Venezia 2012 Second Best Analysis in a Non-Modigliani-Miller World

7/27/2019 Venezia 2012 Second Best Analysis in a Non-Modigliani-Miller World

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11th International ConferenceCredit 2012

Sovereign Risk and its Consequences for Financial Markets, Institutions and Regulation

Venezia, 27-28 September 2012

Second Best Analysis in a Non-Modigliani-Miller WorldFinancial implications of real economic disequilibria

Massimo Cingolani - EIB (*)

(*) Opinions expressed are personal


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OutlineI. General Equilibrium: inter-temporal vs temporary

II. Equilibrium, efficiency and second best.III. Relevance of the Efficiency Market Hypothesis (EMH).

Non-ergodicity Failure to achieve eductive stability

o New Financial Instruments

o Prices and the transmission of informationo Long-lived agents

Empirical evidenceo The equity premium puzzle

o Excess volatility

IV. The consequences of no-arbitrage pricing in a non-MM world Insights from Pasinettis structural dynamics A two goods macro-monetary model without technical progress A worked example from the monetary circuit

V. Conclusions2

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Introduction

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Starting point: invited lecture at GRETA 2011:Admati. DeMarzo, Hellwig &, Pfleiderer. 2011. Fallacies, Irrelevant Facts, and Myths in the Discussion of CapitalRegulation: Why Bank Equity is Not Expensive, The Rock Center for Corporate Governance at Stanford UniversityWorking Paper Series No. 86 Stanford GSB Research Paper No. 2063.

In essence the argument of this paper is:No problem to increase the regulatory capital of banks, because in anycase by the Modigliani Miller theorem this is does change their cost ofcapital. The authors note (p. 18):

The assumptions underlying the Modigliani-Miller analysis are in factthe very same assumptions underlying the quantitative models thatbanks use to manage their risks, in particular, the risks in their tradingbooks.Anyone who questions the empirical validity and relevance ofan analysis that is based on these assumptions is implicitly

questioning the reliability of these quantitative models and theiradequacy for the uses to which they are put including that ofdetermining required capital under the model-based approach formarket risks. If we cannot count on markets to correctly price riskand adjust for even the most basic consequences of changes inleverage, then the discussion of capital regulation should be far

more encompassing than the current debate.


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Equilibrium: different possible definitions

Simple linear model (Marglin, 1984):

- same variables

- different separationbetween endogenous andexogenous

Neoclassicalequilibrium

Neo-Keynesian

equilibriumMarxian equilibrium

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Equilibrium as solution of a system of simultaneous equations

Allais (1943, 1983) neoclassical equilibrium of maximum efficiency:i. there exists a system of prices that clears all markets, present and future,

implying notably the equality between investment and savings;

ii. marginal distribution relations hold (the remuneration of different

production factors is equal between them and proportional to their

marginal productivities);

iii. profits vanish, at least in the long-term when technology is fixed;iv. production factors are fully employed.

Neoclassical equilibrium


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Hicks (1939) notion of neoclassicalequilibrium

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Under the assumptions of the single good,week-economy, intertemporal generalequilibrium and temporary equilibrium coincide

under perfect foresight.

Spot economy

All transactions are for

immediate delivery, without

forward trading. They relate

to the same date.

Temporary EquilibriumSpot Prices

Futures economy

Everything is fixed up in advance, with all goods being

bought and sold forward, allowing not only current

demand and supplies be matched, but also planned

demand and supplies

Equilibrium over Time orIntertemporal General Equilibrium Prices

Assume you know all demand and supply until the end of time. Relative prices that clear all presentand future markets are intertemporal general equilibrium prices. They are consistent with spot

prices under the rational expectations hypothesis (REH), a strong form of which is perfect foresight.

By examining what system of prices would be fixed up in a futures economy, we can find what system of prices would maintain equilibrium over time under agiven set of changing conditions. Economists have often toyed with the idea of a system where all persons trading have perfe ctforesight. This leads to

awkward logical difficulties, but the purpose for which they have invented such systems can be met by our futures economy. Whenever the question is asked:What movement of prices, if it had been expected, could have been carried out through without disequilibrium? This is the sort of way it can be tackled (Hicks,1939, 140).


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Correct expectations equilibrium (Magill and Quinzii, 2008)

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In a spot-financial market equilibrium, for a temporary equilibrium to coincide withan intertemporal equilibrium, there must also exist a set of securities traded in

forward markets open at the same time as those of current goods that covercompletely every possible future condition of the economy in any of its contingentstates :

the financial markets must be complete, and agents must correctly anticipate at theinitial date the spot prices of every good and the payoff of every security at every date-event in the future.(2008, p. 2)

A correct expectations equilibriumis defined such a way: that this concept permits agents to hold different probability assessments regarding

future events: in case where all agents hold common probability assessments the conceptreduces to the equilibrium referred to in macroeconomics as a rational expectationsequilibrium

Removing the assumption of correct anticipations leads to the theory of temporaryequilibrium, which focuses on the minimal conditions on agents expectations of future

prices which permit current markets to clear. Maintaining the assumption of correctanticipations of future prices while dropping the assumption that financial markets arecomplete leads to the theory of general equilibrium with incomplete markets (Magilland QuinziiM&Q - 2008, p. 3)

Malinvaud (2008) notes that for the coincidence between intertemporal andtemporary equilibria time must be infinite.


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General equilibrium as a situation of maximum efficiency

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MaximumEfficiency(Pareto

optimality)

IntertemporalEquilibrium

Debreu (1959)

TemporaryEquilibrium

Arrow (1953)

Rational

or correct

expectations,

+ other ...


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Second best and no arbitrage efficiency

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Non-ergodicity implies no rational expectations

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A non-ergodic model, is a stochastic modelwhere both the errors and the parameters of

the model depend on time. In this caserational expectations are impossible andhence there is no way to assume them as

endogenous to the model, as the REHrequires. (Davidson, 1983)

Hence there are also no correct expectations,

which is a basic condition for no-arbitrage. Thisbreaks the equivalence between both the firstbest general intertemporal equilibrium and the

Pareto constrained Financial MarketEquilibrium on the one hand and the equilibriumin sequential time prevailing in the real economy,which will become a temporary equilibrium in

the sense of M&Q (see slide 6)


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Eductive stability also questions the REH and the EMH

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New Financial Instruments: Guesnerie-Rochet (1993) have shown that the REHequilibrium is such that opening afuturesmarket for the storable good decreasesthe variance of its price, thus confirmingthe result of Friedman that speculation isgood. However the likelihood of this REHequilibrium decreases due to a reductionin its stability, assessed in eductiveterms. Therefore speculation andincreasing the supply of new financialproducts can be destabilizing as theymake the RE coordination less plausible.

Prices and the transmission of

information: Desgranges, Geoffard

and Guesnerie (2003) show that evenwhen unique REH equilibria exist, theaggressive search of information cankill their eductive stability. In otherterms one cannot trust too much themarket if everybody else trust it toomuch: trusting it leads to dismissyour individual information and ifeverybody does that, the market willreceive little information, acontradiction.

Long-lived agents: Buiter (2009) criticizedthe implicit assumption of long-lived

agents retained by the Efficient MarketHypothesis. Evans, Guesnerie and McGough (2011) show that with long-livedagents, the coordination of expectationsaround a Real Business Cycle equilibriumis dubious. There is no collective image ofthe future, close but not identical to the"true", self-fulfilling, image, which is ableto trigger a common knowledge of the selffulfilling image. An expectational crisis" isunavoidable in the model retained.

NoREHnor

EMH


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Empirical refutation of EMH : equity premium puzzle

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The equity premium puzzle: over decades the return to equity exceeds substantially the long-term risk-freeinterest rate, which indicates a failure of arbitrage to reach equilibrium in the rate of return of various assets.The equity premium in the US is estimated between 6-7% per year for periods going back over 100 years and13% in more recent years. The original article of Mehra, R., and E.C. Prescott (1985), showed that the premiumwas not compatible with estimates of households risk aversion derived from neoclassical theory.

The mean risk premia associated with the size effect (SmB) and the value effect (HmL) should be zero if theCAPM is correct. Consistent with the research described above, SmB and HmL are both positive. For theperiod January 1927December 2005 the monthly mean (t-value) is 0.25 per cent (2.01) for SmB and 0.48 percent (3.64) for HmL, and the correlation between the two premia is 0.13. Figure 1 plots the time series of theintra-year monthly means of the two premia. The figure shows that (a) both premia display substantialvariability over time and (b) the two series display a considerable common co-movement despite the low

estimated correlation. (Keim, 2008, pp. 3-4 of 14)


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Empirical refutation of EMH : excess volatility

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Shiller (2003, p. 90) concludes:After all the efforts to defend the

efficient markets theory, there is stillevery reason to think that, whilemarkets are not totally crazy, theycontain quite substantial noise, sosubstantial that it dominates themovements in the aggregate market.The efficient markets model, for theaggregate stock market, has still neverbeen supported by any study effectivelylinking stock market fluctuations withsubsequent fundamentals.

LeRoy (2008) concludes his survey ofthe matter: Most analysts believethat no single convincing explanation

has been provided for the volatility ofequity prices. The conclusion thatappears to follow from the equitypremium and price volatility puzzles isthat, for whatever reason, prices offinancial assets do not behave as thetheory of consumption-based asset

pricing predicts.


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Temporary equilibrium is out of neoclassical equilibrium

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Recent research in finance has revealed stock price behaviour that is inconsistentwith the predictions of familiar models. The research on time series predictability, asa whole, is convincing evidence that expected returns are not constant through time.

There are reasonable business conditions stories that can account for time variationin expected returns. However, some of the temporal patterns in returns in particularthose relating to calendar turning points are troubling as they defy economicinterpretations. The evidence on cross-sectional anomalies poses a significantchallenge to well-established asset pricing paradigms. Yet, despite mounting

evidence, there is little consensus on alternative theoretical models. As such, the

focus of future research should be on developing such models. (Keim, 2008, p. 9 of14).

What is suggested here is that the group of hypothesis that underlie the neoclassicalparadigm in the core general equilibrium real version or in its financial extensionsbased on the Efficient Market Hypothesis should be rejected. The rejection of theRational Expectations Hypothesis in particular should open the way to more trulyKeynesian models based on the production paradigm (Pasinetti, 1975), where

fundamental uncertainty plays a role (Fontana, 2009), in a monetary production

economy (Graziani, 2003; Parguez and Seccareccia, 2000). Some examples areprovided below. They should be better systematized, expanded and consolidated in

future research.


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Pasinettis structural dynamics

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The efficiency (equilibrium) criteria relevant in structural dynamics is that of full employment,which is only one of the several conditions necessary for the obtainment of the neoclassicalequilibrium and therefore generalizes the latter. For full employment to be achieved, all

incomes distributed in the period must be spent, which happens when natural prices andprofits prevail. Natural rates of profitare such that they are different in each sector, and equalto the sum of the rate of growth of population and the per capita growth of consumption in thatparticular sector.

When there is uniformity of the sectoral profit rates, in general the full employment condition

will not be met and therefore the economy is out of the dynamic equilibrium. If only a singleprofit rate prevails in the economy, the only way to fulfill the full employment condition is thatthis uniform profit rate be the natural uniform profit rate, which is given also by the so-calledCambridge equation (Pasinetti, 1962; Bortis, 1993). The latter in a single good economy statesthat the full employment rate of profit pe is equal to the rate of growth of output (itself equalto the sum of the rate of growth of population g and the weighted average rate of growth ofper capita consumption r*) divided by the propensity to save of capitalists:

p e = 1sC

g+ r*( )

When the uniform rate of profit diverges from pe, either from below or from above,unemployment will develop, or in other words the more general concept of efficiency applicableto the dynamics of structural change will not be observed. The analysis of Pasinetti shows that,

due to diverging rates of technical progress and sectoral consumption growth, this will happen allthe time. Out of equilibrium allocation and distribution cannot be separated anymore.

p i*= g + ri


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Parguez 4 regimes

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Parguez develops a model of the monetary circuit where rent (return in excess ofthe long-term interest rate) increases unemployment, in other words where itbrings the economy far away from the dynamic equilibrium path. In this model, inaddition to the 3 usual regimes of fix-price models (pure Keynesian case, pureclassical case and the classical-Keynesian case, Parguez introduces a 4th regime, the"Rentier-Led" Case:

This case is the result of both an increase in rentiers' share of aggregateincome and a more constraining price target. Rentiers strive to increase theirown income by pushing upwards (with the support of the Central Bank) therate of interest. Abstracting from the impact on the required rate, of return, therise in the rate of interest imposes a higher cost multiplier, kc, which increasesunemployment, as shown by the employment function. For a given rate of

saving, a rise in kc, signals to firms that they need a lower wage-bill, and thus alower employment, to meet their short-term profit target. This negative impactof the rise in kc, is worsened by the required fall in the wage rate, for a givenprice constraint, whose effect is to engineer a "classical-Keynesian"unemployment. (Parguez, 1996a)


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The Monetary Production Economy (Graziani, 2003)

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An illustrative worked example: Assume an economy that produces and consumes widgets where labour productivity is 5widgets per hour and where wages are equal to 10 euro per hour. A temporary monetary equilibrium of the kind studied by thetheory of the monetary circuit is assumed. At the beginning of the day enterprises decide to employ workers for 8 hours, i.e.

their expectations are thus that it is profitable to produce 40 widgets. They are ready to pay a salary of 10 Euros per hour andanticipate that households will save 20% of their incomes. Since unit labour costs are 2 Euros per unit produced, if they want toachieve a target 25% profit rate they must set the selling price of widgets at 2.5. Therefore households consumption will be 64Euros and savings 16 Euros. To balance their accounts at the end of the period, enterprises must borrow from households thetotal amount of their savings. These savings can be viewed as a security that gives right to 16 in time 1, state 0, for which tosimplify the interest rate is assumed to be zero. Since at a price of 2.5 households consume only 26 widgets, enterprisesaccumulate stocks for 14, which have a value of 36, but since they have a debt of 16 to households, their profit is 20. At time 1,state 0, expectations are fulfilled, consumers receive the 16 from the security they bought in the previous period. With stationarydemand forecasts, the rest of the variables remain more or less the same. Households consumption and incomes increase and

the profit rate decreases, indicating a tendency towards convergence to a long-term equilibrium with zero profits.

Assume now that the price at whichsecurity was sold in time zero wasactually wrong. It was sold for 16because it was supposed to give 16 instate 0, but in fact in state 1 it entailed acapital loss of 35. In this case

households consumption and incomesdecrease and enterprises accumulateunplanned stocks. The share of workersin total income decreases and that ofenterprises increases, indicating a moveaway from equilibrium (away from thezero profit condition).


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The world of the Modigliani Miller theorem is a world where there is almost completeanalogy between the static first best intertemporal equilibrium and the dynamic temporary

equilibria that would be achieved in a symmetric sequential economy. This correspondence requires complete markets to exists, perfect expectations and infinite

lived agents. If these assumptions are relaxed, one obtainsa) finance equilibria if markets are incomplete; and,b) true temporary equilibria if the assumptions of perfect forecast and no arbitrage

are abandoned.

Both the current crisis, the critiques that one can develop on rational expectations and anumber of unexplained empirical puzzles concerning the EMH justify that the economicreality does not respect the conditions for the market efficiency hypothesis.

In such circumstances, pricing securities under a no arbitrage assumption when in fact thisassumption does not hold can bring the economy further away from equilibrium viadistribution effect that increase rent to the detriment of wages and entrepreneurial profits.These should be expected to increase unemployment in a monetary economy evolving out

of the out of the neoclassical equilibrium. In other words, pricing under no arbitrage assumptions in a non Modigliani-Miller world

could have contributed to the accumulation of economic and financial imbalances in recentyears. This was illustrated in the paper based on three different arguments that concur inbuilding an intuition that must be verified in the light of more systematic future analyses.

It also points to the need (and urgency) of developing an alternative finance theory thatholds out of the equilibrium conditions of the market efficiency hypothesis.

Conclusions


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Admati, Anat R., Peter M. DeMarzo, Martin F. Hellwig, Paul Pfleiderer. 2011. Fallacies, Irrelevant Facts, and Myths in the Discussion of Capital Regulation: Why Bank Equityis Not Expensive, The Rock Center for Corporate Governance at Stanford University Working Paper Series No. 86 Stanford GSB Research Paper No. 2063.

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Venezia 2012 Second Best Analysis in a Non-Modigliani-Miller World