Allan W. Gregory

Residual-based tests for cointegration in models with regime shifts

In this paper we examine tests for cointegration which allow for the possibility of regime shifts. We propose augmented Dickey-Fuller (ADF) and Phillips type tests designed to test the null of no cointegration against the alternative of cointegration in the presence of a possible regime shift. In particular we consider cases where the intercept and/or slope coefficients have a single break of unknown timing. A formal proof is provided for the limiting distributions of the various tests for the regime shift model (both a level and slope change). Critical values are calculated for the tests by simulation methods and a simple Monte Carlo experiment is conducted to evaluate finite sample performance. In the limited set of experiments, we find that the tests can detect cointegrating relations when there is a break in the intercept and/or slope coefficient. For these same experiments, the power of the conventional ADF test with no allowance for regime shifts falls sharply. As an illustration we test for structural breaks in the U.S. long-run money-demand equation using annual and quarterly data.

Risk Premiums in the Term Structure: Evidence from Artificial Economies

We compare the stattstical properties of prices of US Treasury bills to those generated by a theoretical dynamic exchange economy wrth complete markets. We show that the model can account for netther the sign nor the magmtude of average risk premiums in forward prices and holding-period returns. The economy is also incapable of generating enough variation in risk premmms to account for reJections of the expectations hypotheses with Treasury bill data These conclusions add to the growing list of empiricat deficiencies of the representative agent model of asset pricmg

Testing for structural breaks in cointegrated relationships

Abstract The purpose of this paper is to investigate the tests of Hansen (1992) to detect structural breaks in cointegrated relations using Monte Carlo methods. The evaluation takes place within the linear quadratic model. We study models that generate cointegrated relations with single and multiple regressors. The evidence with multiple regressors suggests that the tests have proper size but the power is low when the cost of adjustment is high. In addition to the tests of Hansen, we consider the sensitivity of the augmented Dickey-Fuller (ADF) test for cointegration in the presence of a structural break. Given a break, our Monte Carlo experiments show that the rejection frequency of the ADF test decreases substantially. Thus the ADF test correctly indicates that the constant parameter cointegrating relationship is not appropriate.

Measuring World Business Cycles

Using Kalman filtering and dynamic factor analysis, we decompose fluctuations in real aggregate output, consumption, and investment for the G7 countries into factors that are (i) common across all countries and aggregates, (ii) common across aggregates within a country, and (iii) specific to each data series. In quarterly data for the period 1970-1993, fluctuations in all of the aggregates contain world and country-specific common components which are significant both statistically and economically. Over this period all seven countries experience business cycle episodes primarily attributable to the world cycle and other episodes driven primarily by the country-specific factor. The share of the variance of aggregate output accounted for by the world business cycle in our estimates ranges from 13% for the U.K. to 67% for France. Also, the world common component in growth rates is more strongly serially correlated than is output growth in any of the seven countries.

Theoretical Relations Between Risk Premiums and Conditional Variances

Many statistical models of time-varying risk premiums, including the autoregressive conditional heteroscedasticity (ARCH)-in-mean, attempt to exploit a relation between risk premiums and conditional variances or covariances of asset returns. We examine this relation in numerical versions of a dynamic asset-pricing theory and show that it can be increasing, decreasing, flat, or nonmonotonic. Its shape depends on both the preferences of the representative agent and the stochastic structure of the economy. Without additional structure, the theory does not provide either a general foundation for ARCH-in-mean specifications or a simple interpretation of their parameters.

Realistic cross-country consumption correlations in a two-country, equilibrium, business cycle model

A well-known feature of one-good, multi-agent, Arrow-Debreu economies with identical additively-separable, homothetic preferences is that the consumptions of all agents are perfectly correlated. Such economies are widely used in interpreting business cycles but seem to be inconsistent with observed cross-country correlations of aggregate consumption. This paper provides an example of a two-country real business cycle model in which preferences are not separable between consumptions and labor supply. The model has a simple closed-form solution, and allows for fluctuations in labor supply in equilibrium. Moreover, it generates correlations between national consumption rates which are close to some of those observed in historical data.

Testing for Cointegration in Linear Quadratic Models

This paper evaluates the finite sample performance of various tests for cointegration by Monte Carlo methods. The evaluation takes place within the linear quadratic model. The results indicate sharp differences in the tests to detect cointegrating relations especially when the cost of adjustment term and the number of regressors are large. Although no single test dominates for all the parameter settings considered, overall the augmented Dickey-Fuller and the Phillips type of test (1987) seem the most reliable in terms of test size and power.

Calibration as Testing: Inference in Simulated Macroeconomic Models

A stochastic macroeconomic model with no free parameters can be tested by comparing its features, such as moments, with those of data. Repeated simulation allows exact tests and gives the distribution of the sample moment under the null hypothesis that the model is true. The authors calculate the size of tests of the model studied by R. Mehra and E. C. Prescott. The approximate size of their test (which seeks to match model-generated, mean, risk-free interest rates and equity premia with historical values) is zero, although alternate empirical representations of this model economy or alternate moment-matching tests yield large probabilities of the type I error.

Common and country-specific fluctuations in productivity, investment, and the current account

Dynamic factor analysis and Kalman filtering are used to construct a measure of common economic activity for the G7 countries. Common movements are important in productivity, but account for a substantially smaller share of movements in investment, and virtually none of the variation in the current accounts. For all seven countries, country-specific investment fluctuations have a significant negative impact on the current account, while country-specific productivity movements have little effect. A multi-country dynamic general equilibrium model is analyzed which is consistent with our qualitative findings. The model overstates, however, the quantitative importance of investment fluctuations for movements in the current account.

Calibration as estimation

One aspect of calibration in macroeconomics is the notion that free parameters of models should be chosen by matching certain moments of the simulated models with those of actual data. We formally examine this notion by treating the process of calibration as an econometric estimator. A numerical version of the Mehra-Prescott (1985) economy is the setting for an evaluation of calibration estimators via Monte Carlo methods. While these estimators sometimes have reasonable finite-sample properties they are not robust to mistakes in setting non-free parameters. In contrast, generalized method of moments (GMM) estimators have satisfactory finite-sample properties, quick convergence, and informational requirements less stringent than those of consistent calibration estimators. In dynamic equilibrium models in which GMM is infeasible we offer some suggestion for improving estimates based on calibration methodology.