Panel data panel data set not

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Marilynn Harmon
5 years ago
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1 Panel data A panel data set contains repeated observations on the same units collected over a number of periods: it combines cross-section and time series data. Examples The Penn World Table provides national income accounts for all the countries of the world for as many recent years as possible. There are also within-country panels. The British Household Panel Survey follows the same representative sample of individuals over a period of years. When it started in 1991 the panel consisted of 5,500 households and 10,300 individuals drawn from 250 areas of Great Britain. Each household completed a questionnaire on its demographic composition, its sources of income and its labour market experience. Barro (1991) had access to panel data but did not exploit it fully as Temple observes.

2 I will describe the basic panel data methods and give an application from Distribution and Development by Gary Fields (see above). Basic models Time series data takes the form y 1,..., y T, x 1,..., x T for the case of T observations on 2 variables (to keep it simple) on a single unit (country, say). Cross section data takes the form y 1,..., y n, x 1,..., x n for the case of 2 variables and n units. In a panel each observation has a unit subscript i and a time subscript t. So panel data takes the form y it, x it for i 1,..., n and t 1,..., T. One way of modelling panel data is to pool the data and treat the nt observations as coming from the same population. In the case of 2 variables we would have y it x it it for i 1,..., n & t 1,..., T i.e. ordinary regression with nt

3 observations. The parameters would be estimated by least squares. At the other extreme is the specification where parameter values change across time and across units as in y it it it x it it. This model cannot be estimated because every observation has its own parameters it and it! Intermediate cases include T unrelated cross-sections or n unrelated time series y it t t x it it : t 1,..., T y it i i x it it : i 1,..., n Panel data methods treat the case where there is some constancy across units and across time. The most common specification is y it i x it it where each unit has its own intercept but the slope is identical across units. The parameter i captures all the influences that act only on the i-th unit. These influences are permanent and do not

4 change with time. The varying intercept can be handled using dummy variables with y it 1 2 D 2i... N D Ni x it it where the dummies are defined so D 2i 1 if i 2 0 otherwise,..., D Ni 1 if i N So the intercept for unit 1 is 1, for unit 2 it is 1 2, etc. In panel data analysis this specification is called the fixed effects model. The alternative random effects model treats the changing i of y it i x it it 0 otherwise in a different way. Instead of treating the i as unknown constants, it assumes they are generated at random from a population of s. An advantage of this formulation is that it is more economical with parameters: instead of n intercept parameters there are only 2 for the mean and variance of the distribution. The random effects formulation is not often used when the units are

5 countries. Fields on the Kuznets curve The relationship between income inequality and development as measured by income per head has been investigated using cross-section, time series and panel data. The findings often conflict and Fields ch 3 reviews the research on the topic. The Kuznets curve (see above for K s observations on inequality) is an inverted U relation between income inequality and income: it is an expression of K s observation that as income increases, inequality increases but then falls as income rises further. One possible specification is Ey x x 2 with 0. Here y is a measure of inequality such as the Gini coefficient and x is a measure of income, such as GDP per head. Here is a scatter plot (p. 38) from one cross-section study

6 The small dots represent countries and the big dots groups of countries. The small dots are widely dispersed but there is some inverted U-shape pattern to the big dots. The K hypothesis is a generalisation covering all countries but pure cross-section analysis does not seem appropriate for a hypothesis about how inequality varies over time. Table 3.1 of Fields compares least squares estimates for pooled data with a country fixed-effects specification:

7 The results are quite different and the significantly negative coefficient on GNP 2 has disappeared.

Poverty, Inequality and Growth: Empirical Issues

Poverty, Inequality and Growth: Empirical Issues Start with a SWF V (x 1,x 2,...,x N ). Axiomatic approaches are commen, and axioms often include 1. V is non-decreasing 2. V is symmetric (anonymous) 3.