Research Database

[Please note that the following Greek lettering is improperly transcribed.] If [0,1] is a measure space of agents and X---- a collection of pairwise uncorrelated random variables with common finite mean U and variance a , one would like to establish a law of large numbers () Xdl = U. In this paper we propose to interpret () as a Pettis integral. Using the corresponding Riemann-type version of this integral, we establish (*) and interpret it as an L2-law of large numbers. Intuitively, the main idea is to integrate before drawing an W, thus avoiding well-know measurability problems. We discuss distributional properties of i.i.d. random shocks across the population. We given examples for the economic interpretability of our definition. Finally, we establish a vector-valued version of the law of large numbers for economies.

Although the role of financial constraints on entrepreneurial choices has received considerable attention, the effects of these constraints on aggregate capital accumulation and wealth inequality are less known. Entrepreneurship is an important determinant of capital accumulation and wealth concentration and, conversely, the distribution of wealth affects entrepreneurial choices in presence of borrowing constraints. We construct a model that matches wealth inequality very well, both for entrepreneurs and non-entrepreneurs, and find that more restrictive borrowing constraints generate less wealth concentration, but also reduce average firm size, aggregate capital and the fraction of entrepreneurs. We also find that voluntary bequests are an important channel that allows some high-ability workers to establish or enlarge an entrepreneurial activity: with accidental bequests only, there would be fewer large firms, fewer entrepreneurs, and less aggregate capital, but also less wealth concentration.

Sudden Stops are financial crises defined by a large, sudden current-account reversal. They occur in both advanced and emerging economies and result in deep recessions, collapsing asset prices, and real exchange-rate depreciations. They are preceded by economic expansions, current-account deficits, credit booms, and appreciated asset prices and real exchange rates. Fisherian models (i.e. models with credit constraints linked to market prices) explain these stylized facts as an outcome of Irving Fisher's debt-deflation mechanism. On the normative side, these models feature a pecuniary externality that provides a foundation for macroprudential policy (MPP). We review the stylized facts of Sudden Stops, the evidence on MPP use and effectiveness, and the findings of the literature on Fisherian models. Quantitatively, Fisherian amplification is strong and optimal MPP reduces sharply the size and frequency of crises, but it is also complex and potentially time-inconsistent, and simple MPP rules are less effective. We also provide a new MPP analysis incorporating investment. Using a constant debt-tax policy, we construct a crisis probability-output frontier showing that there is a tradeoff between financial stability and long-run output (i.e., reducing the probability of crises reduces long-run output).

We study a random-matching, absence-of-double-coincidence environment in which people cannot precommit and in which there are two imperfect ways of keeping track of what other people have done in the past: money and a public record of all past actions that is updated with an average lag. We study how the magnitude of that lag affects the allocations that are optimal from among allocations that are stationary and feasible and that satisfy incentive constraints which arise from the absence of commitment and the imperfect ways of keeping track of what others have done in the past.

'Structural unemployment' is said to occur in regions or 'sectors' of the economy as a consequence of technological changes. In this paper we present a model which provides an environment which gives rise to unemployment which could be labelled structural unemployment. There is exogenous technological change and vintage specific human capital. Unemployment arises as workers specialized in a particular technology within a vintage decide to search for a job within their vintage, so that their previously acquired special skills are used, instead of getting employed as unskilled workers in the newest vintage. As the rate of technological change increases, the incentives to reassign specialized workers to their same vintage, inccuring therefore in search costs, becomes less attractive, and in consequence the fraction of specialized workers doing search activities decreases. This provides some rationale for the negative correlation between rates of growth and unemployment observed in the data.

It is often argued that with a positively skewed income distribution (median less than mean) a majority voting over proportional tax rates would result in higher tax rates than those that maximize average welfare, and will accordingly reduce aggregate savings. We reexamine this view in a capital accumulation model, in which distorting redistributive taxes provide insurance against idiosyncratic shocks, and income distributions evolve endogenously. We find small differences of either sign between the tax rates set by a majority voting and a utilitarian government, for reasonable parametric specifications. We show how these differences reflect a greater responsiveness of a utilitarian government to the average need for the insurance provided by the tax-redistribution scheme. These conclusions remain true despite the fact that the model simulations produce positively skewed distributions of total income across agents.

When the zero lower bound on nominal interest rates binds, monetary policy cannot provide appropriate stimulus. We show that, in the standard New Keynesian model, tax policy can deliver such stimulus at no cost and in a time-consistent manner. There is no need to use inefficient policies such as wasteful public spending or future commitments to low interest rates.

In 1950 Mexico entered an economic takeoff and grew rapidly for more than 30 years. Growth stopped during the crises of 1982–1995, despite major reforms, including liberalization of foreign trade and investment. Since then growth has been modest. We analyze the economic history of Mexico 1877–2010. We conclude that the growth 1950–1981 was driven by urbanization, industrialization, and education and that Mexico would have grown even more rapidly if trade and investment had been liberalized sooner. If Mexico is to resume rapid growth — so that it can approach U.S. levels of income — it needs further reforms.

We evaluate reforms to the U.S. tax system in a dynamic setup with heterogeneous married and single households, and with an operative extensive margin in labor supply. We restrict our model with observations on gender and skill premia, labor force participation of married females across skill groups, and the structure of marital sorting. We study four revenue-neutral tax reforms: a proportional consumption tax, a proportional income tax, a progressive consumption tax, and a reform in which married individuals file taxes separately. Our findings indicate that tax reforms are accompanied by large and differential effects on labor supply: while hours per-worker display small increases, total hours and female labor force participation increase substantially. Married females account for more than 50% of the changes in hours associated to reforms, and their importance increases sharply for values of the intertemporal labor supply elasticity on the low side of empirical estimates. Tax reforms in a standard version of the model result in output gains that are up to 15% lower than in our benchmark economy.

Technical details and specific data sources are provided for “Facts and Myths about the Financial Crisis of 2008” by V. V. Chari, Lawrence Christiano, and Patrick J. Kehoe.

This paper presents a completely worked example applying the frequency domain estimation strategy proposed by Hansen and Sargent [1980, 1981a]. A bivariate, high order continuous time autoregressive moving average model is estimated subject to the restrictions implied by the rational expectations model of the term structure of interest rates. The estimation strategy takes into account the fact that one of the data series are point-in-time observations, while the other are time averaged. Alternative strategies are considered for taking into account nonstationarity in the data. Computing times reported in the paper demonstrate that estimation using the techniques of Hansen and Sargent is inexpensive.

Although employment at individual firms tends to be highly non-stationary, the employment size distribution of all firms in the United States appears to be stationary. It closely resembles a Pareto distribution. There is a lot of entry and exit, mostly of small firms. This paper surveys general equilibrium models that can be used to interpret these facts and explores the role of innovation by new and incumbent firms in determining aggregate growth. The existence of a balanced growth path with a stationary employment size distribution depends crucially on assumptions made about the cost of entry. Some type of labor must be an essential input in setting up new firms.

Economic development is typically accompanied by a very pronounced migration of labor from rural to urban employment. This migration, in turn, is often associated with large scale urban underemployment. Both factors appear to play a very prominent role in the process of development. We consider a model in which rural-urban migration and urban underemployment are integrated into an otherwise conventional neoclassical growth model. Unemployment arises not from any exogenous rigidities, but from an adverse selection problem in labor markets. We demonstrate that, in the most natural case, rural-urban migration—and its associated underemployment—can be a source of multiple, asymptotically stable steady state equilibria, and hence of development traps. They also easily give rise to an indeterminacy of perfect foresight equilibrium, as well as to the existence of a large set of periodic equilibria displaying undamped oscillation. Many such equilibria display long periods of uninterrupted growth and rural-urban migration, punctuated by brief but severe recessions associated with net migration from urban to rural employment. Such equilibria are argued to be broadly consistent with historical U.S. experience.

We analyze the optimal design of monetary rules. We suppose there is an agreed upon social welfare function that depends on the randomly fluctuating state of the economy and that the monetary authority has private information about that state. We suppose the government can constrain the policies of the monetary authority by legislating a rule. In general, well-designed rules trade-off the need to constrain policymakers from the standard time consistency problem arising from the temptation for unexpected inflation with the desire to give them flexibility to react to their private information. Surprisingly, we show that for a wide variety of circumstances the optimal rule gives the monetary authority no flexibility. This rule can be interpreted as a strict inflation targeting rule where the target is a prespecified function of publicly observed data. In this sense, optimal monetary policy is transparent.

In empirical studies of the CAPM, it is commonly assumed that (a) the return to the value weighted portfolio of all stocks is a reasonable proxy for the return on the market portfolio of all assets in the economy, and (b) betas of assets remain constant over time. Under these assumptions, Fama and French (1992) find that the relation between average return and beta is flat. We argue that these two auxiliary assumptions are not reasonable. We demonstrate that when these assumptions are relaxed, the empirical support for the CAPM is surprisingly strong. When human capital is also included in measuring wealth, the CAPM is able to explain 28 percent of the cross sectional variation in average returns in the 100 portfolios studied by Fama and French. When, in addition, betas are allowed to vary over the business cycle, the CAPM is able to explain 57 percent. More important, relative size does not explain what is left unexplained after taking sampling errors into account.

We study the general equilibrium effects of social insurance on the transition in a model in which the process of moving workers from matches in the state sector to new matches in the private sector takes time and involves uncertainty. As to be expected, adding social insurance to an economy without any improves welfare. Contrary to standard intuition, however, adding social insurance may slow transition. We show that this result depends crucially on general equilibrium interactions of interest rates and savings under alternative market structures.

We study models of credit with limited commitment, which implies endogenous borrowing constraints. We show that there are multiple stationary equilibria, as well as nonstationary equilibria, including some that display deterministic cyclic and chaotic dynamics. There are also stochastic (sunspot) equilibria, in which credit conditions change randomly over time, even though fundamentals are deterministic and stationary. We show this can occur when the terms of trade are determined by Walrasian pricing or by Nash bargaining. The results illustrate how it is possible to generate equilibria with credit cycles (crunches, freezes, crises) in theory, and as recently observed in actual economies.

We develop a model of the market for federal funds that explicitly accounts for its two distinctive features: banks have to search for a suitable counterparty, and once they meet, both parties negotiate the size of the loan and the repayment. The theory is used to answer a number of positive and normative questions: What are the determinants of the fed funds rate? How does the market reallocate funds? Is the market able to achieve an efficient reallocation of funds? We also use the model for theoretical and quantitative analyses of policy issues facing modern central banks.

A statistical definition of the natural unemployment rate hypothesis is advanced and tested. A particular illustrative structural macroeconomic model satisfying the definition is set forth and estimated. The model has "classical" policy implications, implying a number of neutrality propositions asserting the invariance of the conditional means of real variables with respect to the feedback rule for the money supply. The aim is to test how emphatically the data reject a model incorporating rather severe "classical" hypotheses.

This paper examines the quantitative importance of temporal aggregation bias in distorting parameter estimates and hypothesis tests. Our strategy is to consider two empirical examples in which temporal aggregation bias has the potential to account for results which are widely viewed as being anomalous from the perspective of particular economic models. Our first example investigates the possibility that temporal aggregation bias can lead to spurious Granger causality relationships. The quantitative importance of this possibility is examined in the context of Granger causal relations between the growth rates of money and various measures of aggregate output. Our second example investigates the possibility that temporal aggregation bias can account for the slow speeds of adjustment typically obtained with stock adjustment models. The quantitative importance of this possibility is examined in the context of a particular class of continuous and discrete time equilibrium models of inventories and sales. The different models are compared on the basis of the behavioral implications of the estimated values of the structural parameters which we obtain and their overall statistical performance. The empirical results from both examples provide support for the view that temporal aggregation bias can be quantitatively important in the sense of significantly distorting inference.

The paper surveys the recent literature on the fiscal implications of central bank balance sheets, with a special focus on political economy issues. It then presents the results of simulations that describe the effects of different scenarios for the Federal Reserve's longer-run balance sheet on its earnings remittances to the U.S. Treasury and, more broadly, on the government's overall fiscal position. We find that reducing longer-run reserve balances from $2.3 trillion (roughly the current amount) to $1 trillion reduces the likelihood of posting a quarterly net loss in the future from 30 percent to under 5 percent. Further reducing longer-run reserve balances from $1 trillion to pre-crisis levels has little effect on the likelihood of net losses.

This paper examines the seasonal pattern of accruals for loan-loss provisions and chargeoffs chosen by bank managers. Using the existing literature on intra-year discretionary accruals, knowledge of the incentive systems used to evaluate bank managers' performance, and various regulatory characteristics, we predict that accruals for provisions and chargeoffs will cluster in the fourth quarter of each year. We examine quarterly data for 105 large bank holding companies from the first quarter of 1980 through the fourth quarter of 1990. Our results indicate that: (1) provisions and chargeoffs are clustered in the fourth quarter, (2) this clustering is not related to the level of business activity of the banks, (3) the proximity of a bank's actual capital to its regulatory capital requirement does not affect this clustering, and (4) current provisions are affected both by current chargeoffs and by expectations about future chargeoffs. To examine whether the systematic characteristics of these loan-loss provision and chargeoff decisions are understood by users, we also estimate a quarterly equity valuation model in which quarterly provisions should be differentially weighted to reflect their seasonal characteristics. We find strong evidence to indicate that equity prices behave as if the market participants take these seasonal properties into account.

A random matching model with money is used to study the nominal yield on small denomination, bearer, safe, discount securities issued by the government. There is always one steady state with matured securities circulating at par and, for some parameters, another with them circulating at a discount. In the former, a necessary and sufficient condition for a positive nominal yield on not-yet-matured securities is exogenous discriminatory treatment of them by the government. In the latter, the post-maturity discount on securities induces a deeper pre-maturity discount even without such discriminatory treatment.

A model is constructed where banks provide access to a communication technology which facilitates trade. Bank liabilities may coexist with alternative means of payment in equilibrium, and there exist regions of the parameter space where banking dominates the payments system and where physical exchange media dominate. The model is consistent with some observations concerning the role of the banking system in economic development, and with characteristics of banking crises. In particular, in early stages of economic development: 1) rapid output growth is accompanied by an increasing share of banking in transactions activity and 2) there are recurrent banking "panics" where reductions in measured aggregate output coincide with increases in the use of alternative means of payment relative to bank liabilities. In later stages of development, growth slackens off, the share of banking in the payments system stabilizes and the economy is less likely to be subject to banking panics.

We describe a simple environment in which assets of varying qualities may be used for transactions and consumption. The quality of an asset is known to the seller but not the buyer. We show that this feature can generate a negative relationship between the transactions velocities of assets and their rates of return. We also discuss several versions of Gresham's Law which hold in this environment.

Economic equilibria are usually solutions to fixed point problems rather than solutions to convex optimization problems. This leads to two difficulties that are closely related: First, equilibria may be difficult to compute. Second, a model economy may have more than one equilibrium. This paper explores these issues for a number of stylized economies, including static economies that involve both pure exchange and production, economies that have infinite numbers of goods because of time and uncertainty, and economies with distortionary taxes and externalities. There are numerous numerical examples that illustrate the theory and could serve as test problems for algorithms.

This paper describes methods for conveniently formulating and estimating dynamic linear econometric models under the hypothesis of rational expectations. An econometrically convenient formula for the cross-equation rational expectations restrictions is derived. Models of error terms and the role of the concept of Granger causality in formulating rational expectations models are both discussed. Tests of hypothesis of strict econometric exogeneity along the lines of Sim’s are compared with a test that is related to Wu’s.

Theory typically does not give us reason to believe that economic models ought to be formulated at the same level of time aggregation at which data happen to be available. Nevertheless, this is frequently done when formulating econometric models, with potentially important specification-error implications. This suggests examining the alternatives, one of which is to model in continuous time. The primary difficulty in inferring the parameters of a continuous time model given sampled observations is the “aliasing identification problem.” This paper shows how the restrictions implied by rational expectations sometimes do, and sometimes do not, resolve the problem. This is accomplished very simply in the context of a hypothesis about the term structure of interest rates. The paper confirms and extends results obtained for another example by Hansen and Sargent.

How should a government use the power to commit to ensure a desirable equilibrium outcome? In this paper, I show a misleading aspect of what has become a standard approach to this question, and I propose an alternative. I show that the complete description of an optimal (indeed, of any) policy scheme requires outlining the consequences of paths that are often neglected. The specification of policy along those paths is crucial in determining which schemes implement a unique equilibrium and which ones leave room for multiple equilibria that depend on the expectations of the private sector.