On the Mechanics of Economic Development

Lucas opens with the magnitude of cross-country income and growth-rate diversity – 1980 per-capita income of about $10,000 for industrial economies against $240 for India and $270 for Haiti, and 1960-80 per-capita growth rates ranging from 1.4 percent (India) to 7.1 percent (Japan) – and states that the consequences for human welfare bound up in such differences are, in his word, staggering (Sec. 1, p. 5). He deliberately narrows “theory” to mean a dynamic system that can literally be put on a computer and run – hence “mechanics” in the title – distinguishing this from looser verbal accounts, and explicitly brackets out monetary factors and the economics of demography (population growth is taken as exogenously given throughout) to keep the exercise tractable.

The model distinguishes growth effects – changes in parameters that alter the growth rate along a balanced path – from level effects – changes that shift the balanced path up or down without changing its slope. Lucas writes that Solow’s 1956 conclusion that changes in savings rates are level effects only “was startling at the time, and remains widely and very unfortunately neglected today”: the influential idea that tax changes making savings more attractive can have large, sustained effects on an economy’s growth rate “sounds so reasonable, and it may even be true” – “but it is a clear implication of the theory we have that it is not” (Sec. 2). In the model, the long-run per-capita growth rate κ depends only on the exogenous rate of technical change λ and labor’s share (κ = λ/(1-β)); the discount rate ρ and risk-aversion coefficient σ affect only the savings rate and hence the level, not the slope, of the balanced path.

Using Denison’s estimates, Lucas sets λ = 0.013, κ = 0.027 (averaging the output- and capital-growth-rate estimates of 0.029 and 0.024), 1-β = 0.75 (labor’s share), and a savings rate s = 0.10, which together imply κ via (9) and a joint restriction ρ + 0.014σ = 0.0675 on the preference parameters via (10). He reports candidly that either output growth is underpredicted or capital growth is overpredicted, and that in the theory of growth “a half a percentage point is a large discrepancy”, also noting that labor’s share is secularly rising across growing economies rather than constant as the model assumes – limitations he attributes partly to capital-stock price deflators failing to correct for quality improvements (citing Griliches and Jorgenson 1967).

Two specific failures are named (Sec. 3): its apparent inability to account for the observed cross-country diversity in income levels and growth rates under plausible parameter variation, and its strong – and, Lucas stresses, evidently counterfactual – prediction that opening international trade should induce rapid movement toward equality in capital-labor ratios and factor prices once factor mobility is allowed. Neither population growth rates nor labor’s income share vary across countries in a way that can account for observed income differentials (poor countries are not systematically those with rapid population growth, and their lower labor shares imply they should grow faster under the model, which is not observed); and the model’s parameter insensitivity, which explains its empirical success in fitting the stable U.S. time series, works against it when trying to explain large cross-country variation.

Lucas documents that nineteenth-century immigration into the labor-scarce Americas, Australia, and South/East Africa, and the twentieth-century movement of U.S. textile mills from New England toward the (lower-wage) South, confirm that factor mobility does equalize factor prices when it occurs: as he puts it, “it makes no difference whether labor moves to join capital or the other way around” (Sec. 3). Yet once international labor mobility was “largely shut off” in the twentieth century, capital movements did not substitute for it: if moving a textile mill from New England to South Carolina is profitable, Lucas asks why it should not be more profitable still to move it to Mexico. He states that he does not have a satisfactory answer to this question, but that it seems to him to be a major – perhaps the major – discrepancy between the predictions of neoclassical theory and the patterns of trade actually observed, and that dealing with this issue is, in his view, a minimum requirement for a theory of economic development (Sec. 3, pp. 16-17).

Lucas replaces the exogenous technology term A(t) with a structure in which each worker’s human capital h(t) has both an “internal effect” on that worker’s own productivity and an “external effect” – operating through the average skill level h_a – on the productivity of all factors in production (eq. 11). Human capital accumulates according to h-dot(t) = h(t)^γ G(1-u(t)), where 1-u(t) is the fraction of time devoted to human-capital accumulation rather than current production; Lucas shows that diminishing returns in this accumulation technology (γ < 1) cannot sustain growth on their own, so the Uzawa (1965) linear case (γ = 1) is adopted as the one capable of generating “sustained per-capita income growth from endogenous human capital accumulation alone: no external ’engine of growth’ is required.”

Fitting (10), (21), and (26) to Denison’s U.S. estimates (λ = 0.013, κ = 0.014, β = 0.25, s = 0.1, and a 0.009 estimate for the growth rate of human capital from schooling) yields an estimated external-effect elasticity of γ = 0.417, an implied fraction of time devoted to goods production of u = 0.82, and a joint preference restriction ρ + σκ = 0.0675. Under log utility (σ = 1), the efficient human-capital growth rate implied by the model is ν* = 0.009 + 0.0146/σ, which Lucas reports means that the U.S. economy “ought” to “devote nearly three times as much effort to human capital” accumulation “as it does, and” – by the same logic – “ought” to “enjoy growth in per-capita consumption about two full” percentage points higher than it has actually had in the past – a gap between the competitive equilibrium and the efficient outcome that arises precisely because the external effect (γ > 0) is not priced by individual agents.

Lucas is direct: asked what can be concluded from these exercises, he answers, normatively, hardly anything at all, because “the model I have just described has exactly the same ability to fit U.S. data as does the” Solow model, “in which equilibrium and efficient growth rates coincide.” The aggregate time series cannot discriminate between a model with a large external effect and one without, since both fit equally well (Sec. 4). The model’s distinguishing analytical contribution, rather, is that it is “consistent with the permanent maintenance of per-capita income differentials of any size” – though not with differences in growth rates – making some progress toward the paper’s original goal of accounting for persistent cross-country income gaps, even without pinning down why.

Lucas sets up a two-good Ricardian economy in which good i is produced as c_i(t) = h_i(t) u_i(t) N(t), and specialized human capital h_i(t) grows according to h-dot_i(t) = h_i(t) δ_i u_i(t) – i.e., learning-by-doing, where skill in a good accumulates fastest when more effort is currently devoted to producing it (rather than when effort is withdrawn from it, as in the schooling model of Section 4), with good 1 assumed to be the higher-technology good (δ_1 > δ_2). Because comparative advantage and relative productivity are determined by the history of which good a country has specialized in, the terms of trade a country’s government chooses to allow or distort (through tariffs or export subsidies) directly shape which good gets produced, and therefore which rate of human-capital accumulation, and hence which long-run growth rate, the economy ends up on – so that, unlike in the exogenous-technology models of Sections 2-4, the growth rate itself becomes something a country’s trade policy can move.

No – he states that his objective, in this section, has been “to offer one example of a theoretical model in which rates of growth differ across countries, and not to offer policy advice.” He notes that the classic case for infant-industry protection based on external learning effects “does not become either more or less valid, empirically, by being embedded in a slightly new framework” – and that even with the flexibility of export-promotion-style terms-of-trade manipulation, growth-increasing and welfare-improving policies need not coincide, though Lucas allows that they certainly might (Sec. 5). His substantive question is instead whether large cross-country growth differences can be explained without invoking some form of external effect of the kind the model postulates: “I have not seen it done.”

Lucas, following Jane Jacobs’s “The Economy of Cities” (1969), argues that external human-capital effects cannot be cleanly classified as either fully internalizable within a family or firm, or else fully global in scope (“exogenous” technology); some operate at the scale of neighborhoods, industries, or cities. He likens a city, economically, to the nucleus of an atom: on the usual list of economic forces alone, land being always cheaper outside cities than inside them, “cities should fly apart” – yet they do not, which is the puzzle Jacobs’s work is organized around. Lucas suggests urban land rents could, in principle, provide an indirect empirical measure of the external human-capital force (γ), by analogy to the way schooling-induced earnings differentials measure the productive effects of internal human capital, though he stresses that exploiting this “would require a much more detailed theory of the external effects of human capital than anything I have provided.”

Lucas states plainly that “the model that I think is central was developed in section 4” – the human-capital-externality model – built around two state variables: physical capital, accumulated and used in production under a familiar neoclassical technology, and human capital, which raises the productivity of both labor and physical capital and accumulates according to a law with the crucial property that a constant level of effort can sustain growth indefinitely (Sec. 7). He frames the overall project modestly, describing the lectures’ aim as having been “taken about as far as I am able to take it, at present,” and acknowledges that the external effect’s calibrated size (γ = 0.4) is a number he does not know how to independently validate against evidence outside the aggregate time series he used to estimate it – a question he poses to the reader but leaves open.