Econometrics/Fall2017 Homework Set #3 This assignment is due in with a hard copy or electronic Bb depositing before 12 AM Sunday

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Econometrics/Fall2017 Homework Set #3

This assignment is due in with a hard copy or electronic Bb depositing before 12 AM Sunday. You are welcome to turn it in before the deadline.

a. Find one scholarly empirical article from an economics journal with a study similar to this assignment and summarize it (its expectations, methodology and equation and results in a paragraph as much as you can make sense of it).

An Empirical Analysis of the Determinants of poverty and household welfare in South Africa

Abstract: The data used for our analysis is drawn from the first four waves of the National Income Dynamic Study to determine the factors that influence poverty and household welfare in South Africa. They have applied ordinary least squares and probit/logit models on cross-sectional data, this analysis captures unobserved individual heterogeneity and endogeneity, both via fixed effect, and via a robust alternative based on random effect probit estimation. The results from fixed effect and random effect probit indicate that levels of education of the household head, some province dummies, and race of the household head, dependency ratio, and gender of the household head, employment status of the household head and marital status of the household head are statistically significant determinants of household welfare.

Literature review

In measuring poverty and welfare, scholars often adopt various approaches. Some studies have embraced a non-monetary approach – computing an asset index which gives socio-economic status of each household in the sample

The determinants of poverty and household welfare have been modelled using two alternative approaches. The first approach employs probit/logit models to examine the determinants of the probability of a households being poor. The second alternative approach models the determinants of welfare as measured by consumption or income using Ordinary Least Square (OLS).

Methodology

We captures unobserved individual heterogeneity and endogeneity, both via fixed effect, and via a robust alternative based on random effect probit estimation. First a random effect probit model was estimated, with the probability of a household being poor as the dependent variable and a set explanatory variables: levels of education of the household head, province dummies, race of the household head, dependency ratio, indicator variables for location of the household — rural or urban, gender of the household head, employment status of the household head, marital status of the household head, asset ownership, household size and age of the household head (see table 1 above). Given the dichotomous nature of the outcome variable, we assigned a value of 1 if the household is poor and 0 otherwise.

 

Results

It is evident that most of the explanatory variables are statistically significant at 1%, with expected signs. More specifically, the results indicate that unmarried (divorced, never married or widowed and living with a partner) head of households, were significantly more likely to be poor than their counterpart (married head of households). As expected, female-headed households are more likely to be poor than male-headed households.

The results also show that educational levels (primary, secondary, matric and tertiary) of the household head significantly reduce the probability of being poor, implying that a higher level of education provides greater opportunities for a better job and, subsequently, a higher income

The results also indicate that race dummies have an important influence on poverty incidence. In comparison with Black population group, Whites, Indians and Colored population groups, are less likely to be poor.

 

Conclusion

The issue of poverty remains on the agenda of the government and is of paramount importance to policy-makers, academics and development practitioners. In this paper, we employed a methodology for estimating both poverty and household welfare using the National Income Dynamic Study. More importantly we found that compared to traditional rural areas, households living in urban and farms are less likely to be poverty stricken. Moreover, we found that, educational levels (primary, secondary, matric and tertiary) of the household head reduce the probability of being poor.

 

 

 

 

 

b. Start with the data set you tabulated for the previous assignment—‘for U.S. states find time-series (historic) data for the most recent 30 years on poverty rate, state unemployment rate, and transfer payments. Raise the number of states at least to 35 (for d.f issues). Add two variables state inflation rate and the percentage of college graduation completion rate in the state.

 

c. Set expectations and hypothesis testing—again the poverty rate being the dependent variable and four independent variables (including both new and the previously used variables).

- + -

 

We let our model to be linear, here is the estimated poverty rate in State i, is the intercept here, is the coefficient of Transfer Payment Spending variable, is the coefficient of unemployment rate variable, is the coefficient of inflation rate variable and is the coefficient of Percentage of College Graduate is the stochastic error term

The signs above the coefficients indicate the expected impact of that particular independent variable on the dependent variable, holding constant the other explanatory variable, and is a typical stochastic error term.

 

Transfer Payment Spending

We expect the sign of Transfer Payment Spending to be weakly negative because transfer payment spending can’t have much impact on the poverty rate. Transfer Payment can’t help in reducing the poverty rate, it is just the program to help poor old people, disabled people through Social Security. So, I expect this to be weakly negatively related with poverty rate.

The Hypothesis will be

Null Hypothesis:

Alternate Hypothesis:

Type 1 Error- Reject the Null hypothesis when it is actually true

Type 2 Error - Failing to reject the null hypothesis ( ) when it is actually false.

 

Unemployment rate

We expect the sign of Unemployment to be strongly positively because generally unemployment creates Poverty. Unemployment leads to financial crisis and reduces the overall purchasing capacity of a nation. This in turn results in poverty followed by increasing burden of debt. Lack of employment opportunities and the consequential income disparity bring about mass poverty in most of the developing and under developed economies of the world.

The Hypothesis will be

Null Hypothesis:

Alternate Hypothesis:

Type 1 Error- Reject the Null hypothesis when it is actually true

Type 2 Error - Failing to reject the null hypothesis when it is actually false.

 

Inflation rate

We expect the sign of inflation to be positively related to poverty because inflation creates poverty but not strongly positively related because Inflation tends to hit not the poorest in society, but, the middle classes with savings. If you have cash savings, high inflation can destroy your wealth. The poorest often have little savings and are so not affected by inflation. Moderately higher inflation rate doesn’t necessarily increase poverty.

The Hypothesis will be

Null Hypothesis:

Alternate Hypothesis:

Type 1 Error- Reject the Null hypothesis when it is actually true

Type 2 Error - Failing to reject the null hypothesis when it is actually false.

 

Percentage of College Graduate

We expect this to strongly negatively relate with the poverty because if we have States with greater no of Percentage of Graduation rate (%) then we also expect those states to be highly educated, lower poverty and better employment.

The Hypothesis will be

Null Hypothesis:

Alternate Hypothesis:

Type 1 Error- Reject the Null hypothesis when it is actually true

Type 2 Error - Failing to reject the null hypothesis when it is actually false.

 

d. Set hypotheses, run two regressions: one with all the variables--poverty rate being the dependent variable--and another without the state inflation rate (now you have three regressions including the one from the previous assignment.) properly report results (based on convention)

 

1. With All Variables

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.794812926
R Square	0.631727587
Adjusted R Square	0.584208567
Standard Error	2.522905876
Observations	36
ANOVA
	df	SS	MS	F	Significance F
Regression	4	338.4733241	84.61833	13.2942	2.03571E-06
Residual	31	197.3166759	6.365054
Total	35	535.79
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	78.4949794	13.83711067	5.672787	3.12E-06	50.27400613
Transfer Payment Spending per capita(2016)	2.58915E-05	0.000143635	0.180259	0.858122	-0.000267054
% of College Graduation Completion Rate	-0.792271315	0.149072106	-5.31469	8.71E-06	-1.09630588
Unemployment Rate(%,2016)	0.997586884	0.460949625	2.164199	0.038269	0.057473927
Inflation Rate (%)	-0.109729749	0.653763679	-0.16784	0.867797	-1.443089563

 

2. Excluding Inflation rate

 

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.794602365
R Square	0.631392919
Adjusted R Square	0.596836005
Standard Error	2.48430063
Observations	36
ANOVA
	df	SS	MS	F	Significance F
Regression	3	338.2940121	112.7647	18.2711	4.33446E-07
Residual	32	197.4959879	6.17175
Total	35	535.79
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	78.34798677	13.59805873	5.761704	2.17E-06	50.64964753
Transfer Payment Spending per capita(2016)	1.82553E-05	0.000134154	0.136077	0.892613	-0.000255008
% of College Graduation Completion Rate	-0.792761225	0.146762879	-5.40165	6.17E-06	-1.091707426
Unemployment Rate(%,2016)	0.995369439	0.453709751	2.193846	0.035625	0.071192918

 

 

3. Previous Part Output

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.5597449
R Square	0.313314353
Adjusted R Square	0.264265378
Standard Error	2.991051756
Observations	31
ANOVA
	df	SS	MS	F	Significance F
Regression	2	114.2952566	57.1476283	6.387786	0.005183362
Residual	28	250.4989369	8.94639061
Total	30	364.7941935
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	4.931478982	2.200006073	2.24157517	0.0330969	0.42497083	9.4379871
Transfer Payment Spending per capita(2016)	-0.000121021	0.000157333	-0.7692043	0.4482125	-0.0004433	0.0002013
Unemployment Rate(%,2016)	1.902967826	0.539592063	3.52667868	0.0014707	0.79766359	3.0082721

 

 

e. Interpret the results of the full equation based on expectations (based on a theoretical/literature backing), and on statistical grounds (robustness of individual estimated coefficients of the parameters and overall fitness also see if there is possible of multicollinearity).

Solution:

Here R-Square (Coefficient of determination) is 0.7948 or 79.48%, which means our model is 79.48% explained and remaining variation of 20.52% remain unexplained.

Standard error of estimate is 2.52291 which tells us that the average distance of the data points from the fitted line is about 2.55291% poverty rate. So, we can say that our model needs to be more precise

The degree of freedom of regression is 4 because we have two independent groups

The degree of freedom of residual is 31 (35-4).

The F ratio is the test statistic used to decide whether the model as a whole has statistically significant predictive capability, that is, whether the regression SS is big enough, considering the number of variables needed to achieve it. F is the ratio of the Model Mean Square to the Error Mean Square. Here F ratio 13.2942 and significant F is 0.0000 which indicate the model is significant.

The Equation (Consider all variables)

 

If and

 

 

 

 

 

 

The Correlation matrix would be

	Poverty Rate(%,2016)	Transfer Payment Spending per capita(2016)	% of College Graduation Completion Rate	Unemployment Rate(%,2016)	Inflation Rate (%)
Poverty Rate(%,2016)	1
Transfer Payment Spending per capita(2016)	0.010143587	1
% of College Graduation Completion Rate	-0.748387295	0.152794561	1
Unemployment Rate(%,2016)	0.515076867	0.336325191	-0.355197879	1
Inflation Rate (%)	-0.012642756	0.361285749	0.062429354	0.141139956	1

 

From the table, there is no variables which are related to each other, so no case of multicollinearity

In Hypothesis we expect the sign of to be negative, sign of to be positive, to be negative and to be positive.

Here (positive) (But not significant variable)

(Positive)

(Negative)

(Negative)

However the P value which denotes the lowest significance at which Hypothesis can be rejected is 0.8581 for the Transfer Payment Spending variable which indicates the variable is not significant and can’t be used in the model. P value for the unemployment rate is 0.0383 which is significant enough and thus this variable can be used in the model and thus results confirm our Expectation. P value for the % of College graduation is 0.0000 means variable is significant, P value for the % Inflation rate is 0.8678, indicates variable is not significant.

 

f. If the base for comparisons is the equation with three dependent variables, establish if there is a reason to believe your original equation is understated--with an (an) omitted variable(s). Also establish if the equation with four independent variables might have an irrelevant variable.

Solution: No, I don’t believe our original equation is understated and have an omitted variable because correlation between independent variable is not so high which indicates the possibility of an omitted variable

Yes, equation with four independent variables have an irrelevant variables of Inflation rate because its p value is high.

 

g. If you were to correct for an omitted variable, how would you establish the ‘expected bias?’

Solution: The expected bias equals the coefficient of the omitted variable times a function of the correlation between the included and omitted variables.

This bias exists unless:

1. the true coefficient equals zero,

2. the included and omitted variables are uncorrelated in the sample

The term is the amount of expected bias introduced into the estimate of the coefficient of the included variable by leaving out the omitted variable.

 

f. Visually decide (with a scatter diagram if one of the variables may have a nonlinear relationship with the dependent variable—in reality this is done with all of the independent variables)?

Solution: No, there is no variable which have Non Linear Relationship with the Poverty variable.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

References

Sources

http://www.worldatlas.com/articles/us-poverty-rate-by-state.html

https://www.bls.gov/web/laus/laumstrk.htm

https://www.theatlantic.com/business/archive/2014/05/which-states-are-givers-and-which-are-takers/361668/

https://en.wikipedia.org/wiki/List_of_U.S._states_by_educational_attainment

https://www.bls.gov/cpi/

https://academlib.com/1012/economics/omission_relevant_variable

https://are.berkeley.edu/courses/EEP118/current/handouts/OVB%20versus%20Multicollinearity_eep118_sp15.pdf

 

 

 

 

 

Make sure all work is supported (and data provided) with a print out (attached in an appendix).

ScatterPlot

Poverty Rate(%,2016) 88.4 89.3 86.9 85.4 91 89.5 87.9 87.8 91.5 90.2 84.2 83.4 91.6 89.4 89.8 89.6 92.4 82.3 88.4 92.8 90.7 85.1 85 84.2 85.5 86.9 81.900000000000006 92 88.6 11.6 16.3 13 15.4 9.3000000000000007 11.1 12.1 11.8 9.8000000000000007 11.2 15.2 20.2 12.7 7.1 9.6 11.1 8.6999999999999993 21.1 13 11.7 9.6 10.1 20.6 20 17.3 17.3 16.399999999999999 6.4 9.4

% of College Graduation

 

 

Poverty

 

 

 

ScatterPlot

Poverty Rate(%,2016) 4866.8 5163.8 3160.8 3135.9 6152 5716.1 7501.4 8095 24675 3699.2 3724.7 8072.5 4114.3 6031.9 4262.1000000000004 5871.1 4389 8427.6 5206.8999999999996 5385.4 6646.9 8684 5309.8 5522.3 5774 4796.6000000000004 5824.4 4883.1000000000004 4115.8 4545.2 5002 3935 6264 5555 5253.5 6306.4 16.2 12.6 16.100000000000001 16 13.9 8.5 9.8000000000000007 11.6 16.3 13 15.4 9.3000000000000007 11.1 12.1 11.8 9.8000000000000007 11.2 15.2 20.2 12.7 7.1 9.6 11.1 8.6999999999999993 21.1 13 11.7 9.6 10.1 20.6 20 17.3 17.3 16.399999999999999 6.4 9.4

Transfer Payment Spending

 

 

Poverty

 

 

 

Scatterplot

Poverty Rate(%,2016) 2 1.5 2.7 1.6 1.5 1.1000000000000001 2.1 3.1 3.7 2.8 2.7 2.6 1.4 1.9 1.2 0.9 3.1 3 2.7 2.6 1.8 1.6 2.2000000000000002 2.4 2.5 2.7 3 2.8 2.9 1.5 1 1.7 2.4 2.2999999999999998 2.7 2.8 16.2 12.6 16.100000000000001 16 13.9 8.5 9.8000000000000007 11.6 16.3 13 15.4 9.3000000000000007 11.1 12.1 11.8 9.8000000000000007 11.2 15.2 20.2 12.7 7.1 9.6 11.1 8.6999999999999993 21.1 13 11.7 9.6 10.1 20.6 20 17.3 17.3 16.399999999999999 6.4 9.4

Inflation rate

 

 

Poverty

 

 

 

ScatterPlot

Poverty Rate(%,2016) 4.2 7.2 5 3.5 5.0999999999999996 2.4 4.8 4.9000000000000004 6.4 4 4.7 2.6 2.9 5 3.5 3.3 3.9 5.4 5.3 3.8 3.9 4.2 3.9 3.8 5.3 4 3.9 2.8 4.9000000000000004 5.0999999999999996 6.2 3 4.5 4 2.7 4.5 16.2 12.6 16.100000000000001 16 13.9 8.5 9.8000000000000007 11.6 16.3 13 15.4 9.3000000000000007 11.1 12.1 11.8 9.8000000000000007 11.2 15.2 20.2 12.7 7.1 9.6 11.1 8.6999999999999993 21.1 13 11.7 9.6 10.1 20.6 20 17.3 17.3 16.399999999999999 6.4 9.4

Unemployment Rate (%)

 

 

Poverty