Introduction
Many scholars have studied the relationship between income tax revenues and income tax rates,the most notable among them being Economist Arthur Laffer who coined the concept of Laffer curve.The laffer curve shows that tax revenues usually increase at low levels as tax rates. The graph eventually reaches a maximum amount of revenue known as the optimal tax rate. When tax rates go beyond that level, the tax revenue will start decreasing as many people will not see the reason to work leading to an economic slowdown (Badel & Huggett, 2017).This study will investigate whether the Laffer curve exits in USA and if a positive relationship exists between income tax revenues and income tax rates.
Methods
Overview
This research attempts to directly estimate the relationship between tax rates and tax revenues and test the Laffer curve theory. The hypothesis is that there is a positive relationship between tax rates and tax revenue and that Laffer curve exits in the USA. Regression analysis will be performed, tax revenue will the dependent variable while the independent variables will be the tax rate. Regression analysis is used to model the relationship between dependent and independent variables ( Schroeder et al., 2017) .
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Data
This study will cover a time period starting from 1980 to 2015, so a time series data will be used in this analysis. The data series for tax revenue and tax rates are obtained from the IRS database. The IRS publishes annual data on US tax returns.
Statistical Analysis
The statistical package STATA (version 13.0) was used to for all analyses. Time series plots for each variables was obtained since it reveals the features of the data. In this study the variables; tax revenue and tax rates vary greatly in size, so a log-log regression equation is used to test the hypothesis that a positive relationship exists between the variables. Quadratic function was used to model the Laffer curve, as it fits the upside-down “U” shape of Laffer curve.
Results and Discussion
Time series plots.
Figure (1) shows that tax revenue variable “trends” over time while Figure (2) shows tax rate variable is “wandering” over time. Both variables are non-stationary and the data lead to spurious regression problem. The variables are therefore made stationary by getting the difference before carrying out regression.
Regressions and Interpretations.
Log-log regression equation
Equation 1:
Equation (1) shows the log-log relationship between tax revenue and tax rate. This regression is used to test the hypothesis that as the tax rate of personal income increases, tax revenue will also increase. Therefore, the coefficient ( ) should be positive.
The results for this equation is shown in table (1) in the appendix. The regression equation is
R 2 = 0.7168
(t) (7.55) (9.14)
The coefficient of the tax rate and constant term are statistically significant. A unit increase in tax rate will increase tax revenue by approximately 1.5 percent.R 2 is 0.7168, tax rate explains 71.68% of the variability in tax revenue. Since 71.68% is more close to 100% than 0%, this model is adequate in showing the relationship between tax rates and tax revenue.
Quadratic regression equation.
Equation 2:
Equation (2) tests the link between tax rate and tax revenue beyond the optimal tax rate level. The coefficient ( ) should be positive since Laffer curve says that tax revenues usually increase at low levels as tax rates .The coefficient ( ) should be negative to depict that increased tax rates lowers tax revenue.
The results for this equation is shown in table (2) in the appendix. The regression equation is
R 2 = 0.7183
(t) (7.41) (1.97) (-1.30)
The regression does not support Laffer curve theory because the coefficient of taxrate 2 and tax rate are not statistically significant.
Conclusions
The results of quadratic regressions are not significant. The hypotheis that Laffer curve exists in the US is not supported empirically. The hypothesis that a positive relationship exists between tax rates and tax revenue was not rejected.
References
Badel, A., & Huggett, M. (2017). The sufficient statistic approach: Predicting the top of the Laffer curve. Journal of Monetary Economics , 87 , 1-12.
Chatfield, C. (2018). Statistics for technology: a course in applied statistics . Routledge.
Historical Income Tax Rates and Brackets, 1862-2013 - Tax Foundation. (2018).
US Inflation Calculator. (2018).
Rich, J. S., & Jones, J. P. (2018). Cornerstones of financial accounting .
Schroeder, L. D., Sjoquist, D. L., & Stephan, P. E. (2017). Understanding regression analysis: An introductory guide .
Appendix
Figure 1: Time series plot of tax revenue variable
Figure 2: Time series plot of tax rate variable
Table 1: Results of Equation 1
reg D.lntaxrevenue D.lntaxrate
Source | SS df MS Number of obs = 35
-------------+------------------------------ F( 1, 33) = 83.54
Model | .144530418 1 .144530418 Prob > F = 0.0000
Residual | .05709118 33 .001730036 R-squared = 0.7168
-------------+------------------------------ Adj R-squared = 0.7083
Total | .201621598 34 .005930047 Root MSE = .04159
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D. |
lntaxrevenue | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lntaxrate |
D1. | 1.448936 .1585248 9.14 0.000 1.126415 1.771457
|
_cons | .0531374 .0070369 7.55 0.000 .0388207 .067454
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Table 2: Results of Equation 2
reg D.lntaxrevenue D.Taxrate D.taxrate2
Source | SS df MS Number of obs = 35
-------------+------------------------------ F( 2, 32) = 40.81
Model | .144834628 2 .072417314 Prob > F = 0.0000
Residual | .05678697 32 .001774593 R-squared = 0.7183
-------------+------------------------------ Adj R-squared = 0.7007
Total | .201621598 34 .005930047 Root MSE = .04213
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D. |
lntaxrevenue | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Taxrate |
D1. | 31.17169 15.84922 1.97 0.058 -1.112105 63.45549
|
taxrate2 |
D1. | -75.42432 58.08127 -1.30 0.203 -193.732 42.88335
|
_cons | .0528687 .0071391 7.41 0.000 .0383269 .0674105
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