We build up from the plant level an "aggregate(d) Solow residual" by estimating every U.S. manufacturing plant's contribution to the change in aggregate final demand between 1976 and 1996. We decompose these contributions into plant-level resource reallocations and plant-level technical efficiency changes. We allow for 459 different production technologies, one for each 4- digit SIC code. Our framework uses the Petrin and Levinsohn (2008) definition of aggregate productivity growth, which aggregates plant-level changes to changes in aggregate final demand in the presence of imperfect competition and other distortions and frictions. On average, we find that aggregate reallocation made a larger contribution than aggregate technical efficiency growth. Our estimates of the contribution of reallocation range from 1:7% to2:1% per year, while our estimates of the average contribution of aggregate technical efficiency growth range from 0:2% to 0:6% per year. In terms of cyclicality, the aggregate technical efficiency component has a standard deviation that is roughly 50% to 100% larger than that of aggregate total reallocation, pointing to an important role for technical efficiency in macroeconomic fluctuations. Aggregate reallocation is negative in only 3 of the 20 years of our sample, suggesting that the movement of inputs to more highly valued activities on average plays a stabilizing role in manufacturing growth.
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Are We Undercounting Reallocation's Contribution to Growth?
January 2013
Working Paper Number:
CES-13-55R
There has been a strong surge in aggregate productivity growth in India since 1990, following
significant economic reforms. Three recent studies have used two distinct methodologies to decompose the sources of growth, and all conclude that it has been driven by within-plant increases in technical efficiency and not between-plant reallocation of inputs. Given the nature of the reforms, where many barriers to input reallocation were removed, this finding has surprised researchers and been dubbed 'India's Mysterious Manufacturing Miracle.' In this paper, we show that the methodologies used may artificially understate the extent of reallocation. One approach, using growth in value added, counts all reallocation growth arising from the movement of intermediate inputs as technical efficiency growth. The second approach, using the Olley-Pakes decomposition, uses estimates of plant-level total factor productivity (TFP) as a proxy for the marginal product of inputs. However, in equilibrium, TFP and the marginal product of inputs are unrelated. Using microdata on manufacturing from five countries ' India, the U.S., Chile, Colombia, and Slovenia ' we show that both approaches significantly understate the true
role of reallocation in economic growth. In particular, reallocation of materials is responsible for over half of aggregate Indian manufacturing productivity growth since 2000, substantially larger than either the contribution of primary inputs or the change in the covariance of productivity and size.
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Macro and Micro Dynamics of Productivity: From Devilish Details to Insights
January 2017
Working Paper Number:
CES-17-41R
Researchers use a variety of methods to estimate total factor productivity (TFP) at the firm level and, while these may seem broadly equivalent, how the resulting measures relate to the TFP concept in theoretical models depends on the assumptions about the environment in which firms operate. Interpreting these measures and drawing insights based upon their characteristics thus must take into account these conceptual differences. Absent data on prices and quantities, most methods yield 'revenue productivity' measures. We focus on two broad classes of revenue productivity measures in our examination of the relationship between measured and conceptual TFP (TFPQ). The first measure has been increasingly used as a measure of idiosyncratic distortions and to assess the degree of misallocation. The second measure is, under standard assumptions, a function of funda-
mentals (e.g., TFPQ). Using plant-level U.S. manufacturing data, we find these alternative
measures are (i) highly correlated; (ii) exhibit similar dispersion; and (iii) have similar relationships with growth and survival. These findings raise questions about interpreting the first measure as a measure of idiosyncratic distortions. We also explore the sensitivity of estimates of the contribution of reallocation to aggregate productivity growth to these alternative approaches. We use recently developed structural decompositions of aggregate productivity growth that depend critically on estimates of output versus revenue elasticities. We find alternative approaches all yield a significant contribution of reallocation to
productivity growth (although the quantitative contribution varies across approaches).
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Declining Dynamism, Allocative Efficiency, and the Productivity Slowdown
January 2017
Working Paper Number:
CES-17-17
A large literature documents declining measures of business dynamism including high-growth young firm activity and job reallocation. A distinct literature describes a slowdown in the pace of aggregate labor productivity growth. We relate these patterns by studying changes in productivity growth from the late 1990s to the mid 2000s using firm-level data. We find that diminished allocative efficiency gains can account for the productivity slowdown in a manner that interacts with the within firm productivity growth distribution. The evidence suggests that the decline in dynamism is reason for concern and sheds light on debates about the causes of slowing productivity growth.
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Misallocation or Mismeasurement?
February 2020
Working Paper Number:
CES-20-07
The ratio of revenue to inputs differs greatly across plants within countries such as the U.S. and India. Such gaps may reflect misallocation which hinders aggregate productivity. But differences in measured average products need not reflect differences in true marginal products. We propose a way to estimate the gaps in true marginal products in the presence of measurement error. Our method exploits how revenue growth is less sensitive to input growth when a plant's average products are overstated by measurement error. For Indian manufacturing from 1985'2013, our correction lowers potential gains from reallocation by 20%. For the U.S. the effect is even more dramatic, reducing potential gains by 60% and eliminating 2/3 of a severe downward trend in allocative efficiency over 1978'2013.
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The Dynamics of Plant-Level Productivity in U.S. Manufacturing
July 2006
Working Paper Number:
CES-06-20
Using a unique database that covers the entire U.S. manufacturing sector from 1976 until 1999, we estimate plant-level total factor productivity for a large number of plants. We characterize time series properties of plant-level idiosyncratic shocks to productivity, taking into account aggregate manufacturing-sector shocks and industry-level shocks. Plant-level heterogeneity and shocks are a key determinant of the cross-sectional variations in output. We compare the persistence and volatility of the idiosyncratic plant-level shocks to those of aggregate productivity shocks estimated from aggregate data. We find that the persistence of plant level shocks is surprisingly low-we estimate an average autocorrelation of the plantspecific productivity shock of only 0.37 to 0.41 on an annual basis. Finally, we find that estimates of the persistence of productivity shocks from aggregate data have a large upward bias. Estimates of the persistence of productivity shocks in the same data aggregated to the industry level produce autocorrelation estimates ranging from 0.80 to 0.91 on an annual basis. The results are robust to the inclusion of various measures of lumpiness in investment and job flows, different weighting methods, and different measures of the plants' capital stocks.
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Decomposing Aggregate Productivity
July 2022
Working Paper Number:
CES-22-25
In this note, we evaluate the sensitivity of commonly-used decompositions for aggregate productivity. Our analysis spans the universe of U.S. manufacturers from 1977 to 2012 and we find that, even holding the data and form of the production function fixed, results on aggregate productivity are extremely sensitive to how productivity at the firm level is measured. Even qualitative statements about the levels of aggregate productivity and the sign of the covariance between productivity and size are highly dependent on how production function parameters are estimated. Despite these difficulties, we uncover some consistent facts about productivity growth: (1) labor productivity is consistently higher and less error-prone than measures of multi-factor productivity; (2) most productivity growth comes from growth within firms, rather than from reallocation across firms; (3) what growth does come from reallocation appears to be driven by net entry, primarily from the exit of relatively less-productive firms.
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The Micro-Level Anatomy of the Labor Share Decline
March 2020
Working Paper Number:
CES-20-12
The labor share in U.S. manufacturing declined from 62 percentage points (ppts) in 1967 to 41 ppts in 2012. The labor share of the typical U.S. manufacturing establishment, in contrast, rose by over 3 ppts during the same period. Using micro-level data, we document five salient facts: (1) since the 1980s, there has been a dramatic reallocation of value added toward the lower end of the labor share distribution; (2) this aggregate reallocation is not due to entry/exit, to 'superstars" growing faster or to large establishments lowering their labor shares, but is instead due to units whose labor share fell as they grew in size; (3) low labor share (LL) establishments benefit from high revenue labor productivity, not low wages; (4) they also enjoy a product price premium relative to their peers, pointing to a significant role for demand-side forces; and (5) they have only temporarily lower labor shares that rebound after five to eight years. This transient pattern has become more pronounced over time, and the dynamics of value added and employment are increasingly disconnected.
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Do Firms Mitigate or Magnify Capital Misallocation? Evidence from Plant-Level Data
January 2017
Working Paper Number:
CES-17-14
Almost two thirds of the cross-plant dispersion in marginal revenue products of capital occurs
across plants within the same firm rather than between firms. Even though firms allocate investment very differently across their plants, they do not equalize marginal revenue products across their plants. We reconcile these findings in a model of multi-plant firms, physical adjustment costs and credit constraints. Credit constrained multi-plant firms can utilize internal capital markets by concentrating internal funds on investment projects in only a few of their plants in a given period and rotating funds to another set of plants in the future. The resulting increase in within-firm dispersion of marginal revenue products of capital is hence not a symptom of misallocation within the firm, but rather actions taken by the firm to mitigate external credit constraints and adjustment costs of capital. Economies with multi-plant firms produce more aggregate output despite higher dispersion in marginal revenue products of capital compared to economies with single-plant firms. Because emerging economies are predominantly populated by single-plant firms, the gains from reducing their distortions to the level of developed are
larger than previously thought.
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Automation, Labor Share, and Productivity:
Plant-Level Evidence from U.S. Manufacturing
September 2018
Working Paper Number:
CES-18-39
This paper provides new evidence on the plant-level relationship between automation, labor and capital usage, and productivity. The evidence, based on the U.S. Census Bureau's Survey of Manufacturing Technology, indicates that more automated establishments have lower production labor share and higher capital share, and a smaller fraction of workers in production who receive higher wages. These establishments also have higher labor productivity and experience larger long-term labor share declines. The relationship between automation and relative factor usage is modelled using a CES production function with endogenous technology choice. This deviation from the standard Cobb-Douglas assumption is necessary if the within-industry differences in the capital-labor ratio are determined by relative input price differences. The CES-based total factor productivity estimates are significantly different from the ones derived under Cobb-Douglas production and positively related to automation. The results, taken together with earlier findings of the productivity literature, suggest that the adoption of automation may be one mechanism associated with the rise of superstar firms.
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Rising Markups or Changing Technology?
September 2022
Working Paper Number:
CES-22-38R
Recent evidence suggests the U.S. business environment is changing, with rising market concentration and markups. The most prominent and extensive evidence backs out firm-level markups from the first-order conditions for variable factors. The markup is identified as the ratio of the variable factor's output elasticity to its cost share of revenue. Our analysis starts from this indirect approach, but we exploit a long panel of manufacturing establishments to permit output elasticities to vary to a much greater extent - relative to the existing literature - across establishments within the same industry over time. With our more detailed estimates of output elasticities, the measured increase in markups is substantially dampened, if not eliminated, for U.S. manufacturing. As supporting evidence, we relate differences in the markups' patterns to observable changes in technology (e.g., computer investment per worker, capital intensity, diversification to non-manufacturing) and find patterns in support of changing technology as the driver of those differences.
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