Misallocation and Manufacturing TFP in China and India

Misallocation across firms rather than inefficiency within the representative firm. The paper opens by noting that research on the causes of TFP differences “has largely focused on differences in technology within representative firms,” citing models of slow technology diffusion, and that “these are models of within-firm inefficiency, with the inefficiency varying across countries” (§I, pp. 1403-1404). The alternative it takes from Restuccia and Rogerson (2008) is illustrated with a two-firm example: identical technologies, but one firm has political connections and gets subsidised credit from a state-owned bank while the other can borrow only at high rates informally. “Assuming that both firms equate the marginal product of capital with the interest rate, the marginal product of capital of the firm with access to subsidized credit will be lower… This is a clear case of capital misallocation: aggregate output would be higher if capital was reallocated from the firm with a low marginal product to the firm with a high marginal product.” Real-world analogues are cited from the McKinsey Global Institute, including Brazilian labour regulation that raises supermarkets’ labour costs relative to informal retailers’ and so lets low-productivity informal retailers hold a large share of the sector.

A monopolistic-competition model with heterogeneous firms – Melitz (2003) without international trade – whose key result is that revenue productivity should be equalised across plants within an industry in the absence of distortions. A representative competitive firm combines S industry outputs Cobb-Douglas; each industry output is a CES aggregate of differentiated products; each product is produced Cobb-Douglas in plant TFP, capital and labour, with capital and labour shares allowed to differ across industries but not across plants within an industry (§II, pp. 1406-1407). Because there are two factors, the paper can separate distortions that raise both marginal products proportionally – an output distortion – from those that raise the marginal product of capital relative to labour, a capital distortion. Profit maximisation gives the familiar markup pricing and yields marginal revenue products proportional to revenue per worker and to the revenue-capital ratio respectively: “the after-tax marginal revenue products of capital and labor are equalized across firms. The before-tax marginal revenue products must be higher in firms that face disincentives, and can be lower in firms that benefit from subsidies” (§II, p. 1408). The paper also notes the model is “a cousin to the Lucas (1978) span-of-control model” in its size distribution, and Appendix I shows the two formulations are isomorphic for aggregate TFP, with the chosen elasticity of substitution of 3 corresponding to returns to scale of 0.5 – “quite low, even compared to studies such as Atkeson and Kehoe (2005), who chose [returns to scale of at least 0.8].”

Because plant-specific deflators are generally unavailable, so plant prices show up inside measured productivity – and it is precisely that price component that reveals the wedge. Following Foster, Haltiwanger and Syverson (2008), TFPQ is what a plant-specific deflator gives and TFPR is what an industry deflator gives (§II, pp. 1409-1410). “In our simple model, TFPR does not vary across plants within an industry unless plants face capital and/or output distortions. In the absence of distortions, more capital and labor should be allocated to plants with higher TFPQ to the point where their higher output results in a lower price and the exact same TFPR as at smaller plants.” TFPR is proportional to a geometric average of the plant’s marginal revenue products of capital and labour, and hence to the capital wedge raised to the capital share divided by one minus the output wedge, so “high plant TFPR is a sign that the plant confronts barriers that raise the plant’s marginal products of capital and labor, rendering the plant smaller than optimal.” One measurement note matters for interpretation: labour input is measured as the wage bill “to crudely control for differences in human capital,” i.e. as a common wage per unit of human capital times effective labour.

Under joint lognormality of physical and revenue productivity, aggregate industry TFP equals a productivity index minus the elasticity of substitution over two, times the variance of log TFPR. “In this special case, the negative effect of distortions on aggregate TFP can be summarized by the variance of log TFPR. Intuitively, the extent of misallocation is worse when there is greater dispersion of marginal products” (§II, p. 1411). Three modelling properties are then flagged. First, with Cobb-Douglas aggregation across sectors, each sector’s share of aggregate labour and capital is unaffected by misallocation as long as average marginal revenue products are unchanged – unit-elastic demand means “an industry that is 1% more efficient has a 1% lower price index and 1% higher demand, which can be accommodated without adding or shedding inputs” – and this assumption is relaxed later. Second, the baseline conditions on a fixed aggregate capital stock; endogenising capital through a consumption Euler equation makes the output elasticity with respect to TFP equal to one over one minus the average capital share, “reminiscent of a one-sector neoclassical growth model.” Third, the number of firms is assumed unaffected by misallocation, which the paper shows holds in a model of endogenous entry with entry costs in labour, while noting it lacks Melitz’s overhead costs and therefore lacks endogenous exit: “We leave it as an important topic for future research to investigate the impact of distortions on aggregate productivity and welfare through endogenous entry and exit.”

India’s ASI for 1987-88 to 1994-95, China’s Annual Surveys of Industrial Production for 1998-2005, and the US Census of Manufactures for five years from 1977 to 1997 – and the Chinese sampling frame excludes small private firms, which affects what can be compared. The ASI is a census of registered plants with more than fifty workers (one hundred without power) plus a random one-third sample of registered plants between ten (twenty without power) and fifty (or one hundred) workers, with sampling weights applied; the raw data are about 40,000 plants a year (§III, pp. 1412-1413). The Chinese survey is a census of all nonstate firms with more than 5 million yuan of revenue (about $600,000) plus all state-owned firms, running from over 100,000 firms in 1998 to over 200,000 in 2005. The US Census covers all manufacturing plants, leaving over 160,000 a year after dropping small Administrative Records plants. Two data repairs are notable. The Chinese data report only wage payments, and the median plant labour share of about 30 percent is far below the roughly 50 percent aggregate manufacturing labour share in Chinese input-output tables and national accounts, so nonwage benefits are imputed as a constant fraction of wages chosen so that the total equals 50 percent of aggregate value added. US plant age is imputed from first appearance in the data, since the US census does not report it. The paper also flags that its Chinese ownership data “may understate the extent of privatization,” citing a 2005 survey finding 15 percent of firms officially classified as state-owned had in fact been privatised.

The rental rate at 0.10, the elasticity of substitution at 3, and industry capital elasticities from US labour shares scaled up by 3/2. The rental rate reflects “a 5% real interest rate and a 5% depreciation rate,” and the paper notes the efficiency gains do not depend on it because “our hypothetical reforms collapse [the capital distortion] to its average in each industry,” so a wrong rental rate “affects only the average capital distortion, not the liberalization experiment” (§IV, p. 1414). The elasticity of substitution is set to 3 deliberately low: “The gains from liberalization are increasing in [the elasticity]… and so we made this choice conservatively,” against trade and IO estimates that “typically range from three to ten,” with the honest concession that the elasticity surely differs across goods so “our single [elasticity] is a strong simplifying assumption.” Industry capital elasticities come from one minus the US industry labour share in the NBER Productivity Database, not from Indian or Chinese labour shares, “precisely because we think distortions are potentially important in China and India” and because “we cannot separately identify the average capital distortion and the capital production elasticity in each industry”; because the Census/ASM labour share is about two-thirds of the NIPA share, each industry’s share is scaled up by 3/2. Finally, because a modest elasticity of 3 implies large markup rents, those rents are assumed to accrue pro rata to labour and capital, so “our assumed value of [the elasticity] has no impact on our production elasticities.”

From residuals in the plants’ own first-order conditions, following Chari, Kehoe and McGrattan (2007) – with one assumption that should be stated plainly. A capital distortion is inferred “when the ratio of labor compensation to the capital stock is high relative to what one would expect from the output elasticities with respect to capital and labor,” and an output distortion is inferred “when labor’s share is low compared with what one would think from the industry elasticity of output with respect to labor” (§IV, p. 1415). The assumption: “A critical assumption embedded in (18) is that observed value-added does not include any explicit output subsidies or taxes.” Physical productivity is recovered from nominal revenue by raising it to the power of the elasticity over the elasticity minus one, because “plants with high real output… must have a lower price to explain why buyers would demand the higher output,” so “we infer price vs. quantity from revenue and an assumed elasticity of demand.” The paper stresses how little this step needs: the productivity equation “requires only our assumptions about technology and demand plus profit maximization; we need not assume anything about how inputs are determined.” Before computing gains the 1 percent tails of relative TFPR and relative TFPQ are trimmed, which removes up to 6 percent of observations in total because the output and capital distortions are trimmed separately.

Substantially, in both physical and revenue productivity, though the physical-productivity comparison is contaminated for China by its sampling frame. For physical productivity, the 75th-to-25th-percentile ratio in the latest year is 5.0 in India, 3.6 in China and 3.2 in the United States, with standard deviations of log TFPQ of 1.23 (India 1994), 0.95 (China 2005) and 0.84 (US 1997) (§IV, Table I, pp. 1416-1418). The paper is careful: “There is manifestly more TFPQ dispersion in India than in China, but this could reflect the different sampling frames (small private plants are underrepresented in the Chinese survey). The U.S. and Indian samples are more comparable,” and India’s much thicker left tail is “consistent with policies favoring the survival of inefficient plants in India relative to the United States.” It also confronts a discrepancy with earlier work head-on: its US TFPQ standard deviation of about 0.80 far exceeds the roughly 0.22 reported by Foster, Haltiwanger and Syverson, explained by its own measure reflecting “the quality and variety of a plant’s products, not just its physical productivity” and by that paper analysing a dozen industries “specifically chosen because their products are homogeneous.” For revenue productivity, the 75/25 ratios are 2.2 (India), 2.3 (China) and 1.7 (US), and the 90/10 ratios 5.0, 4.9 and 3.3 – “consistent with greater distortions in China and India than the United States” (§IV, Table II).

Barely: dummies for ownership, age, size and region together explain under 5 percent of within-industry TFPR variance in India and about 10 percent in China. The cumulative shares are 0.58 percent for ownership alone in India against 5.25 percent in China, rising to 4.71 and 10.01 percent once age, size and region are added (§IV, Table III, pp. 1419-1420). The paper also pauses over an interpretation its framework does not accommodate: government-guaranteed monopoly power would show up as higher TFPR and possibly higher TFPQ, so “whereas we frame high TFPR plants as being held back by policy distortions, such plants may in fact be happily restricting their output.” Its response is not to dismiss this but to note the welfare implication is the same: “Still, such variation in TFPR is socially inefficient, and aggregate TFP would be higher if such plants expanded their output.”

86-115 percent in China and 100-128 percent in India – but also 31-43 percent in the United States, which is why the paper benchmarks against the US instead. Fully equalising TFPR within industries would raise manufacturing TFP by 115.1 percent in China in 1998, 95.8 in 2001 and 86.6 in 2005; 100.4 percent in India in 1987, 102.1 in 1991 and 127.5 in 1994; and 36.1, 30.7 and 42.9 percent in the United States in 1977, 1987 and 1997 (§IV, Table IV, pp. 1420-1421). The paper’s caveat is unusually blunt: “We freely admit this exercise heroically makes no allowance for measurement error or model misspecification. Such errors could lead us to overstate room for efficiency gains from better allocation.” The US benchmark exists precisely because of this: it matters “because there may be measurement error and factors omitted from the model (such as adjustment costs and markup variation) that generate gaps in marginal products even in a comparatively undistorted country such as the United States” (§I, p. 1405). Relative to the US in 1997 – chosen as “a conservative point of comparison because U.S. gains are largest in 1997” – the gains are 50.5, 37.0 and 30.5 percent for China and 40.2, 41.4 and 59.2 percent for India (§IV, Table VI, pp. 1423-1424). And the paper draws the obvious defensive inference: “If measurement and modeling errors are to explain these results, they clearly have to be much bigger in China and India than the United States.”

Chinese allocative efficiency improved about 2 percent a year from 1998 to 2005; India’s deteriorated about 1.8 percent a year from 1987 to 1994. “Compared to the 1997 U.S. benchmark, Chinese allocative efficiency improved 15% (1.5/1.3) from 1998 to 2005, or 2.0% per year,” while for India “we find no evidence of improving allocations… The implied decline in allocative efficiency of 12%, or 1.8% per year from 1987 to 1994, is surprising given that many Indian reforms began in the late 1980s” (§IV, p. 1424). The paper benchmarks these against measured TFP growth using Bosworth and Collins (2007), who report Chinese industry TFP growth of 6.2 percent a year over 1993-2004 and Indian industry TFP growth of 0.3 percent a year over 1978-1993: “our point estimate for China (2% per year) would suggest that perhaps one-third of its TFP growth could be attributed to better allocation of resources. For India, our evidence for worsening allocations might help to explain its minimal TFP growth.” It also checks that the Indian time variation is not a sampling artefact: restricting to larger census plants gives gains of 89-123 percent rather than 100-128 (§IV, fn. 16).

Roughly 49 percent of the US-China gap and 35 percent of the US-India gap, on the paper’s own crude estimate of those gaps. US manufacturing TFP in 1997 is estimated as 130 percent above China’s in 1998 and 160 percent above India’s in 1994, giving shares of log(1.5)/log(2.3) and log(1.4)/log(2.6) respectively (§IV, p. 1424). The word “crudely” is the paper’s, and the footnote details why: Indian prices are deflated to US prices using the 1985 Penn World Table tradable-goods price, Chinese prices are converted using the Indian tradable-goods price for want of Chinese manufacturing deflators, and manufacturing capital-output ratios and human capital are assumed equal to their economy-wide counterparts, with human capital built from average years of schooling assuming a 10 percent Mincerian return (§IV, fn. 17).

Roughly squared, because average capital shares are about half in both countries. “In India’s case the average capital share was 50% in 1994-1995, and so the TFP gains are roughly squared. The same goes for China, because its average capital share was 49% in 2005. Thus a 30% TFP gain in China could yield a 67% long-run gain in manufacturing output, whereas a 59% TFP gain in India could ultimately boost its manufacturing output by 153%” (§IV, p. 1424). This is the long-run response that holds the rental price of capital constant, not a claim about the transition.

More dispersed than the actual one, with fewer mid-sized plants and more small and large plants – and in China and India most plants of every initial size quartile would shrink, including state-favoured large ones. Tabulating plants by initial value-added quartile against the ratio of efficient to actual output, “in China and India the most populous column is 0%-50% for every initial size quartile. Although average output rises substantially, many plants of all sizes would shrink. Thus many state-favored behemoths in China and India would be downsized” (§IV, Table V, pp. 1421-1423). The systematic pattern is nonetheless the expected one: “initially large plants are less likely to shrink and more likely to expand in both China and India (a pattern much less pronounced in the United States). Thus TFPR increases with size more strongly in China and India than in the United States.” The paper links the Indian version of this to prior work: “The positive size-TFPR relation in India is consistent with Banerjee and Duflo’s (2005) contention that Indian policies constrain its most efficient producers and coddle its least efficient ones.”

Highly sensitive to the elasticity of substitution within industries; robust to capital valuation, labour measurement, and the elasticity across sectors. Adjusting book capital to current market values using country capital deflators and imputed capital age changes almost nothing (China 29.8 against 30.5 percent baseline; India 59.9 against 59.2) (§IV, p. 1425). Measuring labour as employment rather than the wage bill lowers the gains (China 25.6 against 30.5; India 57.4 against 59.2), which the paper reads as meaning “wage differences appear to amplify TFPR differences rather than limit them” – the opposite of the rent-sharing concern that motivated the check. The elasticity is the fragile parameter: “China’s hypothetical TFP gain in 2005 soars from 87% under [an elasticity of] 3 to 184% with [5], and India’s in 1994 from 128% to 230%,” with the intuition that at higher elasticities “TFPR gaps are closed more slowly in response to reallocation of inputs from low- to high-TFPR plants, enabling bigger gains.” Replacing Cobb-Douglas across sectors with CES matters much less: with sectors as complements the gains fall modestly in China (82 against 87 percent) and appreciably in India (108 against 128), because sectors with larger productivity gains shed inputs; with sectors more substitutable the gains rise (90 and 142 percent).

The paper runs seven distinct checks and concludes they are “inconclusive” – neither establishing nor ruling out the explanation. Trimming 2 percent rather than 1 percent tails (up to 12 percent of observations) cuts the full-equalisation gains from 87 to 69 percent for China in 2005 and from 128 to 106 percent for India in 1994, so “measurement error in the remaining 1% tails could well be important, but does not come close to accounting for the big gains” (§V, p. 1426). Under classical error TFPR should be unrelated to ownership, and it is strongly related: in China state-owned plants have 41 percent lower TFPR “as if they received subsidies to continue operating despite low profitability,” collectives 11 percent higher, and foreign-owned plants 23 percent higher TFPQ but 13 percent lower TFPR, possibly reflecting credit access or export-processing-zone treatment; Chinese exporters have 46 percent higher TFPQ and 14 percent lower TFPR, whereas US exporters have a similar TFPQ advantage but higher TFPR (§V, Table VII, pp. 1426-1427). In India all forms of public involvement carry lower TFPR (29 percent for central-government plants, 8 for local, 16 for joint) and 40-70 percent higher TFPQ, “although this might reflect monopoly rights that guarantee demand.” Lower TFPR predicts exit in all three countries (coefficients -0.011 China, -0.019 India, -0.011 US), which argues TFPR is a real profitability signal rather than noise. Two-way regressions of revenue on inputs and inputs on revenue give “mixed evidence”: classical error might add 5 percent to the variance of log revenue in India and 3 percent in China, but appears to lower the variance of log inputs in India by 10 percent relative to the US. Growth-rate dispersion is also mixed – input growth varies much less in China and India than in the US, revenue growth much more. And instrumenting with lagged variables cuts the gains proportionally more in the US (43 to 26 percent) than in China (87 to 72) or India (127 to 108), so “by this metric, measurement error accounts for a bigger fraction of the gains in the United States than in China or India.” The summary is honest: “the statistics in this subsection are inconclusive. They do not provide clear evidence that the signal-to-noise ratio for TFPR is higher in the United States than in China and India, but neither do they entirely rule out the possibility. In addition, we cannot rule out nonclassical measurement error.”

Partially: state ownership in China and the interaction of delicensing with size restrictions in India – and the paper calls this “a first pass.” In China the share of plants that are private domestic rises from 15.9 percent in 1998 to 62.5 percent in 2005 while state ownership falls from 29.0 to 8.1 percent and collective from 35.1 to 7.5 percent (§VI, Table XI, p. 1431). Sector TFPR dispersion rises with the state-ownership share, and equalising TFPR only within ownership categories lowers the measured gains by 8.2 percent in 1998 and 2.4 percent in 2005, so “of the 15% reduction in potential gains from reallocation in China from 1998 to 2005, we calculate that 39% (5.8/15.0) comes from the shrinking TFPR gap between SOEs and other plants” (§VI, p. 1433). For India, roughly 40 percent of industries by value-added were delicensed in 1985 and 42 percent in 1991, while size restrictions were lifted only over 1997-2005, “which unfortunately we are unable to analyze because our data end in 1994-1995”; across industries the mean share of value added subject to size restrictions was 21 percent with a standard deviation of 16 (§VI, pp. 1433-1434). The findings are layered: industries delicensed in 1991 show lower TFPR dispersion but not specifically after 1991 – “It is as if licensed industries had lower TFPR dispersion despite their licensing restrictions, and the delicensing did not affect this” – while size-restricted industries show higher dispersion, and the triple interaction shows that “industries delicensed in 1991 who face size restrictions do indeed display more TFPR dispersion from 1991 onward.” A complementary result: among industries delicensed in 1991, the relationship between TFPR and TFPQ growth flattens after delicensing, with the 90th-versus-10th-percentile TFPR gap falling from 1.2 to 0.6 log points. Several candidate policy correlates come up empty: “We find little evidence that TFPR dispersion is correlated with measures of geography, industry concentration, and (in India) labor-market regulation,” with average TFPR levels differing within 10 percent across Chinese provinces and Indian states, no relationship to an industry Herfindahl index, and no significant relationship to a value-added-weighted Besley-Burgess labour-regulation index.

Four are examined – varying markups, adjustment costs, unobserved investments and plant-specific capital shares – and in each case the cross-country pattern points the wrong way for the alternative. On markups, under linear demand markups rise with size, which would inflate TFPR dispersion where size dispersion is wider; but “whereas TFPR is strongly increasing in percentiles of plant size (value added) in India and mostly increasing in plant size in China, if anything TFPR decreases with plant size in the United States. If linear demand applied everywhere, then TFPR should increase with size in the United States, too. The fact that China and India differ not only quantitatively but qualitatively from the United States suggests more than just amplification of usual U.S. forces” (§VII.A, p. 1436). On adjustment costs, “TFPR steadily increases with plant age in India, contrary to this story,” while “only the United States exhibits the predicted pattern of steadily falling TFPR with age”; input growth varies more across US plants than Chinese or Indian ones, so “the United States displays more churning, and so, if anything, should have more TFPR variation because of convex adjustment costs.” Replicating Cooper and Haltiwanger’s estimation of idiosyncratic profitability shocks yields similar parameters across countries (US serial correlation 0.81 and innovation standard deviation 0.56; China 0.79 and 0.59; India 0.84 and 0.57), with overall shock standard deviations only 1 percent higher for China and 10 percent higher for India against TFPR standard deviations over 50 percent higher – so “plants in China and India face greater barriers to reallocation as opposed to bigger shocks with the same costs of reallocation” (§VII.B, pp. 1436-1439). Median plant age is 5 years in China, 12 in India and 10 in the US; median size 160, 33 and 47 employees; equalising TFPR only within size and age quartiles lowers the gains only about 5 percent in each country. On unobserved investments such as R&D or customer-base building, low TFPR should predict high subsequent TFPQ growth, and that is exactly what the US shows “but the opposite pattern in China and India” (§VII.C, pp. 1440-1441). Finally, attributing all within-industry variation in capital-labour ratios to plant-specific capital shares rather than distortions still leaves gains of 23-45 percent for China and 32-39 percent for India against the 30-50 and 40-60 percent baselines, with the majority then coming from output rather than capital distortions (§VII.D, pp. 1441-1442).

It names four limitations in its own conclusion and describes the whole exercise as a first pass. “There could well be greater measurement error in the Chinese and Indian data than in the U.S. data. The static monopolistic competition model we deploy could be a poor approximation of all three countries. Although we provided reassuring evidence on these concerns, our investigation was very much a first pass.” The two forward-looking items are that “future work could try to relate differences in plant productivity to observable policy distortions much more than we have,” and that “we neglected the potential impact of distortions on plant entry and exit, an important topic for future research” (§VIII, p. 1443). None of the paper’s magnitudes should be read as estimates of the effect of any actual policy; they are the output of a counterfactual reallocation within a specified model.