The Return to Capital in Capital-Scarce Countries

That the Lucas paradox had been largely dissolved by the finding that marginal products of capital are not in fact higher in poor countries – and the paper accepts the logic of that dissolution while questioning its premise. “An emerging body of empirical work based on national income accounts suggests that the neoclassical predictions about capital scarcity and higher rates of return do not hold up in the macro data… If recent empirical studies are accurate then it is unsurprising that capital does not flow from rich to poor countries; with equalized marginal products, it has little incentive to do so” (§1, p. 2). But the paper observes that each of those results requires a specific adjustment – “(i) the capital per effective worker and a human capital externality (Lucas, 1990), (ii) non-reproducible capital and the price of capital goods (Caselli and Feyrer, 2007), or (iii) technology catch-up and distortions in saving and investment decisions (Gourinchas and Jeanne, 2013)” – and that aggregate data cannot test the first-order condition that all of this rests on.

That the financial return equals the marginal product of capital minus depreciation – a condition which, if it fails, breaks the inference from marginal products to where capital should go. “In a one-sector neoclassical model, a firm’s first-order condition states that the marginal product of capital and the financial return should differ only by the depreciation rate, which is often assumed constant across countries… Therefore, theory predicts that high financial returns and high marginal products of capital should go hand in hand. If this link breaks down (i.e., if a high marginal product of capital does not turn into high financial returns), it is not clear that capital ought to flow to countries with high marginal products of capital” (§1, p. 2). The derivation shows where the condition comes from: “the key determinant of the relationship between the period marginal product of capital and the investment return is the capital accumulation equation. Thus, if friction exists in the capital accumulation process, then the cross-country investment return and marginal product of capital patterns may diverge” (§2.1.1, p. 9).

Because aggregate capital stocks are themselves built by assuming the accumulation process the test is about – and because index returns and national-accounts marginal products come from different samples. “With aggregate data, estimates of the aggregate capital stock are constructed from aggregate investment data (such as from the Penn World Tables) using the perpetual inventory method, which requires one to posit a capital accumulation process. Since this process is typically assumed to follow a model where a unit increase in investment leads to a unit increase in capital stock, the aggregate capital stock estimate itself implicitly relies on the assumption that the link between marginal product of capital and the investment return holds” (§1, p. 5). Firm data let capital stocks be observed from accounting and market values instead. The second advantage is matching: “Alternative methods that compare investment returns estimates from the MSCI index with marginal product of capital estimates from aggregate macro data suffer from a sample mismatch problem as investment returns estimates use a subset of public firms and the marginal product of capital is estimated using both public and private firms. In this case, the gap between investment returns and the marginal product of capital may be due to capital accumulation frictions, or due to sample differences.” The paper’s own method “does not suffer from this mismatch problem as the investment return and the marginal product of capital estimates use the same sample of firms.”

Return on assets as the marginal product, and an internal rate of return on value as the financial return, both scaled by the prior year’s market value of assets. Return on assets is EBITDA adjusted for extraordinary items over the previous year’s market value of assets, where that market value is the book value of debt plus the market value of equity (§2.2, pp. 11-12). Interest is not deducted, following Fama and French (1999) rather than Gilchrist and Himmelberg (1995), because the capital definition here includes debt as well as the capital stock. Pre-tax earnings are used to minimise cross-country tax differences. The denominator uses market rather than book assets on two grounds: book assets are carried at acquisition cost, so they “may not correctly reflect current values,” and market values capture intangibles the accounts expense. That second point cuts in a specific direction worth noting – “in many R&D intensive industries, the book value of firm assets is often substantially lower than market values. The accounting treatment of R&D can potentially inflate the marginal product of capital in developed countries especially in R&D intensive industries” – so the choice works against the paper’s own finding. The internal rate of return adds to EBITDA the change in the market value of assets less the depreciation-adjusted change in book value, the latter standing in for gross investment at current prices; the paper explains why it uses the change in book value rather than capital expenditure (“capital expenditures only capture investments in fixed assets. As our definition of capital is not limited to fixed assets”), and both measures are inflation-adjusted. It also notes that market values of capital assets “implicitly adjust for differences in the relative price of capital goods across countries.”

Listed firms in MSCI developed and emerging countries, 1997-2014, giving 334,471 firm-years across 42 countries – with several limitations the paper states itself rather than leaving to the reader. The country restriction is defended on data grounds (many developing exchanges are new or tiny – Laos opened in 2011, Syria 2009, Somalia 2012; the Maldives exchange had five listed firms in 2008) and on relevance grounds: “as Reinhart and Rogoff (2004) suggest, roughly 25 emerging markets account for the bulk of international financial flows” (§1, p. 5; §3, pp. 14-15). The post-1996 window reflects unavailability of reliable emerging-market firm data before 1995. Firms are sorted into the 48 Fama-French industries, of which 44 remain after dropping financials, and Saudi Arabia is dropped for data availability; data are winsorized at 1 and 99 percent by country, with the paper noting that major outliers arise from mergers and that results are unchanged without winsorization. Sample sizes vary enormously, from 68,438 US firm-years and 52,501 Japanese to 365 for Colombia, and industry coverage varies too – all 44 industries appear in Canada, Japan, the UK and the US, but only 23 in Hungary. The conceded limits: “our conclusions about the Lucas paradox are restricted to the sample of public firms”; “available firm-level data do not provide insight into the productivity of self-employed workers or informal sector firms. This is a significant drawback as these types of households and firms make up a large part of the economy in developing countries”; firm market variables “are also susceptible to market volatility”; overseas subsidiaries of listed firms “could influence the outcome of analysis”; and “the capital flows in our sample are restricted to those received by the private sector and do not cover sovereign flows.” Against this the paper argues the restriction is partly the point: “it is precisely the firms in the formal economy that are the beneficiaries of foreign capital flows.”

By using Worldscope, which standardises reported figures, and then by re-running the analysis on IFRS adopters alone. Datastream “aims to ‘provide the data in a manner that allows maximum comparability between one company and another, and between various reporting regimes’,” with the consequence that “the numbers reported in the firm’s annual/quarterly audit reports could differ from the numbers provided by Worldscope, which adjusts the data to make the definitions more comparable to their U.S. counterparts” (§1, p. 6; §3, pp. 13-14). Since IFRS was adopted by EU countries by 2005 and a majority of MSCI developed and emerging countries by 2011, while the US has not adopted it, restricting to IFRS adopters is a direct test, and “we find that the main results remain robust.” A further check runs the analysis within industries unlikely to contain multinationals, such as utilities, again leaving “the main findings… intact.”

Return on assets of 9.2 percent and internal rate of return of 8.3 percent on average, with emerging markets showing higher return on assets and lower internal rates of return than developed markets. “While this pattern is consistent with the benchmark model, two notable patterns emerge from the data. First, emerging market countries have a higher ROA, but lower IRR compared with developed countries. This pattern holds for both average and median values and suggests that a potential explanation for the Lucas Paradox may lie in the gap between investment return and marginal product of capital” (§3.1, pp. 16-17). The second pattern is a caution about using means: among developed countries the average internal rate of return exceeds the average return on assets, contrary to the benchmark, “likely due to the right skewness in the distribution of investment returns” – and indeed “even for developed countries, the median ROA is higher than the median IRR.” This skewness is why the paper leans on quantile regressions. In the two-way plots, return on assets slopes steeply down against log GDP per capita with a narrow confidence interval, while the internal rate of return slopes up with a wide one – a positive mean trend which “contradicts the predictions of the neoclassical model” but “is consistent with the uphill international capital flows pattern documented in Prasad et al. (2007).”

Return on assets or internal rate of return on log GDP per capita, with time and industry dummies and firm controls, standard errors clustered at the country-year level – and no country fixed effects in the benchmark. The firm controls are size (log book assets in dollars, CPI-adjusted), leverage (book debt to assets) and the equity price-to-book ratio, “from Fama and French (1992) to proxy for alternative firm-level risks” (§4.1, pp. 17-18). Errors are clustered by country-year “rather than country due to the limited number of country clusters.” The omission is explained and then checked: “We do not include country fixed effects in the benchmark regression due to the relatively limited time dimension of the dataset (less than 20 years). The Appendix presents regression results with country clusters and with country fixed effects. The main findings remain robust.” GDP per capita is used as the labour-productivity proxy following Banerjee and Duflo (2005) and Gourinchas and Jeanne (2013), with the paper noting the alternatives’ own problems – output per worker misses home production and is complicated by cross-country differences in employment definitions – and checking both alternatives anyway.

Yes, robustly: the coefficient on GDP per capita is negative and significant at 1 percent, and the result holds across quantiles, industries, years, periods and accounting regimes. In the quantile regressions the coefficient is significant at the 25th, 50th and 75th percentiles, “most negative for firms in the 75th percentile of ROA, and there is little difference in the coefficients between the 25th and the 50th percentiles,” which the paper reads as meaning “the effect of the changes in the aggregate output per unit labor is most acutely apparent for the most productive firms in the economy” (§4.1, pp. 18-19). Across industries, 40 of the 44 non-financial Fama-French industries show statistically significant negative coefficients at 5 percent, “and only one industry (aircraft manufacturing) has a statistically significant positive coefficient,” with the most negative coefficients in defence and medical/pharmaceutical industries, “both of which require high levels of human and physical capital” (§4.1, pp. 19-20). Year by year, “yearly point estimates and confidence intervals (whiskers) all lie below zero between 1997 and 2014,” with the slope steepest during the 2007-2010 crisis and the early-2000s recession, flattening in recoveries, and relatively flat during the 1997 Asian crisis. The post-crisis 2011-2014 window, the IFRS subsample and the MSCI EU 2006-2014 subsample all confirm it, with Greece excluded from the post-crisis and EU samples “because of the Greek government-debt crisis that severely affected its stock market and firm performance between 2011 and 2013.”

No – and this null is the paper’s central result. “Despite the statistically significant negative relationship with marginal product of capital observed in the previous subsection, the coefficient on per capita GDP is not statistically significant when controlling for firm- and industry-specific factors. This result implies that the cross-country marginal product of capital and investment return patterns do not necessarily mirror each other – as the neoclassical model predicts. The finding also suggests that even accurate measures of marginal products of capital may not explain patterns of international capital flows, as the marginal product of capital may itself be an inaccurate proxy for investment returns” (§4.2, pp. 20-21). The inferential consequence for the Lucas paradox is stated directly: “if investment returns are inversely correlated with per capita GDP, capital ought to flow from developed to emerging countries and any deficiencies in these flows imply international financial market frictions. However, the results… suggest that the investment returns are roughly equal across developed and emerging countries. Therefore, an incentive may not exist for capital to flow to emerging markets, since opportunities that deliver similar investment returns also exist within developed economies.”

Essentially yes, which is what makes the contrast informative rather than a power problem. In quantile regressions the coefficient is “positive and statistically significant at the 5% level for the bottom 25th percentile and statistically insignificant for firms in the 50th and 75th percentile,” which the paper reads as “even the best-performing firms within emerging countries cannot successfully translate their higher marginal products of capital to higher investment returns. A potential resolution to the Lucas paradox may therefore lie in macroeconomic factors that affect all firms within emerging economies” (§4.2, p. 21). Industry by industry, the coefficient is insignificant in 42 of 44 industries, with only defence significantly negative – “this pattern for cross-industry firm-level IRR estimates contrasts sharply with Figure 3(a), in which 40 industries have a statistically significant negative coefficient.” Year by year, the coefficient is “statistically insignificant or positive and significant for 10 years,” negative and significant for eight, of which four cluster around the crisis (2006-2008 and 2010), with the steepest negative slopes in 2006 and 2007. The post-crisis, IFRS and EU subsamples all return insignificant coefficients.

Alternative productivity measures, tax adjustment, industry composition, and an explicit comparison with a contrary finding in the literature. Replacing GDP per capita with output per worker leaves the return-on-assets coefficient negative and significant and the internal-rate-of-return coefficient insignificant, in both the main sample and the post-crisis IFRS subsample (§4.3.1, p. 23). Output per hour worked, reported in the appendix, gives the same split and a steeper negative slope for return on assets, with China dropped for lack of hours data and some interpolation required. Adjusting income by a three-year average income tax rate – three-year rather than annual “to smooth large variations,” with firm-years above 100 percent excluded – cuts the sample to 122,465 firm-years across 42 countries and again leaves return on assets negatively and significantly related to income and the internal rate of return insignificant (§4.3.2, p. 24). The paper also notes that corporate tax rates “tend to be lower in emerging markets relative to developed countries, which suggests that tax rate differences are an unlikely friction in the international flow of capital.” On composition, repeating the analysis by industry shows “the investment returns wedge is remarkably consistent across industries, with a few exceptions only, and suggests that cross-country differences in industry portfolios are not the main driver behind the observed patterns” (§1, fn. 4). And the paper confronts David, Henriksen and Simonovska (2016), who find emerging-market MSCI indices outperform: the difference is attributed to sample and method – more countries but a shorter period here, developed markets having “substantially outperformed emerging market countries in the recent decade,” and, most importantly, “our measure computes the total asset return, which tends to be lower and less volatile relative to equity returns” (§3, fn. 7).

A capital accumulation friction: if a unit of investment does not deliver a unit of installed capital, the marginal product of capital and the financial return no longer differ by depreciation alone. Via Cochrane’s (1991) decomposition, the return can be written in terms of the price of installed capital measured in current output; “with a standard capital accumulation equation, [that price] = 1 for all t, which suggests that buying a unit of period t installed capital costs a unit of period t − 1 consumption good; therefore cross-country differences in the price of installed capital are perfectly correlated with cross-country differences in the price of output. However, if friction exists in the capital accumulation process, the relative price of capital can diverge from a unity” (§5.1, pp. 25-26). This is the paper’s unification claim: a relative-price wedge of the Caselli-Feyrer kind can arise “even in a one-sector case,” where their correction had no role, and “with adjustment costs, [the marginal contribution of capital] is no longer constant… This divergence between the marginal product of capital and the investment return is consistent with the capital wedge in Gourinchas and Jeanne (2013)” – so “using a capital accumulation friction, we explicitly depict how a within-country capital market friction can generate the capital wedge.” The paper adds a supporting observation about the data those literatures use: the International Comparison Program prices behind the Penn World Tables explicitly include “import duties and other product taxes actually paid by the purchaser, the costs of transporting the asset to the place where it will be used, and any charges for installing the asset,” and “the transportation/installation costs are some of the most commonly cited sources of the capital accumulation friction.”

A quadratic adjustment term – investment squared over the capital stock – with no sign restriction, because a unit of investment could plausibly yield either less or more than a unit of capital. The term is quadratic to capture “the nonlinear costs incurred in the installation process” and inversely proportional to existing capital because “firms are less affected by the reallocation of resources when they have a large capital base” (§5.2, pp. 27-28). Quadratic costs follow Chirinko (1993), Gilchrist and Himmelberg (1995) and Jin (2010); Cochrane (1991) uses cubic, and “the results, however remain robust even with a cubic adjustment cost.” On the sign: “the investment theory literature assumes that [the coefficient] is negative, as it is the cost incurred in the installation process. However, extensive research in the finance literature studies potential synergies in corporate mergers… Therefore, we are agnostic about placing restrictions on the sign.” Negative means a friction, positive a synergy. The resulting expression makes the adjustment term bear on returns twice, “indirectly through the marginal product of capital price adjustment; and… directly as an investment wedge.”

That the squared investment-to-capital ratio is significantly related to the growth of capital at market prices, so the linear accumulation process is rejected – with the sign of the friction depending on the specification. The test regresses the growth rate of the market value of assets on the depreciation-adjusted change in book value over lagged market assets and its square, plus industry and time fixed effects and firm controls. “Column (1) of Table 5 shows that [the squared term] is positive and statistically significant between 1997 and 2014. This finding suggests that the aggregate capital estimates, which rely on a linear capital accumulation process, require modification,” and this survives restricting to IFRS countries and replacing the investment measure with capital expenditure over lagged market assets – a substitution motivated by the fact that in-house R&D is expensed while purchased patents are capitalised, so the capex measure “is shielded from the differential treatment of the intangible assets” (§5.3, pp. 28-29). The heterogeneity test is where the sign changes: interacting the squared term with log GDP per capita, “[the squared term] is negative and statistically significant, suggesting a friction in a capital accumulation process. However, the interaction… is positive and statistically significant during the sample period,” which the paper reads as “while most emerging market countries may suffer from capital accumulation friction, the effect slowly dissipates as the economy develops.” The interaction result is not significant in the post-crisis IFRS subsample, which the paper attributes to “the limited number of observations and a high correlation between” the squared term and the interaction. Readers should note the paper does not itself reconcile the positive sign in the pooled specification with the negative sign in the interacted one. One further piece of reasoning is worth carrying: the paper argues the missing-R&D problem cannot generate this result, because “omitted R&D investment may affect the level of [the investment ratio], but it should not affect the curvature of the capital accumulation process.”

That the explanation for missing capital flows may be domestic rather than international, stated as a suggestion rather than a demonstration. “We suggest that the marginal product of capital patterns do not mirror investment return patterns because of cross-country differences in capital accumulation efficiency. Sufficiently large capital adjustment costs can decouple the cross-country financial returns pattern from the marginal product of capital. This finding also suggests that a key explanation for the pattern of international capital flows may indeed be domestic rather than international frictions that affect the capital accumulation process. Thus, what matters is not only factors that affect productive efficiency but also those that affect capital accumulation efficiency” (§6, p. 30). The paper’s own read of its relation to the prior literature is that it confirms rather than overturns one part of it: “the results confirm the view that there is no prima facie evidence that international credit frictions play a major role in preventing capital flows from rich to poor countries (Caselli and Feyrer, 2007)” – but by a different route, since here the marginal products do differ and it is the returns that are equalised. The stated next step is to extend beyond listed firms: “future research using data that encompasses unlisted firms and self-employed workers may help increase our understanding of domestic capital market frictions.”