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IS MACROECONOMICS TAKING AN AUSTRIAN TURN? Nicolás Cachanosky Department of Economics Metropolitan State University of Denver Campus Box 77, P.O. Box 173362 Denver, CO 80217 [email protected] Roger Koppl Department of Finance Syracuse University 721 University Avenue, Syracuse University Syracuse, NY 13244 [email protected] 9-Sep-17 Abstract Abstract text Jel codes:

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Page 1: IS MACROECONOMICS TAKING AN AUSTRIAN TURN?€¦ · IS MACROECONOMICS TAKING AN AUSTRIAN TURN? ... advocates for a full rejection of DSGE modeling and replace it with one that

IS MACROECONOMICS TAKING AN AUSTRIAN TURN?

Nicolás Cachanosky Department of Economics

Metropolitan State University of Denver Campus Box 77, P.O. Box 173362

Denver, CO 80217 [email protected]

Roger Koppl

Department of Finance Syracuse University

721 University Avenue, Syracuse University Syracuse, NY 13244

[email protected]

9-Sep-17

Abstract Abstract text Jel codes:

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1. Introduction

Almost ten years have passed since the 2008 crisis, this provides a time frame long enough

to observe the effects that the Great Recession had in macroeconomics and business cycle

theory. According to observed reactions, the largest impact produced by the crisis has been

to the status of dynamic stochastic general equilibrium (DSGE) models. In words of

(Stiglitz, 2011, p. 592), if prediction is the standard test of a scientific theory, then

macroeconomic models such as DSGE have failed “miserably.” DSGE models proved

inadequate to predict, explain, and remedy one of the largest crises in the twentieth

century.

This situation has produced a different set of reactions with respect to what changes

should macroeconomics go through to fill the gap between what macroeconomics can

explain and what it should explain. These reactions can be divided in three groups. The first

one consists in continue applying macroeconomic theory such as DSGE models as if nothing

had happened. The 2008 crisis was a big albeit rare even that does not justify making

significant changes to macroeconomic theory. The second type of reaction consists in fixing

and expanding the DSGE model to take into account the missing pieces that would allow for

this theory to better fit into how business cycles can evolve. The third type of reaction

advocates for a full rejection of DSGE modeling and replace it with one that is better suited

to deal with real world events.

Following (Caballero, 2010), we locate DSGE models in the core of macroeconomic theory

being other models and non-DSGE research the periphery of the field. Interestingly, some of

the reactions in the macroeconomic literature have stepped outside conventional

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macroeconomic theory (into the periphery of the periphery) to bring new theoretical

insights into business cycle theory. This is because there are two important characteristics

present in the 2008 crisis that do not have room in DSGE modeling; (1) the development of

a cluster of errors and (2) a cascade effect. The incipient Austrian turn in macroeconomics

observed after the 2008 crisis is pointed to deal with these issues. A number of scholars

have turned to the Austrian literature, in particular to the Austrian Business Cycle Theory

(ABCT) as a way to explain what went wrong in the 2008 crisis.

We argue that in conventional macroeconomics there is still room for a sharper Austrian

turn. In other words, there are still gains from trade on engaging issues that have been

traditionally present in the Austrian literature. Following the macroeconomic literature

discussed below, we rely on the ABCT to account for the cluster of errors and on Fisher’s

debt-deflation (FDD) theory to describe the cascade effect that can be observed during a

crisis.

The paper is divided into two main sections. The first one reviews the situation of

macroeconomics after the crisis, with an emphasis on its core, DSGE models. The second

one discusses the contributions that can take place with a deeper Austrian turn in

macroeconomics. We divide these contributions in five: (1) Hayek’s knowledge problem

applied to monetary policy, (2) the rule of law versus the rule of experts in monetary

policy, (3) the loss of confidence and the cascade effect, (4) the Wicksell Effect, and (5) the

average period of production during a business cycle. The last section concludes.

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2. Macroeconomics after the Crisis

The 2008 crisis challenged well-grounded conventional macroeconomic knowledge. The

core, rather than a mere component of the periphery, received a significant empirical

disconfirmation. The crisis showed that a stable low inflation is no guarantee that serious

imbalances are not growing in the economy and that the credit allocation through the

financial market can be a key component of business cycles. This characteristic of the crisis

contrasts with how common is for DSGE models to be modelled without money. The Great

Moderation period that preceded the crisis seems to have feed false confidence in the DSGE

and core of macroeconomic theory (Blanchard, 2014; Blanchard, Dell’Ariccia, & Mauro,

2010).

After the crisis, a series of criticisms to DSGE modeling have been raised by a number of

scholars. (Blanchard, 2016; Keen, 2018) question the lack of reality of the assumptions

used in this type of modeling. The issue with the assumptions used in the core of

macroeconomics is not that they simplify the economic reality, which is what assumptions

are used for. The problem is that they are unreal and therefore the model does not depict

the economic process as it occurs in the real world. A map, for instance, is a simplification

of the real world if its assumptions do not alter the geographical accidents to the point

where the map becomes a reflection of a difference world. Similarly, the issue with DSGE

modeling is that it does not offer a fair representation of the problems faced by the policy

maker. This means that even if the model is calibrated to fit real world data, its foundations

have no anchor to reality and the stance of the economy might become misjudged. If the

reality of the model is an important issue, then there is no clear way to discern which one

of all different potential models is the correct one. The prioritization of mathematical

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tractability over reality of the assumptions lead macroeconomics to develop complex

models that rely on assumptions that are not easy to adjust in isolation from the rest of the

model.

Concerns about DSGE modeling do not rest only on academic discussions about the reality

of the assumptions used. (Canova & Sala, 2009; Romer, n.d.; Stiglitz, 2011), for instance,

point to the problem of model identification already noted by (Liu, 1960; Sims, 1980). This

issue is not a minor one. A Walrasian DSGE model with n equations and n unknowns needs

𝑛2 parameters to be identified with values exogenously given information. The

identification requirement increases even further with the inclusion of rational

expectations into the model. This means that the more accurate and subtle the models are,

the more exogenous information is needed. Different calibrations can yield results that look

correct even if their internal dynamics do not reflect the market process accurately. But, it

remains unknown whether or not the calibrated values are correct. Calibrated values may

rest on a strong intuition, but as strong as this intuition is it may be can still be mistaken.

Looking for answers, macroeconomists have turned into the ABCT as a theory useful to

explain why the 2008 crisis happened. Just at first sight, data matches the general pattern

of this theory. A low interest rate policy contributed to build the housing bubble that burst

after the Federal Reserve started to increase the Federal funds rate. Another reason for this

endorsement is that the DSGE modeling is not well suited to deal with the cluster of errors

observed in the housing bubble, but the ABCT does offer an explanation for such clustering.

Some of this literature offers an explicit endorsement to the ABCT (Borio & Disyatat, 2011;

Diamond & Rajan, 2009a; Hume & Sentance, 2009; Leijonhufvud, 2009a; W. R. White,

2012). Probably the most friendly exposition to the ABCT explanation of the 2008 crisis is

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(Calvo, 2013). But in other cases, even though an explicit endorsement to the ABCT is

absent, still a very Austrian-friendly explanation is offered (Diamond & Rajan, 2009b;

Gjerstad & Smith, 2009; McKinnon, 2010; Meltzer, 2009; Schwartz, 2009; Taylor, 2009).

This suggests that insights from this theory are already more present in macroeconomics

than is usually acknowledge.1 Note, also, that while the DSGE modeling usually does not use

financial markets as a channel of a crisis, credit is at the core of the ABCT. This has probably

been the most appealing angle found in the ABCT to make sense of the 2008 crisis.

(Cachanosky & Salter, 2017) offer a more detailed analysis of the literature discussed in

this paragraph.

3. Austrian Insights into Macroeconomics

3.1. The Knowledge Problem

(Hayek, 1948) knowledge problem is well known in the context of the socialist economic

calculation debate. However, some of his arguments also apply to the making of monetary

policy. To understand why Hayek’s problem also has implications to monetary policy we

need first to focus on two of his main points

The first one, and the probably the more familiar one, is about the dispersion of

information across the economy. Information is not given to economic agents in the same

way it is “given” to the economist who is building a model. Information is an unintended

1 In some sense this is not much of a surprise. For isntance, (Lewin, 1999, pp. 73–75) argues that Böhm-

Bawerk’s average period of production is compatible with the neoclassical tradition leading to growth theory.

According to (L. H. White, 2016), Lucas’ influential islands model is inspired in Hayek, even though posterior

development turned business cycle theory towards real business cycle (RBC) and DSGE models.

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spontaneous outcome of the market process. Hayek’s point, however, is not just that

information is disperse as small bits of information, but that such information cannot exist

outside the market process. Without private property, there can be no transaction, and

without transactions there is no information to recollect in the first place.

The second point in Hayek’s argument, is the distinction between information and

knowledge (Zanotti, 2011). The former is objective and quantitative, such as prices and

quantities. As such, it can be complete (perfect) or incomplete (imperfect.) The latter is

subjective and qualitative, it can be neither complete nor incomplete. Information does not

speak by itself, it requires interpretation which depends on knowledge (i.e. a theory that

makes sense of the data.) This distinction between information and knowledge is

important because it shows that to assume perfect information is not enough to guarantee

that the economy will reach equilibrium. How to read the information correctly and, in

particular, how to discover market disequilibria that remain invisible to other economic

agents is the role of the entrepreneur (Kirzner, 1973).

There are a few ways this relates to central banking and the doing of monetary policy. A

main difference is that there is no market process through which to filter inefficient policy

makers in a similar way market competition drives out inefficient entrepreneurs. In

addition, the presence itself of a central bank eliminates the market process through which

the money and credit market converges towards equilibrium (more on this in the next

section.) This means that entrepreneur and the central bank face knowledge problems of

different difficulty. The former uses market information such as prices and quantities as an

input to discover market disequilibria. This alertness, in turn, is subject to market

competition. The central bank, however, cannot rely on credit market information because

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their policy decisions do not go through market competition. Different to a market with

freedom of entry and exit, what is considered a good monetary policy depends on the

knowledge of the time, not on an objective market outcome such as profits and losses.

From this discussion, it follows that a policy makers does not only need to be a good

technician knowledgably of monetary theory. He also needs to have a type of alertness that

is superior to entrepreneurial alertness in the sense that the central bank needs to be able

to read the market disequilibria correctly, but without being motivated by competition and

without the market information that the entrepreneur has access to.

The central bank knowledge problem is further increased by its condition of being a Big

Player (Koppl, 2002, Chapter 7). An economic agent is a Big Player if its behavior can

produce a Lucas-critique type of effect in the economy. An entrepreneur in a competitive

market takes the market dynamics and incentives as given. A Big Player action, however,

can change either market dynamics or incentives (i.e. a change in policy or regulation). The

central bank is in a more difficulty position than forming a pattern prediction of the

economy situation in the foreseeable future with the market dynamics taken as given. The

Big Player needs to forecast the intended and unintended consequences of his action and

from there the reaction of the economic agents.

3.2. Rule of Law versus the Rule of the Experts

The more is asked for a central bank, and the more costly deviations from monetary

equilibrium are, the more important it becomes for the monetary authority to follow a

well-designed rule rather than rely on discretion. If we lack the sort of knowledge assumed

to be in standard models, then a rules-based approach to macroeconomics has a stronger

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case. Note that the models assume that the economic agents know the model they are living

in. This is the distinction mentioned above between information (economic data) and

knowledge (what the data means.) Even if we assume incomplete information, the model

still assumes economic agents have the right knowledge.

The rule of law has a distinctive presence in the Austrian institutional literature. Hayek is

probably the most important rule of law theorist since Dicey. (Hayek, 1976)

Denationalisation of Money can be seen as a radical reform that moves issuer banks

towards being under the law rather than allowing them to set their objectives and rules.

Some of these Austrian ideas has been extended to monetary policy as well, in particular by

(L. H. White, 2010).

To be under the rule of law is a more strict deviation from discretion than it is to choose

and follow a rule. Under the rule of law the policy maker has no discretion to update or

deviate from the law even if there are short-run benefits by doing so. The reason is that the

cost of devaluing the law by each discretionary deviation has a long-run costs that can

more than offset the short-run benefit. An example would be applying Bagehot’s rule,

where only solvent but illiquid banks should be eligible for a bailout loan. Under the rule of

law there would be no deviation from this principle even if the failure of a bank could

impose costs in the short-run. The long-run costs through moral hazard behavior on part of

the banks can easily become a larger problem than the short-run bank failure.2 The cost-

benefit analysis of rule deviation should also include the cost of eroding the rule.

2 It should be noted that Bagehot did not endorse the need of having a central bank to perform as a lender of

last resort. Rather, Bagehot position was that taken a central bank as given, its behavior shouold be to let

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If there is no rule of law, then the alternative is the rule of the experts. Macroeconomic

theory has evolved around the latter concept rather than the former. Either discretion or

rules in the traditional debate requires an expert to either be discretionary or chose and

implement the right rule. A rule of law evolution of macroeconomics would be more

focused on studying the market process than in controlling it through policy in a similar

way a biologist studies an ecosystem but does neither create it nor rule it. The fact that

macroeconomics has evolved with the rule of expert as part of its core makes it particular

challenging to adopt the alternative rule of law; hence the opportunity to turn to the

Austrian literature on this issue.

One way to move monetary policy closer to rule of law outcome would be for central banks

to target the same outcome that a free market of money and banking under the rule of law

produces. This is where the literature on free banking becomes informative, for which the

self-regulation mechanism of a free market of money and banking is the main topic.3 One of

the outcomes of this research is that the financial market spontaneously stabilizes nominal

income without the need to target it in the first place. In terms of contemporary debates,

this is the idea behind Market Monetarism’s NGDP Targeting (Sumner, 2012, 2013).4

However, since the Keynesian revolution monetary policy is more focused on price level

insolvent banks fail. See the comment in (Selgin, 1996, p. 228). According to (Bagehot, 1873, pp. 65–69) own

words, free banking would be the first best scenario, Bagehot’s rule becomes the second best choice in a world

of central banks as given institutions. Bagehot might be wrong in seeing free banking as superior to central

banking, but it does not follow from his writing that central banking was his recommendation.

3 For a more detailed analysis of free banking see (Cachanosky, 2010; Dowd, 1992; Hasan, 1994; Laidler,

2005; Sechrest, 1993; Selgin, 1988, 1996, Chapters 1, 2; Smith, 1936; L. H. White, 1984).

4 Even though the idea of NGDP Targeting has seen a renewed interest in recent years, the idea had some

presence as well prior to the 2008 crisis (Bean, 1983; Bradley & Jansen, 1989; Feldstein & Stock, 1994; Hall &

Mankiw, 1994; Kahn, 1988; Taylor, 1985).

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stability and unemployment than on nominal income stability. Price level stability,

however, is consistent with monetary equilibrium only if certain conditions hold. In

particular, in the presence of productivity gains an increase in money supply that offsets a

fall in prices produces an excess of money supply with respect to money demand (Selgin,

1996, Chapter 7, 1997).5 This one of the reasons why (Hayek, 1931, p. 124, 1937, pp. 83–

84) refers as a neutral monetary policy keeping nominal income (money supply times

velocity of circulation) constant in per capita terms. The difference between Market

Monetarism’s NGDP Targeting and Hayek’s rule rests on the target growth rate of NGDP.6

As (Selgin, 1996, Chapter 8) argues, before the Keynesian revolution, Hayek’s

recommendation to stabilize nominal income was shared among a number of monetary

scholars rather than being just an Austrian position. As (L. H. White, 2008) shows, to

sustain that either the ABCT or Hayek are in favor of a “do nothing” policy when a crisis

triggers is a misinterpretation of this theory. What Hayek opposes is to increase M beyond

the fall in V as a monetary stimulus policy. (Selgin, Beckworth, & Bahadir, 2015) argue that

a higher rate of productivity gains in the years prior to the 2008 crisis misled the Federal

Reserve into assuming that the monetary policy was in the right track, while the case was

that the inflationary effect of a loose monetary policy was being offset by the gains in

5 Note that this bening deflation does not produce a depression; prices fall because there is an increase in

productivity, not because money demand is increasing (a fall in money velocity). For an empirical study see

(Atkenson & Kehoe, 2004).

6 While for NGDP Targeting nominal income should grow at a 5-percent per year, for Hayek NGDP per capita

should be constant. Later in his carrer, however, Hayek changed his mind towards price level stability (L. H.

White, 1999).

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productivity.7 This is the concern behind monetary rules such as NGDP Targeting and

Hayek’s rule. This situation has also been considered by the ABCT literature.

3.3. Confidence and Cascade Effect

A loss of confidence (i.e. a Minsky moment) can trigger a cascade effect with significant

economic consequences. This is a situation for which DSGE models usually are not well

equipped to deal with. Writing in the context of the Great Depression, (Fisher, 1933) argues

that the combination of over-indebtness and deflation is what makes a crisis so acute. The

combination of these two issues trigger a sequential chain of events where debt and

deflation feed on each other. For Fisher (1933, p. 345) the Great Depression is an example

of the “most serious sort” of crisis. Fisher’s debt-deflation (FDD) theory can be described in

the following way. Starting from a point of over-indebtness, a loss of confidence puts into

motion a chain of events that can be logically ordered in the following nine steps:

1. Liquidation of debt (triggered by the debtor or creditor) leads to a fire sale of stock

in order to increase cash holdings.

2. Increase in money demand makes money velocity fall, and debt liquidation reduces

the money multiplier.

3. Because of (2), price deflation occurs (assuming the central bank does not interfere

with an expansionary policy.)

4. Deflation produces a great fall in the net worth of firms precipitating bankruptcies

due to insolvency.

7 Through a different argument, (Leijonhufvud, 2009a, 2009b) also argues that the focus on price level

stability misled the Federal Reserve.

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5. Because of deflation revenue also falls, this leads again to fire sales (number 1) and

profitable firms become unprofitable.

6. Output falls and unemployment rises. The rise in unemployment produces a fall in

the demand of final goods.

7. Fall in output and rise in unemployment produces pessimism and loss of confidence.

8. Situation number 7 leads to a further fall of money velocity (and therefore to an

increase in deflationary pressure.)

9. The 8-point logical sequence described above leads to “complicated” disturbances in

the interest rate, where nominal interest rates fall and real interest rises.

While Fisher presents this sequence of nine steps as a logical chain of events, he

acknowledges that empirically or chronologically the order might be somewhat altered and

that some steps might repeat (for instance point number five triggering the effect in point

number one again.) Fisher’s nine steps should be interpreted as a pattern effect rather than

as a precise prediction.8 A savvy monetary policy would cut this sequence of events if, for

instance, the monetary authority offsets the fall in the price level with an expansionary

monetary policy such that the deflation component of the theory is cancelled. This, of

course, is Hayek’s rule and NGDP Targeting prescription for monetary policy. The negative

effects of the reduction in the net worth are particularly clear in the case of financial

markets, which played a central role in both the Great Depression and the Great Recession.

ABCT and FDD can easily complement each other. A first point of connection between these

two theories is the required initial over-indebtness situation in the market. According to

8 The problem of point versus pattern prediction in economcis was a also a concern for (Hayek, 1967,

Chapters 1, 2).

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the ABCT, the excess of debt comes from an exogenous expansionary monetary policy

performed by the monetary authority. Fisher, however, gives more weight to origin of the

over-indebtness into investors’ enthusiasm of profits into new opportunities with high

profit expectations (this still resonates with (Hayek, 1933, Chapter IV) endogenous version

of the ABCT where banks issue more credit when misled by productivity gains). New

technological discoveries or an increase in total factor productivity (TFP) can lead firms to

issue too much debt under the expectation of receiving high rates of return.

Still, (Fisher, 1933) exposition does not imply that the only reason for over-indebtness is

through investor’s enthusiasm. In fact, in the first paragraph of the section that discusses

debt starters, (Fisher, 1933, p. 348) also sustains that “[e]asy money is the great cause of

over borrowing” and that “this was a prime cause leading to the over-indebtness of 1929.

Inventions and technological improvements created wonderful investment opportunities,

and so caused big debts” (p. 348, emphasis added.)

The second point of contact between the ABCT and FDD is that while the former is a theory

of unsustainable booms that little says about how a bust will play out, the former is focused

on the bust and less on the boom. In (Garrison, 2001, p. 120) words, the ABCT “is a theory

of the unsustainable boom. It is not a theory of the depression per se. In particular, it does

not account for the severity and possible recalcitrance of the depression that may follow in

the heels of the bust.” In short, FDD starts where the ABCT story stops.

3.4. The Wicksell Effect

(Borio, 2011, 2012, 2016), and in particular (Borio & Disyatat, 2011), refer to (Wicksell,

1898) natural rate of interest and the Wicksell Effect that occurs when there is a market

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deviation from it.9 Wicksell’s natural rate of interest is the rate level that equilibrates price

of goods across time. In other words, since the interest rate is the price of time, the natural

rate of interest is the level that equilibrates the allocation of time in production and

consumption. This is why for the ABCT a monetary policy that reduces interest rates might

produce an “over consumption” of time, which occurs as investment in projects that are too

long or too capital intense (for a more detailed exposition see next section.)

This is also why Hayek favors a stable nominal income as a neutral monetary policy that

would avoid interest rate deviations from its natural level. The fact that the natural rate is

ultimately unobservable is also a reason why a monetary rule that would let market forces

converge to the natural rate is likely to be more efficient than a discretionary approach.

While Hayek’s knowledge problem points to the convenience of a rule of law in the sphere

of monetary policy, (Borio & Shim, 2007, p. 12) are more inclined towards a discretionary

approach. The reason rests the “difficulties in designing built-in stabilisers.” The monetary

rule itself, however, does not need to be complex in the sense of being very specific on its

effects on different industries. Changes in money supply ultimately affect the whole

economy, not a single industry. What a monetary policy needs to do is actually target

monetary equilibrium, which is what Hayek’s rule and NGDP Targeting do. Other concerns

such as loan provisions, minimum capital requirements, loan-to-value rations, and

currency mismatching among others can be part of the discussion of financial regulation

without the need to be embedded in a rule that makes money supply match money

demand. It is even possible to have central banks focus only on monetary equilibrium and

another agency worry about financial stability.

9 On the natural rate of interest see (Anderson, 2005; Barro & Gordon, 1983; Garrison, 2012; Williams, 2003).

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3.5. The Average Period of Production

The most questionable aspect of the ABCT is the lack of tractability of its most distinctive

component, the average period of production (APP) or roundaboutness.10 The lack of

tractability of APP makes it a challenge to be included in a formal model, DSGE or

otherwise. This problem was early recognized, and in a lost contribution, (Hicks, 1939, p.

138) offers a measurement of APP that is the equivalent of what is today known as the

modified duration of a cash-flow.

There are two key intuitions in the APP. The first one is that a fall of interest rates

incentivize in increase in the period of production. The second one is that a fall of interest

rates also incentivize more capital intense production. (Cachanosky & Lewin, 2014, 2016b;

Lewin & Cachanosky, 2017) show that these two intuitions can in fact be captured in a

financial framework and that the ABCT can be framed in financial terms. Finance provides a

well-known measure of the average period of a cash-flow, which is the Macaulay duration.

Cachanosky and Lewin show that under ceteris paribus, the cash-flow with a longer life has

a larger Macaulay duration. The second intuition requires transforming the usual free-cash-

flow (FCF) into its equivalent Economic Value Added (EVA®) representation.11 By doing

this, the cash-flow now has an explicit measurement of financial capital. Cachanosky and

Lewin show that, ceteris paribus, the cash-flow with a larger financial capital also has a

larger Macaulay duration.

10 This issue has been present in three capital debates since Böhm-Bawerk’s work to the Cambridge

controversy. See (Cohen, 2008, 2010; Cohen & Harcourt, 2003; Lewin & Cachanosky, n.d.).

11 On EVA® applications ot corporate finance see (Ehrbar, 1998; Stern, Shiely, & Ross, 2003; Young &

O’Byrne, 2000). For an application to economics and market process see (Cachanosky, 2017).

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But this analysis has a dual result that coincides with Hick’s contribution. In both cases,

either longer or larger financial capital, these cash-flows also have a larger modified

duration, which is a measure of the present value sensitivity to changes in the interest

rate.12 This means that even though a fall in interest rates makes all present values

increase, those of cash-flow that are either longer or require a larger investment increase

more than shorter cash-flows and small projects. Then, modified duration is the financial

equivalent to Böhm-Bawerk’s APP.

This means that Wicksell Effect can actually be captured through the effects of monetary

policy on the present value of the cash-flows of different and competing investment

opportunities in the portfolio of investors. A reduction in interest rates makes the relative

price of longer and larger investment to increase with respect to shorter and smaller

projects. A reversion of the monetary policy produces the opposite movement in the

relative prices of these two projects which signals to investors that resources need to be

reallocated, which can be costly if investment is irreversible (Dixit & Pyndick, 1994).

Furthermore, (Cachanosky & Lewin, 2016a) show that in the years of low interest rates

prior to the 2008 crisis, economic profits as perceived by firms, is higher on larger firms

than on smaller firms. These empirical results match the Wicksell Effect in the ABCT.

4. Conclusions

12 In continuous time, Macualay duration and modified duration are equal.

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