1 Econ 122B Problem Set 3 Name(Print)______________________ Due in class on May 25 UCI ID____________________________ 1-3 are based on the following information. Each question is independent. Suppose that you collect data on 1,000 households in CA on their consumption and income information as well as their size. You are intended to estimate Cons Inc Size u = + + + , αβ β 1 2 where Inc is disposable income, Cons is consumption expenditure, and Size is the adult equivalent number of people in a household. 1. Suppose that unfortunately, you notice that there are reporting errors in disposable income. Which of the following is correct? a) If the reporting error is random, OLS estimates of coefficients would not be biased. b) If the reporting error is random, OLS estimates of coefficients tend to be biased. c) OLS estimates will be unbiased, but less efficient. d) None of the above. 2. Suppose that there are missing values on Size. Which of the following is correct? a) If those values are missing at random, then OLS estimates of all coefficients would not be biased. b)Regardless of whether those values are missing randomly or non-randomly, OLS estimates of all coefficients would not be biased. c) Only OLS estimate of β2 will be biased, but not that of β1 . d) As long as we don’t have missing values on Cons, OLS will be unbiased. 3. If one only includes in the sample those households with 2 or more people, then a) this would lead to a sample selection bias. b) the estimation results would not have internal validity. c) this would not lead to a sample selection bias. d) this will lead to more precise estimates of the coefficients. 2 4. Suppose you are interested in learning how recession could change people’s charitable donation behavior. Suppose you have data on individual’s dollar amount donated to some good cause (Don) and individual’s income (Inc), in dollars, for the United States for the period 1979-1985. In 1982 the United States suffered a very bad recession, an event that might disturb the relationship between Don and Inc. To see if this happened, you estimate a simple savings function that relates Don to Inc. 1 23 log( ) log( ) log( ) * , Don =+ + + + αβ β β Inc D Inc D u where D=1 for 1979-1981, and 0 for 1982-1985. (1) What is the impact of the recession (D) on donations? Write down the expression for it. (2)How would you test the null hypothesis that the donation-income relationship did not change before and after the 1982 recession? Write down the null hypothesis and determine if you need to perform a t test or an F test. 5. You are curious about female labor supply, so you estimate the following model, 12 3 hours female married female married u =+ − − + αβ β β *, Below is what you get,  2 300 500 300 800 * , (30) (350) (100) (320) n=526, R .208 hours =− + − female married female married = where hours is the number of hours per year one works; female is a dummy equal to 1 if female and 0 otherwise; and married is a dummy indicating one is married or not, and married is 1 if married and 0 otherwise. (1) Based on the above estimated equation, complete the following table Table 1: Average hours per year: 3 non-married married male ______ _____ female ______ _____ (2) How would you interpret all the estimated coefficients? (3) How would you determine whether gender difference in the hours of working depends significantly on marital status? Write down the null hypothesis, determine if you need a t or an F test, and what is your conclusion? 5. In February 1992, New Jersey (NJ) increased the state minimum wage from $4.25 to $5.05, but in Pennsylvania (PA) minimum wage stayed at $4.25. Do minimum wages decrease employment in low wage labor markets (e.g. fast-food restaurant industry)? This is a classical yet controversial question. Suppose you estimate 12 3 FTE NJ Post NJ Post u =+ − − + *, αβ β β where FTE is the number of employees in a restaurant. NJ is a dummy that is 1 if a restaurant is in NJ, and 0 if it is in PA. Post is a dummy that is 1 if it is from the year after the minimum wage increase and is 0 if it’s from the year before. (1) How would you interpret β1 and β1 ? (2) How would you interpret β3 ? (3) Which coefficient captures the impact of the minimum wage increase on the average number of restaurant employees?

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1 Econ 122B Problem Set 3 Name(Print)______________________ Due in class on May 25 UCI ID____________________________ 1-3 are based on the following information. Each question is independent. Suppose that you collect data on 1,000 households in CA on their consumption and income information as well as their size. You are intended to estimate Cons Inc Size u = + + + , αβ β 1 2 where Inc is disposable income, Cons is consumption expenditure, and Size is the adult equivalent number of people in a household. 1. Suppose that unfortunately, you notice that there are reporting errors in disposable income. Which of the following is correct? a) If the reporting error is random, OLS estimates of coefficients would not be biased. b) If the reporting error is random, OLS estimates of coefficients tend to be biased. c) OLS estimates will be unbiased, but less efficient. d) None of the above. 2. Suppose that there are missing values on Size. Which of the following is correct? a) If those values are missing at random, then OLS estimates of all coefficients would not be biased. b)Regardless of whether those values are missing randomly or non-randomly, OLS estimates of all coefficients would not be biased. c) Only OLS estimate of β2 will be biased, but not that of β1 . d) As long as we don’t have missing values on Cons, OLS will be unbiased. 3. If one only includes in the sample those households with 2 or more people, then a) this would lead to a sample selection bias. b) the estimation results would not have internal validity. c) this would not lead to a sample selection bias. d) this will lead to more precise estimates of the coefficients. 2 4. Suppose you are interested in learning how recession could change people’s charitable donation behavior. Suppose you have data on individual’s dollar amount donated to some good cause (Don) and individual’s income (Inc), in dollars, for the United States for the period 1979-1985. In 1982 the United States suffered a very bad recession, an event that might disturb the relationship between Don and Inc. To see if this happened, you estimate a simple savings function that relates Don to Inc. 1 23 log( ) log( ) log( ) * , Don =+ + + + αβ β β Inc D Inc D u where D=1 for 1979-1981, and 0 for 1982-1985. (1) What is the impact of the recession (D) on donations? Write down the expression for it. (2)How would you test the null hypothesis that the donation-income relationship did not change before and after the 1982 recession? Write down the null hypothesis and determine if you need to perform a t test or an F test. 5. You are curious about female labor supply, so you estimate the following model, 12 3 hours female married female married u =+ − − + αβ β β *, Below is what you get,  2 300 500 300 800 * , (30) (350) (100) (320) n=526, R .208 hours =− + − female married female married = where hours is the number of hours per year one works; female is a dummy equal to 1 if female and 0 otherwise; and married is a dummy indicating one is married or not, and married is 1 if married and 0 otherwise. (1) Based on the above estimated equation, complete the following table Table 1: Average hours per year: 3 non-married married male ______ _____ female ______ _____ (2) How would you interpret all the estimated coefficients? (3) How would you determine whether gender difference in the hours of working depends significantly on marital status? Write down the null hypothesis, determine if you need a t or an F test, and what is your conclusion? 5. In February 1992, New Jersey (NJ) increased the state minimum wage from $4.25 to $5.05, but in Pennsylvania (PA) minimum wage stayed at $4.25. Do minimum wages decrease employment in low wage labor markets (e.g. fast-food restaurant industry)? This is a classical yet controversial question. Suppose you estimate 12 3 FTE NJ Post NJ Post u =+ − − + *, αβ β β where FTE is the number of employees in a restaurant. NJ is a dummy that is 1 if a restaurant is in NJ, and 0 if it is in PA. Post is a dummy that is 1 if it is from the year after the minimum wage increase and is 0 if it’s from the year before. (1) How would you interpret β1 and β1 ? (2) How would you interpret β3 ? (3) Which coefficient captures the impact of the minimum wage increase on the average number of restaurant employees?

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