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Hausman (1978) represented a tectonic shift in inference related to the specification of econometric models. The seminal insight that one could compare two models which were both consistent under the null spawned a test which was both simple and powerful. The so-called ‘Hausman test’ has been applied and extended theoretically in a variety of econometric domains. This paper discusses the basic Hausman test and its development within econometric panel data settings since its publication. We focus on the construction of the Hausman test in a variety of panel data settings, and in particular, the recent adaptation of the Hausman test to semiparametric and nonparametric panel data models. We present simulation experiments which show the value of the Hausman test in a nonparametric setting, focusing primarily on the consequences of parametric model misspecification for the Hausman test procedure. A formal application of the Hausman test is also given focusing on testing between fixed and random effects within a panel data model of gasoline demand.

This chapter revisits the Hausman (1978) test for panel data. It emphasizes that it is a general specification test and that rejection of the null signals misspecification and is not an endorsement of the fixed effects estimator as is done in practice. Non-rejection of the null provides support for the random effects estimator which is efficient under the null. The chapter offers practical tips on what to do in case the null is rejected including checking for endogeneity of the regressors, misspecified dynamics, and applying a nonparametric Hausman test, see Amini, Delgado, Henderson, and Parmeter (2012, chapter 16). Alternatively, for the fixed effects die hard, the chapter suggests testing the fixed effects restrictions before adopting this estimator. The chapter also recommends a pretest estimator that is based on an additional Hausman test based on the difference between the Hausman and Taylor estimator and the fixed effects estimator.

This paper examines the diffusion of Jerry Hausman's econometric ideas using citation counts, citing authors, and source journals of his most referenced citers. Bibliographic information and citation counts of references to econometrics papers were retrieved from Thomson Reuters Web of Science and analyzed to determine the various ways in which Hausman's ideas have spread in econometrics and related disciplines. Econometric growth analysis (Gompertz and logistic functions) is used to measure the diffusion of his contributions. This analysis reveals that the diffusion of Hausman's ideas has been pervasive over time and disciplines. For example, his seminal 1978 paper continues to be strongly cited along exponential growth with total cites mainly in econometrics and other fields such as administrative management, human resources, and psychology. Some of the more recent papers have a growth pattern that resembles that of the 1978 paper. This leads us to conclude that Hausman's econometric contributions will continue to diffuse in years to come. It was also found that five journals have published the bulk of the top cited papers that list Hausman as a reference, namely, Econometrica, Journal of Econometrics, Review of Economic Studies, Academy of Management Journal, and the Journal of Economic Literature. “Specification tests in econometrics” is Hausman's dominant contribution in this citation analysis. We found no previous research on the econometric modeling of citation counts as done in this paper. Thus, we expect to stimulate methodological improvements in future work.

In this chapter we investigate the finite sample properties of a Hausman test for the spatial error model (SEM) proposed by Pace and LeSage (2008). In particular, we demonstrate that the power of their test could be very low against a natural alternative like the spatial autoregressive (SAR) model.

We provide straightforward new nonparametric methods for testing conditional independence using local polynomial quantile regression, allowing weakly dependent data. Inspired by Hausman's (1978) specification testing ideas, our methods essentially compare two collections of estimators that converge to the same limits under correct specification (conditional independence) and that diverge under the alternative. To establish the properties of our estimators, we generalize the existing nonparametric quantile literature not only by allowing for dependent heterogeneous data but also by establishing a weak consistency rate for the local Bahadur representation that is uniform in both the conditioning variables and the quantile index. We also show that, despite our nonparametric approach, our tests can detect local alternatives to conditional independence that decay to zero at the parametric rate. Our approach gives the first nonparametric tests for time-series conditional independence that can detect local alternatives at the parametric rate. Monte Carlo simulations suggest that our tests perform well in finite samples. We apply our test to test for a key identifying assumption in the literature on nonparametric, nonseparable models by studying the returns to schooling.

We compare environmental impacts associated with incoming foreign direct investment versus domestic capital in China. We use aggregate data on Chinese provinces’ economic and pollution indicators to explore the effects of the financial origin of fixed capital. Our simultaneous models consider three prime channels through which these effects work: economic scale, sectoral composition, and pollution intensity. Results show that emissions associated with foreign financed capital are lower than with domestically financed capital for some but not all of the considered types of pollution.

Purpose – This chapter considers a Hausman and Taylor (1981) panel data model that exhibits a Cliff and Ord (1973) spatial error structure.

Methodology/approach – We analyze the small sample properties of a generalized moments estimation approach for that model. This spatial Hausman–Taylor estimator allows for endogeneity of the time-varying and time-invariant variables with the individual effects. For this model, the spatial fixed effects estimator is known to be consistent, but its disadvantage is that it wipes out the effects of time-invariant variables which are important for most empirical studies.

Findings – Monte Carlo results show that the spatial Hausman–Taylor estimator performs well in small samples.

Purpose: In reality, financial decisions are made under conditions of asymmetric information that results in either favorable or adverse selection. As far as financial decisions affect growth of the firm, the latter must also be affected by either favorable or adverse selection. Therefore, the core objective of this chapter is to examine the determinants of each financial decision and the effects on growth of the firm under conditions of information asymmetry.

Design/Methodology/Approach: This chapter uses data for the non-financial firms listed in S&P 500. The data cover quarterly periods from 1989 to 2014. The statistical tests include linearity, fixed, and random effects and normality. The generalized method of moments estimation method is employed in order to examine the relative significance and contribution of each financial decision on growth of the firm, respectively. Standard and proposed proxies of information asymmetry are discussed.

Findings: The results conclude that there is a variation in the impact of financial variables on growth of the firm at high and low levels of information asymmetry especially regarding investment and financing decisions. A similar picture emerges in the cases of firm size and industry effects. In addition, corporate dividen d policy has a similar effect on firm growth across all asymmetric levels. These findings prove that information asymmetry plays a vital role in the relationship between corporate financial decisions and growth of the firm. Finally, the results contribute to the vast literature on the estimation of information asymmetry by demonstrating that the classical and standard proxies for information asymmetry are not consistent in terms of the ability to differentiate between favorable or adverse selection (which corresponds to low and high level of information asymmetry).

Originality/Value: This chapter contributes to the related literature in two ways. First, this chapter offers updated empirical evidence on the way that financing, investment, and dividends decisions are made under conditions of favorable and adverse selection. Other related studies deal with each decision separately. Second, the study offers new proxies for measuring information asymmetry in order to reach robust estimates of the effects of financial decisions on growth of the firm under conditions of agency problems.

The Hausman test is used in applied economic work as a test of misspecification. It is most commonly thought of as a test of whether one or more explanatory variables in a regression model are endogenous. The usual Hausman contrast test requires one estimator to be efficient under the null hypothesis. If data are heteroskedastic, the least squares estimator is no longer efficient. The first option is to estimate the covariance matrix of the difference of the contrasted estimators, as suggested by Hahn, Ham, and Moon (2011). Other options for carrying out a Hausman-like test in this case include estimating an artificial regression and using robust standard errors. Alternatively, we might seek additional power by estimating the artificial regression using feasible generalized least squares. Finally, we might stack moment conditions leading to the two estimators and estimate the resulting system by GMM. We examine these options in a Monte Carlo experiment. We conclude that the test based on the procedure by Hahn, Ham, and Moon has good properties. The generalized least squares-based tests have higher size-corrected power when heteroskedasticity is detected in the DWH regression, and the heteroskedasticity is associated with a strong external IV. We do not consider the properties of the implied pretest estimator.