Proper Time Series Analysis

Macro economic variables consist of GNP, unemployment, inflation, interest rate, exchange rate, balance of payments, etc.

Unacceptable levels (think high inflation) or instability (think alternating periods of high and low growth) in any of the above variables can be very distressing for the people (think prices increasing by 20% every month OR being fired from your job due to low revenue growth prospects of your employer due to recession)

Hyperinflation in Zimbabwe:

! From New York Times, “at a supermarket near the centre of this tatterdemalion capital, toilet paper costs $417. No, not per roll. Four hundred seventeen Zimbabwean dollars is the value of a single two-ply sheet. A roll costs $145,750 — in American currency, about 69 cents. The price of toilet paper, like everything else here, soars almost daily, spawning jokes about an impending better use for Zimbabwe's $500 bill, now the smallest in circulation.”

! 100 Trillion Zimbabwean dollar bills were in circulation

! In November 2008, inflation hit a high of 79.6 billion percent. So $Z 79600000000 would have to be paid in Nov 2008 for a pen priced at $Z1 in Nov 2007

The Great Recession (2007-2009)1. US unemployment rate rose from 5% in 2008 pre-crisis to 10%

by late 20092. Post recession Income levels of the median male worker was

down to 1968 levels3. Approximately 5.4 million people have been added to federal

disability rolls4. U.S. total national debt rose from 66% GDP in 2008 pre-crisis to

over 103% by the end of 2012

Macro variables reflect different aspects of the same economy so they are interconnected and fluctuations in one can quickly translate into fluctuations in the others

Consider this situation: When inflation is high, people may lose confidence in money as the real value of savings is severely reduced

This discourages savings due to the fact that the money is worth more presently than in the future

This expectation reduces economic growth because the economy needs a certain level of savings to finance investments which boosts economic growth.

Also, inflation makes it harder for businesses to plan for the future. It is very difficult to decide how much to produce, because businesses cannot predict the demand for their product at the higher prices they will have to charge in order to cover their costs.

Savings

Growth

Investment

To stabilize the economy over time, governments need to formulate policy to control the macro variables for which they need to understand the long term relation between them. Is this possible?

The most powerful tool to understand the relation between crucial macro variables is Time Series Analysis: a branch of Econometrics or statistical analysis of economic variables

• Nelson and Plosser (1982) argued that almost all macroeconomic time series, have a unit root

What does this mean:• In the absence of unit root (stationary), the series fluctuates around a constant long-

run mean and implies that the series has a finite variance which does not depend on time.

• On the other hand, non-stationary series have no tendency to return to long-run deterministic path and the variance of the series is time dependent.

• Non-stationary series suffer permanent effects from random shocks and thus the series follow a random walk

• Think tourist arrivals at a destination over time. If this series is non-stationary, then in case of random shocks like terrorist attacks or natural disaster, the number of tourist arrivals never revert to their original mean, but if the series was stationary they would have.

• If this were true, there is no use to policy anymore. The effects of hyperinflation or a recession on the economy are permanent and incurable and we are doomed to be on a low level path forever.

• Such a Greek tragedy scenario where you are completely at the mercy of the Gods doesn’t seem relevant for current times

Perron (1989), argued that in the presence of a structural break, the standard ADF tests for unit root are biased towards the non-rejection of the null hypothesis

The series on the left is non-stationary but the one on the right is not.. However, ADF tests might misleadingly point out the series on the right to be non-stationary as well

Testing for structural breaks is extremely important while analyzing long time series. Otherwise, all subsequent analysis might be misleading

For instance, two series are cointegrated if they are individually I(1), but some vector of coefficients exists to form a stationary linear combination of them

However, in the presence of structural breaks, unless proper testing is done, the individual series might mistakenly by labeled I(1)

Test Model Software

Perron (1989)** Exogenous with one break

Zivot and Andrews (1992)*Endogenous with one break Eviews

Lumsdaine and Papell (1997)*Endogenous with two breaks GAUSS

Lee and Strazicich (2003)**Endogenous with two breaks RATS

Gregory and Hansen (1996)One Endogenous break in cointegration framework Eviews

Saikkonen and Lütkepohl (2000)One Endogenous break in cointegration framework GAUSS

Bai and Perron (2003)Endogenous multiple breaks RATS,Eviews

* Assume no break(s) under the null hypothesis of unit root

** Assume break(s) under both the null and the alternative hypothesis

The Indian Ministry of Statistics and Program Implementation has just introduced a structural break in the GDP series. Read up and be careful

The tests in the earlier slide are quite technical. But expectedly anyone interested in this issue is likely to have a technical appetite. Hence happy reading. Zivot & Andrews (intensely mathematical) is good place to start

Tests for panel data are a different set. Search Westlund, Levin-Lin-Chu, Pedroni etc.