Econometrics Project Completed

in USA

Project prepared for Dr John Stinespring

12/11/2013

I. Introduction

The share of young adults between the age group of 24 and 34 living with

parents have edged up last year despite improvements in the economy. A new study

from Pew research has estimated that a total of 21 million young adults are living with

parents, a clear sign that effects of recession are still lingering. “Although the media at

times present a picture of an increasing proportion of young adults living in their

parent’s home, Messineo and Wojkiewicz (2004) finds that the increase in propensity

from 1960 to 1990 for young adults age 19 to 30 to live with parents was largely due to

an increasing proportion of young adults over this time period who were never married,

or formerly married – groups that are much more likely to reside with their parents”

Kreider, M said in a speech at the ASA annual meetings in New York, August 12, 2007.

The predicted percentage of young male adults living at home is of particular

importance in determining the loss of potential productivity faced by The United States

every year. While there is a substantial literature which examines the home-leaving

(and returning) behavior of young adults, little work has been done to show the socio-

economic reasons behind the rising trend over the last decade.

This paper provides new empirical evidence on the relationship between

percentage of males within the age group of 18 and 34 living at home and limited labor

market outcomes, average marriage age for young people, and rent of house to price of

house ratio in the United States. I use this evidence to argue that percentage of males

between the age group of 18 and 34 are affected by these key socio-economic variables.

To understand the relationship it is necessary to understand the uncertainties and

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opportunities that exist for young adults in the labor market. I based my research

paper primarily on one paper, written by Liu, Yang, Di Zhu “Young American Adults

living in Parental Homes,” (2011). The data I used was for the United States as a

country dating back to 1983 through 2012 and primarily sourced from The Bureau of

Labor Statistics (BLS), The Current Population Survey (CPA) and American Housing

Survey (AHS).

II. Literature review

The basis of my research and calculations are from a paper entitled “Young

American Adults living in parental homes” written by Zhu Xiao Di, Yi Yang and

Xiaodong Liu. Their paper, written in 2002 reviewed the literature of young adults

(ages 25-34) living in parental homes in regard to gender difference, racial difference,

family structure variation, parental resource gap, personal income gap, and the long-

term trend. They test to see the effect of personal income, parental resource, and race

on the living arrangements of young adults. They based their research on data collected

from The Current Population Survey (CPS). One of the limitations they faced while

using CPS data for their analysis is that the data did not have information on rent. To

amend, they generated a median monthly contract rent variable based on the American

Housing Survey (AHS) of 1999 which was adjusted for four regions and metropolitan

status, namely inner cities, suburbs, and non-metro areas. For each dataset, they

estimated the effect of various factors on the probability of young adults living at

parental homes, controlling for selected demographic young adults living at parental

homes, controlling for selected demographic characteristics. Their dependent variable

is whether the young adult lives in parental home (1=yes, 0=no). Independent variables

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include young adults’ personal income, average rent in an area (For CPS 2001 data),

parental resources (for PSID data), age, gender, race, educational attainment, marital

status, and regional and urban variation (for PSID data). Their analysis confirms as

pointed out in their research by Liu, Yang, Di Zhu (2002) “their belief that personal

income is one of the most important factors explaining the living arrangements of

young adults (ages 25-34)” (p. 40). Controlling for parental resources and selected

demographic factors, those with lower personal income are more likely to live in

parent’s home. Even though their U-shaped pattern representing the long term trends

of co-residence was in line with the overall economic conditions in income distribution

such as family income inequality, low-wage share of total employment, inequality in

wages and salaries, and the number of persons below the poverty level, their

conclusions do not give us a numerical prediction of the percentage of big babies living

at home.

The Liu, Yang, Di Zhu paper wasn’t the only paper used in my research, but the

theory served as the back bone of my model. The strong relationship between living

arrangements and personal income encouraged me to observe what other socio-

economic factors can affect this relationship and change the percentage of young adults

living at home. Another piece used as a reference was published by the Fertility and

Family Statistics Branch, U.S. Census Bureau and presented by Rose M. Krieder in

August of 2012 and was titled “Young Adults Living in Their Parent’s Home”. Her

literature “Young Adults Living in Their Parent’s Home” (2007) examined how “…

[T]he characteristics of young adults living in their parents’ home might differ from

young adults living elsewhere” (p.1). Krieder’s findings indicate that the profile of

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young adults living in their parents’ home suggests that young adults often live in their

parents’ home for their own benefit. Another paper I found interesting was,

“Intergenerational Transfers and Household Structure Why Do Most Italian Youths

Live With Their Parents?” by Marco Manacorda and Enrico Moretti (2002). I did not

focus entirely on this due to the geographical relevance and it used independent

variables which are primarily social factors that are typical characteristics of Italian

Youths only. Their basic analysis was that Italy is an outlier in terms of the living

arrangements of its young man.

III. Methodology and Data

To test the hypothesis that socio-economic factors have a greater impact on

percentage of young adults (18-34), I created a total of three linear-logged model based

on the model used in the Liu, Yang, Di Zhu paper, but I added different independent

variables and expressed my dependent variable as a percentage of young adults (18-34)

living at home. My models attempt to estimate the impact of socio-economic factors

including rent to price ratio of housing, labor market participation ratio of people over

the age of 65, average marriage age of males and real weekly wage of adults (18-34).

Percentage of young adults living at home denoted by PHt, rent to price ratio of housing

as RPt, average marriage age of males as AVGMt, labor market participation ratio of

people over the age of 65 as LPt, and real weekly wage as RWt all of which I expect to

have a significant impact on percentage of young adults living at home.

The idea to start with a linear-logged model came from Liu, Yang, Di Zhu paper

and I also thought the variables should have a linear-logged relationship with my

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dependent variables and the errors to be normally distributed. I have run a Jarque-

Bera Normality test to show that my errors are normally distributed. I decided to log

some of the independent variables in the model because of the fact that the regressand

and some of the regressors are in different units. Logging some of the regressors will

help me minimize the spread of the data and attempt to get the data on a comparable

scale.

The linear-logged model is written as follows:

Model I: PHt = β0 + β1 Log (RPt) + β2 Log (AVGMt) + β3 LPt + β4 Log (RWt) +Ut

From this point I developed my second model which is essentially the same as my

original model but controlling for the independent variable, labor force participation ratio

of people over the age of 65(LPt).

Firstly, the introduction of this control variable will enable me to predict the long-

run trend of the percentage of young adults (18-34) living at home without taking into

consideration a phenomenon which has been only recently observed in the labor market

and might not hold in the long-run with the economy emerging out of the Great Recession.

Secondly, another reason behind dropping the independent variable, labor force

participation ratio of people over the age of 65(LPt) in the second model is entirely based

on suspecting multicollinearity between LPt and one or more independent variables

such as average marriage age of males as people are less likely to get married if they do

not have a stable job. I included tests results in the appendix section to show evidence of

multicollinearity.

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The second model is as follows:

Model II: PHt = β0 + β2 Log (RPt) + β3 Log (AVGMt) + β4 Log (RWt) + Ut

Building up on this model a dummy variable was added to make a third model

and to account for any impact that a recession may have on real wages and

coincidentally affect the dependent variable, percentage of young adults (18-34) living

at home. We added this variable on the account that recessions would have a qualitative

impact on percentage of young adults (18-34) living at home, one that couldn’t be

measured by adding numerical data. The third model is still controlling for the

independent variable, labor force participation ratio of people over the age of 65(LPt):

Model III: PHt = β0 + β1 Log (RPt) + β2 Log (AVGMt) + β3 Log (RWt) + β4

(Recession*Log (RWt)) +Ut

All models underwent a series to test to verify their legitimacy and to ensure no

models contained underlying problems, resulting in biased predictions. The first test

was for normality which was done by looking at the probability of the Jarque-Bera

Normality Test. It is important that the error terms u are normally distributed. In the

classical normal linear regression model (CNLRM) it is assumed that the error terms

follow the normal distribution (with zero mean and constant variance). Using the

central limit theorem (CLT) to justify the normality of the error term, I was able to

show the OLS estimators themselves are normally distributed. This in turn allowed us

to use the t and F statistics in hypothesis testing in small, or finite, samples like my

samples. Therefore the role of the normality assumption is very critical. Due to the

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small size of the samples I ran a Jarque-Bera Normality Test and it showed that the

errors were normally distributed. All the Jarque-Bera Test error terms output gave me

probabilities of more than 20% as shown in the table below:

Figure 1

The errors are normally distributed because the likelihood of getting a Jarque-

Bera score of 1.5654 (approximately) and the errors being normally distributed is

45.72% (approximately).

Secondly, I tested the slopes of the regression line to see if there is a significant

relationship between the independent and dependent variable. Just because the slope

coefficients are not equal to zero, it doesn’t mean that there is a statistically significant

relationship. To evaluate I conducted t-tests for each slope coefficients of the

independent variables. All my slope coefficients had t-statistics greater than the t-

critical value at 5% significance level. So I rejected the null hypothesis and I could

statistically conclude that there is a relationship between the independent and

dependent variables. My F-statistic computed was also greater than F-critical which

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determined that there is a significant relationship between the dependent variable and

any of the independent variables in our model. The adjusted R2 of all three of my

models were high, which was an excellent indicator that our regression line was much

better than simply using the average value of the dependent variable for prediction

purposes.

Next was to test for multicollinearity this was conducted in many steps. My first

model showed low t-stats for some of the independent variables with high probability

and R2 and F-statistics were high which were good signs indicating that the model

suffers from multicollinearity. After noticing that two of my independent variables Log

RPt and LPt were showing low t-stats with high probability I conducted a simple pair-

wise correlation test and it confirmed that the independent variables Log AVGMt is

highly collinear with Log RWt and LPt as shown in the table underneath.

LOG(RWt) LOG(RPt) LOG(AVGMt) LPt

LOG(RWt) 1.000000 -0.531632 0.835753 0.746151LOG(RPt) -0.531632 1.000000 -0.318637 -0.411232

LOG(AVGMt) 0.835753 -0.318637 1.000000 0.906715LPt 0.746151 -0.411232 0.906715 1.000000

Table 1

I further confirmed my doubts by using confidence ellipses to decipher which

variables had a possibility of being collinear, which was indicated by an elliptical shape

as opposed to a circular one, where a circular shape would have indicated no

multicollinearity. It confirmed my simple-pair wise correlation test.

I regressed the independent variables on the other independent variables. Upon

regressing Log AVGM on Log RW I got an auxiliary regression R2 = 0.698483 which is

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less than the adjusted R2 of the original model indicating that there is no problematic

collinearity between these two independent variables. However, upon regression Log

AVGMt on LPt I got an auxiliary regression R2 of 0.822132. Using Klein’s Rule of

Thumb I can conclude that there is high collinearity between the two independent

variables.

I had two options for correcting the multicollinearity. According to O.J.

Blanchard, Comment, Journal of Business and Economic Statistics, multicollinearity is

essentially a data deficiency problem (micronumerosity). Faced with micronumerosity I

decided to drop the independent variable LPt in my second model although carefully

checking for specification bias. Even though economic theory suggest that the labor

force participation of people over the age of 65 is important, out limitation in having a

priori information on how much it will affect the dependent variable I dropped the

variable. It corrected for multicollinearity in the first model and the ensuing models.

Since all my data was collected for the same population over a period of time the

variables were of similar orders of magnitude, as a result of which I did not face any

trouble with Heteroscedasticity.

The next test was for autocorrelation. I started detecting for autocorrelation by

plotting the residuals against time, the time sequence plot as show overleaf:

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Figure 2

Examining the time sequence plot as above, I observed that our estimated error

terms exhibit a pattern (negative runs to the positive runs) suggesting that perhaps our

error terms are not random.

Then we conducted a Durbin-Watson test to check if the d-statistic shows results

of autocorrelation. The calculated d-statistic for all our models were close 2.00

indicating there is no autocorrelation. To avoid some of the limitations of the Durbin-

Watson d test for autocorrelation, I also used a Breusch-Godfrey (BG) Test to further

verify our observation. Using Breusch-Godfrey test we fail to reject the null hypothesis

of no auto correlation. I also checked each model more model misspecification using a

Ramsey RESET test.

As mentioned earlier our data includes percentage of young adults (18-34) PH,

Rent to Price of houses ratio (RP), average marriage age of males (AVGM), labor

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market participation ratio of people over the age of 65 (LP), real weakly wage (RW),

and a dummy variable indicating recessions. All the data was collected primarily from

The Bureau of Labor Statistics (BLS), The Current Population Survey (CPA) and

American Housing Survey (AHS) expressed annually between the years or 1983 to

2012. I would also like to acknowledge Associate Professor John Stinespring, on his

contribution with reliable dataset for years 1983 to 2011. The descriptive statistics of all

our variables is listed below.

PH RP AVGM LP RW

Mean 14.761 4.699 26.843 13.300 572.952

Median 14.548 4.938 26.850 12.238 588.375

Maximum 18.695 5.327 29.100 17.800 689.000

Minimum 12.859 3.098 25.400 10.775 419.250

St. Dev. 1.400 0.628 0.923 2.279 88.305

Skewness 1.267 -1.376 0.480 0.853 -0.222

Kurtosis 4.730 3.800 2.983 2.274 1.512

Jarque-Bera 11.765 10.262 1.152 4.296 3.014

Probability 0.003 0.006 0.562 0.117 0.222

Sum442.83

4140.979

805.30

0399.010 17188.550

Sum Sq. Dev. 56.853 11.082 24.714 150.644 226135.000

Observations 30 30 30 30 30

Table 2

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IV. Results

The results of my models showed different beta values for each variable depending

on the model.

The first model had betas were all statistically significant and had a good Durbin-Watson

score of almost 2.00.

PHt = -179.3907 + 1.658688 Log RPt + 77.72824 Log AVGMt – 0.206411 LPt -9.676319 Log RWt

(-8.342) (2.079) (9.279) (-2.070) (-7.960)

Adjusted R2 = 0.88 DW = 2.03

After the variables in the linear model were tested for their significance the model

indicates that the average marriage age of males and the real wage of adults are the most

significant variables with probability of being equal to zero is 0.0000. Even though the

model wasn’t represented in any of the papers I used as reference, it confirms Rose M.

Krieder’s claim that average marriage age of males have a significant impact on their

decision to live at home with their parents. My findings also confirms Liu, Yang, Di Zhu’s

finding that personal income is one of the most important factors explaining the living

arrangements of young adults.

The intercept fail to infer any economically significant prediction because the

percentage of young adults living at home cannot be negative. However analyzing the

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other slope coefficients, we can start interpreting them. When the rent to house price ratio

goes up by 1 percent, on average, the percentage of young adults living at home goes up by

1.659% which meets my apriori expectation that as rent of houses increase the percentage

of young adults living at home should increase as well. The average marriage age of males

is a highly economical and statistically significant variable as its slope co-efficient shows. It

indicates that as the average marriage age of males increase by 1%, on average, the

percentage of young adults living at home will increase by 77.3% hence the most important

determinant of a young adult’s decision to continue to live at home with their parents. As I

mentioned it verifies Rose M. Krieder’s claim that average marriage age of males have a

significant impact on their decision to live at home with their parents. As labor force

participation rate of people over the age of 65 goes up by 1%, on average, the percentage of

young adults living at home decreases by .206%. It is interesting to see that this

independent variable shows such results as it contradicts my apriori expectation of how

this variable would affect the percentage of young adults living at home. Real wages also

show an interesting relationship indicating that as real wages go up by 1%, on average,

percentage of young adults living at home will decrease by 9.676%.

Model II: PHt = -140.8271 + 2.295887 Log (RPt) + 63.65141 Log (AVGMt) -9.042724 β3 Log (RWt) +

Ut

(-12.356) (2.940) (12.263) (-7.242)

Adjusted R2 = 0.870 DW = 1.591

After testing for the significance of the slope coefficients we get very similar results as

model I predictions. It also confirms Rose M. Krieder’s claim that average marriage age of

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males have a significant impact on their decision to live at home with their parents. My

findings also confirms Liu, Yang, Di Zhu’s finding that personal income is one of the most

important factors explaining the living arrangements of young adults.

The intercept once again fail to infer any economically significant prediction because the








percentage of young adults living at home will increase by 63.651% hence once again

verifying the most important determinant of a young adult’s decision to continue to live at

home with their parents. As real wages goes up by 1% the percentage of young adults

living at home decreases by 9.043%.

Model III: PHt = -141.1819 + 2.371887 Log (RPt) + 63.35958 Log (AVGMt) – 8.848407 Log (RWt) -

0.243939 +Ut

(-12.323) (3.000) (12.136) (-6.975) (-0.876)Adjusted R2 = 0.869 DW = 1.754

After introducing the dummy variable in our third model the slope coefficient fails

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to pass the significance test suggesting that the percentage of young males living at home

are not affected by the decrease in real wage due to recession.

After testing for the significance of the remaining slope coefficients we get very

similar results as model II predictions. It also confirms Rose M. Krieder’s claim that

average marriage age of males have a significant impact on their decision to live at home

with their parents. My findings also confirms Liu, Yang, Di Zhu’s finding that personal

income is one of the most important factors explaining the living arrangements of young

adults.

The intercept once again fail to infer any economically significant prediction because the








percentage of young adults living at home will increase by 63.384% hence once again

verifying the most important determinant of a young adult’s decision to continue to live at

home with their parents. As real wages goes up by 1% the percentage of young adults

living at home decreases by 8.864%.

V. Conclusion

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After comparing two ensuing models with my original model (Model I) we find very

similar results as predicted by Rose M. Krieder and Liu, Yang, Di Zhu papers. My slope

coefficients have only slightly changed across the model however none of the models are

hugely different from each other when it came to explaining the variability of the predicted

dependent variable. However it is important to note that our independent variable LPt

from our first model showed a negative relationship with our dependent variable

suggesting that as labor force participation of people over 65 is negatively related with

percentage of people living at home. As mentioned before this is a very new phenomenon

observed in the US economy especially since “The Great Recession”. It will be interesting

to see if this relationship changes as more and more young adults will start looking for jobs

in the next few years with 3rd quarter economic report suggesting that two more million

jobs will be created in the next coming years. (As I caught up with next research I found

out that the jobs added on the month of august 2014, the job number is only 142,000

compared to jobs added in the economy in the preceding month to be well over 250,000.

This is an alarming figure and needs to be further worked on).

Looking at the statistical significance of the model the adjusted R2 suggest that they

are all great prediction models for the percentage of young adults (18-34) living at home

with their parents. Logically it would be advisable to use the simpler model with the fewest

independent variables based on the idea of Parsimony, however I would suggest using

Model I as it captures more independent variable giving a higher Adjusted R2. Also the

slope coefficient of LPt is statistically significant. I would also ignore the effect of recession

in predicting the percentage of young adults living at home as the slope coefficient is not

statistically different from zero at the 5% significance level.

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If I had more time to allocate to this study we would be able to identify more socio-

economic indicators affecting the young adults decision to stay at home and sacrificing

independence of living alone. At this point more research needs to be conducted before a

conclusion can be made as to whether what other socio-economic factors have an influence

on the percentage of young adults (18-34) living at home.

Appendix

Section I:

Slope significance test for Model I:

Dependent Variable: PHSample: 1983 2012Included observations: 30

Variable Coefficient Std. Error t-Statistic Prob.

C -179.3907 21.50475 -8.341911 0.0000LOG(RP) 1.658688 0.797686 2.079375 0.0480

LOG(AVGM) 77.72824 8.376944 9.278829 0.0000LP -0.206411 0.099724 -2.069826 0.0490

LOG(RW) -9.676319 1.215673 -7.959638 0.0000

R-squared 0.900528 Mean dependent var 14.76113Adjusted R-squared 0.884613 S.D. dependent var 1.400155S.E. of regression 0.475614 Akaike info criterion 1.502592Sum squared resid 5.655217 Schwarz criterion 1.736124Log likelihood -17.53887 Hannan-Quinn criter. 1.577301F-statistic 56.58197 Durbin-Watson stat 2.028597Prob(F-statistic) 0.000000

H0 : β1 = β2 = β3 = β4 = 0

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H0 : β1 = β2 = β3 = β4 ≠ 0

α = 5%

Degree of freedom (d.f.) = n-k = 30-4 = 26

tcrit5% = 2.056

All our |tstat| >|tcrit|, so we reject the null hypothesis and we can be at least 95% confidence

that our estimated betas are statistically significant from zero.

Slope significance test for Model II:



C -140.8271 11.39716 -12.35633 0.0000LOG(RP) 2.295887 0.780982 2.939743 0.0068

LOG(AVGM) 63.65141 5.190515 12.26302 0.0000LOG(RW) -9.042724 1.248598 -7.242301 0.0000


H0 : β1 = β2 = β3 = 0

H0 : β1 = β2 = β3 ≠ 0

α = 5%

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d.f. = n-k = 30-3 = 27

tcrit5% = 2.052

All our |tstat| >|tcrit|, so we reject the null hypothesis and we can be at least 95% confidence

that our estimated betas are statistically significant from zero.

Slope significance test for Model III:



C -141.1575 11.45478 -12.32303 0.0000LOG(RP) 2.366142 0.788595 3.000455 0.0060

LOG(AVGM) 63.38360 5.222882 12.13575 0.0000LOG(RW) -8.863524 1.270809 -6.974712 0.0000

RECESSION -0.243939 0.278525 -0.875826 0.3895


H0 : β1 = β2 = β3 = β4 = 0

H0 : β1 = β2 = β3 = β4 ≠ 0

α = 5%

d.f. = n-k = 30-4 = 26

tcrit5% = 2.056

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Since all our |tstat| are not greater than |tcrit| so we fail to reject the null hypothesis and we

can be at least 95% confidence that our estimated betas are statistically significant from

zero.

Section II:

Pair wise test for model, confidence ellipse and auxiliary regression results:

LOG(RP) LOG(AVGM) LP LOG(RW)LOG(RP) 1.000000 -0.318637 -0.411232 -0.531632

LOG(AVGM) -0.318637 1.000000 0.906715 0.835753LP -0.411232 0.906715 1.000000 0.746151

LOG(RW) -0.531632 0.835753 0.746151 1.000000

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Auxiliary regression of Log (AVGMt) on LPt

Dependent Variable: LOG(AVGM)Sample: 1983 2012Included observations: 30


C 3.108717 0.016111 192.9586 0.0000LP 0.013589 0.001194 11.37630 0.0000

R-squared 0.822132Adjusted R-squared 0.815780

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Auxiliary regression of Log (AVGMt) on LPt

Dependent Variable: LOG(AVGM)Sample: 1983 2012Included observations: 30


C 2.150726 0.141433 15.20670 0.0000LOG(RW) 0.179642 0.022305 8.053795 0.0000

R-squared 0.698483Adjusted R-squared 0.687714

Section III:

Model I:

Breusch-Godfrey Serial Correlation LM Test:

F-statistic 0.441716 Prob. F(3,22) 0.7255Obs*R-squared 1.704359 Prob. Chi-Square(3) 0.6360

Test Equation:Dependent Variable: RESID

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Sample: 1983 2012Included observations: 30Presample missing value lagged residuals set to zero.


C -4.502255 22.99093 -0.195827 0.8465LOG(RP) -0.265268 0.860940 -0.308115 0.7609

LOG(AVGM) 2.671937 9.164657 0.291548 0.7734LP -0.021390 0.105820 -0.202139 0.8417

LOG(RW) -0.568701 1.374306 -0.413810 0.6830RESID(-1) -0.086486 0.221765 -0.389987 0.7003RESID(-2) -0.197194 0.224157 -0.879716 0.3885RESID(-3) -0.190655 0.230274 -0.827946 0.4166

R-squared 0.056812 Mean dependent var -1.66E-14Adjusted R-squared -0.243293 S.D. dependent var 0.441597S.E. of regression 0.492394 Akaike info criterion 1.644102Sum squared resid 5.333933 Schwarz criterion 2.017755Log likelihood -16.66153 Hannan-Quinn criter. 1.763637F-statistic 0.189307 Durbin-Watson stat 2.063198Prob(F-statistic) 0.984705

Model II:



Test Equation:Dependent Variable: RESIDSample: 1983 2012

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Included observations: 30Presample missing value lagged residuals set to zero.


C 1.719738 11.93287 0.144118 0.8867LOG(RP) -0.007951 0.814401 -0.009763 0.9923

LOG(AVGM) -0.680223 5.388396 -0.126238 0.9006LOG(RW) 0.083450 1.294370 0.064472 0.9492RESID(-1) 0.178384 0.208116 0.857135 0.4002RESID(-2) -0.068794 0.217944 -0.315650 0.7551RESID(-3) -0.162499 0.217271 -0.747910 0.4621


Model III:



Test Equation:

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Dependent Variable: RESIDSample: 1983 2012Included observations: 30Presample missing value lagged residuals set to zero.


C 0.382405 12.21984 0.031294 0.9753LOG(RP) 0.008127 0.840510 0.009669 0.9924

LOG(AVGM) -0.130788 5.535181 -0.023629 0.9814LOG(RW) 0.005049 1.356372 0.003722 0.9971

RECESSION 0.029965 0.320852 0.093393 0.9264RESID(-1) 0.098099 0.216814 0.452459 0.6554RESID(-2) 0.004921 0.236883 0.020775 0.9836RESID(-3) -0.117395 0.224004 -0.524075 0.6055


Section IV:

Model I:

Ramsey RESET TestEquation: UNTITLEDSpecification: PH C LOG(RP) LOG(AVGM) LP LOG(RW)Omitted Variables: Powers of fitted values from 2 to 4

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Value df ProbabilityF-statistic 1.217814 (3, 22) 0.3267Likelihood ratio 4.609060 3 0.2028

F-test summary:

Sum of Sq. dfMean

SquaresTest SSR 0.805389 3 0.268463Restricted SSR 5.655217 25 0.226209Unrestricted SSR 4.849828 22 0.220447Unrestricted SSR 4.849828 22 0.220447

LR test summary:Value df

Restricted LogL -17.53887 25Unrestricted LogL -15.23434 22

Unrestricted Test Equation:Dependent Variable: PHSample: 1983 2012Included observations: 30


C -36549.10 83177.65 -0.439410 0.6647LOG(RP) 330.2806 752.6735 0.438810 0.6651

LOG(AVGM) 15497.79 35286.09 0.439204 0.6648LP -41.21711 93.76256 -0.439590 0.6645

LOG(RW) -1929.148 4392.295 -0.439212 0.6648FITTED^2 -18.72183 44.26227 -0.422975 0.6764FITTED^3 0.778442 1.909809 0.407602 0.6875FITTED^4 -0.012026 0.030760 -0.390962 0.6996


Model II:

Ramsey RESET TestEquation: UNTITLEDSpecification: PH C LOG(RP) LOG(AVGM) LOG(RW)Omitted Variables: Powers of fitted values from 2 to 4

Value df ProbabilityF-statistic 1.872391 (3, 23) 0.1624

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Likelihood ratio 6.555385 3 0.0875

F-test summary:

Sum of Sq. dfMean






C 77573.20 56626.82 1.369902 0.1839LOG(RP) -1231.602 898.7099 -1.370411 0.1838

LOG(AVGM) -34156.05 24912.76 -1.371026 0.1836LOG(RW) 4852.880 3539.113 1.371214 0.1835FITTED^2 53.73434 37.97062 1.415156 0.1704FITTED^3 -2.374822 1.630973 -1.456077 0.1589FITTED^4 0.039146 0.026168 1.495956 0.1483


Model III:

Ramsey RESET TestEquation: UNTITLEDSpecification: PH C LOG(RP) LOG(AVGM) LOG(RW) RECESSIONOmitted Variables: Powers of fitted values from 2 to 4

Value df Probability

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F-statistic 1.345720 (3, 22) 0.2853Likelihood ratio 5.054468 3 0.1679

F-test summary:

Sum of Sq. dfMean






C 56587.14 54350.69 1.041148 0.3091LOG(RP) -923.9276 887.0017 -1.041630 0.3089

LOG(AVGM) -24759.77 23758.50 -1.042144 0.3087LOG(RW) 3462.787 3322.301 1.042286 0.3086

RECESSION 95.36145 91.38539 1.043509 0.3080FITTED^2 39.46957 36.45807 1.082602 0.2907FITTED^3 -1.757769 1.569674 -1.119831 0.2749FITTED^4 0.029177 0.025237 1.156148 0.2600


Bibliography

A) Liu, Yang, Di Zhu, “Young American Adults living in Parental Homes,”

(2011), Harvard University

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B) Kreider, Rose, “Young Adults Living in Their Parent’s Home”, U.S. Census

Bureau, Presented at the ASA annual meetings in NY, August 12, 2007

C) Gujarati, Damodar N., and Dawn C. Porter. Basic Econometrics. Boston:

McGraw-Hill Irwin, 2009. Print

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Econometrics Project Completed

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Transcript of Econometrics Project Completed