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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.

We investigate the question of whether investing in a child’s development by having a parent stay at home when the child is young is correlated with the child’s adult outcomes. Specifically, do children with stay-at-home mothers have higher adult earnings than children raised in households with a working mother? The major contribution of our study is that, unlike previous studies, we have access to rich longitudinal data that allows us to measure both the parental earnings when the child is very young and the adult earnings of the child. Our findings are consistent with previous studies that show insignificant differences between children raised by stay-at-home mothers during their early years and children with mothers working in the market. We find no impact of maternal employment during the first five years of a child’s life on earnings, employment, or mobility measures of either sons or daughters. We do find, however, that maternal employment during children’s high school years is correlated with a higher probability of employment as adults for daughters and a higher correlation between parent and daughter earnings ranks.

This chapter proposes semiparametric estimation of the relationship between growth rate of GDP per capita, growth rates of physical and human capital, labor as well as other covariates and common trends for a panel of 23 OECD countries observed over the period 1971–2015. The observed differentiated behaviors by country reveal strong heterogeneity. This is the motivation behind using a mixed fixed- and random coefficients model to estimate this relationship. In particular, this chapter uses a semiparametric specification with random intercepts and slopes coefficients. Motivated by Lee and Wand (2016), the authors estimate a mean field variational Bayes semiparametric model with random coefficients for this panel of countries. Results reveal nonparametric specifications for the common trends. The use of this flexible methodology may enrich the empirical growth literature underlining a large diversity of responses across variables and countries.

This paper seeks to explain the serial persistence as well as the substantial number of zeros characterizing global bilateral investment holdings. We explore the different sources of serial persistence in the data (unobserved country pair effects, genuine state dependence, and transitory shocks) and examine the crucial factors affecting the decision to invest in a host country.

Based on a gravity setup, we consider investment behavior at the extensive (participation) margin and employ dynamic first-order Markov probit models, controlling for unobserved cross-sectional heterogeneity and serial correlation in the transitory error component, in order to explore the sources of persistence. Within this modeling framework we explore the importance of institutional quality of the host country in attracting foreign investment.

The data support that the strong persistence is driven by true state dependence, implying that past investment experiences strongly impact on the trajectory of future investment holdings. Institutional quality appears to play a significant role to attract foreign investment.

The empirical findings suggest that due to the existence of genuine state dependence, inward-investment stimulating policy measures could have a more pronounced effect since they are likely to induce a permanent change to the future trajectory of inward investment.

Both the substantial number of zeros and the salient persistence characterizing bilateral investment holdings decision have been previously overlooked in the literature. A study modeling jointly the levels and the selection mechanism could prove a fruitful direction for future research.

An adverse health event can affect women’s work capacity as they need time to recover. The institutional framework in the Netherlands provides employment protection during the first two years after the diagnosis. In this study, we have assessed the extent to which women’s employment is affected in the short- and long term by an adverse health event. We have used administrative Dutch data which follow women aged 25 to 55 years for four years after a medical diagnosis. We found that diagnosed women start leaving employment during the protection period and four years later they were about one percentage point less likely to be employed. Women in permanent employment did not reduce their employment during the protection period and reduced their employment with less than 0.5 percentage points thereafter. Furthermore, we found minor adjustments in the working hours in the short term and no adjustments in the long term. Lastly, we found that for wages, and not for employment and hours, adjustments could be related to the severity of the health condition: women diagnosed with temporary health conditions experienced a short-term wage penalty of about 0.5–1.7 percent and those diagnosed with chronic and incapacitating conditions experienced a long-term wage penalty of about 0.5 percent, while women diagnosed with some chronic and nonincapacitating conditions, such as respiratory conditions, experienced no wage changes in the short or long term.

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.

In this chapter, we utilize the residual concept of productivity measures defined in the context of normal-gamma stochastic frontier production model with heterogeneity to differentiate productivity and inefficiency measures. In particular, three alternative two-way random effects panel estimators of normal-gamma stochastic frontier model are proposed using simulated maximum likelihood estimation techniques. For the three alternative panel estimators, we use a generalized least squares procedure involving the estimation of variance components in the first stage and estimated variance–covariance matrix to transform the data. Empirical estimates indicate difference in the parameter coefficients of gamma distribution, production function, and heterogeneity function variables between pooled and the two alternative panel estimators. The difference between pooled and panel model suggests the need to account for spatial, temporal, and within residual variations as in Swamy–Arora estimator, and within residual variation in Amemiya estimator with panel framework. Finally, results from this study indicate that short- and long-run variations in financial exposure (solvency, liquidity, and efficiency) play an important role in explaining the variance of inefficiency and productivity.

We examine the roles of sample initial conditions and unobserved individual effects in consistent estimation of the dynamic binary response panel data model. Different specifications of the model are estimated using female welfare and labor force participation data from the Survey of Income and Program Participation. These include alternative random effects (RE) models, in which the conditional distributions of both the unobserved heterogeneity and the initial conditions are specified, and fixed effects (FE) conditional logit models that make no assumptions on either distribution. There are several findings. First, the hypothesis that the sample initial conditions are exogenous is rejected by both samples. Misspecification of the initial conditions results in drastically overstated estimates of the state dependence and understated estimates of the short- and long-run effects of children on labor force participation. The FE conditional logit estimates are similar to the estimates from the RE model that is flexible with respect to both the initial conditions and the correlation between the unobserved heterogeneity and the covariates. For female labor force participation, there is evidence that fertility choices are correlated with both unobserved heterogeneity and pre-sample participation histories.

We present Bayesian models for finding the longitudinal causal effects of a randomized two-arm training program when compliance with the randomized assignment is less than perfect in the training arm (but perfect in the non-training arm) for reasons that are potentially correlated with the outcomes. We deal with the latter confounding problem under the principal stratification framework of Sommer and Zeger (1991) and Frangakis and Rubin (1999), and others. Building on the Bayesian contributions of Imbens and Rubin (1997), Hirano et al. (2000), Yau and Little (2001) and in particular Chib (2007) and Chib and Jacobi (2007, 2008), we construct rich models of the potential outcome sequences (with and without random effects), show how informative priors can be reasonably formulated, and present tuned computational approaches for summarizing the posterior distribution. We also discuss the computation of the marginal likelihood for comparing various versions of our models. We find the causal effects of the observed intake from the predictive distribution of each potential outcome for compliers. These are calculated from the output of our estimation procedures. We illustrate the techniques and ideas with data from the 1994 JOBS II trial that was set up to test the efficacy of a job training program on subsequent mental health outcomes.