Panel Data Summary

Panel Data Summary Advantages : - Control of heterogeneity More variability and degrees of freedom Capture the change dynamics Minimizes aggregation bias associated with individual data Disadvantages : - Presence of outliers lead to disturbances in quality of estimates Existence of unbalanced panels Types : 1) 2) 3) 4) 5) Balanced Unbalanced : missing values w zebi Typical : large N, small T Rotating : a sub-sample of individuals replaced at each period Pseudo : obtained by merging cross sections at different times using different individuals ● General Model : with unobservable factors taken into account it becomes : Assumptions : - Explanatory variables are non stochastic and the corresponding matrices are full rank (no multicollinearity) Explanatory variables are uncorrelated with error terms The different assumptions on the distribution of the errors terms and the degree of variability of the coefficients → Panel data models provide a solution to the correlation between explanatory variables and error terms due to the presence of unobservable factors. ● Types of models Pooled regression : Pooled model is one where the data on different units are pooled together with no assumption on individual differences. Individual Regression Assumptions of classical OLS hold which enables us to use an OLS estimator.. Test Advantages Disadvantages - *Easy to compute *Homogeneity of observation and behavior of individuals over time *Parsimonious model *ignores heterogeneity Explanatory variables depend on the individuals. - *Easy to compute *Perfect for modeling individual heterogeneity Var Cov Matrix depends on Omega. APPLIED WHEN THERE IS CORRELATION BETWEEN INDIVIDUAL EFFECTS AND REGRESSORS (u(i) and x (it)) Estimated models only differ in value of constant term. There is an individual effect fixed over time. → If errors are homoskedastic, we use LSDV or within estimator (also called *Individual estimation only possible if T>K+1 *Does not take into consideration interdependence of individual behavior We use a GLS estimator. Fixed effects *Large number of parameters to estimate 1) We use Student’s test (t stat) : to test whether α(i) = 0 2) We use Fisher’s test to test if there are differences between the n groups α(i) = α(j) If there are omitted variables, and these variables are correlated with the variables in the model, then fixed effects models may provide a means for controlling for omitted variable bias. *When N is large, the number of parameters to be estimated is prohibitive *We cannot take into account variables which do not vary across time An individual intercept (αi) is included to control for individual-specific and time-invariant characteristics. That intercepts are called fixed effects. fixed effects estimator). Random effects We have a composite error term. APPLIED WHEN THERE IS NO CORRELATION BETWEEN INDIVIDUAL EFFECTS AND REGRESSORS (u(i) and x (it)) The error component (ut) is the sum of the individual specific random component Thus, the main benefit of fixed effects estimations is that the potential sources of biases in the estimations are limited in comparison to classical OLS models. → If errors are heteroskedastic, we use GLS. We estimate it using GLS. We use the Breusch Pagan test with Lagrange Multiplier. H0 : sigma²= 0 H1 : sigma ² =! 0 You run the OLS, get the residuals, regress them on explanatory variables supposed to be responsible for heteroskedasticity, get *Random effect models assist in controlling for unobserved heterogeneity when the heterogeneity is constant over time and not correlated with independent variables. *RE model makes it possible to take into account Assumption that independence between individual random effect and regressors exists is difficult to accept (µi) and idiosyncratic disturbance (εi,t). = The RE model assumes the independence between specific individual effects zi and exogenous variables xit the R², compute LM, compare with X². variables which do not vary over time ● FIXED EFFECTS ESTIMATORS : 1) Least Squares Dummy Variables : The natural way to estimate fixed effects for all individuals is to include an indicator variable. For example, for the first unit: The number of dummy variables equals N-1 (idk exactly but there is one that is not accounted for, either tekhou N-1 wala loula omitted). It is not feasible to use the least square dummy variable estimator when N is large. The model becomes : 2) Within estimator : We average the observations across time and subtract them from the original model. Our new estimated model becomes : → Both estimators yield the same result. NOTE 1 : There is an estimator called Between Estimator that uses group means. We do not use Between Estimator with FE models as they yield inconsistent estimators. NOTE 2 : Total deviation from the sample mean is as follows : ● Two way fixed effects : We add the temporal effects to the fixed effects. To avoid multicollinearity, we add only T-1 temporal effects. We estimate it using partitioned regression.