1. Econometric Analysis of Panel Data
William Greene Department of Economics Stern School of Business

2. Dear Professor Greene, I have to apply multiplicative heteroscedastic models, that I studied in your book, to the analysis of trade data. Since I have not found any Matlab implementations, I am starting to write the method from scratch. I was wondering if you are aware of reliable implementations in Matlab or any other language, which I can use as a reference. 

3. a “multi-level” modelling feature along the following lines
a “multi-level” modelling feature along the following lines? My data has a “two level” hierarchical structure: I'd like to perform an ordered probit analysis such that we allow for random effects pertaining to individuals and the organisations they work for.

7. -----------------------------------------------------------------------------
Random Coefficients  OrdProbs Model
Dependent variable                 HSAT
Log likelihood function    
Estimation based on N =    947, K =  14
Inf.Cr.AIC  =   AIC/N =    3.951
Unbalanced panel has    250 individuals
Ordered probit (normal) model
LHS variable = values 0,1,...,10
Simulation based on    200 Halton draws
        |                  Standard            Prob.      95% Confidence
    HSAT|  Coefficient       Error       z    |z|>Z*         Interval
        |Nonrandom parameters
Constant|    ***          16.05  .0000       
     AGE|    ***           .0000       
    EDUC|     ***           4.33  .0000         
        |Scale parameters for dists. of random parameters
Constant|    ***          27.57  .0000        
        |Standard Deviations of Random Effects
R.E.(01)|     *             1.71  .0877        
        |Threshold parameters for probabilities
  Mu(01)|     **            2.53  .0113         
  ...
Mu(09)|    ***          39.20  .0000       

8. Agenda Single equation instrumental variable estimation Panel data
Exogeneity
Instrumental Variable (IV) Estimation
Two Stage Least Squares (2SLS)
Generalized Method of Moments (GMM)
Panel data
Fixed effects
Hausman and Taylor’s formulation
Application
Arellano/Bond/Bover framework

9. Structure and Regression

10. Exogeneity

11. An Experimental Treatment Effect

12. Instrumental Variables
Instrumental variable associated with changes in x, not with ε
dy/dx = β dx/dx + dε /dx = β + dε /dx. Second term is not 0.
dy/dz = β dx/dz + dε /dz. The second term is 0.
β =cov(y,z)/cov(x,z) This is the “IV estimator”
Example: Corporate earnings in year t Earnings(t) = β R&D(t) + ε(t) R&D(t) responds directly to Earnings(t) thus ε(t) A likely valid instrumental variable would be R&D(t-1) which probably does not respond to current year shocks to earnings.

13. Least Squares

14. The IV Estimator

15. A Moment Based Estimator

16. Cornwell and Rupert Data
Cornwell and Rupert Returns to Schooling Data, 595 Individuals, 7 Years Variables in the file are
EXP = work experience, EXPSQ = EXP2 WKS = weeks worked 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 FEM = 1 if female UNION = 1 if wage set by unioin contract ED = years of education LWAGE = log of wage = dependent variable in regressions
These data were analyzed in Cornwell, C. and Rupert, P., "Efficient Estimation with Panel Data: An Empirical Comparison of Instrumental Variable Estimators," Journal of Applied Econometrics, 3, 1988, pp  See Baltagi, page 122 for further analysis.  The data were downloaded from the website for Baltagi's text.

17. Wage Equation with Endogenous Weeks
logWage=β1+ β2 Exp + β3 ExpSq + β4OCC + β5 South + β6 SMSA + β7 WKS + ε
Weeks worked is believed to be endogenous in this equation.
We use the Marital Status dummy variable MS as an exogenous variable.
Wooldridge Condition (5.3) Cov[MS, ε] = 0 is assumed.
Auxiliary regression: For MS to be a ‘valid’ instrumental variable,
In the regression of WKS on [1,EXP,EXPSQ,OCC,South,SMSA,MS, ]
MS significantly “explains” WKS.
A projection interpretation: In the projection
XitK =θ1 x1it + θ2 x2it + … + θK-1 xK-1,it + θK zit , θK ≠ 0.
(One normally doesn’t “check” the variables in this fashion.

18. Auxiliary Projection
| Ordinary least squares regression |
| LHS=WKS Mean = |
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
Constant
EXP
EXPSQ
OCC
SOUTH
SMSA MS

19. Application: IV for WKS in Rupert
| Ordinary least squares regression |
| Residuals Sum of squares = |
| Fit R-squared = |
| Adjusted R-squared = |
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] |
Constant
EXP
EXPSQ D
OCC
SOUTH
SMSA
WKS

20. Application: IV for wks in Rupert
| LHS=LWAGE Mean = |
| Standard deviation = |
| Residuals Sum of squares = |
| Standard error of e = |
| Fit R-squared = |
| Adjusted R-squared = |
| Not using OLS or no constant. Rsqd & F may be < 0. |
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] |
Constant
EXP
EXPSQ D
OCC
SOUTH
SMSA
WKS
OLS
WKS

21. Generalizing the IV Estimator-1

22. Generalizing the IV Estimator - 2

23. Generalizing the IV Estimator

24. The Best Set of Instruments

25. Two Stage Least Squares

26. 2SLS Estimator

27. 2SLS Algebra

28. A General Result for IV
We defined a class of IV estimators by the set of variables
The minimum variance (most efficient) member in this class is 2SLS (Brundy and Jorgenson(1971)) (rediscovered JW, 2000, p )

29. GMM Estimation – Orthogonality Conditions

30. GMM Estimation - 1

31. GMM Estimation - 2

32. IV Estimation

33. An Optimal Weighting Matrix

34. The GMM Estimator

35. GMM Estimation

36. Application - GMM NAMELIST ; x = one,exp,expsq,occ,south,smsa,wks$
NAMELIST ; z = one,exp,expsq,occ,south,smsa,ms,union,ed$
2SLS ; lhs = lwage ; RHS = X ; INST = Z $
NLSQ ; fcn = lwage-b1'x
; labels = b1,b2,b3,b4,b5,b6,b7
; start = b
; inst = Z
; pds = 0$

37. Application - 2SLS

38. GMM Estimates

39. 2SLS
GMM with Heteroscedasticity

40. Testing the Overidentifying Restrictions

41. Inference About the Parameters

42. Specification Test Based on the Criterion

43. Extending the Form of the GMM Estimator to Nonlinear Models

44. A Nonlinear Conditional Mean

45. Nonlinear Regression/GMM
NAMELIST ; x = one,exp,expsq,occ,south,smsa,wks$
NAMELIST ; z = one,exp,expsq,occ,south,smsa,ms,union,ed$
? Get initial values to use for optimal weighting matrix NLSQ ; lhs = lwage ; fcn=exp(b1'x) ; inst = z
; labels=b1,b2,b3,b4,b5,b6,b7 ; start=7_0$
? GMM using previous estimates to compute weighting matrix
NLSQ (GMM) ; fcn = lwage-exp(b1'x) ; inst = Z
; labels = b1,b2,b3,b4,b5,b6,b7 ; start = b
; pds = 0 $ (Means use White style estimator)

46. Nonlinear Wage Equation Estimates NLSQ Initial Values

47. Nonlinear Wage Equation Estimates 2nd Step GMM

48. IV for Panel Data