1. Econometric Analysis of Panel Data Instrumental Variables in Panel Data –Assumptions of Instrumental Variables –Fixed Effects Model –Random Effects Model –First Difference Model

2. Instrumental Variables in Panel Data The Model with Random Regressors Instrumental Variables –Instrumental variables can be obtained through use of exogenous regressors X1 in periods other than the current period, using the exogeneity assumption.

3. Assumptions of Instrumental Variables Summation Assumption –Exogenous variables X1 are included in Z. –Z may include excluded exogenous variables (other than X1), although they are difficult to find.

4. Assumptions of Instrumental Variables Contemporary Exogeneity Assumption –Any time-invariant exogenous variables in X1 can be used only once as an instrument.

5. Assumptions of Instrumental Variables Weak Exogeneity Assumption (Predetermined Instruments Assumption)

6. Assumptions of Instrumental Variables Strong Exogeneity Assumption –For dynamic models, at most weak exogeneity of instruments can be assumed. –Time invariant instruments can be used only once.

7. IV for Fixed Effects Model Fixed Effects Model –Strong exogeneity of instrumental variables must be assumed for the fixed effects model so that the within estimates are consistent.

8. IV for Random Effects Model Random Effects Model –Strong exogeneity of instrumental variables must be assumed for the random effects model so that the GLS parameter estimates are consistent.

9. IV for First Difference Model First Difference Model

10. IV for First Difference Model First Difference Model –No time-invariant variables. –To consistently estimate the first-difference model, we need only the Weak Endogeneity assumption for the instrumental variables.

11. Example: Returns to Schooling Cornwell and Rupert Model (1988) Data (575 individuals over 7 years) –Dependent Variable y it : LWAGE = log of wage –Explanatory Variables x it : Time-Variant Variables x1 it : –EXP = work experience WKS = weeks worked  endogenous OCC = occupation, 1 if blue collar, IND = 1 if manufacturing industry SOUTH = 1 if resides in south SMSA = 1 if resides in a city (SMSA) MS = 1 if married UNION = 1 if wage set by union contract Time-Invariant Variables x2 i : –ED = years of education  endogenous FEM = 1 if female BLK = 1 if individual is black

12. Example: Returns to Schooling Labor Market Equilibrium Model –Labor Demand Equation lwage = exp exp2 wks occ ind south smsa ms union [blk fem ed] –Labor Supply Equation wks = lwage union [fem ed] –Endogenous or predetermined variable: [ed]