Ch. 11 Panel Data model Data sets that combine time series and cross sections are common in econo- metrics. For example, the published statistics of the OECD contain numerous series of economic aggregate observed yearly for many countries. The PSID is a studies of roughly 6000 families and 15000 individuals who has been interviews periodically from 1968 to the present. Panel data sets are more oriented toward cross-section analysis; they are wide but typically short(relatively). Hetero- geneity across units is an integral part of the analysis Recall that the(multiple) linear model is used to study the relationship be- tween a dependent variable and several independent variables. That is ∫(x1,x2,…,xk)+E B1x1+B2x2+….+Bkxk+E xB+ where y is the dependent or explained variable, i, i=l,.,k are the independent or the explanatory variables and Bi, i=1, ..,k are unknown coefficients that we are interested in learning about, either through estimation or through hypothesis testing. The term e is an unobservable random disturbance. In the following, we will see the panel data sets provide a richer source of information and the needin f some complex stochastic specifications. el data set of that it will allow the researcher greater fexibility in model difference in behavior across individuals. The basic framework for this statistical model is of the form t=xtB+z1a+et,i=1,2,…,N;t=1,2,…,T. There are k regressor in xit, not including a constant term. The heterogene- ity, or individual effect is za where zi contains a constant term and a set of individual or group specific variables, which may be obser location. an so on or unobserved as family specific characteristics, individ ual heterogeneity in skill or preference, and so on, all of which are taken to be constant over time t. the various cases we will consider areCh. 11 Panel Data Model Data sets that combine time series and cross sections are common in econo￾metrics. For example, the published statistics of the OECD contain numerous series of economic aggregate observed yearly for many countries. The PSID is a studies of roughly 6000 families and 15000 individuals who has been interviews periodically from 1968 to the present. Panel data sets are more oriented toward cross-section analysis; they are wide but typically short (relatively). Hetero￾geneity across units is an integral part of the analysis. Recall that the (multiple) linear model is used to study the relationship be￾tween a dependent variable and several independent variables. That is y = f(x1, x2, ..., xk) + ε = β1x1 + β2x2 + ... + βkxk + ε = x 0β + ε where y is the dependent or explained variable, xi , i = 1, ..., k are the independent or the explanatory variables and βi , i = 1, ..., k are unknown coefficients that we are interested in learning about, either through estimation or through hypothesis testing. The term ε is an unobservable random disturbance. In the following, we will see the panel data sets provide a richer source of information and the needing of some complex stochastic specifications. The fundamental advantage of a panel data set over a cross section is that it will allow the researcher greater flexibility in model difference in behavior across individuals. The basic framework for this statistical model is of the form yit = x 0 itβ + z 0 iα + εit, i = 1, 2, ..., N; t = 1, 2, ..., T. There are k regressor in xit, not including a constant term. The heterogene￾ity, or individual effect is z 0 iα where z 0 i contains a constant term and a set of individual or group specific variables, which may be observed, such as race, sex, location, an so on or unobserved, such as family specific characteristics, individ￾ual heterogeneity in skill or preference, and so on, all of which are taken to be constant over time t. The various cases we will consider are: 1