Part 11: Heterogeneity [ 1/36] Econometric Analysis of Panel Data William Greene Department of Economics Stern School of Business

Part 11: Heterogeneity [ 2/36] Agenda  Random Parameter Models Fixed effects Random effects  Heterogeneity in Dynamic Panels  Random Coefficient Vectors-Classical vs. Bayesian  General RPM Swamy/Hsiao/Hildreth/Houck  Hierarchical and “Two Step” Models  ‘True’ Random Parameter Variation Discrete – Latent Class Continuous  Classical  Bayesian

Part 11: Heterogeneity [ 3/36] A Capital Asset Pricing Model

Part 11: Heterogeneity [ 4/36] Heterogeneous Production Model

Part 11: Heterogeneity [ 5/36] Parameter Heterogeneity

Part 11: Heterogeneity [ 6/36] Parameter Heterogeneity

Part 11: Heterogeneity [ 7/36] Fixed Effects (Hildreth, Houck, Hsiao, Swamy)

Part 11: Heterogeneity [ 8/36] OLS and GLS Are Inconsistent

Part 11: Heterogeneity [ 9/36] Estimating the Fixed Effects Model

Part 11: Heterogeneity [ 10/36] Partial Fixed Effects Model

Part 11: Heterogeneity [ 11/36] Heterogeneous Dynamic Models

Part 11: Heterogeneity [ 12/36] Random Effects and Random Parameters

Part 11: Heterogeneity [ 13/36] Estimating the Random Parameters Model

Part 11: Heterogeneity [ 14/36] Estimating the Random Parameters Model by OLS

Part 11: Heterogeneity [ 15/36] Estimating the Random Parameters Model by GLS

Part 11: Heterogeneity [ 16/36] Estimating the RPM

Part 11: Heterogeneity [ 17/36] An Estimator for Γ

Part 11: Heterogeneity [ 18/36] A Positive Definite Estimator for Γ

Part 11: Heterogeneity [ 19/36] Estimating β i

Part 11: Heterogeneity [ 20/36] Baltagi and Griffin’s Gasoline Data World Gasoline Demand Data, 18 OECD Countries, 19 years Variables in the file are COUNTRY = name of country YEAR = year, LGASPCAR = log of consumption per car LINCOMEP = log of per capita income LRPMG = log of real price of gasoline LCARPCAP = log of per capita number of cars See Baltagi (2001, p. 24) for analysis of these data. The article on which the analysis is based is Baltagi, B. and Griffin, J., "Gasoline Demand in the OECD: An Application of Pooling and Testing Procedures," European Economic Review, 22, 1983, pp The data were downloaded from the website for Baltagi's text.

Part 11: Heterogeneity [ 21/36] OLS and FGLS Estimates | Overall OLS results for pooled sample. | | Residuals Sum of squares = | | Standard error of e = | | Fit R-squared = | |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Constant LINCOMEP LRPMG LCARPCAP | Random Coefficients Model | | Residual standard deviation =.3498 | | R squared =.5976 | | Chi-squared for homogeneity test = | | Degrees of freedom = 68 | | Probability value for chi-squared= | |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | CONSTANT LINCOMEP LRPMG LCARPCAP

Part 11: Heterogeneity [ 22/36] Country Specific Estimates

Part 11: Heterogeneity [ 23/36] Estimated Γ

Part 11: Heterogeneity [ 24/36] Two Step Estimation (Saxonhouse)

Part 11: Heterogeneity [ 25/36] A Hierarchical Model

Part 11: Heterogeneity [ 26/36] Analysis of Fannie Mae  Fannie Mae  The Funding Advantage  The Pass Through Passmore, W., Sherlund, S., Burgess, G., “The Effect of Housing Government-Sponsored Enterprises on Mortgage Rates,” 2005, Federal Reserve Board and Real Estate Economics

Part 11: Heterogeneity [ 27/36] Two Step Analysis of Fannie-Mae

Part 11: Heterogeneity [ 28/36] Average of 370 First Step Regressions SymbolVariableMeanS.D.CoeffS.E. RMRate % JJumbo LTV175%-80% LTV281%-90% LTV3>90% NewNew Home Small< $100, FeesFees paid MtgCoMtg. Co R 2 = 0.77

Part 11: Heterogeneity [ 29/36] Second Step

Part 11: Heterogeneity [ 30/36] Estimates of β 1

Part 11: Heterogeneity [ 31/36] A Hierarchical Linear Model German Health Data Hsat = β 1 + β 2 AGE it + γ i EDUC it + β 4 MARRIED it + ε it γ i = α 1 + α 2 FEMALE i + u i Sample ; all$ Reject ; _Groupti < 7 $ Regress ; Lhs = newhsat ; Rhs = one,age,educ,married ; RPM = female ; Fcn = educ(n) ; pts = 25 ; halton ; pds = _groupti ; Parameters$ Sample ; 1 – 887 $ Create ; betaeduc = beta_i $ Dstat ; rhs = betaeduc $ Histogram ; Rhs = betaeduc $

Part 11: Heterogeneity [ 32/36] OLS Results OLS Starting values for random parameters model... Ordinary least squares regression LHS=NEWHSAT Mean = Standard deviation = Number of observs. = 6209 Model size Parameters = 4 Degrees of freedom = 6205 Residuals Sum of squares = Standard error of e = Fit R-squared = Adjusted R-squared = Model test F[ 3, 6205] (prob) = 142.0(.0000) | Standard Prob. Mean NEWHSAT| Coefficient Error z z>|Z| of X Constant| *** AGE| *** MARRIED|.29664*** EDUC|.14464***

Part 11: Heterogeneity [ 33/36] Maximum Simulated Likelihood Normal exit: 27 iterations. Status=0. F= Random Coefficients LinearRg Model Dependent variable NEWHSAT Log likelihood function Estimation based on N = 6209, K = 7 Unbalanced panel has 887 individuals LINEAR regression model Simulation based on 25 Halton draws | Standard Prob. Mean NEWHSAT| Coefficient Error z z>|Z| of X |Nonrandom parameters Constant| *** AGE| *** MARRIED|.23427*** |Means for random parameters EDUC|.16580*** |Scale parameters for dists. of random parameters EDUC| *** |Heterogeneity in the means of random parameters cEDU_FEM| *** |Variance parameter given is sigma Std.Dev.| ***

Part 11: Heterogeneity [ 34/36] “Individual Coefficients” --> Sample ; $ --> create ; betaeduc = beta_i $ --> dstat ; rhs = betaeduc $ Descriptive Statistics All results based on nonmissing observations. ============================================================================== Variable Mean Std.Dev. Minimum Maximum Cases Missing ============================================================================== All observations in current sample BETAEDUC|

Part 11: Heterogeneity [ 35/36] A Hierarchical Linear Model  A hedonic model of house values  Beron, K., Murdoch, J., Thayer, M., “Hierarchical Linear Models with Application to Air Pollution in the South Coast Air Basin,” American Journal of Agricultural Economics, 81, 5, 1999.

Part 11: Heterogeneity [ 36/36] HLM