Problem Set #3 Economics 43

Due Friday, October 24^th at the start of class Prof. Stephen Schmidt

The United States has a federal form of government, meaning that there is a central national government and state governments below that. Within each state, there are still smaller governing units – cities, counties, towns, school districts, and others. All of these units of government spend money. They raise some of that money themselves, but most of them also receive money from other units of government. In particular, most school districts in the United States receive money from state governments, which they spend on education in that particular school district.

Economists who study public finance have asked several questions about the effects of state aid to schools on education spending, and about the effects of grants from one level of government to another generally. Some argue that state aid and local taxes are substitutes. They argue that if school districts receive more aid from the state, they simply reduce their local tax collections by an equal amount of money, leaving the total amount of money spent on education unchanged. Others argue that giving aid to school districts increases the total amount of resources available to the school district, and thus increases total education spending. In this problem set we’ll look at a sample of data on 50 states, and see how much (if at all) education spending rises in states with higher amounts of state aid to school districts. If you would like to read more about this topic, you can look at the paper “Federal Aid and Public Education: An Empirical Look at the New Fiscal Federalism” by Stephen Craig and Robert Inman, which is available in JSTOR and is linked from the Eco 43 course page. However, you do not need to read that paper to do this problem set.

1. The data for this problem set is found on the Union academic server, in the Courses file, in the economics file, in the eco43 file, in the file schoolspend.xls. This is an Excel file. Double-clicking on this file should open it in Excel. The file has observations on 8 variables for all 50 states. The variables are:

Totalspend – Total spending on education in the state, $millions

Totalstateaid – Total aid from the state government to schools, $millions

Schoolage – Percentage of the state’s population that is age 6 to 18

Elderly – Percentage of the state’s population that is age 65 and older

Income – Total income in the state, $millions

Minority – Percentage of the state’s population that is nonwhite
Population – Of the state, in millions

Salary – Average salary of a public school teacher, in dollars per year

a) How much money does New York spend on education? What is New York’s population? Calculate the amount of money spent per capita.
b) What is the average teacher’s salary in New York? Is this higher than most states, or lower? What is the average teacher’s salary in Mississippi? What is the average teacher’s salary in your home state? (Include the name of the state in your answer. If you are from New York or Mississippi, look up the average teacher salary in California.)
To run regressions, you need to load the data into Eviews. Follow the directions given on the “Loading Excel data into Eviews” handout given out in class (copies are available on the table outside my office). The Eviews workfile should be undated with 50 observations. The series are in columns, the first data cell is B2, and there are 8 series to be loaded. After you have loaded the data, select the View menu, and choose “Select All (except C-RESID)”. Then double-click on the variables to open a group. Click on the View button in the group, select Descriptive Statistics, and select Common Sample. Print the resulting window, and hand in the printout along with your answers. You will probably want to save your Eviews data file to a floppy disk, so you can work on the problem set later without having to reload the data from Excel to Eviews.

c) Open the totalspend variable and display its histogram and statistics. How much money is spent on schools in the average state? (Be sure to get the units right.) How much is spent in the state that spends the most? How much is spent in the state that spends the least? Look in the Excel file and find out what states spend the most and the least. Which are they? Why do you think these particular states spend the most and the least respectively?

2. Using Eviews, estimate the regression

Totalspend_i = b₀ + b₁*totalstateaid_i + b₂*schoolage_i + b₃*salary_i + b₄*income_i +
b₅*population_i + b6*minority_i + b7*elderly_i + e_i

Print your regression result and turn it in along with your answer.

a) How many of the estimated parameters are statistically significantly different from zero, and how many are not? Which of these variables appear to affect total spending, and which appear not to affect it?
b) How many degrees of freedom does this regression have? Test the null hypothesis that b₁=0 against the alternative that b₁¹0. Do you reject, or fail to reject? On the basis of this test, does an increase in state aid increase spending, decrease it, or have no effect?
c) Perhaps one problem with this regression is that we have included some irrelevant right-hand side variables. In particular, perhaps population demographics don’t actually matter. If so, then it must be that b6=b7=0. Estimate the regression

Totalspend_i = b₀ + b₁*totalstateaid_i + b₂*schoolage_i + b₃*salary_i + b₄*income_i +
b₅*population_i + e_i

Print your regression result and turn it in along with your answer. Using an F-test, test whether this model is an acceptable restriction of the regression in part a. Do you conclude that minority and elderly do not affect spending, or that they do?
d) Continue dropping variables whose parameters are not statistically significantly different from zero, making appropriate tests to see that dropping them is acceptable, until all remaining parameters are statistically significantly different from zero at the 5% level. Print your final regression and turn it in with your answers. Perform an F-test to make sure this final regression is an acceptable restriction of the original one from part a.

e) On the basis of your final regression, if population rises by 1000 people, how much does total spending rise? Does this seem like a reasonable amount or not? If total state aid rises by 1 million dollars, how much does total spending rise? How do you know?

3. The regression from problem 2 suffers from the problem that it tries to compare large states to small states. This may be obscuring the effect of state aid on spending. In this problem we’ll try looking at aid per student and spending per student, which may make large and small states easier to compare. First, we need to calculate some new variables. Type the following commands at the Eviews command line:

genr students = population*schoolage/100
genr incomepc = income/population

genr spendps = totalspend/students

genr stateaidps = totalstateaid/students

a) Double-click on the variable stateaidps, and display its histogram and statistics. What is its mean value? (Its standard deviation should be 800.7193. If not, you probably made a mistake generating it. Check your work, and fix errors until you get that standard deviation.)
b) Double-click on the variable spendps, and display its histogram and statistics. What is the mean value of spending per student? In the average state, what fraction of spending is paid for with state aid? What is the highest value of spending per student, and what is the lowest value? Does this seem like a small amount of variation across states in spending on education per student, or a lot? Explain your answer.
c) Click on incomepc, then hold down the control key and click on spendps. Open them as a group, press the View button, and graph them as a scatter graph. Print the graph and turn it in along with your answers. Do the variables appear to be strongly correlated or weakly correlated? Do states with higher incomes per person appear to spend more money per student on education, or less?

4. Now we can analyze spending and state aid using variables that are more comparable across states than the first set of variables were. Estimate the regression

Spendps_i = b₀ + b₁*stateaidps_i + b₂*schoolage_i + b₃*salary_i + b₄*incomepc_i +
b₅*population_i + b6*minority_i + e_i

a) How many of the parameters are statistically significantly different from zero, and how many are not? Which variables affect spending per students, according to this model? Is this more variables or fewer than in the regression from question 2a? Are you surprised by any of the variables that do not affect spending? Briefly explain why.
b) Click on the variable incomepc, then hold down the control key and click on the variable salary. Open them as a group, click the View button, and select Correlations. What is the correlation of these variables? Why might be correlated in this way? Explain why this correlation might cause incomepc to be insignificant in the regression in part a.
c) Test the null hypothesis that b₁=0 against the alternative that b₁¹0. Do you reject, or fail to reject? On the basis of this test, does an increase in state aid increase spending, decrease it, or have no effect?
d) Test the null hypothesis that b₁=1 against the alternative that b₁¹1. Do you reject, or fail to reject? If state aid increases by $1 per student, does total spending increase by $1, by more than $1, or less than $1?
e) Calculate a 95% confidence interval for the true value of b₁. Is it reasonable to believe that a $1 increase in state aid produces a 10 cent increase in total spending? Is it reasonable to believe that a $1 increase in state aid produces a 75 cent increase in total spending?
f) If state aid increases by $100 per student, how much do you predict total spending rises? If so, then what must happen to local taxes for schools when state aid increases by $100?

5. a) The regression from problem 3 still contains some insignificant variables on the right-hand side. Re-estimate this regression, dropping insignificant variables, until all remaining variables are significant at the 5% level. Using an F-test, test whether this model is an acceptable restriction of the regression in problem 3. If it is not, you probably dropped a significant variable by mistake, or you dropped two variables at once when you should have kept one of the two. Keep trying until you get an acceptable final regression by the F-test. Print your final regression (several different answers are possible) and turn it in along with your answers.
b) How many variables affect spending in your final model? For each variable other than state aid, does an increase in that variable increase or decrease total spending? Give a short explanation (not more than two or three sentences) of why you think that each significant variable might affect spending.
c) Has your estimated value of b₁ changed much as a result of simplifying the model? On the basis of this model, does a $1 increase in state aid increase total spending, or not? If it does, does it increase it by more than $1 or less than $1? Support your answers with appropriate test statistics.
d) Write a short (two or three paragraph) essay answering the following questions. Use the econometric results of this problem set to justify your answers.

When state governments increase state aid to school districts, do school districts use the increased state aid to reduce local tax collections or not? If so, how much? Are state aid and local school taxes substitutes or not? Is it beneficial for states to give aid to school districts or not? Why or why not?