Kalyn LeBlanc

ECO-625

5-1 Problem Set

14.1, 14.2,

14.3, E14.1, E14.2, & E14.3

14.1: The following two equations

describe property crime and police expenditures across U.S. cities:

Consistency of

OLS

Sample and mean

parameter to be consistent because increase in no income, increase in no

crime, increase in police expenditure, and increase in liberal is positively

related.

2SLS Consider

If is

a linear function of it

violates the OLS estimator, it is biased we can consider age of people as and

independent variable.

14.2:

A public health researcher is trying to estimate the determinants of fertility

rates in developing countries. She proposes the following model:

1. The simultaneity bias causes the

estimates of B to no longer be consistent or efficient. In the case when OLS

estimates are no longer blue the preferred use of measure is induced least

square theory of estimation or ILS.

2. Measurement error will decrease the

efficiency of the estimate by increasing the estimates variance this can be

minimized by selection of time, using accurate samples, accurate questionnaire,

and awareness of all factors affecting the variables under consideration.

3. The consequences of measurement error in

this current problem are increased estimated variance and increased probability

of type 1 error.

14.3: The following two equations

describe the interactions between fertility rates and average income of women

in a cross-section of countries:

1.

Substitute

Fertility

Incomei

is a linear function of this will be correlated with . This violates the model assumptions and

the OLS estimator will be biased.

An

assumption of OLS regression is independent variables are not strongly

correlated, income and education are independent variables of the first

equation, fertility and education are independent in second equation. This is a

not a good model or parameter estimate would not be consistent.

2. Educationi and Rurali are predetermined

variables in the system

Slope

coefficient in equation one = 3

Slope

coefficient in equation two = 2

Number

of slope coefficients in equation one is greater than the total number of

predetermined variables in the system it is not exactly identified.

Number

of slope coefficients in equation two is the same as the total number of

predetermined variables in the system it is exactly identified.

3.

4.

if

we find variable Zi the equation will be written

Estimate

equation OLS, GDP and Education are exogenous

This

estimates will not be biased the two conditions Zi must satisfy

Corrected(GDPi,

Fertilityi) = 0

Corrected(GDPi,

Incomei) 0

Assumptions:

GDPi

and Fertilityi correlation is 0

GDPi

and Income correlation is not 0

E14.1: Use the data in Education.xls to

run 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, when

introduction a new variable the education variable becomes insignificant and

the standard error also increases. It can be concluded that the dummy variable

is not a valid instrument variable since dummy variable is uncorrelated with

years of education and correlated with the error term in the regression of part

a.

E14.2: Use the data in Demand.xls to run

an instrumental variable regression.

1.

Regression

Equation:

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 Measurement

Error.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 regression

model on experience, occupation, industry, union, education, and black is

2.

Estimated

Regression model of spouse experience on other independent variables is

Predicted value

=

Predicted value

for experience, education, occupation, industry, married, union, and black