thurman model 1 cross sectional ecn 405

Elizabeth Thurman ECN 405 2L

Model 1 Paper

Cross Sectional

Introduction:

The cost of housing is an important factor when choosing where to live and also

in considering the economic well-being of a state. High housing costs can be an

indication of higher paying jobs and higher prices in general in a particular area. When

housing prices are increased, it indicates an increased demand for housing in that area.

Often, when prices are high, one must achieve a certain level of education in order to

obtain a high paying job in a high-priced area.

The question I would like to analyze is how personal income affects housing

prices in a state, and also how level of education ties in with level of income to affect

said housing prices. Therefore, in this paper, I will be using personal income and level

of education as my testing variables in a regression analysis to see if the amount of

money a consumer makes, and their level of education will have an effect on the

dependent variable, housing prices.

Also, I will be exploring the impact of income and education on home mortgages

throughout this paper by using five related studies in the form of journal articles. I will

be exploring how each article relates and shapes my model and question. I will then

pose my economic model that I will use to answer my question along with its estimation

and corresponding graphs.

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Further, I will test to see if I have evidence of heteroscedasticity which could

imply that I have a violation of constant variance in my error terms. I will then test for

endogeneity which will allow me to assess whether there is a correlation between an

independent variable and an error term. If the test results show that I do have an

endogenous model, my regression coefficient would cause the model to be biased, and

therefore violating the OLS rules for being the best estimator.

After testing for homoscedasticity and endogeneity, I will do a Ramsey reset test

for zero mean to see if my model is specified correctly, test for normality, and preform a

Wald test. Then, I will perform a final weighted estimation on my variables and then test

a binary model for states west versus east of the Mississippi River.

Review of the literature:

The article by Stephen Malpezzi, "Housing prices, externalities, and regulation in

US metropolitan areas" analyzes the determinants of housing prices which vary widely

across the United States. The study focuses mainly on city and metropolitan areas. It

uses a simple supply and demand framework to assess how regulatory actions effect

housing prices and uses factors such as income and population changes.

This article has helped me to shape my model because of the use of population

and income in relation to housing prices. I have included both as variables in my model

to study their effect. In Malpezzi’s article, I like that he related the housing prices to

metropolitan areas and chose to do my binary testing based on states east and west of

the Mississippi. This is because although both coasts tend to have a relatively large

number of metropolitan areas compared to the “inner states”, the east coast states

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seem to have more populated areas throughout. Highly populated areas tend to have

high demand for housing, thus increasing the prices of homes (or other housing

amenities). This is why I especially wanted to include population; however, I used

population for an entire state which will not give me the more specific relation to housing

prices that I would have liked.

The article "Education and income" by Hendrik S. Houthakker, analyzes income

levels in relation to a person’s level of education. It is performed as a cross sectional

analysis of different age groups across a single year. The article concludes that “capital

values increase uniformly as education increases”. However, it finds that those with

college levels 1-3 do not fare as well as those with only a high school diploma.

This concept led me to use the testing variable ‘level of education’ because those

who afford higher priced homes may be correlated with higher paying jobs which would

most likely require more than a high school diploma. Because the study found a

positive correlation between level of education and level of income, I decided it would

be a reasonable variable to use along with the amount of personal income.

In the article "Valuation of education and crime neighborhood characteristics

through hedonic housing prices" by Robin A. Dubin and Allen C. Goodman, housing

prices are studied as a bundle of neighborhood characteristics. Among the

characteristics in the bundle are those of crime and neighborhood schools. The study

found that housing values were influenced in the Baltimore metropolitan area

significantly when the two variables were studied together.

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This article inspired me to use state crime rates in 2010 to see how it affects the

cost of housing. Because one would intuitively guess that housing prices are cheaper

where there is more crime, I would like to test for a correlation. Many homeowners want

to live in an area where there is low crime not only for the safety of their family and safe

schools, but also for the safety of their belongings. Areas with high breaking and

entering rates may also drive the nearby cost of housing down. However, sometimes it

costs more to live in a city where the crime rates tend to be higher. This is another

reason I would also like to add crime rates as a variable. However, I will be using crime

as the amount of burglaries and will use it as a state data and not specifying it to

suburban, city, or rural housing, although this would be an interesting study.

The article "Housing and income" by Alan R. Winger finds that income and

housing do have a relationship and should involve other factors such as the permanent

income of an individual. In the past, studies have concluded that there is a relationship;

however, the specific factors involved where not clear. The article notes that you must

take into account that the decision to purchase a home was made in the past relative to

when each study is performed. Therefore it is harder to conclude what factors are

considered when a consumer decides to buy their home. The article mentions a paper

by Margaret Reid who studied the effects and also found that there is a strong

correlation between income and the housing market.

Because a strong correlation was found, and the two variables of housing related

to income are widely studied, I was inspired to also test for a correlation between the

two. If I were to analyze a second model, I would include a test for income over a

certain time period to see if it fluctuates with housing prices because income can also

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fluctuate. Thus, what a consumer may be able to afford in one year, may not be true in

the next.

Similarly, in the article, "Housing and permanent income: Tests based on a

three-year re-interview survey” by Lee, Tong Hun, the author points out that as

consumption is tested against income, income is usually tested at a point in time.

Instead, he notes, particularly with the consumption and purchase of mortgage loans

(housing), it is better to test the relationship with a fixed income over time. This is

because purchasing power may fluctuate and although a consumer may be making a lot

in a particular year, they may not make as much in following years and therefore not

affect the mortgage market as greatly.

This article gave some great insight into the notion that it must be kept in mind

we are testing income and housing at one point in time. Although results were found,

indication that income over time is a more accurate measure when related to housing

consumption, I decided to keep my variable of income because I am interested to see if

there is any correlation with housing prices combined with other factors such as the

population’s level of education, level of crime, GDP per capita, etc.

The Model:

Y(House Prices) = B0 + B1(Personal Income) + B2(Level of Education) + B3(State

Taxes) + B4(Unemployment Rate) + B5(GDP) + B6(Population) + B7(Burglary) + U

This is a cross sectional model measuring 2010 data on average housing costs

in relation to income and level of education in each of the 50 states. (Data used can be

found in Appendix A)

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Assumptions about disturbance term:

1. Linearity – The expected value of Y is linearly associated given the X’s. Also, the

average value of the error term is equal to zero given X.

2. Unbiased – Error terms are independent of one another.

3. Homoscedasticity - Constant error variance. This means that the variance of the

errors is the same regardless of X. V(ε|xi)=σε2. The degree of random noise is

the same regardless of the value of the X’s.

4. Mean Independence – The error term is independent of the X variables.

5. Normality – The error terms are normally distributed.

Variables:

House Price Index: This is the dependent variable (Y).

Personal Income per capita: This is a testing independent variable. This should have a

positive effect on housing prices because the greater purchasing power consumers

have, the more housing they will buy, thus increasing demand and therefore pricing of

houses.

Level of Education: This is another testing independent variable. It should have a

positive effect on housing prices. Those who obtain a higher level of education tend to

earn higher income, thus have higher purchasing power driving up demand and prices

of housing.

Total State Taxes: Independent variable. This should have a positive impact on

housing prices. As taxes increase, so do property taxes.

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Unemployment Rate: This is another independent variable. If the unemployment rate is

low, the housing rate may be higher because more people are able to earn a living, thus

driving demand for housing.

GDP per capita: Independent variable. This should have a positive effect on housing

prices. Economically healthy states who have higher GDP may have higher costs of

living due to its many consumers earning a living.

Population: This is an independent variable. The population in a state may cause

higher costs for housing because with more people comes a higher demand for

housing. When supply is limited, and housing demand increases, so must the price.

State Total Burglary: Independent variable. This may have a negative impact on home

prices because housing tends to be cheaper if there is a higher rate of crime in the area.

The demand for housing in these types of areas is lower than safer areas.

I will use this model to answer my question by testing the independent variables,

Personal Income and Level of Education against Housing Prices. I will test to see how

correlated the variables are and whether they are significant.

I will then do a test on a binary variable for which I chose to use states west and

states east of the Mississippi river. I chose this criteria for my binary because I wanted

to compare if there was a difference between the west coast and east coast. The

United States tends to be split with higher populations toward each coast, having lots of

land with lower populations throughout its middle section. This is why I chose to

compare the large populations of California and Texas (these are the states with the

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higher population data on the west coast) to the states Florida, New York, Ohio,

Pennsylvania and Illinois (higher population data on the east coast).

Initial estimation and hypothesis testing:

Dependent Variable: CPIHOUSING

Method: Least Squares

Date: 12/11/14 Time: 16:48

Sample: 1 50

Included observations: 50

Variable Coefficient Std. Error t-Statistic Prob.

C -115.4761 88.06088 -1.311322 0.1967

INCOME 0.003878 0.003856 1.005642 0.3202

EDUCATION 10.95013 2.965625 3.692351 0.0006

TAXES 2.28E-06 8.96E-07 2.543248 0.0147

BURGLARY -0.000868 0.000305

-2.840839 0.0068

CAPITAGDP -0.001513 0.001888 -0.801578 0.4272

UNEMPLOYMENT 7.641442 4.836332 1.580008 0.1214

R-squared 0.654494 Mean dependent var 329.1984

Adjusted R-squared 0.606284 S.D. dependent var 94.81226

S.E. of regression 59.49163 Akaike info criterion 11.13873

Sum squared resid 152187.9 Schwarz criterion 11.40641

Log likelihood -271.4681 Hannan-Quinn criter. 11.24066

F-statistic 13.57588 Durbin-Watson stat 1.928779

Prob(F-statistic) 0.000000

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When testing the dependent variable (housing prices) against all other variables,

initially I find that burglary has a negative correlation with housing prices. This was as I

expected. All variables seem to have a correlation with my dependent variable;

however, GDP per capita seems to have the least correlation when compared with other

variables. Also, this variable has a negative beta, which I expected the correlation to be

positive because the income of a state increases as taxes increase which would mean

the housing costs more.

The following are correlation graphs. This gives a visual display the relationship

between each variable against the dependent variable.

Personal income appears to have a generally positive correlation, as expected.

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It appears as though total state taxes remain around one area with varying house

prices. This makes sense since state income may be in the same general area, the

prices of its houses vary much more greatly.

Level of education appears to have a positive correlation with housing prices, as

expected.

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State burglary appears to vary. As burglary levels remain around a certain number,

house prices seem to vary. However, it appears as burglary rates increase, housing

prices don’t stay at high levels.

GDP per capita appears to have a roughly positive correlation, however not very

strongly. I expected a stronger correlation.

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Unemployment rate does not appear to have a very strong correlation; however unemployment tends to stay around a certain level while house prices vary.

The population variable does not appear to have a high correlation with the housing

price variable.

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Conclusion/Test Results:

In conclusion, I have found that housing prices are more correlated with my

testing variable income, than with the testing variable level of education. In my final

estimation I found that my variables are significant, and that burglary is negatively

correlated as I expected.

Due to the high F-stat in my Breusch-Pagan-Godfrey test for heteroscedasticity

(Appendix B), I find that I reject the null concluding that my model has implication of

heteroscedasticity. Therefore, my error terms may be correlated to some degree and

also have varying distributions and variances.

In my test for endogeniety found in (Appendix B) I found that because my t-stat of

-0.586935 was less than my t-crit of 2.02, I fail to reject the null, concluding that I do not

have endogeneity. Therefore, my variables are not correlated with the error term.

In the Ramsey reset test for zero mean I find that my model is specified correctly.

The normality test shows that my model is not a normal distribution. The Wald test

shows that my testing variables are not jointly significant at a value of 0. In the final

weighted estimation I found that most all of my variables tend to be significantly

correlated with the exception of GDP per capita, as it was in my initial estimation.

Therefore, I would conclude that while I would want to include more data

variables, housing prices are related to the level of one’s income. There is also a higher

correlation between housing prices and burglary rates. It has a negative correlation,

meaning as burglary rates are higher, housing prices tend to be lower. If I created a

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new model, or added onto this model, I would do more testing for crime rates and use it

as a testing variable rather than a control variable.

References:

Article 1

Dubin, Robin A., and Allen C. Goodman. "Valuation of education and crime neighborhood characteristics through hedonic housing prices." Population and environment 5.3 (1982): 166-181.

Article 2

Houthakker, Hendrik S. "Education and income." The Review of Economics and Statistics (1959): 24-28.

Article 3

Lee, Tong Hun. "Housing and permanent income: Tests based on a three-year reinterview survey." The Review of Economics and Statistics (1968): 480-490.

Article 4

Malpezzi, Stephen. "Housing prices, externalities, and regulation in US metropolitan areas." Journal of Housing Research 7 (1996): 209-242.

Article 5

Winger, Alan R. "Housing and income." Economic Inquiry 6.3 (1968): 226-252.

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Appendix A:

State

House Price Index (in hundreds)

Personal Income per capita ($)

level of Education

Total State Taxes (in thousands)

Unemployment Rate

GDP per capita

Population

State Total Burglary

Binary: West=1, East=0

Alabama 291.11 33,894 21.9 8,419,911 9.3 36156 4,785,570 42,034 0Alaska 280.23 45,565 27.9 4,522,927 7.9 68656 713,868 3,105 1Arizona 263.87 33,993 25.9 10,719,958 10.4 38222 6,408,790 50,771 1Arkansas 245.27 32,017 19.5 7,559,898 7.9 37658 2,922,280 32,511 1California 411.31 42,282 30.1 107,195,465 12.3 51546 37,333,601 228,857 1Colorado 342.25 41,689 36.4 8,575,262 9 49923 5,048,196 26,153 1Connecticut 409.47 55,216 35.5 12,344,106 9.3 64766 3,579,210 15,172 0Delaware 437.58 40,969 27.8 2,763,032 8 62994 899,711 7,515 0Florida 296.59 38,478 25.8 30,484,883 11.3 38258 18,846,054 169,119 0Georgia 284.15 34,341 27.3 14,782,779 10.2 41894 9,713,248 96,723 0Hawaii 448.63 41,668 29.5 4,837,862 6.8 48694 1,363,731 8,663 1Idaho 278.66 32,100 24.4 2,951,703 8.7 34825 1,570,718 6,502 1Illinois 318.26 42,033 30.8 27,795,759 10.4 50296 12,839,695 75,399 0Indiana 245.34 34,344 22.7 13,795,221 10.1 43207 6,489,965 47,115 0Iowa 246.02 39,033 24.9 6,809,344 6.3 46052 3,050,314 16,656 1Kansas 234.66 38,811 29.8 6,492,996 7.1 43556 2,858,910 19,404 1Kentucky 287.18 32,929 20.5 9,531,404 10.2 37746 4,347,698 30,311 0Louisiana 241.53 37,199 21.4 8,758,633 7.4 48594 4,545,392 45,435 1Maine 462.13 37,213 26.8 3,489,953 8.2 38374 1,327,366 7,359 0Maryland 423.05 50,035 36.1 15,237,748 7.8 54080 5,787,193 36,542 0Massachusetts 617.39 51,487 39 20,090,563 8.3 60354 6,563,263 37,767 0Michigan 241.09 35,082 25.2 22,208,870 12.7 39056 9,876,149 73,868 0Minnesota 312.11 42,572 31.8 17,208,877 7.4 50641 5,310,337 24,415 1Mississippi 243.14 30,834 19.5 6,268,823 10.5 31331 2,970,047 30,444 0Missouri 278.25 36,606 25.6 9,707,053 9.3 42610 5,996,063 44,043 1Montana 353.21 34,612 28.8 2,142,809 6.7 36918 990,527 3,654 1Nebraska 252.66 39,926 28.6 3,864,897 4.7 49119 1,829,838 8,326 1Nevada 216.76 36,657 21.7 5,835,963 13.8 44102 2,703,230 22,226 1N Hampshire 404.59 44,963 32.8 2,271,936 6.1 47224 1,316,614 5,441 0New Jersey 485.57 50,941 35.4 25,927,891 9.6 56025 8,802,707 38,732 0New Mexico 299.21 33,175 25 4,295,237 7.9 39316 2,064,982 21,014 1New York 576.76 49,582 32.5 63,807,610 8.6 60974 19,398,228 64,973 0N Carolina 314.54 35,435 26.5 21,514,930 10.8 43778 9,559,533 102,690 0N Dakota 254.68 43,275 27.6 2,645,695 3.8 51254 674,344 1,966 1Ohio 245.55 36,199 24.6 23,583,596 10 42342 11,545,435 106,521 0Oklahoma 203.06 35,912 22.9 7,082,161 6.9 39377 3,759,263 37,476 1Oregon 373.79 35,898 28.8 7,475,135 10.7 49538 3,837,208 19,637 1Pennsylvania 373.96 41,635 27.1 30,169,122 8.4 45976 12,710,472 55,171 1Rhode Island 474.92 43,013 30.2 2,568,759 11.7 46277 1,052,669 6,121 0S Carolina 317.6 32,669 24.5 7,242,724 11.2 35078 4,636,361 46,156 0S Dakota 290.44 40,613 26.3 1,321,228 5.1 46507 816,211 3,181 1Tennessee 288.17 35,426 23.1 10,513,788 9.8 39649 6,356,683 64,235 0Texas 223.8 38,065 25.9 39,516,186 8.2 47617 25,245,178 228,597 1Utah 320.5 32,447 29.3 5,237,427 8.1 42075 2,774,424 15,017 1Vermont 436.9 40,134 33.6 2,511,387 6.4 42097 625,793 3,366 0Virginia 403.22 44,836 34.2 16,411,055 7.1 52084 8,024,417 30,629 0Washington 414.56 42,547 31.1 16,106,154 9.9 52850 6,742,256 55,164 1W Virginia 217.41 31,798 17.5 4,803,704 8.4 34818 1,854,146 10,756 0Wisconsin 303.86 38,728 26.3 14,368,569 8.5 44431 5,689,060 26,566 0Wyoming 274.93 45,025 24.1 2,158,260 7 66256 564,222 2,149 1

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Appendix B:

Test for Heteroscedasticity:

Heteroscedasticity Test: Breusch-Pagan-Godfrey

F-statistic 6.258169 Prob. F(1,42) 0.0163

Obs*R-squared 5.705965 Prob. Chi-Square(1) 0.0169

Scaled explained SS 3.957595 Prob. Chi-Square(1) 0.0467

Test Equation:

Dependent Variable: RESID^2


Date: 12/11/14 Time: 14:53

Sample: 1 50



C -6821.033 4419.425 -1.543421 0.1302

CAPITAGDP 0.236573 0.094568 2.501633 0.0163




Sum squared resid 1.17E+09 Schwarz criterion 20.10639




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Date: 12/11/14 Time: 14:55

Sample: 1 50


Weighting series: ABS(VRES)

Weight type: Variance (average scaling)


C -108.2291 52.54895 -2.059586 0.0463

INCOME 0.012422 0.002053 6.050098 0.0000

TAXES 2.13E-06 5.89E-07 3.615020 0.0009

BURGLARY -0.000847 0.000182 -4.642958 0.0000

CAPITAGDP -0.002872 0.001753 -1.638338 0.1096

UNEMPLOYMENT 9.806262 3.717914 2.637571 0.0120

Weighted Statistics







Prob(F-statistic) 0.000000 Weighted mean dep. 313.1386

Unweighted Statistics



S.E. of regression 69.00406 Sum squared resid 180939.3

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Durbin-Watson stat 2.070976

Test for Endogeniety:



Date: 12/11/14 Time: 14:08

Sample: 1 50



C -122.7353 100.7347 -1.218402 0.2310

INCOME -0.008659 0.022321 -0.387937 0.7003

TAXES 2.01E-06 1.15E-06 1.752352 0.0882

EDUCATION 11.58633 4.461864 2.596747 0.0135

CAPITAGDP 0.008608 0.017224 0.499797 0.6203

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BURGLARY -0.000785 0.000376 -2.088543 0.0439

UNEMPLOYMENT 9.239402 5.959531 1.550357 0.1298

IVRES -0.010193 0.017367 -0.586935 0.5609








Test for Zero Mean:

Ramsey RESET Test

Equation: UNTITLED

Specification: CPIHOUSING C INCOME TAXES EDUCATION CAPITAGDP

BURGLARY UNEMPLOYMENT

Instrument specification: C INCOME TAXES EDUCATION CAPITAGDP

BURGLARY POPULATION

Omitted Variables: Powers of fitted values from 2 to 4

Value df Probability

F-statistic 2.214646 (3, 34) 0.1043

Likelihood ratio 7.853523 3 0.0491

F-test summary:

Sum of Sq. dfMean

Squares

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Test SSR 24134.14 3 8044.714

Restricted SSR 147639.3 37 3990.252

Unrestricted SSR 123505.2 34 3632.506

LR test summary:

Value df

Restricted LogL -241.0367 37

Unrestricted LogL -237.1100 34

Unrestricted Test Equation:



Date: 12/11/14 Time: 14:20

Sample: 1 50



C 11126.00 7566.153 1.470497 0.1506

INCOME -0.245853 0.165883 -1.482087 0.1475

EDUCATION -585.4722 400.5812 -1.461557 0.1530

TAXES -0.000137 9.33E-05 -1.469711 0.1508

CAPITAGDP 0.081795 0.055551 1.472444 0.1501

BURGLARY 0.051451 0.035064 1.467355 0.1515

UNEMPLOYMENT -441.7197 300.9174 -1.467910 0.1513

FITTED^2 0.275000 0.179630 1.530927 0.1350

FITTED^3 -0.000558 0.000353 -1.579705 0.1234

FITTED^4 4.15E-07 2.54E-07 1.635528 0.1112



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Normality:

Wald Test:

Equation: Untitled

Test Statistic Value df Probability

F-statistic 28.84905 (2, 38) 0.0000

Chi-square 57.69810 2 0.0000

Null Hypothesis: C(2)=C(3)=0

Null Hypothesis Summary:

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Normalized Restriction (= 0) Value Std. Err.

C(2) 0.012422 0.002053

C(3) 2.13E-06 5.89E-07

Restrictions are linear in coefficients.

Final Weighted Estimation:



Date: 12/11/14 Time: 14:55

Sample: 1 50


Weighting series: ABS(VRES)

Weight type: Variance (average scaling)


C -108.2291 52.54895 **-2.059586 0.0463

INCOME 0.012422 0.002053 ***6.050098 0.0000

TAXES 2.13E-06 5.89E-07 ***3.615020 0.0009

BURGLARY -0.000847 0.000182 ***-4.642958 0.0000

CAPITAGDP -0.002872 0.001753 *-1.638338 0.1096

UNEMPLOYMENT 9.806262 3.717914 ***2.637571 0.0120

Weighted Statistics





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Prob(F-statistic) 0.000000 Weighted mean dep. 313.1386

Unweighted Statistics



S.E. of regression 69.00406 Sum squared resid 180939.3

Durbin-Watson stat 2.070976

*Reject at alpha = 0.10

**Reject at alpha = 0.05

***Reject at alpha = 0.01

Binary Estimation:



Date: 12/11/14 Time: 16:30

Sample: 1 50



C 59.01909 118.0173 0.500089 0.6198

INCOME 0.008922 0.004040 2.208542 0.0332

INCOME*BINARY -0.001853 0.005813 -0.318785 0.7516

TAXES 1.84E-06 1.47E-06 1.249160 0.2191

TAXES*BINARY 5.24E-07 1.89E-06 0.277112 0.7832

BURGLARY -0.000798 0.000511 -1.562475 0.1263

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BURGLARY*BINARY 4.04E-05 0.000684 0.059132 0.9531

CAPITAGDP 0.000345 0.003074 0.112353 0.9111

CAPITAGDP*BINARY -0.002311 0.004385 -0.527089 0.6011

UNEMPLOYMENT -6.536023 8.989954 -0.727036 0.4715

UNEMPLOYMENT*BINARY 13.60267 9.166913 1.483888 0.1459








Appendix C:

Test for heteroscedasticity:

H0: The model contains homoscedasticity

H1: The model contains heteroscedasticity

Critical value F(1,42): 4.07

F Statistic: 6.258169

Therefore reject null. Conclude the model is heteroscedastic

Test for endogeniety:

H0: The model is not endogenous

H1: The model is endogenous

DF: 36

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Tcritical: 0.10, 0.05, 0.01 = 1.302, 1.683, 2.422 respectively.

Tstat: |-0.586935|

Therefore, conclude that the model is not endogenous.

Test for zero mean:

H0: Γ = 0 (model is specified correctly)

H1: Γ ≠ 0 (model is not specified correctly)

Fstatistic = 2.214646 < Tcritical = 2.89

Therefore, fail to reject H0.

Normality:

H0: skewness & kurtosis = 0

H1: otherwise

Tcritical: 1.696 < Jarque-Bera: 3.1858

Therefore, reject H0, conclude my model is not normal.

Wald test:

H0: B1=B2=0

H1: Otherwise

Fcritical: 3.24 < Fstatistic: 28.84905

Therefore reject Ho. My testing variables are not jointly significant at a value of 0.

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thurman model 1 cross sectional ecn 405

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