Testing the lucas critique: A review

Claims that the parameters of an econometric model are invariant under changes in either policy rules or expectations processes entail super exogeneity and encompassing implications. Super exogeneity is always potentially refutable, and when both implications are involved, the Lucas critique is also refutable. We review the methodological background; the applicability of the Lucas critique; super exogeneity tests; the encompassing implications of feedback and feedforward models; and the role of incomplete information. The approach is applied to money demand in the u.S.A. to examine constancy, exogeneity, and encompassing, and reveals the Lucas critique to be inapplicable to the model under analysis.     

A note on super exogeneity in linear regression models

This note considers how hypotheses of invariance and super exogeneity may be formulated and tested in elliptical linear regression models. It is demonstrated that for jointly elliptical random variables super exogeneity will only hold under normality.     

The Quantitative Significance of the Lucas Critique

Doan, Litterman, and Sims (DLS) have suggested using conditional forecasts to do policy analysis with Bayesian vector autoregression (BVAR) models. Their method seems to violate the Lucas critique, which implies that coefficients of a BVAR model will change when there is a change in policy rules. In this article, we attempt to determine whether the Lucas critique is important quantitatively in a BVAR macro model that we construct. We find evidence following two candidate policy rule changes of significant coefficient instability and of a deterioration in the performance of the DLS method.     

Testing exogeneity in overidentified models

Summary In this paper we analyse the consequences of model overidentification on testing exogeneity, when maximum likelihood techniques for estimation and inference are used. This situation is viewed as a particular case of the more general problem of considering how restrictions on nuisance parameters could help in making inference on the parameters of interest. At first a general model is considered. A suitable likelihood function factorization is used which allows a simple derivation of the information matrix and others tools useful for building up joint tests of exogeneity and overidentifying restrictions both of Wald and Lagrange Multiplier type. The asymptotic local power of the exogeneity test in the justidentified model is compared with that in the overidentified one, when we assume that the latter is the true model. Then the pseudo-likelihood framework is used to derive the consequences of working with a model where overidentifying restrictions are erroneously imposed. The inconsistency introduced by imposing false restrictions is analysed and the consequences of the misspecification on the exogeneity test are carefully examined.     

Testing for Full Insurance Using Exogenous Information

We strongly reject the full-insurance hypothesis, using testing variables that are not decision variables for the households under investigation. We find that households are not insured against changes in the unemployment rate associated with the household head's occupational category. Using this exogenous information, we also investigate the appropriateness of exogeneity assumptions on idiosyncratic variables that have been used as testing variables in the full-insurance literature. It is shown that several exogeneity assumptions made in the existing literature are potentially problematic.     

Likelihood-Based Inference for Weak Exogeneity in I(2) Cointegrated VAR Models

This article develops limit theory for likelihood analysis of weak exogeneity in I(2) cointegrated vector autoregressive (VAR) models incorporating deterministic terms. Conditions for weak exogeneity in I(2) VAR models are reviewed, and the asymptotic properties of conditional maximum likelihood estimators and a likelihood-based weak exogeneity test are then investigated. It is demonstrated that weak exogeneity in I(2) VAR models allows us to conduct asymptotic conditional inference based on mixed Gaussian distributions. It is then proved that a log-likelihood ratio test statistic for weak exogeneity in I(2) VAR models is asymptotically χ² distributed. The article also presents an empirical illustration of the proposed test for weak exogeneity using Japan's macroeconomic data.     

A Bayesian analysis of exogeneity in models pooling time-series and cross-sectional data

The analysis of exogeneity in econometric time-series models as formalized in the seminal paper by Engle et al. [Econometrica 51 (1983), 277–304] is extended to cover a more general class of models, including error-components models. The Bayesian framework adopted here allows us to take full advantage of a number of statistical tools, related to the reduction of Bayesian experiments, and motivates a careful consideration of prediction issues, leading to a concept of predictive exogeneity. We also adapt the formal definitions of weak and strong exogeneity introduced in Engle et al. (1983), and provide a naturally nested set of definitions for exogeneity. An example highlights the main implications of our analysis for econometric modelling.     

Simple Tests for Exogeneity of a Binary Explanatory Variable in Count Data Regression Models

This article investigates power and size of some tests for exogeneity of a binary explanatory variable in count models by conducting extensive Monte Carlo simulations. The tests under consideration are Hausman contrast tests as well as univariate Wald tests, including a new test of notably easy implementation. Performance of the tests is explored under misspecification of the underlying model and under different conditions regarding the instruments. The results indicate that often the tests that are simpler to estimate outperform tests that are more demanding. This is especially the case for the new test.     

习惯形成下中国城乡居民预防性储蓄研究

本文将习惯偏好引入传统的预防性储蓄模型,构造出检验具有习惯偏好居民的预防性储蓄动机的计量方程。然后利用中国26个省1999-2011年城乡居民消费数据进行实证分析。回归结果发现,在控制了习惯形成效应后,城乡居民依然存在显著的预防性储蓄动机,但是该动机强度比无习惯偏好时降低了约1/2。同时,城乡对比结果表明,在绝对层面,农村居民具有更大的衡量预防性储蓄动机强度的绝对谨慎系数,其值约为城镇居民的1.5倍;然而基于现有消费,农村居民衡量预防性储蓄量的相对谨慎系数则要小于城镇居民,约为后者的60%。本文最后在城乡二元结构背景下对上述结果进行解释,并给出相应的政策建议。     

A robust test of exogeneity based on quantile regressions

In this paper, we propose a robust test of exogeneity. The test statistics is constructed from quantile regression estimators, which are robust to heavy tails of errors. We derive the asymptotic distribution of the test statistic under the null hypothesis of exogeneity at a given quantile. The finite sample properties of the test are investigated through Monte Carlo simulations that exhibit not only good size and power properties, but also good robustness to outliers.     

Autoregressive distributed lag models and cointegration

Summary This paper considers cointegration analysis within an autoregressive distributed lag (ADL) framework. First, different reparameterizations and interpretations are reviewed. Then we show that the estimation of a cointegrating vector from an ADL specification is equivalent to that from an error-correction (EC) model. Therefore, asymptotic normality available in the ADL model under exogeneity carries over to the EC estimator. Next, we review cointegration tests based on EC regressions. Special attention is paid to the effect of linear time trends in case of regressions without detrending. Finally, the relevance of our asymptotic results in finite samples is investigated by means of computer experiments. In particular, it turns out that the conditional EC model is superior to the unconditional one. We thank Vladimir Kuzin for excellent research assistance and Surayyo Kabilova for skillful word processing. Moreover, we are grateful to an anonymous referee for clarifying comments.     

Asymptotic Inference on Cointegrating Rank in Partial Systems

The likelihood ratio test for cointegrating rank is analyzed for partial (or conditional) systems in the vector autoregressive error-correction model. Under the assumption of weak exogeneity for the cointegrating parameters, the asymptotic distributions are given and tables of critical values are provided. A discussion is given of some of the assumptions of the model, why they are needed, and how they are tested.     

The Time-Varying-Parameter Model for Modeling Changing Conditional Variance: The Case of the Lucas Hypothesis

The main econometric issue in testing the Lucas (1973) hypothesis in a time series context is estimation of the forecast-error variance conditional on past information. The conditional variance may vary through time as monetary policy evolves and agents are obliged to infer its present state. Under the assumption that a monetary policy regime is continuously changing, a time-varying-parameter model is proposed for the monetary-growth function. Based on Kalman-filtering estimation of recursive forecast errors and their conditional variances, the Lucas hypothesis is tested for the U.S. economy (1964:1–1985:4) using monetary growth as aggregate demand variable. The Lucas hypothesis is rejected in favor of Friedman's (1977) hypothesis—the conditional variance of monetary growth affects real output directly, not through the coefficients on the forecast-error term in the Lucas-type output equation.     

Regression spline bivariate probit models: A practical approach to testing for exogeneity

Bivariate probit models can deal with a problem usually known as endogeneity. This issue is likely to arise in observational studies when confounders are unobserved. We are concerned with testing the hypothesis of exogeneity (or absence of endogeneity) when using regression spline recursive and sample selection bivariate probit models. Likelihood ratio and gradient tests are discussed in this context and their empirical properties investigated and compared with those of the Lagrange multiplier and Wald tests through a Monte Carlo study. The tests are illustrated using two datasets in which the hypothesis of exogeneity needs to be tested.     

On the interactions of unit roots and exogeneity

The paper considers the impact on estimation and inference of interactions between the existence of unit roots in a data generation process and the presence or absence of weak and strong exogeneity of conditioning variables for the parameters of interest in individual cointegrated linear relationships. The asymptotic distributions of estimators for single equation conditional linear relations are analyzed in conjunction with a Monte Carlo study. The results confirm the important role of weak exogeneity in single equation estimation from integratedcointegrated data; highlight the advantages of using an asymptotic analysis to understand the complicated interactions observed; and reveal the accuracy of the limiting distributions in characterizing finite sample behaviour.     

On the interactions of unit roots and exogeneity

The paper considers the impact on estimation and inference of interactions between the existence of unit roots in a data generation process and the presence or absence of weak and strong exogeneity of conditioning variables for the parameters of interest in individual cointegrated linear relationships. The asymptotic distributions of estimators for single equation conditional linear relations are analyzed in conjunction with a Monte Carlo study. The results confirm the important role of weak exogeneity in single equation estimation from integratedcointegrated data; highlight the advantages of using an asymptotic analysis to understand the complicated interactions observed; and reveal the accuracy of the limiting distributions in characterizing finite sample behaviour.     

Identification of average marginal effects under misspecification when covariates are normal

A previously known result in the econometrics literature is that when covariates of an underlying data generating process are jointly normally distributed, estimates from a nonlinear model that is misspecified as linear can be interpreted as average marginal effects. This has been shown for models with exogenous covariates and separability between covariates and errors. In this paper, we extend this identification result to a variety of more general cases, in particular for combinations of separable and nonseparable models under both exogeneity and endogeneity. So long as the underlying model belongs to one of these large classes of data generating processes, our results show that nothing else must be known about the true DGP—beyond normality of observable data, a testable assumption—in order for linear estimators to be interpretable as average marginal effects. We use simulation to explore the performance of these estimators using a misspecified linear model and show they perform well when the data are normal but can perform poorly when this is not the case.     

Cross-Sectional Dependence in Panel Data Analysis

This article provides an overview of the existing literature on panel data models with error cross-sectional dependence (CSD). We distinguish between weak and strong CSD and link these concepts to the spatial and factor structure approaches. We consider estimation under strong and weak exogeneity of the regressors for both T fixed and T large cases. Available tests for CSD and methods for determining the number of factors are discussed in detail. The finite-sample properties of some estimators and statistics are investigated using Monte Carlo experiments.     

A finite mixture model for multivariate counts under endogenous selectivity

We describe a selection model for multivariate counts, where association between the primary outcomes and the endogenous selection source is modeled through outcome-specific latent effects which are assumed to be dependent across equations. Parametric specifications of this model already exist in the literature; in this paper, we show how model parameters can be estimated in a finite mixture context. This approach helps us to consider overdispersed counts, while allowing for multivariate association and endogeneity of the selection variable. In this context, attention is focused both on bias in estimated effects when exogeneity of selection (treatment) variable is assumed, as well as on consistent estimation of the association between the random effects in the primary and in the treatment effect models, when the latter is assumed endogeneous. The model behavior is investigated through a large scale simulation experiment. An empirical example on health care utilization data is provided.     

Evaluating the performance of simple estimators for probit models with two dummy endogenous regressors

This study considers the small sample performance of approximate but simple two-stage estimators for probit models with two endogenous binary covariates. Monte Carlo simulations show that all the considered estimators, including the simulated maximum-likelihood (SML) estimation, of the trivariate probit model are biased in very small samples (N=100). With moderately small samples (N=500), some of the approximations perform as well as the SML estimator when the degree of endogeneity is not very large. Some of the approximations seem robust with higher correlations and are also promising for testing the exogeneity of binary covariates. The methods are used to estimate the impact of employment-based health insurance and health care (HC) on HC use, where the approximations seem to work at least as well as the SML and in some cases better.