E13 | Macro Paper Warehouse

A Contribution to the Empirics of Economic Growth

This 1992 Quarterly Journal of Economics paper by Mankiw, Romer, and Weil tests whether Robert Solow’s (1956) neoclassical growth model, augmented to include accumulation of human as well as physical capital, can account for the enormous cross-country variation in income per capita. Using Summers-Heston national accounts data for three samples of countries (98 non-oil countries, a 75-country intermediate sample excluding low-data-quality and very small countries, and 22 OECD countries) over 1960-1985, the authors first show that the textbook Solow model (with only physical capital) gets the signs of the effects of the investment rate and population growth right and explains a majority of cross-country income variation, but implies an unrealistically high capital share of income – roughly 0.6-0.8 in the estimated regressions rather than the roughly one-third value implied by independent data on factor shares. Adding a proxy for human-capital investment (the fraction of the working-age population enrolled in secondary school) to the regression raises the explained variance to about 80 percent and brings the implied capital and human-capital shares close to their independently known values of about one-third each, without rejecting the restriction that the model’s coefficients should sum to zero. The paper further argues that the well-documented absence of unconditional convergence across countries does not contradict the Solow model, because the model predicts only “conditional convergence” – convergence toward each country’s own steady state, determined by its own saving, population growth, and human-capital investment rates – and the data show a statistically and economically significant conditional convergence at a rate, implying a roughly 35-year half-life to steady state, reasonably close to what the augmented model predicts. Finally, the paper argues that apparently puzzling patterns in international interest-rate differentials and capital flows (the Feldstein-Horioka finding that capital does not flow from high-saving to low-saving countries) do not straightforwardly contradict the model once one allows for imperfect capital markets and expropriation risk, and that direct evidence on profit rates and returns to schooling is, if anything, consistent with the Solow model’s prediction of higher returns to capital in poorer countries. The authors are careful to note that this defense of the Solow model does not make it a complete theory of growth, since it still treats saving rates, population growth, and worldwide technological change as exogenous, and that endogenous-growth models may still be needed to explain those more fundamental determinants.

A Contribution to the Theory of Economic Growth

Robert Solow’s 1956 paper argues that the Harrod-Domar model’s famous conclusion – that steady economic growth is only ever balanced on a “knife-edge,” liable to tip into growing unemployment or prolonged inflation – follows specifically from its assumption that capital and labor must be combined in fixed proportions, with no possibility of substitution between them. Solow keeps every other Harrod-Domar assumption (a single composite commodity, a constant savings ratio s applied to output Y, an exogenously growing labor force L(t) = L0e^(nt)) but replaces fixed-coefficient technology with a standard neoclassical production function Y = F(K,L), homogeneous of degree one. Substituting the labor-force path into the savings identity and converting to the capital-labor ratio r = K/L yields a single first-order differential equation, r-dot = sF(r,1) - nr, whose qualitative behavior can be studied graphically by comparing the curve sF(r,1) against the ray nr. Under the “normal” case illustrated in Figure I (essentially the Cobb-Douglas case), this equation has a unique, globally stable equilibrium capital-labor ratio r*: starting from any positive initial ratio, the economy converges to balanced growth in which capital, labor, and output all expand at the labor force’s natural rate n, so that “no simple opposition between natural and warranted rates of growth is possible.” Solow is careful to show this stability is not automatic for every conceivable production function – Figure II exhibits a case with three equilibria (two stable, one unstable, so initial conditions determine which stable path is reached) and Figure III exhibits cases with no equilibrium at all, where the capital-labor ratio either grows or shrinks without bound. Three worked examples (fixed-proportions/Harrod-Domar, Cobb-Douglas, and a two-parameter constant-elasticity-of-substitution family) make the algebra explicit, including the specific redundant-labor and redundant-capital sub-cases that arise in the fixed-proportions case when the natural and warranted rates diverge. Section V shows that competitive factor prices (real wage and real rental) adjust smoothly along the way to equilibrium – directly contradicting a claim by Harrod that a perpetually falling interest rate would be needed to sustain balance. Section VI extends the model to neutral technical progress (which raises the asymptotic growth rate above n), a wage-elastic labor supply, a capital-yield-dependent savings ratio, income taxation, and endogenous (income-dependent) population growth, the last of which can produce a low unstable threshold capital-labor ratio separating permanent stagnation from self-sustaining growth. Section VII explicitly limits the claim to a frictionless, full-employment “neoclassical side of the coin,” noting that rigid real wages, liquidity-trap-like asset preferences, and the general absence of perfect foresight can each still generate unemployment or excess capacity through familiar Keynesian channels.

A Mathematical Theory of Saving

Frank Ramsey’s 1928 paper asks how much of its income a nation ought to save, and derives a rule – that the rate of saving times the marginal utility of consumption should equal the gap between attainable “Bliss” and the community’s actual current rate of enjoyment – valid, he shows, “under conditions of surprising generality.” The setup assumes a community that persists forever without changing in numbers or tastes, whose enjoyments and sacrifices at different times can be added independently, and which – crucially – does not discount later enjoyments merely because they are later, a practice Ramsey calls “ethically indefensible” and traceable only to “the weakness of the imagination” (though Section II relaxes this to allow a constant positive discount rate). Denoting consumption x(t), labour a(t), and capital c(t), with income f(a,c) satisfying the accounting identity that savings plus consumption equal income, and given utility of consumption U(x) and disutility of labour V(a), Ramsey defines “Bliss” (B) as the maximum obtainable rate of net enjoyment U(x)-V(a), which the community either reaches in finite time or approaches asymptotically forever; because only reaching or approaching Bliss keeps the cumulative shortfall from Bliss, summed over all time, finite, the paper argues the community is bound to save enough to do so. Solving the resulting calculus-of-variations problem (jointly with an optimal labour-supply condition equating the marginal disutility of labour to the marginal efficiency of labour times the marginal utility of consumption) yields the headline rule: the rate of saving times the marginal utility of consumption should always equal Bliss minus the actual rate of utility enjoyed – a result Ramsey also derives, via a suggestion from Keynes, by a much simpler direct argument comparing the loss from postponing consumption by an infinitesimal interval. The rule’s most striking feature, Ramsey notes, is that it is independent of the production function except through Bliss, and independent of the current rate of interest (when the future is not discounted) except where that rate is exactly zero; a numerical illustration using an assumed utility schedule implies saving roughly three-fifths of income at a family income of 500 pounds, “greatly in excess of that which anyone would normally suggest.” Section II specializes to a linear income function f(a,c) = pa + rc (constant wage and interest rates) to give a graphical solution, extend the analysis to an individual with a finite lifetime who wishes to leave a bequest, and rework the rule under constant time-discounting of future utility – showing the discounted version depends only on the ratio of the discount rate to the interest rate, and that if the interest rate is smaller than the discount rate, consumption is driven toward bare subsistence and debt accumulates without limit. Section III turns to how the interest rate itself is determined, showing that out of equilibrium the interest rate behaves as a demand price for the whole stock of capital but a supply price for the flow of new saving, so it can substantially exceed what would ultimately be needed to induce thrift; and that when different individuals apply different constant discount rates, a stationary equilibrium divides the community into a class that reaches Bliss and a class driven down to bare subsistence, rather than settling on some common intermediate standard.

Economic Growth and Capital Accumulation

Trevor Swan’s 1956 paper illustrates, with two diagrams, the connexion between capital accumulation and the growth of the productive labour force in a one-sector economy, then devotes a long appendix to defending the neoclassical treatment of capital as a factor of production against Joan Robinson’s contemporaneous critique. In the main text, output is produced from capital K and labour N under a constant-returns production function Y = K^a * N^b (a+b=1), giving the growth-accounting identity y = as(Y/K) + bn, where s is the saving ratio and n the (initially constant) rate of growth of the labour force. Plotting growth rates against the output-capital ratio, the growth line of capital (a ray of slope s through the origin), the horizontal growth line of labour (at n), and the growth line of output (their weighted average) must intersect at a single point, where the output-capital ratio settles and the whole economy grows at rate n regardless of the saving ratio – a higher saving ratio permanently raises the level of output per head reached along the way, and briefly accelerates growth during the transition, but does not raise the long-run equilibrium growth rate itself. Adding a constant rate of “neutral” technical progress shifts the growth line of output upward and establishes a new equilibrium at which output per head is not merely permanently higher but perpetually rising, at a rate that exceeds the rate of technical progress itself because capital’s own growth is sustained at a higher level too. Introducing land as a third, fixed factor (Section 3) converts the model into an explicitly classical one: the growth line of capital now lies everywhere above the “Ricardian line” (the locus of population-growth/output-capital-ratio combinations consistent with a constant standard of living), so that, absent technical progress, the output-capital ratio falls indefinitely toward a stationary state at the origin – a mechanism Swan reads as the formal counterpart of the classical doctrine that accumulation ultimately leads to stagnation, checked only if technical progress raises the Ricardian line fast enough. Section 4 shows the model is formally equivalent to Harrod’s warranted/natural-rate apparatus, with the growth line of capital as Harrod’s warranted rate and the growth line of output as the natural rate. The paper’s substantial Appendix, “Notes on Capital,” then takes up Joan Robinson’s contemporaneous claim that Capital cannot be given an operative meaning as a factor of production even in a stationary state: using a “scarecrow” model of durable, freely-reshapable “meccano set” capital, Swan argues that at the margin of a single stationary equilibrium capital can validly be measured as “an equilibrium dollar’s worth” without needing a natural technical unit, reworks Wicksell’s point-input/point-output and Akerman durable-equipment models to show the same marginal-productivity apparatus applies there too, and shows that the “Wicksell effect” – part of an increase in social capital being absorbed by rising wages and falling interest rather than appearing as extra physical capital – can run in either direction (the “Wicksell effect in reverse”), which he takes as evidence against Robinson’s claim that the effect is “the key to the whole theory of accumulation and of the determination of wages and profits.”

Endogenous Technological Change

This 1990 Journal of Political Economy paper by Paul Romer models long-run growth as driven by technological change that arises from intentional research investment by profit-maximizing firms, treating technology – specifically, a design for a new producer durable – as a nonrival but only partially excludable good: once created, a design can be used in production without limit, but because it cannot be perfectly kept secret its benefit to future researchers is nonexcludable even though its use in manufacturing the specific patented good is legally protected. Because a nonrival input makes the aggregate production function nonconvex, Romer shows that ordinary price-taking competition cannot be supported and instead builds an equilibrium with monopolistic competition, in which firms that have purchased a patented design earn a markup over marginal cost that is bid away, in present-value terms, by free entry into the market for designs. Solving for a balanced-growth-path equilibrium, the paper’s central result is a growth equation that depends on the interest rate and on the total stock of human capital devoted to research, but not on the size of the labor force or on the unit cost of manufacturing new capital goods, implying that a country’s raw population is not the relevant scale variable for growth and that, if the total stock of human capital is too low, the model can generate no growth at all. Two distinct externalities – spillovers from a new design onto future researchers’ productivity, which are entirely nonexcludable, and the wedge introduced by monopoly markup pricing in the market for durables – cause equilibrium research investment to fall short of the socially optimal level. Romer argues that, in contrast to his own earlier (1986) model or Arrow’s (1962) learning-by-doing model, in which knowledge accumulation was forced by assumption to move in step with physical capital accumulation, a subsidy to physical capital is here a poor and possibly counterproductive substitute for a direct subsidy to research, and that integration into world markets speeds growth for any country – including a populous one such as China or India – by pooling the effective supply of human capital available for research, a claim supported with historical evidence from Sokoloff (1988) on U.S. counties gaining access to navigable waterways.

Home Bias in Open Economy Financial Macroeconomics

This is a survey of the “home bias” puzzle: the well-documented fact that investors everywhere hold a disproportionate share of their wealth in domestic equities, bonds and bank assets, well beyond what standard portfolio theory recommends. Coeurdacier and Rey organize the literature into three broad classes of explanation – hedging motives in frictionless financial markets, asset trade costs, and informational frictions and behavioral biases – and give particular attention to a “new” macroeconomics literature they label Open Economy Financial Macroeconomics, which embeds non-trivial international portfolio choice into standard two-country DSGE models. Using such a model with both bonds and equities, they show that once real-exchange-rate risk is hedged through bond positions, the remaining equity position optimally hedges human-capital risk conditional on bond payoffs – a channel that, unlike the unconditional hedge used in earlier equity-only models, robustly generates home bias in both the model and in the authors’ own new cross-country evidence. The survey also reviews the transaction-cost literature (concluding that plausible costs are generally too small to explain observed home bias, except when diversification gains are themselves small), the literature on informational asymmetries and endogenous information acquisition, and behavioral explanations built on differences in investor beliefs. It closes by presenting new descriptive evidence on cross-border bond holdings, bank lending and institutional (mutual fund) holdings, and by arguing that “the home bias puzzle is now less of a puzzle” than it once was, while flagging major open areas – modeling the official sector, financial intermediaries, delegated investment and heterogeneous investors – for future work.

Increasing Returns and Long-Run Growth

This 1986 Journal of Political Economy paper by Paul Romer builds a fully specified competitive-equilibrium model of long-run growth in which knowledge is an input to production with increasing marginal productivity, in contrast to the diminishing-returns assumption underlying the standard Ramsey-Cass-Koopmans growth model. Growth is driven by profit-maximizing firms that invest forgone consumption in a research technology exhibiting diminishing returns (so the proportional growth rate of a firm’s own knowledge is bounded above by a constant), while the resulting stock of knowledge generates a positive externality across firms because it cannot be perfectly patented or kept secret; production of the consumption good is globally convex, not concave, in the aggregate stock of knowledge. Romer proves that a finite-valued social optimum exists despite the global increasing returns, because diminishing returns in research bound the feasible growth rate of knowledge, and that – under an additional asymptotic-growth condition – a suboptimal competitive equilibrium with externalities also exists, in which private agents underinvest in research relative to the social optimum because they do not internalize the externality. Historical productivity data for the three successive “leader” countries since 1700 (the Netherlands, the United Kingdom, and the United States), decade-by-decade U.S. per capita growth since 1800, a nonparametric test for trend across eleven countries’ growth rates, and the repeated failure of growth-accounting exercises to explain measured output growth from measured input growth are all offered as evidence consistent with, though the paper is careful to say not decisive proof of, increasing rather than diminishing returns. Under linear or sufficiently weakly curved utility, per capita consumption and output can grow at a rate that is monotonically increasing over time toward an asymptotic upper bound, small current or anticipated future disturbances can have permanently amplified aggregate effects, and – in a multicountry extension with imperfectly mobile knowledge – countries starting from identical initial conditions can diverge permanently, with the composite knowledge/capital good flowing toward the initially more developed country. Romer is explicit that these unbounded-growth and instability results depend on the specific functional forms and utility restrictions used in the worked examples (e.g., logarithmic versus linear utility) and that the model is deliberately restricted to a single state variable (knowledge), holding population and physical capital fixed, for analytical tractability.

Investment, Capacity Utilization, and the Real Business Cycle

In the real business cycle models of Kydland-Prescott and Long-Plosser, cycles come from shocks to the production function; this paper instead adopts Keynes’s view that it is shocks to the marginal efficiency of investment that drive output fluctuations, and asks whether such shocks can be made to work inside a neoclassical framework. The obstacle is well known and the authors state it up front: in a standard model an investment shock raises the return to investment, which induces intertemporal substitution that persuades people to work more now but also to consume less now, so consumption moves countercyclically; and because labour expands against a fixed capital stock, labour productivity falls. Both contradict the evidence. The paper’s answer is to make the rate at which installed capital is used a choice variable. Production depends on capital services – the capital stock times a utilization index – and higher utilization causes faster depreciation, which is Keynes’s own notion of user cost. The shock is a technological change that raises the productivity of newly produced capital goods only, entering as a multiplicative factor on gross investment in the capital accumulation equation and reaching output only after a time-to-build delay taken to be about a year. The mechanism then runs as follows. A positive shock lowers the replacement cost of old capital in terms of new, so it becomes optimal to run old capital harder and depreciate it off faster. Because capital and labour services are complements under constant returns, higher utilization raises the marginal product of labour, employment rises, and average labour productivity rises with it – all without relying on intertemporal substitution in labour supply, which the paper’s preference specification (utility in consumption less a convex function of labour effort) deliberately eliminates. The higher marginal product of labour also creates an intratemporal substitution away from leisure and toward consumption, which is what makes it possible for consumption and investment to rise together. The authors are explicit that the restriction to new capital is load-bearing: if the technological shift is applied to installed capital as well, the shock drops out of the utilization and labour conditions entirely, and “the positive effects of a technological shift on h, l, y, and productivity, in addition to the procyclical effect on consumption, are all lost.” Quantitatively, the model is parameterised annually (discount factor 0.96, capital share 0.29 from the average 1950-85 U.S. figure, labour supply elasticity 1.7, depreciation elasticity 1.42 chosen to deliver a steady-state depreciation rate of 0.1), solved exactly by computing the stationary joint distribution of capital and the two-state shock over a discretised state space, and calibrated so that it reproduces the standard deviation and first-order autocorrelation of detrended U.S. output for 1948-85 – and nothing else. It then reproduces qualitatively the relative volatilities of consumption, investment and hours, though it exaggerates them, and it ranks the persistence of consumption, productivity and investment correctly. Fit is better at a risk aversion of 2 than of 1: the correlation of consumption with output rises from 0.50 to 0.79 against an actual 0.74, and the standard deviation of investment falls from 14.7 to 11.6 percent against an actual 10.5. A notable auxiliary finding is that the required exogenous persistence is far lower than in conventional Solow-residual-driven models: the fitted annual autocorrelation of the shock is 0.47 or 0.51, against Hansen’s quarterly 0.95, which implies a four-quarter figure of 0.81. On shock size the authors concede no advantage – the ratio of shock to output standard deviation, 1.47, sits inside Hansen’s range of 1.3 to 1.7 – but argue that a shock of a given size is a weaker requirement here because it applies only to new capital goods. The paper’s own conclusion is hedged throughout: variable capacity utilization “may be important” and “may allow for a smaller burden to be placed on intertemporal substitution.”

Optimum Growth in an Aggregative Model of Capital Accumulation

David Cass’s 1965 paper elaborates Frank Ramsey’s 1928 optimum-saving problem inside Robert Solow’s aggregative growth model, showing that maximizing the discounted stream of utility from per-capita consumption yields a unique optimum growth path that converges to a “quasi-stationary” balanced path determined by the economy’s effective social discount rate. The setup is a centralized, closed one-sector economy in which output per worker y=f(k) satisfies standard neoclassical conditions (positive but diminishing marginal product, with the marginal product going to infinity as capital per worker k goes to zero and to zero as k grows without bound), population and the labor force grow exogenously at rate n, and a central planning board allocates output between per-capita consumption c and gross investment z, with capital per worker evolving as k-dot = z - (n+depreciation)k. Social welfare is the integral of a concave, time-invariant utility index of per-capita consumption U(c), weighted by population and discounted at a constant rate p that is required to exceed the population growth rate n, so the effective discount rate on per-capita welfare is a = p - n > 0. Applying Pontryagin’s Maximum Principle, Cass derives necessary and (given the concavity assumptions) sufficient conditions for an optimum path involving a continuous “imputed price” of capital q(t): the price evolves so that its own rate of return, adjusted for depreciation, equals the marginal product of capital net of the effective discount rate, subject to a transversality condition that the discounted imputed price vanishes as time recedes to infinity, and current output is allocated to maximize the imputed value of net national product at every instant. Ignoring the historically given initial capital stock, there is a unique “quasi-stationary” path (c*, z*, k*) at which the imputed price is constant, characterized by setting the marginal product of capital equal to the effective discount rate plus population growth and depreciation; this path is independent of the specific shape of the utility function, depending only on the effective social discount rate, and as that discount rate is sent to zero the quasi-stationary path converges to the “golden rule” path previously identified by Phelps (1961). Linearizing the dynamic system around this point, Cass shows the two characteristic roots are real and of opposite sign, so the quasi-stationary point is a saddle point; examining the phase diagram in the capital/imputed-price plane, he shows the stable saddle-path is exactly the unique optimum growth path for any historically given initial capital-labor ratio, with capital and consumption per head both monotonically increasing if the initial capital-labor ratio is below its quasi-stationary value, and both monotonically decreasing if it starts above. A further result, established without additional assumptions on the shapes of the utility and production functions, is that the behavior of the optimum gross saving rate along the way to the steady state is in general ambiguous – it need not move monotonically even though capital and consumption per head do – though for the Cobb-Douglas/constant-relative-risk-aversion special case the saving rate can rise, fall, or stay constant depending on parameter values. In the limiting case where the discount rate is sent to zero, Cass shows – extending a result Tjalling Koopmans had proved rigorously at essentially the same time – that the limiting optimum path is the one that maximizes the discounted-free integral of the excess of actual utility over golden-rule utility, connecting the paper’s framework back to Ramsey’s original Bliss-based formulation with golden-rule welfare playing the role Ramsey’s Bliss played.

Technical Change and the Aggregate Production Function

Robert Solow’s 1957 paper proposes a simple method for separating shifts in the aggregate production function (“technical change,” broadly defined) from movements along it caused by capital accumulation, and applies it to U.S. private non-farm output from 1909-1949, finding that seven-eighths of the doubling in output per worker-hour is attributable to technical change and only one-eighth to increased capital per worker. Starting from an aggregate production function Q=F(K,L;t), Solow specializes to the case of neutral technical change, Q=A(t)f(K,L), where neutrality means the shift “leaves marginal rates of substitution untouched” and simply scales output at any given capital-labor ratio; under the standard (and, he argues, practically unavoidable) assumption of constant returns to scale and competitive factor markets paying marginal products, this yields a simple decomposition of the growth rate of output per worker, q-dot/q, into a technical-change term A-dot/A and capital’s income share times the growth rate of capital per worker, w_k*(k-dot/k) – requiring, to estimate it, only time series of output per worker, capital per worker, and capital’s share of income, and one new assumption (competitive factor pricing), without needing to specify the exact functional form of the production function. Applying this to U.S. private non-farm GNP per man-hour, an estimate of the capital stock (Goldsmith’s data, crudely corrected for unemployment but not for wartime multi-shift operation) and factor-share data for 1909-1949, Solow reconstructs the cumulative shift factor A(t) year by year; a scatter of the year-to-year technical-change term against the capital-labor ratio shows essentially no relationship, so he concludes technical change over the period was, on average, neutral, though the average annual rate of shift roughly doubled between the first and second halves of the sample (about 1 to 1.2 percent per year before 1929 versus roughly 2 percent per year after 1930). The paper’s headline growth-accounting result compares the near-doubling of output per man-hour ($0.623 to $1.275) against the roughly 80 percent cumulative rise in A(t): correcting the 1949 output figure for the estimated technical-change factor implies that about one-eighth of the 40-year increase in output per hour is attributable to increased capital intensity and the remaining seven-eighths to technical change broadly defined. Dividing the resulting technical-change-corrected output-per-worker series by A(t) and plotting it against capital per worker (Chart 4) reveals a scatter with a distinct, though not violent, curvature consistent with diminishing returns; several two-parameter curves (including Cobb-Douglas, semi-logarithmic, and others with upper asymptotes) fit this corrected scatter about equally well, with the linear specification performing noticeably worse, and the data show no sign of approaching capital saturation within the observed range. Solow flags a cluster of wartime and postwar observations (1943-1949) as anomalously high relative to the rest of the scatter, likely reflecting underestimated capital utilization from unmeasured multi-shift wartime operation, and, after experimentation, excludes these years from the regressions reported in the paper’s tables.

The Ramsey steady-state conundrum in heterogeneous-agent economies

When macroeconomists solve for optimal capital and labor taxation in Aiyagari-style heterogeneous-agent, incomplete-markets economies, they routinely assume – without proving it – that the long-run “Ramsey steady state” exists and is well-behaved (interior), a step Aiyagari (1995) himself admitted was hard to justify. This paper proves that assumption is generally false in the standard Aiyagari model with constant-relative-risk-aversion preferences: for the empirically normal case of risk aversion sigma >= 1, no interior Ramsey steady state exists at all, and the only steady state the Ramsey planner can reach has aggregate consumption collapsing to zero and the labor tax rising to 100%, because the planner has a permanent incentive to borrow cheaply against a market interest rate that sits below the household discount rate, front-loading consumption until public debt becomes unsustainable. Using a modified, analytically tractable version of the Aiyagari model that nests the standard model as a limiting case, the authors then show that when an interior steady state does exist (under a feasibility condition on public debt capacity), it features a zero long-run capital tax – the opposite of Aiyagari’s celebrated positive-capital-tax result – with the modified golden rule instead satisfied purely through a high steady-state labor tax and public debt; for the alternative low-risk-aversion case (sigma < 1), an interior steady state can exist but only with a divergent Ramsey multiplier and a violation of the modified golden rule. The paper’s conclusions rest on a standard incomplete-markets model with CRRA power utility, ad hoc borrowing constraints, and a Ramsey planner maximizing time-zero discounted welfare; the authors are explicit that their results do not apply to Ramsey plans that instead maximize only steady-state welfare, where the incentive to front-load consumption disappears.

The Return to Capital in Capital-Scarce Countries

The recent resolution of the Lucas paradox has been that the marginal product of capital is not actually higher in poor countries once measurement is done properly, so there was never much incentive for capital to flow there. This paper reopens the question by measuring both quantities that the neoclassical first-order condition links – the marginal product of capital and the financial return – on the same firms, using Worldscope accounting and stock-market data for listed firms in MSCI developed and emerging countries from 1997 to 2014 (334,471 firm-years across 42 countries). The marginal product is proxied by earnings before interest, tax, depreciation and amortisation over the previous year’s market value of assets (debt at book plus equity at market); the financial return is that plus the capital gain net of new investment, following Fama and French’s internal-rate-of-return-on-value construction; both are inflation-adjusted. The results split the two apart. Consistent with the neoclassical prediction, firm-level return on assets is significantly negatively related to GDP per capita, and this holds after firm, industry and time controls, in 40 of 44 non-financial Fama-French industries, in every single year of the sample, in the post-crisis window, among IFRS adopters, in the EU subsample, using output per worker or per hour instead of per capita, and after adjusting income for corporate tax. The internal rate of return shows nothing of the kind: the coefficient on GDP per capita is statistically insignificant in the main specification and in every robustness variant, insignificant in 42 of 44 industries, and insignificant or positive in 10 of 18 years. Averaged across the sample, return on assets is 9.2 percent and the internal rate of return 8.3 percent, with emerging markets showing higher return on assets but lower internal rates of return than developed markets, in means and medians alike. Quantile regressions sharpen the point: the negative relation with income is strongest for the most profitable firms, yet even those firms show no corresponding advantage in realised returns – “even the best-performing firms within emerging countries cannot successfully translate their higher marginal products of capital to higher investment returns.” The proposed mechanism is a capital accumulation friction: adding a quadratic adjustment term to the accumulation equation breaks the constant-depreciation link, and a firm-level test finds the squared investment-to-capital ratio significantly related to the growth of capital at market prices, so the linear accumulation process implicit in perpetual-inventory capital stocks needs modification. The implication the paper draws is a redirection rather than a solution: “a key explanation for the pattern of international capital flows may indeed be domestic rather than international frictions.” Its own stated limits are firm: the sample is listed firms only, so “our conclusions about the Lucas paradox are restricted to the sample of public firms,” and firm data say nothing about the self-employed or informal sector that “make up a large part of the economy in developing countries.”

Time to Build and Aggregate Fluctuations

This 1982 Econometrica paper by Finn Kydland and Edward Prescott builds an equilibrium growth model, fitted to post-war U.S. quarterly data, in which business-cycle fluctuations arise from technology shocks propagating through two departures from the standard growth model: a time-to-build technology, in which new productive capital requires multiple periods (calibrated to four quarters) of construction and only finished capital counts as productive, and a non-time-separable utility function in which current leisure’s marginal value depends on a distributed lag of past leisure choices, admitting substantially greater intertemporal substitution of leisure than a standard time-separable specification. The technology shock is decomposed into a highly persistent (autoregressive, calibrated at 0.95 per quarter) permanent component and a transitory component, both observed only through a noisy indicator at the time labor-supply and new-investment decisions are made, so the model incorporates a signal-extraction problem alongside its intertemporal optimization. Because there are no externalities, the authors compute the competitive equilibrium as the solution to a representative-household planning problem, approximated by a quadratic objective and linear constraints around the model’s deterministic steady state so that equilibrium decision rules are linear and second moments can be computed analytically; nearly all parameters are calibrated from steady-state national-accounts ratios and evidence from other applied literatures (e.g., surveyed construction lags of about two years) rather than formally estimated, leaving a small number of free parameters chosen to match the model’s simulated second moments to Hodrick-Prescott-filtered U.S. data for 1950:1-1979:2. The fitted model reproduces, surprisingly well given its simplicity, the U.S. economy’s pattern of output autocorrelation over six lags, the relative volatility ranking across output components (investment about three times as volatile as output, consumption about half as volatile), the strong procyclicality of consumption and hours, and the fact that cyclical output variation comes mainly from variation in hours worked rather than in labor productivity. The paper directly tests time-to-build against the leading alternative propagation mechanism, a quadratic adjustment-cost technology, and finds that even a small adjustment cost badly distorts the model’s implied comovements – making output driven mainly by productivity rather than hours, and making consumption too volatile and investment too smooth relative to the data – concluding that adjustment costs “were not a substitute for the time-to-build assumption in explaining the data.”

Time to Plan and Aggregate Fluctuations

Studies of major capital projects report two facts about investment gestation: projects take longer than a quarter to complete, and they open with a lengthy planning phase – drawing plans, arranging finance, obtaining permits – during which the direct resource cost is small relative to the project total. Kydland and Prescott’s Time to Build built the first fact into a macro model; this paper argues the second is the one that matters quantitatively, and that the first “per se has relatively modest implications for business cycle dynamics.” The authors take Christiano and Eichenbaum’s divisible-labour model with technology and government consumption shocks and compare three investment technologies: one-period completion; Kydland and Prescott’s four-period gestation with resource weights of 0.25 in each quarter (time to build); and the same four-period gestation reweighted to 0.01, 0.33, 0.33, 0.33 so that the first quarter consumes almost nothing (time to plan). The empirical basis is explicit – in Mayer’s (1960) data projects took 22 months on average with the first 7 months a preconstruction planning phase, and Krainer (1968) finds that in all 25 projects he studies less than 5 percent of total cost was incurred in the first three months, and in 18 of them less than 2.5 percent. The mechanism the planning phase supplies is a delay in the response of hours worked. In a standard model a positive technology shock makes households work harder to accumulate the investable resources needed to exploit the higher return on investment; with a planning phase there is little to do with those resources in the period of the shock, so hours worked actually falls a little, investment barely moves, and much of the extra output is simply consumed. That delay in hours translates into a delay in output, and produces three matches to U.S. quarterly data for 1947:1-1995:1. First, persistence: the first-order autocorrelation of U.S. GDP growth is 0.37 (standard error 0.07), the one-period and four-period even-weight models produce essentially zero even though the exogenous technology growth rate is serially uncorrelated, and the time-to-plan model produces 0.36. Second, the timing of productivity and hours: because hours are damped on impact while productivity jumps, productivity comes to lead hours worked, and the contemporaneous hours-productivity correlation falls from roughly 0.90 in the other two models to 0.28 – the U.S. figure being near zero with a significantly positive correlation between productivity and future hours. Third, investment now lags output, which is counterfactual for aggregate investment but matches the behaviour of business investment in structures and equipment, the components for which a planning period is most plausible. The authors are careful about what does not work: consumption leads the cycle and is far too volatile in the time-to-plan model, both counterfactual, and they attribute this to the level of aggregation rather than to the mechanism, conjecturing that a model separating business structures from residential investment and household durables would fix it. Adding government consumption shocks – which in their specification are temporary – cuts persistence rather than raising it, because with no investment margin available hours must rise sharply to absorb the shock; it also reduces the excess volatility of consumption, and contributes almost nothing to output volatility. They describe the work as “primarily as preliminary and, we hope, suggestive.”