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Sunday, July 31, 2011

Differences in saving rates

Consider two countries that are equal in every respect but have different saving rate. The country with the higher saving rates accumulates more capital and therefore converges to an higher level of capital stock and output per worker.

This prediction of the model seems roughly consistent with the empirical evidence that emerges from looking at a cross section of countries. Statistics suggest that high investment rates are associated with high level of GDP per capita. But does the picture really tells us that if Gambia increases its saving rate from 5% to 10% this will lead to a doubling of GDP per capita in Gambia? We will go back to this point later. For now keep in mind that this relation has motivated many policy choices.

The Stalin 5 years plans in the thirties were basically based on this theory and a lot of programs in developing countries in the 60s had as a main goal the increase in saving (even forced saving though taxes) to increase capital stock and achieve a higher output per worker. Even more recently the IMF has stated that "To achieve gains in real per capita GDP an expansion in private saving and investment is key".

The Golden rule of saving

An interesting question is whether higher saving, even if it always yields higher levels of steady state income, always yields higher steady state consumption. The answer is no and the intuition comes from the fact that returns to capital are decreasing.
Increasing my saving by 5% always reduces my consumption by 5% but the benefit it will bring in terms of future consumption depend on the returns to capital. If I have little capital returns to capital are high and my consumption will eventually increase.

If I have a lot of capital returns to capital are low, the benefits of additional saving are low and consumption might actually decline. The steady state level of consumption depends on the saving rate. It reaches a maximum at the point in which the marginal product of capital is equal to the depreciation rate. This saving for which the maximum consumption is achieved is called the “golden rule" of saving.


But if savings and investment is so important why do some countries (for example the African countries) fail to realize that and do not save and invest? So far we've been treating savings as an exogenous variable and so we are not really equipped to answer this question. A first simple theory of saving rates might be based on basic needs: some countries do not save simply because they are too poor to save. Suppose that when people have very low income they need all their income to satisfy their basic needs (like food) and thus their saving rate is 0 (They consume all their income).

When income reaches a basic level people start saving and save a constant fraction of their income as in the previous example. Also assume that this rate is the same across countries.

The model will display two steady states. Notice that the one steady state (the one with low capital) is unstable in the sense that if capital is above it , it will move toward the higher capital steady state but if a country starts with a capital below that level that country will converge toward a level of 0 capital stock. The situation depicted is called a poverty trap. Countries that start with a level of capital stock that is very low will never take off. Notice that here we have reversed the causality: it is not that countries are poor because they don't save but they do not save because they are poor.

The poverty trap model has been the rational for the kind of policy denominated big push, that is a massive investment from abroad that is able to raise the capital stock just above the first steady state so convergence to the higher steady state can happen. The big problem with this theory has been that even though these type of big push policies have been tried repeatedly (from Zambia in the 60s to Cambodia or Lithuania in the 1990s) they do not seem to have generated sustained growth. For example in the period 1960-1988 of 87 developing countries (income per capita below US$ 5000) 47 of them have failed to even improve their standard of living. So why are some countries unable to takeoff even with massive foreign aid?

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