Estimating the effective tax rates in OECD countries

When studying public economics, researchers often need to calibrate their model so that the effective tax rates implied by the model are consistent with the national accounts and government revenue statistics. One of the most widely used method for effective tax rate estimation was proposed by Mendoza, Razin, and Tesar (1994). In this note, I briefly explain its methodology using the national income identity.

1. National Income Identity without Taxes

First, recall the national income identity:

$Y = C + I + G$

$Y = wL + (r + \delta)K + \pi$

For simplicity we do not consider any taxes or international trade at this moment. On the left-hand side of the identity stands the gross domestic product (Y), which refers to the value of services and final products produced by a country within a certain period of time. The right-hand side of the identity can contain different terms, depending on the accounting approach the statistics authority uses:

Expenditure approach. In this case the right-hand side of the identity contains the following terms: household consumption (C), investment (I), government consumption (G). (If there is any international trade there will be net export on the right-hand side as well.)
Income approach. In this case there are three terms on the right-hand side of the identity. They are: labor compensation (wL), depreciation of fixed asset (δK), and operating surplus (rK + π).

In theory, the two approaches should yield identical estimates of gross domoestic product (GDP). This can be illustrated by the following example.

Suppose the national economy is made up by a representative household and a representative firm. The representative household’s budge constraint is:

$C + I = wL + rK + \pi$

which says that the representative household’s consumption and investment should be financed by its labor income, its capital income, and the representative firm’s profit (the representative firm is owned by the representative household). The representative firm’s profit function is

$\pi = Y - wL - (r + \delta)K$

The firm’s profit is defined as the residual value after the firm deducts wage compensation and capital rent from its sales revenue.

Recall that investment is defined as the difference between next period’s capital stock and current period’s undepreciated capital stock:

$I = K' - (1 - \delta)K$

Substituting the above three equations into either of the national income identity yields