Cesar Perez Lopez - ECONOMETRIC MODELS WITH PANEL DATA. APPLICATIONS WITH STATA

ECONOMETRIC MODELS WITH PANEL DATA. APPLICATIONS WITH STATA Csar Prez Lpez Models WITH PANEL data The data panels are a special type of samples in which the behavior of a certain number of economic agents is followed over time. In this way, the researcher can perform economic analysis and specify models with the data of cross section that are obtained when all operators are considered in an instant of time. Different patterns of behaviour of all agents together studied in the different temporal moments may thus be assessed. Alternatively, you can perform the same analysis considering time series given by the evolution of each economic agent throughout all the periods of the sample. Therefore, an essential feature of the structure of panel data is its two-dimensionality.

The list of individuals (or economic agents) constitutes a dimension and form another dimension the instants of time. Consider as an example the case of the panel of the income tax of the people physical (income tax panel) which develops the Institute of Fiscal Studies Spanish and which aims to have a database with the statements of the tax on the income of the same individuals every year. Different individuals are income tax payers and the time interval varies at present between 1999 and 2012. In them paragraphs following is delves a little more in the structures of data immersed in the two dimensions of a set of data of panel. On the one hand the data of cutting cross or section Cross and on the other hand them data of series temporary. Within the structures of data more important, typical in the work in economy applied, have the cross-sectional data.

A set of data of cross-section is a sample composed by individuals, families, companies, cities, States, countries u another type of units very varied collection in a time certain of the time. General can assume that the data of cross-section is have retrieved through a sampling random of the population underlying. For example, if we get information about wages, education, experience and other characteristics by choosing random 500 people of the employed population, we can say that we have a random samples of the population that has a job. In the case of income from income tax panel, we consider all the variables included in the model of tax and will be analysed for a given year. Considering the different years have all cross sections every year. The cross-sectional data are very often used in economics and other social sciences.

In economics, the analysis of cross-sectional data is closely related to various branches of the applied microeconomics, as tax analysis, the economics of labour, both State and local public finance industrial organization, the urban economy, demography and health economics. Data on individuals, families, companies and cities at a given moment of time are important to compare micro-economic hypotheses and assess economic and fiscal policies. A time series data set consists of observations on a variable or variables over time. Typical examples of time series data are gross domestic product, the money supply, consumer price indexes, annual rates of homicide or car sales figures. Time series data are more used in macroeconomic analysis, as opposed to the cross-sectional data, which are used mostly in microeconomic analysis. Time series tend to be more difficult to analyze than the cross-sectional data since we can almost never assume that economic observations are temporarily independent.

In the case of samples of income tax we can consider time series measuring the evolution of each variable of the tax over the period 1999-2012. A combination of cross sections or data pool is a fusion of several cross-sections of data collected at different points in time in the same population (but not for the same individuals). For example, suppose that two surveys of cross section on families in a country, one in 1985 and another in 1990 are. In 1985, a survey with a random sample is made to obtain variables such as the level of income, savings, the size of families, etc. In 1990, a new random sample of families is made and the same questions that in 1985 to do the survey are used. In order to increase the size of the sample, we can form a set of fused data of cross section by combining data from two years.

The fusion of different years often cross-sectional data is useful to analyze the effects of government policies. The idea is to collect data from the years before and after a key political change. Usually, fused cross-sectional data are analyzed very similar to conventional cross-sectional data, except that we often need to take into account differences in variables over time. In fact, in addition to increasing the size of the sample, the cross section data fusion aims often observe also how a key relationship has changed over time. However, by combining cross sections obtained by random sampling from the same population at different moments of time, we will have a sample of observations distributed independently but not identically. In the case of income tax could form a data pool joining all samples selected annually.

Obviously IRPF samples randomly selected each year do not correspond to the same individuals. A set of panel data, or longitudinal data, consists of a time series for each unit of a cross section (or set of cross-sectional data). A panel of data is a fusion of several cross-sections of data collected at different points in time (or in different geographical units or for different companies, etc.) in the same town for the same individuals. As an example, suppose that we have a record of data on wages, education, and the employment history of a set of individuals followed for a period of ten years. Also could collect information on them data financial or of investment of a same set of companies during a period of five years (therefore those individuals not have why be people). Panel data can also be collected about geographic units.

For example, we may collect data on flows of immigration, level of taxation, wages, cost of Government, etc., in the same set of countries of the European Union for the years 1990, 1995 and 2000. The key feature of the panel data, which differentiates them from the fused data of cross section, is the fact that is collected information of the same cross section (individuals, companies, countries, etc) units in the different moments of time. But we must not forget that the essential characteristic of a panel is its temporal dimension, given that is formed with observations on great variety of individuals taken at different moments of time, usually years. However, made differentiator of a panel is that usually the observations come from the same individuals at different moments in time . In addition, when the source of information that feeds the panel are administrative records there is virtually no response, which allows to form compact panels ideal for exempt of missing values and atypical data analysis without the application of methods of imputation of missing information be required. The stage of exploratory data analysis, prior to any application with panel data and decisive results, looks like this strongly favoured.

The double dimensionality of a panel leads us to consider the regression model with panel data as a set of models for each value of the temporary variable. Note that what we call here a temporary variable can be any other variable that classify individuals in various significant groups, for example geographical regions, companies, etc. However, for simplicity we will continue referring to this second dimension of the panel as a temporal dimension. Consider that we start from the regression model that has as the dependent variable the variable and independent variables x 1 , x 2 ,, x k , given by the equation: Given a set of N observations for each of the variables endogenous and exogenous, we can write the model as follows: i =1,, N Consider now the previous model for each temporary unit where t =1, 2,3,, T . This model, called panel data model, can be written as follows: or in closed notation: where i = 1,, N sample observations and t = 1,, T temporary moments. It is that u it are the terms of error at each time instant.