Part 4A: GMM-MDE[ 1/33] Econometric Analysis of Panel Data William Greene Department of Economics Stern School of Business

Part 4A: GMM-MDE[ 2/33] Chamberlain’s Model and Minimum Distance Estimation  Chamberlain (1984) “Panel Data,” Handbook of Econometrics  Innovation: treat the panel as a system of equations: SUR Models, See Wooldridge, Ch. 7 through p  Assumptions: Balanced panel Minimal restrictions on variances and covariances of disturbances (zero means, finite fourth moments)  Model the correlation between effects and regressors

Part 4A: GMM-MDE[ 3/33] Chamberlain (2)

Part 4A: GMM-MDE[ 4/33] Chamberlain (3) - Data

Part 4A: GMM-MDE[ 5/33] Chamberlain (4) Model

Part 4A: GMM-MDE[ 6/33] Chamberlain (5) SUR Model

Part 4A: GMM-MDE[ 7/33] Chamberlain (6)

Part 4A: GMM-MDE[ 8/33] Chamberlain (7) Estimation of Σ

Part 4A: GMM-MDE[ 9/33] Chamberlain (8) Estimation of Π  FGLS. Use the usual two step GLS estimator.  OLS. System has an unrestricted covariance matrix and the same regressors in every equation. GLS = FGLS = equation by equation OLS. Denote the T OLS coefficient vectors as P = [p 1, p 2, p 3 …, p T ]. Unconstrained OLS will be consistent. Plim p t = π t, t=1,…,T OLS is inefficient. There are T(T-1) different estimates of  in P and T-1 estimates of each δ t.

Part 4A: GMM-MDE[ 10/33] Chamberlain Estimator: Application Cornwell and Rupert: Lwage it = α i + β 1 Exp it + β 2 Exp it 2 + β 3 Wks it + ε it α i projected onto all 7 periods of Exp, Exp 2 and Wks. For each of the 7 years, we regress Lwage it on a constant and the three variables for all 7 years. Each regression has 22 coefficients.

Part 4A: GMM-MDE[ 11/33] Chamberlain Estimator

Part 4A: GMM-MDE[ 12/33] Efficient Estimation of Π  Minimum Distance Estimation: Chamberlain (1984). (See Wooldridge, pp ) Asymptotically efficient Assumes only finite fourth moments of v it  Maximum likelihood Estimation: Joreskog (1981), Greene (1981,2008) Add normality assumption Identical asymptotic properties as MDE (!)  Which is more convenient?

Part 4A: GMM-MDE[ 13/33] MDE-1 Cornwell and Rupert. Pooled, 7 years |Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X| Constant| EXP | EXPSQ | D WKS | OCC | IND | SOUTH | SMSA | MS | FEM | UNION | ED |

Part 4A: GMM-MDE[ 14/33] MDE-2 Cornwell and Rupert. Year |Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X| Constant| EXP | EXPSQ | WKS | OCC | IND | SOUTH | SMSA | MS | FEM | UNION | ED |

Part 4A: GMM-MDE[ 15/33] MDE-3 Cornwell and Rupert. Year |Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X| Constant| EXP | EXPSQ | WKS | OCC | IND | SOUTH | SMSA | MS | FEM | UNION | ED |

Part 4A: GMM-MDE[ 16/33] MDE-4

Part 4A: GMM-MDE[ 17/33] MDE-5

Part 4A: GMM-MDE[ 18/33] MDE-6

Part 4A: GMM-MDE[ 19/33] MDE-7 S 11 S 21 S 12 S 22

Part 4A: GMM-MDE[ 20/33] MDE-8

Part 4A: GMM-MDE[ 21/33] MDE-9

Part 4A: GMM-MDE[ 22/33] Minimum Distance Estimation

Part 4A: GMM-MDE[ 23/33] Carey Hospital Cost Model

Part 4A: GMM-MDE[ 24/33] Multiple Estimates (25) of 10 Structural Parameters

Part 4A: GMM-MDE[ 25/33] Appendix I. Chamberlain Model Algebra

Part 4A: GMM-MDE[ 26/33] MDE (2)

Part 4A: GMM-MDE[ 27/33] MDE (3)

Part 4A: GMM-MDE[ 28/33] Maximum Likelihood Estimation

Part 4A: GMM-MDE[ 29/33] MLE (2)

Part 4A: GMM-MDE[ 30/33] Rearrange the Panel Data

Part 4A: GMM-MDE[ 31/33] Generalized Regression Model

Part 4A: GMM-MDE[ 32/33] Least Squares

Part 4A: GMM-MDE[ 33/33] GLS and FGLS