A Quantitative Evaluation

As a final exercise, let us investigate whether the quantitative implications of the neo­classical growth model are reasonable. For this purpose, consider a world consisting of a collection J of closed neoclassical economies (with all the caveats of ignoring technological, trade and financial linkages across countries, already discussed in Chapter 3; see also Chap­ter 19).

Let us assume that there is no population growth, so that Cj is both total and per capita consumption. Equation (8.55) imposes that all countries have the same discount rate ρ (see Exercise 8.30).

All countries also have access to the same production technology given by the Cobb- Douglas production function

with Hj representing the exogenously given stock of effective labor (human capital). The accumulation equation is

The only difference across countries is in the budget constraint for the representative household, which takes the form

where Tj is the (constant) tax on investment. This tax varies across countries, for example because of policies or differences in institutions/property rights enforcement. Notice that 1+ Tj is also the relative price of investment goods (relative to consumption goods): one unit of consumption goods can only be transformed into 1/ (1 + Tj) units of investment goods.

The right-hand side of the budget constraint (8.57) is still Yj (t), which implicitly assumes thatis wasted, rather than being redistributed back to the representative household.

The competitive equilibrium can be characterized as the solution to the maximization of (8.55) subject to (8.57) and the capital accumulation equation. With the same steps as above, the Euler equation of the representative household is

So countries with higher taxes on investment will have a lower capital stock in steady state. Equivalently, they will also have lower capital per worker, or a lower capital output ratio (using (8.56) the capital output ratio is simply K/Y = (K/AH)^α).

Now substituting this into (8.56), and comparing two countries with different taxes (but the same human capital), and denoting the steady-state income level of a country with a tax rate equal to τ by Y (τ), we obtain the relative steady-state income differences as

This equation therefore summarizes the intuitively obvious notion that countries that tax investment, either directly or indirectly, at a higher rate will be poorer. More interestingly, this equation can be used for a quantitative evaluation of how large the effects of these types of policies might be. The advantage of using the neoclassical growth model for quantitative evaluation relative to the Solow growth model is that the extent to which different types of distortions (here captured by the tax rates on investment) will affect income and capital accu­mulation is determined endogenously.

How large are the effects of tax distortions captured by eq. (8.58)? Put differently, can the neoclassical growth model combined with policy differences account for quantitatively large cross-country income differences?

The advantage of the current approach is its parsimony. As eq. (8.58) shows, only differences in τ across countries and the value of the parameter α matter for this comparison. Recall also that a plausible value for α is 2/3, since this is the share of labor income in national product which, with Cobb-Douglas production function, is equal to α, so this parameter can be easily mapped to data.

Where can we obtain estimates of differences in τ^,s across countries? There is no obvious answer to this question. A popular approach in the literature is to obtain estimates of τ from the relative price of investment goods (as compared to consumption goods), motivated

by the fact that in eq. (8.57) τ corresponds to a distortion directly affecting investment expenditures. Therefore, we may expect τ to have an effect on the market price of investment goods. Data from the Penn World tables suggest that there is a large amount of variation in the relative price of investment goods. For example, countries with the highest relative price of investment goods have relative prices almost eight times as high as countries with the lowest relative price.

Then, using α = 2/3, eq. (8.58) implies that the income gap between two such countries should be approximately threefolds:

Therefore, differences in capital-output ratios or capital-labor ratios caused by taxes or tax-type distortions, even by very large differences in taxes or distortions, are unlikely to account for the large differences in income per capita that we observe in practice.

Nevertheless, many economists have tried (and still try) to use versions of the neoclassical model to go further. The motivation is simple. If instead of using α = 2/3, we take α = 1 /3, the ratio of incomes in the two countries would be

Therefore, if there is any way of increasing the responsiveness of capital or other factors to distortions, the predicted differences across countries can be made much larger. How could we have a model in which α = 1 /3? Such a model must have additional accumulated factors, while still keeping the share of labor income in national product roughly around 2/3. One possibility might be to include human capital (see Chapter 10 below). Nevertheless, the discussion in Chapter 3 showed that human capital differences appear to be insufficient to explain much of the income per capita differences across countries. Another possibility is to introduce other types of capital or perhaps technology that responds to distortions in the same way as capital. While these are all logically possible, a serious analysis of these issues requires models of endogenous technology, which will be our focus in the next part of the book.

8.11.