Laffer curve is the theory indicating that there should be an optimum level of tax rate which maximises the tax revenue. It claims that the tax rate should be neither lower or higher than this optimum tax rate to maximise the tax revenue. Therefore, in terms of what Laffer Curve theory indicates, the correlation between the tax revenue and the tax rate is the up-facing parabolic equation shown by the graph above. (Y denotes the tax revenue, and X denotes the rate of the tax on income and profit (From OECD, 2004-2011)) The countries whose data is missing for 2011, it refers to the data in 2010.
Then, in order to find out the optimum tax rate, this formula is factorised as follows.
f1
g2
Therefore, the optimum tax rate is denoted as Beta divided by bracket two times Alpha. This value shows the average across all countries and times.
These countries might have a different rate of the optimum tax rate due to their geographic characteristics and political situations. So, the deviation of their own optimum level from the average rate is denoted, where the sum of ±D is zero, as follows:
g3
In order to create the formula suitable for the regression analysis, the formula involving ±D is expanded as follows:
f2
In order to simplify and avoid the multicolliearity problem, both the left side and the right side of this equation is divided by X. At this time, both sides of the equation involves the variable X, there is a worry about the simultaneous equation problem. So, in order to verify that the simultaneous equation problem is avoided at 95% confidence level, the Generalised Least Squares (GLS) model is used to assess this equation in order to use its Hausman test (The test assessing whether the analysis is consistent or inconsistent). The other reason to use the GLS model is that the sum of the dummy variables has to be zero because the barometer "Beta divided by bracket two times Alpha" is supposed to be shown as the average of all these countries across all the years.
f3
f4
GLS Result
The GLS model in this software can only regress on the time dummy variables of the fixed effects (I.e. The random effect of the time dummies cannot be used). The dummy variables of the time effect are excluded from this model because the Wald Omit Test showed that the time dummies are not significant (See below).
The Breusch-Pagan test (p-value 0.025 < 0.05 ) indicates that, at the 5% significance level, the unit specific effects (The Random Effect) exist. So, the optimum tax revenue for some countries can be significantly different from the average optimum tax revenue. The Hausman test (p-value 0.94 > 0.05 ) indicates that, the estimates are consistent. This claims that the previously mentioned simultaneous equation problem is avoided, and there is no concern about any other inconsistency problem such as the serial correlation.
The following process is to transforming the equation for the GLS back to the original parabolic equation, and then factorise it to find out the optimum tax rate.
Result
Tax Rate minus the optimum rate (16.55)
The ranking of the optimisation
