Wouter J. Den Haan

Solving the Stochastic Growth Model by Parameterizing Expectations

This article describes a method for solving the one-good stochastic growth model by parameterizing the expectations part of the stochastic Euler equation. The conditional expectation is specified as a function of the state of the system, and the parameters of that function are estimated to solve the model. The article includes a discussion of how to find the parameters of the function and determine systematically the complexity of the functional form necessary to solve the model.

A Practitioner's Guide to Robust Covariance Matrix Estimation

This paper develops asymptotic distribution theory for generalized method of moments (GMM) estimators and test statistics when some of the parameters are well identified, but others are poorly identified because of weak instruments. The asymptotic theory entails applying empirical process theory to obtain a limiting representation of the (concentrated) objective function as a stochastic process. The general results are specialized to two leading cases, linear instrumental variables regression and GMM estimation of Euler equations obtained from the consumption-based capital asset pricing model with power utility. Numerical results of the latter model confirm that finite sample distributions can deviate substantially from normality, and indicate that these deviations are captured by the weak instruments asymptotic approximations.

Accuracy in Simulations

Since the actual solution to intertemporal rational expectations models is usually not known, it is useful to have criteria for judging the accuracy of a given numerical solution. In this paper we propose a test for accuracy that is easy to implement and can be applied to a wide class of models without knowledge of the exact solution. We discuss the power of the test by simulating several models with the linear-quadratic approximation and with the method of parameterized expectations. We conclude that the test is powerful.

The Role of Debt and Equity Finance Over the Business Cycle

This paper documents that debt and equity issuance are procyclical for most size-sorted firm categories of listed U.S. firms. The procyclicality of equity issuance decreases monotonically with firm size. At the aggregate level, however, the results are not conclusive. The reason is that issuance is countercyclical for very large firms which, although few in number, have a large effect on the aggregate because of their enormous size. We show that the shadow price of external funds is procyclical if firms use the standard one-period contract. This model property generates procyclical equity and - as in the data - the procyclicality decreases with firm size. Another factor that causes equity to be procyclical in the model is a countercyclical cost of equity issuance. The calibrated model (i) generates a countercyclical default rate, (ii) generates a stronger cyclical response for small firms, and (iii) magnifies shocks, whereas the model without equity as an external financing source does the exact opposite.

Small Sample Properties of GMM for Business Cycle Analysis

We investigate, by Monte Carlo methods, the finite sample properties of GMM procedures for conducting inference about statistics that are of interest in the business cycle literature. These statistics include the second moments of data filtered using the first difference and Hodrick-Prescott filters, and they include statistics for evaluating model fit. Our results indicate that, for the procedures considered, the existing asymptotic theory is not a good guide in a sample the size of quarterly postwar U.S. data.

The optimal inflation path in a Sidrauski-type model with uncertainty

Abstract In this paper it is shown that in a Sidrauski-type model with uncertainty, the Chicago Rule remains valid as a prescription for the average rate of inflation, although there is a systematic difference between the perfect-foresight and the uncertainty case. Quantitatively, however, the difference turns out to be very small. The paper shows how to calculate the optimal monetary policy as a function of the state variables using the method of parameterized expectations. In terms of expected utility, the optimal policy is as good as the simple policy that reduces the money supply at the rate of time preference.

The comovement between real activity and prices in the G7

Abstract In this paper, we study the short-run and long-run comovement between prices and real activity in the G7 countries during the postwar period using vector autoregressive systems and frequency-domain filters. We find several patterns that are robust across countries and time periods. Typically, the correlation coefficients at long-run horizons are significantly negative and the correlation coefficients at short-run horizons are substantially higher. Additionally, there is evidence of positive correlation at short-run forecast horizons for some countries.

The importance of the number of different agents in a heterogeneous asset-pricing model ☆

In this paper, I compare a two-agent asset-pricing model with the corresponding model with a continuum of agents. In a two-agent economy, interest rates respond to idiosyncratic income shocks because each agent represents half of the population. These interest rate effects facilitate consumption smoothing. An agent in a two-agent economy, however, can never lend more than the other agent is allowed to borrow, which prevents him from building a buffer stock of assets. For most parameter values, the first effect is more important. For some parameter values, the interest rate effects in the two-agent economy are so strong that a relaxation of the borrowing constraint reduces an agents utility.In contrast to these differences, I find that for most parameter values there are no large differences in average interest rates across the two types of economies. In addition, I analyze the business cycle behavior of interest rates in an incomplete markets economy with a continuum of agents. The dynamic response of interest rates to aggregate shocks is a lot more complicated than the response in a complete markets economy and the magnitude of the response is bigger.

Turbulence and Unemployment in a Job Matching Model

According to Ljungqvist and Sargent (1998), high European unemployment since the 1980s can be explained by a rise in economic turbulence, leading to greater numbers of unemployed workers with obsolete skills. These workers refuse new jobs due to high unemployment benefits. In this paper we reassess the turbulence-unemployment relationship using a matching model with endogenous job destruction. In our model, higher turbulence reduces the incentives of employed workers to leave their jobs. If turbulence has only a tiny effect on the skills of workers experiencing endogenous separation, then the results of Ljungqvist and Sargent (1998, 2004) are reversed, and higher turbulence leads to a reduction in unemployment. Thus, changes in turbulence cannot provide an explanation for European unemployment that reconciles the incentives of both unemployed and employed workers.

Job Destruction and the Experiences of Displaced Workers

This paper evaluates a class of endogenous job destruction models based on how well they explain the observed experiences of displaced workers. We show that pure reallocation models in which relationship-specific productivity drifts downward over time are difficult to reconcile with the evidence on postdisplacement wages and displacement rates. Pure reallocation models with upward drift can explain the evidence, but implausibly large and persistent negative productivity shocks are required to generate displacements. Combining upward drift with outside benefits or moral hazard as additional motives for displacement makes it possible to explain the evidence with much smaller shocks. Propagation of aggregate shocks, welfare implications of displacement, upgrade of relationships in lieu of displacement, and learning effects are also discussed.