Solutions to Problem Set 3 Economics 43

1a) New York spends $25,786,820,000 (about $26 billion) on education. New York’s population is 18,058,000 (18 million people). This means about $1428 per person.
b) The average New York teacher salary is $42,080 per year. In Mississippi it is $24,366 per year. Your home state’s teacher salary varies with the state you’re from; the value for my home state (Wisconsin) is $33,100 and the value for California is $39,598.

1c) The mean value is $4,865,940,000. The maximum is $26.537 billion and the minimum is $467 million. The state that spends the maximum is California, and the state that spends the minimum is North Dakota. Big states spend more than small ones; California is the most populous state and North Dakota is one of the least populous.

2a) Three parameters are significant, five are not. Population and teacher salaries matter, and the others do not. (The third significant parameter is the intercept.)
2b) 50 observations – 8 parameters = 42 degrees of freedom. The t-statistic is –0.433 and the critical value is 2.02. Therefore we fail to reject the null hypothesis. State aid appears to have no effect on spending.
2c) The SSR from the restricted regression is 91066410. The SSR from the unrestricted is 83330417. The F-statistic is (91066410-83330417)/2 / (83330417/42) = 0.92. The critical value for 2,42 degrees of freedom is 3.23. We fail to reject the null hypothesis. Dropping these variables is acceptable; we conclude that they do not affect spending.
2d) Answers depended on the final regression you ended up with. Most people should have found that only salary and population matter.
2e) Answer depended on your final regression; most people should have gotten a rise of $929,000, which is fairly reasonable. Most people should have found that a rise in state aid has no effect on spending, because it was dropped from the regression.

3a) The mean value of state aid is $2284 per student.
3b) The mean value of spending is $5114 per student. In an average state, the state pays 2284/5114 = 44.7% of the costs. The highest value is $9159 per student (in New Jersey), the lowest is $2993 (in Utah). This is an enormous variation; some states spend more than three times as much educating their children as others do.
3c) The variables are fairly strongly correlated, positively. States with higher incomes per capita spend more per student.

4a) Four parameters are significant, three are not. State aid, school age fraction, salary, and minority affect spending, income per capita and population do not. This is two more than in the previous regression. It is surprising that income per capita does not affect spending; one would think richer states could afford more education spending.
4b) The correlation is 0.82. They are probably correlated because in a high income area, you need to pay teachers more to get them to take teaching jobs. Cost of living may be higher in those areas also, requiring higher teacher salaries. Because incomepc and salary are highly correlated, we cannot include both in this regression. By dropping incomepc we attribute all income effects to teacher salaries.
4c) The test statistic is 2.12 against a critical value of 2.02. We reject this null hypothesis, albeit not by much. Increases in state aid do increase total spending.
4d) The test statistic is (0.289-1)/0.136 = -5.228. We reject this null hypothesis also. A $1 increase in state aid increases total spending by less than $1.
4e) The 95% confidence interval is 0.289 +/- 2.02*0.136 = [0.014, 0.564]. A 10 cent increase is a reasonable belief; a 75 cent increase is not reasonable.
4f) Predict a rise of $100*0.289 = $28.90. Local taxes must be reduced by $71.10 in that case.

5. Answers to this problem varied depending on what regression you ended up with. Most people should have ended up keeping stateaidps, schoolage, salary, and minority. States with many schoolchildren have lower education spending per student, either because large classes are cheaper or because states with many children can’t be as generous with each one. Salary matters because if you have to pay teachers more, education costs more. It is not clear why minority matters, but several explanations are possible. It is probably not due to lower income for minorities, because incomepc dropped out of the equation. It may have something to do with poor inner city schools, or with a lower willingness to pay for education in states with large minority populations. Your essay should have concluded that local governments do reduce their own taxes when they get state aid, by about 70 cents for each dollar of state aid. State aid helps but only at about 30 cents on the dollar because of this substitution.