Kalyn LeBlanc ECO-6255-1 Problem Set14.
1, 14.2,14.3, E14.
1, E14.2, & E14.3 14.1: The following two equationsdescribe property crime and police expenditures across U.S. cities: Consistency ofOLS Sample and meanparameter to be consistent because increase in no income, increase in nocrime, increase in police expenditure, and increase in liberal is positivelyrelated. 2SLS Consider If isa linear function of itviolates the OLS estimator, it is biased we can consider age of people as andindependent variable.
14.2:A public health researcher is trying to estimate the determinants of fertilityrates in developing countries. She proposes the following model: 1. The simultaneity bias causes theestimates of B to no longer be consistent or efficient. In the case when OLSestimates are no longer blue the preferred use of measure is induced leastsquare theory of estimation or ILS.2. Measurement error will decrease theefficiency of the estimate by increasing the estimates variance this can beminimized by selection of time, using accurate samples, accurate questionnaire,and awareness of all factors affecting the variables under consideration.
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3. The consequences of measurement error inthis current problem are increased estimated variance and increased probabilityof type 1 error. 14.3: The following two equationsdescribe the interactions between fertility rates and average income of womenin a cross-section of countries: 1. SubstituteFertility Incomeiis a linear function of this will be correlated with . This violates the model assumptions andthe OLS estimator will be biased.
Anassumption of OLS regression is independent variables are not stronglycorrelated, income and education are independent variables of the firstequation, fertility and education are independent in second equation. This is anot a good model or parameter estimate would not be consistent. 2. Educationi and Rurali are predeterminedvariables in the system Slopecoefficient in equation one = 3Slopecoefficient in equation two = 2 Numberof slope coefficients in equation one is greater than the total number ofpredetermined variables in the system it is not exactly identified.Numberof slope coefficients in equation two is the same as the total number ofpredetermined variables in the system it is exactly identified. 3. 4.
ifwe find variable Zi the equation will be written Estimateequation OLS, GDP and Education are exogenous Thisestimates will not be biased the two conditions Zi must satisfy Corrected(GDPi,Fertilityi) = 0Corrected(GDPi,Incomei) <> 0 Assumptions:GDPiand Fertilityi correlation is 0GDPiand Income correlation is not 0 E14.1: Use the data in Education.xls torun an instrumental variable regression. 1. General Regression Analysis Logwage = 10.3677 +0.0160087 Experience + 0.009419 Occupation-0.
0123508 + Industry + 0.00138175 Married – 0.0240935 Union + 0.047123 Education – 0.
0030976 Black Coefficients Term Coefficient SE Coefficient T P Constant 10.3677 0.103125 100.535 0 Experience 0.016 0.001487 10.767 0 Occupation 0.0094 0.
040337 0.234 0.816 Industry -0.0124 0.035292 -0.35 0.727 Married 0.
0014 0.025613 0.054 0.957 Union -0.0241 0.033444 -0.
72 0.472 Education 0.0471 0.007838 6.012 0 Black -0.0031 0.
03154 -0.098 0.922 Logwage=10.3677+0.0160087Experience + 0.009419Occupation – 0.
0123508Industry + 0.00138175Married – 0.0240935Union + 0.047123Education – 0.
0030976Black 2. General Regression Analysis Logwage = 11.9946 +0.
0226049 Experience – 0.0697049 Occupation + 0.0508124 Industry + 0.0463796 Married – 0.057606 Union – 0.081351 FITS1 – 0.0200051 Black Coefficients Term Coefficient SE Coefficient T P Constant 11.
9946 1.28376 9.34338 0 Experience 0.0226 0.
00543 4.15965 0 Occupation -0.0697 0.
07628 -0.91383 0.362 Industry 0.0508 0.06291 0.
80767 0.42 Married 0.0464 0.
04514 1.02753 0.306 Union -0.0576 0.04511 -1.
27709 0.203 Education -0.0814 0.10135 -0.80269 0.423 Black -0.
02 0.037 -0.54066 0.589 Summary of Model S = 0.184062 R-Sq = 47.99% R-Sq (adj) = 45.
94% PRESS = 6.58590 R-Sq (pred) = 43.20% Logwage = 11.9946 + 0.026049Experience – 0.
0697049Occupation + 0.050812Industry + 0.0463796Married – 0.
057606Union – 0.081351FITS1 – 0.0200051Black 3.
Concluding, whenintroduction a new variable the education variable becomes insignificant andthe standard error also increases. It can be concluded that the dummy variableis not a valid instrument variable since dummy variable is uncorrelated withyears of education and correlated with the error term in the regression of parta. E14.2: Use the data in Demand.xls to runan instrumental variable regression. 1. RegressionEquation: 2. SUMMARY OUTPUT Regression Statistics Multiple R 0.
058326856 R Square 0.003402022 Adjusted R Square 0.000344973 Standard Error 0.57485567 Observations 328 ANOVA df SS MS F Significance F Regression 1 0.367749736 0.
367749736 1.112845133 0.292245496 Residual 326 107.7296475 0.330459041 Total 327 108.0973973 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.
0% Intercept 2.949777668 0.184926156 15.95111112 9.65337E-43 2.585978447 3.313576889 2.
585978447 X Variable 1 -0.013551115 0.012845696 -1.054914751 0.
292245496 -0.038822036 0.011719807 -0.038822036 E14.
3: Use the data in MeasurementError.xls to correct for measurement error. 1.
SUMMARY OUTPUT Regression Statistics Multiple R 0.16589325 R Square 0.02752057 Adjusted R Square 0.022235356 Standard Error 8.936851618 Observations 186 ANOVA df SS MS F Significance F Regression 7 6.
563684 0.937669 33.17884 3.
10255xE-29 Residual 178 5.030772 0.028263 Total 185 11.59446 Coefficients Standard Error t Stat P-value Lower 95% Intercept 10.36773 0.103125 100.
5355 9.50E-15 10.16422708 Experience 0.016009 0.001487 10.
76713 3.87E-21 0.01307465 Occupation 0.009419 0.
040337 0.23351 0.815634 -0.070180548 Industry -0.01235 0.035292 0.34996 0.
726783 -0.081995368 Married 0.001382 0.025613 0.053948 0.
957037 -0.049161513 Union -0.02409 0.033444 -0.
72041 0.47222 -0.090091863 Education 0.047123 0.007838 6.011812 1.01E-08 0.
031654871 Black -0.0031 0.03154 -0.09821 0.921876 -0.06533871 Estimated regressionmodel on experience, occupation, industry, union, education, and black is 2. EstimatedRegression model of spouse experience on other independent variables is Predicted value= Predicted valuefor experience, education, occupation, industry, married, union, and black
