CPANEL Procedure

The CPANEL procedure analyzes a class of linear econometric models that arise when time series and cross-sectional data are combined. This type of data is called panel data. Typical examples of panel data include observations over time on people, households, countries, or firms. For example, in the case of survey data on household income, the panel is created by repeatedly surveying the same households over many years. The individual entities that are followed over time are called cross sections.

Regression models for panel data are characterized by an error structure that can be divided into a cross-sectional component, a time component, and an observation-level component. Panel data models can be categorized by the exact structure of the error term and how it interacts with the regression equation. The CPANEL procedure supports the following models:

A one-way model depends only on the cross section to which the observation belongs. A two-way model depends on both the cross section and the time period to which the observation belongs. The models are called fixed-effects models if the effects are nonrandom and are called random-effects models otherwise.

If the effects are fixed, the models are essentially regression models with dummy variables that correspond to the effects. For fixed-effects models, ordinary least squares (OLS) estimation, with some facility for absorbing the dummy variables, is the best linear unbiased estimator. Random-effects models use a two-stage approach. In the first stage, variance components are estimated by your choice of the methods described by Swamy and Arora (1972); Fuller and Battese (1974); Wansbeek and Kapteyn (1989); Wallace and Hussain (1969); Nerlove (1971). In the second stage, variance components are used to standardize the data, and then OLS regression is performed.

Random-effects models are more efficient than fixed-effects models, and they can estimate effects for variables that do not vary within cross sections. The cost of these added features is that random-effects models carry much more stringent assumptions than their fixed-effects counterparts. The CPANEL procedure also supports models that blend the desirable features of random and fixed effects. These hybrid models are described by Hausman and Taylor (1981) and Amemiya and MaCurdy (1986).

Instrumental variables (IV) models are models that introduce auxiliary regression variables to deal with endogenous regressors—regressors that are correlated with the residual errors. The CPANEL procedure supports IV generalizations of the pooled regression model, the between-groups regression model, the one-way fixed-effects model, the one-way random-effects model, the two-way fixed-effects model, and the two-way random-effects model. For the one-way random-effects model, PROC CPANEL uses methods that were developed by Baltagi (1981). PROC CPANEL can also estimate these models by using the efficient generalized method of moments (GMM).

Dynamic panel models are autoregression models that include lagged versions of the dependent variable as regressors. Examples of such models can be found in Arellano and Bond (1991) and Blundell and Bond (1998). The CPANEL procedure fits these models by using the generalized method of moments (GMM). You can perform GMM on either the difference equations or the full system of difference and level equations.