Econometric Models on PerCapita Public Expenditure
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Transcript of Econometric Models on PerCapita Public Expenditure
Econometrics Final Project Jack Teller, Mike Weisenburger, and Christian Huitz
Dr. Leonard
May 2, 2016
Research Question
How do region, residents in urban areas, per capita income, and number of residents per
thousand under 18 years of age effect per capita expenditure on public education? Going into the
project, we anticipated that a higher per capita income would result in a higher per capita
expenditure on public education (Fernandez et. al). We also anticipated a higher number of
residents per thousand under 18 to result in a higher per capita expenditure on public education.
We anticipated both region and residents in urban areas to both be less important variables, with
the exception of the Northeast, due to research done prior to our own (Thomas).
Data
‘Residents in urban areas’ is the amount of residents in the region who reside in an urban
area as opposed to other areas. ‘Per capita income’ is the per capita income for every resident in
the region. This includes all residents who are not making an income such as children, retired
people, etc. ‘Number of residents per thousand under 18 years of age’ is the number of residents
in the region under the age of 18 for every thousand residents of the region. Per capita
Table 1: Summary Statistics
Variable Mean Std. Dev. Min. Max.
Per Capita Expenditure on Public Education in 1975 284.6 61.34014 208 546
Residents In Urban Areas 1970 657.8 145.0164 322 909
Per Capita Personal Income 1973 4675.12 644.5063 3448 5889
NorthEast NA NA 0 1
MidWest NA NA 0 1
South NA NA 0 1
Number of Residents Under 18 Years of Age in 1974 325.74 19.42312 287 386
expenditure on public education is the amount that the population of the region pays toward the
public education. The regions being studied are broken into; North East, Midwest, and South.
The data for ‘residents in urban areas’ was taken from 1970, ‘per capita income’ was taken from
1973, ‘number of residents per thousand under 18’ was taken from 1974, and ‘per capita
expenditure’ was taken from 1975
Model 1 analyzes all of our variables together. Model 2 analyzes all of the variables with
the exception of ‘residents in urban areas’. Model 3 analyzes the USA across the board as we
drop all of the region variables. Model 4 analyzes all of our variables, but is a log-linear model.
In Model 1, all of our variables are included. The public expenditure decreases $0.0345
for every unit increase in ‘residents in urban areas’. It increases $.0720 for every unit increase in
‘per capita income’. In the North East, public expenditure is only decreased by $18.596, where it
is decreased by $27.34 in the South and by $34.324 in the Midwest. The public expenditure
increases $1.301 for every one unit increase ‘residents per thousand under 18 years of age’.
In Model 2, we dropped the variable ‘residents in urban areas’. With that variable gone,
the public expenditure increases $0.0674 for every $1 increase in ‘per capita personal income’.
The North East only decreases the public expenditure by $16.4709 while the South decreases it
by $25.78973 and the Midwest decreases the most by $30.86958. The public expenditure
increases $1.349 for every one unit increase ‘residents per thousand under 18 years of age’.
In Model 3, we dropped the variables ‘North East’, ‘South’, and ‘Midwest’. The public
expenditure decreases $0.00427 for every unit increase in ‘residents in urban areas’. It increases
$0.0724 for every unit increase in ‘per capita income’. The public expenditure increases $1.552
for every one unit increase ‘residents per thousand under 18 years of age’.
In Model 4, we included all of the variables, but instead created a log linear regression by
taking the log of the dependent variable, public expenditure. Under this model, the public
expenditure increased by 39.3e-05% with a one unit increase in residents in urban areas.
Regarding income, a one unit change in income led to a 0.002136% change in the public
expenditure. The region variables all effected the percent change in public expenditures to go
down relative to a one unit change: Northeast would make it go down by about 7%, the Midwest
by about 11.5%, the South by about 11%. When the number of residents under the age of 18
increased by one unit, the public expenditure would go up by about 0.03%.
Methods & Results
The variable ‘Residents in urban areas’ is not statistically significant at a 90% confidence
interval in any of the models. ‘Per capita personal income’ is very statistically significant at a
99.9% confidence interval in every model. ‘North East’ is not statistically significant at a 90%
confidence interval in any of the models. ‘Midwest’ is very close to being statistically significant
at a 90% confidence interval in models 1 and 2 and is statistically significant at 95% in model 4.
Table 2: Estimation Results
Model 1 Model 2 Model 3 Model 4
Residents In Urban Areas 1970 -0.0345577 -0.004269 3.93e-06
(0.053188) (0.0513929) (.0001679)
Per Capita Personal Income 1973 0.0720355*** 0.0673588*** 0.0723853*** 0.02136***
(0.013051) (0.010815) (0.0116024) (0.0000412)
NorthEast -18.59675 -16.4709 -0.0698282
(19.688370) 19.28668 (0.0621423)
MidWest -34.32416+ -30.86958+ -0.1153706*
(17.494600) (16.55725) (0.0552181)
South -27.23673 -25.78973 -0.112916*
(17.453680) (17.196960) (0.055089)
Number of Residents Under 18 Years of Age in 1974
1.301458*** 1.349506*** 1.552054*** .0036186**
(0.357166) (0.347125) (0.3146716) (0.0011273)
Constant -433.0787** -451.2727** -556.568*** 3.527505***
(147.2736) (143.6343) (123.19530) (.4648389)
Standard Errors In Parentheses *** p<0.001, ** p<0.01, * p<0.05, +p<0.10
‘South’ is not statistically significant in models 1 or 2, but is statistically significant at 95% in
model 4. ‘Number of residents under 18 years of age’ is statistically significant at 99.9% in
models 1, 2 and 3 and at 99% in model 4.
Since model 4 contains the most statistically significant coefficients, we look to model 4
to answer our research question. Per capita personal income has the greatest positive affect on
public expenditure and living in the Midwest has the greatest negative effect on public
expenditure.
Model 1 ----------------------------------------------------------------------------------------------
Percapitaexpenditureonpublic | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-----------------------------+----------------------------------------------------------------
ResidentsinUrbanAreasinTho | -.0345577 .0531881 -0.65 0.519 -.1418217 .0727063
PerCapitaPersonalincome1973 | .0720355 .0130507 5.52 0.000 .0457163 .0983547
northEast | -18.59675 19.68837 -0.94 0.350 -58.30213 21.10863
Midwest | -34.32416 17.4946 -1.96 0.056 -69.60538 .957064
South | -27.23673 17.45368 -1.56 0.126 -62.43543 7.961967
NumberofResidentsperthousand | 1.301458 .3571664 3.64 0.001 .5811636 2.021753
_cons | -433.0787 147.2736 -2.94 0.005 -730.0842 -136.0731
Public_Expenditure = -433.08 - 0.035Urban Residents +.072Income - 18.597NorthEast -
34.32Midwest -27.23673South + 1.30 Res_under_18
Model 2 ----------------------------------------------------------------------------------------------
Percapitaexpenditureonpublic | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-----------------------------+----------------------------------------------------------------
PerCapitaPersonalincome1973 | .0673588 .0108145 6.23 0.000 .0455637 .089154
northEast | -16.4709 19.28668 -0.85 0.398 -55.34065 22.39886
Midwest | -30.86958 16.55725 -1.86 0.069 -64.23853 2.499364
South | -25.78973 17.19696 -1.50 0.141 -60.44793 8.868459
NumberofResidentsperthousand | 1.349506 .3471245 3.89 0.000 .6499229 2.04909
_cons | -451.2727 143.6343 -3.14 0.003 -740.7486 -161.7968
----------------------------------------------------------------------------------------------
Public_Expenditure = -451.27 - 0.067Income -16.47NorthEast – 30.87Midwest – 25.79South
+ 1.35 Res_under_18
Model 3 ----------------------------------------------------------------------------------------------
Percapitaexpenditureonpublic | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-----------------------------+----------------------------------------------------------------
ResidentsinUrbanAreasinTho | -.004269 .0513929 -0.08 0.934 -.1077175 .0991794
PerCapitaPersonalincome1973 | .0723853 .0116024 6.24 0.000 .0490308 .0957398
NumberofResidentsperthousand | 1.552054 .3146716 4.93 0.000 .9186534 2.185456
_cons | -556.568 123.1953 -4.52 0.000 -804.5472 -308.5889
Public_Expenditure = -556.57 - 0.004Urban Residents +.072Income + 1.55 Res_under_18
Model 4 ----------------------------------------------------------------------------------------------
lnPercapitaexpenditureonpu~c | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-----------------------------+----------------------------------------------------------------
ResidentsinUrbanAreasinTho | 3.93e-06 .0001679 0.02 0.981 -.0003346 .0003425
PerCapitaPersonalincome1973 | .0002136 .0000412 5.19 0.000 .0001305 .0002967
northEast | -.0698282 .0621423 -1.12 0.267 -.1951501 .0554936
Midwest | -.1153706 .0552181 -2.09 0.043 -.2267285 -.0040127
South | -.112916 .055089 -2.05 0.047 -.2240135 -.0018186
NumberofResidentsperthousand | .0036186 .0011273 3.21 0.003 .0013451 .005892
_cons | 3.527505 .4648389 7.59 0.000 2.590068 4.464942
----------------------------------------------------------------------------------------------
Public_Expenditure = 3.5 - 3.93e-06Urban Residents +.0002Income - .069NorthEast -
.115Midwest -.11South + .0036 Res_under_18
Conclusion
After looking at each model, determining that model 4 was the most reliable and told us
the most about the data, we were able to conclude that the various regions, per capita personal
income in 1973, and the number of residence per thousand all play a role when looking at
determining the per capita expenditure on public education. It seems that the South spends the
least on education (decreasing per capita by about 11.5% relative to the rest of the model) , while
the Northeast would seem to spend the most. While the variable Northeast is only significant at a
75% confidence interval, this result is most likely due to a low degrees of freedom. Limits of the
model are for one, the fact that the data was compiled in 1975, but drew from data that was
gathered as far back as 1970. Other limitations we discovered in our research is that state wealth
isn’t the sole predictor of public expenditure. The effort the state makes towards its school
system has an effect on public education expenditure (Baker, et. al). Also, school district
organization, a variable not analyzed in our models, also seems to play a role in how the income
in the state is allocated towards education according to some sources (Littlefield).
Citations
Baker, Bruce, David Sciarra, and Danielle Farrie. "S School Funding Fair? A National Report
Card." Schoolfundingfairness.org. Education Law Center, Sept. 2010. Web. 2 May 2016.
<http://www.schoolfundingfairness.org/National_Report_Card.pdf>.
Fernandez, Raquel, and Richard Rogerson. "The Determinants of Public Education
Expenditures: Evidence from the States, 1950-1990." The National Bureau of Economic
Research 5995 (1997): 1-18. Nber.org/papers. Web. 2 May 2016.
<http://www.nber.org/papers/w5995.pdf>.
Littlefield, Larry. "Local Government Education Expenditures: 2012 Census of Governments
Data." Saying the Unsaid in New York. Wordpress, 10 Mar. 2015. Web. 03 May 2016.
<https://larrylittlefield.wordpress.com/2015/05/10/local-government-education-
expenditures-2012-census-of-governments-data/>.
Thomas C. Frohlich, 24/7 Wall St. "States Spending the Most on Education." USA Today.
Gannett, 2014. Web. 03 May 2016.