Q2. Time Series Analysis: Capital Gains Realizations and the Average Effective Tax Rates Q2.

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1 Econ 74 Public Economics Assignment #3 Q. Time Series Analysis: Capital Gains Realizations and the Average Effective Tax Rates Q. a) The time series of realizations of capital gains as a percentage of GDP (PGDP) and the average effective tax rates (MTR) is plotted in the graphs below. The first graph shows the returns with positive net capital gains, including returns with positive total net capital gains, both short and long term, as a percentage of nominal GDP and the average effective rates from 1954 to 005; the second graph shows the long term capital gains, including returns with positive long term gains in excess of any short term losses, as a percentage of nominal GDP. I also add four reference lines of Year 1981, , 1997, and 003, when the maximum tax rate on long term capital gains went through significant changes. In 1981, the maximum tax rate reduced from 8% to 0%; later on, the rate jumped back to 8% in The maximum tax rate increases gradually up to 9.19% in 1997 and then reduced to 1.19% in the same year. Finally in 003, the maximum tax rate decreased from 1.05% to 16.05% Eyeballing the data with the focus on the four major time reference points, it appears that the realization of capital gains moves at an opposite direction of the average effective tax rates. Returns with Positive Net Capital Gains Long Term Capital Gains % Yr Yr PGDP MTR PGDP MTR b) Time series analysis: Most of prior research using time series analysis used the long term capital gains as the dependent variable, and my analysis below will also focuses on the long term capital gains using the data from 1977 to 005 in order to determine the permanent effect of the change in average effective tax rates on the realizations of capital gains. Using the specifications of CBO (1988) 1, Auerback (1989) and my own adjustments, I obtained the stimates of coefficients of different specifications in Table A below: 1 Congressional Budget Office, 1988, How Capital Gains Tax Rates Affect Revenues: the Historical Evidence, March. Alan J. Auerbach, 1989, Capital Gains Taxation and Tax Reform, National Tax Journal, 4, 3, P

2 Econ 74 Public Economics Assignment #3 Q. Time Series Analysis Table A. Time Series Regressions of Long Term Capital Gains Realizations [1] [] [3] [4] [5] [6] [7] [8] [9] [10] VARIABLES lnncg lnncg lnrcg lnrcg dlnncg dlnncg dlnncg dlnrcg dlnrcg dlnrcg dlnprice [3.035] [3.9] [.537] dlnrce_d [0.363] [0.480] [0.366] [0.58] [0.411] [0.37] dlnrgdp 9.719** 9.513** * 6.185* ** [.759] [.459] [3.654] [3.47] [.978] [3.865] [3.077] [3.63] dlnnyse * * [0.79] [0.947] [0.597] [0.66] [0.834] [0.514] dmtr * 0.187** 0.09** * 0.186** ** [0.0369] [0.057] [0.034] [0.0354] [0.0508] [0.0310] dmtr * ** 0.08 [0.046] [0.0548] [0.0474] [0.0443] [0.055] [0.0458] L.dlnNCG * [0.18] [0.47] [0.183] lnprice [1.188] [1.65] lnrce_d * ** [0.77] [0.181] [0.64] [0.178] lnrgdp [1.36] [1.486] [0.660] [0.451] MTR * * 0.055** ** [0.0181] [0.0166] [0.0154] [0.0143] L.dlnRCG * 0.38* [0.195] [0.34] [0.166] Constant * 0.45 [10.47] [1.88] [.564] [.164] [0.168] [0.183] [0.136] [0.167] [0.140] [0.141] Observations R squared Robust standard errors in brackets ** p<0.01, * p<0.05 D.W AIC BIC

3 Econ 74 Public Economics Assignment #3 In specifications 1 through 4, I use CBO specifications by taking log of the values of variables before running the regression. The estimations are as follows: (1) Ln( NCG) = Ln Pr ice LnRCE LnRGDP MTR, DW.. = (0.0166) (10.47) (1.188) (0.77) (1.36) (0.0181) () Ln( NCG) = Ln Price LnRCE LnRGDP dLnRGDP MTR, DW.. = 1.83 (1.88) (1.65) (0.181) (1.486) (.759) (3) Ln( RCG) = LnRCE LnRGDP 0.055MTR, DW.. = 0.77 (.564) (0.64) (0.66) (0.0154) (4) Ln( RCG) = LnRCE LnRGDP dLnRGDP MTR, DW.. = (.164) (0.178) (0.451) (.459) (0.0143) Variable Definitions: Ln(NCG) = logarithm of nominal net long term capital gains, in excess of net short term losses; LnPRICE = logarithm of the GDP deflator using Year 000 as the base year; LnRCE = logarithm of the real value of corporate equities directly held by households and nonprofit organizations GDP (using Year 000 as the base year); LnRGDP = logarithm of real GDP (using Year 000 as the base year); dlnrgdp = change in the logarithm of GDP (using Year 000 as the base year) MTR = average effective tax rate on capital gains; and Ln(RCG) = logarithm of real net long term gains, in excess of net short term losses (using Year 000 as the base year). The Durban Watson d statistics of CBO specifications indicate that the regressions may have positively serial correlation issues. After running the augmented Dickey Fuller test, it also indicated the level logarithm value of the realization of capital gains, in both nominal and real terms, is not stationary. In order to address the non stationary and serial correlation issue, specification 5 followed Auerback s original specification by taking the first difference of the logarithm of the values of most variables, except of the average effective tax rates. After taking the first difference, the data available for the analysis is from 1979 to 005. Auerbach s specification is as follows:

4 Econ 74 Public Economics Assignment #3 (0.168) (3.035) (0.363) (3.654) (0.79) dMTR 0.046( 1) 0.347dLnCG( 1), (0.0369) (0.046) (0.18) (5) dln( NCG) = dLn Pr ice 0.007LnRCE dLnRGDP dLnNYSE + + R = 0.567, DW.. =.075, AIC = 7.917, BIC = dln(ncg) = change of the logarithm of nominal net long term capital gains, in excess of net short term losses; dlnprice = change of the logarithm of the GDP deflator using Year 000 as the base year; dlnrce = change of the logarithm of the real value of corporate equities directly held by households and nonprofit organizations GDP (using Year 000 as the base year); dlnrgdp = change of the logarithm of real GDP (using Year 000 as the base year); dlnnyse = change of the logarithm of the New York Stock Exchange Index; dmtr = change of the average effective tax rate on capital gains; d MTR(+1) = change in the average effective tax rate one year ahead; dlncg( 1) = change of the lagged value of capital gains realizations. In this original specification, since realizations of capital gain is in nominal term, we need a price index to control for inflation and therefore GDP deflator using 000 as the base year is included in the right hand side. Further, the corporate equity held directly by individual and non profit organization is added since the realization could fluctuates with the shares these people holds. Real GDP is included to control the economic growth as a benchmark of capital gains realization, and the NYSE index is included since stock price is the key determinant in terms of selling decision of stocks. Auerbach also includes a lead variable of the change of future tax rate to gauge the issue of forward looking nature in stock market; i.e. if people expect the future tax rate to rise, they may act before the timing of its realization. Last, the lagged of capital gains realizations is also included since it may affect the current capital gains realization (if people sold majority shares in last period without replacing the portfolio with new purchases of other stocks, the capital gains realizations may hence reduce.) One particular concern with Auerbach s initial specification is the endogeneity issue. Since capital gains realizations affect the average effective tax rate, we may need to consider using instrumental variables to get around with this issue. I suggest using the maximum tax rate on long term capital gain as our IVs for the estimates. As the maximum tax rate changes may happen in the middle of a year, I used either the old tax rate as the IV in equation 6, or the new tax rate as the IV in equation 7 when such scenario occurs. (6) dln( NCG) = dLn Price 0.635LnRCE dLnRGDP dLnNYSE 0.187dMTR R (0.183) (3.9) (0.48) (3.47) (0.947) (0.057) 0.138( 1) (0.057) 0.488dLnCG( 1), (0.47) + + = 0. (7) dln( NCG) = dLn Price 0.041LnRCE dLnRGDP dLnNYSE 0.09dMTR (0.0474) (0.183) (0.136) (.537) (0.366) (.978) (0.597) (0.034) ( + 1) 0.309dLnCG( 1), R = 0.553

5 Econ 74 Public Economics Assignment #3 To make the model more parsimonious, I revised Auerback s specification and replaced the dependent variable by replacing the nominal value of the realization of capital gains with the real value of the realization of capital gains using the GDP deflator of base year 000. (8) dln( RCG) = LnRCE dLnRGDP dLnNYSE dMTR (0.0443) (0.195) (0.167) (0.58) (3.865) (0.66) (0.0354) ( + 1) 0.361dLnCG( 1), R DW AIC BIC = 0.574,.. =.049, = 5.73, = (9) dln( RCG) = LnRCE dLnRGDP dLnNYSE 0.186dMTR (0.055) (0.34) (0.14) (0.411) (3.077) (0.834) (0.0508) ( + 1) 0.485dLnCG( 1), R = 0.1 (10) dln( RCG) = LnRCE dLnRGDP dLnNYSE dMTR (0.0458) (0.166) (0.141) (0.37) (3.63) (0.514) (0.031) ( + 1) 0.38dLnCG( 1), R = 0.56 dln(rcg) = change of the logarithm of real net long term gains, in excess of net short term losses (using Year 000 as the base year). All other variables are defined in the same way in Equation 5. Using the same IV strategy, we have equation 9 and 10 as the counterpart to equation 6 and 7 when the change of tax rate took place in the middle of a particular year. Using the change of the old maximum tax rates (equation 6 and equation 9) when the tax rate change occurred in the middle of a year as the IV significantly reduced the R, but in contrast, using the new maximum tax rates as the IV does not substantially change the R and it addressed the endogeneity issue since the maximum tax rate is truly exogenous to the realization of capital gains. Therefore, my final model would be equation 10.

6 Econ 74 Public Economics Assignment #3 Using Auerbach s elasticity calculations method, the estimated elasticity of realizations with respect to effective tax rates would be as follow 3 : MTR = 15% MTR = 0% MTR = 5% Elasticity using Equation Elasticity using Equation Elasticity using Equation Elasticity using Equation c) The optimal tax rate would be 15.3% using the specification in equation 8, and 14% using equation 10; compared with 15.15% using equation 5 (estimates without IVs) and 14.3% using equation 7 (estimate using IVs). If the current MTR is 15%, it is very close to the optimal tax rate and therefore the government shall keep the tax rate no lower than 14%. Any further adjustment of the tax rate will cause a reduction in the capital gains realizations and hence might reduce the total tax revenues. d) The elasticity estimates from the time series analysis above is between Burman and Randolph s estimate of the elasticity of the permanent tax effect, approximately 0.18, and the elasticity of transitory effect, approximately 6.4. Burman and Randolph s results may be more reliable than my estimates since they separate the effects into permanent and transitory effects that may capture some short term responses in individuals behaviors to the change of tax policies and explain the inverse relationship we observed in the graphs in part a). Second, Burman and Randolph s model overcomes the shortcoming of aggregation bias that my model may have via using an aggregated data. Last, Burman and Randolph s model is less sensitive to sample period that time series models typically does. On the other hand, my results will be more reliable than the results of Burman and Randolph s in terms of the following perspectives: first of all, time series analysis estimates long run realization elasticities better. In Burman and Randolph s paper, their data sets do not encompass a long enough time period (they had the data of tax returns from ) to be able to reliably separate out long run from transitory elasticities. Furthermore, the cross state differences in tax rates that they use as an IV for permanent tax effect may not affect taxpayers' behavior in the same way as a change in the tax rate, especially if the state taxes are correlated with other characteristics of the state residents or if capital gains realizations are not in equilibrium. Last but not least, in the time series model, we are able to allow the elasticities to vary depending on the current tax rate would provide a better indictor in policy decision. 3 Follow Auerbach s method to calculate the elasticity as the dmtr coefficient divided by 1 plus the coefficient of lagged capital gains, all multiplied by the MTR rate itself.