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 ----------------------------------------------------------------------------------------------


-----------------------------+----------------------------------------------------------------


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


_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 ----------------------------------------------------------------------------------------------


-----------------------------+----------------------------------------------------------------

ResidentsinUrbanAreasinTho | -.004269 .0513929 -0.08 0.934 -.1077175 .0991794



_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


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.

Econometric Models on PerCapita Public Expenditure

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