On price exogeneity in complete demand systems

Complete demand systems have always been estimated under the assumption that either prices or quantities were exogenous. In this paper, we introduce some explicit price adjustment process and test the assumption of exogeneity of prices. Comparing the model with endogenous prices to the model with exogenous prices will reveal that the assumption of the exogeneity of prices is not a very dramatic one as both estimated models are very similar in many experiments with American and Canadian data. Applying a system-wide Wu-Hausman test and a likelihood ratio test, will always lead us to reject the exogeneity of prices in three-commodity models, while at the more disaggregated level, prices may often be considered as exogenous.     

Testing for serial correlation in simultaneous equation models: Some further results

In this paper approximate counterparts of the exact tests earlier proposed by the authors are examined. Type 1 error probabilities and test powers are estimated and compared using Monte Carlo experiments. The effect on the Type 1 error probabilities of the misspecification which results when serial correlation is present elsewhere in the system is also investigated.     

Testing for exogeneity in limited dependent variable models using a simplified likelihood ratio statistic

A simple likelihood-ratio statistic for the weak exogeneity of the continuously observed endogenous variables is presented for the limited information simultaneous equations models in which a single endogenous variable is censored. The statistic is a likelihood ratio test statistic for the exclusion of the reduced form residuals of the continuously observed endogenous variables and is asymptotically locally most powerful. The procedure is illustrated by an application to a model of female labour supply.     

FIML estimation of the dynamic simultaneous equations model with ARMA disturbances

A method is presented for the estimation of the parameters in the dynamic simultaneous equations model with vector autoregressive moving average disturbances. The estimation procedure is derived from the full information maximum likelihood approach and is based on Newton-Raphson techniques applied to the likelihood equations. The resulting two-step Newton-Raphson procedure involves only generalized instrumental variables estimation in the second step. This procedure also serves as the basis for an iterative scheme to solve the normal equations and obtain the maximum likelihood estimates of the conditional likelihood function. A nine-equation variant of the quarterly forecasting model of the US economy developed by Fair is then used as a realistic example to illustrate the estimation procedure described in the paper.     

Several efficient two-step estimators for the dynamic simultaneous equations model with autoregressive disturbances

Several asymptotically efficient methods are suggested on both the full and the limited information approach to estimate the simultaneous equations model in which the lagged endogenous variables and the autoregressive disturbances coexist. They are two-step procedures and do not involve iterations. A method is suggested also for the case where any portion of the autoregressive parameter matrix is specified to be zero. Since the consistency and efficiency depend upon the asymptotic, local identifiability, the necessary and sufficient condition is derived for it. It does not depend on the exclusion of the lagged endogenous variables.     

Testing the specification of multivariate models in the presence of alternative hypotheses

In this paper we propose a non-nested hypothesis test for testing the specification of a multivariate econometric model in the presence of an alternative model which purports to explain the same phenomenon. We demonstrate that the new test statistic tends to minus the same random variable as the CPD test statistic introduced by Pesaran and Deaton (1978), provided that the truth is ‘close’ to the null hypothesis. Since the new test is simpler to compute than the multivariate CPD test, it would seem to be the procedure of choice.     

A note on simultaneous equation estimation techniques applications with a regional econometric model

A large-scale regional econometric model is estimated using six estimation techniques, including Iterated Instrumental Variables and Iterated Two-Stage Least-Squares. Following estimation the model is simulated and a seventh technique called PANGLOSS is derived. The seven techniques are then compared in ex post and ex ante tests.     

Testing a linear dynamic panel data model against nonlinear alternatives

The most popular econometric models in the panel data literature are the class of linear panel data models with unobserved individual- and/or time-specific effects. The consistency of parameter estimators and the validity of their economic interpretations as marginal effects depend crucially on the correct functional form specification of the linear panel data model. In this paper, a new class of residual-based tests is proposed for checking the validity of dynamic panel data models with both large cross-sectional units and time series dimensions. The individual and time effects can be fixed or random, and panel data can be balanced or unbalanced. The tests can detect a wide range of model misspecifications in the conditional mean of a dynamic panel data model, including functional form and lag misspecification. They check a large number of lags so that they can capture misspecification at any lag order asymptotically. No common alternative is assumed, thus allowing for heterogeneity in the degrees and directions of functional form misspecification across individuals. Thanks to the use of panel data with large $N$ and $T$, the proposed nonparametric tests have an asymptotic normal distribution under the null hypothesis without requiring the smoothing parameters to grow with the sample sizes. This suggests better nonparametric asymptotic approximation for the panel data than for time series or cross sectional data. This is confirmed in a simulation study. We apply the new tests to test linear specification of cross-country growth equations and found significant nonlinearities in mean for OECD countries’ growth equation for annual and quintannual panel data.     

Two tests for strict exogeneity in a correlated random effects panel data Tobit model

This paper presents two tests for strict exogeneity of the covariates in a correlated random effects panel data Tobit model. The tests are applied in an analysis of hours of work of US women. Estimation procedures when a model does not pass a test for strict exogeneity are discussed.     

The existence of moments of some simple Bayes estimators of coefficients in a simultaneous equation model

In this paper a simple modification of the usual k-class estimators has been suggested so that for 0 ≦ k ≦ 1 the problem of the non-existence of moments disappears. These modified estimators can be interpreted either as Bayes estimators or as constrained estimators subject to the restriction that the squared length of the coefficient vector is less than or equal to a given number.     

Model selection test procedures in a single linear equation of a dynamic simultaneous system and their defects in small samples

A variety of asymptotically valid tests for orthogonality, serial correlation, predictive failure, and of coefficient restrictions are presented, and their rejection probabilities are assessed in linear structural models with lagged dependent and (possibly) jointly dependent variables by Monte Carlo methods. For all test procedures the small-sample distribution under the null usually deviates substantially from the asymptotic distribution; this impedes their use in a reliable model selection strategy for econometric time-series analysis. Despite the harassing dependence of type I errors on factors generally unknown to the practitioner, inconsistencies originating from specification errors or from disregarded simultaneity may be detected by particular tests in particular situations. From this study some clues emerge on how to interpret (in)significant values of the various test statistics.     

Identification and stochastic specification in Rosen's hedonic price model

The use of an explicitly specified utility function to derive the inverse demand functions in S. Rosen's hedonic price model provides considerable insight into the correct stochastic specification of the model. It turns out that except in special cases, the inverse demand equations are nonlinear in parameters and cannot be formulated conveniently as regression models. Moreover, the inverse demand functions and the hedonic price function must be estimated simultaneously to obtain consistent estimates of the parameters of these functions. A tractable estimation technique is described. It is desirable to derive the inverse demand functions from a utility specification that is not a strongly separable function of houses' attributes since strong separability implies the existence of deterministic relations among incomes, prices, and observed housing attributes that may fail to hold in applications. Finally, it is shown that the use of an explicitly specified utility function does not guarantee identification of the parameters of Rosen's model.     

The relationship between health and labour force participation: Evidence from a panel data simultaneous equation model

A concern when estimating the effect of health on labour supply is that health might be endogenous, and in particular that people might use poor health to justify non-participation. This would result in the effect of health being overestimated if health were treated as exogenous. The paper employs a simultaneous equation model to explore the relationship between health and labour force status, allowing for the endogeneity of health. In addition, the paper takes advantage of panel data to control for unobserved heterogeneity so that more efficient estimation results can be obtained than using cross-sectional data. The results confirm the finding in the literature that health has a positive and significant effect on labour force participation for both males and females. As for the reverse effect, it is found that labour force participation has a negative effect on male health but a positive effect on female health, implying that the justification hypothesis is rejected for males but not for females. The exogeneity hypothesis on the health variable is rejected for both samples based on a joint test.     

On the consequences of planning interval specification error for the estimation of dynamic models

In recent years, it has become customary to derive dynamic behavioral relationships from intertemporal utility maximization. Since the planning interval for which decisions are made is unknown, a likely specification error in dynamic models is that the period for which data are available is longer than the planning interval. This paper brings out the consequences of this specification error for the estimation of dynamic models derived from intertemporal utility maximization.     

Asymptotic expansions of the distributions of the estimates of coefficients in a simultaneous equation system

In this paper asymptotic expansions are derived for the density functions of the TSLS and LIML estimates of coefficients in a simultaneous equation system when the sample size increases and the effect of the exogenous variables increases along the sample size. These approximations are used to compare the asymptotic moments of the TSLS and LIML estimates and the concentration of probability around the true value of the estimates.     

Testing for structural breaks in dynamic factor models

In this paper we investigate the consequences of structural breaks in the factor loadings for the specification and estimation of factor models based on principal components and suggest procedures for testing for structural breaks. It is shown that structural breaks severely inflate the number of factors identified by the usual information criteria. The hypothesis of a structural break is tested by using LR, LM and Wald statistics. The LM test (which performs best in our Monte Carlo simulations) is generalized to test for structural breaks in factor models where the break date is unknown and the common factors and idiosyncratic components are serially correlated. The proposed test procedures are applied to datasets from the US and the euro area.