Statistical and Econometric Methods for Transportation Data Analysis

Transcription

1 Statistical and Econometric Methods for Transportation Data Analysis Chapter 5 Simultaneous-Equation Models Example 5.2 (with 3SLS Extensions) Using 2017 USF Survey data Seemingly Unrelated Regression Estimation and 3SLS A survey of 226 people was conducted at the University of South Florida in the Fall of One element of the survey was to find out how fast people drove on interstate highways with speed limits of 55 mph, 65 mph and 70 mph. Your task is to first estimate a seemingly unrelated regression model to determine the normal driving speed of individuals in this data sample. The equation system: Speed = β Z + α X + ε Speed = β Z + α X + ε Speed = β Z + α X + ε In these equations, Speed70, Speed65 and Speed55 are the number of miles per hour respondents normally drive above the speed limit (with little traffic) for 70, 65, and 55 mph speed limits, respectively. These variables can take on positive values if respondents normally drive above the speed limit and negative values if they normally drive below it. Also in these equations, Z is a vector of driver and driver-household characteristics, X is a vector of vector of driver preferences and opinions, β's, α's, are vectors of estimable parameters, and ε's are disturbance terms. Next, estimate the same modeling system using three-stage least squares (3SLS), that is: Speed = λ Speed + β Z + α X + ε Speed = λ Speed + λ Speed + β Z + α X + ε Speed = λ Speed + β Z + α X + ε Then, provide a write up to inlcude: 1. The results of your best model specification. 2. A discussion of the logical process that led you to the selection of your final specification (the theory behind the inclusion of your selected variables). Include t-statistics and justify the signs of your variables.

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4 -> read;nvar=39;nobs=226;file=u:\00work-purdue\new_laptop\cgn6933\srv17.txt$ -> skip -> reject;x39=1$ -> create;agel=x25-x38$ -> create;if(agel>17)late=1$ -> create;if(x23=2)male=1$ -> create;if(x24=1)married=1$ -> create;mo70=x1-70$ -> create;mo65=x2-65$ -> create;mo55=x3-55$ -> dstat;rhs=mo70,mo65,mo55$ - Standard Missing Variable Mean Deviation Minimum Maximum Cases Values - MO MO MO Descriptive Statistics for 3 variables DSTAT results are matrix LASTDSTA in current project. -> reject;x1=-999$ -> reject;x2=-999$ -> reject;x3=-999$ -> reject;x25=-999$ -> reject;x38=-999$ -> reject;x23=-999$ -> reject;x37=2$ -> Sure;lhs=mo70,mo65,mo55 ;eq1=one,x25,x32,late,x33 ;eq2=one,male,x25,x32,late,x33 ;eq3=one,x36,late,x33$ Deleted 2 observations with missing data. N is now 202 Criterion function for GLS is log-likelihood. Iteration 0, GLS = Iteration 1, GLS = Iteration 2, GLS = Iteration 3, GLS = Iteration 4, GLS = GLS has converged. Estimates for equation: MO70... Generalized least squares regression... LHS=MO70 Mean = Standard deviation = Number of observs. = 202 Model size Parameters = 5 Degrees of freedom = 197 Residuals Sum of squares = Standard error of e = Fit R-squared = Adjusted R-squared = Model test F[ 4, 197] (prob) = 1.1(.3424) Log W Log-Likelihood = Durbin-Watson Autocorrelation =.2139

5 MO70 Coefficient Error z z >Z* Interval Constant *** X X LATE * X Estimates for equation: MO65... Generalized least squares regression... LHS=MO65 Mean = Standard deviation = Number of observs. = 202 Model size Parameters = 6 Degrees of freedom = 196 Residuals Sum of squares = Standard error of e = Fit R-squared = Adjusted R-squared = Model test F[ 5, 196] (prob) = 2.4(.0423) Log W Log-Likelihood = Durbin-Watson Autocorrelation =.1557 MO65 Coefficient Error z z >Z* Interval Constant *** MALE X X LATE ** X Estimates for equation: MO55... Generalized least squares regression... LHS=MO55 Mean = Standard deviation = Number of observs. = 202 Model size Parameters = 4 Degrees of freedom = 198 Residuals Sum of squares = Standard error of e = Fit R-squared = Adjusted R-squared = Model test F[ 3, 198] (prob) = 3.2(.0236) Log W Log-Likelihood = Durbin-Watson Autocorrelation =.1162

6 MO55 Coefficient Error z z >Z* Interval Constant *** X LATE *** X > 3sls;lhs=mo70,mo65,mo55 ;eq1=one,mo65, x25,x32,late,x33 ;eq2=one,mo70,mo55,male,x25,x32,late ;eq3=one,mo65,x36,late,x33 ;Inst=male,married,late,x25,x30,x31,x32,x33,x34,x35,x36,x37,x38 ;maxit=1$ Deleted 4 observations with missing data. N is now 200 Criterion function is max(abs(%chg in b(i))). Iteration 0, 3SLS = Iteration 1, 3SLS = Estimates for equation: MO70... InstVar/GLS least squares regression... LHS=MO70 Mean = Standard deviation = Number of observs. = 200 Model size Parameters = 6 Degrees of freedom = 194 Residuals Sum of squares = Standard error of e = Fit R-squared = Adjusted R-squared = Model test F[ 5, 194] (prob) = 143.1(.0000) Durbin-Watson Autocorrelation =.0879 MO70 Coefficient Error z z >Z* Interval Constant MO *** X X LATE X

7 Estimates for equation: MO65... InstVar/GLS least squares regression... LHS=MO65 Mean = Standard deviation = Number of observs. = 200 Model size Parameters = 7 Degrees of freedom = 193 Residuals Sum of squares = Standard error of e = Fit R-squared = Adjusted R-squared = Model test F[ 6, 193] (prob) = 155.5(.0000) Durbin-Watson Autocorrelation =.0040 MO65 Coefficient Error z z >Z* Interval Constant MO *** MO *** MALE X X LATE Estimates for equation: MO55... InstVar/GLS least squares regression... LHS=MO55 Mean = Standard deviation = Number of observs. = 200 Model size Parameters = 5 Degrees of freedom = 195 Residuals Sum of squares = Standard error of e = Fit R-squared = Adjusted R-squared = Model test F[ 4, 195] (prob) = 98.9(.0000) Durbin-Watson Autocorrelation = MO55 Coefficient Error z z >Z* Interval Constant MO *** X LATE X