Sequel of Econometric Experiment of Laffer Curve

* Please could you read this previous post before reading this one:
Econometric Experiment of Laffer Curve

The previous post shows the optimum tax rate maximising the tax revenue. The optimum tax rate is 16.55%.

This entry tries to investigate that there can be some sort of cost when tax is increased. So, in order to find out the optimum tax rate which maximises the net gain of the tax revenue instead of the gross gain shown previously. The national dept % GDP (The public deficit) is denoted as the cost of high taxation. The GLS estimate below is the regression of the national dept % GDP on the tax rate and the lags of this explanatory variable.

The tax rate levied in 3 years ago is highly correlated. The estimate is also detected as consistent.

So, the higher tax rate causes the higher loss in 3 years later. This can be because that, when the government is too used to rely on the high tax revenue, then it may cause the decline in the private sector activities. Also, when the volume of the reliance on the government expenditure does not seem to be robust. Furthermore, when this volume of the reliable becomes bigger, the volatility of the reliance also become bigger. All in all, the prediction cost becomes bigger when the size of the public sector economy becomes bigger.

In order to find out the optimum tax rate which maximises the profit from the taxation i.e. the tax revenue minus the tax cost = the deficit in 3 years ago. As shown below, both functions are differentiated by means of the tax rate. At the tax rate where the differentiated tax revenue equals the differentiated deficit, the net gain from the taxation is maximised.

Owing to the result, when the tax rate is 10.5%, the net gain is maximised. This tax rate 10.5% is lower than 16.55%, the tax revenue maximising the gross gain shown in the previous post.