Panel Data

# Panel Data - Economics 245A Panel Data Models To understand...

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Economics 245A Panel Data Models To understand panel data models it is helpful to begin with the following i) A sequence of random variables f Y i g n i =1 is said to be a cross-section data set if the subscript i indexes distinct observations made at the same point in time. ii) A sequence of random variables f Y t g T t =1 is said to be a time-series data set if the subscript t indexes observations made at distinct points in time. iii) A sequence of random variables f Y i;t g t =1 ;:::;T i =1 ;:::;n is said to be a cross-section time-series data set if the subscript i;t indexes distinct observations at each of T points of time. iv) A sequence of random variables f Y i;t g t =1 ;:::;T i =1 ;:::;n is said to be a panel data set if the subscript i;t indexes observations on the same set of n individuals at each of T points of time. Example. If we sample students from the freshmen class at UCSB in each of two years, UCSB in their freshmen year, and sample the same &ve students in their sopho- more year, then we have a panel data set. As the example makes clear, a panel data set is a special case of a cross-section time-series data set. What advantages arise from sampling data in this way? The most substantial advantage is that stronger identi&cation can be obtained from panel data sam- role in the recent literature on testing for unit roots but is not part of the older literature on panel data models, is empirical ±identi&cation². Empirical identi&- cation is obtained as in the following Example. Let Y i;t be the observation for country i in period t . Initially, we gather data for only one country ( i = 1 ) and estimate Y 1 ;t = & 0 + 1 X 1 ;t + U 1 ;t ; where t = 1 ;:::T . Unfortunately, T is not large enough to learn much about 1 , that is, the variance of the estimator of 1 is quite large. We need to increase the sample size. Yet we must wait one period for each addition to T (and in many cases a period is a year), so increasing T takes too long. If we believe that the

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same relation holds for another country ( i = 2 ), then we have 2 T observations to estimate 1 . obtained as in the following Example. Let Y i;t be the wage for individual i in year t . Let X i;t be the education of individual i in year t . If we believe that the e/ect of education on wage is di/erent for each individual, then in a given year Y i = & 0 + 1 ;i X i + U i : Because 1 ;i di/ers over individuals, we cannot identify the marginal e/ect of education on a worker by studying educational di/erences across workers. Rather, we must study the same worker at multiple time periods. If we move from a cross- section to a panel data set, we can identify (and estimate)
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Panel Data - Economics 245A Panel Data Models To understand...

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