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Ramb&Reitzig – Non Linear Functions in Panel Data Models Non Linear Functions in Panel Data Models - Algorithm Using Stata Presentation at the Stata User Group Meeting in Berlin 8. April 2005 Fred Ramb and Markus Reitzig

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Ramb&Reitzig – Non Linear Functions in Panel Data Models Theoretical models often are nonlinear e.g. in economics the well known q-model Micro panel data NLLS estimator is biased Fixed effects estimator is efficient Standard software package is not available Overview

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Ramb&Reitzig – Non Linear Functions in Panel Data Models Motivation Theory q Model Linearized Fixed Effects Estimator Stata Code Pooled Cross Sectional Nonlinear Least Squares Panel Data Random Effects and Fixed Effects Empirical Results Summary Overview

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Ramb&Reitzig – Non Linear Functions in Panel Data Models Cobb-Douglas Production function Theory (I): q Model Logarithmic transformation With for small x:

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Ramb&Reitzig – Non Linear Functions in Panel Data Models Theory (II): Algorithm with: Logarithmic transformation With for larger x, linearized version is estimated:

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Ramb&Reitzig – Non Linear Functions in Panel Data Models program nlacc if "`1'" =="?" { global S_1 "B_0 X1 C1 C2 C3 T1 T2 T3 T4 T5" global B_0= 0 global X1= 0 global C1= 0 global C2= 0 global C3= 0 global T1= 0 global T2= 0 global T3= 0 global T4= 0 global T5= 0 exit } replace `1'=$B_0 + ln(1+($X1*x2)) + $C1*control1+$C2*control2 + $C3*control3 /* */ + $T1*dyear1 + $T3*dyear2 + $T3*dyear3 + $T4*dyear4 + $T5*dyear5 end nl acc y Stata Code: NLLS

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Ramb&Reitzig – Non Linear Functions in Panel Data Models xtreg y x control1 control2 time*, fe Stata Code: Fixed Effects gen ex = _b[x] gen y_s = y - (log(1+ex*x)) gen x_s = x / (1+ (ex*x)) log off local i=1 while `i' < 50 { quietly xtreg y_s x_s control1 control2 time*, fe quietly replace ex = ex + _b[x_s] quietly replace y_s = y - (log(1+ex*x)) quietly replace x_s = x2 / (1+ (ex*x)) local i = `i' + 1 } log on replace y_s = y - (log(1+ex*x)) + (ex*(x / (1+ (ex*x)))) xtreg y_s x_s control1 control2 time*, fe

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Ramb&Reitzig – Non Linear Functions in Panel Data Models xtreg y x control1 control2 time*, re gen exr = _b[x] gen y_sr = y - (log(1+exr*x)) gen x_sr = x / (1+ (exr*x) log off local i=1 while `i' < 50 { quietly replace exr = exr + _b[x_sr] quietly replace y_sr = y-(log(1+exr*x)) quietly replace x_sr = x / (1+ (exr*x)) quietly xtreg y_sr x_sr control1 control2 time*, re local i = `i' + 1 } log on replace y_sr = y-(log(1+exr*x)) + (exr*(x / (1+ (exr*x)))) xtreg y_sr x_sr control1 control2 time*, re xttest0 Stata Code: Random Effects

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Ramb&Reitzig – Non Linear Functions in Panel Data Models xtreg y_s x_s control1 control2 time*, fe est store fixed xtreg y_sr x_sr control1 control2 time*, re hausman fixed Stata Code: Hausman Test

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Ramb&Reitzig – Non Linear Functions in Panel Data Models Empirical Results: Dataset Sources Hoppenstedt: accounting data Datastream: stock market data Sample 1997-2003 Consolidated financial statements Manufacturing sector Estimation Sample 2,786 observations / 676 firms (Overall) 1,463 observations / 325 firms (HGB) 532 observations / 139 firms (IAS) 791 observations / 212 firms ( US-GAAP)

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Ramb&Reitzig – Non Linear Functions in Panel Data Models Empirical Results: Example 1

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Ramb&Reitzig – Non Linear Functions in Panel Data Models Empirical Results: Example 2

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Ramb&Reitzig – Non Linear Functions in Panel Data Models Pros Different results by estimating pooled cross sectional nonlinear least squares on the one hand and by estimating fixed effects using the algorithm on the other hand. Results using the algorithm are more efficient Summary Cons Do-File is limited to the q-model Heteroskedasticity? Robust estimation is necessary Local or global maximum? Bootstrap is necessary Dynamics? GMM is necessary

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Ramb&Reitzig – Non Linear Functions in Panel Data Models Thank you for your attention

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Ramb&Reitzig – Non Linear Functions in Panel Data Models Appendix (I)

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Ramb&Reitzig – Non Linear Functions in Panel Data Models

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Appendix (III)

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1 FE Panel Data assumptions. 2 Assumption #1: E(u it |X i1,…,X iT, i ) = 0.

1 FE Panel Data assumptions. 2 Assumption #1: E(u it |X i1,…,X iT, i ) = 0.

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