Economics 310

Lecture 11Dummy variables and Varying

Parameters models

Multiple dummy variables

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More than one Qualitative Variable

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Testing for Structural StabilityChow-Test

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Dummy variables and heteroscedasticity To do the Chow test, we must assume

that the variance of the disturbance in each regression is same.

This holds for dummy variable test for structural change. We can’t have heteroscedasticity.

Can test this assumption with F-test.

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Piecewise Linear Regression

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Piecewise Linear Regression

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Sample data for Piecewise regression

D D*(Output-50) Output Cost0 0 11.90594 24.264041 6.431719981 56.43172 127.47890 0 37.05464 80.300880 0 34.72284 70.062820 0 34.10817 74.702631 47.47867085 97.47867 269.35941 9.159162062 59.15916 133.80120 0 23.26331 52.236751 40.11877492 90.11877 243.41511 27.62116352 77.62116 202.21690 0 38.57961 80.12890 0 11.50201 28.551891 32.33868592 82.33869 219.37531 19.36715023 69.36715 171.53351 25.9150599 75.91506 198.81251 32.93600216 82.936 217.55930 0 35.60991 75.342690 0 46.10208 100.09411 39.64945331 89.64945 241.9891 18.41368224 68.41368 170.4956

Results of Piecewise Regression

SUMMARY OUTPUT

Regression StatisticsMultiple R 0.998R Square 0.996Adjusted R Square 0.996Standard Error 6.179Observations 20

ANOVAdf SS MS F Significance F

Regression 2 170903.2 85451.6 2238.0 0.0Residual 17 649.1 38.2Total 19 171552.3

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%Intercept 3.409 3.164 1.077 0.296 -3.266 10.084D*(Output-50) 1.873 0.192 9.754 0.000 1.468 2.278Output 2.016 0.101 19.914 0.000 1.802 2.230

Interpretation of dummy variable in semi-log regression

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Semi-log ExampleSUMMARY OUTPUT

Regression StatisticsMultiple R 0.824525R Square 0.6798415Adjusted R Square 0.6594059Standard Error 0.0926684Observations 51

ANOVAdf SS MS F Significance F

Regression 3 0.857045296 0.285682 33.26743 1.09956E-11Residual 47 0.40360922 0.008587Total 50 1.260654516

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%Intercept 9.6243101 0.054469323 176.6923 5.29E-68 9.514732087 9.733888south 0.0118063 0.031304883 0.377139 0.707768 -0.05117096 0.074784west 0.063115 0.032704045 1.929885 0.059669 -0.00267696 0.128907spend 0.0001199 1.29663E-05 9.248157 3.75E-12 9.38294E-05 0.000146

Interpretation of Coefficients

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