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This chapter reviews the recent developments in the estimation of panel data models in which some variables are only partially observed. Specifically we consider the issues of censoring, sample selection, attrition, missing data, and measurement error in panel data models. Although most of these issues, except attrition, occur in cross-sectional or time series data as well, panel data models introduce some particular challenges due to the presence of persistent individual effects. The past two decades have seen many stimulating developments in the econometric and statistical methods dealing with these problems. This review focuses on two strands of research of the rapidly growing literature on semiparametric and nonparametric methods for panel data models: (i) estimation of panel models with discrete or limited dependent variables and (ii) estimation of panel models based on nonparametric deconvolution methods.

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 chapter develops a set of two-step identification methods for social interactions models with unknown networks, and discusses how the proposed methods are connected to the identification methods for models with known networks. The first step uses linear regression to identify the reduced forms. The second step decomposes the reduced forms to identify the primitive parameters. The proposed methods use panel data to identify networks. Two cases are considered: the sample exogenous vectors span Rn (long panels), and the sample exogenous vectors span a proper subspace of Rⁿ (short panels). For the short panel case, in order to solve the sample covariance matrices’ non-invertibility problem, this chapter proposes to represent the sample vectors with respect to a basis of a lower-dimensional space so that we have fewer regression coefficients in the first step. This allows us to identify some reduced form submatrices, which provide equations for identifying the primitive parameters.

This chapter describes how to use popular software programs (Hierarchical Linear Modeling, LISREL) to analyze multiwave panel data. We review prevailing methods for panel data analyzes in strategic management research and identify their limitations. Then, we explain how multilevel and latent growth modeling provide more rigorous methodologies for studying dynamic phenomena. We present an example illustrating how firm performance can initiate temporal change in the human and social capital of members of Board of Directors, using hierarchical linear modeling. With the same data set, we replicate this test with first-order factor latent growth modeling (LGM). Next, we explain how to use second-order factor LGM with panel data on employee cognitions. Finally, we review the relative advantages and disadvantages of these new data-analytical approaches.

Numerous empirical studies have been conducted to analyze the impact of board gender diversity (BGD) on firm performance without being able to establish a clear relationship. In this paper, we reassess the relationship between BGD and firm performance by using a quantile regression approach. Our results indicate that BGD matters only across a subset of the firm performance distribution. Moreover, when the possible endogeneity of the relationship between BGD and firm performance is taken into account, there are some conditions under which a positive and significant relationship is observed for the eight lowest quantiles.

A semiparametric stochastic frontier model is proposed for panel data, incorporating several flexible features. First, a constant elasticity of substitution (CES) production frontier is considered without log-transformation to prevent induced non-negligible estimation bias. Second, the model flexibility is improved via semiparameterization, where the technology is an unknown function of a set of environment variables. The technology function accounts for latent heterogeneity across individual units, which can be freely correlated with inputs, environment variables, and/or inefficiency determinants. Furthermore, the technology function incorporates a single-index structure to circumvent the curse of dimensionality. Third, distributional assumptions are eschewed on both stochastic noise and inefficiency for model identification. Instead, only the conditional mean of the inefficiency is assumed, which depends on related determinants with a wide range of choice, via a positive parametric function. As a result, technical efficiency is constructed without relying on an assumed distribution on composite error. The model provides flexible structures on both the production frontier and inefficiency, thereby alleviating the risk of model misspecification in production and efficiency analysis. The estimator involves a series based nonlinear least squares estimation for the unknown parameters and a kernel based local estimation for the technology function. Promising finite-sample performance is demonstrated through simulations, and the model is applied to investigate productive efficiency among OECD countries from 1970–2019.

The objective of this chapter is to introduce the reader to Spatial Health Econometrics (SHE). In both micro and macro health economics there are phenomena that are characterised by a strong spatial dimension, from hospitals engaging in local competitions in the delivery of health care services, to the regional concentration of health risk factors and needs. SHE allows health economists to incorporate these spatial effects using simple econometric models that take into account these spillover effects. This improves our understanding of issues such as hospital quality, efficiency and productivity and the sustainability of health expenditure of regional and national health care systems, to mention a few.