Cross-equation Restrictions Research Articles

U.S. Wage and Price Dynamics: A Limited Information Approach

This paper analyzes the dynamics of prices and wages using a limited information approach to estimation. I estimate a two-equation model for the determination of prices and wages derived from an optimization-based dynamic model in which both goods and labor markets are monopolistically competitive; prices and wages can be reoptimized only at random intervals; and, when prices and wages are not reoptimized, they can be partially adjusted to previous-period aggregate inflation. The estimation procedure is a two-step minimum distance estimation that exploits the restrictions imposed by the model on a time-series representation of the data. In the first step, I estimate an unrestricted autoregressive representation of the variables of interest. In the second, I express the model solution as a constrained autoregressive representation of the data and define the distance between unconstrained and constrained representations as a function of the structural parameters that characterize the joint dynamics of inflation and labor share. This function summarizes the cross-equation restrictions between the model and the time-series representations of the data. I then estimate the parameters of interest by minimizing a quadratic function of that distance. I find that the estimated dynamics of prices and wages track actual dynamics quite well and that the estimated parameters are consistent with the observed length of nominal contracts.

Tests of the Present-Value Model of the Current Account: A Monte Carlo Study

Using a Monte Carlo approach, we evaluate the small-sample properties of four different tests of the present-value model (PVM) of the current account: the non-linear Wald, linear Wald, Lagrange multiplier, and likelihood ratio tests. We find that the non-linear Wald test is biased towards over-rejecting the cross-equation restrictions implied by the PVM, and that the test statistic is uncorrelated with the goodness of fit of the PVM. The three alternative tests are essentially equivalent and are more reliable in evaluating the PVM.

Monetary Policy Inertia or Persistent Shocks?

In this paper, we propose a simple econometric framework to disentangle the respective roles of monetary policy inertia and persistent shocks in interest rate rules. The procedure exploits the cross-equation restrictions provided by a DSGE model which is confronted to a monetary SVAR. We show that, provided enough informative variables are included in the formal test, the data favour a monetary policy representation with low inertia and highly serially correlated monetary shocks. To the contrary, when the procedure is based solely on the dynamic behavior of the nominal interest rate, no clear-cut conclusion can be reached as to the correct representation of monetary policy.

VAR-based estimation of Euler equations with an application to New Keynesian pricing

VAR-based estimation of Euler equations exploits cross-equation restrictions that the theory imposes on a vector-autoregressive (VAR) process for market expectations. This paper shows that Sargent's (1979. A note on maximum likelihood estimation of the rational expectations model of the term structure. Journal of Monetary Economics 5, 133–143.) original approach of imposing these restrictions on the endogenous variable of the Euler equation (i.e. computing the rational expectations solution) implies multiple solutions and is therefore impracticable. The paper shows that this identification problem can be circumvented by reverse-engineering the cross-equation restrictions on the forcing variable of the Euler equation. The proposed reverse-engineering approach contrasts with the conventional approach in the literature that avoids the identification problem by constraining the system formed by the Euler equation and the VAR process to yield a unique stable rational expectations equilibrium. This uniqueness condition makes little economic sense because the VAR process is just a reduced-form approximation of true market expectations, and a simulation experiment shows that imposing uniqueness can lead to severe misspecification bias. The severity of this misspecification bias is illustrated in practice with an application to Gali and Gertler's (1999. Inflation dynamics: a structural econometric analysis. Journal of Monetary Economics 44, 195–222.) hybrid New Keynesian Phillips Curve.

Dynamic discrete choice and dynamic treatment effects

This paper considers semiparametric identification of structural dynamic discrete choice models and models for dynamic treatment effects. Time to treatment and counterfactual outcomes associated with treatment times are jointly analyzed. We examine the implicit assumptions of the dynamic treatment model using the structural model as a benchmark. For the structural model we show the gains from using cross-equation restrictions connecting choices to associated measurements and outcomes. In the dynamic discrete choice model, we identify both subjective and objective outcomes, distinguishing ex post and ex ante outcomes. We show how to identify agent information sets.

Term structure estimation without using latent factors

A combination of observed and unobserved (latent) factors capture term structure dynamics. Information about these dynamics is extracted from observed factors using restrictions implied by no-arbitrage, without specifying or estimating any of the parameters associated with latent factors. Estimation is equivalent to fitting the moment conditions of a set of regressions, where no-arbitrage imposes cross-equation restrictions on the coefficients. The methodology is applied to the dynamics of inflation and yields. Outside of the disinflationary period of 1979 through 1983, short-term rates move one-for-one with expected inflation, while bond risk premia are insensitive to inflation.

Monetary Policy Analysis with Potentially Misspecified Models

Policy analysis with potentially misspecified dynamic stochastic general equilibrium (DSGE) models faces two challenges: estimation of parameters that are relevant for policy trade-offs, and treatment of the deviations from the cross-equation restrictions. Using post-1982 US data, we study the robustness of the policy prescriptions from a state-of-the-art DSGE model with respect to two approaches to model misspecification pursued in the recent literature: (i) adding shocks to the DSGE model and/or generalizing the processes followed by these shocks; and (ii) explicit modeling of deviations from cross-equation restrictions (DSGE-VAR). (JEL C51, E13, E43, E52, E58)

Simultaneous equations in ordered discrete responses with regressor‐dependent thresholds

Summary The parameters of ordered discrete response (ODR) models are identified only up to a positive scale. In this paper, we examine the identification issue for simultaneous equations with ODR, where the well-known identification problem in simultaneous equations of recovering structural-form parameters from reduced-form parameters is compounded with the ODR identification problem. We allow the thresholds in ODR to be regressor dependent as well as constant; the former is particularly challenging because threshold parameters get mixed with regression parameters, adding one more dimension to the identification problem. We also explore a cross-equation restriction on threshold differences, under which the structural form parameters are fully identified as if the dependent variables are continuously distributed. An empirical example with farm–household joint labour supply is provided to illustrate the identification issues, to show how our proposals work and to apply tests devised for the threshold constancy and cross-equation restrictions.

Inventories, Employment and Hours

The purpose of this paper is to develop a model that integrates inventory and labor decisions. We extend a model of inventory behavior to include a detailed specification of the role of labor input in the production process and of the costs associated with it. In particular, we distinguish between employment, hours and effort per worker, and allow for adjustment costs associated with employment changes. We assume that the requirement function for effective hours has a general trans-logarithmic form, and derive an estimable system of Euler equations for inventories and employment with implied cross-equation restrictions. The econometric results shed light on several important topics, including the shape of the marginal cost of output and the role of labor hoarding as an explanation of procyclical productivity and the persistence of inventory stocks. Moreover, they raise questions about the adequacy of commonly used specifications such as Cobb-Douglas approximations to the production process and the definition of labor input as the product of employment and effective hours worked per worker.

Equity returns of financial institutions and the pricing of interest rate risk

This study investigates the issue of whether financial intermediaries’ common stock returns incorporate a risk premium for their inherent exposure to unexpected changes in interest rates. A wide range of financial institutions is employed to test the hypothesis that the interest rate risk is priced by capital markets. In addition, the above sample is extended by incorporating firms from the non-financial sector. A two-factor model with the market portfolio and the changes in market yields, as exogenously specified risk variables, is employed. The model is estimated via a seemingly unrelated regression estimation (SURE) framework with both cross-equation restrictions and within equation nonlinear constraints on the parameters. The findings indicate that financial institutions’ equity returns incorporate a risk premium for their exposure to market yields’ surprises. The return generating function of the insurance business could be further explained by an additional factor such as currency movements. It is a...

Inventories, employment and hours

This paper develops a model that integrates inventory and labor decisions. We extend a model of inventory behavior to include a detailed specification of the role of labor input in the production process, distinguishing between employment, hours and effort per worker. We estimate jointly the Euler equations for inventories and employment, a labor compensation schedule, and an hours requirement function with the cross-equation restrictions imposed. The econometric results shed light on several important topics, including the shape of the marginal cost of output, the role of labor hoarding as an explanation of pro-cyclical productivity, and the persistence of inventory stocks.

Changing beliefs and the term structure of interest rates: Cross-equation restrictions with drifting parameters

This paper shows how to estimate a Bayesian VAR with drifting parameters and nonlinear cross-equation restrictions. The restrictions promote parsimony by reducing the dimension of the drifting component in conditional mean parameters. As an application, the paper investigates an anticipated-utility version of the expectations model of the term structure. The estimates suggest that changing beliefs matter for understanding the yield curve and point to an intriguing clue about risk premia. Local approximations to the mean yield spread are highly correlated with the variance of the trend short rate, suggesting a connection between uncertainty about the long-run target of monetary policy and risk premia on long-term bonds.

Dynamic Discrete Choice and Dynamic Treatment Effects

This paper considers semiparametric identification of structural dynamic discrete choice models and models for dynamic treatment effects. Time to treatment and counterfactual outcomes associated with treatment times are jointly analyzed. We examine the implicit assumptions of the dynamic treatment model using the structural model as a benchmark. For the structural model we show the gains from using cross equation restrictions connecting choices to associated measurements and outcomes. In the dynamic discrete choice model, we identify both subjective and objective outcomes, distinguishing ex post and ex ante outcomes. We show how to identify agent information sets.

On the Fit and Forecasting Performance of New Keynesian Models

The Paper provides new tools for the evaluation of DSGE models, and applies it to a large-scale New Keynesian dynamic stochastic general equilibrium (DSGE) model with price and wage stickiness and capital accumulation. Specifically, we approximate the DSGE model by a vector autoregression (VAR), and then systematically relax the implied cross-equation restrictions. Let delta denote the extent to which the restrictions are being relaxed. We document how the in- and out-of-sample fit of the resulting specification (DSGE-VAR) changes as a function of delta. Furthermore, we learn about the precise nature of the misspecification by comparing the DSGE model’s impulse responses to structural shocks with those of the best-fitting DSGE-VAR. We find that the degree of misspecification in large-scale DSGE models is no longer so large to prevent their use in day-to-day policy analysis, yet it is not small enough that it cannot be ignored.

Maximum Likelihood Estimation of Dynamic Stochastic Theories with an Application to New Keynesian Pricing

This paper proposes a novel Maximum Likelihood (ML) strategy to estimate Euler equations implied by dynamic stochastic theories. The strategy exploits rational expectations cross-equation restrictions, but circumvents the problem of multiple solutions that arises in Sargent's (1979) original work by imposing the restrictions on the forcing variable rather than the endogenous variable of the Euler equation. The paper then contrasts the proposed strategy to an alternative, widely employed method that avoids the multiplicity problem by constraining the ML estimates to yield a unique stable solution. I argue that imposing such a uniqueness condition makes little economic sense and can lead to severe misspecification. To illustrate this point, I estimate Gali and Gertler's (1999) hybrid New Keynesian Phillips Curve using labor income share as the measure of real marginal cost. My ML estimates indicate that forward-looking behavior is predominant and that the model provides a good approximation of U.S. inflation dynamics. By contrast, if the same estimates are constrained to yield a unique stable solution, forward-looking behavior becomes much less important and the model as a whole is rejected.

A Structural Estimation and Interpretation of the New Keynesian Macro Model

We formulate and solve a Rational Expectations New Keynesian macro model that implies non-linear cross-equation restrictions on the dynamics of inflation, the output gap and the Federal funds rate. Our maximum likelihood estimation procedure fully imposes these restrictions and yields asymptotic and small sample distributions of the structural parameters. We show how the structural parameters shape the responses of the macro variables to the structural shocks. While the point estimates imply that the Fed has been stabilizing inflation fluctuations since 1980, our econometric analysis suggests considerable uncertainty regarding the stance of the Fed against inflation.

Using Placebo Laws to Test "More Guns, Less Crime"

Abstract We reexamine Mustard and Lott’s controversial study on the effect of “shall-issue” gun laws on crime using an empirical standard error function randomly generated from “placebo” laws. We find that the effect of shall-issue laws on crime is much less well-estimated than the Mustard and Lott (1997) and Lott (2000) results suggest. We also find, however, that the cross equation restrictions implied by the Lott-Mustard theory are supported. A boomlet has occurred in recent years in the use of quasi-natural experiments to answer important questions of public policy. The intuitive power of this approach, however, has sometimes diverted attention from the statistical assumptions that must be made, particularly regarding standard errors. Failing to take into account serial correlation and grouped data can dramatically reduce standard errors suggesting greater certainty in effects than is actually the case. We find that the placebo law technique (Bertrand, Duflo and Mullainathan 2002) is a useful addition to the econometrician’s toolkit.

Reaching Inflation Stability

Inflation volatility has significantly declined over the last 20 years in the U.S. To find out why, I follow a structural approach. I estimate a complete New Keynesian model which imposes cross-equation restrictions on the time series of inflation, the output gap and the interest rate. I perform counterfactual analysis with the most commonly used measures of inflation: Consumer Price Index (CPI) and Gross Domestic Product Deflator (GDPD). While the change in the propagation mechanism of the economy induced most of the CPI volatility drop, it played a smaller role in the reduction of GDPD volatility. Our maximum likelihood estimates imply that the most important factor behind the drop in inflation volatility was the more forward-looking price setting behavior of the 80s and 90s.

Testing poolability in a system of dynamic regressions with nonspherical disturbances

This study analyzes the testing of cross-equation restrictions within a set of regression equations. Through Monte Carlo experiments we examine the actual size of various asymptotic procedures for testing the poolability hypothesis, i.e., equal slope vectors across individual equations. Regression models with both lagged dependent variable regressors and nonspherical disturbances are considered. In these models we find that the performance in finite samples of classical asymptotic test procedures using critical values from either ℱ or χ2 approximations is often rather poor. However, employing the original test statistics with bootstrapped critical values leads to much more accurate inference in finite samples. In an empirical analysis of panel data on GDP growth and unemployment rates in OECD countries it is shown that classical asymptotic tests and bootstrap procedures may lead to conflicting test outcomes.

Discrete policy interventions and rational forecast errors in foreign exchange markets: the uncovered interest parity hypothesis revisited

AbstractThis paper combines policy response explanations of the uncovered interest parity puzzle with a time series approach that accounts for discrete central bank interventions. When monetary authorities manage the interest rate differential through an anti‐inflationary policy rule, which allows for discrete shifts, then a stochastic segmented trends representation seems appropriate for the exchange rate and the interest rate differential series. In this setting, rational forecast errors are possible, and a test of the uncovered parity hypothesis, based on the cross‐equation restrictions on a Markov switching process, suggests that the parity relationship cannot be rejected for three European currencies vis‐à‐vis the US dollar. Copyright © 2002 John Wiley & Sons, Ltd.