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«Abstract We study a model with heterogeneous producers that face collateral and cash in advance constraints. A tightening of the collateral ...»

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Liquidity Traps and Monetary Policy: Managing a

Credit Crunch

∗ †

Francisco Buera Juan Pablo Nicolini

January 15, 2016

Abstract

We study a model with heterogeneous producers that face collateral and

cash in advance constraints. A tightening of the collateral constraint results

in a credit-crunch generated recession that reproduces several features of the

financial crisis that unraveled in 2007. The model can suitable be used to study the effects on the main macroeconomic variables and of alternative policies following the credit crunch. The policy implications are in sharp contrast with the prevalent view in most Central Banks, based on the New Keynesian explanation of the liquidity trap.

∗ Federal Reserve Bank of Chicago; francisco.buera@chi.frb.org † Federal Reserve Bank of Minneapolis and Universidad Di Tella; juanpa@minneapolisfed.org.

‡ We want to thank Marco Basetto, Jeff Campbell, Gauti Eggertsson, Jordi Gali, Simon Gilchrist, Hugo Hopenhayn, Oleg Itskhoki, Keichiro Kobayashi, Pedro Teles. The views expressed in this paper do not represent the Federal Reserve Bank of Chicago, Minneapolis, or the Federal Reserve System.

1 Introduction In this paper, we study the effect of monetary and debt policy following a negative shock to the efficiency of the financial sector. We build a model that combines the financial frictions literature, like in Kiyotaki (1998), Moll (2014) and Buera and Moll (2015) with the monetary literature, like Lucas (1982), Lucas and Stokey (1987) and Svensson (1985). The first branch of the literature gives rise to a non-trivial financial market by imposing collateral constraints on debt contracts. The second gives rise to a money market by imposing cash-in-advance constraint in purchases. We show that the model qualitatively reproduces several aspects of the recent great recession.

More importantly, we also show that a calibrated version can quantitatively match many salient features of the US experience since 2007. Finally, we use the model to learn about the effects of alternative policies.

The year 2008 will long be remembered in the macroeconomics literature. This is so not only because of the massive shock that hit global financial markets, particularly the bankruptcy of Lehman Brothers and the collapse of the interbank market that immediately followed, but also because of the unusual and extraordinary policy response that followed. The Federal Reserve doubled its balance sheet in just three months—from $900 billion on September 1 to $2.1 trillion byDecember 1, and it reached around $3 trillion by the end of 2012. At the same time, large fiscal deficits implied an increase in the supply of government bonds, net of the holdings by the Fed, of roughly 30% of total output in just a few years, a change never seen during peace time in the United States. Similar measures were taken in other developed economies.

Somewhat paradoxically, however, the prominent models used for policy evaluation by the main Central Banks at the time of the crisis ignored the financial sector in one hand, and the role of changes in outside liquidity on the other.1 There were good historical reasons for both: big financial shocks have seemed to belong exclusively to emerging economies since the turbulent 1930s. In addition, monetary economics developed during the last two decades around the central bank rhetoric of exclusively emphasizing the short-term nominal interest rate, while measures of liquidity These models have been further adapted to try to address these issues (see Curdia and Woodford (2010), Christiano et al. (2011) or Werning (2011)). As we will discuss, our model captures different effects and the policy implications differ substantially.

or money were completely ignored as a stance of monetary policy.2 But 2008 seriously challenged those generally accepted views. Consequently, we need general equilibrium models that can be used for policy evaluation during times of financial distress. The purpose of this paper is to provide one such model and to analyze the macroeconomic effects of alternative policies.

An essential role of financial markets is to reallocate capital from wealthy individuals with no profitable investment projects to individuals with profitable projects and no wealth. The efficiency of these markets determines the equilibrium allocation of physical capital across projects and therefore equilibrium intermediation and total output. The financial frictions literature, from which we build, studies models of intermediation with these properties, the key friction being an exogenous collateral constraint on investors.3 The equilibrium allocation critically depends on the nature of the collateral constraints: The tighter the constraints, the less efficient the allocation of capital and the lower are total factor productivity and output, so a tightening of the collateral constraint creates disintermediation and a recession. We interpret this reduction in the ability of financial markets to properly allocate capital across projects as the negative shock that hit the US economy at the end of 2007.4 We modify this basic model by imposing a cash-in-advance constraint on households. Monetary policy has real effects, not only because of the usual well-understood distortionary effects of inflation in a cash-credit world, but, more importantly, because of the zero bound constraint on nominal interest rates that naturally arises in monetary models. Conditional on policy, the bound on the nominal interest rate may become a bound on the real interest rate. For example, imagine a policy that successfully targets a constant price level: if inflation is zero, the Fisher equation implies a zero lower bound on the real interest rate. The way in which negative real interest rates interact with the zero bound on nominal interest rates, given a target for inflation, is at the heart of the mechanism by which policy affects outcomes in the model A likely reason is that the empirical relationship between monetary aggregates, interest rates, and prices, which remained stable for most of the 20th century, broke down in the midst of the banking deregulation that started in the 1980s. For a detailed discussion, as well as a reinterpretation of the evidence that strongly favors the view of a stable money demand relationship, see Lucas and Nicolini (2015).





We closely follow the work of Buera and Moll (2015) who study business cycles in the framework developed by Moll (2014) to analyze credit markets in development. See Kiyotaki (1998) for an earlier version of a related framework.

As we explain in detail in Section 4.1, the behavior of the real interest rate, the variable we use to identify the shock, dates the begging of the recession in the third quarter of 2007.

discussed in the paper.

The exogenous nature of both frictions raises legitimate doubts regarding the policy invariant nature of them. Precise micro-foundations for the collateral or the cash-in-advance constraints have been hard to develop in macro models that remain tractable and general enough to provide insights on the effects of the policies we study in this paper. We thus view this as a first exploration into the the role of the above mentioned monetary and debt policies, hoping that the answers we provide, both positive and normative, can shed light into the questions we pose, as in Robert E. Lucas (2000), and Alvarez and Lippi (2009) for models with cash-in-advance constraints, and Kiyotaki (1998) or Moll (2014) for models with collateral constraints.

As we show in a simplified version of the model that can be solved analytically, if the shock to the collateral constraint that causes the recession is sufficiently large, the equilibrium real interest rate becomes negative and persistent as long as the shock is persistent. We find this property of the model particularly attractive, since a very special feature of the last years is a substantial and persistent gap between real output and its trend, together with a substantial and persistent negative real rate of interest.

This feature is specific to the credit crunch: If the recession is driven by an equivalent but exogenous negative productivity shock, the real interest rate remains positive.

The reason for the drop in real interest rates is that savings must be reallocated to lower productivity entrepreneurs, but they will only be willing to do it for a lower interest rate. To put it differently, the “demand” for loans falls, which in turn pushes down the real interest rate. Several other properties of the recession generated by a tightening of the collateral constraint in the model are in line with the events that have unfolded since 2008, such as the sustained periods with an effective zero bound on nominal interest rates, and the substantial drops in investment and total factor productivity, all of these driven by a single shock. In addition, the model implies the need of a very large increases in liquidity while the zero bound binds to stabilize prices, two features present in the crisis.

A calibrated version of the full model can quantitatively account for the behavior of the real interest rate, output, capital, total factor productivity and, with somewhat less success, measures of leverage, since 2007. The one variable the model misses is labor input, that dropped substantially in the US following 2007 and is constant in the model. We find this quantitative performance remarkable, given that it is driven by a single shock. We also find it reassuring in using the model to perform policy analysis.

The paper proceeds as follows. In Section 2 we present the model. In Section 3, we define an equilibrium and characterize its properties for a particular case that, by shutting down the endogenous evolution of the wealth distribution, can be solved analytically. In Section 4 we calibrate the full model and show that, once the monetary and debt policies implemented by the US authorities are taken into account, it can explain the evolution of all relevant macro-variables, the exception being labor input as we already mentioned. In solving the model, we study the deterministic equilibrium path following the shock to intermediation. In looking at the data, we focus at the medium frequency evolution of the data, which is the frequency the model implies we should focus on, as we explain in detail. In particular, we ignore the high frequency business cycle fluctuations that are the focus of the RBC literature.

In Section 5, we perform several policy counterfactuals that help put the policies undertaken in the United States starting in 2008 into perspective. First, we solve for the equilibrium in the absence of a policy reaction. Specifically, we assume that there is no injection of liquidity on impact and that there is no further increase in the stock of government bonds (safe assets). The model implies that there will be an initial deflation, followed by an inflation rate that is higher that the steady state. These effects are the natural response of the no arbitrage condition between money and bonds. In the case that private debt contracts are indexed to the price level, the real effects are minor. On the contrary, in the more realistic case in which debt obligations are in nominal terms, the deflation strongly accentuates the recession well beyond the one generated by the credit crunch, due to a debt deflation problem. A similar result obtains with sticky wages, commonly assumed in modern monetary models. We then study active inflation-targeting policies for low values of the inflation target. In these cases, the deflation with its associated real effects can be avoided by a sufficiently large increase in the supply of government liabilities that must accommodate the credit crunch. This exercise is reminiscent of the discussion in Friedman and Schwartz, who argued that the Fed should have substantially increased its balance sheet in order to avoid the deflation during the Great Depression.5 Was the different monetary policy In 2002, Bernanke, then a Federal Reserve Board governor, said in a speech in a conference celebrating Friedman’s 90th birthday, “I would like to say to Milton and Anna: Regarding the Great Depression. You’re right, we did it. We’re very sorry. But thanks to you, we won’t do it again” (speech published in Milton Friedman and Anna Jacobson Schwartz, The Great Contraction, 1929-1933 ) (Princeton, NJ: Princeton University Press, 2008), 227.

recently adopted the reason why the Great Contraction was much less severe than the Great Depression? Our model suggests this may well be the case.6 In studying inflation targeting policies, we show that the number of periods that the economy will be at the zero bound and the amount of liquidity that must be injected depend on the target for the rate of inflation. The evolution of output critically depends on the increase in liquidity. The target for inflation and the zero bound constraint on nominal rates imply a floor on how low the real interest rate can be. But for this to be an equilibrium, private savings must end up somewhere else: this is the role of the increase in government liabilities. In this heterogeneous credit-constrained agents model, outside liquidity affects equilibrium interest rates even if taxes are lump sum: Ricardian equivalence does not hold if agents discount future flows at different rates, as is the case when collateral constraints bind. As a consequence, the issuance of government liabilities (money or bonds, which are perfect substitutes at the zero bound) crowds out private investment and slows down capital accumulation. But increases in liquidity have an additional effect. In the model, a credit crunch generates a recession because total factor productivity falls. The reason, as we mentioned above, is that capital needs to be reallocated from high productivity entrepreneurs for which the collateral constraint binds to low productivity entrepreneurs for which the collateral constraint does not bind. An increase in liquidity prevents the real interest rate from falling too much, and ameliorates the drop in productivity.



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