## 2.1 Aggregate productivity

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### Aggregate patterns since 2000
- Productivity measure: real output per hours worked (labor productivity) for the non-farm business sector.
- Two main patterns observed:
  - A slowdown of productivity growth since around 2005:
    - Productivity growth from 2005 to 2019 was 1.5 percent.
    - Post-war (1950-2009) average productivity growth was 2.2 percent.
    - Average productivity growth from 1996 to 2004 was 3.2 percent.
  - Counter-cyclicality of productivity:
    - After the Great Financial Crisis in 2009 and the pandemic recession in 2020, productivity rose markedly and then returned to trend.
    - These cyclical rises have been linked to "excess layoffs" and a cleansing effect of recessions (low productivity firms dropping out).
- Levels and recent growth:
  - By 2024Q1, productivity is 6.5 percent above its 2019Q4 level.
  - Productivity is at its 2005 to 2019 trend as of the latest observation.
  - Average productivity growth since 2019Q4 was about 1.6 percent, close to the 2005Q1–2019Q4 average of 1.5 percent and the 2015Q1–2019Q4 average of 1.6 percent.

### Between-within decomposition (aggregate change since 2019Q4)
- Decomposition separates contributions to aggregate productivity change into between (sectoral composition) effects and within (industry-specific productivity growth) effects.
- Key observations:
  - The sudden lockdown in 2020Q2 produced a sharp compositional increase in aggregate productivity as low-productivity, contact-intensive services were shut down.
  - The between-component contribution waned as services reopened; within-industry productivity gains then took hold.
  - Within-industry productivity:
    - Increased until late 2021 (consistent with a cleansing effect).
    - Declined in 2022.
    - Grew consistently since late 2022 through 2023Q4.
    - Ended 2023 at a level more than 5 percent higher than before the pandemic.
- Historical comparison:
  - Over 2007Q4 to 2019Q4, the between component played a more important role, dragging aggregate productivity down by 17 percent of the total productivity increase over that period.

### Sectoral productivity patterns (2019Q4–2023Q4 vs 2015Q1–2019Q4)
- Cross-sector findings:
  - Productivity growth since the pandemic has been most pronounced in high-skilled services and low or negative in contact-intensive and lower-skilled service sectors.
  - Information and Professional Services combined contributed over 70 percent of overall productivity growth from end-2019 to end-2023.
  - Construction experienced worsening productivity.
- Cross-sectional stability:
  - Sectors that saw faster productivity growth since the pandemic were also those with faster productivity growth prior to the pandemic — sectoral pattern remained largely unchanged despite large compositional shifts.

### Salient drivers
- Telework
  - Telework is a major structural change after the pandemic, with implications for work, housing, mobility, amenities, and wage bargaining.
  - Preliminary cross-sectional observation:
    - Among industries with the fastest productivity growth since the pandemic, a majority (8 out of the top 10) are those with predominantly teleworkable jobs (using the Gordon and Sayed (2022) teleworkability classification).
  - Formal analysis controls for other drivers in regressions.
- Digitalization (investment in IPP/ICT)
  - Overall investment declined since the mid-2000s, but investment in intellectual property products (IPP) rose since 2015.
  - IPP investment growth accelerated in 2020 and was maintained through the pandemic and post-pandemic period.
  - IPP includes software and R&D; IPP investment facilitates workplace digitization and is recognized as important for productivity, particularly in modern services.
  - Industry-level real investment rates for software capital, ICT capital, and IPP capital are constructed; the IPP dataset is available at annual frequency with latest data in 2022.
- Labor market churn
  - Pandemic and post-pandemic years saw increased churn: quits rates, vacancy rates (as share of employment or ratio to unemployment), hiring, business applications, and firm births.
  - Historically, higher churn correlates with higher productivity due to upgraded employer-employee matches and higher wages for job switchers; higher churn can also spur capital investment.
  - Documented broad-based increase in job-to-job quits across industries.
  - Time-series variation in job-to-job churn has been correlated with productivity growth over time.
- New business formation
  - Sharp increase in business applications and start-up rates since late 2021, concentrated in IT-intensive sectors.
  - This increase in firm formation correlates with overall productivity growth over time.

### Empirical analysis: data, specifications, and main results
- Data and construction
  - Real value added per hour: BEA GDP by industry combined with BLS hours worked by industry.
  - Digitalization measures: BEA’s Detailed Data for Fixed Assets and Consumer Durable Goods.
  - Constructed real investment rates for software capital, ICT capital, and IPP capital; annual frequency, latest data 2022.
  - Labor churn measures: JOLTS vacancy rate and quits rate (BLS); job-to-job separation/quits rate from Longitudinal Employer-Household Dynamics (Census).
  - Firm churn: business applications from Business Formation Statistics (Census); measured relative to sector real value added.
  - Teleworkability: Dingel and Neiman (2020) index (0 to 100), time-invariant, aggregated to sector level using 2019 real output weights.
  - Analysis aggregated to 14 sectors (roughly NAICS 2) and drops Agriculture, Mining, and Public Administration.
- Regression specification
  - Panel regressions estimated: Y_it = α_i + τ_t + X'_{i,t-k} β + ε_{i,t}
    - Y_i,t: productivity growth (or investment rate).
    - X: explanatory variables (teleworkability, investment rates, labor churn, firm churn).
    - Lag structure: variables entered with a lag of two years (k = 2).
    - Industry fixed effects (α_i) and time fixed effects (τ_t) included in various specifications.
  - Annual sample: 2011 to 2023.

### Main regression findings and magnitudes
- Key explanatory variables (lagged two years): vacancy rate, quits rate (JOLTS), job-to-job quits rate (Census), Firm Apps/VA, IPP/VA.
- Consistent results:
  - IPP investment rate (IPP/VA) and labor churn measures are most consistently related to productivity growth.
  - Pooled regressions: investment rates and labor churn measures generally significant at least at the five percent level.
  - Panel regressions with time fixed effects: similar findings; industries with more pronounced labor churn experienced faster productivity growth conditional on IPP investment rates.
  - Industry fixed effects alone: labor churn variables significantly related to productivity growth.
  - Adding both industry and time fixed effects generally weakens significance, except for job-to-job quits rates.
- Selected coefficient estimates (Table 1 and related tables; standard errors in parentheses):
  - Vacancy Rate: 0.533*** (0.166) in one pooled specification; other specifications report 1.020*** (0.244) and 0.401** (0.167) among examples.
  - Quits Rate: 0.968** (0.431) in one specification; other examples 1.093*** (0.392), 0.902** (0.425).
  - J2J Quits Rate: 0.410*** (0.152) in one column; 1.132*** (0.349) in another; other examples 0.380** (0.150), 0.948*** (0.288), 1.624* (0.753).
  - IPP/VA: 0.233*** (0.040) in column (1); similar magnitudes 0.246*** (0.040), 0.259*** (0.039); other tables report 0.247*** (0.044), 0.267*** (0.044).
  - Firm Apps/VA: coefficients generally small and statistically insignificant (examples: 0.005 (0.012); 0.002 (0.012)).
- Economic magnitudes:
  - Using time series variation (column 11), a one percentage point increase in the job-to-job quits rate is associated with a 1.1 percentage point increase in productivity growth.
  - The (unweighted) sector average job-to-job quits rate was 5.5 percent in 2019 and increased to 6 percent in 2022; the associated increase in the fitted value of productivity growth is 0.55 percentage points.
- Robustness:
  - Adding non-IPP investment leaves IPP coefficients generally stable while non-IPP investment coefficients are insignificant — suggesting IPP (digital capital and innovation) matters more for productivity growth than other capital types.
  - ICT investment results (Tables 3 and 5) show similar positive associations for ICT/VA: examples 0.289*** (0.043), 0.318*** (0.048), 0.324*** (0.045).
  - Non-ICT/VA or Non-IPP/VA coefficients often negative or insignificant (examples: -0.055 (0.039); -0.070* (0.037); -0.077** (0.037)).

### Teleworkability, IPP, and labor churn (selected statistics)
- Teleworkability index descriptive statistics:
  - The average teleworkability index in the sample is 30, the standard deviation is 23.
  - Regression coefficient in column (1): 0.023** (0.012). Interpretation: an increase in the index by one unit is associated with a 0.023 percentage point increase in the annual productivity growth rate.
  - A one standard deviation increase in the teleworkability index is associated with an about 0.5 percentage point increase in the annual productivity growth rate.
- Joint interpretation:
  - The Dingel-Neiman teleworkability index is positively related to productivity growth in simple specifications, and the positive association has not changed since the start of the pandemic.
  - Once real investment rates in IPP capital, labor churn, and firm churn are included, the teleworkability index is only weakly associated with productivity growth — teleworkable industries tend to have higher productivity growth largely because of other attributes (e.g., higher IPP investment and labor churn).
  - Labor churn was particularly pronounced in industries amenable to telework and/or with high rates of digital investment.

### Cross-sectional decomposition of productivity growth
- Fitted contribution of explanatory variable X for industry i:
  - ∆ˆg_X_A,i ≡ β_X [ ̄X_i − ̄ ̄X ], where averages use 2018-2021.
- Cross-sectional findings:
  - Strong productivity growth in the information sector, relative to the cross-industry average, is almost entirely accounted for by the higher rate of IPP investment in the IT sector; labor churn contributes negatively to this sector.
  - Job-to-job quits rate is important to account for stronger productivity growth in professional services, entertainment and recreation, and retail trade relative to the cross-sectional average.
  - The cross-sectional regression can account well for productivity growth in professional services, wholesale trade, and real estate and rental, but performs poorly for manufacturing and construction (large residuals).

### Time-series decomposition and implied fits
- Time-delta for churn-driven productivity change:
  - ∆ˆg_churn_A,i,t ≡ β_churn [ churn_i,t − churn_i,t−1 ] with β_churn from panel estimates.
- Aggregate implied change constructed as weighted average using previous-year output shares.
- Time-series findings:
  - The fitted value using job-to-job quits mirrors realized productivity with varying magnitudes.
  - The large increase in productivity in 2020 and 2021 is largely not attributable to job-to-job quits; sectoral composition shifts and other factors played bigger roles during the height of the pandemic and early re-opening.
  - Labor churn enters with a lag of 2 years, so sharp changes in 2020 are not immediately reflected.
  - Small positive contribution from labor churn to productivity in 2020–2021 due to a hot labor market and elevated churn prior to the pandemic.
  - Fall in productivity in 2022 is consistent with the fall in churn in 2020; contribution from labor churn in 2023 is sizeable, consistent with increases in job-to-job quits above pre-pandemic levels by 2021.
  - Overall, the increased rate of job-to-job reallocation since 2020 can explain more than 80 percent of the cumulative increase in labor productivity from 2020 to 2023.
  - Compared to labor churn measures, the rate of IPP investment explains less of the time-series variation than it does in the cross-section.
  - The burst in business formation, while concentrated in industries with higher productivity growth on average, does not (yet) appear to drive recent productivity growth within industries in the available short time series.

### Additional empirical notes and selected sample statistics
- The mean IPP investment rate over sectors is about 4 percent in the sample, with a standard deviation of 5.8 percent.
- A one standard deviation increase in the IPP investment rate would therefore be associated with a 1.45 increase in productivity growth (using the reported coefficient magnitudes).
- Industry average growth rate of business applications: 15 percent for 2020–2021 vs 2.9 percent for 2015–2019 (unweighted industry averages).
- Cross-sectional results for business formation:
  - For 2020-2023, Business Apps 20-21: coefficients 0.182** (0.080), 0.187** (0.074), 0.169** (0.072) in selected specifications.
  - Interpretation: a one percentage point increase in the average growth rate of business applications in 2020–2021 is associated with a 0.17 to 0.18 percentage point increase in annual productivity growth.

### Conclusion and implications
- Rising productivity since end-2022 has provided considerable tailwind to US GDP growth during a period of high interest rates.
- Recent productivity increases are concentrated in industries that had relatively strong productivity growth before the pandemic: industries with higher rates of IP investment and amenable to telework (notably Information Technology and Professional Services).
- Both IP investment and transition to telework accelerated further since the pandemic, lifting productivity after an initial volatile adjustment period.
- A new reinforcing trend has been the sharply increased rate of worker churn across jobs; worker churn has had a more positive effect on productivity across a broader set of industries than IP investment, explaining a large share of aggregate productivity increase in recent years.
- Increased firm churn (surge in business formation) has also been concentrated in industries with higher productivity growth, though its within-industry impact is not yet notable given the short time series.
- By the end of the sample, labor productivity for the non-farm business sector has merely returned to the pre-pandemic trend.
- Without high rates of IP investment and labor reallocation, productivity would have drifted below trend in recent years (as observed in other advanced economies, e.g., the euro area).
- Sustainability of the higher productivity growth rate is uncertain:
  - Downside risks: IPP investment may slow; rates of worker churn have already normalized to a great extent.
  - Upside possibilities: new technologies (AI) and continued high rates of new business formation may provide a new impulse for productivity growth, especially once interest rates come down and financial conditions for start-ups become more favorable.

_Extracted from "2.1 Aggregate productivity" and adjacent sections of the provided IMF PDF chapter._

### 2.1  Aggregate productivity

### 2.1 Aggregate productivity

### Aggregate patterns since 2000
- Productivity measure: real output per hours worked (labor productivity) for the non-farm business sector.
- Two main patterns observed:
  - A slowdown of productivity growth since around 2005.
    - Productivity growth from 2005 to 2019 was 1.5 percent.
    - Post-war (1950-2009) average productivity growth was 2.2 percent.
    - By contrast, average productivity growth from 1996 to 2004 was 3.2 percent.
  - Counter-cyclicality of productivity:
    - After the Great Financial Crisis in 2009 and the pandemic recession in 2020, productivity rose markedly and then returned to trend.
    - These cyclical rises have been linked to "excess layoffs" and a cleansing effect of recessions (low productivity firms dropping out).
- Levels and recent growth:
  - By 2024Q1, productivity is 6.5 percent above its 2019Q4 level.
  - Productivity is at its 2005 to 2019 trend as of the latest observation.
  - Average productivity growth since 2019Q4 was about 1.6 percent, close to the 2005Q1–2019Q4 average of 1.5 percent and the 2015Q1–2019Q4 average of 1.6 percent.

### Between-within decomposition (aggregate change since 2019Q4)
- Decomposition separates contributions to aggregate productivity change into:
  - Between (sectoral composition) effects.
  - Within (industry-specific productivity growth) effects.
- Key observations:
  - The sudden lockdown in 2020Q2 produced a sharp compositional increase in aggregate productivity as low-productivity, contact-intensive services were shut down.
  - The between-component contribution waned as services reopened; within-industry productivity gains then took hold.
  - Within-industry productivity:
    - Increased until late 2021 (consistent with a cleansing effect).
    - Declined in 2022.
    - Grew consistently since late 2022 through 2023Q4.
    - Ended 2023 at a level more than 5 percent higher than before the pandemic.
- Historical comparison:
  - Over 2007Q4 to 2019Q4, the between component played a more important role, dragging aggregate productivity down by 17 percent of the total productivity increase over that period.

### Sectoral productivity patterns (2019Q4–2023Q4 vs 2015Q1–2019Q4)
- Cross-sector findings:
  - Productivity growth since the pandemic has been most pronounced in high-skilled services and low or negative in contact-intensive and lower-skilled service sectors.
  - Information and Professional Services combined contributed over 70 percent of overall productivity growth from end-2019 to end-2023.
  - Construction experienced worsening productivity.
- Cross-sectional stability:
  - Sectors that saw faster productivity growth since the pandemic were also those with faster productivity growth prior to the pandemic — sectoral pattern remained largely unchanged despite large compositional shifts.

### Salient drivers

- Telework
  - Telework is a major structural change after the pandemic, with implications for work, housing, mobility, amenities, and wage bargaining.
  - Preliminary cross-sectional observation:
    - Among industries with the fastest productivity growth since the pandemic, a majority (8 out of the top 10) are those with predominantly teleworkable jobs (using the Gordon and Sayed (2022) teleworkability classification).
  - A formal analysis follows in later sections controlling for other drivers.

- Digitalization (investment in IPP/ICT)
  - Overall investment declined since the mid-2000s, but investment in intellectual property products (IPP) rose since 2015.
  - IPP investment growth accelerated in 2020 and was maintained through the pandemic and post-pandemic period.
  - IPP includes software and R&D; IPP investment facilitates workplace digitization and is recognized as important for productivity, particularly in modern services.
  - Industry-level real investment rates for software capital, ICT capital, and IPP capital are constructed; the IPP dataset is available at annual frequency with latest data in 2022.

- Labor market churn
  - Pandemic and post-pandemic years saw increased churn: quits rates, vacancy rates (as share of employment or ratio to unemployment), hiring, business applications, and firm births.
  - Historically, higher churn correlates with higher productivity due to upgraded employer-employee matches and higher wages for job switchers; higher churn can also spur capital investment.
  - Documented broad-based increase in job-to-job quits across industries.
  - Time-series variation in job-to-job churn has been correlated with productivity growth over time.

- New business formation
  - Sharp increase in business applications and start-up rates since late 2021, concentrated in IT-intensive sectors.
  - This increase in firm formation correlates with overall productivity growth over time.

### Empirical analysis: data, specifications, and main results

- Data and construction
  - Real value added per hour: BEA GDP by industry combined with BLS hours worked by industry.
  - Digitalization measures: BEA’s Detailed Data for Fixed Assets and Consumer Durable Goods.
  - Constructed real investment rates for software capital, ICT capital, and IPP capital; annual frequency, latest data 2022.
  - Labor churn measures: JOLTS vacancy rate and quits rate (BLS); job-to-job separation/quits rate from Longitudinal Employer-Household Dynamics (Census).
  - Firm churn: business applications from Business Formation Statistics (Census); measured relative to sector real value added.
  - Teleworkability: Dingel and Neiman (2020) index (0 to 100), time-invariant, aggregated to sector level using 2019 real output weights.
  - Analysis aggregated to 14 sectors (roughly NAICS 2) and drops Agriculture, Mining, and Public Administration.

- Regression specification
  - Panel regressions estimated: Y_it = α_i + τ_t + X'_{i,t-k} β + ε_{i,t}
    - Y_i,t: productivity growth (or investment rate).
    - X: explanatory variables (teleworkability, investment rates, labor churn, firm churn).
    - Lag structure: variables entered with a lag of two years (k = 2).
    - Industry fixed effects (α_i) and time fixed effects (τ_t) included in various specifications.
  - Annual sample: 2011 to 2023.

- Main regression findings (Table 1 highlights)
  - Explanatory variables: vacancy rate, quits rate (JOLTS), job-to-job quits rate (Census), firm applications relative to real value added (Firm Apps/VA), real IPP investment as share of real value added (IPP/VA); all lagged by two years.
  - IPP investment rate (IPP/VA) and labor churn measures are most consistently related to productivity growth.
  - Pooled regressions (columns 1, 5, 9): investment rates and labor churn measures are generally significant at least at the five percent level.
  - Panel regressions with time fixed effects (columns 2, 6, 10): similar findings; industries with more pronounced labor churn experienced faster productivity growth conditional on IPP investment rates.
  - Specifications with industry fixed effects alone (columns 3, 7, 11): labor churn variables are significantly related to productivity growth.
  - Adding both industry and time fixed effects generally weakens significance, except for job-to-job quits rates.
  - Selected coefficient estimates (from Table 1; standard errors in parentheses):
    - Vacancy Rate: 0.533*** (0.166) in column (1).
    - Quits Rate: 0.968** (0.431) in column (2) or related specifications.
    - J2J Quits Rate: 0.410*** (0.152) in column (3) and 1.132*** (0.349) in another specification.
    - IPP/VA: 0.233*** (0.040) in column (1); similar magnitudes in related columns (e.g., 0.246*** (0.040) and 0.259*** (0.039) in other columns).
    - Firm Apps/VA: coefficients generally small and statistically insignificant in these specifications.
  - Economic magnitudes:
    - Using time series variation (column 11), a one percentage point increase in the job-to-job quits rate is associated with a 1.1 percentage point increase in productivity growth.
    - The (unweighted) sector average job-to-job quits rate was 5.5 percent in 2019 and increased to 6 percent in 2022; the associated increase in the fitted value of productivity growth is 0.55 percentage points.
  - Robustness:
    - Adding non-IPP investment leaves IPP coefficients generally stable while non-IPP investment coefficients are insignificant — suggesting IPP (digital capital and innovation) matters more for productivity growth than other capital types.
    - Table 3 (appendix) shows corresponding results with ICT investment; Table 4 and Table 5 (appendix) report related robustness checks.

- Sample and estimation notes
  - Annual sample covers 2011 to 2023.
  - Explanatory variables entered with a lag of two years to capture delayed impacts.
  - Regressions performed at NAICS 2 industry classification aggregated to the study’s sector scheme; Agriculture, Mining, and Public Administration excluded.

_Italic source attribution: Extracted from "2.1 Aggregate productivity" and adjacent sections of the provided IMF PDF chapter._

### 0.25 percentage point higher productivity growth rate. The mean IPP investment rate over sectors

### wpiea2024124-print-pdf - 0.25 percentage point higher productivity growth rate. The mean IPP investment rate over sectors

### Key empirical findings
- The mean IPP investment rate over sectors is about 4 percent in our sample, with a standard deviation of 5.8 percent.
- A one standard deviation increase in the IPP investment rate would therefore be associated with a 1.45 increase in productivity growth.
- Firm churn, measured by business applications relative to real value added, is not significantly related to productivity growth in the panel regressions covering 2011 to 2023.
- Cross-sectional evidence in Appendix A.2 indicates that increased firm churn since the COVID-19 pandemic could have had a positive impact on productivity growth.
- Prior to the pandemic, the rate of business creation was low and varied little across industries.
- The surge in business application and formation since late 2020 is a clear structural shift and explains why firm churn has become a significant driver of productivity growth across sectors during the time since the pandemic.

### Teleworkability, investment (IPP), and labor churn (panel regression results)
- Data and specification:
  - Dependent variable: productivity growth (g_A).
  - Explanatory variables: Dingel-Neiman teleworkability index (Telework), vacancy rate, quits rate (JOLTS), job-to-job separation rate (J2J Quits Rate; Census), real investment in IPP as share of real value added (IPP/VA), business applications relative to real value added (Firm Apps/VA).
  - All explanatory variables lagged by two years (except Telework).
  - By NAICS2 industry classification. Annual sample, 2011 to 2023.
- Teleworkability index descriptive statistics:
  - The average teleworkability index in the sample is 30, the standard deviation is 23.
  - Regression coefficient in column (1) implies that an increase in the index by one unit is associated with a 0.023 percentage point increase in the annual productivity growth rate.
  - A one standard deviation increase in the teleworkability index is associated with an about 0.5 percentage point increase in the annual productivity growth rate.
- Regression coefficients and significance (selected):
  - Telework coefficient (column 1): 0.023** (standard error 0.012).
  - Telework (other columns): 0.024* (0.012), 0.002 (0.010), 0.020* (0.011), 0.017 (0.011).
  - Telework × post-2019 interactions: coefficients small and not significant (e.g., -0.001 (0.028), 0.020 (0.023), 0.010 (0.023), 0.004 (0.024)).
  - Vacancy Rate: 1.020*** (0.244) in column with vacancy rate.
  - Quits Rate: 1.093*** (0.392).
  - J2J Quits Rate: 0.399*** (0.131).
  - Firm Apps/VA: 0.005 (0.012), 0.002 (0.012), 0.002 (0.012) across specifications.
  - IPP/VA: 0.239*** (0.040), 0.251*** (0.040), 0.247*** (0.040) across specifications.
  - Constants range: -1.077* (0.637), -1.092* (0.655), -3.042*** (0.837), -3.355*** (0.923), -3.147*** (0.859).
- Model diagnostics:
  - Observations: 182 in each specification.
  - R-squared: 0.049, 0.043, 0.245, 0.227, 0.216 across columns (1)–(5).
  - Industry fixed effects included in specifications marked N; Year fixed effects included (Y) in all.
  - Robust standard errors in parentheses. Significance: *** p<0.01, ** p<0.05, * p<0.1.
- Interpretation:
  - The Dingel-Neiman teleworkability index is positively related to productivity growth in simple specifications, and the positive association has not changed since the start of the pandemic.
  - Once real investment rates in IPP capital, labor churn, and firm churn are included, the teleworkability index is only weakly associated with productivity growth.
  - This suggests teleworkable industries tend to have higher productivity growth largely because of other attributes (e.g., higher IPP investment and labor churn).
  - Labor churn was particularly pronounced in industries amenable to telework and/or with high rates of digital investment.

### Contributions to the change in productivity growth — cross-sectional decomposition
- Fitted value for contribution of an explanatory variable X to cross-sectional productivity variation for industry i:
  - ∆ˆg_X_A,i ≡ β_X [ ̄X_i − ̄ ̄X ]
  - ̄X_i is the explanatory variable for industry i averaged over 2018-2021; ̄ ̄X = (1/I) Σ_i ̄X_i is the cross-industry average (averages use 2018-2021 because explanatory variables enter lagged by two years).
  - β_X is the coefficient estimate for explanatory variable X from columns 2, 6, and 10 in Table 1.
- Cross-sectional findings (Figure 8 discussion):
  - The strong productivity growth in the information sector, relative to the cross-industry average, is almost entirely accounted for by the higher rate of IPP investment in the IT sector; labor churn contributes negatively to this sector.
  - The job-to-job quits rate is important to account for stronger productivity growth in professional services, entertainment and recreation, and retail trade relative to the cross-sectional average.
  - The cross-sectional regression can account well for productivity growth in professional services, wholesale trade, and real estate and rental, but performs poorly for manufacturing and construction (large residuals).

### Contributions to the change in productivity growth — time-series decomposition
- Time-delta for churn-driven productivity change for industry i in year t:
  - ∆ˆg_churn_A,i,t ≡ β_churn [ churn_i,t − churn_i,t−1 ]
  - β_churn uses parameter estimates from columns 3, 7, and 11 in Table 1.
- Aggregate implied change:
  - ∆ˆg_A,t = (1/I) Σ_i ω_i,t ∆ˆg_churn_A,i,t, where ω_i,t = y_i,t−1 / Σ_i y_i,t−1 (weights are previous-year output shares).
- Constructed implied productivity growth series:
  - ˆg_A,2020 = g_A,2019 + ∆ˆg_A,2020
  - ˆg_A,t = ˆg_A,t−1 + ∆ˆg_A,t
  - Compare cumulative implied productivity to actual within-sector productivity increases.
- Time-series findings (Figure 9 discussion):
  - The time series variation of the fitted value using job-to-job quits mirrors realized productivity with varying magnitudes.
  - The large increase in productivity in 2020 and 2021 is largely not attributable to job-to-job quits; sectoral composition shifts and other factors played bigger roles during the height of the pandemic and early re-opening.
  - Labor churn enters with a lag of 2 years, so sharp changes in 2020 are not immediately reflected.
  - There is a small positive contribution from labor churn to productivity growth in 2020–2021 due to a hot labor market and elevated churn prior to the pandemic.
  - The fall in productivity in 2022 is consistent with the fall in churn in 2020; the contribution from labor churn in 2023 is sizeable, consistent with increases in job-to-job quits above pre-pandemic levels by 2021.
  - Overall, the increased rate of job-to-job reallocation since 2020 can explain more than 80 percent of the cumulative increase in labor productivity from 2020 to 2023.
  - Compared to labor churn measures, the rate of IPP investment explains less of the time-series variation than it does in the cross-section.
  - The burst in business formation, while concentrated in industries with higher productivity growth on average, does not (yet) appear to drive recent productivity growth within industries in the available short time series.

### Conclusion and implications
- Rising productivity since end-2022 has provided considerable tailwind to US GDP growth during a period of high interest rates.
- Recent productivity increases are concentrated in industries that had relatively strong productivity growth before the pandemic: industries with higher rates of IP investment and amenable to telework (notably Information Technology and Professional Services).
- Both IP investment and transition to telework accelerated further since the pandemic, lifting productivity after an initial volatile adjustment period.
- A new reinforcing trend has been the sharply increased rate of worker churn across jobs; worker churn has had a more positive effect on productivity across a broader set of industries than IP investment, explaining a large share of aggregate productivity increase in recent years.
- Increased firm churn (surge in business formation) has also been concentrated in industries with higher productivity growth, though its within-industry impact is not yet notable given the short time series.
- By the end of the sample, labor productivity for the non-farm business sector has merely returned to the pre-pandemic trend.
- Without high rates of IP investment and labor reallocation, productivity would have drifted below trend in recent years (as observed in other advanced economies, e.g., the euro area).
- Sustainability of the higher productivity growth rate is uncertain:
  - Downside risks: IPP investment may slow; rates of worker churn have already normalized to a great extent.
  - Upside possibilities: new technologies (AI) and continued high rates of new business formation may provide a new impulse for productivity growth, especially once interest rates come down and financial conditions for start-ups become more favorable.

*Source: wpiea2024124-print-pdf - 0.25 percentage point higher productivity growth rate. The mean IPP investment rate over sectors*

### References

### References

### Bibliographic entries
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### Appendix A.1 — Between-within decomposition (methodology and interpretations)
- Definitions and notation:
  - A_t = Y_t / h_t (equation 6)
  - g_A,t+h = A_{t+h} / A_t − 1 (equation 7)
  - s_it = h_it / Σ_i h_it (equation 8)
  - Y_t = Σ_i Y_it (equation 9)
  - A_it = Y_it / h_it (equation 10)
- Decomposition goal: decompose aggregate cumulative productivity growth g_A,t+h into within-sector component g_W,t+h and between-sector component g_B,t+h such that g_A,t+h = g_W,t+h + g_B,t+h.
- Aggregation constructs:
  - A^B_{t+h} = Σ_i A_it s_{i,t+h} (equation 11)
  - ˜g^B_{t+h} = A^B_{t+h} / A_t − 1 (equation 12)
  - A^W_{t+h} = Σ_i s_it A_{i,t+h} (equation 13)
  - ˜g^W_{t+h} = A^W_{t+h} / A_t − 1 (equation 14)
  - Rescaled components:
    - g_B,t+h = ˜g^B_{t+h} / (˜g^B_{t+h} + ˜g^W_{t+h}) * g_A,t+h (equation 15)
    - g_W,t+h = ˜g^W_{t+h} / (˜g^B_{t+h} + ˜g^W_{t+h}) * g_A,t+h (equation 16)
- Sector contribution decomposition:
  - ˜g^A_{i,t+h} = (A_it / A_t) s_it (A_{i,t+h} − A_{i,t}) + (A_it − Ȧ_t)(s_{i,t+h} − s_{i,t}) / A_it (equation 17)
  - g^A_{i,t+h} = ˜g^A_{i,t+h} / (˜g^B_{t+h} + ˜g^W_{t+h}) * g_A,t+h (equation 18)
  - Ȧ_t = (1/I) Σ_i A_it (equation 19)
- Empirical note: Figure 11 (2007Q4 to 2019Q4) shows a substantially negative between effect over the pre-pandemic period; service sectors with below average productivity increased their hours-share, contributing to a negative between component.
- Empirical note: Figure 12 reports sector contributions to aggregate productivity growth for 2019Q4–2023Q4 (percentage points, annualized) across listed sectors (Wholesale; Construction; Transportation and warehousing; Other private services; Education, healthcare, social assistance; Art, Ent, Rec, Accommodation and food; Finance; Manufacturing; Retail; Professional services; Information). Sub-sectors “Mining” and “Utilities” not shown.

### Appendix A.2 — Panel regressions: labor churn, firm churn, and investment (summarized empirical findings)
- General setup (notes):
  - Dependent variable: productivity growth (g_A).
  - Explanatory variables include vacancy rate, quits rate (Source: JOLTS), job-to-job separation rate (J2J Quits Rate; Source: Census), investment shares (ICT/VA, IPP/VA, Non-IPP/VA), business applications relative to real value added (Firm Apps/VA); all lagged by two year unless noted.
  - By NAICS2 industry classification. Annual sample, 2011 to 2023 for main panels; 2020–2022 for some investment-on-churn panels.
  - Robust standard errors reported. Significance: *** p<0.01, ** p<0.05, * p<0.1.
- Selected coefficient estimates from Table 3 (Panel: Labor churn, firm churn, and investment (ICT), 2011-2023):
  - Vacancy Rate: 0.401** (column 1, standard error (0.167)); 0.693*** (column 2, (0.266)); 0.424*** (column 9, (0.136)).
  - Quits Rate: 0.902** (column 1, (0.425)); 0.779** (column 2, (0.391)).
  - J2J Quits Rate: 0.380** (column 1, (0.150)); 0.307** (column 2, (0.137)); 0.948*** (column 9, (0.288)); 1.624* (column 12, (0.753)).
  - ICT/VA: 0.289*** (column 1, (0.043)); 0.295*** (column 5, (0.040)); 0.372** (column 9, (0.165)); 0.548** (column 11, (0.196)).
  - Firm Apps/VA coefficients generally small and statistically insignificant (examples: 0.002 (column 1, (0.011)); -0.032 (column 3, (0.023))).
  - Sample observations: 182 in each reported regression.
- Selected coefficient estimates from Table 4 (IPP & non-IPP), 2011-2023:
  - Vacancy Rate: 0.542*** (column 1, (0.166)); 0.980*** (column 2, (0.263)); 0.494*** (column 3, (0.148)).
  - Quits Rate: 0.984** (column 1, (0.432)); 0.832** (column 2, (0.400)).
  - J2J Quits Rate: 0.413*** (column 1, (0.151)); 0.327** (column 2, (0.138)); 1.080*** (column 9, (0.358)); 1.642** (column 12, (0.740)).
  - IPP/VA: 0.247*** (column 1, (0.044)); 0.267*** (column 2, (0.044)); note some columns report negative or insignificant IPP/VA coefficients in extended specifications (e.g., -0.175 (column 3, (0.630))).
- Selected coefficient estimates from Table 5 (ICT & non-ICT), 2011-2023:
  - Vacancy Rate: 0.381** (column 1, (0.172)); 0.638** (column 2, (0.281)); 0.423** (column 3, (0.155)).
  - Quits Rate: 0.904** (column 1, (0.425)); 0.774** (column 2, (0.391)); 1.279** (column 3, (0.570)).
  - J2J Quits Rate: 0.377** (column 1, (0.150)); 0.298** (column 2, (0.137)); 0.989** (column 3, (0.354)).
  - ICT/VA: 0.318*** (column 1, (0.048)); 0.324*** (column 2, (0.045)); 0.371** (column 3, (0.157)).
  - Non-ICT/VA: coefficients often negative or small (examples: -0.055 (column 1, (0.039)); -0.070* (column 5, (0.037)); -0.077** (column 6, (0.037))).
- Teleworkability (Table 6: Teleworkability, churn, and investment (ICT), 2011-2023):
  - Telework coefficient: 0.023** (column 1, (0.012)); 0.024* (column 2, (0.012)); other columns report smaller or insignificant Telework effects (e.g., 0.003 (column 3, (0.010))).
  - ICT/VA remains significant in several specifications: 0.287*** (column 3, (0.041)); 0.313*** (column 4, (0.039)); 0.310*** (column 5, (0.039)).
  - Individual churn measures significant when included: Vacancy Rate 0.736*** (column 4, (0.247)); Quits Rate 1.009*** (column 4, (0.385)); J2J Quits Rate 0.367*** (column 4, (0.128)).
- Cross-sectional results on business formation and investment (Table 7):
  - For 2015-2019, Business Apps 15-19 coefficients negative or insignificant (example: -0.161 (column 1, (0.100))).
  - For 2020-2023, Business Apps 20-21: 0.182** (column 4, (0.080)); 0.187** (column 5, (0.074)); 0.169** (column 6, (0.072)).
  - IPP/VA 20-22: 0.171*** (column 5, (0.030)); ICT/VA 20-22: 0.172*** (column 6, (0.045)).
  - Industry average growth rate of business applications: 15 percent for 2020–2021 vs 2.9 percent for 2015–2019 (unweighted industry averages).
  - Interpretation provided: a one percentage point increase in the average growth rate of business applications in 2020–2021 is associated with a 0.17 to 0.18 percentage point increase in annual productivity growth.
- Investment-on-churn correlations (Tables 8–9, 2020–2022 sample):
  - Table 8 (IPP/VA): Vacancy Rate coefficients small or negative (example: 0.037 (column 1, (0.032)); -0.143* (column 3, (0.074))). Quits Rate: 0.081 (column 1, (0.119)); -0.359** (column 3, (0.143)).
  - Table 9 (ICT/VA): Vacancy Rate: 0.071 (column 1, (0.047)); -0.138 (column 2, (0.094)); Quits Rate: 0.170 (column 1, (0.147)); -0.406** (column 3, (0.196)).
  - Overall interpretation: IPP/ICT investment was somewhat less intensive in industries with higher quits during the pandemic, but magnitudes are not large and correlations are not consistent across churn measures.

### Appendix A.3 — Figures: sector contributions and aggregate fits (descriptive notes)
- Figure 13: Contributions to average productivity growth from labor churn (quits rate) and investment, by sector. Notes explain plotting: actual average productivity growth (black dot), fitted value for IPP Investment (green bar), fitted value for Quits (orange bar), residual (gray bar). Averages from 2020 to 2023, in deviation from the industry average for 2020 to 2023.
- Figure 14: Contributions to productivity growth from labor churn (vacancy rate) and investment, cross-sectional variation. Same plotting conventions and averaging period as Figure 13.
- Figure 15: Time series of contributions from quits rate. Figure shows for each year the increase in productivity in percent relative to 2019, both actual and fitted value using quits rate. Aggregation uses weighted average of sectors, weights = real value added.
- Figure 16: Time series of contributions from vacancy rate. Figure shows for each year the increase in productivity in percent relative to 2019, both actual and fitted value using vacancy rate. Aggregation uses weighted average of sectors, weights = real value added.

*Post-pandemic Productivity Dynamics in the United States Working Paper No. WP/2024/124*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024124-print-pdf.pdf_