Keywords: autoregressive models, covariance structures, error components, generalized method of moments, individual effects, measurement error, optimal instruments, panel data, predetermined variables, unobserved heterogeneity.


I  Static Models

2  Unobserved Heterogeneity

Chapter 2 begins by introducing the problem of unobserved heterogeneity in regression analysis and how the availability of panel data helps to solve it. Correlated effects are motivated as an instance of endogenous regressors, and compared with other approaches to endogeneity in econometrics. Within-group or fixed effects estimation is discussed and motivated from short and long panel perspectives in least squares and likelihood contexts. The implications of heteroskedasticity and serial correlation for valid inference and optimal estimation are considered, as well as extensions to non-linear models with additive effects, including small and long T robust standard errors, and minimum distance methods.

Keywords: endogenous regressors, fixed effects, heteroskedasticity, minimum distance, optimal estimation, robust standard errors, serial correlation, unobserved heterogeneity bias, within-group estimation.


3  Error Components

This chapter is devoted to error component models. These are initially motivated from an interest in distinguishing permanent from transitory components of variation in such areas as the analysis of wage inequality and mobility. Next, they are regarded as a special case of the unobserved heterogeneity model in which the effects are uncorrelated with the regressors. Tests of these restrictions and extensions to models with a subset of uncorrelated regressors are discussed. Finally, nonparametric estimation of the error component distributions is considered.

Keywords: error components models, models with information in levels, nonparametric estimation, tests of uncorrelated effects, wage inequality and mobility.


4  Error in Variables

The last chapter in Part I deals with error in variables in panel data. The central theme here is that regressions in levels and deviations may not only differ because of unobserved heterogeneity but also as a result of magnification of measurement error bias in the regressors in changes. Conditions under which panel data provides internal instrumental variables are discussed and a firm money demand illustration provided.

Keywords: error in variables, internal instrumental variables, firm money demand, measurement error bias, regressions in levels and deviations.


II  Time Series Models with Error Components

5  Covariance Structures for Dynamic Error Components

Part II deals with time series models with error components. Chapter 5 opens up with an informal discussion of the problem of distinguishing between unobserved heterogeneity and individual dynamics in short panels. Next, modelling strategies of time effects, moving average models, and inference from covariance structures are considered. Then an illustration is provided by considering tests of the permanent income hypothesis from household panel data.

Keywords: covariance structures, moving average models, permanent income hypothesis, time effects, time series with error components.


6  Autoregressive Models with Individual Effects

Chapter 6 considers the specification and estimation of autoregressive models with heterogeneous intercepts. Within-group biases in short panels are discussed. Fixed T consistent estimation from GMM and likelihood perspectives is considered. The discussion clarifies the impact of assumptions about initial conditions and heteroskedasticity on estimation. Particular attention is paid to unit roots and to estimation under mean stationarity. The chapter concludes with a detailed tutorial on the estimation and testing of VAR models using firm-level panel data.

Keywords: autoregressive models, firm-level panel data, initial conditions, mean stationarity, time series heteroskedasticity, unit roots, VAR models, within-group biases.


III  Dynamics and Predeterminedness

7  Models with both Strictly Exogenous and Lagged Dependent Variables

The subject of Part III is dynamics and predeterminedness. Chapter 7 deals with models with both strictly exogenous and lagged dependent variables allowing for autocorrelation of unknown form. In contrast to the autoregressive models of Part II, here lagged dependent variables appear in a structural role. Their effects are identified regardless of the form of serial correlation thanks to the availability of strictly exogenous regressors. Estimation is discussed from short and long panel perspectives in GMM and likelihood contexts. A model of cigarette addiction is used as an illustration.

Keywords: autocorrelation of unknown form, cigarette addiction, lagged dependent variables, short and long panels, strictly exogenous regressors.


8  Predetermined Variables

Chapter 8 deals with models in which the errors are mean independent of current and lagged values of certain conditioning variables, but not with their future values. Partial adjustment, Euler equations, and cross-country growth are discussed as examples.  Alternative approaches to estimation from small and large T perspectives are considered. Special attention is given to estimators that use information on the levels of the variables. Such topics as the irrelevance of filtering and optimal instruments with sequential moment conditions are also considered.

Keywords: cross-country growth, Euler equations, information on the levels of the variables, irrelevance of filtering, partial adjustment, optimal instruments, predetermined variables, sequential moment conditions.


IV  Appendices

A  Generalized Method of Moments Estimation

Part IV contains two additional chapters that review the main results in the theory of generalized method of moments estimation and optimal instrumental variables. The purpose of these chapters is to make the book reasonably self-contained. The first one begins by introducing method of moments estimation problems, followed by a general formulation of GMM estimation and testing, using 2SLS and 3SLS as examples. The chapter deals with consistency, asymptotic normality, asymptotic variance estimation, optimal weight matrix, and Sargan tests of overidentifying restrictions.

Keywords: asymptotic variance estimation, generalized method of moments, moments estimation problems, overidentifying restrictions, Sargan tests.


B  Optimal Instruments in Conditional Models

This chapter considers models defined by conditional moment restrictions. The focus of the discussion is in finding the optimal instruments for each type of model that is considered. The problem is first solved for the linear regression model, which is the most familiar context, and then the same procedure is used for increasingly more complex models.

Keywords: conditional moment restrictions, conditional models, linear regression, optimal instruments.