Productivity Dynamics in U.S. Manufacturing: An Industry-Based Analysis

Sponsored by Rockwell Automation

Executive Summary
Productivity growth in the computer and electronic products subsector, once the principal driver of productivity performance in the manufacturing sector, has experienced significant waning in recent years. Consequently, the U.S. manufacturing productivity outlook has become murky. This is a challenging trend for our society, because increased productivity growth helps lift living standards. The good news is that empirical evidence put forth in this paper shows that innovation and capital investment play a key role in accelerating multifactor productivity growth (i.e., output per unit of a combined set of inputs including labor, materials, and capital) in a wide range of manufacturing industries. I also find that the proportion of educated workers (B.A. degree and higher) in the manufacturing labor force is an important driver of labor productivity performance across a wide range of subsectors. The analysis suggests that focusing on boosting just one of these productivity catalysts would be less effective than focusing on multiple drivers.

A beneficial policy response must consist of a coordinated program that stimulates manufacturing equipment investment as well as innovation investment and increases the supply of educated labor in the broad economy. An optimal return on policy efforts requires public and private decision-makers to structure resource allocations in a manner that accounts for the likely linkages of productivity determination across manufacturing subsectors.

Major findings include:

  1. While the computer and electronic products subsector has historically played an outsized role in the relatively strong productivity performance of the broader manufacturing sector, productivity growth in the information technology space has slowed dramatically in recent years. This has happened as the high-impact innovation that led to persistent and rapid increases in computer processing speeds, which are necessarily accounted for in the calculation of computer-sector productivity growth, naturally reached physical limits. This is reducing manufacturing’s rate of productivity growth.
  2. Though the machinery and transportation equipment subsectors have shown notable improvement in their productivity performance over the past 15 years, it has not been enough on an absolute basis to make up for diminishing computer subsector productivity; overall manufacturing productivity growth is therefore languishing at historically weak rates.
  3. More than two decades’ worth of government statistics and regression analysis demonstrate that innovation and capital investment are directly correlated to and thus play a significant role in driving multifactor productivity growth in a wide range of manufacturing subsectors.
  4. An increase in the labor force participation rate of those with a B.A. degree and higher correlates to faster labor productivity growth in multiple industries. The supply of educated labor plays a definitive role in driving labor productivity growth across diverse subsectors.
  5. Statistical analysis shows a strong interconnectedness of productivity performance across subsectors. This evidence supports the hypothesis that because of supply chain linkages, innovation spillovers, cluster impacts, and trade channels, productivity determination is not independent across manufacturing industries. When changes are made in one industry that promote productivity, these can affect productivity performance in other industries as well.

Abstract
This paper is the first in a series of MAPI Foundation studies whose goal is to shed light on productivity dynamics in the manufacturing sector from the perspective of questions that are unique to the present-day economic and technological climate. The current study makes use of an expanding dataset on productivity growth in detailed manufacturing industries to analyze the industry pattern of the U.S. manufacturing productivity evolution. The results of a dynamic ranking analysis of manufacturing subsector productivity performance, and performance along a number of variables that are known to impact productivity, are first discussed. This is followed by a presentation of the results of estimating one-equation models designed to identify key drivers of multifactor productivity growth and labor productivity growth in select manufacturing subsectors. Finally, modest statistical evidence is offered to support the hypothesis of cross-industry impacts of productivity determination.

The results suggest an uncertain outlook for U.S. manufacturing productivity performance in the wake of a sharp deceleration in the growth of labor productivity in the computer and electronic products subsector, which has played an outsized role in total manufacturing productivity strength. Findings point to the need for a program that stimulates capital investment, innovation investment, and workforce human capital in a unified approach for enhancing U.S. manufacturing productivity performance during this period of global integration and disruptive technological advancement.

Section 1
Introduction: Slowing Productivity Meets Disruptive Technology

For all of its importance, productivity is a straightforward concept. It is a measure of the output of the economy—or a sector of the economy—produced by a given amount and combination of inputs. Symptomatic of an increasingly data-rich period, there has been growth in the number of metrics used to gauge productivity performance. Two metrics, however, remain critical and dominate economic analysis as well as public discourse. Chief among them is labor productivity, defined as the ratio of the output of goods and services to the labor hours used in their production. Most commonly, labor productivity is measured as the output per hour of “all persons.” A second measure, multifactor (or sometimes called “total factor”) productivity, measures the output generated by a combination of inputs. In U.S. data, this combination consists of capital, labor, energy, raw materials, and business services (often denoted by the acronym KLEMS). Productivity performance matters directly for such outcomes as long-term economic growth, wage growth, and competitiveness. The potential growth of an economy, which is the sustainable rate of output gain without inflation, is the sum of the growth of labor productivity and the growth of labor hours.

At a time when short-term U.S. and global economic outlook risks are increasingly raising red flags about the long-term future, productivity is not getting the discussion that it merits. In the manufacturing sector, strong productivity performance is needed to meet the globally driven challenges of cost pressures and competitiveness. For both manufacturing and the economy as a whole, the dramatic slowdown in productivity growth in the years following the deep and destabilizing 2008-2009 recession is of increasing concern partially because it is a key factor behind slow output growth and slow wage growth. The troubles brought about by an elevated dollar and a wide range of difficult economic adjustments in key regions of the world highlight the need for U.S. policymakers to once again focus on competitive performance—and that requires productivity strength.

Fortunately, while worries about manufacturing productivity are growing, so are opportunities for real change. Rapid and potentially disruptive technological advancement is holding out the prospect of significant evolution in the very nature of manufacturing. The range of such advancements that are slowly working their way into goods supply chains around the world is daunting. With opportunities stemming from such innovations as 3D printing, robotics, and software-led factories, technology is high on the list of topics for all who focus on the future of manufacturing in the United States. While such technologies by no means provide the answer to all U.S. competitive challenges, if they are used in combination with other important policy programs, most notably human capital development, they can very well be part of an effective solution matrix for improving the trajectory of U.S. industrial growth.

The combination of slowing productivity growth and advancing manufacturing technology compels careful study to add to our understanding of the unique dynamics of productivity performance in the manufacturing sector. This paper makes use of the growing span of data on the productivity growth of manufacturing subsectors and detailed industries to remedy what has been a lack of focus on industry-specific dynamics and the interaction between industries.

The results of this research give rise to five conclusions:

  1. While the computer and electronic products subsector has played an outsized role in the relatively strong productivity performance of the overall manufacturing sector in recent decades, productivity growth in the information technology space is now slowing dramatically, presenting a difficult challenge for the manufacturing outlook.
  2. The machinery and transportation equipment subsectors have shown relative improvement in their productivity performance, but not nearly enough—yet—to replace the thrust from computer subsector productivity.
  3. While results are distinctly subsector-specific and must be viewed in the context of data constraints, I find a significant role for innovation and capital investment in driving multifactor productivity growth in a wide range of manufacturing industries.
  4. I also find a critical role for the economy’s supply of educated labor in accelerating labor productivity growth throughout diverse manufacturing industries.
  5. Finally, modest evidence raises the question of whether productivity outcomes are completely independent across manufacturing subsectors. When changes are made in one industry that promote productivity, these seem to affect productivity performance in other industries as well.

Section 2 of this paper provides an overview of key literature on the generators, measurement, and implications of productivity performance. Section 3 reviews the history of non-farm and manufacturing productivity in the United States. Using data on three-digit manufacturing subsector productivity performance, output growth, capital intensity, human capital, and patents, Section 4 provides a wide range of rankings to draw a picture of subsector dynamics in the U.S. productivity evolution. Section 5 postulates a testable framework for identifying key drivers of labor productivity growth and multifactor productivity growth for a sample of manufacturing subsectors. Section 6 provides the empirical results of these tests. Section 7 offers conclusions and policy implications.

Section 2
Productivity Research: An Overview of Key Literature

Since the pioneering work of Nobel laureate Robert Solow in the late 1950s, productivity has been a major area for research in economics. Solow was the first to suggest the role of technological change in long-run economic growth. Subsequent sophisticated analysis has considered the complex questions surrounding the relationship between technology, human capital, and productivity. For this paper, I focus on seven articles whose collective insight is pertinent to the question of productivity performance in the manufacturing sector.

A recent paper by Eichengreen, Park, and Shin (2015)1 examines the global dimension of the current productivity slump. The authors note that total factor productivity (TFP) growth has been slowing around the world in both advanced and developing economies. They constructed a country database, examined the global and country-specific correlates of total factor productivity slumps, and then studied the persistence of these episodes. Their findings are germane to a broad understanding of the productivity question in a modern global context. First, they find that episodes of TFP weakness are far from unprecedented. Such episodes of slowing total factor productivity growth appeared in the first half of the 1970s as well as in the late 1980s, the early and late 1990s, and on the eve of the 2008-2009 financial crisis.

Their findings on the correlates of TFP slumps will likely enhance future research. They note a negative association between the incidence of TFP weakness and educational attainment. In addition, countries with high investment shares of GDP appear to be more susceptible to productivity deceleration. And political systems matter. On a positive note, they explain that while there have been slumps, there have also been periods of acceleration. While productivity has thus far been thought of as a structural variable, research such as this gives rise to legitimate discussions of productivity cycles.

Jorgenson, Ho, and Stiroh (2008)2 focus on the lessons of recent U.S. history. They note that labor productivity growth surged after 1995, averaging 2.8% from 1996 to 2000. As a result, persistent frustration that the benefits of computerization would never show up in productivity data yielded to optimism about a productivity resurgence, led by information technology (IT). But this did not last long. The acceleration in productivity growth lasted through the middle of 2004. Subsequent data were weaker.

The authors assert that the sources of productivity growth changed twice since 1995. IT dominated the productivity picture between 1995 and 2000. After 2000, TFP growth outside of IT production accelerated. Like the Eichengreen paper, this study suggests a shifting and dynamic process through time that gives rise to productivity volatility—and unpredictability.

Stiroh (2001)3 and Syverson (2011)4 abstract from historical specifics to consider the fundamental question of the forces that shape productivity performance. Stiroh discusses the two competing models that dominate the economics literature. In the neoclassical model, capital accumulation drives productivity growth in the short run but capital succumbs to diminishing returns. Thus, long-run productivity growth is entirely driven by exogenous technical progress. In the more recent “new growth” theory, as expounded by economists such as NYU’s Paul Romer, productivity growth can continue indefinitely without exogenous technical progress. Stiroh notes that both paradigms offer important insights and they are not mutually exclusive. Common to both models is the critical insight that investment is fundamental to productivity performance. But there has been growing recognition that “investment” is a broad term that can, for example, include human capital investment as well as research and development investment in addition to the more well-understood business equipment expenditure and deployment. Stiroh notes that growing consideration of the broad heterogeneity of investment has allowed for significant advances in the understanding of productivity growth.

Syverson’s 2011 paper leverages the growing supply of firm-level productivity data, the existence of which has spawned numerous research programs. He outlines one of the most compelling mysteries in productivity research, noting that economists have persistently documented large measured productivity differences across producers even within narrowly defined industries. In this paper, Syverson cites one of his earlier works that found that within narrowly defined industries in the U.S. manufacturing sector, a plant at the 90th percentile of the productivity distribution generates almost twice as much output with the same measured inputs as a plant in the 10th percentile. Remarkably, U.S. manufacturing is not exceptional in this regard. If anything, plant-level productivity dispersion is small relative to manufacturing sectors in other countries.

Motivated by global evidence of this wide dispersion, Syverson offers a framework that begins to explain its existence. The resulting model implies that for any industry there will be a critical productivity level such that if a firm operates below it, it will have negative profits. The threshold productivity level depends on industry-specific factors as well as wage rates and fixed costs common to all producers. Within the confines of producing above the critical productivity threshold in industry equilibrium, industry conditions allow for a wide range of performances partially because the most productive firms simply cannot service the entire market.

Bernanke (1981),5 Steindel (1992),6 and Leonard and Waldman (2007)7 consider the calculus of productivity-related forces specific to the manufacturing sector. In a prescient 1981 paper, Ben Bernanke considered the variables that impact manufacturing productivity and discussed important method issues. He asserts that while growth accounting, which decomposes economic growth into major sources (labor inputs, capital inputs, and residuals) is a good descriptor, this much-used framework does not enlighten on the causes of productivity change. He explains that in standard analysis, the levels of capital and labor inputs are thought of as jointly endogenous with productivity. It is not typical to think of capital or labor as “causing” productivity.

Bernanke studies productivity in the U.S. manufacturing sector from 1947 to 1980. He uses a modeling approach that explicitly recognizes that measured productivity levels are not a given to the manufacturing sector but rather represent choices made by workers and firms in response to exogenous constraints. He finds that the two most impactful sources of productivity change are the collective factors that directly affect the sector’s production possibilities—i.e., technology and the cost of capital, including utilization costs. Product demand, the business cycle, and labor supply are found to be less important to the manufacturing productivity outcome.

Steindel (1992) explores issues connected with manufacturing productivity growth and “high-tech” capital, generally meaning information processing capital. He finds evidence of a positive relationship between high-tech capital usage and productivity in manufacturing industries. The impact is sufficiently large to account for a nontrivial fraction of the growth of productivity in manufacturing industries from the first half to the second half of the 1980s, even though other factors played more substantial roles and the bulk of the acceleration in growth remains “difficult to explain.” In something of a testimonial to the complexity of productivity determination, Steindel concludes his article by noting that while his evidence does not show that high-technology adoption was a decisive element in the improvement in manufacturing productivity growth during the 1980s, the results do suggest that high-tech equipment may have made a larger contribution than previous research would suggest.

Leonard and Waldman offer useful revelations for empirical manufacturing productivity research by estimating a simple model of innovation in the U.S. manufacturing sector. The authors model process and product innovation in a framework in which patents are used as a proxy for product innovation and multifactor productivity in the U.S. manufacturing sector is used as a proxy for process innovation. The estimated equation for process innovation is thus of interest for the current study. Their explanatory variables are the growth rate of investment in equipment and software in the entire economy (in present form and lagged three years), a five-year lag on the growth rate of dollar expenditures on university- and college-performed basic research, and a two-year lag on the growth rate of full-time equivalent scientists and engineers in R&D-performing companies. In effect, this specification reflects inputs from the essential “ingredients” for innovation as well as the dispersion of innovation through capital deployment.

Section 3
The History of U.S. Non-Farm and Manufacturing Productivity Performance

One challenge with understanding the drivers of labor productivity progress is the relatively short history of the data. Further, the data, even on an annual basis, are remarkably volatile. As a means of smoothing the volatility, Figure 1 shows a four-year moving average of the growth of non-farm labor productivity in the United States. The data extend back to 1951. As discussed in Eichengreen (2015), history supports the notion of productivity cycling, with pronounced slumps followed by pronounced accelerations.

Figure 1 – U.S. Non-Farm Labor Productivity Growth, Four-Year Moving Average

Source(s): U.S. Bureau of Labor Statistics

Source(s): U.S. Bureau of Labor Statistics

For much of the 1950s, there was a slowing trend in labor productivity growth that reversed after 1959 and peaked in 1964 and 1965. Volatility aside, it is clear that from the mid-1960s to the early 1980s, there was a sustained slowing in labor productivity growth to near zero in 1982 before a partial rebound kept productivity growth in a moderate range until the mid-1990s.

Subsequently, the now well-recognized information technology boom catalyzed a reacceleration of productivity growth to the peak levels of the 1960s. The post-1996 productivity acceleration reached an apex during 2003. This was followed by a lengthy slowdown that bottomed in 2008. A short-lived post-recession bounce peaked in 20108 and was followed by dramatic slowing that took labor productivity growth to 0.45% for the latest data in 2014.

Figure 2 shows a four-year moving average of labor productivity growth in the U.S. manufacturing sector. Unfortunately, these data extend back only to 1991. As is the case for the total economy, the data point to an IT-led productivity acceleration that peaked in 2005, decelerated to 1.7% by 2009, and then experienced a post-recession bounce to 3.5% in 2010. In spite of an upward blip to 4.4% during 2013, labor productivity growth in manufacturing decelerated to 2.1% by 2014, the weakest in this history apart from 1991 and 2009.

Figure 2 – U.S. Manufacturing Labor Productivity Growth, Four-Year Moving Average

Source(s): U.S. Bureau of Labor Statistics

Source(s): U.S. Bureau of Labor Statistics

Section 4
The Sector Dynamics of U.S. Manufacturing Productivity Performance

The overall history of manufacturing productivity growth masks an interesting volatility among major subsectors that tells a deeper story and thus offers greater insight. In this section, I consider the industry dynamic along a number of important parameters. In doing so, I rank the 21 major manufacturing subsectors at key points in time.9

Table 1 shows the ranking of a four-year moving average of labor productivity growth for four years—1993, 1999, 2005, and 2014. The years were chosen in part to avoid business cycle distortions. As shown, the computer and electronic products subsector ranked first in labor productivity growth throughout this period. The machinery and textile product mills subsectors are notable for improvements in their rankings. The machinery subsector, an increasingly important driver of U.S. manufacturing growth, climbed from a ranking of 18 in 1993 and 15 in 1999 to 6 in both 2005 and 2014. The transportation equipment subsector scored relatively high throughout this period, never falling below a ranking of 5. By contrast, the electrical equipment, appliance, and component subsector fell from a second place ranking in 1993 to 16 by 2014. The chemicals subsector remained a laggard throughout.

Table 1 – Ranking by Four-Year Moving Average of Labor Productivity Growth

Source(s): MAPI Foundation and U.S. Bureau of Labor Statistics

Source(s): MAPI Foundation and U.S. Bureau of Labor Statistics

A more quantitative perspective on the dynamic is shown in Figure 3, which displays the recent history of labor productivity growth in the consistently first-place computer and electronic products subsector as well as the machinery and transportation equipment subsectors, chosen for their relative improvement, and chemicals and fabricated metal products, whose relative productivity performance has been lagging. As shown, labor productivity growth in the computer and electronic products subsector peaked at a virtually unprecedented 21% in 2000 and has since experienced a pronounced slowdown as the high-impact innovation that led to persistent and rapid increases in computer processing speeds, which are necessarily accounted for in the calculation of computer-sector productivity growth, naturally reached physical limits. Nothing yet seems to be compensating for this dramatic waning of IT subsector productivity. Even as machinery and transportation equipment began to experience a measure of productivity acceleration after 2011, their productivity growth never pulled away from the relatively weaker chemicals and fabricated metal products subsector and weakened during 2014.

Figure 3 – Labor Productivity Growth in Select U.S. Manufacturing Subsectors, Four-Year Moving Average

Source(s): U.S. Bureau of Labor Statistics

Source(s): U.S. Bureau of Labor Statistics

To build on the insights offered by Figure 3, Table 2 shows two measures of dispersion among the major manufacturing subsectors in their labor productivity performance. Given the disproportionate role of computer and electronic products, the data were calculated with and without this subsector. With all subsectors included, the simpler of the two measures, which is the percentage point difference in the labor productivity growth of the highest-ranked and lowest-ranked subsectors, peaked at 23.8 in 1999. Excluding the computer subsector, this measure is less than half of that at 10.5 percentage points. As computer manufacturing productivity growth has waned, the “top minus bottom” metric including the computer subsector has converged on the top minus bottom metric whose calculation excludes computer and electronic products.

The second measure in Table 2 is the standard deviation of labor productivity performance among the 21 major manufacturing subsectors. A measure of dispersion around the mean, it peaked at 4.4 percentage points in 1999 when computers are included but narrowed dramatically to 1.5 percentage points by 2014. Since 1999, the standard deviation has narrowed even when excluding the computer and electronic products subsector, perhaps suggesting a convergence driven by an interindustry dynamic that will be analyzed later in the paper.

Table 2 – Dispersion Measures of Labor Productivity Growth Across Manufacturing Subsectors, Percentage Points

Source(s): MAPI Foundation and U.S. Bureau of Labor Statistics

Source(s): MAPI Foundation and U.S. Bureau of Labor Statistics

Table 3 shows rankings of multifactor productivity growth. While not perfectly aligned, these data tell much the same story as the labor productivity rankings. The computer and electronic products subsector dominated while the transportation equipment and machinery subsectors displayed relative improvement. Further, the chemicals subsector showed relative weakness, as did fabricated metal products, although the latter climbed in the ranking in 2014.

Table 3 – Ranking by Four-Year Moving Average of Multifactor Productivity Growth

Source(s): MAPI Foundation and U.S. Bureau of Labor Statistics

Source(s): MAPI Foundation and U.S. Bureau of Labor Statistics

Tables 4 through 7 show rankings by variables that are thought to have impacts on productivity performance. The literature is clarifying as to the presumed importance of a wide range of investments that broaden the production possibility frontier and distribute new capital. These include equipment investment, research and development spending, and human capital investment. Along these lines, Table 4 shows subsector rankings by a 10-year moving average of utility patent grants, a well-accepted proxy for innovation output. Computer and electronic products as well as machinery are, relatively speaking, the star performers, although fabricated metal products and chemicals, which exhibit relatively weak productivity performance, are also impressive in terms of their relative standings in patent generation.

Table 4 – Ranking by 10-Year Moving Average of Utility Patent Awards

Source(s): MAPI Foundation and U.S. Patent and Trademark Office

Source(s): MAPI Foundation and U.S. Patent and Trademark Office

Table 5 puts the manufacturing innovation picture into further perspective by showing the share of total manufacturing utility patents accounted for by each subsector. Computer and electronic products and machinery are the relatively strong performers and have dominated innovation output in an absolute sense. In 2012, these two sectors alone accounted for 56% of total manufacturing sector utility patent awards. Machinery has waned in its patent share, while an increasingly large share has come from the computer and electronic products subsector. A number of other subsectors had interesting shares, including fabricated metal products and plastics and rubber products. Nonetheless, it is clear that significant innovation output has been contained to a few dynamic manufacturing industries.

Table 5 – Share of Total Manufacturing Utility Patent Awards (%)

Source(s): MAPI Foundation and U.S. Patent and Trademark Office

Source(s): MAPI Foundation and U.S. Patent and Trademark Office

Table 6 shows subsector rankings by a four-year moving average in the growth of capital intensity, a ratio of the change in capital deployment to the change in labor deployment. Computer and electronic products and chemicals are the relatively strong performers, while miscellaneous manufacturing, which broadly consists of medical equipment and a variety of other difficult to classify industries, has been rising in relative capital intensity growth performance.

Table 6 – Ranking by Four-Year Moving Average of Capital Intensity Growth

Source(s): MAPI Foundation and U.S. Bureau of Labor Statistics

Source(s): MAPI Foundation and U.S. Bureau of Labor Statistics

Table 7 considers the human capital component of the productivity picture. It shows the rankings of major manufacturing subsectors by the share of their respective workforces with a B.A. degree and higher; the span of these data is limited and extends back only to 2000. Computer and electronic products and chemicals have the relatively more educated workforces. Paradoxically, while machinery is quite strong in patent performance, it ranks in the middle of the pack in its share of educated labor. Transportation equipment ranked fourth in 2013. Beverage and tobacco products, a poor productivity performer, ranked a high number three in both 2005 and 2013. Food, furniture, and wood are the relatively weak subsectors in educated labor shares.

Table 7 – Ranking by Share of Workforce With a B.A. Degree or Higher

Source(s): MAPI Foundation and U.S. Bureau of Labor Statistics

Source(s): MAPI Foundation and U.S. Bureau of Labor Statistics

The rankings of output growth, shown in Table 8, are basically consistent with rankings of productivity growth. Computer and electronic products is basically the strong player, but output growth in this subsector slipped from first to fourth in the wake of the Great Recession. The relative strength of output growth in machinery and transportation equipment has moved up markedly, while chemicals slid considerably in its relative output growth after 2009. Fabricated metal products moved up in its relative output growth rankings in spite of its low ranking in labor productivity growth.

Table 8 – Ranking by Average Annual Output Growth

Source(s): MAPI Foundation and Federal Reserve Board

Source(s): MAPI Foundation and Federal Reserve Board

Both the consistencies and the inconsistencies in these ranking results testify to the need for a broad and integrated, if simple, statistical framework for evaluating the drivers of productivity outcomes. This challenge is addressed in the next two sections.

Section 5
Identifying Key Drivers: A Testable Model

Testing the drivers of productivity dynamics in the context of the current study involves a mixture of the old and the new. The “old” comes from well-established concepts in the productivity literature, outlined in Section 2. And while the subsector-level productivity series aren’t new, as they span back to the late 1980s, we are just now at the leading edge of having enough data points to begin to credibly estimate evidence-generating one-equation models. While one-equation specifications do not always offer the most definitive insights, multiple estimations across subsectors provide an opportunity for meaningful comparisons.

The current study makes use of five subsectors for statistical analysis. They are computer and electronic products, due to its dominance in the manufacturing productivity picture; machinery and transportation equipment, whose relative productivity performance has improved; and chemicals and fabricated metal products, whose productivity performance has been relatively lagging. For simplicity, the assumption of a linear functional form is employed. The relatively limited dataset allows for only a few explanatory variables in each equation. Partially motivated by this constraint, I estimate one equation for multifactor productivity growth and two alternative equations for labor productivity growth.

Along the lines of Bernanke, Stiroh, and Leonard/Waldman, some combination of investment variables was deemed appropriate for the multifactor productivity equations. Leonard and Waldman used the growth of university-level research and development expenditures and the growth of the R&D workforce in their multifactor productivity specification for the total manufacturing sector. But such data are not easily available on the subsector level. Instead, I make use of a rich dataset on utility patents by subsector. Patents are a well-accepted proxy for innovation output and, at the very least, track innovation. Further, empirical employment of patents is conceptually consistent with Leonard and Waldman’s specification and with Bernanke’s finding that expansion of the production possibility frontier, which innovation can bring, is a critical source of productivity change. Motivated by Robert Solow’s notion that innovation is embedded in new capital investment, I chose the growth of equipment investment in the given subsector as the other explanatory variable for the multifactor productivity equation.

For labor productivity, a reading of the literature combined with data constraints suggests that one variable for human capital and one variable for non-labor investment is the optimal specification for a one-equation model. Unfortunately, as mentioned, workforce educational attainment data on the subsector level extend back only to 2000. Thus, I take a macro approach and use the labor force participation rate of workers with a B.A. degree and higher. In effect, this is the economy’s supply of educated labor and is partially reflective of the skills market that all sectors and subsectors face. A comparison of this estimate across the five manufacturing subsectors will be most revealing. In the first of the two labor productivity equations, the growth of capital intensity is chosen as the other variable in that it is a reasonable proxy for capital per worker, a known and logical influence on labor productivity, as it somewhat reflects the productive capital that the workforce has at their disposal. In the second equation, I employ an innovation framework and select patents as the second variable.

Finally, I test for cross-sector productivity impacts. The logic of innovation spillovers, supply chains, and the simple fact that medium-sized and large manufacturers often have businesses in multiple industries all suggest that productivity performance outcomes across major manufacturing subsectors are not completely independently determined. Future research should explore this question in more sophisticated frameworks. For the purposes of the current study, I offer a range of simple correlations along with univariate regression estimates.

Section 6
Empirical Results

As per the specification outlined in the previous section, I first estimated an equation with a four-year moving average of multifactor productivity growth as the endogenous variable.10 The explanatory variables11 are a 10-year moving average of utility patent grants for the individual subsector and annual growth in equipment investment for the subsector. Explanatory variable lags were tested on a trial and error basis, as no predetermined dynamic structure was employed for the estimation. A well-accepted method was used to correct for serial correlation when needed.12

The results of estimating the multifactor productivity equation for each of the chosen five subsectors are shown in Table 9. Not surprisingly, the results vary. In the computer and electronic products subsector, the two explanatory variables account for 85% of the variation in multifactor productivity growth (as indicated by the adjusted R-squared). Nonetheless, both coefficients have unexpectedly negative signs. And while the patents variable has a high level of statistical significance (meaning that the coefficient can be generalized to some extent, that it is not simply a random accident of these data),13 the investment variable is not significant at all.

Table 9 – Drivers of Multifactor Productivity Growth in Select Manufacturing Subsectors
Dependent Variable: Four-Year Moving Average of Multifactor Productivity Growth
Sample: 1992-2012, Annual Data (t-statistics in parentheses)

Statistical Significance: ***1% level or less, **5% level or less but >1%, *10% level or less but >5% Source(s): MAPI Foundation

Statistical Significance: ***1% level or less, **5% level or less but >1%, *10% level or less but >5%
Source(s): MAPI Foundation

In the other four subsectors, both the patents and investment variables have the expected positive sign. The variables show encouraging levels of statistical significance, with the exception of the investment variable in the equation for the chemicals subsector and the patents variable in the machinery equation. The adjusted R-squared is generally impressive, especially in the machinery equation. While more sophisticated work will build on these results, it seems clear that an investment program with both an innovation and an equipment deployment component will play a role in broadening productivity strength across a range of goods-producing industries.

Two alternative specifications were estimated with a four-year moving average of labor productivity growth as the endogenous variable. In the first, a four-year moving average of the growth in capital intensity was paired with the labor force participation rate of workers with a B.A. degree and higher (“educated labor”) as the explanatory variables. Table 10 shows the results. With the exception of the transportation equation, the two variables explain a significant share of the variation in labor productivity growth in these sectors.

Beyond this, the results in Table 10 are surprising and even provocative. The capital intensity variable has an unexpectedly negative sign. This can sometimes be a function of statistical noise; the small sample must also be kept in mind. By contrast, the educated labor variable has the expected positive sign in all five equations, with a reasonable statistical significance posture, save for the serial correlation trouble in the computer and electronic products equation.

Table 10 – Drivers of Labor Productivity Growth in Select Manufacturing Subsectors
Dependent Variable: Four-Year Moving Average of Labor Productivity Growth
Sample: 1992-2013, Annual Data (t-statistics in parentheses)

Statistical Significance: ***1% level or less, **5% level or less but >1%, *10% level or less but >5% Source(s): MAPI Foundation

Statistical Significance: ***1% level or less, **5% level or less but >1%, *10% level or less but >5%
Source(s): MAPI Foundation

The second labor productivity equation uses a 10-year moving average of patents in the place of a four-year moving average of capital intensity. As shown in Table 11, there is a varying degree of statistical success. The overall regression did not explain much of the variation in labor productivity growth in machinery and transportation but it certainly did in the other three equations. The patents variable has an unexpected negative sign in all but the transportation equation. As with the first labor productivity equation, the educated labor variable has a positive sign in all equations along with a reasonably solid profile of statistical significance.

Table 11 – Drivers of Labor Productivity Growth in Select Manufacturing Subsectors
Dependent Variable: Four-Year Moving Average of Labor Productivity Growth
Sample: 1992-2013, Annual Data (t-statistics in parentheses

Statistical Significance: ***=1% level or less, **5% level or less but >1%, *10% level but >5% Source(s): MAPI Foundation

Statistical Significance: ***=1% level or less, **5% level or less but >1%, *10% level but >5%
Source(s): MAPI Foundation

The expected and consistent behavior of the human capital variable in the two labor productivity equations reinforces the need for human capital strength as a central input for labor productivity improvement even in a time of rapid technological change in manufacturing. The persistently falling labor force participation rate of workers with a B.A. degree and higher, shown in Figure 4, is clearly disturbing for the productivity outlook. It remains above the overall labor force participation rate, shown in Figure 5. But the direction gives cause for concern.

Figure 4 – Labor Force Participation Rate, Bachelor’s Degree and Higher, Ages 25+

Source(s): U.S. Bureau of Labor Statistics

Source(s): U.S. Bureau of Labor Statistics

Figure 5 – Labor Force Participation Rate, Ages 16+

Source(s): U.S. Bureau of Labor Statistics

Source(s): U.S. Bureau of Labor Statistics

Finally, I offer results on potential cross-subsector productivity impacts. Figure 6 shows, for each of the 21 major manufacturing subsectors, the number of correlations a subsector’s labor productivity growth has with labor productivity growth in each of the other 20 subsectors that are at or above 0.5. While bivariate correlations should be seen as suggestive and never dispositive, the fact that 11 subsectors have 10 or more cross-subsector labor productivity correlations that are at or above 0.5 is certainly at least interesting.

Figure 6 – Number of Correlations of Subsector Labor Productivity Growth With Other Manufacturing Subsectors That Are at or Above 0.5

Source(s): U.S. Bureau of Labor Statistics and MAPI Foundation

Source(s): U.S. Bureau of Labor Statistics and MAPI Foundation

Further evidence in the form of univariate regressions is shown in Tables 12 and 13. The strategy was simply to estimate one-variable regressions of productivity growth in one subsector as a function of productivity growth in another subsector. Table 12 shows the results for multifactor productivity growth. Once again, the computer and electronic products subsector is challenging in its results. A four-year moving average of multifactor productivity (MFP) growth in the machinery subsector by itself explains 72% of the variation in a four-year moving average of multifactor productivity growth in computer and electronic products. But the variable is at best marginally significant. By contrast, the machinery multifactor productivity variable is significant at the 1% level in the equation in which the endogenous variable is a four-year moving average of multifactor productivity growth in the transportation equipment sector. And machinery MFP growth explains just under half of the variation in transportation equipment MFP growth.

Table 12 – One-Variable Specifications for Cross-Subsector Impacts of Multifactor Productivity Growth
Dependent & Independent Variable: Four-Year Moving Average of Multifactor Productivity Growth
Sample: 1992-2013, Annual Data (t-statistics in parentheses)

Statistical Significance: ***1% level or less, **5% level or less but >1%, *10% level or less but >5% Source(s): MAPI Foundation

Statistical Significance: ***1% level or less, **5% level or less but >1%, *10% level or less but >5%
Source(s): MAPI Foundation

Table 13 shows cross-subsector univariate estimations for labor productivity growth. As shown, fabricated metal products is the explanatory variable for machinery, machinery is the explanatory variable for transportation equipment, and computer and electronic products is the explanatory variable for fabricated metal products, all explaining nontrivial shares of the variation in their respective endogenous variables.

Table 13 – One-Variable Specifications for Cross-Subsector Impacts of Labor Productivity Growth
Dependent & Independent Variable: Four-Year Moving Average of Labor Productivity Growth
Sample: 1991-2013 Annual Data (t-statistics in parentheses)

Statistical Significance: ***1% level or less, **5% level or less but >1%, *10% level or less but >5% Source(s): MAPI Foundation

Statistical Significance: ***1% level or less, **5% level or less but >1%, *10% level or less but >5%
Source(s): MAPI Foundation

These correlations and single-variable equations, while not completely dispositive by any means, are likely indicative of a manufacturing sector that is evolving into an increasingly interconnected labyrinth of supply chains, innovation spillovers, clusters, and trade channels. It is certainly a reasonable hypothesis, supported by this evidence, that productivity growth outcomes across manufacturing subsectors have an interesting degree of interrelationship.

Section 7
Conclusions and Implications

While the computer and electronic products subsector has played a critical role in the relatively strong productivity performance of the overall U.S. manufacturing sector in recent decades, productivity in this subsector is slowing markedly. Computer subsector productivity growth in excess of 20% was not sustainable, even for an innovative, forward-looking industry. And this remarkable performance masked a less than exciting profile for much of the manufacturing sector. U.S. manufacturing, in effect, could be said to have been in a productivity bubble. Post-bubble periods, of course, give rise to great concern about the outlook. The machinery and transportation equipment subsectors have shown relative improvement in their productivity performance, but not nearly enough on an absolute basis—yet—to replace the thrust from computer subsector productivity.

At this critical and difficult juncture, what is the policy prescription? The analysis presented in this paper supports the significant role of innovation and capital investment in driving multifactor productivity growth in a wide range of manufacturing subsectors. More robust statistical results point to the definitive role played by the economy’s supply of educated labor in driving labor productivity growth across a wide range of manufacturing industries. In this time of exciting technological advancement, policymakers and business decision-makers need to be aware that optimal returns on technology investment will come from a multilayered program that smartly recognizes and incorporates the role of workforce skills in the evolving production environment.

One such approach would be to promote industrial clusters, which should be the model for the public end of stimulating a new technology program that will enhance competitiveness. Clusters maximize the benefits of geographic proximity by coordinating resource use. I suggest an approach that makes use of regional centers to evolve and disperse new technologies in a cluster-specific manner. If this is coordinated with stimulating area schools to offer programs that produce a technology-ready workforce, then the cluster will be strong and competitive. Taken over all clusters, this will optimize the national result.

If public investments are made, how should they be targeted? The statistical evidence presented in this paper raises the question of whether productivity outcomes are completely independent across manufacturing subsectors. A manufacturing sector that is becoming integrated along a growing number of parameters testifies to the complexity of productivity determination. Major subsectors are not independent in this regard. An identification of the most connected industries will be enlightening as to the structure of optimal and cost-effective productivity-enhancing investments.

The productivity research program needs to widen in scope as the recognition of industry-specific productivity dynamics grows. Economists, for example, are beginning to rigorously study the role of management behavior in productivity outcomes. An understanding of management practices across manufacturing subsectors will add to the empirical framework put forth in this paper.


Footnotes

1. Barry Eichengreen, Donghyun Park, and Kwanho Shin, “The Global Productivity Slump,” NBER Working Paper no. 21556, September 2015.

2. Dale W. Jorgenson, Mun S. Ho, and Kevin J. Stiroh, “A Retrospective Look at the U.S. Productivity Growth Resurgence,” Journal of Economic Perspectives 22, no. 1 (Winter 2008): 3-24.

3. Kevin J. Stiroh, “What Drives Productivity Growth?,” Federal Reserve Bank of New York Economic Policy Review 7, no. 1 (March 2001): 37-59.

4. Chad Syverson, “What Determines Productivity?,” Journal of Economic Literature 49, no. 2 (2011): 326-365.

5. Ben S. Bernanke, “The Sources of Labor Productivity Variation in U.S. Manufacturing, 1947-80,” NBER Working Paper no. 712, July 1981.

6. Charles Steindel, “Manufacturing Productivity and High-Tech Investment,” Federal Reserve Bank of New York Quarterly Review 17, no. 2 (Summer 1992).

7. Jeremy Leonard and Cliff Waldman, “An Empirical Model of the Sources of Innovation in the U.S. Manufacturing Sector,” Business Economics 42, no. 4 (October 2007): 33-45.

8. After most recessions, output recovers before employment, creating an arithmetic bounce in productivity growth that is not necessarily indicative of a significant shift.

9. For certain parameters a number of subsectors are combined, making for less than 21.

10. The endogenous variable is the one on the left side of the equation. It is the variable that we are trying to explain or predict with the regression exercise.

11. Explanatory variables are those that appear on the right side of the equation. They are the variables that are being tested for their statistical association with the endogenous variable.

12. Serial correlation is a statistical issue whereby the error terms from the regression are sequentially correlated. This causes the standard errors of the regression coefficients to be understated, often leading to an erroneous conclusion of statistical significance. The most common test for first-order serial correlation is the Durbin–Watson statistic. In the absence of serial correlation, the Durbin–Watson is in and around 2.0.

13. Significance has a descending scale. A lower number indicates superior statistical significance.

Kristin Graybill