Kalyn people as and independent variable. 14.2: A

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