Exam 2 Solutions: Monday, April 2 8:30-9:50 AM

Amherst College Department of Economics Economics 360 Spring 2012 Name: Exam 2 Solutions: Monday, April 2 8:30-9:50 AM Cigarette Consumption Data: Cross section of per capita cigarette consumption and prices in fiscal year 2008 for the 50 states and the District of Columbia. Cigarette consumption per capita in state t (packs) Price of cigarettes in state t received by suppliers (dollars per pack) State t Name of state t Cigarette tax rate in state t (dollars per pack) Per capita tobacco production in state t (pounds) The price of cigarettes faced by consumers equals the sum of the price received by cigarette manufacturers (PriceSupplier) and the tax rate (Tax). The next x questions explore the possibility that consumers 1. (15 points) Consider the following theory: Theory: Consumers do not distinguish between price received by cigarette manufacturers and the tax on cigarettes. For example, a $1.00 increase in the price tobacco makers receive would have the same effect on cigarette consumption as a $1.00 increase in the cigarette tax; in either case, the price paid by consumers would rise by $1.00. a. Consider the following linear model: + β PriceSup Which parameters of the model are relevant to this theory? β PriceSup and β Tax What does the theory imply about these parameters? β PriceSup = β Tax

2 b. Use the ordinary least squares estimation procedure to estimate the values of the model s parameters. Interpret the numerical value of the coefficient estimate for 1) β PriceSup : We estimate that a $1.00 increase in the price of cigarettes decreases per capita cigarette consumption by 30.4 packs annually assuming that the other explanatory variables remain constant. 2) β Tax : We estimate that a $1.00 increase in the cigarette tax decreases per capita cigarette consumption by 10.7 packs annually assuming that the other explanatory variables remain constant. 3) β TobProd : We estimate that a 1 pound increase in per capita tobacco production increases per capita cigarette consumption by.74 packs annually assuming that the other explanatory variables remain constant. Dependent Variable: CIGCONSPC Date: 03/31/12 Time: 08:54 Sample: 1 51 Included observations: 51 PRICESUPPLIER -30.39686 10.32414-2.944251 0.0050 TAX -10.65007 3.961551-2.688358 0.0099 TOBPRODPC 0.740987 0.316474 2.341388 0.0235 C 188.9528 37.70800 5.010949 0.0000 c. What are the appropriate null and alternative hypotheses to access the theory? H 0 = β Tax H 1 β Tax d. What does the Prob[Results IF H 0 True] equal?.11 EViews Wald Test: C(1) = C(2) Wald Test: Equation: Untitled Test Statistic Value df Probability t-statistic -1.613066 47 0.1134 F-statistic 2.601981 (1, 47) 0.1134 Chi-square 2.601981 1 0.1067

3 2. (20 points) Consider a theory advocated by a state legislator: Theory: Since the revenue collected from the cigarette tax is used to finance schools, roads, etc. consumers know that it is going toward a good cause. Consequently, they will be less sensitive to the tax placed on cigarettes than on the price received by the cigarette manufacturers. Consider the same linear model that was introduced in the first question: + β PriceSup a. Do your coefficient estimates from question 1 lend support to this second theory? X Yes Explain. The estimate of β PriceSup is 30.4 and the estimate of β Tax is 10.7. This suggests that consumers are more sensitive to the price received by suppliers than the tax. b. What does the second theory imply about the relationship between the actual values of the No relevant coefficients? β PriceSup < β Tax c. Cleverly modify the model by introducing a new parameter that will enable you to assess the second theory. Modified Model: β Clever = β PriceSup β Tax β PriceSup = β Clever + β PriceSup + (β Clever ) ( + ) where = + Dependent Variable: CIGCONSPC Date: 03/31/12 Time: 09:12 Sample: 1 51 Included observations: 51 PRICESUPPLIER -19.74679 12.24178-1.613066 0.1134 PRICECONSUMER -10.65007 3.961551-2.688358 0.0099 TOBPRODPC 0.740987 0.316474 2.341388 0.0235 C 188.9528 37.70800 5.010949 0.0000 d. Use the ordinary least squares estimation procedure to estimate the values of the modified model s parameters. Interpret the numerical value of the new parameter: Estimate of β Clever = 19.7: We estimate that a $1.00 increase in the cigarette tax decreases per capita cigarette consumption by 19.7 fewer packs than a $1.00 increase in the price cigarette suppliers receive.

4 e. What are the appropriate null and alternative hypotheses to access the second theory expressed in terms of the original parameter and the new parameter? H 0 = β Tax β Clever = 0 H 1 < β Tax β Clever < 0 f. What does the Prob[Results IF H 0 True] equal?.1134 2 =.057 Smoking Rate Data: Cross section of smoking rates and prices in fiscal year 2008 for the 50 states and the District of Columbia. Note that there are a total of 102 observations: 51 observations for adults and 51 observations for youths Price of cigarettes in state t paid by consumers (dollars per pack) SmokeRate t Percent of those who smoke in state t Youth t 1 if observation t is a youth, 0 otherwise State t Name of state t 3. (20 points) Consider the following theory. Theory: The price of cigarettes impacts youth more strongly than adults. More specifically, the smoking rates of youths are more sensitive to the price of cigarettes than the rates for adults. a. Devise a linear model to assess this theory: SmokeRate t + β PriceCon + β PriceCon_Youth1 PriceCon_Youth1 t where PriceCon_Youth1 t = Youth1 t b. Use the ordinary least squares estimation procedure to estimate the values of the modified model s parameters. Interpret the numerical value of each coefficient estimate: Estimate of β PriceCon = 1.72: We estimate that a $1.00 increase in the cigarette tax decreases the adult smoking rate by 1.72 percentage points. Estimate of β PriceCon_Youth1 =.22: We estimate that a $1.00 increase in the cigarette tax decreases the youth smoking rate by 1.72 +.22 or 1.94 percentage points. Dependent Variable: SMOKERATE Date: 03/31/12 Time: 09:27 Sample: 1 102 Included observations: 102 PRICECONSUMER -1.721962 0.373635-4.608679 0.0000 PRICECON_YOUTH1-0.219780 0.131153-1.675749 0.0969 C 28.70768 1.879599 15.27330 0.0000 c. What are the appropriate null and alternative hypotheses to access this theory? H 0 : β PriceCon_Youth1 = 0 H 1 : β PriceCon_Youth1 < 0 d. What does the Prob[Results IF H 0 Ture] equal?.0969 2 =.048

5 Crime Data for California: Annual time series data of crime and economic statistics for California from 1989 to 2008. CrimesAll t UnemRate t State t Year t Crimes per 100,000 persons in year t Unemployment rate in year t (percent) Name of state t Year 4. (25 points) We wish to estimate that effect that time has on crime after accounting for unemployment. a. Using the available data devise a model that estimate the effect of time (Year) in percentage terms after accounting for unemployment. log(crimesall t ) + β Year Year t + β Unem UnemRate t b. Use the ordinary least squares estimation procedure to estimate the values of the modified model s parameters. Interpret the numerical value of each coefficient estimate: Estimate of β Year =.036: We estimate that the crime rate decreases by 3.6 percent per year. Estimate of β Unem =.039: We estimate that a 1 percentage point increase in the unemployment rate increases the crime rate increases by 3.6 percent. Dependent Variable: LOGCRIMESALL Date: 03/31/12 Time: 09:39 Sample: 1989 2008 Included observations: 20 YEAR -0.036114 0.003001-12.03367 0.0000 UNEMRATE 0.039019 0.011504 3.391867 0.0035 C 80.35511 6.033100 13.31904 0.0000 c. What issue often arises with time series data? Autocorrelation

6 d. Investigate the possibility that this issue is relevant. If it is an issue, use the appropriate steps to account for it. If not, explain why it is not an issue. Plot the residuals from the ordinary least squares (OLS) regression:.15.10.05.00 -.05 -.10 -.15 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 LOGCRIMESALL Residuals Typically, a positive residual is followed by a positive residuals and a negative residual is followed by a negative residuals. This suggests that autocorrelation may be present. Conduct a Lagrange Multplier Test: Test Equation: Dependent Variable: RESID Date: 03/31/12 Time: 09:47 Sample: 1989 2008 Included observations: 20 Presample missing value lagged residuals set to zero. YEAR -0.000837 0.001874-0.446794 0.6610 UNEMRATE -0.008131 0.007321-1.110718 0.2831 C 1.731923 3.767842 0.459659 0.6519 RESID(-1) 0.815643 0.154368 5.283761 0.0001 Estimate the value of ρ:.779 Dependent Variable: RESIDUAL Date: 04/12/12 Time: 08:40 Sample (adjusted): 1990 2008 Included observations: 19 after adjustments RESIDUALLAG 0.779559 0.134368 5.801667 0.0000

7 Apply the Generalized least Squares (GLS) Estimation Procedure: Generate the new dependent and explanatory variables: AdjLogCrimesAll = LogCrimesAll.780 LogCrimesAll( 1) AdjYear = Year.780 Year(-1) AdjUnemRate = UnemRate.780 UnemRate ( 1) Dependent Variable: ADJLOGCRIMESALL Date: 04/12/12 Time: 08:43 Sample (adjusted): 1990 2008 Included observations: 19 after adjustments ADJYEAR -0.031818 0.007797-4.080702 0.0009 ADJUNEMRATE 0.030037 0.010154 2.958236 0.0093 C 15.79709 3.440152 4.591974 0.0003