Economics 15 Professor Zabel Basic Econometrics Fall 2010

Exam 1 Answer Key

1.(30) Students who apply to college typically need to take the SAT exam. Exams are given in math and reading and scores on the exams range between 200 and 800. Suppose that you are interested in estimating the effect on hours spent in an SAT preparation course (HOURS) on total SAT scores (SAT). The population is all college-bound high school seniors for a particular year. A.(10) Suppose you are given a grant to run a controlled experiment. Explain how you would structure the experiment in order to estimate the causal effect of HOURS on SAT. Explain how you would use the results of the experiment to estimate this causal effect. Answer: I would take a random sample of all college-bound high school seniors. Then I would randomly divide the sample of students into two groups and each group would receive a different number of hours of an SAT preparation course, say h1 > h2 (note that h2 could be zero). Because of this randomized experiment the number of SAT preparation course hours would be uncorrelated with any other variable, including the error term. In this case the difference in the average value of SAT scores, diff = across the two groups can be attributed to the difference in HOURS. That is, the effect of studying h2 versus h1 hours would lead to a change in the SAT score of diff. Consider a more realistic case where students choose how much time to spend in a preparation course, and you can only randomly sample SAT and HOURS from the population of all college-bound high school seniors. In this case, the population model can be expressed as

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B.(5) Write down the interpretation of and . What is the expected sign of ? Why? Answer: is the average value of SAT given no hour spent in the preparation course. An increase of one hour in a preparation course will lead to a change in SAT score of , on average. The expected sign of is positive. This is because an additional hour of preparation should provide the person with greater knowledge to better on the SAT test. C.(5) Explain how you would determine if this effect is statistically/economically significant Answer: To determine if this effect is statistically significant, test the hypothesis

A rejection of this hypothesis will indicate that the impact is statistically significant. To determine if this effect is economically significant, calculate the standardized coefficient

I would NOT calculate the elasticity since the units of measurement of SAT is not meaningful.

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D.(5) Do you think that the above model allows one to measure the causal relationship between HOURS and SAT? Why or why not? Be as specific as possible in giving reasons for your answer. Answer: It is unlikely that measures the causal relationship between HOURS and SAT. This is because the students that take the preparation course are not a random sample from the population of students who will take the SAT. For example, one might expect that these students have a lower GPA on average than students who do not take the course. Thus, one could get the result that the average SAT score for the students who take the course is lower than for the students who do not take the course and hence the estimate of could be negative. 2.(10). What is the standard error of the regression? (Explain in words, just writing down the formula is not good enough). How does it relate to the goodness of fit of the regression? Explain how the SER is used in hypothesis testing. Answer: The standard error of the regression (SER) is an estimator of the standard deviation of the error term in the linear regression model. The formula is

Since the variance of y conditional on x is equal to the variance of the error term, the standard error is an estimator of how spread out the observed values of Y are around its conditional (on X) mean conditional. So the larger the SER, the worse the fit of the regression. When carrying out hypothesis tests about the coefficients in the regression model using the OLS estimators of these coefficients, we need the standard deviations of the OLS estimators. These standard deviations are a function of the standard deviation of the error term. Since the standard deviation of the error term is not observed, we use the SER to estimate it.

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3.(50). Suppose you work for the Justice Department and you are investigating price discrimination in the retail market. In particular, you are interested in determining if fast-food restaurants charge higher prices in the areas with larger concentrations of blacks. You collect data at the zip code level on prices for various items at fast food restaurant along with characteristics of the population in each zip code in New Jersey and Pennsylvania. You form the following model A.(5) Interpret the coefficient estimates for pctncar, income, and hrsopen. Answer: A one percentage point increase in pctncar will lead to a $0.0059 decrease in the price of an entre, on average and all other regressors held constant. A $10,000 increase in median family income will lead to a $0.063 decrease in the price of an entre, on average and all other regressors held constant. If stores stay open one more hour per day, the price of an entre will decrease by $0.143, on average and all other regressors held constant.

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B(10). Show that the R2 for the regression is 0.412 and interpret this result. Carry out a test for the overall significance of the regression at the 1% significance level. Interpret the result of this test. Answer:

This implies that 41.2% of the variation in the price if an entre is explained by the regression. The test for the overall significance of the regression at the 1% significance level

The result is

Hence, we reject the null hypothesis that the slope coefficients are jointly zero. This means that the regressors significantly explain the variation in pentree.

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C(10). Test the hypothesis at the 1% significance level that there is price discrimination against blacks in fast food stores in New Jersey and Pennsylvania. What is the result? Is the result economically significant (why or why not)? Answer:

The result is

The result is that there is evidence of discrimination against blacks in fast food stores in New Jersey and Pennsylvania. To determine economic significance, we calculate the elasticity

Or the standardized coefficient

Thus, using the elasticity, the impact of pctblack on the price of an entre IS NOT economically significant. BUT using the standardized coefficient, the impact of pctblack on the price of an entre IS economically significant

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D.(10). Calculate the expected difference in the price of an entree for zip codes that differ in the median household income by $20,000. Test at the 5% significance level the hypothesis that the magnitude of this difference is at least 10 cents. Calculate the p-value of the test and interpret your result. Answer: E[entre|income = x + 2] - E[entre|income = x] = 2 =2-0.063=-0.126 Hypothesis test:

The result is

The p-value = P(Z > 0.44) = 0.33. This implies that the smallest significance levels at which the null hypothesis will be rejected is 0.33. E.(10). The variables pctpov, pctncar, and crimerate capture local economic conditions. Carry out a test at the 5% significance level of whether or not the local economic conditions affect the price of an entre. Answer:

The result is

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Table3:RegressionResults

DependentVariable:PriceofanEntreeVariables (1) (2)pctblack 0.0070 0.0050 (0.0020) (0.0016)income 0.0630 0.0135 (0.0296) (0.0230)crimerate 1.4208 (0.8869) wagest 0.0111 0.0285 (0.0798) (0.0796)hrsopen 0.1435 0.1435 (0.0098) (0.0097)pctpov 0.0120 (0.0120) pctncar 0.0059 (0.0064) nstores 0.0651 0.0513 (0.0163) (0.0148)Constant 3.8355 3.4235 (0.4344) (0.3949)Observations 377 377Rsquared 0.400StandarderroroftheRegression 0.5018 TotalSumofSquares 157.61 Standarderrorsinparentheses