Problem Set #2 Economics 43

Due Tuesday, October 7th at the start of class Prof. Stephen Schmidt

The amount of money the Federal government receives in tax collections depends on the amount of income people earn. If income rises, tax collections will rise also; the amount by which tax collections rise, when income rises by $1, is called the effective marginal tax rate. It is difficult to know exactly how increases in income will change tax collections. Different households are in different tax brackets, so the increase in tax collections from an additional dollar of income (which is called the effective marginal tax rate) depends on who earns it. Also, households that earn additional income may increase their tax deductions or hide their income from taxes in other ways. On the other hand, as income rises, households rise into higher tax brackets and face a higher rate than previously. For all these reasons, it is not a simple matter to calculate the effective marginal tax rate; that is, to find out how much tax collections will rise if income rises.

In this problem set we’ll use with data from the US economy to estimate the effective marginal tax rate. We’ll take a relatively simple approach to the problem using the econometrics tools we’ve learned so far in class. If you’d like to see how economists study the problem, you can take a look at the paper “Measuring the Average Marginal Tax Rate from the Individual Income Tax” by Robert Barro and Chaipat Sahasakul (Journal of Business, 1983, vol. 56, no. 4, p. 419-452) which is available through JSTOR at the URL:

http://www.jstor.org/view/00219398/di993836/99p0089l/0

and is linked from the course web page. However, you do not need to read this article to do the problem set.

1. The first step is to load the data, which comes from the DRI Economic Database, into Eviews. To do this, go to the Statlab (the DRI database may not be available elsewhere), and:

a) Start Eviews.
b) Under the File menu, select New, then Workfile to create a new Eviews workfile.
c) Select “Annual” for the data frequency, and type 1947 for the start date, and 2002 for the end date. Then hit OK to continue.
d) From the File menu, select Import, then select DRI Basic Economics Database. For Series names, type ggfr ggfit ggfca gdp gwy gpbt punew. These variables are:

ggfr: Federal tax receipts, $billions
ggfit: Income tax receipts, $billions
ggfca: Corporate profits tax receipts, $billions
gdp: US gross domestic product, $billions
gwy: US wage and salary income, $billions
gpbt: Corporate profits before taxes, $billions
punew: Consumer price index (CPI), 100=1983
To avoid the problem of inflation, we will convert all variables to real values. To do that, type the following commands at the command line in Eviews:

genr realreceipts = ggfr/punew*179.8
genr realinctax = ggfit/punew*179.8
genr realcorptax = ggfca/punew*179.8
genr realgdp = gdp/punew*179.8
genr realwages = gwy/punew*179.8
genr realprofits = gpbt/punew*179.8

Multiplying by 179.8 (rather than 100) gives us values in real 2002 dollars rather than real 1983 dollars.

a) Double-click on the realgdp variable to open it, then select View… Descriptive Statistics… Histogram and Stats to see its statistics. What is the average value of realgdp? (If you don’t get $5651 billion, you probably made a mistake generating the variable. Check your work carefully, and keep trying until you do get this value.) Do the same for the realreceipts variable. What is the average value of realreceipts? On average, what fraction of income is taken by the Federal government as taxes?
b) Double-click on the realwages and realprofits variables. What are their mean values? On average, what percentage of US GDP takes the form of real wages? What percentage takes the form of corporate profits?
c) Double-click on the realinctax variable. What was its value in 2002? What fraction of 2002 total Federal tax receipts was this? Was it higher or lower than the previous year? Double-click on the realcorptax variable. What was its value in 2002, and what fraction of total Federal tax receipts was this?
d) Type the commands

genr inctaxfrac = realinctax/realreceipts
genr corptaxfrac = realcorptax/realreceipts

Double-click on the inctaxfrac variable, then select View.. Graph... Line Graph to display its values over time. Print the graph, and hand it in along with your answers. Is the fraction of Federal taxes collected from the income tax rising, falling, or staying steady over time? Do the same for the corptaxfrac variable. Is it rising, falling, or staying steady over time? Does it change sharply in any one year or years? If so, can you think of anything that might have happened then to cause the change?
e) Select inctaxfrac, then hold down the Control key and select corptaxfrac. (Those two variables should light up and no others). Double-click on either one to open a group containing those two variables. Then select View... Graph... Scatter... Simple Scatter. Print the graph, and hand it in along with your answers. Do these variables appear to be positively correlated or negatively correlated? Is the correlation strong or weak? Why do you think they are correlated in this way? (Hint: If you add them up, what must be true?) Click the View button, then select Correlations to calculate their correlation coefficient. What is its value?

2. a) Consider the economic model

TR = b₀ + b₁*GDP

where TR is tax receipts and GDP is, of course, GDP. According to this model, if GDP rises by $1 billion, how much should Federal tax receipts rise? (The answer is a parameter, not a number.) Would you expect the value of this parameter to be positive or negative? Why? Would you expect it to be bigger than 1 or smaller than 1? Why? What range of values might you expect it to fall into, and what information do you have that makes you think so?
b) Estimate the econometric model

TR_t = b₀ + b₁*GDP_t + e_t

What is your value for? What is your value for? What is the standard error of your estimate for? On a graph with GDP (the independent variable) on the horizontal axis and TR (the dependent variable) on the vertical axis, graph the estimated line. (Draw the graph by hand, not in Eviews.)
c) Test the null hypothesis that b₁=0. Do you reject this hypothesis or fail to reject it? Did you get the result you expected? Also test the null hypothesis that b₁=1.Do you reject this hypothesis or fail to reject it, and did you get the result you expected? Calculate a 95% confidence interval for the true value of b₁.
d) Based on the regression from part b, what is your estimate of the effective marginal tax rate in the United States economy as a whole? Is this larger or smaller than the average rate you calculated in question 1a?
e) What is the value of R² for the regression in part b? Does the model fit the data well, or not very well?
f) To predict values of tax receipts for a given year, we use the equation



In 2002, US GDP was $10,437 billion. What value does the model predict for tax receipts in that year? (Be sure to get the units right.) Find the actual value (double-click on realreceipts and use the Spreadsheet view). How close is it to the actual value? How large is the residual for this observation? Is it positive or negative? We don't know the value of GDP for 2003. If it is $10,700 billion, what would you predict for tax receipts? If it is $10,900 billion, what would you predict?

3. The effective marginal tax rate might be different for different taxes, since the rates and the exemptions are different. First we’ll calculate the effective marginal tax rate of the income tax. Estimate the regression

ITR_t = b₀ + b₁*WAGES_t + e_t

where ITR is real income tax receipts and WAGES is real wages. What is your estimate of the effective marginal tax rate of the income tax? Test the null hypothesis that the effective marginal tax rate of the income tax is equal to 20%. What do you conclude?
b) Calculate a 95% confidence interval for the true value of the effective marginal tax rate of the income tax. Does this confidence interval overlap, or not overlap, the one you calculated for the effective marginal tax rate for all taxes in problem 2c? Does it appear that the effective marginal tax rate on wages is about the same as the effective tax rate for all components of GDP?
c) Now we’ll calculate the effective marginal tax rate of the corporate income tax. Estimate the regression

CTR_t = b₀ + b₁*PROFITS_t + e_t

where CTR is real corporate tax receipts and PROFITS is real wages. What is your value for from this regression? What is your estimate of the effective marginal tax rate of the corporate tax? Calculate a 95% confidence interval for the true value of the effective marginal tax rate of the corporate tax. Does this confidence interval overlap, or not overlap, the one you calculated for the effective marginal tax rate for income tax in part b? Does it appear that the effective marginal tax rate on corporate profits is about the same as the effective tax rate on wages?
d) Who pays a higher marginal tax rate on income, workers or firms? Or does there not appear to be a statistically significant difference? Justify your answer with the results of your analysis.

4. The regressions we’ve run so far assume that the effective marginal tax rate of the US economy is constant over the entire time period from 1947 to 2002. That assumption is almost certainly not literally true, for many reasons. As incomes rise, taxpayers find themselves in higher brackets; on the other hand, the brackets and the legal tax rates change over time as well. Also, the way exemptions are calculated changes periodically, and occasionally the entire tax system is reformed (this last occurred in 1986). In this problem we’ll look to see if the effective tax rate appears to be changing over time. The most substantial changes to the tax code in recent history (with the possible exception of the ones the Bush administration has implemented) were made by Ronald Reagan, so we’ll look to see if the effective tax rate has changed since he took office in 1981.

a) In the worksheet window (the one with all the variables listed) click on the Sample button, and change the Sample to 1947 1980 (instead of 1947 2002). Estimate the equation

TR_t = b₀ + b₁*GDP_t + e_t


What is your value for from this regression? What is your value for ? Is your estimated value for the effective marginal tax rate higher or lower than the value you got when you estimated the effective marginal tax rate for the entire period 1947 to 2002?
b) In 1981, real GDP (2002 dollars) was $6191. Using this regression, predict what tax collections would have been in 1981 if the effective tax rate had been the same as it was from 1947 to 1980.
c) Now click on the Sample button and change the sample to 1981 2002, the period since Reagan was elected. Estimate the regression

TR_t = b₀ + b₁*GDP_t + e_t

for the post-Reagan era. What is your value for from this regression? What is your value for ? Is the marginal tax rate higher or lower since Reagan than it was before? How has the intercept changed? Compared to the standard errors of the estimates, are the differences small, or large? Using this regression, predict the value of tax receipts for 1981 with the post-Reagan tax structure. What value do you get? Did the Reagan changes increase or decrease total tax collections in 1981?
d) On a large graph with GDP on the horizontal axis and tax receipts on the vertical axis, draw the estimated line for the period 1947 to 1980 (using the regression parameters from part a) and for the period 1981 to 2002 (using the parameters from part c). Then write a short (one or two paragraph) essay answering the following question: On the basis of these regressions, how did Ronald Reagan change the tax structure of the US economy? Focus on both the change in the marginal tax rate, and in total tax collections, in your answer.