## 1. Deceleration in Average TFP Growth, 2005–2010 vs. 1996–2004

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### Productivity slowdown — overview
- U.S. total factor productivity (TFP) growth slowed since the mid-2000s: after growing at about 1¾ percent per year during 1996–2004, the average TFP growth rate has halved since 2005.
- The slowdown appears to go beyond the effects of the Great Recession and is central to assessing future potential growth.
- Explanations surveyed include:
  - Reduced ability to benefit from technological advances (Gordon, 2012 and 2013).
  - Return to more normal rates after an extraordinary IT-led decade (Fernald, 2014).
  - Continued potential for technology-driven gains, especially in services or from ongoing IT innovations (Baily, Manyika, and Gupta, 2013; Byrne, Oliner, and Sichel, 2013; Bernanke, 2013).
- TFP reflects more than technological innovation and depends on factors affecting the efficiency of combining labor and capital, including competition, administrative burden, infrastructure, and access to finance.

### Empirical strategy (three stages)
- Estimate state-level TFP growth using a standard Cobb-Douglas production function with time-varying and state-specific labor shares.
- Use stochastic frontier analysis (SFA) to decompose TFP growth into common technological trends and state-specific technical efficiency.
- Analyze determinants of TFP growth across U.S. states using panel data models relating TFP growth to human capital, innovation (R&D), infrastructure, taxation, and regulatory framework.

### Measurement caveats and robustness
- No direct state-level capital stock or capital services data; capital allocated across states using national industry capital shares (Garofalo and Yamarik (2002); Yamarik (2013)), assuming identical capital-to-output ratios within industries across states.
- Labor input is private-sector employment (not hours); changes in hours per worker enter TFP estimates.
- Robustness checks: GDP-weighted average of state TFP growth closely matches national aggregate TFP estimates; strong correlation with Caliendo and others (2014) state-level TFP.

### Cross-state variation and IT specialization
- For the U.S. as a whole, TFP growth slowed about 1¾ percentage points on average in 2005–2010 relative to 1996–2004.
- State-level deceleration ranged:
  - Decline of over 3 percentage points in New Mexico and South Dakota.
  - A relatively modest (below 1 percent) decline in ten states.
  - Oregon was an outlier with sustained high TFP growth over the whole period.
- Little evidence that the TFP slowdown was significantly larger in states most specialized in IT production or intensive in IT usage.
  - IT production is more geographically concentrated than IT usage across states.
  - Statistical tests show no significant additional TFP deceleration for IT-producing or IT-intensive states.
  - Example: New Mexico and Oregon had similar degrees of IT-production specialization and IT-intensity but very different productivity outcomes.

### SFA decomposition: technological progress versus efficiency
- SFA framework: inefficiencies create a wedge between actual production and the production frontier; technological progress shifts the frontier; improvements in technical efficiency move states closer to the frontier.
- Rolling-window SFA estimates (1995–2010) indicate:
  - Production frontier has been shifting up at a relatively constant rate of about 1 percent per year.
  - Estimated technical efficiency declined over time; the average state moved slightly away from the frontier.
- Cross-state variation in estimated technical efficiency:
  - Delaware found to be quite close to the production frontier on average.
  - Oklahoma, West Virginia, and Montana found furthest from the frontier.
- Aggregate implication:
  - Staff estimates that if all states with lower-than-average efficiency converged to the average efficiency, average aggregate output per worker would have been about 3 percent higher than its actual level in 2010.

### Determinants of inefficiency and state-level TFP growth
- SFA with conditional inefficiency effects (Battese and Coelli, 1995) links state inefficiencies to observable factors; estimated results show:
  - Greater human capital (proxied by years of schooling, especially elementary and tertiary educational attainment) is associated with smaller inefficiencies.
  - A greater share of total R&D spending in GDP tends to lower inefficiencies and potentially contributes positively to technological progress.
  - States with larger financial sectors tend to be more efficient, possibly reflecting the role of financial intermediation in resource allocation.
- Magnitudes and illustrative estimates:
  - A one year increase in average years of schooling is associated with about 10 percent decrease in technical inefficiency.
- Panel-data analysis of TFP growth (fixed-effects with three-year averages and a mean group model allowing heterogeneity and cross-sectional dependence) confirms that investment in human capital and R&D/innovation are important factors associated with TFP growth.

### Human capital and TFP (cross-state facts)
- Average years of schooling: range from below 12.5 years in Mississippi and West Virginia to over 14.5 years in the District of Columbia and Massachusetts.
- Conditional-inefficiency results:
  - Schooling coefficient −0.12*** (mean inefficiency estimates), indicating higher schooling is associated with lower technical inefficiency.
  - Tertiary educational attainment coefficient −0.01***; Elementary educational attainment coefficient −0.01*** (reported in conditional inefficiency effects).

### R&D, innovation, and TFP (facts and findings)
- Total R&D expenditure in the U.S.: about 2½ percent of GDP per year in 1996–2010.
  - About three-quarters of total R&D performed by business sector.
  - Business R&D declined as share of GDP in 2000–05 and was at 2 percent of GDP in 2012 close to its 2000 peak.
- State extremes:
  - New Mexico: highest total R&D at 7.5 percent of GDP and government R&D at 4.4 percent of GDP.
  - Michigan: highest business R&D at 4.2 percent of GDP.
- Empirical findings:
  - Some support for a positive impact of both business R&D expenditure and, more importantly, of government R&D spending on TFP growth.
  - Including interaction terms for both types of R&D expenditure makes their combined effects statistically insignificant.
  - Examples from reported specifications: Business R&D expenditure 0.36**, Total R&D expenditure 0.40*, Government R&D expenditure −0.52*** in one specification and 0.61*** in another.

### Sectoral patterns and slowdown
- The slowdown in TFP has not been confined to IT-producing or IT-intensive user states; estimated pace of technological progress remained broadly unchanged since mid-1990s.
- Evidence points to increasing inefficiencies and slower catching-up across states, which may be associated with divergence in educational attainment and R&D spending.
- Dummy-variable and interaction tests indicate a post-2005 deceleration in TFP growth (Post-2005 dummy coefficients reported as statistically significant across many specifications, e.g., Post-2005 dummy 1.70*** in several models).

### Policy implications and recommendations
- While empirical associations are not definitive causal claims, the findings suggest:
  - Policies that promote investment in human capital may reduce technical inefficiencies and help boost aggregate TFP growth.
  - Policies that support innovation, including both business and government R&D, could raise aggregate TFP, though interactions between R&D types warrant careful assessment because combined effects may be statistically insignificant.
- The analysis highlights scope for policies to tackle inefficiencies and help boost productivity across states.

### Data sources, specialization indices, and model notes
- Output: Gross domestic product by state in chained (2005) dollars, private industries, from the BEA (NAICS series spliced with SIC-based series where noted).
- Labor input: Employment in the private sector constructed as sum of farm employment and private nonfarm employment from the BEA (NAICS spliced with SIC where noted).
- Capital input: Net private capital stock by state in chained 2005 dollars from Yamarik (2013) with extension for 2008–2010 by the author.
- Labor and capital shares: labor share computed as ratio of private sector compensation of employees to private sector output minus ‘ambiguous labor income’; three-year moving average used.
- Specialization indices:
  - IT-producing: share of “Computer and electronic product manufacturing” (NAICS 334) in private industries relative to U.S. (index averaged over 2002–04).
  - ICT-producing: composite “Information, Communication, and Technology” sector relative share (synthetic index construction analogous to IT-producing).
  - IT-intensive user states: share of sectors identified in Jorgenson, Ho, and Samuels (2010, Table 1) relative to U.S.; reference year 2005.
- Educational attainment: average years of schooling from Turner et al. (2006) extended with OECD Regional Database; tertiary assigned 20.52 years for attainment series.
- Innovation indicators (R&D): OECD Regional Database and original NSF/SRS data covering 1990–2010/2011 (R&D expenditure by sector, R&D personnel, employment in high-tech sectors, patent applications, ownership).
- Additional state indicators: infrastructure spending, tax burden, own-source revenue, government size score, poverty rate, financial sector share (sources noted in Appendix 1).
- Key empirical model notes:
  - Models estimated include fixed-effects with five-year averages, dynamic panel data models using system-GMM, time-varying inefficiency stochastic-frontier models with convergence, and conditional inefficiency specifications.
  - Stochastic frontier frontier estimates report plausible output elasticities: Log labor ~0.57–0.63***; Log capital ~0.45–0.49*** across subperiods.
  - Conditional inefficiency regressions show statistically significant associations of schooling and R&D with inefficiency measures and confirm role of Great Recession dummy (GR dummy positive and significant in inefficiency equations).

*Source: IMF staff estimates, chapter "1. Deceleration in Average TFP Growth, 2005–2010 vs. 1996–2004" (PDF).*

### 1. Deceleration in Average TFP Growth, 2005–2010 vs. 1996–2004

### 1. Deceleration in Average TFP Growth, 2005–2010 vs. 1996–2004

### Productivity slowdown — overview
- U.S. total factor productivity (TFP) growth slowed since the mid-2000s: after growing at about 1¾ percent per year during 1996–2004, the average TFP growth rate has halved since 2005.
- The slowdown appears to go beyond the effects of the Great Recession and is central to assessing future potential growth.
- Explanations surveyed in the chapter include:
  - Reduced ability to benefit from technological advances (Gordon, 2012 and 2013).
  - Return to more normal rates after an extraordinary IT-led decade (Fernald, 2014).
  - Continued potential for technology-driven gains, especially in services or from ongoing IT innovations (Baily, Manyika, and Gupta, 2013; Byrne, Oliner, and Sichel, 2013; Bernanke, 2013).
- TFP reflects more than technological innovation and depends on factors affecting the efficiency of combining labor and capital, including competition, administrative burden, infrastructure, and access to finance.

### Empirical strategy (three stages)
- Estimate state-level TFP growth using a standard Cobb-Douglas production function with time-varying and state-specific labor shares.
- Use stochastic frontier analysis (SFA) to decompose TFP growth into common technological trends and state-specific technical efficiency.
- Analyze determinants of TFP growth across U.S. states using panel data models relating TFP growth to human capital, innovation (R&D), infrastructure, taxation, and regulatory framework.

### Caveats on measurement
- No direct state-level capital stock or capital services data; capital allocated across states using national industry capital shares (Garofalo and Yamarik (2002); Yamarik (2013)), assuming identical capital-to-output ratios within industries across states.
- Labor input is private-sector employment (not hours), so changes in hours per worker enter TFP estimates.
- Two robustness checks: GDP-weighted average of state TFP growth closely matches national aggregate TFP estimates; strong correlation with Caliendo and others (2014) state-level TFP.

### Key empirical questions addressed
- Has the TFP growth slowdown been similar across U.S. states?
- To what extent can aggregate TFP benefit from convergence of low-productivity states to high-productivity ones (frontier shifts vs. closing frontier gaps)?
- Which state-level factors and policies are associated with TFP growth, exploiting cross-state variation?

### Summary finding relevant for policy
- Policies promoting investment in human capital and research and development (R&D) are highlighted as especially beneficial for TFP growth.

### Final high-level finding
- The slowdown in U.S. TFP growth from the mid-2000s has been widespread across states and owes more to declining efficiency in combining factors of production than to a diminishing pace of technological progress.

---

### Cross-state variation and IT specialization
- For the U.S. as a whole, TFP growth slowed about 1¾ percentage points on average in 2005–2010 relative to 1996–2004.
- State-level deceleration ranged:
  - Decline of over 3 percentage points in New Mexico and South Dakota.
  - A relatively modest (below 1 percent) decline in ten states.
  - Oregon was an outlier with sustained high TFP growth over the whole period.
- Little evidence that TFP slowdown was significantly larger in states most specialized in IT production or intensive in IT usage.
  - IT production is more geographically concentrated than IT usage across states.
  - Statistical tests show no significant additional TFP deceleration for IT-producing or IT-intensive states.
  - Example: New Mexico and Oregon had similar degrees of IT-production specialization and IT-intensity but very different productivity outcomes.

---

### SFA decomposition: technological progress versus efficiency
- Framework: SFA assumes inefficiencies create a wedge between actual production and the production frontier; technological progress shifts the frontier; improvements in technical efficiency move states closer to the frontier.
- Rolling-window SFA estimates (1995–2010) indicate:
  - Production frontier has been shifting up at a relatively constant rate of about 1 percent per year.
  - Estimated technical efficiency declined over time; the average state moved slightly away from the frontier.
- Large cross-state variation in estimated technical efficiency:
  - Delaware found to be quite close to the production frontier on average.
  - Oklahoma, West Virginia, and Montana found furthest from the frontier.
- Aggregate implication:
  - Staff estimates that if all states with lower-than-average efficiency converged to the average efficiency, average aggregate output per worker would have been about 3 percent higher than its actual level in 2010.

---

### Determinants of inefficiency and state-level TFP growth
- SFA with conditional inefficiency effects (Battese and Coelli, 1995) links state inefficiencies to observable factors; estimated results show:
  - Greater human capital (proxied by years of schooling, especially elementary and tertiary educational attainment) is associated with smaller inefficiencies.
  - A greater share of total R&D spending in GDP tends to lower inefficiencies and potentially contributes positively to technological progress.
  - States with larger financial sectors tend to be more efficient, possibly reflecting the role of financial intermediation in resource allocation.
- Magnitudes and illustrative estimates:
  - A one year increase in average years of schooling is associated with about 10 percent decrease in technical inefficiency.
- Panel-data analysis of TFP growth (fixed-effects with three-year averages and a mean group model allowing heterogeneity and cross-sectional dependence) confirms that investment in human capital and R&D/innovation are important factors associated with TFP growth (see Appendix 2, Table A5 for details).

---

*Source: IMF staff estimates, chapter "1. Deceleration in Average TFP Growth, 2005–2010 vs. 1996–2004" (PDF).*

### 13.8 in 2010 (albeit slowing in 2004–06), but substantial variation remains across states:

### _wp15116 - 13.8 in 2010 (albeit slowing in 2004–06), but substantial variation remains across states:

### Human capital and TFP
- Average years of schooling: range from below 12.5 years in Mississippi and West Virginia to over 14.5 years in the District of Columbia and Massachusetts.
- The study finds a strong positive relation between the indicator of human capital and TFP growth.
- Stochastic-frontier / conditional-inefficiency results:
  - Mean inefficiency estimates: Schooling coefficient −0.12*** (z-statistic reported), indicating higher schooling is associated with lower technical inefficiency.
  - Tertiary educational attainment coefficient −0.01***; Elementary educational attainment coefficient −0.01*** (reported in conditional inefficiency effects).

### R&D, innovation, and TFP
- Total R&D expenditure in the U.S.: about 2½ percent of GDP per year in 1996–2010.
  - About three-quarters of total R&D performed by business sector.
  - Business R&D declined as share of GDP in 2000–05 and was at 2 percent of GDP in 2012 close to its 2000 peak.
- State extremes:
  - New Mexico: highest total R&D at 7.5 percent of GDP and government R&D at 4.4 percent of GDP.
  - Michigan: highest business R&D at 4.2 percent of GDP.
- Empirical findings:
  - Some support for a positive impact of both business R&D expenditure and, more importantly, of government R&D spending on TFP growth.
  - Including interaction terms for both types of R&D expenditure makes their combined effects statistically insignificant.
  - Table A5 reports business R&D and total R&D coefficients positive in some specifications (e.g., Business R&D expenditure 0.36**, Total R&D expenditure 0.40*), while government R&D shows mixed signs across specifications (e.g., Government R&D expenditure −0.52*** in one specification and 0.61*** in another).

### Sectoral patterns and slowdown
- The slowdown in TFP has not been confined to IT-producing or IT-intensive user states; estimated pace of technological progress remained broadly unchanged since mid-1990s.
- Evidence points to increasing inefficiencies and slower catching-up across states, which may be associated with divergence in educational attainment and R&D spending.
- Dummy-variable and interaction tests (Appendix 2, Tables A1–A2) indicate a post-2005 deceleration in TFP growth (Post-2005 dummy coefficients reported as statistically significant across many specifications, e.g., Post-2005 dummy 1.70*** in several models).

### Policy implications and recommendations
- While empirical associations are not definitive causal claims, the findings suggest:
  - Policies that promote investment in human capital may reduce technical inefficiencies and help boost aggregate TFP growth.
  - Policies that support innovation, including both business and government R&D, could raise aggregate TFP, though interactions between R&D types warrant careful assessment because combined effects may be statistically insignificant.
- The analysis highlights scope for policies to tackle inefficiencies and help boost productivity across states.

### Data sources and measurement notes
- Output: Gross domestic product by state in chained (2005) dollars, private industries, from the BEA (NAICS series spliced with SIC-based series where noted).
- Labor input: Employment in the private sector constructed as sum of farm employment and private nonfarm employment from the BEA (NAICS spliced with SIC where noted).
- Capital input: Net private capital stock by state in chained 2005 dollars from Yamarik (2013) with extension for 2008–2010 by the author.
- Labor and capital shares: labor share computed as ratio of private sector compensation of employees to private sector output minus ‘ambiguous labor income’; three-year moving average used.
- Specialization indices:
  - IT-producing: share of “Computer and electronic product manufacturing” (NAICS 334) in private industries relative to U.S. (index averaged over 2002–04).
  - ICT-producing: composite “Information, Communication, and Technology” sector relative share (synthetic index construction analogous to IT-producing).
  - IT-intensive user states: share of sectors identified in Jorgenson, Ho, and Samuels (2010, Table 1) relative to U.S.; reference year 2005.
- Educational attainment: average years of schooling from Turner et al. (2006) extended with OECD Regional Database; tertiary assigned 20.52 years for attainment series.
- Innovation indicators (R&D): OECD Regional Database and original NSF/SRS data covering 1990–2010/2011 (R&D expenditure by sector, R&D personnel, employment in high-tech sectors, patent applications, ownership).
- Additional state indicators: infrastructure spending, tax burden, own-source revenue, government size score, poverty rate, financial sector share (sources noted in Appendix 1).

### Key empirical model notes
- Models estimated include fixed-effects with five-year averages, dynamic panel data models using system-GMM, time-varying inefficiency stochastic-frontier models with convergence, and conditional inefficiency specifications (see Appendix 2, Tables A3–A5).
- Stochastic frontier (time-varying inefficiency) frontier estimates report plausible output elasticities: Log labor ~0.57–0.63***; Log capital ~0.45–0.49*** across subperiods.
- Conditional inefficiency regressions show statistically significant associations of schooling and R&D with inefficiency measures and confirm role of Great Recession dummy (GR dummy positive and significant in inefficiency equations).

*Source: IMF staff estimates and empirical results presented in the content unit.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15116.pdf_