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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The Impact of Plant-Level Resource Reallocations and Technical Progress on U.S. Macroeconomic Growth
December 2009
Working Paper Number:
CES-09-43
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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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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Good Dispersion, Bad Dispersion
March 2024
Working Paper Number:
CES-24-13
We document that most dispersion in marginal revenue products of inputs occurs across plants within firms rather than between firms. This is commonly thought to reflect misallocation: dispersion is 'bad.' However, we show that eliminating frictions hampering internal capital markets in a multi-plant firm model may in fact increase productivity dispersion and raise output: dispersion can be 'good.' This arises as firms optimally stagger investment activity across their plants over time to avoid raising costly external finance, instead relying on reallocating internal funds. The staggering in turn generates dispersion in marginal revenue products. We use U.S. Census data on multi-plant manufacturing firms to provide empirical evidence for the model mechanism and show a quantitatively important role for good dispersion. Since there is less scope for good dispersion in emerging economies, the difference in the degree of misallocation between emerging and developed economies looks more pronounced than previously thought.
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Reallocation, Firm Turnover, and Efficiency: Selection on Productivity or Profitability?
September 2005
Working Paper Number:
CES-05-11
There is considerable evidence that producer-level churning contributes substantially to aggregate (industry) productivity growth, as more productive businesses displace less productive ones. However, this research has been limited by the fact that producer-level prices are typically unobserved; thus within-industry price differences are embodied in productivity measures. If prices reflect idiosyncratic demand or market power shifts, high 'productivity' businesses may not be particularly efficient, and the literature's findings might be better interpreted as evidence of entering businesses displacing less profitable, but not necessarily less productive, exiting businesses. In this paper, we investigate the nature of selection and productivity growth using data from industries where we observe producer-level quantities and prices separately. We show there are important differences between revenue and physical productivity. A key dissimilarity is that physical productivity is inversely correlated with plant-level prices while revenue productivity is positively correlated with prices. This implies that previous work linking (revenue-based) productivity to survival has confounded the separate and opposing effects of technical efficiency and demand on survival, understating the true impacts of both. We further show that young producers charge lower prices than incumbents, and as such the literature understates the productivity advantage of new producers and the contribution of entry to aggregate productivity growth.
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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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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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Materials Prices and Productivity
June 2012
Working Paper Number:
CES-12-11
There is substantial within-industry variation, even within industries that use and produce homogeneous inputs and outputs, in the prices that plants pay for their material inputs. I explore, using plant-level data from the U.S. Census Bureau, the consequences and sources of this variation in materials prices. For a sample of industries with relatively homogeneous products, the standard deviation of plant-level productivities would be 7% lower if all plants faced the same materials prices. Moreover, plant-level materials prices are both persistent across time and predictive of exit. The contribution of net entry to aggregate productivity growth is smaller for productivity measures that strip out di'erences in materials prices. After documenting these patterns, I discuss three potential sources of materials price variation: geography, di'erences in suppliers. marginal costs, and suppliers. price discriminatory behavior. Together, these variables account for 13% of the dispersion of materials prices. Finally, I demonstrate that plants.marginal costs are correlated with the marginal costs of their intermediate input suppliers.
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Productivity Dispersion and Plant Selection in the Ready-Mix Concrete Industry
September 2011
Working Paper Number:
CES-11-25
This paper presents a quantitative model of productivity dispersion to explain why inefficient producers are slowly selected out of the ready-mix concrete industry. Measured productivity dispersion between the 10th and 90th percentile falls from a 4 to 1 difference using OLS, to a 2 to 1 difference using a control function. Due to volatile productivity and high sunk entry costs, a dynamic oligopoly model shows that to rationalize small gaps in exit rates between high and low productivity plants, a plant in the top quintile must produce 1.5 times more than a plant in the bottom quintile.
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Has toughness of local competition declined?
May 2022
Working Paper Number:
CES-22-13
Recent evidence on rm-level markups and concentration raises a concern that market
competition has declined in the U.S. over the last few decades. Since measuring competition is difficult, methodologies used to arrive at these findings have merits but also raise technical concerns which question the validity of these results. Given the significance of documenting how competition has changed, I contribute to this literature by studying a different measure of competition. Specifically, I estimate the toughness of local competition over time. To derive this estimate, I use a generalized monopolistic competition model with variable markups. This model generates insights that allows me to measure competition as the sensitivity of weighted-average markup to changes in the number of competitors using directly observable variables. Compared to firm-level markups estimation, this method relaxes the need to estimate production functions. I then use confidential Census data to estimate toughness of local competition from 1997 to 2016, which shows that local competition has decreased in non-tradable industries on average in the U.S. during this time period.
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