Economics 345 Applied Econometrics

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1 Economics 345 Applied Econometrics Lab Exam Version 1: Solutions Fall 2016 Prof: Martin Farnham TAs: Joffré Leroux Rebecca Wortzman Last Name (Family Name) First Name Student ID Open EViews, and open the EViews workfile, smoke.wf1. These data, along with all of the data for this course, should be on the Network Drive sfgclients on 'uvic\storage' (S:) Your computer should be mapped to this drive. Browse to this drive and to the folder \social sciences\economics\econ 345\Wooldridge EViews Files\ Introduction: A standard 8.5x11 inch (2-sided) "cheat sheet" will be permitted in the exam. You may not have any application open while writing the exam. You may access websites cited in this exam for purposes of looking up statistical tables. You may not access any other websites (other than the browser homepage) while writing the exam. You may NOT access the course website or any files downloaded from the course website. You may not look at any other student's computer screen or paper. Students who violate these rules will receive a score of zero on the exam. Throughout the exam, if you have trouble answering a question (for instance, if EViews won't execute a command you've given), sketch briefly for me or the TA what you are trying to do. You may be able to get partial credit for writing down the syntax you attempted to use. The exam is worth 45 points. You should budget approximately 1 minute per point to complete the exam on time. Open EViews, and open the EViews workfile, smoke.wf1 A major goal of public health policymakers in countries like Canada is to reduce smoking. The primary economic justifications for reducing smoking are twofold: 1) there is a direct externality from second hand smoke that affects the health of non-smokers; and 2) there is a fiscal

2 externality from health problems that smokers experience. Because taxpayers foot the bill for lung disease in Canada, one person's smoking affects everyone else's tax bill. These are both negative externalities and so government policy to reduce smoking is arguably justified on economic grounds. (some have noted that smokers die more cheaply than non-smokers and actually save taxpayers money by smoking we ll leave that debate for another time) A number of questions that we can start to answer with data are of interest to policymakers. First, how responsive is smoking to the price of cigarettes? This will inform the decision of how high to set taxes on cigarettes. Second, what effect do various demographic factors (age, race, income) have on the quantity of cigarettes smoked? Answers to this question may help target advertising campaigns. Third, do policies such as restricting smoking in restaurants reduce the amount that individuals smoke? This lab exam will center around these questions. For purposes of this study, data were collected on individuals (both smokers and non-smokers). The number of cigarettes smoked per day, age, education, income, and white vs. nonwhite status is recorded for each individual. A dummy variable equal to 1 if the person lives in a state (these are US data) with smoking restrictions is also included. Therefore, we have a dataset on individuals and their smoking habits and characteristics that may allow us to gain some insight into the questions noted above. 1) 37 points total The determinants of daily cigarettes smoked. Suppose that the true model of the daily number of cigarettes smoked is given by: cigs= β 0 + β 1 educ+ β 2 age+ β 3 agesq+ β 4 cigpric+ β 5 income+ β 6 restaurn+u where variables are defined as follows: cigs: daily # of cigarettes smoked by individual educ: individual's education (in years) age: individual's age (in years) agesq: individual's age squared (in years) cigpric: average price of cigarettes in individual's state of residence (in cents per pack) income: annual income of individual (in dollars) restaurn: dummy equal to 1 if the individual's state restricts smoking in restaurants; =0 otherwise Estimate this model by OLS (note: if you take more econometrics, you'll learn that OLS isn't the best estimating approach when you have a variable like cigs which has mostly zero values--for today assume OLS is the best approach): a) 3 points Write down the estimated coefficient on cigpric

3 b) 3 points Interpret this coefficient. State clearly (making reference to correct units) the estimated effect of cigpric on the daily number of cigarettes smoked. Note: I graded this leniently. I expect people to do better on the final. This is the correct answer For every one cent per pack increase in average price of cigarettes in one s state of residence, daily number of cigarettes smoked by an individual increases by cigarettes on average. (That s the interpretation of the coefficient. But note that the coefficient estimate is statistically insignificant.) If you can t get close to a correct interpretation, you should not be passing this course. Some people are in bad shape on this front, judging from the lab exams. c) 6 points Perform the following hypothesis test at the 5% significance level (you may reference the following website to obtain critical values for your test: ): H 0 : β 2 =0, β 3 =0 H 1 : the null hypothesis is not true. State whether or not you reject the null hypothesis, and provide sufficient evidence to back your claim. This would include the value of your test statistic, the degrees of freedom, and the critical value against which you are comparing the test statistic. Fcrit 3.0 Fstat 15.2 df=800 I reject the null at the 5% significance level. age and agesq are jointly statistically significant. d) 2 points Draw a clearly labelled picture of the relevant distribution. Show the rejection region and the value of your test statistic in the picture. Standard F diagram (see midterm 2, for example of drawing). Rejection region in right tail above Fcrit. Fstat in this case lies well to the right of Fcrit, so in rejection region.

4 Note horizontal axis should be labeled F. Vertical axis should be labeled f(f), because this is a pdf of the F statistic under the null. Note that drawings that show the F-statistic taking on negative values received 0 points, because F can only be positive. e) 2 points Now consider the estimated coefficient on educ. Write down, as a formal statement, the null and alternative hypotheses for a two-sided test of whether years of education affects the daily number of cigarettes smoked. H 0 :β 1 = 0 H 1 :β 1 0 Note that some people stated the alternative as H0 is false. You ve been asked to state the alternative for a two-sided test. So you can be more specific than saying H0 is false. f) 6 points Does education have a statistically significant effect on the number of cigarettes smoked, according to your results? Test at the 5% significance level. Clearly justify your answer (citing test statistic and critical value). There are 2 ways to do this. You can either compare the two-sided p-value from EViews to the alpha of 0.05 implied by a 5% significance level; or you can do a t-test. p-value approach: p=0.0034<0.05èestimated coeff on educ is statistically significant at the 5% level. t-test approach: tcrit=1.96 (plus or minus, because the test is two-sided) t=-2.94 t is larger in magnitude than tcrit (more negative), therefore lies in the left-tail rejection regionè estimated coeff on educ is statistically significant at the 5% level. Either way you conclude that education has a statistically significant effect on the number of cigarettes smoked. g) 2 points What is the lowest significance level at which you can reject the null that education has no effect on the number of cigarettes smoked (assuming a 2-sided test)? p=0.0034, so you can reject the null at significance levels as low as 0.34%.

5 h) 3 points Based on the coefficient estimate you observe on cigpric, does the demand curve for cigarettes slope downward? No. The coefficient estimate on cigpric is positive. This implies that the demand curve slopes upward. As one student noted, this would make cigarettes a Giffen good. However, we should also note that the coefficient estimate is statistically insignificant. i) 3 points Does income have a statistically significant effect on the daily number of cigarettes smoked? Justify your answer clearly. No. Again, two ways to do this (see (f) above). p-value=0.34. Assuming a 2-sided alternative (it s standard to assume this unless told otherwise), this is way higher than the alpha=0.10 of a test at the 10% significance level. tstat= This is way too small in magnitude to lead us to reject the null at standard significance levels (1%, 5%, or 10%). So income does not have a statistically significant effect on the daily number of cigarettes smoked. j) 3 points Do restrictions on restaurant smoking appear to reduce smoking? Explain. They do. The coefficient estimate is -2.85, which suggests that states with restaurant smoking restrictions have lower rates of smoking (about 3 cigs a day on average), holding other variables in the model constant. Note the statements like A 1 unit increase in smoking restrictions causes don t really make sense. Smoking restrictions are a binary thing either on or off. So it doesn t make sense to think of units of smoking restrictions. Think carefully about the variables you re dealing with (a dummy variable in this case) when interpreting coefficient estimates. It s also worth noting here that the coefficient estimate on restaurn is statistically significant (pvalue=0.01). Technically, if the estimate wasn t statistically significant, you should conclude that these restrictions have no effect. k) 4 points

6 Consider that state restrictions on restaurant smoking are usually approved by voters in the state. Does this give you any reason to suspect that the coefficient on restaurn might be biased? Clearly explain. People struggled with this. The idea is fairly simple. Whether a state has restaurant smoking restrictions is not randomly assigned (restaurn is not exogenous, it s endogenous). Voters decide on these restrictions. Naturally you would expect states with lots of nonsmokers to pass these restrictions at the ballot box, and you would expect states with lots of smokers to reject these restrictions at the ballot box. So it could be that the outcome variable, cigs, is actually causing the policy variable, restaurn, rather than the other way around. Of course we see less smoking in states with smoking restrictions that s because the states that imposed those restrictions already had less smoking when they imposed the restrictions than states without the restrictions. Consider a residence hall where student residents vote to make it no-substance (no drugs or alcohol). You would expect to see residents of such no-substance residence halls drink and do drugs less than residents of regular residence halls. But it s not necessarily the policy that causes the behaviour. It may well be the behaviour that causes the policy. The policy might actually have zero effect on behaviour, but because it s endogenous, we d likely see a negative coefficient on the policy variable (implying, possibly incorrectly, that the policy reduces substance use). 2) 8 points total Does smoking differ by race? Policymakers may wish to target anti-smoking campaigns at different demographic groups. If one racial group has higher rates of smoking than another, it might be worth targeting advertising at that group. a) 2 points Using the model above as a basis for your analysis, write down a model that allows you to test whether whites and non-whites smoke different amounts (holding the same things constant as were held constant above). Do not use any interaction terms in this specification. cigs = β 0 + β 1 educ + β 2 age + β 3 agesq+ β 4 cigpric + β 5 income + β 6 restaurn+ β 7 white +u Here we just include a dummy equal to 1 if the person is white and equal to 0 if non-white. b) 2 points Estimate the model you've written down and write down clearly the difference in daily cigarettes smoked between whites and nonwhites, holding other things constant

7 This just says that holding other variables in the model constant, whites smoke on average fewer cigarettes a day than non-whites. c) 4 points Now write down a variant of the model from (2a) that allows whites to respond differently to cigarette prices than non-whites do. Estimate this model. If you were advising policymakers, would you (based on your findings) be inclined to advise them that whites respond differently to changes in cigarette prices than non-whites do? Explain clearly. In the previous question we wanted to see if whites smoked different amounts than non-whites, holding other variables in the model constant. In other words, we wanted to see if the intercept for whites and non-whites was different. In this question we want to see whether whites respond differently to price changes than nonwhites, holding other variables in the model constant. In other words, we want to see if the slope (with respect to cigpric) is different for whites and non-whites. This requires an interaction term: cigs = β 0 + β 1 educ + β 2 age + β 3 agesq+ β 4 cigpric + β 5 income + β 6 restaurn+ β 7 white +β 8 white*cigpric +u If whites and non-whites respond differently to price changes, then the coefficient estimate for beta8 will be statistically significant. As it turns out the coefficient estimate for beta4 is and the coefficient estimate for beta8 is Going purely on the coefficient estimates this suggests that the demand curve slopes down for non-whites and slopes up for whites (because >0). However, the coefficient estimate for beta8 is not statistically significant (look at the p-value or t-statistic). Therefore I would tell policymakers that there is no statistical evidence that whites respond differently to price changes than non-whites.

Final Exam - section 2. Thursday, December hours, 30 minutes

Final Exam - section 2. Thursday, December hours, 30 minutes Econometrics, ECON312 San Francisco State University Michael Bar Fall 2011 Final Exam - section 2 Thursday, December 15 2 hours, 30 minutes Name: Instructions 1. This is closed book, closed notes exam.