Author: Serob Asatrjan Supervisor: Dr. M.A.J. Theebe

Student number: 6092411 Second reader: Prof. dr. M.K. Francke

Faculteit Economie & Bedrijfskunde

Business Economics, Real Estate Finance

Universiteit van Amsterdam

November 2010

EX ANTE IDENTIFICATION OF HOUSING BUBBLES:

INTRODUCING THE MOVING EXTREMA APPROACH

Master’s Thesis

ABSTRACT

In this thesis, I propose an early warning system for identifying bubbles in house

prices – the moving extrema approach. This methodology monitors a number of

indicators that were noted to display certain directional dynamics prior to the

occurrence of housing bubbles in the past. The dynamics in question – the moving

extremum cycle phases – are moving intervals of time where the last value is the

largest or the smallest among other values (each extrema seen as a signal). When the

same moving extremum cycle phases in a time series of a variable occur within a

fixed number of periods prior to every bubble (i.e. signaling horizon), such signals

are tested for the randomness of their occurrence. To reduce the number of false

signals (noise) in those variables that were proven to issue signals non-randomly,

several variables are tested in combination, bound by the length of their signaling

horizons. When these variables achieve their predetermined extrema within specific

for each variable cycle phases, such co-movements are interpreted as signals for an

upcoming bubble. This method was tested on the US long-term data (24 variables for

the period of 1890-2007 and 16 variables for the period of 1930-2007). The

indicators that displayed the best performance within the in-sample tests were: a) 2-

year lagged real house price, residential investment to GDP, real residential

investment, and nominal exchange rate of GDPUSD currency pair – all expressed as

growth rates [based on the long sample of 1890-1990]; b) real farm value of land and

improvements per acre expressed as growth rates, and price-to-rent ratio in levels

[based on the short sample of 1930-1990]. Their out-of-sample performance was

exceptionally good – the bubble that occurred in the US in the beginning of the 21st

century was called with no false alarms.

KEYWORDS

Moving extrema approach, housing bubbles, early warning system, long-term data

ACKNOWLEDGEMENTS

I want to thank dr. Marcel Theebe for support and guidance in the right direction, for

patience and encouragement to develop something new. I am also thankful to prof. dr.

Marc Francke for useful corrections and remarks.

TABLE OF CONTENTS

INTRODUCTION ....................................................................................................... 4

1. OVERVIEW OF THE LITERATURE................................................................. 9 1.1 What is a bubble? .................................................................................................................9 1.2 Housing bubble identification methodologies....................................................................10

1.2.1 Fundamental price models ..........................................................................................10 1.2.2 Logit/probit models.....................................................................................................12

1.3 Ex post bubble identification..............................................................................................13 1.4 Variables explaining house prices......................................................................................18

2. METHODOLOGY................................................................................................ 21 2.1 Kaminsky-Lizondo-Reinhart leading indicators ................................................................21

2.1.1 One-indicator KLR .....................................................................................................22 2.1.2 Composite KLR indicator ...........................................................................................25

2.2 From KLR thresholds to moving extrema..........................................................................25 2.3 Moving Extrema approach .................................................................................................29

2.3.1 In-sample application: one-indicator moving extrema ...............................................31 2.3.2 In-sample application: composite indicator ................................................................33 2.3.3 Out-of-sample application ..........................................................................................35

3. EMPIRICAL ANALYSIS..................................................................................... 37 3.1 Data and variables ..............................................................................................................37

3.1.1 Variables .....................................................................................................................37 3.2 In-sample analysis and results............................................................................................41

3.2.1 1890-1990 (long sample) ............................................................................................41 3.2.2 1930-1990 (short sample) ...........................................................................................45

3.3 Out-of-sample analysis and results ....................................................................................50 3.3.1 1991-2007 (long sample) ............................................................................................50 3.3.2 1991-2007 (short sample) ...........................................................................................52

3.4 Comparing composite indicators........................................................................................54

CONCLUSION.......................................................................................................... 56

REFERENCES .......................................................................................................... 59

DATA SOURCES...................................................................................................... 65

APPENDICES............................................................................................................ 68

INTRODUCTION

Relevance of housing bubbles

It is intuitively clear that the information about the existence or the build-up of a

housing bubble would interest the most prospective buyers (buy-side investors) both

because of the potential negative gearing and margin calls in case of mortgage

financing, or the consequent loss of equity in case the property is bought out with

cash. Such information may also influence sell-side decisions, as it would be

convenient to sell during overvaluation and repurchase after the bust. It would also be

of interest to mortgage portfolio holders or any market participant who may be

exposed to the risk of lending without sufficient future asset coverage, which includes

investors who take positions in the housing market via RMBS.

In the light of the severe worldwide recession that started in 2007, the question of

central banks’ intervention into the formation of housing bubbles during the boom

stages is becoming gradually one of the hottest topics for academicians and central

bankers.1 While some specialists advise non-intervention and others propagate

policies of “leaning against the wind”2, such attention to housing bubbles arises from

the macroeconomic consequences that they tend to bring forth. Black et al. (2005: 10)

stated that housing crashes lasted on average for 5 years with the average aggregate

price depreciation of 30%.3 Cecchetti (2006: 3) concluded that as opposed to equity

booms, house price booms that ended with a bust were “bad in virtually every way

imaginable”: decreasing the output gap, while increasing its volatility and GDP at

risk, such housing booms downgraded economic growth outlook for several years

ahead. Adalid and Detken (2007: 17) distinguished between high and low-cost booms

with the main criterion being the post-boom 3-year period GDP growth. They found

that high-cost booms were associated with much larger residential investment during

the boom episodes and much deeper declines in house prices during the bust. Bunda

and Ca’Zorzi (2009: 15) found that a booming housing market signaled 81% of the

episodes of financial pressure (decline in nominal exchange rate and currency

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

1 The number of papers concerned with monetary policy influence on house prices published by the researchers from BIS, ECB,

FED, etc. speaks in support of this statement.

2 Ahearne et al. (2005).

3 Industrial countries, 1970-2002.

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reserves) or even banking crisis.4 Andre and Girouard (2008: 19) noted that the

potential negative outcomes for the economic growth, employment and the stability of

the financial infrastructure caused by house price busts could justify the actions taken

by central bankers to reduce price escalation; another question being the effectiveness

of such intervention.

Identification of housing bubbles

As about half of the total household wealth depends on the movement of house

prices5 and housing bubbles may have such vicious consequences on the economy, it

is surprising, that no method for preventing bubble formation has yet been introduced

during the preceding years. A key issue here is the ability to prove the existence or the

absence of a bubble with a sufficient degree of confidence. The main argument of the

skeptics of “real time” bubble exploration is that it is hard to exclude the possibility of

a major shift in the underlying fundamentals even for the most famous events

generally perceived as bubbles6; that the ability to predict or identify bubbles by

central banks (as the institutions responsible for price stability) would imply an

informational advantage over the private markets; and that detecting bubbles using

econometric methods is impossible with a sufficient level of confidence7. These views

could be summed up by Malkiel’s words: asset price bubbles are “virtually impossible

to identify ex ante” (Malkiel 2010: 17).

Still, there were those who were warning of the existence of a bubble in several

countries already in 2002-2003, both in the media8 and more importantly in the

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

4 Despite the fact, that no causality was set out to be proven, the occurrence of such events in a successive pattern should not be

ignored.

5 Wolff (2010) showed that the gross value of the principal residences in the US in 2007 constituted 33% of the total household

wealth, reaching 44% if accounted for other real estate holdings; Goldbloom and Craston (2008) stated that the total dwelling

assets in the aggregate portfolio of Australian households constituted 66% of the total wealth in 2007; Halifax report (2010) on

the household wealth in the United Kingdom indicated that the housing assets in 2009 comprised approximately 48% of the total

household wealth.

6 Garber (1990) provided explanations for the three most prominent events perceived as bubbles, namely the Dutch Tulipmania

(1634-1637), the Mississippi Bubble (1719-1720) and the South Sea Bubble (1720), stating that, for example, the annual

depreciation of the price of a tulip bulb during the “bubble” period did not differ so categorically from that registered in the 18th

century.

7 See, for example, Gurkaynak (2005).

8 Krugman (2005) suggested that there was a bubble in the US both in geographically and zoning-restricted areas with inelastic

supply and the midland cities, remarking though, that the prices and sales volumes were already deteriorating.

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academic circles9. These studies prove that “real time” identification of bubbles in the

housing markets is not impossible.

Aim and research questions

The aim of this thesis is to propose a specific early warning system for timely (ex

ante) identification of housing bubbles – the moving extrema approach – targeted at

homebuyers as the primary users.

The following research questions were addressed in this paper:

1. What are the available methodologies for identifying housing bubbles?

2. How does the moving extrema approach work?

3. How did the moving extrema approach perform in out-of-sample mode?

An overview of the proposed methodology

The moving extrema approach was inspired by another early warning system

developed initially for currency crisis ex ante identification by Kaminsky, Lizondo

and Reinhart in 1998. The main idea of the moving extrema approach is to seek for

association between the dynamics of certain explanatory variables and the occurrence

of housing bubbles, and exploit that association to identify housing bubbles ex ante.

The dynamics in question – the moving extremum cycle phases – are moving

intervals of time where the last value is the largest or the smallest among other values

– thus, either moving maximum or minimum. Observing data this way allows

extracting certain directional movements in explanatory variables. When the same

moving extremum cycle phases of a variable occur within certain signaling horizons

(fixed number of periods prior to each bubble), such a variable is filtered out and

tested for the randomness of such occurrences to establish if the same cycle phase is

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9 Among others, Baker (2002) stated that the nominal house prices in the US had risen by 47% in the period of 1995-2001, of

which the inflationary increase had been only 18%, the 29% gap could be explained by only 10% increase in rents and the

remaining 19% increase of price of owning relative to renting was a bubble. Case and Shiller (2003) also concluded that the US

housing market concealed regional bubbles. Bodman and Crosby (2003) found that houses in the two of the five most populated

cities in Australia were overvalued by 15% and 25%. Hawksworth (2004) suggested that the UK market was overpriced by 20-

40%, and Black et al. (2005) calculated the premium of actual house prices over their fundamental value in the same market

being around 25% by the third quarter of 2004. Ayuso and Restoy (2006) reported that the price-to-rent ratio in the Spanish

housing market was about 24-32% higher than its long-term equilibrium value.

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occurring in a variable mostly prior to bubbles or all the time – randomly. To bring

the number of false signals down, several variables are tested in combination, bound

by the same length of signaling horizon – when all of these variables achieve their

respective largest or smallest values at the same time (within specific for each

variable cycle phases), such co-movements are interpreted as signals for an upcoming

bubble. The aim of this approach is to find such co-movements that lower the number

of false alarms, but are still able to call all the bubble episodes inside the sample.

Then there is sufficient evidence to use these variables trying to identify bubbles ex

ante.

Data

An important condition set for the moving extrema approach is to analyze as long

time series as possible, for that reason and the issue of public availability of data in

English, the US housing market was chosen. I would like to stress the amount of work

undertaken to acquire data series for 24 variables for the period of 1890-2009, which

taking into account different transformations and rationing were compiled into 70

time series, which then entered the analysis. Data for another 16 variables,

unavailable from 1890, were collected for the period of 1930-2009, resulting in 71

time series after various transformations (in total 40 variables and 141 series).

Results

The best-performing composite indicators, based on in-sample tests, were both 3-year

signaling-horizon indicators (bubble imminent to occur in a 3-year time window after

the signal):

• 2-year lagged real house price, residential investment to GDP, real residential

investment, and nominal exchange rate of GDPUSD currency pair – all

expressed as growth rates [based on the long sample of 1890-1990];

• real farm value of land and improvements per acre expressed as growth rates,

and price-to-rent ratio in levels [based on the short sample of 1930-1990].

The out-of-sample results were more than satisfactory: both composite indicators

named above were successful at identifying the out-of-sample bubble with no false

alarms. A potential user – homebuyer – could have benefited greatly relying on

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forecasts of these indicators, as the whole of the housing bubble that occurred in the

beginning of the 21st century could have been avoided.

Structure of the paper

The remainder of this thesis is organized as follows: chapter 1 is concerned with the

overview of literature, chapter 2 describes the methodological issues, and chapter 3

the empirical analysis.

Chapter 1 deals with the definition of a bubble (section 1.1); discusses the existing

“real time” and ex ante bubble identification approaches most commonly applied to

house prices (section 1.2); describes the choice of ex post bubble dating methodology

used in the thesis (section 1.3); and lists the variables considered and found

significant as explanatory variables of house prices (section 1.4).

Chapter 2 describes the starting point of the proposed approach – the KLR

methodology (section 2.1); explaines the transition from thresholds to moving

extrema (section 2.2); and gives a thorough overview of the proposed methodology

(section 2.3).

Chapter 3 describes the data and the variables tested in the thesis (section 3.1);

describes the in-sample analysis of single indicators, on which the composite

indicators are based (section 3.2); discusses the out-of-sample performance of the

composite indicators (section 3.3); and compares the composite indicators with a

potential competitor (section 3.4).

An overview of the completed work and results together with suggestions regarding

further development of the ideas raised in the thesis at hand is presented in the final

section i.e. Conclusions.

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1. OVERVIEW OF THE LITERATURE

The literature overview chapter is divided into four sections: 1) issues of definition; 2)

overview of the most frequently used methods for identifying housing bubbles in the

“real time” and ex ante; 3) methods for dating bubbles ex post; 4) variables that have

been found effective in explaining house price dynamics.

1.1 What is a bubble?

Before approaching the issues of bubble detection, it is necessary to answer the

question: What is the concept of a bubble? In their 2003 paper, Karl Case and Robert

Shiller studied the origin of the term “housing bubble” collecting data on its

occurrence in the major English language newspapers from 1980-2003, and found

that the term had almost been not used at all until 200210

contrary to the “housing

boom”, which had been very popular since 1980s. They suggested that journalists did

not want to use the word “bubble” without very strong evidence of the magnitude of

the stock market crashes in 1987 and 2000. Nevertheless, the concept of a bubble in

asset prices has pervaded the academic literature and there are plenty of sources to

which to refer.

There are numerous definitions of an asset price bubble. The most famous definition

is the one by Stiglitz (1990): “if the reason that the price is high today is only because

investors believe that the selling price will be high tomorrow – when “fundamental”

factors do not seem to justify such a price – then a bubble exists”. This could be

understood as a substitution of fundamentals with expectations. Such a formulation

does not require a decline in prices to prove the existence of a bubble: if it is possible

to show that the prices have grown out of line with fundamentals, such an

overvaluation could go on for extended periods of time and still qualify as a bubble.

Another prominent definition was presented by Kindleberger in 1987: “a sharp rise in

price of an asset in a continuous process, with the initial rise generating expectations

of further rises and attracting new buyers – generally speculators interested in profits

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10 Case and Shiller (2003) stated that the term “housing bubble” came up several times after the stock market crash in 1987, but

vanished shortly after.

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from trading rather than in its use or earning capacity. The rise is then followed by a

reversal of expectations and a sharp decline in price often resulting in severe financial

crisis.”11

This implies that an important condition for identifying the existence of a

bubble is the bursting. The definition of a bubble for this study is derived by further

abandoning the expectations component from Kindleberger’s formulation. The

reasoning is that the prospective end-users of the model presented in this paper – buy-

side investors – would not discriminate between fundamentally sound price and

overpricing (a bubble) that would go on for the next two centuries (meaning that the

price would not drop for 200 years ahead), as concrete evidence of a bubble, that

could hurt their interests, can only emerge through a burst.12

Thus, the definition

chosen for this paper stipulates the following: when there is a sufficient (in terms of

magnitude) spike-like movement in the price, it can be defined as a bubble.

1.2 Housing bubble identification methodologies

The most commonly implemented methodologies dealing with house price bubble

identification are, first of all, the fundamental price approach and then probit

modeling. In the two following sections, the general idea of these methodologies is

described along with several examples from the respective studies.

1.2.1 Fundamental price models

A frequently used “umbrella” of methodologies for house price bubble exploration is

the fundamental price approach. Its root is to model the fundamental (equilibrium)

price and then compare it to the actual price. A good example of such a model can be

found in Case and Shiller (2003). In this paper, the regional US house prices were

regressed on the following fundamentals: percentage change in population and

employment, mortgage and unemployment rates in levels, number of housing starts,

income per capita, and the ratio of the latter to annual mortgage payments. The

positive difference between the actual price and the fundamental price calculated this

way was interpreted as overvaluation. The authors concluded that a bubble was

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11 Several other definitions can be found in Flood and Hodrick (1990), Muellbauer and Murphy (2008), Shiller (2007), Smith

and Smith (2006).

12 In addition, the ax ante signaling approach presented in this paper is not based on the concept of deviation from fundamentals,

but merely on the property of certain dynamics in various macroeconomic and other variables to lead house price bubbles.

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concealed in several cities – in addition to the regression results, this conclusion was

supported by the existence of “elements of speculative bubbles – the strong

investment motive, the high expectations of future price increases, and the strong

influence of word-to-mouth discussion”, which they derived from their survey (Case

and Shiller 2003: 341).

An essential part of fundamental price models is the error term specification that

seeks to explain the gap between the actual and the fundamental price. An often-cited

example was demonstrated in a study by Abraham and Hendershott (1996), where an

error term was set to account for the bubble-building lagged house price growth and

the bubble-bursting difference between the lagged fundamental and actual price. The

higher the appreciation rate of house prices in the previous period, the more it would

be likely for the price to develop into a bubble during the current period. On the other

hand, the larger the gap between the actual price and the fundamental lagged price,

the stronger the pressure on the bubble to burst.

The next level is not just to explain the gap, but to model the short-term dynamics of

the price adjusting back to equilibrium – such models are called error correction

models (ECM). Malpezzi (1999) proposed, in addition to a linear error correction

model, an ECM using cubic terms to enforce the notion, that a larger positive gap

between actual and fundamental price implied larger (faster) adjustment effects than

smaller overvaluation. Despite the fact, that only the linear adjustment was found

statistically significant, the idea of proportional reactions is worth mentioning. For

other examples of ECM, see, among others, Abelson et al. (2005), Cameron et al.

(2005), Sorbe (2008).

An important prerequisite for the error correction models to be viable is cointegration

between the dependent and the independent variables, meaning that they act within a

long-term relationship and cannot wonder apart for too long without a bound. If the

latter is true, the deviations between such variables are temporary and can be

explained by an error correction term. When it comes to cointegration between house

prices and (assumed) fundamentals, various empirical studies report both the

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existence and the lack of such relationships.13

Despite the mixed results, fundamental

price models remain a widely accepted and used methodology.

1.2.2 Logit/probit models

While fundamental price models set out to establish the equilibrium price of housing

for a certain moment in time and the bubble is exposed via the positive gap between

the actual and the calculated fundamental price, logit/probit models are constructed to

indicate the probability of events14

. Thus, it is not the difference between the positive

and the normative, but the association between events that matters within the latter

methodology. Logit/probit models are limited dependent variable models that are

programmed to calculate the probability of an event using the cumulative logistic

distribution in the case of logit models, and the cumulative normal distribution in the

case of probit models. This solves the problem of the linear probability model,

transforming the probability function into an S-shaped curve bound between 0 and 1.

The two studies that are relevant to the theme of this paper were conducted by

Agnello and Schuknecht (2009) and Noord (2006). Both studies applied probit

analysis to house prices, with the former study concentrating on booms and busts and

the latter on house price peaks. Agnello and Schuknecht (2009: 28) included the

following variables in their probit model: growth rate of real GDP per capita; growth

rate of global-liquidity variable (growth of broad money aggregate M3 of the

countries in the sample other than (minus) the respective national M3 of the particular

country under observation); level of nominal short-term interest rate; growth of

working-age population; banking crisis dummy and market deregulation dummy. All

variables entered the analysis with a lag. This model was tested on panel data of 18

countries (including the US) for the period of 1980-2007. Panel data were used to

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13 For example, Black et al. (2005: 15) found cointegration between UK house prices and real disposable income for a period of

31 years; Abelson et al. (2005: 15) reported cointegration between Australian house prices and explanatory variables for a period

of 33 years. Gallin (2003: 3) found no cointegration between the US national-level house price and the assumed economic

fundamentals such as income per capita, population, stock market index, construction wages and personal consumption deflator

within a period of 27 years. Schnure (2005: 11) reported that cointegration tests for regional housing prices and income in the US

(for a period of 26 years) failed to find evidence of such a relationship. Mikhed and Zemcik (2007: 12) further supported Gallin’s

findings, having found no cointegration between aggregate house prices and personal income per capita, consumer price index,

population, mortgage rate, construction wage, the stock market and rent in the US for a period of 24 years.

14 Such events may occur in “real time”, but due to their latent nature, cannot be observed directly, or they may occur in a

certain time window – dependent on the setup of the model.

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enhance the robustness of the model, as the sample period was too short to extract

reliable results on single-country basis.

The probit regression with house price booms being the dependent variable returned

the following results: all variables were found significant at 1% apart from real credit

growth, which was found significant at 5% and deregulation dummy variable, which

was found significant at 10%. Regarding the bust sequence being the dependent

variable: all variables were significant at 1% apart from population growth, which

was significant at 10% and the deregulation dummy, which was not significant even

at 10% level. The model performed extremely well predicting booms in the US house

prices during 1982-2007 issuing only one false signal in 1997. The prediction of busts

was somewhat less successful with two false signals in the beginning of the period

and, more importantly, failure to indicate a bust during 1993-1997.

Noord’s (2006: 15) probit regression with the dependent variable being the peaks in

the US house prices included the following variables: simple average of short- and

long-term interest rate; real house price gap (calculated as the log of real house price

minus the log-linear trend of real house price); and inflation, which were all found

significant at 5%. The conclusions reported were generally successful: as of the end

of the 4th

quarter of 2005, the real house price gap (overvaluation) was found to be

26%. The probability of a peak in house prices was calculated to be 98,5%. This

probability was upgraded to 100% if the housing prices were to increase in 2006 at

the same pace as in 2005 and/if the interest rates were to increase by 100-200 basis

points. Although the timing of the peak was not forecasted precisely – the peak, as we

know now, occurred in 2007 – the conclusion of this paper could have been quite

useful for buy-side decisions.

1.3 Ex post bubble identification

Although it may seem easy to identify asset price bubbles ex post, there are several

issues that need prior clarification. The definition of a bubble elected for this paper

doesn’t require delving deeper into the matters of explaining prices – what matters is

the fact that there was a sufficient boom and a bust. But how much does the price

have to increase and decline and in what time frame for an episode to qualify as a

boom/bust sequence (a bubble)? There are two main approaches commonly used by

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academicians; one of them is for purely ex post decisions and the other for “real time”

estimation.

Bry and Boschan’s (1971) algorithm is the more frequently encountered approach that

deals with the identification of turning points ex post.15

The algorithm prescribes the

exact procedures for identification: correction for outliers, identification of peaks and

troughs, alternation condition, phase and total cycle length etc. The main problem of

this methodology is that it leaves the ends of the series unused, which is somewhat

inappropriate for this thesis, as using this methodology would exclude the last bubble

episode (the one in the beginning of the 21st century) from analysis and that episode is

chosen as the out-of-sample test event.

The second approach is based on a “normal” level and a deviation threshold for time

series for recursive estimations, meaning that the available data is sufficient to

conclude if there is a boom or a bust at a given period. The root of the method is to

establish a deviation threshold from some long-term average or moving average,

which, if crossed, would mean a boom or a bust.16

Adalid and Detken (2007) studied the impact of liquidity shocks on asset price cycles,

defining a boom as at least 4 consecutive quarters where the price index exceeds its

very slow adjusting trend (Hodrick-Prescott filter with !=100,000) by minimum 10%.

This is the most suitable methodology to date bubbles in this thesis in my view, as a

smoothed price trend would reveal the long-term price dynamics which buyers have

to face, and the temporary deviations from this price trend by more than a certain

percentage would mean being exposed to a possibility of a bubble.

Identifying US housing bubbles

The foundation for the upcoming analysis is the house price series produced by Case

and Shiller. First of all, it is necessary to check if the series are stationary, as such a

case would imply mean reverting price dynamics and any major deviation from the

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15 Noord (2006) dated booms and busts in house prices using the Bry-Boschan procedures and defined a peak as a period, prior

and preceding which the price had been rising and then falling for at least 6 quarters. In addition, prices had to rise at least 15%

to qualify as a boom phase. Among other papers, where Bry-Boschan algorithm was implemented, are Girouard (2006), OECD

(2007), Helbling and Terrones (2003).

16 The following papers are a few who have used this method: Alessi and Detken (2009), Bordo and Jeanne (2002), Gerdesmeier

et al. (2009).

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mean could then be seen as a bubble. The traditional Augmented Dickey-Fueller test

was implemented to test for unit roots in the real price series. The results are

presented in appendix 1 and show that there is a unit root in the levels, so the test is

repeated in differences (house prices are expressed in natural logs) and the more

negative value of the test statistic than the critical value at 99% confidence level

allows to reject the unit root in the growth rates of house prices. Thus, the series is

integrated in the order of 1, allowing for an important conclusion that the series is not

mean reverting – at least, based on the analyzed data.

The definition of a bubble in this paper states that a bubble is any sufficient spike-like

movement in real house prices in terms of magnitude. To date the bubbles in the

house price series for the US market, this definition is taken as the basis together with

the threshold method described previously. Within the threshold methodology, the

series are to be smoothed using the Hodrick-Prescott filter to reveal the long-run

dynamics of the series. No assumptions are made if this long-term path is in

accordance with the fundamentals – only the facts based on data. Agnello and

Schuknecht (2009) and Adalid and Detken (2007) used very strong smoothing

parameters of !=10,000 and of !=100,000, applying which smoothes the series too

much, approaching a more “linear” shape the higher the parameter is set (see figure

1).

Figure 1. The real house price index (1890=100) and the smoothed series using HP

filter with !=10,000 and 100,000, period of 1890-2009

Source: S&P / Case-Shiller Home Price Index, author’s calculations

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Setting the filter parameter to !=100, generates a more reasonable result with the

smoothed series moving closer to the actual price, smoothing out the excess volatility

(see figure 2).17

Figure 2. The real house price index (1890=100) and the smoothed series using HP

filter with !=100, period of 1890-2009

Source: Ibid., author’s calculations

Next, the difference between the smoothed values and the actual prices are calculated

for each year. It is, thus, needed to choose a minimum deviation value between these

two series for an episode to qualify as a bubble. Adalid and Detken (2007: 14) set the

deviation threshold of their composite index of asset prices from the smoothed trend

to 10%; Noord (2006: 8) used the value of 15% for the sequence to qualify as a boom

or a bust. In this case, it is not the difference between the trough and the peak that

needs to be considered, but the positive gap between the actual price and the

smoothed series, so the threshold of 10% was considered at first. The bubbles

identified in such a way are shown in table 1 - the overvaluation is shown for every

year, where the actual price exceeded the smoothed series by more than 10%.

Table 1. Bubble episodes from 1890-2007 with 10% deviation threshold

1894 1895 1907 1916 1946 1947 1989 2004 2005 2006 2007

20.7% 13.4% 10.3% 10.1% 15.4% 14.3% 10.7% 10.5% 21.8% 29.5% 11.5%

Source: S&P / Case-Shiller Home Price Index, author’s calculations

Comparing the deviations shown in table 5 with the deviations of actual price from

smoothed series in figure 2, it becomes obvious that the bubble in the end of the 70’s

is left unaccounted. Decreasing the threshold to 9%, brings the episode into the

observations, without adding any other event into the picture (see table 2).

""""""""""""""""""""""""""""""""""""""""""""""""""""""""

17 !=100 is also the default setting for annual data smoothing within statistical software packages.

" &#"

Table 2. Bubble episodes and overvaluation in each year with 9% deviation threshold

1894 1895 1907 1916 1946 1947 1979 1989 1990 2004 2005 2006 2007

20.7% 13.4% 10.3% 10.1% 15.4% 14.3% 9.3% 10.7% 9.8% 10.5% 21.8% 29.5% 11.5%

Source: Ibid.

The duration and the magnitude of the bubbles are denoted in figure 3 bubble

episodes are marked with red arrows. These are the final episodes, around which all

of the following analysis is constructed.

Figure 3. The real house price index (1890=100), the smoothed series using HP filter

with !=100, and the bubble episodes during the period of 1890-2009

Source: Ibid., author’s calculations

A problem with HP filter treating the beginning and the end parts of the sample with a

bias towards the values at those ends was described in St-Amant and Norden (1997:

13). This problem may have an impact on this particular analysis, as the beginning of

the overpriced periods is of primary interest. If the house price in the coming future

(beyond 2010) were to decrease further, the smoothed series would look much flatter

closer to the end of the series, meaning that the overvaluation period had started

earlier - closer to 2000. It would also mean that the market was still overvalued after

2007 - under the present assumptions the overvaluation ended in 2007. An attractive

alternative solution that could reduce the above-mentioned problem is the unobserved

component model (see, for example, Harvey (2006)). Nevertheless, as HP filter was

used in numerous studies with similar aims and is easier to implement and

understand, it is chosen as the preferred methodology for this thesis.

&$"

1.4 Variables explaining house prices

In this section, various variables from academic sources that were found significant in

explaining house prices or predicting housing boom/bust episodes are presented in a

way that mimics that of Lestano and Kuper (2003: 7), where potential indicators were

listed with the general interpretation of each variable and its respective references.18

Table 3. Variables explaining house prices from existing research with comments and

references

Variable Comments References

1 After-tax interest rate The default assumption of interest rates’ impact on housing prices is

that low and/or declining rates favor house price appreciation, as cheap

credit increases demand. An important issue here is the tax burden,

which in the US is lowered due to mortgage interest deductibility.

Abraham and

Hendershott

(1996)

2 Budget balance Fiscal deficit narrows prior to the peak and widens considerably

afterwards.

Ahearne et al.

(2005)

3 Construction cost Growing construction costs, ceteris paribus, increase house prices, as

the reproduction cost becomes higher and arbitrage opportunities may

arise in case house prices respond with a lag.

Abraham and

Hendershott

(1996)

4 Construction share in

GDP

There is a positive association between construction share and house

prices (in the US): rising house prices push construction up, with the

peak of the construction share in GDP generally occurring in close

proximity to the peak in house prices.

Ahearne et al.

(2005)

5 Current account to GDP It was reported that peaks in house prices were associated with

substantial deterioration in balance of the current account. Although

Kole and Martin (2009) concluded that there was no systematic

relationship between current account and house price, such association

may still be useful within the setup of the model presented in this

paper.

Kole and Martin

(2009)

6 Disposable income Disposable income (after-tax personal income) is one of main

determinants of housing demand, i.e. growing disposable income

pushes housing prices up.

Abelson et al.

(2005),

Sorbe (2008)

7 Employment Employment growth is generally associated with increasing consumer

inflation (Phillips curve), which in its turn increases house prices.

Abraham and

Hendershott

(1996), Case and

Shiller (2003)

8 Exchange rate In large cities of the countries with open economies, decreasing

exchange rates may increase house prices, making housing more

attractive for foreigners. In addition to that, depreciating home currency

supports export growth, resulting in increased economic activity and

higher demand.

Abelson et al.

(2005)

9 Gap between lagged

actual and fundamental

house price

Widening gap implies a bubble and also proximity to the peak of house

prices, as overvaluation cannot go on forever. Tsounta (2009) used

long-run house price instead of the fundamental price.

Abraham and

Hendershott

(1996), Noord

(2006)

10 GDP GDP is, in principle, a business cycle variable. The growth in GDP,

similarly to income growth, ceteris paribus, would imply growth in

house prices via increased economic activity and housing demand.

Prolonged GDP growth may lead to a perception of higher level life-

time income and motivate potential buyers to spend more on housing,

taking on more debt. Tsatsaronis and Zhu (2004) presented the results

of variance decomposition of housing prices, which prescribed rather

moderate 7% in the US house price variance to shocks to GDP (the

number was calculated as an average for the group including the US).

Agnello and

Schuknecht

(2009), Kole and

Martin (2009),

Schnure (2005),

Tsatsaronis and

Zhu (2004)

""""""""""""""""""""""""""""""""""""""""""""""""""""""""

18 Some research involved only comparative analysis without using regression techniques – in such case, the variables

considered there are also listed as significant in table 3.

" &%"

Variable Comments References 11 Government spending/

revenue

Government expenditure was found to have a positive effect on

housing prices: government expenditure fuels economic activity via

investment etc, which transforms into rising house prices. There is an

association between government revenue and housing price, which

could potentially have predictive power - high government revenue is

usually the result of strong economic activity.

Afonso and Sousa

(2009)

12 Housing costs to

consumption

Increased housing expenditures (imputed and tenant-occupied rent) to

consumption could be associated with higher house prices. The ratio of

housing costs to income was used by Hogue (2010) as a measure of

both affordability and overvaluation.

Shiller (2007)

13 Housing starts Increases in house prices (positive returns) bring forth more investment

activity with housing starts’ peaks usually leading house price peaks.

Schnure (2005)

14 Housing stock per capita Housing stock p.c. is a supply variable that is negatively related to

house prices: increase in housing stock per capita, ceteris paribus,

should lead to a decrease in house prices, as demand would not cover

supply.

Abelson et al.

(2005)

15 Income p.c. to annual

mortgage payment ratio

Ratio of income per capita to annual mortgage payment measures

affordability. High ratio suggests possible bubble development, if the

increase comes from low interest rates and softening mortgage

conditions. The subsequent decline in the ratio may indicate the

proximity to the peak in house prices as worries of overpricing result in

tighter credit supply and higher interest rates.

Case and Shiller

(2003)

16 Inflation rate High consumer inflation pushes house prices up as rents are usually

indexed with CPI change and real estate is often perceived as a hedge

against inflation. Tsatsaronis and Zhu calculated the variance

decomposition of the US housing prices and prescribed 42% of house

prices’ total variation to inflation, that was equally the largest

contributor (the number was calculated as an average for the group

including the US).

Noord (2006),

Tsatsaronis and

Zhu (2004)

17 Labor force Labor force is comprised of individuals that are employed or are

seeking employment. Growth in labor force increases house prices via

additional demand.

Schnure (2005)

18 Lagged house price

growth

Lagged house price growth is a primary measure of expectations.

Krainer (2002) concluded that the primary driver of house prices in the

US by the end of 2001 was not the drop in mortgage rates, but price

appreciation in previous periods, implying a bubble based on

expectations.

Abraham and

Hendershott

(1996), Kole and

Martin (2009),

Krainer (2002),

Lecat and

Messonnier

(2005), Sorbe

(2008), Tsounta

(2009)

19 Long-term interest rate Decreasing long-term interest rate in “normal” economic conjuncture

increases house prices, as more entities wish and are able to borrow at

lower cost, which increases the demand for housing. The question often

raised is the applicability of nominal vs. real interest rates: although

theory suggests that real rates are those that should matter to borrowers,

practice shows that nominal rates are more influential, as that is what

mortgagors have to pay and what banks follow within DSCR.

Adalid and Detken

(2007), Afonso

and Sousa (2009),

Kole and Martin

(2009), Noord

(2006),

20 Money aggregate M3 Broad money growth usually peaks before house prices and is

positively correlated with real GDP and household borrowing.

Adalid and Detken

(2007), Agnello

and Schuknecht

(2009), Ahearne et

al. (2005)

21 Mortgage interest rate In general, decreasing or low mortgage interest rates have a positive

impact on house price growth. What makes this variable different from

long-term interest rate is the specific to the housing market risk

premium, which fluctuates depending on the perception of risk in the

housing market.

Abelson et al.

(2005), Cutts and

Nothaft (2005),

Krainer (2002),

Malpezzi (1999),

Sorbe (2008)

22 Moving average of

house price growth

Two-quarter MA of house price growth was found significant for

predicting house price peaks for a panel of 17 countries, but not for the

US within country-specific testing. This variable accounts for

expectations (similar to the lagged price growth), taking into account a

longer base for the development of such expectations. In this thesis,

two-year MA is considered instead of two-quarter variable.

Noord (2006)

23 Output gap Positive output gap (difference between actual and potential GDP) is

associated with house price growth, as during house price booms real

GDP grows faster than potential GDP, which then reverses into a

negative gap after the house price peak.

Ahearne et al.

(2005), Sorbe

(2008)

('"

Variable Comments References

24 Personal income As mentioned under disposable income, income variables are widely

considered as the main determinants of house prices. The difference

between personal and disposable income arises from personal current

taxes – thus, changes in disposable income account for the effects

emerging through the buyers/rents channels, while changes in personal

income reflect on a wider level (somewhat similar to GDP growth, as

the latter includes taxes payable to the government).

Case and Shiller

(2003), Cutts and

Nothaft (2005),

Schnure (2005),

Sorbe (2008)

25 Population Although population is not as good a variable for house prices as

number of households or the ratio of young households to total (the

latter often ignored due to data availability issues), it is a generally

accepted demand determinant, where population growth, ceteris

paribus, increases house price via increased demand.

Case and Shiller

(2003), Cutts and

Nothaft (2005),

Malpezzi (1999),

Tsounta (2009)

26 Price-to-income ratio Substantial upward deviations of price-to-income ratio from its long-

term trend are generally perceived as a sign of overvaluation. Malpezzi

(1999) implemented price-to-income ratio with various lags to account

for different magnitude deviations’ error correction.

Andersen and

Kennedy (1994),

Malpezzi (1999),

Black et al. (2005)

27 Price-to-rent ratio Price-to-rent ratio is the gross rent multiplier, which is the third main

affordability ratio. As in the case of price-to-income ratio, upward

deviations from the long-term trend may indicate a bubble

development.

Ayso and Restoy

(2006), Gallin

(2004), Girouard

(2006)

28 Private sector credit Growth of credit to private sector should be correlated with growing

house prices. Additional “kick” is given by the growing house prices,

which increase the collateral value and that, in is turn, increases house

prices further. Helbling (2005) concluded that private credit booms,

measured via large upward deviations in the credit-to-GDP ratio from

long-term trend, coincided with housing boom-bust cycles.

Agnello and

Schuknecht (2009)

29 Productivity Labor productivity (output per hour of work) influences house prices

via changes in income and expectations of future income growth.

Kahn (2008)

30 Rapid house price

appreciation

Helbling (2005) concluded that rapid house price growth during short

periods (as opposed to extended periods of moderate house price

appreciation) were relatively good indicators of a developing bubble.

Helbling (2005)

31 Residential investment to

GDP

Residential investment is, in its principle, similar to housing starts: the

peaks in residential investment to GDP ratio usually precede the

housing price peaks in the US (Dokko 2009).

Dokko (2009),

Musso et al.

(2010), Shiller

(2007)

32 Short term interest rate Although it is the mortgage rate that seem to matter the most among

different types of interest rates where housing prices are concerned,

short term rate is often monitored as an indicator of monetary policy

direction. Helbling (2005) noted that monetary policy via short rates

tightening triggered the bursting of house price bubbles. Thus, initially

low rates support the boom in house prices, which is later deflated into

a bust by a sharp increase in the short rate.

Agnello and

Schuknecht

(2009), Helbling

(2005), Lecat and

Mesonnier (2005),

Tsatsaronis and

Zhu (2004)

33 Stock market index Using stock prices is a simple way to include fluctuations in wealth.

Another application is reflecting on the possible substitution effects

from stock to housing markets after stock market crashes. Thus, there

are two theoretical principles: first of all, increasing stock prices

increase wealth, which pushes house prices up; secondly, stock market

crashes may cause a flow of funds from stocks to real estate also

increasing the prices of the latter.

Abelson et al.

(2005), Lecat and

Mesonnier (2005)

34 Term spread Term spread is an indicator of future economic growth: narrowing gap

between long and short rates indicates the increased perception of

riskiness by the lenders – proximity of a recession; a widening spread

usually means higher growth in the future, as central banks try to

stimulate the economy lowering the short rate.

Tsatsaronis and

Zhu (2004)

35 Unemployment rate Decreasing unemployment rate usually brings forth increased inflation

(Phillips curve), which is transmitted into higher house prices; also

allows access to ownership to individuals in the labor force that do not

yet own a home, thus increasing demand and house prices.

Abelson et al.

(2005), Case and

Shiller (2003),

Schnure (2005)

36 User cost of housing User cost of housing (mortgage rate adjusted for taxation and inflation

less the lagged capital gains) could be viewed as the negative-signed

net return. Rising user cost decreases housing prices.

Andersen and

Kennedy (1994),

Krainer (2002)

37 Working-age to total

population

Growth in working-age population increases house prices via growing

demand, especially when supply lags are taken into account. Long-term

increase in the working-age to total population ratio implies that the

composition of population is generally on the younger side, which

favors formation of new households that need housing – increasing

demand leads to price appreciation.

Agnello and

Schuknecht

(2009), Andersen

and Kennedy

(1994)

Variables tested within the empirical analysis are based on table 3 with several

exceptions due to the public availability of data in sufficient length.

" (&"

2. METHODOLOGY

As stated in the introduction section, the aim of this paper is to introduce a new early

warning system for identifying housing bubbles ex ante – the moving extrema

approach. The root of this idea is to find regularity in the dynamics of various

indicators and house prices (particularly housing bubbles), so that if certain indicators

act in a specific way, a signal is issued by the system that means that a housing bubble

is imminent in a certain time period. This method was inspired by Kaminsky, Lizondo

and Reinhart’s leading indicators approach (KLR) and several elements of the latter

are taken as the foundation of the moving extrema methodology. This chapter

explains the proposed methodology by, first, describing KLR; then discussing why

KLR is not ideal for dealing with country-specific long-term data; and finally

describing the moving extrema approach itself.

2.1 Kaminsky-Lizondo-Reinhart leading indicators

KLR leading indicators approach is an ex ante signaling model developed by

Kaminsky, Lizondo and Reinhart (1998) for currency crisis and has since been used

for banking, debt crisis and asset price bubble identification. It has not been applied to

housing bubbles so far.

A few words about the background of this method: Stock and Watson (1989: 2)

revisited the leading indexes that were developed by the National Bureau of

Economic Research in 1937 for “summarizing and forecasting the state of

macroeconomic activity”. In 1996, Kaminsky and Reinhart proposed several leading

indicators for their currency and banking crisis prediction methodology, which they

said had taken its roots from the above-mentioned Stock and Watson, and Diebold

and Rudebusch (1989) – both papers concerned with turning points forecasting. In

1998, Kaminsky and Reinhart in cooperation with Lizondo revised the 1996 model

and formulated what is generally referred to as the Kaminsky-Lizondo-Reinhart

leading indicators – in this paper (as in many others) this model is abbreviated to

“KLR”. Two domains of KLR can be differentiated: the traditional approach

introduced in 1996 and developed further in 1998 dealt with single indicators. In

(("

2002, a composite indicator approach was presented by Kaminsky. In the following

paragraphs both of these methods are described in some detail.

2.1.1 One-indicator KLR

KLR “monitors the evolution of a number of economic variables and when one of

these variables deviates from its “normal” level beyond a certain “threshold” value,

this is taken as a warning signal about a possible [currency] crisis within a specified

period of time” (Kaminsky et al. 1998: 15). The general shape of such a process could

be described as follows:

(1)

!

Dumt=1 if

!

"Xt# "X

max/min$threshold{ } ,

where

!

"Xt is the change in the indicator at time t, and

!

"Xmax/min#threshold is the chosen

maximum or minimum threshold, depending on the nature of the indicator.19

Dummy

variable issues a signal, when its value is 1.

Several definitions are specified thereafter. First, the meaning of “crisis” should be

established precisely. Second, the signaling horizon should be chosen, indicating the

number of periods prior to the occurrence of a crisis that an indicator should issue a

signal. Third, the thresholds, as the minimum levels of deviation for an indicator to

issue a signal, are chosen so that the noise-to-signal ratio (explained later on) is the

lowest. Thresholds have to be country-specific and are derived “in relation to

percentiles of the distribution of observations of the indicator” (Ibid.: 17). What it

means is that, for example, 10% or 20% of the highest growth rates up to a certain

point in time registered for one or another indicator were chosen as the threshold –

this also made it possible to analyze 16 variables for 20 countries (320 thresholds),

which would be exceedingly time-consuming to be carried out manually.

The next stage of KLR approach is involved with analyzing the results, trying to

answer the question if the signals are effective via table 4 (the matrix is slightly

modified to account for any event, not only a currency crisis).20

A is the number of

""""""""""""""""""""""""""""""""""""""""""""""""""""""""

19 Several indicators were analyzed in levels – for example, interest rates; others both in levels and first differences of logs.

20 This type of analysis could be implemented to any kind of signaling approach, not only KLR. For example, Gerdesmeier et al.

(2009: 23) applied this matrix to the results of a probit model. Lestano and Kuper (2003) used a similar set-up for comparing

various EWS models (probit, logit and several other signaling approaches).

" ()"

periods (dependent on the specifications) in which the indicator issued a correct signal

(predicted the event), B is the number of periods with false alarms (noise), C is the

number of periods where the event occurred without the indicator’s signal and D is

the number of periods where no signal was needed and neither any was issued. It is

clear that an ideal indicator would generate A- and D-type signals only.

Table 4. KLR indicators’ performance matrix

Event No event

Signal issued A B

No signal issued C D

Source: Kaminsky et al. (1998: 18)

There are three main ratios to assess the efficiency of the model. The measure of

correct signals over all signals that could have been issued correctly:

(2)

!

A

A+C .

The ratio of incorrect signals over all signals that could have been issued falsely:

(3)

!

B

B+D .

The ratio of equation (3) to (2) is the adjusted noise-to-signal ratio:

(4)

!

B

B+D÷

A

A+C ,

which is the nucleus of all performance evaluation in KLR: it shows that the model

issues random signals if the ratio is 1, and the lower the outcome is, the better the

model performs (ideally 0).

Berg and Pattillo (1999: 564) noted that the ratio actually measured the proportion of

correct to incorrect signals (B/A), with the (A+C)/(B+D) being the frequency of the

event in tranquil times that could not be optimized using different thresholds for the

indicators. In addition, neither (B/A) nor the adjusted noise-to-signal ratio account for

missed events – for example, the ratio may be quite low, but the value of such an

indicator system is questionable, if only 70% of the events were predicted and the low

(*"

value of the ratio came from the numerous signals issued correctly for the most, but

not all events in the sample. In this thesis, this problem is tackled seriously, setting the

condition of predicting all the events in the sample as a necessary condition.21

Alessi and Detken (2009: 12) stated that the noise-to-signal ratio below 1 could only

be treated as a necessary and not a sufficient condition. The reasoning behind this

notion is as follows – if the model gives an approximately equal number of correct

and false signals, the potential end-users (in their paper – policy-makers) may be

reluctant to take any notice of it at all. They proposed what they called a “loss

function”:

(5)

!

L ="C

A+C+ (1#" )

B

B+D ,

where

!

" was the user’s relative risk aversion between type I (signaling failed to

indicate the event: C/(A+C)), and type II errors (false alarms: B/(B+D)). If the

relative risk aversion is more than 0,5, then the user is prepared to accept more false

signals, so that she won’t miss the correct ones and vice versa. In addition to this, the

gap between the conditional and the unconditional probabilities – the difference

between the ratio of correct to all issued signals and the ratio of all possible good

signals to the total sample (to see if the there were proportionally more correct signals

than events in the sample) – was proposed in KLR:

(6)

!

A

A+ B"

A+C

A+ B+C +D ,

which shows the increasing quality of the indicator the larger it is and must be at least

non-negative.

""""""""""""""""""""""""""""""""""""""""""""""""""""""""

21 Another efficiency measure proposed in KLR was the average lead-time of each particular indicator, which showed the

number of periods prior to the event when the first signal was issued. Also the persistence of a signal was calculated to see what

was the difference between the “normal” and pre-crisis times in the average number of signals per period. These measures are

not fully applicable to the analysis at hand as an important issue here is the frequency of data – months in KLR, annual data in

this thesis.

" (+"

2.1.2 Composite KLR indicator

In the concluding chapter of their 1998 paper, Kaminsky, Lizondo and Reinhart stated

that the natural extension of their analysis would have been the construction of a

composite index for simultaneous signals. In 2000, Kaminsky presented a paper on

this topic, where she suggested four composite indices for currency and banking

crisis. The only composite indicator, that could be potentially interesting for this

thesis, combined single indicators into a system by weighing their respective

importance using the inverse noise-to-signal ratio:

(7)

!

It =Stj

" j

j=1

m

# ,

where

!

Stj equals 1 if the indicator j crosses the critical threshold in period t,

!

" j is the

noise-to-signal ratio of the indicator j (defined as

!

" j=

B

B+D÷

A

A+C from equation

(4)), and m is the number of observations. This composite indicator has several

advantages and disadvantages: the main disadvantage is that the outcome of this

system is not binary anymore and thus, a threshold for the indicator itself is needed to

decide whenever the probability should be treated as a call for an event. Among the

advantages of this system is the fact, that the same non-binary outcomes

(probabilities) allow for the KLR system to be compared with the logit/probit

methodology using the log and the quadratic probability scores – such formulation

then allows for various ex ante, i.e. logit/probit and signaling-based, systems to be

compared statistically (Kaminsky 2000: 16).

2.2 From KLR thresholds to moving extrema

The unfitness of KLR thresholds to issue a sufficient number of signals working with

long-term country-specific data becomes evident when levels and growth rates of

variables, that were found significant, for example, within the probit models discussed

in section 1.2.2 (house price boom/busts and peaks forecasting), are plotted and

compared in the pre-bubble periods. The idea of using thresholds to indicate a signal,

when deviations in the variable’s dynamics are sufficient (growth rates or the values

(!"

in levels exceed a threshold), can only be justified if the history of such deviations

supports the theory.

Figure 4, where the nominal long-term interest rates are presented in levels (covering

the whole sample), allows for such comparison in combination with Figure 5 - the

same indicator’s values prior to all bubble episodes within 3-year windows,

explaining the aforementioned notion.

Figure 4. Nominal long-term interest rate (in levels), period of 1891-2009

Source: Officer (2010), author’s calculations, bubble episodes (in red)

Figure 5. Nominal long-term interest rates (in levels) during the 3-year windows

preceding each bubble episode, 7 episodes

Source: Ibid.

The default assumptions regarding the long-term interest rate would suggest that the

low/declining rate would boost the demand for housing by lowering the cost of

capital, increasing the demand for loans and creating additional liquidity, with which

potential buyers can bid prices up. Figures 4 and 5, though, clearly show that such a

" (#"

single threshold cannot be defined, as there is no clear pattern for the interest rates

being lower during pre-bubble times than during tranquil times.

Even the usage of percentiles, implemented in KLR, would not give sufficient results,

as it is not the case for, at least, the nominal long rate to have lower level of values

with each bubble episode. Expressing the indicator in percentage change does not

improve the picture either (see figures 6, 7).

Figure 6. Nominal long-term interest rate (growth), period of 1891-2009

Source: Ibid.

Figure 7. Nominal long-term interest rate (growth) during the 3-year windows

preceding each bubble episode, 7 episodes

Source: Ibid.

The long rates do display negative change prior to the bubble episodes (figure 7), but

the magnitude of the decline is not sufficient for determining particular thresholds – in

Figure 6 one could notice many periods of much larger declines during tranquil times.

For a similar display in relation to several other variables found significant predicting

house price peaks and boom/busts, respectively in Noord (2006) and Agnello and

Schuknecht (2009), see Appendix 2.

($"

The ongoing global economic crisis that started in 2007 reminded the market

participants of the cyclicality in economic trends, proving once again that what goes

up, has to come down – despite the magnitude and the persistence of the upward

trend. The cyclical nature of long rate dynamics is barely noticeable in 3-year

windows (as in figure 7), but extending the length of these windows to 8 years,

enables a clearer view (see figure 8 – the cycle phases marked with green have a

purely visualization purpose). It becomes evident that prior to an event of

overvaluation, the growth rate of the nominal long-term interest rate declines. The

same variables from Agnello and Schuknecht (2009) and Noord (2006) are

demonstrated in appendix 3 in support of more general upward/downward phases in

explanatory variables prior to bubbles.

Figure 8. Growth of nominal long-term interest rate (in blue) during the 8-year

windows preceding each of the 7 bubble episodes (in red), and cycle phases (in green)

Source: Officer (2010), author’s calculations

Such cyclicality is practically impossible to include in a long-term model using

thresholds – even if the latter are expressed in percentiles: different cycle phases have

different magnitudes and the large growth rates during preceding boom phases distort

the actual size of the previously chosen percentiles, pushing them too high up. The

notion depicted in figure 8 gave me the impulse to put the KLR threshold concept

aside and consider the local maxima/minima in the cycle phases of various lengths

instead. The method developed this way is referred to as the Moving Extrema.22

""""""""""""""""""""""""""""""""""""""""""""""""""""""""

22 I wish to acknowledge, that the methodology proposed here has been developed independently from the more advanced

moving-maximum models, described in Hall et al. (2002). The derivation of the methodology at hand is extremely simple and

intuitive and any similarities with the named study are either natural or coincidental.

" (%"

2.3 Moving Extrema approach

The moving extrema (ME) approach is an early warning system that, similarly to

KLR, follows the dynamics of several variables that were proven to lead certain

events - housing bubbles. Unlike KLR, the moving extrema approach does not follow

such variables crossing predetermined thresholds, but seeks for certain moving

extremum cycle phases observable prior to bubbles. A moving extremum cycle phase

is a number of periods, where the value (of the variable under observation) in the last

period achieves the highest or the lowest value compared to other values inside the

phase. It is important to note, that inside the local extremum phases, values are not

necessarily moving incessantly in the same direction. A theoretical example of a cycle

phase of incessant growth and a moving maxima cycle phase is presented in figure 9

(two cycle phases are independent).

Figure 9. Incessant growth cycle phase (in red) and a moving maxima cycle phase (in

blue); arrows denote the length of moving maxima cycle phases

What figure 9 shows, is an approach somewhat similar to smoothing of data series. It

would have been perfect if variables were to display continuous-change cycle phases,

which could be associated with certain events, but the reality is that there is a

substantial amount of extraneous deviations in the dynamics of variables. For this

reason, a condition that variables have to grow continuously is replaced with moving

extremum cycle phases: in figure 9 the arrow “5” denotes the maximum within the 5-

period cycle phase; the arrow “9” shows the 9-period maximum cycle phase, i.e. the

maximum value during the last 9 periods. The idea of this method is to find similar

ME cycle phases and associate them with the occurrence of bubbles.

)'"

Herring and Wachter (2002: 7) formulated the underlying postulate regarding the

ability to estimate the probability of an upcoming event23

based on historical data - if

the underlying causal structure of the economic system changes each time an event

occurs, previous events cannot be taken as evidence for new estimations; only if the

structure is stable, probabilities of an event can be estimated with a known

confidence. This is the first assumption for constructing an early warning system: the

causal structure of the underlying economic forces is assumed to be stable through

time.

Developing an early warning system constitutes a tradeoff between the amount of

false signals and episodes predicted. Under the KLR methodology in the literature

review section, the loss function, defined by Alessi and Detken (see equation (5)),

looked into this problem by including the user’s relative risk aversion factor to

differentiate between users that are more neutral towards Type I errors (the indicator

fails to signal the upcoming event) than Type II (false signal). Homebuyers, the

primary intended users of this methodology, would generally try to avoid Type I

errors (missed events) for their wrong decisions to purchase real estate during a

bubble may lead to taking large obligations and the risk of losing a substantial part of

their equity. As in any optimization exercise, it is not possible to optimize both sides

of the problem – one should be fixed and the other minimized or maximized.

Following the homebuyer logic, the condition to be enforced at all times is the

requirement that for any separate or composite indicator to be considered within this

analysis, it should be able to predict all the in-sample bubbles (Type I errors must

equal 0). Only then we can work on minimizing the number of false alarms (Type II

errors).

Below, all stages of the moving extrema methodology are described in some detail:

the process of choosing indicators one by one based on their ability to lead bubbles is

presented in section 2.3.1; the procedure of combining separate indicators into

composite indicators is discussed in section 2.3.2; and the procedures for identifying

oncoming bubbles using the composite indicators developed in the preceding section

are described in section 2.3.3.

""""""""""""""""""""""""""""""""""""""""""""""""""""""""

23 In their formulation, an event was a shock.

" )&"

2.3.1 In-sample application: one-indicator moving extrema

To present this methodology as clearly as possible, keeping in mind the targeted final

users of this approach, the required procedures are presented as a user’s manual

flowchart with concrete steps (see figure 10) and comments to these steps.

Figure 10. A flow diagram explaining the implementation procedure of the one-

indicator stage of the moving extrema approach

Comments to Step 1. The number of countries with the amount of sufficiently long-

term data regarding housing prices and explanatory economic variables is limited.

Some of such countries are the Netherlands, Norway, the United Kingdom and the

United States. Housing bubbles can be dated ex post using methods from chapter 1.3.

Comments to Step 2. The more data sets of explanatory variables there are, the higher

the probability of finding variables able to predict all in-sample events with low

number of false alarms. Therefore, different variations and ratios of the same

variables are considered as separate variables: for example, GDP per capita and GDP

per working age population denoted both in levels and as growth rates are treated as

four separate variables.

)("

Comments to Step 3. The idea of the moving extremum cycle phases was described

above. The lengths of these phases (n) are 2, 3, 4, 5, 6, 7, 8 years, all tested

simultaneously and compared in search of the best-performing phase lengths. A

theoretical example of determining moving extremum cycle phases is presented in

table 5. Hypothetical values of a hypothetical variable are taken for a period of seven

years. The moving extremum cycle phase lengths vary from 2 to 7 years. First of all,

as the values in this short series are alternating, there are both moving minimum and

maximum cycles of 2-year length. There is a 3-year moving minimum cycle phase in

1908. The main purpose of this example is to show that the value of a variable in a

certain year can be a moving extremum cycle phase of various lengths – see how a

variable’s value is a 2-, 3- and 4-year moving maxima phase in 1909. The year in

which we start to count makes all the difference.

Table 5. An example of determining moving extremum cycle phases

Year 1906 1907 1908 1909 1910 1911 1912

Values 5 6 2 7 3 9 1

max2 min2 max2 min2 max2 min2

min3 max3 max3 min3

max4 max4 min4

max5 min5

max6 min6

min7

Comments to Step 4. The signaling horizon indicates the number of periods (m),

during which a bubble is expected after an indicator has issued a signal. Three

signaling horizons are simultaneously tested and compared: 1-, 2- and 3-year

horizons. A 3-year signaling horizon means that if an indicator has issued a signal in

1995, a high probability of a bubble exists in 1996, 1997 and 1998.

Comments to Step 5. It is important to develop the notion suggested under the

comment to Steps 2 and 3. If a number of combinations of moving extremum cycle

phases and signaling horizons of one variable were able to call all the in-sample

events, all of those are considered separately. For example, a variable might have

been able to call all the bubbles via moving minimum cycle phases of 4,5 and 6 years

with signaling horizons of 2 and 3 years. In this case, all 6 combinations of the same

variable make it to the next round. In addition, the moving extremum cycle phase

cannot vary within one successful variable. It means that only cycle phases with the

" ))"

same length, direction (maximum or minimum) and signaling horizon that have called

all the bubbles in the sample are to be seen as successful. For example, each time the

moving maximum of 4-year phase of a variable had been observed and a bubble

within 2-year signaling horizon had occurred - this makes this variable a candidate for

the next round.

Comments to Step 7. Having obtained the noise-to-signal ratios for all of the variables

(keeping in mind various cycle phase lengths and signaling horizons) choose one

best-performing combination using the lowest noise-to-signal ratio for each variable.

In case of identical ratios consult other evaluation procedures: correct to all signals

issued, the average number of wrong signals issued per bubble, and the ratios from

KLR (correct signals to all possible correct signals - equation (2); wrong signals to all

possible wrong signals - equation (3); and the conditional/unconditional probability

gap - equation (6)).24

The end result of the one-indicator stage should emerge as one or several tables

(dependent on the number of signaling horizons) with different variables listed by the

ascending noise-to-signal ratio. The outcome of such analysis, described later on in

this paper, can be seen in appendices 5 and 6.

2.3.2 In-sample application: composite indicator

After the results for all of the variables are obtained from the one-indicator stage,

indicators that succeeded in predicting all the events in the sample with noise-to-

signal ratios below 1 are extracted for analysis at the composite level.

The reasoning behind the composite signal is this: different indicators may display

their local minimum and maximum values influenced by various exogenous factors –

it is when several indicators achieve their local maxima/minima at the same time in a

pattern supported by occurrence of bubble in the past immediately after such co-

movements, it is not unreasonable to expect a bubble in the near future. The final

target in such a case would be to “clean” all the false signals out, lowering the noise-

""""""""""""""""""""""""""""""""""""""""""""""""""""""""

24 See appendix 4 for the summary tables of the variable “Nominal long-term interest rate” in levels – this is a suggestion of how

to organize such an analysis in practice.

)*"

to-signal ratio, though keeping in mind the condition that all the bubbles in the sample

have to be predicted by the composite indicator under consideration.

Constructing such an aggregate system is intuitive: if the one-indicator approach is

able to predict all the preceding events with noise-to-signal ratio lower than 1 (1

would mean random signals), then such single indicators can be connected into

systems by signaling horizons and only those signals counted that had been issued by

all indicators. Indicators are included into the system step by step in the order of the

ascending noise-to-signal ratios. Once again, these procedures are presented as a

flowchart in figure 11.

Figure 11. A flow diagram explaining the development procedure of the composite

indicator stage of the moving extrema approach

At first, the first two variables with the lowest noise-to-signal ratios are combined: if

the resulting composite indicator is still able to predict all the in-sample events with a

synergy in terms of a lower noise-to-signal ratio, then the pair is fixed and the next

indicator is included to try for a 3-indicator system. If the third (or any other

consecutive) variable fails to raise the quality of the composite system in terms of

lowering the noise-to-value ratio, it is ignored and the next one on the list is tested.

The limit for the number of indicators included in the composite system is 4, if the

noise-to-signal of 0 has not been reached first. The reason for the maximum number

" )+"

of variables being fixed to 4 is the fact that the marginal decrease in the noise-to-

signal ratio becomes less than the danger of losing good signals and missing bubbles

somewhere after the fourth indicator.25

The evaluation of these composite indicators

is carried out using the same ratios from the one-indicator stage (see comments to

Step 7 in the previous section). These were the actions to be undertaken to develop

composite indicators. The next section describes the process of implementing these

composite indicators to real-life bubble monitoring.

2.3.3 Out-of-sample application

The purpose of developing an early warning system is to use it in the “real time” to

identify specific upcoming events ex ante. Figure 12 describes the specific actions to

use the composite indicators from the moving extrema approach.

Figure 12. A flowchart explaining the implementation procedure of the composite

indicators to “real-time” data

Comments to Step 1. A rather complicated issue to be assessed before implementation

of the composite indicators out of sample is determining if the bursting stage of the

previous bubble is already over. No comprehensive cross-country approach is

suggested in this paper, but the following remark seems to be proper for the US house

prices: during a period of 1890-2000, each bursting bubble had at least two years of

non-negative price change after the deflation of prices. Similar simple analysis

regarding other countries may be appropriate.

Comments to Step 3. For example, if a composite indicator with a 2-year signaling

horizon contains three single indicators – the nominal mortgage rate (with 4-year

moving minimum cycle phase), the growth rate of housing starts (with 3-year moving

""""""""""""""""""""""""""""""""""""""""""""""""""""""""

25 Data series with few missing values that do not coincide with bubbles can still be included into the composite indicator – the

signals issued by all other variables are analyzed in such cases.

)!"

maximum cycle phase) and the M0 money aggregate growth rate (with 5-year moving

maximum cycle phase), a signal will be issued next time when the nominal mortgage

rate will be at its lowest within a moving time window of 4 years, the housing starts’

growth rate has been the highest within a time window of 3 years and the M0 growth

rate has been the highest within a time window of 5 years. Such a signal means that

during the following 2 years there would be a high probability of overvaluation in

house prices.

Comments to Step 4. If there is more than one composite indicator developed within

the in-sample stage, the signals of all of these composite indicators should be

observed in combination and the conclusions made depending on the in-sample

performance of each composite indicator.

" )#"

3. EMPIRICAL ANALYSIS

3.1 Data and variables

The empirical analysis in its entirety is based on one country – the United States of

America - for the period of 1890-2009. The main reason for this was the author’s

desire and interest to develop an early warning system based on long-term trends of a

single country, rather than merging data from various countries into a panel26

, and the

US is the country with the largest amount of publicly available backward looking

statistics in English. There were doubts about the usage of such data as historical

sources are generally more prone to error, not all time series are available in the

desired length, and many fragments of similar variables are not exactly compatible.

On the other hand, pooling countries together would result in an implicit assumption

that the same economic forces accompany housing prices equally and that might lead

to wrong or unsatisfactory results.27

In addition, the usage of annual frequency makes

the necessity to seasonally adjust data redundant, while keeping in place important

underlying trends.

3.1.1 Variables

The choice of indicators/variables to be tested within this thesis was based on table 3,

limited by the availability (or the quality) of data series with sufficient length. There

are two blocks of data analyzed within this thesis categorized by the length of the

series: 1890-2007 and 1930-2007.28

The first block is further divided by three themes:

macroeconomic, housing sector and other variables; the second has an additional set

of affordability variables (see tables 6 and 7).29

Forty different variables were

collected, 24 of which with the sample length of 1890-2009 and 16 with the sample

""""""""""""""""""""""""""""""""""""""""""""""""""""""""

26 Altough

Fuertes and Kalotychou (2006) expressed their support for the panel analysis and argued that it was much more

efficient in terms of forecast performance.

27 Berg et al. (2008), Bunda and Ca’Zorzi (2009), Calza et al. (2009) among others supported this view.

28 Limiting samples to 2007 is dictated by methodological issues (the bubble dating procedure in section 1.3. were based on full

sample length – i.e. 1890-2009).

29 Demographic variables were listed under the macroeconomic theme.

)$"

length of 1930-2009. Due to the signaling nature of the model developed and tested in

this paper, only those variables are considered in levels that may display sufficient

cyclical dynamics expressed in levels.

Table 6. List of variables with data available for 1890-2007 and the number of time

series that entered the analysis

Macroeconomic Levels Growth No of series

Real consumption per capita + 1

Nominal exchange rate: GBPUSD + + 2

Employed persons + 1

GDP deflator ratio + 1

Real GDP + 1

Real GDP per capita + 1

Real GDP per person in labor force, per employed person + 2

Interest rate: nominal and real: short, long, term spread + + 12

Labor force + 1

Real money supply: M0, M2 + 2

M2 multiplier (M2/M0 ratio) + + 2

Real output gap + + 2

P/E ratio: S&P 500 + + 2

Population + 1

Labor force to population + + 2

Real productivity: nonfarm business output per hour + 1

Stock market index: S&P 500 real price + 1

Unemployment rate + + 2

Inflation rate + 1

TOTAL Macroeconomic 38

Housing sector

Real construction cost + 1

Housing starts + 1

Mortgage rate: nominal, real, gap + + 8

Real residential investment + 1

Share of real residential investment in GDP + + 2

Real residential nonfarm wealth, per capita ratio + 2

Real residential nonfarm wealth to labor force + 1

Real residential nonfarm wealth per employed person + 1

Real residential nonfarm wealth to M0; M2 + + 4

TOTAL Housing Sector 21

Other

Gap between real house price and its 5-year MA + + 2

Lagged real house price (1,2,3-year lags) + 3

Rapid real house price growth (>2%) + 1

2;3- year moving average of growth in real house prices + 2

Real price of gold ounce + 1

House price/gold ounce price (levels and growth) + + 2

TOTAL Other 11

TOTAL 70

* - Data in levels start from 1890; growth rate data start from 1891

" )%"

Table 7. List of variables with data available for 1930-2007 and the number of time

series that entered the analysis

Macroeconomic Levels Growth

No of

Series

Real federal budget balance + 1

Federal budget balance to GDP + 1

Real current account + + 2

Current account to GDP + + 2

Real government expenditure + 1

Government expenditure to GDP + 1

Real government net saving + + 2

Government net saving to GDP + 1

Real government revenue + 1

Government revenue to GDP + + 2

Real personal and disposable income + 2

Real personal and disposable income per capita + 2

Real personal and disposable income to labor force + 2

Real personal and disposable income per employed person + 2

Personal and disposable income to GDP + + 4

Real personal saving + 1

Personal saving to GDP + + 2

Real personal saving per capita + 1

Real personal saving to labor force + 1

Real personal saving per employed person + 1

Real gross private domestic investment + 1

Gross private domestic investment to GDP + + 2

Residential investment to gross private domestic investment + + 2

Real M1 + 1

M1/M0, M2/M1 + + 4

TOTAL Macroeconomic 42

Housing sector

Real rental price of tenant occupied nonfarm housing + 1

Real imputed rental price (owner-occupied) nonfarm housing + 1

Real housing and utilities expenditures growth + 1

Housing and utility expenditures % from disposable income + + 2

Housing and utility expenditures % from consumption + + 2

Real nonfarm mortgage debt + 1

Nonfarm mortgage debt to GDP + + 2

Real nonfarm residential mortgage debt + 1

Nonfarm residential mortgage debt to GDP + + 2

Real mortgage interest cost + 1

TOTAL Housing sector 14

Affordability ratios

Price-to-income + + 2

Price-to-rent + + 2

Total mortgage interest cost to total disposable income + + 2

TOTAL Affordability ratios 6

Other

Gap between actual and 5-year price-to-income, price-to-rent + + 4

Gap between current saving and 5-year MA + + 2

Real farm value (land + buildings) per acre + 1

TOTAL Other 7

TOTAL 71

* - Data in levels start from 1929; growth rate data start from 1930

Where applicable, data is analyzed both in levels and per annum growth rates. The

following variables, listed in table 3 and likewise interesting within this analysis, were

omitted due to the lack of data: after-tax interest rate, credit to the private sector,

housing stock, working age population, and the user cost of housing. Apart from

these, all the variables that were touched upon in table 3 were presented in the

*'"

analysis with some additions. The collected data consist of series extracted from

original sources and those derived from the latter. The description of such data

transformation follows next.

1. The GDP deflator, which is the broader measure of inflation, is calculated as the

ratio of nominal to real GDP.

2. The size of the labor force was calculated using the unemployment rate and the

total persons employed data:

(8)

!

LF = E +uE

1"u ,

where LF is the size of the labor force, u is the unemployment rate, E is the number of

employed persons.

3. The term spread and the mortgage rate spread are calculated as the difference

between respectively the long-term and the short-term interest rate; and the mortgage

rate and the short-term interest rate (separately real and nominal).

Figure 13. Real GDP index (1980=100) and the smoothed trend using HP filter with

!=1600, period of 1890-2009

Source: 1890-1928 – Grebler et al. (1956) Appendix B; 1929-2009 – NIPA: Table 1.1.5; author’s

calculations

4. The real output gap was calculated by smoothing the real GDP series with the

Hodrick-Prescott filter (!=1600) and then the gap between the actual and the

" *&"

smoothed (potential) GDP was divided by the smoothed value (the results are

displayed in figure 3).30

5. A more controversial variable (in terms of reliability and applicability) is the total

real mortgage interest cost and its ratio to the total disposable income. As respective

data could not be obtained for the required period, this variable was calculated as the

product of the mortgage rate and the total amount of residential nonfarm mortgages

outstanding, although it is known that adjustable rate mortgages are not the

predominant product in the US housing market.31

Thus, the conclusions arising from

the possible usage of this variable should be treated cautiously.

3.2 In-sample analysis and results

To assess the fair value of the developed model, the recursive testing could be

implemented for the whole sample period, reproducing the analysis that could have

been performed after the first bubble (in this sample) of 1894-1895, moving further to

predict each following event. On the other hand, 141 data sets available for analysis

make it more reasonable to mimic only the prediction process of the last episode of a

housing bubble that was measured to have started in 2004, trying to see if this

methodology could have helped to predict the bubble in advance of 1-3 years.

3.2.1 1890-1990 (long sample)

One-indicator stage

For the period of 1890-1990 6 bubbles were identified ex post (see table 2 or figure

3). Each time a series from table 6 enters the analysis so that the predictive ability of

those variables can be tested on the sample of the first 6 bubbles in search of existing

cyclical dynamics. If the tests return satisfactory results, meaning that all 6 bubbles

are predicted with the noise-to-signal ratio being lower than 1, a variable can be called

successful, allowing it to qualify for the next round. No assumptions are made about

the direction of extrema (minima or maxima) that would predict all in-sample events

""""""""""""""""""""""""""""""""""""""""""""""""""""""""

30 St-Amant and Norden (1997) concluded that the usage of HP filtering is not always a reliable method to measure the output

gap; nevertheless, within this thesis the output gap is merely a variable among others and an in-depth analysis of the latter using

more sophisticated methodologies would be outside the scope of this paper.

31 Girouard (2006: 28) stated that adjustable rate mortgages constituted only 33% of all mortgages in the US by 2005.

*("

with little noise, as the transition mechanisms for the most of the variables could be

described in both ways. For example, declining interest rate (maximum-type phase)

could be an indication of possible overheating in the housing market, but at the same

time increasing values of this variable could indicate the proximity to the peak of the

housing bubble (minimum-type phase). The summary of the five best-performing

indicators is presented in tables 8 and 9 (see full results in appendix 5).

Table 8. The best five indicators that predicted all 6 bubbles during 1890-1990 with

signal-to-noise ratios lower than 1; 2-year signaling horizon

Name

Growth

/ Levels

Moving

Extremum

Length

of

phase

Noise-

to-

signal

ratio

Good /

All

signals

Wrong

signals

per

called

bubble

Conditional -

Unconditional

Probability

1

3-year lagged real

house price G max 3 0.49 0.26 4.67 0.11

2

Real house price

and 5-year MA gap L max 2 0.58 0.23 6.00 0.08

3

Res. n-f wealth to

M0 G max 2 0.59 0.23 6.17 0.08

4 Real mortgage rate L max 3 0.60 0.23 5.67 0.08

5

Real res. n-f wealth

to labor force G max 2 0.67 0.21 6.33 0.06

Comment: complete results in appendix 5.1

Table 9. The best five indicators that predicted all 6 bubbles during 1890-1990 with

signal-to-noise ratios lower than 1; 3-year signaling horizon

Name

Growth

/ Levels

Moving

Extremum

Length

of

phase

Noise-

to-

signal

ratio

Good /

All

signals

Wrong

signals

per

called

bubble

Conditional -

Unconditional

Probability

1

Real construction

cost G max 4 0.50 0.35 2.50 0.14

2

Nominal long term

rate G min 5 0.53 0.33 2.67 0.12

3

2-year lagged real

house price G max 3 0.55 0.32 4.17 0.11

4 Housing starts G max 3 0.56 0.32 3.50 0.11

5

Residential

investment to GDP G max 3 0.56 0.32 3.50 0.11

Comment: complete results in appendix 5.2

The initial results contained two variables that displayed their best results within 1-

year signaling horizon framework: real and nominal mortgage rate analyzed in levels.

These were merged with the next better-performing horizon – 2-year signaling

window category. Note how with the lengthening signaling horizon increases the

length of cycle phases, giving more space to the latter to be revealed, ignoring the

random exogenous effects. Out of 70 data series, 53 managed to predict all the events

" *)"

in the sample with noise-to-ratios below 1. From these, 8 achieved noise-to-signal

ratios below 0,6 and 19 indicators below 0,7. Each fourth signal issued by the 3-year

lagged real house price is good, and there are approximately 5 false alarms per called

bubble. The real construction cost performs better with each third signal appropriate

and only 2-3 false alarms per called bubble. These results may seem somewhat not

too encouraging at first, but the problem of a large amount of false signals will be

solved within the composite indicator stage.

Composite indicators

The composite indicators are built keeping in mind the respective signaling horizon (2

or 3 years in the case of the long sample), where the single indicators from appendix 5

are added step by step. The results of such composition are presented in tables 10 and

12. The best performing (in terms of noise-to-signal ratios) single-indicators that

entered the 2-year signaling horizon composite indicator were: 1) gap between the

real house price and its 5-year moving average in levels, 2) real residential nonfarm

wealth to labor force expressed in growth rates; 3) real residential nonfarm wealth per

employed person expressed in growth rates; and 4) real price of gold ounce expressed

in growth rates.

Table 10. Composite indicator that predicted all 6 bubbles during 1890-1990; 2-year

signaling horizon

Bubbles

called

Noise-to-signal

ratio

Good to

all

signals

Wrong

signals/

Called

Bubbles

Good/All

Possible

Good

Signals

Conditional -

Unconditional

Probability

Wrong

signals/

Tranquil

times

2 indicators 100% 0.39 0.31 3.33 0.60 0.16 0.24

3 indicators 100% 0.33 0.35 2.83 0.60 0.20 0.20

4 indicators 100% 0.24 0.43 2.00 0.60 0.28 0.14

Indicators in order of inclusion: gap between the real house price and its 5-year moving

average (in levels); real residential nonfarm wealth to labor force (growth); real residential

nonfarm wealth per employed person (growth); real price of gold ounce (growth)

Comparing this composition with table 8, one would notice that several single

indicators that scored lower noise-to-signal ratios than some of those that entered the

composite indicator were excluded from the composite. The reason for that is their

inability to cooperate with other indicators, either failing to predict in-sample events

or under-achieving in terms of reduced level of noise.

**"

The 2-year horizon composite model does not perform ideally in-sample: noise-to-

signal ratio does drop to 0,24, but there are still too many false alarms – 2 per called

bubble. This can be viewed in the following way: 15% of the tranquil times false

alarms arrive, which means that during 1890-1990 (101 years) there were wrong

signals 15 times. The fact that there are quite many signals issued is seen also via the

high number of good to all possible good signals, which is 0,6, good on the one hand,

but also potentially dangerous, as it implies higher proportion of random signals.

Looking at each bubble episode separately gives some insights into the consistency of

the composite indicator’s performance (see table 11). The performance has been quite

homogenous and most of the bubbles had 1-2 false alarms per each bubble episode.

The noise-to-signal ratio has also persisted at the same level, with a large deviation

during the first bubble period mainly due to the length of that period (6 years). The

fact that the period during the 1948-1979 had 5 wrong signals raises some doubt,

although the following prediction of the bubble in the end of the 80s was overall

successful.

Table 11. Composite indicator’s performance over the period of 1890-1990; 2-year

signaling horizon; details for 6 bubble episodes

Bubbles

called

Noise-to-signal

ratio

Good to

all

signals

Wrong

signals/

Called

Bubbles

Good/All

Possible

Good

Signals

Conditional -

Unconditional

Probability

Wrong

signals/

Tranquil

times

TOTAL

PERIOD 6 0.24 0.43 2.00 0.60 0.28 0.14

1890-1895 1 1.50 0.67 1.00 0.67 -0.08 1.00

1896-1907 1 0.20 0.50 1.00 0.50 0.33 0.10

1908-1916 1 0.29 0.50 1.00 0.50 0.28 0.14

1917-1947 1 0.07 0.60 2.00 1.00 0.50 0.07

1948-1979 1 0.33 0.17 5.00 0.50 0.10 0.17

1980-1990 1 0.75 0.33 2.00 0.33 0.06 0.25

Indicators: see footer of table 10

The 3-year signaling horizon composite indicator consists of the following indicators:

1) 2-years lagged house price expressed in growth rates; 2) ratio of residential

investment to GDP expressed in growth rates of the ratio; 3) real residential growth

expressed in growth rates; and 4) nominal exchange rate GBPUSD expressed in

growth rates (see table 12). The results clearly improve with the 3-year signaling

horizon model, where the noise-to-signal ratio declines to the level of 0,13 and there

is a false alarm only per every second bubble.

" *+"

Table 12. Composite indicator that predicted all 6 bubbles during 1890-1990; 3-year

signaling horizon

Bubbles

called Noise-to-signal ratio

Good to

all

signals

Wrong

signals /

Called

Bubbles

Good/All

Possible

Good

Signals

Conditional -

Unconditional

Probability

Wrong

signals/

Tranquil

times

2 indicators 100% 0.30 0.47 1.33 0.33 0.26 0.10

3 indicators 100% 0.27 0.50 1.17 0.33 0.29 0.09

4 indicators 100% 0.13 0.67 0.50 0.29 0.46 0.04

Indicators in order of inclusion: 2-years lagged house price (growth); residential investment

to GDP (growth); real residential investment (growth); nominal exchange rate GBPUSD

(growth)

Table 13. Composite indicator’s performance over the period of 1890-1990; 3-year

signaling horizon; details for 6 bubble episodes

Bubbles

called

Noise-to-signal

ratio

Good to

all

signals

Wrong

signals /

Called

Bubbles

Good/All

Possible

Good

Signals

Conditional -

Unconditional

Probability

Wrong

signals/

Tranquil

times

TOTAL

PERIOD 6 0.13 0.67 0.50 0.29 0.46 0.04

1890-1895 1 N/A 1.00 0.00 0.25 0.00 N/A

1896-1907 1 0.00 1.00 0.00 0.33 0.75 0.00

1908-1916 1 0.50 0.50 1.00 0.33 0.17 0.17

1917-1947 1 0.00 1.00 0.00 0.25 0.87 0.00

1948-1979 1 0.21 0.33 2.00 0.33 0.24 0.07

1980-1990 1 0.00 1.00 0.00 0.25 0.64 0.00

Indicators: see footer of table 12

Table 13 indicates a relatively consistent performance with no false signals in 4 out of

6 bubbles. In addition, the last two bubble episodes were forecasted with low noise-

to-signal ratio. All the performance measures and the length of the signaling window

indicate that this is the reliable model from the long-sample group.

3.2.2 1930-1990 (short sample)

A similar analysis to the one described in the previous section was undertaken for the

short sample (period of 1930-1990). This time there were enough single-indicators

performing well within 1-year signaling horizon to form a separate group. The results

for the first 5 successful indicators with 1-, 2- and 3-year signaling horizons are

presented in tables 14,15,16 (for complete results see appendix 6).

*!"

Table 14. The best five indicators that predicted all 3 bubbles during 1930-1990; 1-

year signaling horizon

Name

Growth

/ Levels

Moving

Extremum

Length

of

phase

Noise-

to-

signal

ratio

Good /

All

signals

Wrong

signals

per

called

bubble

Conditional -

Unconditional

Probability

1

Real government net

saving L max 4 0.25 0.27 3.67 0.18

2

Government net saving to

GDP L max 4 0.27 0.25 4.00 0.17

3

Government expenditure to

GDP G min 4 0.31 0.22 4.67 0.14

4 Personal income to GDP G max 3 0.36 0.20 6.67 0.12

5

Mortgage interest to disp.

Income G max 4 0.38 0.19 7.00 0.11

Comment: complete results in appendix 6.1

Table 15. The best five indicators that predicted all 3 bubbles during 1930-1990; 2-

year signaling horizon

Name

Growth

/ Levels

Moving

Extremum

Length

of

phase

Noise-

to-

signal

ratio

Good /

All

signals

Wrong

signals

per

called

bubble

Conditional -

Unconditional

Probability

1

Price-to-income and 5-year

MA gap L max 7 0.15 0.50 2.33 0.37

2

Price-to-rent and 5-year MA

gap L max 5 0.26 0.36 4.67 0.23

3 Price-to-income L max 3 0.28 0.35 3.67 0.22

4

Federal budget balance to

GDP L max 4 0.33 0.31 3.67 0.18

5 Real federal budget balance L max 3 0.35 0.30 4.67 0.17

Comment: complete results in appendix 6.2

Table 16. The best five indicators that predicted all 3 bubbles during 1930-1990; 3-

year signaling horizon

Name

Growth

/ Levels

Moving

Extremum

Length

of

phase

Noise-

to-

signal

ratio

Good /

All

signals

Wrong

signals

per

called

bubble

Conditional -

Unconditional

Probability

1 Real farm value per acre G max 8 0.18 0.56 1.33 0.38

2 Real government expenditure G min 8 0.22 0.50 1.33 0.32

3 Price-to-rent L max 8 0.25 0.47 3.00 0.29

4

Saving-to-GDP and 5-year

MA gap L min 7 0.26 0.46 2.33 0.28

5 Price-to-income G max 7 0.26 0.45 2.00 0.27

Comment: complete results in appendix 6.3

For the shorter sample, 66 out of 71 time series were able to predict all 3 bubbles, of

which 11 achieved noise-to-signal ratio levels below 0,3. Especially low ratios were

registered for the variables: gap between price-to-income ratio and its 5-year moving

" *#"

average in levels (0,15) and real farm value per acre (0,18) with 2- and 3-year

signaling horizons respectively.

It is crucial to underline the importance of the smaller sample on the reliability of the

results: when there is a decline in sample size in regression models, it results in a

smaller number of degrees of freedom, which then pushes the critical values for the

test statistics up, requiring smaller standard errors of coefficients for the latter to be

statistically significant at the same confidence level. As the moving extrema approach

does not have statistical testing behind it, it is difficult to implement a precise

requirement to account for the shortened sample, although there is one condition that

can be enforced to make the results more viable: to lower the acceptable threshold of

the noise-to-signal ratio - in appendix 6 this is expressed as highlighted areas, where

the indicators that scored noise-to-signal ratios above 0,5 are marked with grey. These

indicators should not be considered as candidates for the composite indicators.

Composite indicators

The larger number of successful indicators with 3 different signaling horizons allows

to built 3 composite indicators on the same principles as described above (see tables

17,19,21).

The 1-year signaling horizon model consists of the following indicators: 1) real

government net savings in levels; 2) government net saving to GDP in levels; 3)

government expenditure to GDP expressed in growth rates; 4) personal income to

GDP expressed in growth rates (see table 17).

Table 17. Composite indicator that predicted all 3 bubbles during 1930-1990; 1-year

signaling horizon

Bubbles

called

Noise-to-signal

ratio

Good to

all

signals

Wrong

signals /

Called

Bubbles

Good/All

Possible

Good

Signals

Conditional -

Unconditional

Probability

Wrong

signals /

Tranquil

times

2 indicators 100% 0.25 0.27 3.67 0.80 0.18 0.2

3 indicators 100% 0.12 0.43 1.33 0.6 0.35 0.07

4 indicators 100% 0.03 0.75 0.33 0.60 0.67 0.02

Indicators in order of inclusion: real government net savings (in levels); government net

saving to GDP (in levels); government expenditure to GDP (growth); personal income to

GDP (growth)

*$"

Table 18. Composite indicator’s performance over the period of 1930-1990; 1-year

signaling horizon; details for 3 bubble episodes

Bubbles

called

Noise-to-signal

ratio

Good to

all

signals

Wrong

signals /

Called

Bubbles

Good/All

Possible

Good

Signals

Conditional -

Unconditional

Probability

Wrong

signals /

Tranquil

times

TOTAL

PERIOD 3 0.03 0.75 0.33 0.60 0.67 0.02

1930-1947 1 0.00 1.00 0.00 0.50 0.88 0.00

1948-1979 1 0.00 1.00 0.00 1.00 0.97 0.00

1980-1990 1 0.22 0.50 1.00 0.50 0.32 0.11

Indicators: see footer of table 17

It is the riskiest indicator of those analyzed in this paper, as it enforces the strictest

condition: the issued signal indicates a bubble within the next year, not during two or

three years. Taking this into account, the model performs very well in-sample: with

the noise-to-signal ratio of 0,03; 3 signals out of 4 being correct, and with only one

wrong signal per 3 bubbles. Also the consistency of predictions is quite good: all

bubbles called with noise-to-signal ratios close to 0 (see table 18). Despite good in-

sample performance, the riskiness of this indicator (due to the signaling horizon and

the sample length) should definitely be treated cautiously while relying on out-of-

sample forecasts.

Table 19. Composite indicator that predicted all 3 bubbles during 1930-1990; 2-year

signaling horizon

Bubbles

called

Noise-to-signal

ratio

Good to

all

signals

Wrong

signals /

Called

Bubbles

Good/All

Possible

Good

Signals

Conditional -

Unconditional

Probability

Wrong

signal /

Tranquil

times

2 indicators 100% 0.11 0.58 1.67 0.88 0.45 0.09

3 indicators 100% 0.09 0.63 1.00 0.63 0.49 0.06

4 indicators 100% 0.05 0.75 0.33 0.38 0.62 0.02

Indicators in order of inclusion: gap between the current price-to-income ratio and its 5-

year moving average (in levels); gap between the current price-to-rent ratio and its 5-year MA

(in levels); price-to-income ratio (in levels); gap between the current price-to-income and its

5-year MA (growth)

The composite indicator based on the 2-year signaling horizon was composed of 1)

the gap between the current price-to-income ratio and its 5-year moving average in

levels; 2) the gap between the current price-to-rent ratio and its 5-year MA in levels;

3) price-to-income ratio in levels; 4) gap between the current price-to-income and its

5-year MA expressed in growth rates (see table 19). A noise-to-ratio level of 0,05 and

only 2% of false signals during tranquil times makes the indicator rather attractive and

" *%"

dependable. The consistency of predictions shown in table 19 is sufficient: two last

bubbles were called with 0 noise-to-signal ratios. It is very similar to the previous

specification in terms of performance, but the 2-year signaling window makes it less

risky.

Table 20. Composite indicator’s performance over the period of 1930-1990; 2-year

signaling horizon; details for 3 bubble episodes

Bubbles

called

Noise-to-signal

ratio

Good to

all

signals

Wrong

signals /

Called

Bubbles

Good/All

Possible

Good

Signals

Conditional -

Unconditional

Probability

Wrong

signals/

Tranquil

times

TOTAL

PERIOD 3 0.05 0.75 0.33 0.38 0.62 0.02

1930-1947 1 0.21 0.50 1.00 0.33 0.32 0.07

1948-1979 1 0.00 1.00 0.00 0.50 0.94 0.00

1980-1990 1 0.00 1.00 0.00 0.33 0.73 0.00

Indicators: see footer of table 19

The 3-year signaling horizon composite indicator displayed the best results within the

in-sample analysis with the following two variables: 1) real farm value (land +

improvements) per acre expressed in growth rates and 2) the price-to-rent ratio in

levels (see tables 21 and 22).

Table 21. Composite indicator that predicted all 3 bubbles during 1930-1990; 3-year

signaling horizon

Bubbles

called

Noise-to-signal

ratio

Good to

all

signals

Wrong

signals /

Called

Bubbles

Good/All

Possible

Good

Signals

Conditional -

Unconditional

Probability

Wrong

signals/

Tranquil

times

2 indicators 100% 0.00 1.00 0.00 0.27 0.82 0.00

Indicators in order of inclusion: real farm value (land + improvements) per acre (growth);

price-to-rent ratio (in levels)

A noise-to-signal of 0,00 means no false alarms. At the same time only 27% of all

possible good signals were issued. It may be due to the cycle phase length of the

variables, 8 years, filtering out the longest phases in the development of these

variables. This is the second most reliable indicator, after the long-sample 3-year

signaling horizon composite indicator and should be considered in a combination with

the latter for more reliable forecasting.

+'"

Table 22. Composite indicator’s performance over the period 1930-1990; 3-year

signaling horizon; details for 3 bubble episodes

Bubbles

called

Noise-to-signal

ratio

Good to

all

signals

Wrong

signals /

Called

Bubbles

Good/All

Possible

Good

Signals

Conditional -

Unconditional

Probability

Wrong

signals/

Tranquil

times

TOTAL

PERIOD 3 0.00 1.00 0.00 0.27 0.82 0.00

1930-1947 1 0.00 1.00 0.00 0.25 0.76 0.00

1948-1979 1 0.00 1.00 0.00 0.33 0.91 0.00

1980-1990 1 0.00 1.00 0.00 0.25 0.64 0.00

Indicators: see footer of table 21

3.3 Out-of-sample analysis and results

The in-sample results are sufficient, but the only way to appraise the predictive

quality of a model is to test (or carry out a simulation simulation of) it in the out-of-

sample mode. The most reliable composite indicators based on in-sample

performance and the intrinsic nature of the signaling horizon were the two 3-year

signaling window models. The importance of the longer signaling horizon in terms of

reliability comes from simple probabilities: if there is a period of 10 years which

contains one event, then an indicator with 3-year signaling horizon is approximately 3

times more likely to randomly predict the event than the 1-year signaling horizon

model.

Below, both long sample models with 2- and 3-year signaling horizons and the three

short sample models with 1-,2- and 3-year signaling horizon are tested, seeking to

find if they were able to predict the bubble that, according to the chosen ex post

identification methodology, had developed in 2004 and continued till 2007.

3.3.1 1991-2007 (long sample)

With the 2-year signaling horizon indicator the expectations of possible mediocre

performance came true (see table 23). In in-sample mode, there were two false alarms

per bubble. The ratio has increased to 2.3 for the complete sample with all seven

bubbles. This was due to the fact that during out-of-sample testing the indicator issued

five signals, only one of which was correct.

" +&"

Table 23. Composite indicator’s performance over the total sample period of 1890-

2007; 2-year signaling horizon; details for 7 bubble episodes

Bubbles

called

Noise-to-signal

ratio

Good to

all

signals

Wrong

signals /

Called

Bubbles

Good/All

Possible

Good

Signals

Conditional -

Unconditional

Probability

Wrong

signals/

Tranquil

times

TOTAL

PERIOD 7 0.33 0.38 2.29 0.50 0.21 0.17

1890-1895 1 1.50 0.67 1.00 0.67 -0.08 1.00

1896-1907 1 0.20 0.50 1.00 0.50 0.33 0.10

1908-1916 1 0.29 0.50 1.00 0.50 0.28 0.14

1917-1947 1 0.07 0.60 2.00 1.00 0.50 0.07

1948-1979 1 0.33 0.17 5.00 0.50 0.10 0.17

1980-1990 1 0.75 0.33 2.00 0.33 0.06 0.25

1991-2007 1 1.67 0.20 4.00 0.20 -0.09 0.33

Indicators in order of inclusion: gap between the real house price and its 5-year moving

average (in levels); real residential nonfarm wealth to labor force (growth); real residential

nonfarm wealth per employed person (growth); real price of gold ounce (growth)

In other words, the 2004-2007 bubble was called, but with way too many false alarms

– 4. With a whopping 1,67 noise-to-signal ratio it can be concluded that this indicator

was overall unsuccessful, though expectedly so. In its defense, it should be

mentioned, that the correct signal was issued in 2002, having predicted the first year

of overvaluation (see table 28).

The more reliable, at least based on the in-sample testing results, 3-year signaling

horizon long-sample indicator was tested next (see table 24).

Table 24. Composite indicator’s performance over the total sample 1890-2007; 3-

year signaling horizon; details for 7 bubble episodes

Bubbles

called

Noise-to-signal

ratio

Good to

all

signals

Wrong

signals /

Called

Bubbles

Good/All

Possible

Good

Signals

Conditional -

Unconditional

Probability

Wrong

signals/

Tranquil

times

TOTAL

PERIOD 7 0.11 0.73 0.43 0.30 0.49 0.03

1890-1895 1 N/A 1.00 0.00 0.25 0.00 N/A

1896-1907 1 0.00 1.00 0.00 0.33 0.75 0.00

1908-1916 1 0.50 0.50 1.00 0.33 0.17 0.17

1917-1947 1 0.00 1.00 0.00 0.25 0.87 0.00

1948-1979 1 0.21 0.33 2.00 0.33 0.24 0.07

1980-1990 1 0.00 1.00 0.00 0.25 0.64 0.00

1991-2007 1 0.00 1.00 0.00 0.33 0.65 0.00

Indicators in order of inclusion: 2-years lagged house price (growth); residential investment

to GDP (growth); real residential investment (growth); nominal exchange rate GBPUSD

(growth)

+("

The model performed very well, having predicted the out-of-sample event with no

false alarms. The in-sample noise-to-signal ratio of 0,13 dropped further to the total

sample ratio of 0,11. Though only every third good signal of all possible good signals

was issued (from possible six signals, that could have been issued for the last bubble,

only two were actually indicated), this result is still more than satisfactory, as the

timing of these signals was very convenient: the first signal was issued in 2002,

meaning that the time-window of 2003-2005 could be potentially bubbly; the second

signal was issued in 2004, covering the period of 2005-2007 (see table 28). As this

indicator was claimed to be the most reliable already during the in-sample tests, a user

(a buy-side investor) consulting this indicator could have avoided making a costly

mistake of entering the overvalued market altogether.

3.3.2 1991-2007 (short sample)

As can be seen from the last row of table 25, there had been cause for alarm that arose

during the in-sample testing – the short sample composite indicator of 1-year

signaling horizon issued no signals during 1991-2007 at all.

Table 25. Composite indicator’s performance over the total sample 1930-2007; 1-

year signaling horizon; details for 4 bubble episodes

Bubbles

called

Noise-to-signal

ratio

Good to

all

signals

Wrong

signals /

Called

Bubbles

Good/All

Possible

Good

Signals

Conditional -

Unconditional

Probability

Wrong

signals/

Tranquil

times

TOTAL

PERIOD 3 0.07 0.67 0.50 0.44 0.55 0.03

1930-1947 1 0.00 1.00 0.00 0.50 0.88 0.00

1948-1979 1 0.00 1.00 0.00 1.00 0.97 0.00

1980-1990 1 0.22 0.50 1.00 0.50 0.32 0.11

1991-2007 0 - - - - - -

Indicators in order of inclusion: real government net savings (in levels); government net

saving to GDP (in levels); government expenditure to GDP (growth); personal income to

GDP (growth)

Fortunately, it was possible to foresee the shortcomings of this indicator already prior

to the tests, and in “real” life the potential user would have been cautious and most

probably consulted it last among others. The 1-year signaling horizon is too narrow

for in-sample testing of only 3 bubbles to give reliable indicator specifications.

" +)"

The 2-year signaling horizon model derived from the short sample variables

performed much better, having predicted the last bubble episode with a noise-to-

signal ratio of 0,42 (see table 26).

Table 26. Composite indicator’s performance over the total sample 1930-2007; 2-

year signaling horizon; details for 4 bubble episodes

Bubbles

called

Noise-to-signal

ratio

Good to

all

signals

Wrong

signals /

Called

Bubbles

Good/All

Possible

Good

Signals

Conditional -

Unconditional

Probability

Wrong

signals/

Tranquil

times

TOTAL

PERIOD 4 0.10 0.67 0.50 0.31 0.50 0.03

1930-1947 1 0.21 0.50 1.00 0.33 0.32 0.07

1948-1979 1 0.00 1.00 0.00 0.50 0.94 0.00

1980-1990 1 0.00 1.00 0.00 0.33 0.73 0.00

1991-2009 1 0.42 0.50 1.00 0.20 0.21 0.08

Indicators in order of inclusion: gap between the current price-to-income ratio and its 5-

year moving average (in levels); gap between the current price-to-rent ratio and its 5-year MA

(in levels); price-to-income ratio (in levels); gap between the current price-to-income and its

5-year MA (growth)

There were two signals issued: one false alarm in 1999, covering the period of 2000-

2001; and the other – a correct signal – in 2004, covering the period of 2005-2006

(see table 28). A potential user basing her decisions purely on this indicator, could

end up having somewhat insufficient forecast material, as year 2004 – the first year of

overvaluation – was not blocked out. Apart from this, the indicator performed rather

well, keeping in mind that it was not considered top quality.

The second most reliable indicator from all five moving extrema approach composite

indicators did not let the potential user down, having predicted the last bubble with no

false alarms, similar to its long sample counterparty (see table 27).

Table 27. Composite indicator’s performance over the total sample 1930-2007; 3-

year signaling horizon; details for 4 bubble episodes

Bubbles

called

Noise-to-signal

ratio

Good to

all

signals

Wrong

signals /

Called

Bubbles

Good/All

Possible

Good

Signals

Conditional -

Unconditional

Probability

Wrong

signal /

Tranquil

times

TOTAL

PERIOD 4 0.00 1.00 0.00 0.29 0.78 0.00

1930-1947 1 0.00 1.00 0.00 0.25 0.76 0.00

1948-1979 1 0.00 1.00 0.00 0.33 0.91 0.00

1980-1990 1 0.00 1.00 0.00 0.25 0.64 0.00

1991-2009 1 0.00 1.00 0.00 0.33 0.65 0.00

Indicators in order of inclusion: real farm value (land + improvements) per acre (growth);

price-to-rent ratio (in levels)

+*"

Of six possible good signals two were issued in a timely manner (see table 28). The

first signal was issued in 2002, preventing the potential user from buying a property

during 2003-2005; the second signal was issued in 2005, covering the period of 2006-

2008. In other words, the buy-side investor having consulted this indicator (especially

in combination with the 3-year signaling horizon composite indicator based on the

long-sample variables) could have successfully avoided the bubbly US housing

market of the first decade of the 21st century.

Table 28. The chronological representation of the issued signals, 1991-2007

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07

2y + + + + + LONG

3y + +

1y

2y + +

Moving

Extrema SHORT

3y + +

Comment: “+” indicates an issued signal; the highlighted gray area and the bold borders

denote the coverage of the correctly issued signals; the diagonal pattern denotes the bubble

3.4 Comparing composite indicators

As we touched upon the composite indicator methodology proposed by Kaminsky

(2000), it is appropriate to compare the outcomes of these two methods. Kaminsky-

type composite indicator (see equation 7) used all the available variables with noise-

to-signal ratio lower than 1 to weigh single-indicators by the inverse of their noise-to-

signal to receive a probability-type distribution (between 0 and 1). After the in-sample

tests are performed, a critical threshold, that would transform the probabilities of an

event into yes/no signals, is to be chosen. This threshold is chosen such that all the in-

sample events are predicted with the lowest possible noise-to-signal. When there is no

marginal gain from raising the threshold (meaning that the noise-to-signal ratio does

not decline any further), its level is fixed for out-of-sample testing.

The summary of the results from such composition is presented in table 29. The in-

sample performance was very good, but not better than the methodology proposed in

this thesis (noise-to-signal ratios for Kaminsky-type indicator were, on average,

higher).

" ++"

Table 29. Performance summary of Kaminsky-type composite indicator

Signaling

horizon IN-SAMPLE

Bubbles

called

Noise-

to-

signal

ratio OUT-OF-SAMPLE

2004-

2007

bubble

called

Noise-

to-

signal

ratio

6 bubbles (1890-

1990)

7 bubbles (1890-

2007)

2y 100% 0.18 NO 0.24

3y 100% 0.19 NO 0.27

3 bubbles (1930-

1990)

4 bubbles (1930-

2007)

1y 100% 0.04 NO 0.07

2y 100% 0.08 YES 0.10

3y 100% 0.07 NO 0.09

Indicators: Long 2-years gap between the real house price and its 5-year moving average

(in levels); real residential nonfarm wealth to labor force (growth); real residential nonfarm

wealth per employed person (growth); real price of gold ounce (growth). Long 3-years : 2-

years lagged house price (growth); residential investment to GDP (growth); real residential

investment (growth); nominal exchange rate GBPUSD (growth). Short 1-year: real

government net savings (in levels); government net saving to GDP (in levels); government

expenditure to GDP (growth); personal income to GDP (growth). Short 2-years: gap between

the current price-to-income ratio and its 5-year moving average (in levels); gap between the

current price-to-rent ratio and its 5-year MA (in levels); price-to-income ratio (in levels); gap

between the current price-to-income and its 5-year MA (growth). Short 3-years: real farm

value (land + improvements) per acre (growth); price-to-rent ratio (in levels).

The out-of-sample performance, on the other hand, was insufficient, with only one of

the indicators being able to predict the bubble of 2004-2007. Not only is this type of

composition unsuitable in terms of results but the manual work behind weighing each

signal by the inverse of its noise-to-signal ratio, is substantial. Moving extrema

composite indicators clearly outperform Kaminsky-type composite indicators. It is

important to note, though, that Kaminsky-type composite indicator approach was

developed for different kind of data – panel medium-term data as opposed to long-

term country-specific data in the case of the moving extrema approach.

+!"

CONCLUSION

The aim of this thesis was to propose an early warning system for timely housing

bubble identification – the moving extrema approach – with homebuyers kept in mind

as the target users.

To do so, three research questions were addressed:

1. What are the available methodologies for identifying housing bubbles?

The two main methodologies most commonly used within house price bubble

identification were discussed: the fundamental price models and probit models. The

fundamental price models compare the positive house prices with the normative

equilibrium prices calculated on a set of assumed economic fundamentals. Some

fundamental models contain error correction specifications (ECM), which are

programmed to explain the path of the price moving back from overvaluation to

equilibrium. Under the limited dependent variable models, two studies that

implemented probit models to identifying housing peaks and house price boom/bust

sequences were described.

2. How does the moving extrema approach work?

The moving extrema approach was inspired by another early warning system

developed initially for currency crisis ex ante identification by Kaminsky, Lizondo

and Reinhart. The root of the moving extrema approach is to find association between

the dynamics of certain explanatory variables and the occurrence of housing bubbles.

Two central definitions were explained: 1) moving extremum cycle phase – a moving

interval of time within which a variable’s value is either the maximum or the

minimum among other values; seven lengths of moving extremum cycle phases were

considered simultaneously in this paper – from 2 to 8 years. Each occurrence of an

extremum in such a moving interval was viewed as a signal; 2) signaling horizon – a

time interval between a signal from moving extremum cycle phase and the occurrence

of a bubble; three signaling horizons were simultaneously tested – 1-, 2- and 3-year

horizons.

" +#"

At first, those variables (with fixed moving extremum cycle phases and signaling

horizons within one series), that were issuing signals prior to each bubble in the

sample, were filtered out as the potentially suitable ones. Then, the noise-to-signal

ratios for each variable were calculated to see if those signals were issued randomly

or if there were relatively more correct signals than wrong ones. Those indicators that

passed this test (didn’t issue signals randomly) were sorted in the ascending order by

the noise-to-signal ratio, divided into groups by signaling horizons.

The best-performing variables were considered within the composite indicators

grouped by the respective signaling horizon: signals issued by two single indicators

with the same signaling horizons were combined and only those counted, that were

issued by both. The requirements for inclusion into a composite indicator were: 1) the

ability to call all bubbles in the sample; 2) synergy from signals issued by several

single indicators in terms of lowered noise-to-signal ratio. The maximum number of

single indicators in the composite indicator was prescribed to 4.

3. How did the moving extrema approach perform out-of-sample?

The best-performing composite indicators, based on in-sample tests, were both 3-year

signaling horizon indicators:

• 2-year lagged real house price, residential investment to GDP, real residential

investment, and nominal exchange rate of GDPUSD currency pair – all

expressed as growth rates [based on the long sample of 1890-1990];

• real farm value of land and improvements per acre expressed as growth rates,

and price-to-rent ratio in levels [based on the short sample of 1930-1990].

These and other less reliable composite indicators were tested under conditions close

to “real”-life, inserting data from 1991 to 2007 to see if these indicators had been able

to identify the bubble that occurred in the beginning of the 21st century if used at the

time. The out-of-sample results were more than satisfactory: both composite

indicators listed above managed to identify the bubble with no false alarms. A

potential user – homebuyer – could have benefited greatly relying on forecasts of

these indicators, as the whole of the housing bubble of 2004-2007 could have been

successfully avoided. Less reliable indicators were not as successful: the riskiest

composite indicator with 1-year signaling horizon failed to indicate the bubble; two

+$"

others did predict the bubble, but issued some false alarms. In defense of this

methodology, it should be said that the potentially unreliable nature of the latter was

obvious already during the in-sample tests.

How could the results of this analysis be used in future?

After the deflation of house prices in the US has stopped and a period of two years of

non-negative growth has been registered, the methodology suggested in this thesis can

be of assistance anew. If one doesn’t wish to carry out all of the analysis undertaken

in this paper to determine the best-performing composite indicators on the new total

sample (including the 1991-2007), and is only interested in checking for a new

possible US housing bubble using the already developed indicators, a shortcut would

be to monitor the developments in the following composite indicators (especially

together):

a) when the 2-years lagged house price growth rate and the growth rate of residential

investment to GDP ratio are both the largest within a 3-year moving cycle phase, the

growth rate of real residential investment is the largest within a 2-year moving cycle

phase and the growth rate of the nominal exchange rate of pound-dollar currency pair

is the largest within a 4-year moving cycle phase, a potential homebuyer should be

cautious of an upcoming bubble during the next 3 years.

b) when the growth rate of real farm value of land and improvements per acre and the

price-to-rent ratio in levels are both the largest within an 8-year moving cycle phase,

once again a bubble is imminent to occur during the following 3 years.

There are many ways in which future research could move further using the outputs

of this thesis. Similar analysis could be carried out on the housing markets of

countries such as the Netherlands, Norway, the UK and others, where data are

available in sufficient length. The moving extrema approach could be developed

further, upgrading the simple method with thresholds, same-direction continuous

change conditions and other modifications to extract maximum utility out of the

cyclical dynamics’ forecasting ability. As this approach lacks the possibilities of

statistical tests, other tests that could help prescribe statistical significance to the

composite and single indicators would be another major improvement.

" +%"

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" !+"

DATA SOURCES Variable Period Source

Real House Price

Index

1890-2009 Online Data Robert Shiller,

http://www.econ.yale.edu/~shiller/data.htm

Real Building

Cost Index

1890-2009 Online Data Robert Shiller,

http://www.econ.yale.edu/~shiller/data.htm

U.S. Population 1890-2009 Online Data Robert Shiller,

http://www.econ.yale.edu/~shiller/data.htm

CPI 1890-2009 Online Data Robert Shiller,

http://www.econ.yale.edu/~shiller/data.htm

Nominal S&P

500 Price

1890-2009 Online Data Robert Shiller,

http://www.econ.yale.edu/~shiller/data.htm

Real p.c.

Consumption

1890-2009 Online Data Robert Shiller,

http://www.econ.yale.edu/~shiller/data.htm

P/E Ratio (S&P) 1890-2009 Online Data Robert Shiller,

http://www.econ.yale.edu/~shiller/data.htm

Long-Term

Interest Rate

1890-2009 Lawrence H. Officer, "What Was the Interest Rate Then?"

MeasuringWorth, 2010. URL:

http://www.measuringworth.org/interestrates/

Short-Term

Interest Rate

1890-2009 Lawrence H. Officer, "What Was the Interest Rate Then?"

MeasuringWorth, 2010. URL:

http://www.measuringworth.org/interestrates/

Mortgage Rate 1890-1952 Grebler, L., Blank, D.M. and Winnick, L. (1956), Capital Formation

in Residential Real Estate: Trends and Prospects. Princeton

University Press, p. 549. Appendix O.

http://www.nber.org/books/greb56-1

Mortgage Rate 1963-2009 Economic Report of the President. Table B-73, Bond yields and

interest rates, 1929-2008.

http://www.gpoaccess.gov/eop/tables09.html

Housing Starts 1890-1952 Grebler, L., Blank, D.M. and Winnick, L. (1956), Capital Formation

in Residential Real Estate: Trends and Prospects. Princeton

University Press, p. 549. Appendix B.

http://www.nber.org/books/greb56-1

Housing Starts 1953-1958 Nonfarm Housing Starts 1889-1958. Bulletin No. 1260.

http://www.michaelcarliner.com/files/Data/BLS59HousingStarts188

9-1958.pdf

Housing Starts 1962-2009 Economic Report of the President. Table B-56, Bond Yields and

Interest Rates, 1929-2008.

http://www.gpoaccess.gov/eop/tables09.html

Federal Budget

Balance

1901-2008 Budget of the US Government. Historical Tables.

http://www.whitehouse.gov/sites/default/files/omb/budget/fy2008/p

df/hist.pdf

Rental of Tenant-

Occupied

Nonfarm Housing

1929-2009 National Income and Product Accounts: Table 2.5.5

http://www.bea.gov/national/nipaweb/SelectTable.asp

Imputed Rent of

Owner-Occupied

Nonfarm

1929-2009 National Income and Product Accounts: Table 2.5.5

http://www.bea.gov/national/nipaweb/SelectTable.asp

Unemployment

rate

1890-1930 Romer, C. (1986), Spurious Volatility in Historical Unemployment

Data. The Journal of Political Economy, 94(1): 1-37.

Unemployment

rate

1931-1939 Coen, R.M. (1973), Labor Force and Unemployment in the 1920's

and 1930's: A Re-Examination Based on Postwar Experience. The

Review of Economics and Statistics, 55(1): 46-55.

Unemployment

rate

1940-2009 Houshold Data Annual Averages. Civilian Labor Force.

ftp://ftp.bls.gov/pub/special.requests/lf/aat1.txt

!!"

Real housing and

utilities

expenditures

1929-2009 National Income and Product Accounts: Table 2.3.3

http://www.bea.gov/national/nipaweb/SelectTable.asp

Nominal GDP 1890-1928 Grebler, L., Blank, D.M. and Winnick, L. (1956), Capital Formation

in Residential Real Estate: Trends and Prospects. Princeton

University Press, p. 549. Appendix B.

http://www.nber.org/books/greb56-1

Nominal GDP 1929-2009 National Income and Product Accounts: Table 1.1.5

http://www.bea.gov/national/nipaweb/SelectTable.asp

Nominal

Residential

Investment

1890-1928 Grebler, L., Blank, D.M. and Winnick, L. (1956), Capital Formation

in Residential Real Estate: Trends and Prospects. Princeton

University Press, p. 549. Appendix B.

http://www.nber.org/books/greb56-1

Nominal

Residential

Investment

1929-2009 National Income and Product Accounts: Table 1.1.5

http://www.bea.gov/national/nipaweb/SelectTable.asp

Nominal

Government

Current Receipts

1929-2009 National Income and Product Accounts: Table 3.1

http://www.bea.gov/national/nipaweb/SelectTable.asp

Nominal

Government

Current

Expenditures

1929-2009 National Income and Product Accounts: Table 3.1

http://www.bea.gov/national/nipaweb/SelectTable.asp

Nominal Net

Government

Saving

1929-2009 National Income and Product Accounts: Table 3.1

http://www.bea.gov/national/nipaweb/SelectTable.asp

Nominal Price of

Gold Ounce

1890-2009 Lawrence H. Officer, "The Price of Gold, 1257-2009,"

MeasuringWorth, 2010. URL:

http://www.measuringworth.org/gold/

Nominal Current

Account

1929-2009 National Income and Product Accounts: Table 4.1

http://www.bea.gov/national/nipaweb/SelectTable.asp

Nominal

Nonfarm

Mortgage Debt

1896-1952 Grebler, L., Blank, D.M. and Winnick, L. (1956), Capital Formation

in Residential Real Estate: Trends and Prospects. Princeton

University Press, p. 549. Appendix L.

http://www.nber.org/books/greb56-1

Nominal

Nonfarm

Mortgage Debt

1953-1954 Economic Report of the President. Table B-75, Bond yields and

interest rates, 1929-2008.

http://www.gpoaccess.gov/eop/tables09.html

Nominal

Nonfarm

Mortgage Debt

1955-2009 US Flow of Funds, Annual Flows and Outstandings.

http://www.federalreserve.gov/releases/z1/current/data.htm

Nominal

Nonfarm

Residential

Mortgage Debt

1896-1952 Grebler, L., Blank, D.M. and Winnick, L. (1956), Capital Formation

in Residential Real Estate: Trends and Prospects. Princeton

University Press, p. 549. Appendix L.

http://www.nber.org/books/greb56-1

Nominal

Nonfarm

Residential

Mortgage Debt

1953-1954 Economic Report of the President. Table B-75, Bond yields and

interest rates, 1929-2008.

http://www.gpoaccess.gov/eop/tables09.html

Nominal

Nonfarm

Residential

Mortgage Debt

1955-2009 US Flow of Funds, Annual Flows and Outstandings.

http://www.federalreserve.gov/releases/z1/current/data.htm

Nominal

GBPUSD

1890-2009 Lawrence H. Officer, "Exchange Rates Between the United States

Dollar and Forty-one Currencies," MeasuringWorth, 2009. URL:

http://www.measuringworth.org/exchangeglobal/

Nominal

Residential

Nonfarm Wealth

1890-1953 Grebler, L., Blank, D.M. and Winnick, L. (1956), Capital Formation

in Residential Real Estate: Trends and Prospects. Princeton

University Press, p. 549. Appendix D.

" !#"

http://www.nber.org/books/greb56-1

Nominal

Residential

Nonfarm Wealth

1955-2009 US Flow of Funds, Annual Flows and Outstandings.

http://www.federalreserve.gov/releases/z1/current/data.htm

Nominal Personal

Income

1929-2009 National Income and Product Accounts: Table 2.1

http://www.bea.gov/national/nipaweb/SelectTable.asp

Nominal

Disposable

Income

1929-2009 National Income and Product Accounts: Table 2.1

http://www.bea.gov/national/nipaweb/SelectTable.asp

Farm Value (land

and buildings)

per acre

1929-2008 Farm Land Values. Department of Agricultural Economics,

University of Missouri.

http://extension.missouri.edu/publications/DisplayPub.aspx?P=G40

4

Owner’s equity

as percentage of

household real

estate

1929-2008 US Flow of Funds, Annual Flows and Outstandings. B-100.

http://www.federalreserve.gov/releases/z1/current/data.htm

Nominal Net

Worth

1929-2008 US Flow of Funds, Annual Flows and Outstandings. B-100.

http://www.federalreserve.gov/releases/z1/current/data.htm

Rent-to-Price

ratio

1960-2009 Davis, Morris A., Lehnert, Andreas, and Robert F. Martin, 2008,

"The Rent-Price Ratio for the Aggregate Stock of Owner-Occupied

Housing," Review of Income and Wealth, vol. 54 (2), p. 279-284;

data located at Land and Property Values in the U.S., Lincoln

Institute of Land Policy http://www.lincolninst.edu/resources/ (data

for the perid of 1930-2009 was calculated using inputs from the

source above.

Nominal Personal

Saving

1929-2009 National Income and Product Accounts: Table 2.1

http://www.bea.gov/national/nipaweb/SelectTable.asp

Gross Private

Domestic

Investment

1929-2009 National Income and Product Accounts: Table 1.1.5

http://www.bea.gov/national/nipaweb/SelectTable.asp

Nonfarm

Business

Productivity

Output per hour

1890-1946 Kendrick, J.W. (1961), Productivity Trends in the United States.

Appendix A. http://www.nber.org/books/kend61-1

Nonfarm

Business

Productivity

Output per hour

1947-2009 Bureau of Labor Statistics. http://www.bls.gov

Employed

Persons in All

Sectors of

Economy

1890-2009 1890-1954: Kendrick, J.W. (1961), Productivity Trends in the

United States. Appendix A. http://www.nber.org/books/kend61-1

1955-2009: OECD: http://www.oecd.org/statsportal

Nominal M1 1929-1935 Friedman, M. and Schwartz, A.J. (1971), A Monetary History of the

United States, 1867-1960. Table A-1.

Nominal M1 1936-1947 Federal Reserve of St. Louis http://www.stlouisfed.org

Nominal M1 1948-2009 Money Stock Measures. Federal Reserve.

http://www.federalreserve.gov/releases/h6/hist/h6hist1.txt

Nominal M2 1890-1946 Anderson, R.G. (2003), Some Tables of Historical US Currency and

Monetary Aggregates Data. Working Paper 006A.

http://research.stlouisfed.org/wp/2003/2003-006.pdf

Nominal M2 1947-1958 Rasche web page.

https://www.msu.edu/~rasche/research/money.htm

Nominal M2 1959-2009 Money Stock Measures. Federal Reserve.

http://www.federalreserve.gov/releases/h6/hist/h6hist1.txt

Monetary Base 1890-1917 Anderson, R.G. (2003), Some Tables of Historical US Currency and

Monetary Aggregates Data. Working Paper 006A.

http://research.stlouisfed.org/wp/2003/2003-006.pdf

Monetary Base 1918-2009 Federal Reserve of St. Louis http://www.stlouisfed.org

!$"

APPENDICES

APPENDIX 1

1.1 ADF test output (natural logs of house prices in levels)

Null Hypothesis: HOUSEPRICE has a unit root

Exogenous: Constant

Lag Length: 1 (Automatic based on SIC, MAXLAG=12)

t-Statistic Prob.*

Augmented Dickey-Fuller test statistic -1.587205 0.4860

Test critical values: 1% level -3.486064

5% level -2.885863

10% level -2.579818

1.2 ADF test output (natural logs of house prices in first differences)

Null Hypothesis: D(HOUSEPRICE) has a unit root

Exogenous: Constant

Lag Length: 0 (Automatic based on SIC, MAXLAG=12)

t-Statistic Prob.*

Augmented Dickey-Fuller test statistic -10.48549 0.0000

Test critical values: 1% level -3.486064

5% level -2.885863

10% level -2.579818

" !%"

APPENDIX 2

2.1 Inflation rate (in levels) during 1891-2009; and the 3-year windows preceding

each bubble episode, 7 bubbles, period of 1891-2003

2.2 2-year moving average of house price growth during 1892-2009; and the 3-year

windows preceding each bubble episode, 7 bubbles, period of 1892-2003

#'"

2.3 Gap between the real house price and its 5-year MA (in levels) during 1890-2009;

and the 3-year windows preceding each bubble episode, 7 bubbles, period of 1891-

2003

2.4 Growth in real GDP per capita during 1891-2009; and the 3-year windows

preceding each bubble episode, 7 bubbles, period of 1891-2003

" #&"

APPENDIX 3

3.1. Inflation rate in levels (in blue): 8-year windows preceding each of the 7 bubble

episodes (in red), cycle phases (in green), period of 1891-2007

Comment: the level of inflation rate declines prior to a bubble

3.2. 2-year moving average of house price growth (in blue): 8-year windows

preceding each of the 7 bubble episodes (in red), cycle phases (in green), period of

1891-2007

Comment: the MA growth mostly increases prior to a bubble

3.3 Gap (%) between the real house price and its 5-year MA in levels (in blue): 8-year

windows preceding each of the 7 bubble episodes (in red), cycle phases (in green),

period of 1891-2007

Comment: the gap increases (or the negative gap decreases) prior to a bubble

The cycle phases marked in green have a purely visualization purpose.

#("

3.4 Growth of real GDP per capita (in blue): 8-year windows preceding each of the 7

bubble episodes (in red), cycle phases (in green), period of 1891-2007

Comment: the cyclicality in this indicator is harder to observe, nevertheless, there is an

upward trend prior to a bubble (taking into account the signaling horizon of 2-3 years)

3.5 Real short-term interest rate in levels (in blue): 8-year windows preceding each of

the 7 bubble episodes (in red), cycle phases (in green), period of 1891-2007

Comment: a mild upward trend prior or during the first years of overvaluation can be

observed clearly

The cycle phases marked in green have a purely visualization purpose.

" #)"

APPENDIX 4

4.1 Moving minima analysis table for the variable nominal long-term interest rate in

levels

MOVING

MINIMA

Horizon of

prediction /

Moving

extremum

Bub

bles

calle

d

Number

of

bubbles

Noise-to-

signal

ratio

Good /

All

signals

Wrong signals per

called bubble

Good

signa

ls /

Possi

ble

good

signa

ls

Bad

signals

/

Possibl

e bad

signals

P(bubble/signal)

-P(bubble)

Formula A' 6

[B/(B+D)

] /

A/(A+C)

A/(A+B

) B/A'

A/(A

+C)

B/(B+

D)

A/(A+B)-(A+C)

/ (A+B+C+D)

1 year

2 Year MM 3 6 1.11 0.08 15.00 0.44 0.49 -0.01

3 Year MM 2 6 1.15 0.08 17.50 0.33 0.38 -0.01

4 Year MM 1 6 1.34 0.07 27.00 0.22 0.30 -0.02

5 Year MM 1 6 1.19 0.08 24.00 0.22 0.26 -0.01

6 Year MM 1 6 1.04 0.09 21.00 0.22 0.23 0.00

7 Year MM 1 6 0.99 0.09 20.00 0.22 0.22 0.00

8 Year MM 1 6 0.99 0.09 20.00 0.22 0.22 0.00

2 year

2 Year MM 6 6 0.78 0.18 6.67 0.60 0.47 0.03

3 Year MM 4 6 0.94 0.16 8.00 0.40 0.38 0.01

4 Year MM 2 6 1.10 0.14 12.50 0.27 0.29 -0.01

5 Year MM 1 6 1.35 0.12 23.00 0.20 0.27 -0.03

6 Year MM 1 6 1.18 0.13 20.00 0.20 0.24 -0.02

7 Year MM 1 6 1.12 0.14 19.00 0.20 0.22 -0.01

8 Year MM 1 6 1.12 0.14 19.00 0.20 0.22 -0.01

3 year

2 Year MM 6 6 0.82 0.24 6.17 0.57 0.47 0.03

3 Year MM 4 6 0.86 0.24 7.25 0.43 0.37 0.03

4 Year MM 3 6 1.02 0.21 7.67 0.29 0.29 0.00

5 Year MM 2 6 1.12 0.19 10.50 0.24 0.27 -0.02

6 Year MM 2 6 0.96 0.22 9.00 0.24 0.23 0.01

7 Year MM 2 6 0.90 0.23 8.50 0.24 0.22 0.02

8 Year MM 2 6 0.90 0.23 8.50 0.24 0.22 0.02

* - pink denotes the best indicator

Comment: the table presents a summary of analysis sheets with 1-, 2- and 3-year signaling

horizons and 2,3,4,5,6,7 and 8-year moving minima. In this particular case, the best settings

were determined as the 2-year moving minima with 100% in-sample prediction performance

(6 out of 6 bubbles called); noise-to-signal ratio of 0,78; almost each 5th

signal issued was

good, and 3 signals out of 5 possible good signals were issued. At the same time, half of all

possible bad signals are present; and per each called bubble there are approximately 7 false

alarms

#*"

4.2 Moving maxima analysis table for the variable nominal long-term interest rate in

levels

MOVING

MAXIMA

Horizon of

prediction /

Moving

extremum

Bub

bles

calle

d

Number

of

bubbles

Noise-to-

signal

ratio

Good /

All

signals Wrong signals per

called bubble

Good

signals

/

Possib

le

good

signals

Bad

signals /

Possible

bad

signals

P(bubble/sign

al)-P(bubble)

Formula A' 6

[B/(B+D)

] /

A/(A+C)

A/(A+B

) B/A'

A/(A+

C) B/(B+D)

A/(A+B)-

(A+C) /

(A+B+C+D)

1 year

2 Year MM 5 6 0.89 0.10 9.00 0.56 0.49 0.01

3 Year MM 5 6 0.65 0.13 6.60 0.56 0.36 0.04

4 Year MM 3 6 1.05 0.09 10.67 0.33 0.35 0.00

5 Year MM 3 6 0.96 0.09 9.67 0.33 0.32 0.00

6 Year MM 3 6 0.96 0.09 9.67 0.33 0.32 0.00

7 Year MM 3 6 0.92 0.10 9.33 0.33 0.31 0.01

8 Year MM 3 6 0.89 0.10 9.00 0.33 0.30 0.01

2 year

2 Year MM 5 6 1.29 0.12 8.80 0.40 0.52 -0.03

3 Year MM 5 6 1.16 0.13 6.60 0.33 0.39 -0.02

4 Year MM 3 6 1.88 0.09 10.67 0.20 0.38 -0.06

5 Year MM 3 6 1.71 0.09 9.67 0.20 0.34 -0.06

6 Year MM 3 6 1.71 0.09 9.67 0.20 0.34 -0.06

7 Year MM 3 6 1.65 0.10 9.33 0.20 0.33 -0.05

8 Year MM 3 6 1.59 0.10 9.00 0.20 0.32 -0.05

3 year

2 Year MM 5 6 1.40 0.16 8.40 0.38 0.53 -0.05

3 Year MM 5 6 1.18 0.18 6.20 0.33 0.39 -0.03

4 Year MM 3 6 1.59 0.14 10.00 0.24 0.38 -0.07

5 Year MM 3 6 1.44 0.16 9.00 0.24 0.34 -0.05

6 Year MM 3 6 1.44 0.16 9.00 0.24 0.34 -0.05

7 Year MM 3 6 1.38 0.16 8.67 0.24 0.33 -0.05

8 Year MM 3 6 1.33 0.17 8.33 0.24 0.32 -0.04

Comment: the table presents a summary of analysis sheets with 1-, 2- and 3-year signaling

horizons and 2,3,4,5,6,7 and 8-year moving maxima

" #+"

APPENDIX 5

5.1. Indicators that predicted all 6 bubbles during 1890-1990 with signal-to-noise

ratios lower than 1; 2-year signaling horizon

Name

Growth

/ Levels

Moving

Extremum

Length

of

phase

Noise-

to-

signal

ratio

Good /

All

signals

Wrong

signals

per

called

bubble

Conditional -

Unconditional

Probability

1

3-year lagged real

house price G max 3 0.49 0.26 4.67 0.11

2

Real house price

and 5-year MA gap L max 2 0.58 0.23 6.00 0.08

3

Res. n-f wealth to

M0 G max 2 0.59 0.23 6.17 0.08

4 Real mortgage rate L max 3 0.60 0.23 5.67 0.08

5

Real res. n-f wealth

to labor force G max 2 0.67 0.21 6.33 0.06

6

Real res. n-f wealth

per employed p. G max 2 0.67 0.21 6.33 0.06

7

Real price of gold

ounce G max 2 0.67 0.21 7.00 0.06

8

Real GDP per

employed person G max 3 0.71 0.20 4.67 0.05

9

Real res. nonfarm

wealth G max 2 0.71 0.20 6.67 0.05

10

Real res. nonfarm

wealth p.c. G max 2 0.71 0.20 6.67 0.05

11

Res. n-f wealth to

M2 G max 2 0.71 0.20 6.00 0.05

12

Nominal mortgage

rate G max 2 0.74 0.19 7.67 0.04

13

Nominal long term

rate L min 2 0.78 0.18 6.67 0.03

14 M2/M0 G min 2 0.78 0.18 6.67 0.03

15 Real output gap L max 2 0.79 0.18 8.17 0.03

16 Real mortgage rate G max 2 0.79 0.18 7.50 0.03

17 Real long term rate G min 2 0.82 0.18 6.17 0.03

18 Real long term rate L max 2 0.84 0.17 7.17 0.02

19

Real GDP per

capita G min 2 0.86 0.17 7.33 0.02

20

Rapid price growth

>2% L max 3 0.86 0.17 7.33 0.02

21

Res. n-f wealth to

M0 L max 2 0.88 0.17 8.33 0.02

22

Nominal mortgage

rate L max 2 0.94 0.16 8.00 0.01

23 Real output gap G min 2 0.98 0.15 8.33 0.00

24

Real GDP to labor

force G max 2 0.98 0.15 6.50 0.00

Comment: the third column shows if the data is expressed in levels or growth rates; the fourth

column marks the direction of the phase; the fifth column marks the length of a phase in

years; the sixth column shows the ratio of good signals to all possible good signals; the

seventh column shows the number of wrongly issued signals per called bubble; the last

column denotes the difference between the conditional and unconditional probabilities: if the

gap is close to zero or negative, it means that signals were issued more or less randomly with

the right predictions happening by chance

#!"

5.2. Indicators that predicted all 6 bubbles during 1890-1990 with signal-to-noise

ratios lower than 1; 3-year signaling horizon

Name

Growth

/ Levels

Moving

Extremum

Length

of

phase

Noise-

to-

signal

ratio

Good /

All

signals

Wrong

signals

per

called

bubble

Conditional -

Unconditional

Probability

1

Real construction

cost G max 4 0.50 0.35 2.50 0.14

2

Nominal long term

rate G min 5 0.53 0.33 2.67 0.12

3

2-year lagged real

house price G max 3 0.55 0.32 4.17 0.11

4 Housing starts G max 3 0.56 0.32 3.50 0.11

5

Residential

investment to GDP G max 3 0.56 0.32 3.50 0.11

6 Real M0 G max 4 0.60 0.31 3.00 0.10

7 GDP defltaor G min 3 0.64 0.29 4.00 0.08

8 Inflation rate L min 3 0.64 0.29 4.00 0.08

9

Real residential

investment G max 2 0.65 0.29 5.33 0.08

10

Nominal short term

rate L min 4 0.66 0.29 3.33 0.08

11

House price to gold

ounce price G max 2 0.69 0.28 5.17 0.07

12

Nominal exchange

rate: GBPUSD L max 3 0.69 0.28 5.17 0.07

13

Nominal exchange

rate: GBPUSD G max 4 0.70 0.28 3.50 0.07

14

Residential

investment to GDP L max 2 0.73 0.27 5.50 0.06

15 Real mortgage gap L max 4 0.73 0.27 3.67 0.06

16 Unemployment rate L min 4 0.74 0.26 4.67 0.05

17 Nominal term spread L min 3 0.78 0.26 5.83 0.05

18

Nominal short term

rate G max 3 0.83 0.24 4.67 0.03

19 P/E ratio G max 2 0.85 0.24 5.83 0.03

20 P/E ratio L max 2 0.86 0.24 6.50 0.03

21 Unemployment rate G max 2 0.87 0.23 6.00 0.02

22 Real term spread L min 3 0.88 0.23 5.50 0.02

23

1-year lagged real

house price G max 2 0.89 0.23 6.67 0.02

24

Labor force to

population G max 3 0.90 0.23 4.50 0.02

25

House price to gold

ounce price L max 3 0.91 0.23 6.83 0.02

26 Real M2 G max 3 0.91 0.23 4.00 0.02

27

Nominal mortgage

gap L max 3 0.92 0.23 5.17 0.02

28 S&P real price G max 2 0.97 0.21 5.50 0.00

29 Productivity G max 2 0.99 0.21 6.83 0.00

" ##"

APPENDIX 6

6.1. Indicators that predicted all 3 bubbles during 1930-1990; 1-year signaling horizon

Name

Growth

/ Levels

Moving

Extremum

Length

of

phase

Noise-

to-

signal

ratio

Good /

All

signals

Wrong

signals

per

called

bubble

Conditional -

Unconditional

Probability

1

Real government net

saving L max 4 0.25 0.27 3.67 0.18

2

Government net saving to

GDP L max 4 0.27 0.25 4.00 0.17

3

Government expenditure to

GDP G min 4 0.31 0.22 4.67 0.14

4 Personal income to GDP G max 3 0.36 0.20 6.67 0.12

5

Mortgage interest to disp.

Income G max 4 0.38 0.19 7.00 0.11

6 Disposable income to GDP G max 3 0.42 0.17 6.33 0.09

7

Real housing and utilities

expendit. G max 3 0.48 0.16 5.33 0.08

8 Real M1 G min 2 0.49 0.15 7.33 0.07

9 Real tenant-oc. rental price G min 2 0.54 0.14 8.00 0.06

10

Hous. and util. exp. to

consumption G min 2 0.54 0.14 8.00 0.06

11 M1/M0 L min 3 0.56 0.14 8.33 0.06

12

Real mortgage interest cost

(calc) G max 2 0.57 0.14 10.67 0.05

13

Real per. income per empl.

person G min 2 0.60 0.13 9.00 0.05

14

Real perosnal income to

labor force G min 2 0.67 0.12 10.00 0.04

15

N-f residential mortgage

debt to GDP L max 2 0.68 0.12 12.67 0.03

16 Real government revenue G max 2 0.71 0.11 8.00 0.03

17

Nonfarm mortgage debt to

GDP L max 4 0.76 0.11 11.33 0.02

18

Mortgage interest to disp.

Income L max 2 0.83 0.10 12.33 0.02

19

Government revenue to

GDP G max 2 0.83 0.10 9.33 0.01

Comment: due to the smaller sample, the noise-to-signal ratio acceptable had to be lowered

from 1 to 0,5. The highlighted indicators therefore do not qualify as sufficient

#$"

6.2. Indicators that predicted all 3 bubbles during 1930-1990; 2-year signaling horizon

Name

Growth

/ Levels

Moving

Extremum

Length

of

phase

Noise-

to-

signal

ratio

Good /

All

signals

Wrong

signals

per

called

bubble

Conditional -

Unconditional

Probability

1

Price-to-income and 5-year

MA gap L max 7 0.15 0.50 2.33 0.37

2

Price-to-rent and 5-year MA

gap L max 5 0.26 0.36 4.67 0.23

3 Price-to-income L max 3 0.28 0.35 3.67 0.22

4

Federal budget balance to

GDP L max 4 0.33 0.31 3.67 0.18

5

Real federal budget balance in

levels L max 3 0.35 0.30 4.67 0.17

6

Real n-f residential mortgage

debt G max 8 0.40 0.27 2.67 0.14

7 Disposable income to GDP L min 5 0.45 0.25 4.00 0.12

8

Real disp. income per empl.

person G max 3 0.48 0.24 5.33 0.11

9

Price-to-income and 5-year

MA gap G min 5 0.49 0.24 4.33 0.10

10

Res.inv. to gross priv. dom.

inv. G min 3 0.51 0.23 5.67 0.10

11 Real disposable income G max 2 0.53 0.22 7.00 0.09

12

Real disposable income per

capita G max 2 0.53 0.22 7.00 0.09

13 Real imputed rental price G max 4 0.53 0.22 4.67 0.09

14

Real disposable income to

labor force G max 4 0.55 0.21 3.67 0.08

15 Real nonfarm mortgage debt G max 4 0.57 0.21 5.00 0.08

16 M1/M0 G min 3 0.60 0.20 5.33 0.07

17 Real government net saving G min 3 0.68 0.18 6.00 0.05

18

Hous. and util. exp. to dispos.

income G max 2 0.75 0.17 10.00 0.04

19 Personal saving to GDP G max 2 0.75 0.17 6.67 0.04

20 M2/M1 L max 2 0.78 0.16 12.00 0.03

21

Real personal saving to labor

force G max 2 0.79 0.16 7.00 0.03

22 Real personal income G max 2 0.87 0.15 7.67 0.02

23

Real personal income per

capita G max 2 0.87 0.15 7.67 0.02

24

Real per. saving per empl.

person G max 2 0.87 0.15 7.67 0.02

Comment: due to the smaller sample, the noise-to-signal ratio acceptable had to be lowered

from 1 to 0,5. The highlighted indicators therefore do not qualify as sufficient

" #%"

6.3. Indicators that predicted all 3 bubbles during 1930-1990; 3-year signaling horizon

Name

Growth

/ Levels

Moving

Extremum

Length

of

phase

Noise-

to-

signal

ratio

Good /

All

signals

Wrong

signals

per

called

bubble

Conditional -

Unconditional

Probability

1 Real farm value per acre G max 8 0.18 0.56 1.33 0.38

2 Real government expenditure G min 8 0.22 0.50 1.33 0.32

3 Price-to-rent L max 8 0.25 0.47 3.00 0.29

4

Saving-to-GDP and 5-year

MA gap L min 7 0.26 0.46 2.33 0.28

5 Price-to-income G max 7 0.26 0.45 2.00 0.27

6

N-f residential mortgage debt

to GDP G max 7 0.28 0.44 1.67 0.26

7 Personal saving to GDP L min 6 0.39 0.36 2.33 0.18

8

Gross priv. domestic inv. to

GDP G max 5 0.39 0.36 2.33 0.18

9

Hous. and util. exp. to

consumption L min 3 0.44 0.33 4.67 0.15

10

Price-to-rent and 5-year MA

gap G max 4 0.50 0.31 3.00 0.13

11

Saving-to-GDP and 5-year

MA gap G max 4 0.50 0.31 3.00 0.13

12 Real current account L min 4 0.51 0.30 4.67 0.12

13

Res.inv. to gross private dom.

Inv. L max 3 0.51 0.30 4.67 0.12

14

Nonfarm mortgage debt to

GDP G max 4 0.53 0.29 4.00 0.11

15 Personal income to GDP L min 5 0.55 0.29 3.33 0.11

16 Real current account G min 3 0.57 0.28 6.00 0.10

17 Price-to-rent G max 3 0.57 0.28 6.00 0.10

18

Real gross priv. domestic

investment G max 2 0.58 0.28 7.00 0.10

19 Government revenue to GDP L max 2 0.83 0.21 10.00 0.03

20 M2/M1 G min 3 0.83 0.21 5.00 0.03

21 Real personal saving G min 2 0.94 0.19 10.00 0.01

22

Real personal saving per

capita G min 2 0.94 0.19 10.00 0.01

23

Hous. and util. exp. to dispos.

income L max 2 0.97 0.18 10.33 0.00

Comment: due to the smaller sample, the noise-to-signal ratio acceptable had to be lowered

from 1 to 0,5. The highlighted indicators therefore do not qualify as sufficient