1) The Effect of Recent Tax Changes on Taxable Income

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1 1) The Effect of Recent Tax Changes on Taxable Income In the most recent issue of the Journal of Policy Analysis and Management, Bradley Heim published a paper called The Effect of Recent Tax Changes on Taxable Income. The abstract is below: This paper estimates the elasticity of taxable income to the net-of-tax share using a panel of tax returns that follows a random sample of taxpayers from 1999 to 2005, spanning the EGTRRA 2001 and JGTRRA 2003 tax changes. Results suggest that the elasticity of taxable income to the current year s net-of-tax share lies between 0.3 and 0.4 overall, and that the elasticity of a broader measure of income falls between 0.1 and 0.2 overall, with substantially higher elasticities for taxpayers reporting income in excess of $500,000. The data consist of a panel of the same taxpayers over six years. The Economic Growth and Tax Relief Reconciliation Act of 2001 (EGTRRA) and the Jobs and Growth Tax Relief Reconciliation Act of 2003 (JGTRRA) constitute what are normally referred to as the Bush tax cuts the decrease in tax rates on the top 10% of earners. The model estimated by Heim if of the form below: 1 1 is the income of the taxpayer at time t. denotes the tax rate at time t, 1 is the take home income. The dependent variable is the log of the ratio of their current income to the income three years previously. Each is a control variable for the following variables: Demographic Variables Mean St Dev Age Age Squared Married Number of Children Child Away from Home Entrepreneur Itemizer AMT Taxpayer Sex of Primary Filer (1 Female) The regression table for six different specifications of his model is on the following page. The first three and second three models use two different definitions of income. The remaining models are estimated using different methods for estimation do not worry about them. Coefficient estimates are next to the variable name; standard error estimates are directly below them. a) Economic theory suggests that the coefficient estimate of can be interpreted as an elasticity: the ratio of the percent change in tax rate to the percent change in earned income. Looking at the coefficient on log 1, Heim concludes:

2 154 / The Effect of Recent Tax Changes on Taxable Income Table 3. Estimation results: Three-year difference. Gross Income Gross Taxable Income (1) (2) (3) (1) (2) (3) ln(1 t) *** 0.184*** *** 0.317*** (0.099) (0.073) (0.071) (0.141) (0.112) (0.111) Married 0.028** 0.068*** 0.074*** *** 0.064*** (0.011) (0.010) (0.011) (0.016) (0.016) (0.017) Age/ *** 0.588*** 0.761*** (0.213) (0.172) (0.169) (0.299) (0.255) (0.253) Age Squared/ *** 0.085*** 0.065*** (0.022) (0.017) (0.016) (0.030) (0.025) (0.025) Sex of Primary Filer (0.013) (0.011) (0.011) (0.018) (0.016) (0.016) Itemizer 0.027*** 0.072*** 0.073*** 0.041*** 0.152*** 0.154*** (0.009) (0.007) (0.007) (0.012) (0.010) (0.011) Number of Children 0.021*** 0.031*** 0.029*** 0.040*** 0.052*** 0.050*** (0.004) (0.003) (0.003) (0.005) (0.005) (0.005) Child away from Home (0.023) (0.028) (0.028) (0.043) (0.048) (0.048) Entrepreneur 0.035*** 0.061*** 0.066*** 0.051*** 0.065*** 0.069*** (0.009) (0.008) (0.008) (0.013) (0.012) (0.012) ln(lagged Income) and yes yes Deviation of ln(income) from ln(lagged Income) 10-piece Spline of ln(lagged Income) and yes yes Deviations of ln(income) from ln(lagged Income) Region Dummies yes yes yes yes yes yes Year Dummies yes yes yes yes yes yes Constant yes yes yes yes yes yes Observations 96,873 96,873 96,873 96,873 96,873 96,873 Notes: Robust standard errors (clustered at the individual level) are in parentheses. The change in the net-of-tax rate is instrumented in all specifications with the change in net-of-tax rate evaluated at the level of income in the base year (inflated by the CPI for the tax calculation in the later year). All specifications include a constant term. * Significant at 10 percent, ** Significant at 5 percent, *** Significant at 1 percent. Looking at the gross income specification without income controls, the estimated elasticity is wrongly signed and insignificant, with a coefficient of This is likely due to incomes decreasing overall at the same time that net-of-tax shares were increasing, suggesting the need for variables to control for exogenous trends in income and mean reversion. When the log of lagged income and deviation from lagged income (or a 10-piece spline in these) are included, the elasticities have the correct sign and are significant. When lagged income and the deviation from lagged income are included, the estimated elasticity is 0.198, whereas when 10-piece splines in these are included, the estimated elasticity drops slightly to Looking at the results for gross taxable income when income controls are included, the magnitudes are larger, as would be expected. The specification with lagged income and the deviation from lagged income yields an elasticity estimate of 0.331, and the specification with 10-piece splines in these yields a slightly smaller estimated elasticity of Journal of Policy Analysis and Management DOI: /pam Published on behalf of the Association for Public Policy Analysis and Management

3 Overall, these results suggest that the recent tax changes induced individuals to increase their income and/or decrease their deductions, credits, and exclusions in response to the lower marginal tax rates. According to the model 2, a one percent increase in the tax rate leads to how big of a percent increase in gross income? (5 pts.) b) Is gross income or gross taxable income more sensitive to changes in the tax rate? How do you know? (5 pts.) c) Find a z value for the coefficient estimate on itemizer, in model two. Construct a 95% confidence interval. (10 pts.) d) In model three, a ten year increase in age leads to about how large of an increase in percent income? (You can ignore the squared term for this problem.) (5 pts.) e) Is the effect of tax rate on log income large relative to sex, itemizer, and number of children? (This is how you see if an effect is substantively important, rather than just statistically significant.) (5 pts.) 2) Why Short People Make More Money Upon completing 818, you decide to conduct an analysis between height, in inches above 5 feet, and income, rounded to the nearest ten thousand dollars, of seven former La Follette graduates, who are also friends of yours. You get the following data: Height Income a) Which is the dependent variable, and which is the independent variable in your model? How do you know, and why? (5 pts.) b) Just looking at it, are the variables positively or negatively correlated? Explain. (5 pts.) c) Given your dependent and independent variable above, specify a model that you want to estimate. (5 pts.) d) Calculate the least squares estimates (the coefficient estimates). (10 pts.) e) What is the sum of your estimated residuals? (No need to do the calculation, if you know the answer) (5 pts.) f) Calculate the residual sum of squares. (5 pts.) g) Calculate the R 2. (5 pts.) h) Interpret your estimated coefficient effect: what is the estimated effect of your independent variable on your dependent variable? Is there a causal story here? Why or why not? (3 5 sentences) (10 pts.)

4 3) Gore v. Bush Every four years, the American National Election Studies asks a random subset of voters a broad array of questions regarding their thoughts towards the president, the elections, and politics in general. This data are from the 2000 version of the survey. The variables used in this analysis are: (high) GoreTherm: A Feeling Thermometer regarding Al Gore, from 0 (low) to 100 (high) ApproveClint: A dummy variable for whether they approve of the job Bill Clinton is doing (0/1). WatchNews: The number of days in the last week you have watched national news (1 7). DemTherm: A Feeling Thermometer regarding the Democratic Party, from 0 (low) to 100 RepTherm: A Feeling Thermometer regarding the Republican Party, from 0 (low) to 100 (high) You take GoreTherm as your dependent variable, and generate the STATA output given below: Source SS df MS Number of obs = F( 5, 821) = Model Prob > F = Residual (a1) R-squared = (a2) Adj R-squared = Total Root MSE = (a3) GoreTherm Coef. Std. Err. t P> t [95% Conf. Interval] ApproveClint (b1) WatchNews (b2) (b3) DemTherm (e1) (e2) (e3) (e4) RepTherm BetOff _cons a) Fill in the missing values for (a1) (a3). (5 pts.) b) Fill in the missing values for (b1) (b3). (5 pts.) c) Fill in the missing values for (e1) (e4). (10 pts.) d) You look at the coefficient for ApproveClint. You believe that ApproveClint equals one only when the respondent approves of the job Bill Clinton has done, but you suddenly worry that your research assistant may have miscoded the variable. Why? (5 pts.) One theory suggests that only political parties affect feelings towards the candidates. A second is that media effects from the news, incumbent effects from Bill Clinton, and economic effects, measured by if you are better off, affect your feeling towards candidates. To compare these two sets of competing theories, you specify a second model, and generate the following output:

5 Source SS df MS Number of obs = F( 2, 1657) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = GoreTherm Coef. Std. Err. t P> t [95% Conf. Interval] DemTherm RepTherm _cons e) You used the exact same data, but the sample size changed dramatically. Why? How might this bias your results? (10 pts.) f) Conduct an F test to compare the two models. (Hint: Use the R 2 version of the test, since the sample sizes are not equivalent.) (10 pts.) g) To test the hypothesis in a different way, you rerun the original model and then generate the following STATA output: test ApproveClint WatchNews BetOff ( 1) ApproveClint = 0 ( 2) WatchNews = 0 ( 3) BetOff = 0 F( 3, 821) = Prob > F = What null hypothesis did you test? What does this tell us about the theory that only parties matter? (5 pts)

6 4) On Wisconsin. You and eight friends attempt to smuggle in flasks into Camp Randall on game day. The flasks are partially designed to keep you warm, and partially designed to help numb your disappointment about the team s performance this year. As you approach the stadium, there are nine different gates. You know that in exactly five of them, you will be frisked, with your contraband taken. In four of them, you will not. You and your friends decide to take one gate each. You form a line and go one at time, not using any gate that had been used previously. a) What is the probability that the first person who selects a gate has their flask taken? (5 pts) b) If the first person does not have their flask taken, what is the probability that the second person does? (5 pts) c) What is the probability that the second person has their flask taken? (10 pts) d) What is the probability that the third person does not have their flask taken, while the first two people do have their flask taken? (5 pts) e) Is this a binomial experiment? Why or why not? (5 pts) 5) Who Does the Dishes? Do women tend to spend more time on housework than men? Based on data from the National Survey of Families and Households, the following summary data was reported regarding the number of hours spent in housework per week women were surveyed, with mean of 32.6 hours per week and a standard deviation of For men, the sample size is 4252, with mean 18.1 hours per week and standard deviation of 12.9 hours. A labor economist has argued that women s labor in the home should count towards GDP. She has stated that she guess that women spend thirty hours a week working. She has also stated that women do twice as much work than men around the house (so fifteen hours). Take these as your null hypotheses. a) What is the distribution of the sample mean for hours per week spent working for women in this model? (5 pts.) b) Can we reject the labor economist s null hypothesis at the five percent level? Is she over or understating how many hours women work? (5 pts.) c) What is the distribution of the difference between the sample means of hours worked for men and for women? (5 pts.) d) Construct a 95% confidence interval for the difference in means between hours worked for men and for women. (5 pts.) You attempt to design an experiment to follow up on these results. You have found a random subset of women who have agreed not to do any housework for a month, and you want to figure out how that effects the amount of hours men work. As you design the experiment, you take as a null hypothesis that men work 18.1 hours per week, with a standard error of 12.9 (so 18.1 and 12.9 are now population parameters).

7 e) Why might your treatment the women stopping their housework cause men to work more? Why might it cause them to work less? So, do you want a one tailed or a two tailed hypothesis? (10 pts) f) Assume you gather data on 500 men in this study. What is the distribution of the sample mean under the null hypothesis? (5 pts) g) You set your critical value of at.05. What are the critical values for this study? (5 pts) h) Consider the alternative hypothesis that men work 20 hours a week. What is the Type II error? What is the power of this study? (10 pts)