Convergence relies on diminishing returns to “capital”. If this is our assumed starting point, the share of capital in national income does give us rough estimates of the concavity
of production in capital. The problem is that the resulting concavity understates observed
variation in cross-country income by orders of magnitude. For instance, Parente and
Prescott (2000) calibrate a basic Cobb-Douglas production function by using reasonable
estimates of the share of capital income (0.25), but then huge variations in the savings
rate do not change world income by much. For instance, doubling the savings rate leads
to a change in steady state income by a factor of 1.25, which is inadequate to explain an
observed range of around 20:1 (PPP). Indeed, as Lucas (1990) observes, the discrepancy
actually appears in a more primitive way, at the level of the production function. For
the same simple production function to fit the data on per-capita income differences, a
poor country would have to have enormously higher rates of return to capital; say, 60
times higher if it is one-fifteenth as rich. This is implausible. And so begins the hunt for
other factors that might explain the difference. What did we not control for, but should
have?
This describes the methodological approach. The convergence benchmark must be pitted
against the empirical evidence on world income distributions, savings rates, or rates of
return to capital. The two will usually fail to agree. Then we look for the parametric
differences that will bridge the model to the data.
“Human capital” is often used as a first port of call: might differences here account for
observed cross-country variation? The easiest way to slip differences in human capital
into the Solow equations is to renormalize labor. Usually, this exercise does not take
us very far. Depending on whether we conduct the Lucas exercise or the PrescottParente
variant, we would still be predicting that the rate of return to capital is far
higher in India than in the U.S., or that per-capita income differences are only around
half as much (or less) as they truly are. The rest must be attributed to that familiar
black box: “technological differences”. That slot can be filled in a variety of ways:
externalities arising from human capital, incomplete diffusion of technology, excessive
government intervention, within-country misallocation of resources, . . . . All of these
— and more — are interesting candidates, but by now we have wandered far from
the original convergence model, and if at all that model still continues to illuminate,
it is by way of occasional return to the recalibration exercise, after choosing plausible
specifications for each of these potential explanations.
This model serves as a quick and ready fix on the world, and it organizes a search for
possible explanations. Taken with the appropriate quantity of salt, and viewed as a first
pass, such an exercise can be immensely useful. Yet playing this game too seriously
reveals a particular world-view. It suggests a fundamental belief that the world economy
is ultimately a great leveller, and that if the levelling is not taking place we must search
for that explanation in parameters that are somehow structurally rooted in a society.
Convergence relies on diminishing returns to “capital”. If this is our assumed starting point, the share of capital in national income does give us rough estimates of the concavityof production in capital. The problem is that the resulting concavity understates observedvariation in cross-country income by orders of magnitude. For instance, Parente andPrescott (2000) calibrate a basic Cobb-Douglas production function by using reasonableestimates of the share of capital income (0.25), but then huge variations in the savingsrate do not change world income by much. For instance, doubling the savings rate leadsto a change in steady state income by a factor of 1.25, which is inadequate to explain anobserved range of around 20:1 (PPP). Indeed, as Lucas (1990) observes, the discrepancyactually appears in a more primitive way, at the level of the production function. Forthe same simple production function to fit the data on per-capita income differences, apoor country would have to have enormously higher rates of return to capital; say, 60times higher if it is one-fifteenth as rich. This is implausible. And so begins the hunt forother factors that might explain the difference. What did we not control for, but shouldhave?This describes the methodological approach. The convergence benchmark must be pittedagainst the empirical evidence on world income distributions, savings rates, or rates ofreturn to capital. The two will usually fail to agree. Then we look for the parametricdifferences that will bridge the model to the data.“Human capital” is often used as a first port of call: might differences here account forobserved cross-country variation? The easiest way to slip differences in human capitalinto the Solow equations is to renormalize labor. Usually, this exercise does not takeus very far. Depending on whether we conduct the Lucas exercise or the PrescottParentevariant, we would still be predicting that the rate of return to capital is farhigher in India than in the U.S., or that per-capita income differences are only aroundhalf as much (or less) as they truly are. The rest must be attributed to that familiarblack box: “technological differences”. That slot can be filled in a variety of ways:externalities arising from human capital, incomplete diffusion of technology, excessivegovernment intervention, within-country misallocation of resources, . . . . All of these— and more — are interesting candidates, but by now we have wandered far fromthe original convergence model, and if at all that model still continues to illuminate,it is by way of occasional return to the recalibration exercise, after choosing plausiblespecifications for each of these potential explanations.This model serves as a quick and ready fix on the world, and it organizes a search forpossible explanations. Taken with the appropriate quantity of salt, and viewed as a firstpass, such an exercise can be immensely useful. Yet playing this game too seriouslyreveals a particular world-view. It suggests a fundamental belief that the world economyis ultimately a great leveller, and that if the levelling is not taking place we must searchfor that explanation in parameters that are somehow structurally rooted in a society.
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