2.2 Panel data models

Equation chapter 1 section 1notes on panel data models

Introduction

Panel data methods are appropriate when the researcher has available observations that are both cross-sectional and time series. For example, one could form a panel data set with observations on the per capita consumption of tobacco for a set of OECD countries over the period 1960 to 2005. Usually the data is “stacked”—that is, all of the observations for country A is listed together in order of year before the data for country B, etc. It is also possible to stack the data by year—countries A to Z for 1960, countries A to Z for 1961, and so on through 2005.

Let $y_{it}$ be the per capita consumption of tobacco for country i in year t . We wish to model the per capita consumption of tobacco as a function of a set of observable independent variables like the price of tobacco, income, restrictions on tobacco advertising, and restrictions on tobacco consumption. Of course there are several sources of unobserved heterogeneity in that data set. In particular, we might expect that systematic differences in consumption patterns would exist due to differences in the customs and mores of the various countries in the sample. It also would be reasonable to assume that these country-level differences are be relatively stable over time. Additionally, we might expect that there would be differences the per capita consumption of tobacco over time due to changes in our understanding of the long run health effects of tobacco consumption. These changes might affect both (1) the level of consumption and (2) the responsiveness of the consumption of tobacco to changes in the explanatory variables.

In these notes we describe some of the ways of modeling panel data sets and discuss some of the issues associated with the estimation of these models. We also discuss how to use Stata to analyze panel data sets. We begin by considering some of the types of panel data model specifications.

Model specification

There are four general specifications of the panel data model available. The differences in these models reflect differing assumptions one might make and are listed below.

1. slope coefficients are constant and the intercept varies over the individuals:

2. slope coefficients are constant and the intercept varies over the individuals and over time:

3. all coefficients vary over individuals:

4. all coefficients vary over time and individuals:

These four models can be classified further, depending on whether the researcher assumes that the coefficients of the model are fixed or random. However, most research in economics is restricted to estimation of (1) and (2) because they strike a reasonable balance between being general enough without introducing unnecessary assumptions that can render estimation extremely difficult.