## _wp16162 - 2012. Main findings of this paper suggest a possible link between the recent global

## Source details

**Canonical URL:** [_wp16162 - 2012. Main findings of this paper suggest a possible link between the recent global](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp16162.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp16162.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp16162.pdf.json)

---

### Main findings and themes
- Core finding: Main findings of this paper suggest a possible link between the recent global productivity slowdown and the global trade slowdown.
- Primary mechanisms studied:
  - Possible link between the recent global productivity slowdown and the global trade slowdown via imported inputs.
  - Firm-level imports, Productivity pro-cyclicality, Aggregate TFP growth.
- JEL Classification Numbers: E3, F1, F4, O4
- Keywords: Firm-level imports, Productivity pro-cyclicality, Aggregate TFP growth
- Authors’ E-Mail Addresses: jahn@imf.org, mjchoi@bok.or.kr

### Data, sample, and price deflators
- Main data source: Survey of Business Activities (SBA) from Statistics Korea (KOSTAT).
- Sample period: 2006 to 2012.
- Sample coverage: manufacturing sector limited to 22 industry categories (24 two-digit KSIC codes 10–33 with industries 12 and 18 excluded).
- Panel: unbalanced panel including 36,310 observations of 8,232 firms.
- Firms covered: all firms with 50 or more employees and 300 million won or greater capital.
- Price deflators:
  - Revenue deflated with sector-level Producer Price Index (PPI) compiled by the Bank of Korea.
  - Capital and investment deflated with domestic PPI for capital goods.
  - Domestic and imported inputs deflated by sector-level effective PPI and Imported Inputs Price Index, respectively, constructed following Amiti and Konings (2007).
- Import intensity definition: import ratio = real imported inputs / real total inputs.
- Summary statistics highlights:
  - Importing firms are larger and more productive than non-importing firms.
  - Importers import one third of their input materials on average.
  - Firms that imported continuously have an average import ratio about 0.4.

### Empirical framework and identification
- Production function: Cobb-Douglas with log output as function of log labor (l), log capital (k), log intermediate inputs (m), and TFP.
- TFP decomposition: TFP = component due to imported inputs (function of import ratio f) + residual TFP from other sources.
- Endogeneity and selection concerns:
  - Simultaneity bias between inputs and unobservable productivity shocks.
  - Sample selection bias from exit decisions correlated with productivity.
- Estimation methodology:
  - Olley-Pakes (O-P) semiparametric approach extended to include import intensity as a state variable (following Kasahara and Rodrigue (2008) and Halpern et al. (2011, 2015)).
  - O-P uses investment (and import ratio) as proxies to control for unobservable productivity by inverting the investment function.
- Aggregation and decomposition:
  - Aggregate TFP = output-share-weighted sum of firm-level TFP.
  - Decomposition of aggregate TFP growth into:
    - Change in unweighted average TFP across firms.
    - Change in covariance between firm output share and firm TFP (efficiency/resource allocation term).
  - Covariance further decomposed into intra-firm efficiency (within-firm TFP changes keeping shares constant, includes exit effect) and inter-firm efficiency (resource reallocation across firms, includes entry effect).

### Key production function estimation results (selected)
- OLS, fixed effects, and Olley-Pakes (O-P) comparisons (dependent variable: log(total real revenue); sample: 36,310 observations, 8,232 firms where indicated):
  - Table 1 (Column highlights):
    - Column (1) OLS: Labor 0.467*** (standard error: -0.006); Capital 0.171*** (-0.004); Materials 0.431*** (-0.005); Observations 36,310; R-squared 0.864.
    - Column (3) firm fixed effects: Labor 0.414*** (-0.021); Capital 0.165*** (-0.014); Materials 0.146*** (-0.012); Observations 36,310; R-squared 0.966.
    - Column (4) sector-year and firm fixed effects: Labor 0.410*** (-0.018); Capital 0.095*** (-0.008); Materials 0.139*** (-0.010); Observations 36,310; R-squared 0.973.
  - Table 4 (with imported inputs ratio):
    - Column (1) OLS: Imported inputs ratio 0.233*** (-0.011); Observations 36,310; R-squared 0.866.
    - Column (4) sector-year and firm FE: Imported inputs ratio 0.075*** (-0.010); Observations 36,310; R-squared 0.973.
    - Column (5) Olley-Pakes: Labor 0.092*** (-0.013); Capital 0.264*** (-0.017); Materials 0.389*** (-0.009); Imported inputs ratio 0.422*** (-0.007); # of firms 8,232; Observations 36,310.
- Stylized estimator biases reported:
  - O-P import ratio coefficient is significantly positive and larger than OLS estimate (O-P controls for simultaneity and selection biases).
  - Labor coefficients: OLS and within estimators tend to be upwardly biased relative to O-P.
  - Capital coefficients: OLS and within estimators tend to be downwardly biased relative to O-P.
- Industry heterogeneity: Industry-specific O-P estimates (16 industries with >100 firms) — import ratio coefficient positive and significant in most industries, magnitudes vary between 0.14 and 0.36.

### Robustness checks (Olley-Pakes extensions)
- Table A3 Olley-Pakes (selected columns):
  - Column (1) (capital and import ratio as state variables): Imported inputs ratio 0.422*** (0.01); # of firms 8,232; Observations 36,310.
  - Column (2) (adds export ratio): Imported inputs ratio 0.270*** (0.01); Export ratio -0.066*** (0.01); # of firms 8,232; Observations 36,310.
  - Column (3) (adds R&D): Imported inputs ratio 0.260*** (0.02); R&D 0.015*** (0.00); # of firms 8,232; Observations 36,310.
  - Column (4) (lagged imported inputs ratio): Imported inputs ratio (t-1) 0.066*** (0.02); # of firms 7,077; Observations 6,956.
- Robustness summary:
  - O-P results remain positive and significant after including export ratio and R&D.
  - Lagged import ratio (1-year lag) shows positive dynamic effects on productivity with smaller magnitude.

### Aggregate TFP accounting: role of imported inputs (2007–2012)
- Table 6 (Aggregate TFP Growth and Contribution of Imported Inputs (%)):
  - 2007: Growth of aggregate TFP (a) 0.59; Contribution of imported inputs (b) -2.02; Excluding contribution of imported inputs (c) 2.60.
  - 2008: (a) 5.49; (b) 4.00; (c) 1.49.
  - 2009: (a) -8.66; (b) -2.87; (c) -5.79.
  - 2010: (a) 12.28; (b) 0.26; (c) 12.01.
  - 2011: (a) 1.52; (b) 0.81; (c) 0.71.
  - 2012: (a) 6.13; (b) 0.22; (c) 5.91.
- Global Financial Crisis (2008–2009) specifics:
  - Aggregate TFP declined by 8.7 percent in 2009 (Table 6 column (a): -8.66).
  - 2.9 percent of the decrease is attributed to shrinkage of import intensity (Table 6 column (b): -2.87) — about one third of the drop.
- Interpretation: imported inputs materially amplified aggregate TFP movements during downturns when import intensity fell among larger firms.

### Decomposition of aggregate TFP growth associated with imported inputs
- Table 7 (Decomposition of Aggregate TFP Growth associated with Imported Inputs (%)):
  - 2007: TFP growth due to imported inputs (a) -25.97; unweighted average (b) 3.92; covariance term (c) -29.88; intra-firm efficiency (d) -30.97; inter-firm efficiency (e) 1.09.
  - 2008: (a) 69.93; (b) 3.38; (c) 66.55; (d) 60.78; (e) 5.77.
  - 2009: (a) -31.11; (b) 1.09; (c) -32.20; (d) -39.31; (e) 7.10.
  - 2010: (a) 3.78; (b) 14.03; (c) -10.25; (d) -12.80; (e) 2.55.
  - 2011: (a) 12.57; (b) -6.72; (c) 19.29; (d) 10.28; (e) 9.01.
  - 2012: (a) 3.10; (b) 4.94; (c) -1.84; (d) -10.16; (e) 8.32.
- GFC interpretation (2008–2009):
  - Growth of aggregate TFP explained by imported inputs dropped by 31 percent in 2009 (Table 7 column (a): -31.11).
  - Decomposition of the -31 percent: unweighted average TFP growth due to imported inputs 1 percent (column (b): 1.09); covariance term -32 percent (column (c): -32.20).
  - Covariance decomposition: intra-firm efficiency -39 percent (column (d): -39.31); inter-firm efficiency 7 percent (column (e): 7.10).
  - Interpretation: the large negative import-related TFP shock during the GFC was driven overwhelmingly by intra-firm declines in import intensity among relatively larger firms; concentration of importing activity in larger firms amplified aggregate TFP losses.

### Industry-level heterogeneity and findings
- Industry selection: nine industries with more than 500 firms reported (industry codes preserved as in source).
- Table 8 (TFP Growth and Contribution of Imported Inputs by Industry (%)) — selected examples:
  - Industry 10, 2007: Growth of sector-level TFP (a) -2.39; Contribution of imported inputs (b) 0.02; Excluding contribution (c) -2.40.
  - Industry 10, 2010: (a) 14.76; (b) 3.03; (c) 11.73.
  - Industry 28, 2008: (a) 38.03; (b) 20.20; (c) 17.83.
  - Industry 26, 2012: (a) 11.17; (b) 0.94; (c) 10.23.
- Table 9 (Industry-level decomposition of TFP growth due to imported inputs) — selected examples:
  - Industry 10, 2008: (a) 46.93; (b) 4.39; (c) 42.53; (d) 16.89; (e) 25.65.
  - Industry 24, 2008: (a) 144.36; (b) 4.95; (c) 139.41; (d) 139.92; (e) -0.51.
  - Industry 28, 2008: (a) 372.89; (b) 28.40; (c) 344.48; (d) -14.12; (e) 358.60.
- Industry-level patterns:
  - Several industries experienced sharp TFP drops in 2009 ranging approximately from 2 percent to 21 percent.
  - Industries 22, 24, 25, and 29 had large TFP drops in 2009; contribution of import ratio to these drops ranged about 0.6 percent to 6 percent.
  - Industry 28 (Electrical equipment) experienced a TFP decrease tied to import ratio and a 16 percent TFP drop in the following year with about half attributed to import ratio.
  - Across industries, import-related TFP declines in 2009 were dominated by negative covariance (efficiency) effects, primarily intra-firm efficiency loss rather than inter-firm reallocation.

### Cross-sector regressions and explanatory power
- Table 10 and Table 11 (industry-level regressions) — selected outcomes:
  - TFP due to imported inputs explains about 20 percent of variation in industry TFP growth across sectors and time on average; other factors account for about 80 percent (Table 10 coefficients: e.g., coefficient on (TFP growth)st = 0.195*** and 0.805*** in different specifications).
  - Covariance term explains around 87 percent of variation in TFP growth due to imported inputs.
  - Over the full sample, intra- and inter-firm efficiency improvements explain roughly equal shares of covariance variation on average, but during turbulent periods (GFC) intra-firm efficiency dominates fluctuations.
  - Table 10 reported Adj R squared up to 0.967 in some specifications; Table 11 reported Adj R squared values ranging from 0.339 to 0.900 across specifications.

### Descriptive statistics (selected table highlights)
- Table 2 (Importer vs. Non-importer):
  - Mean TFP: Importer 0.18; Non-importer -0.17.
  - Mean Size: Importer 0.88; Non-importer 0.08.
  - Mean Import ratio: Importer 0.35; Non-importer 0.08.
  - Observations: Importer 17,521; Non-importer 18,789.
- Table 3a (Average TFP and Firm Size by year, examples):
  - 2006 Importers: Observations 2,309; TFP 0.134; Size 0.71; Import ratio 0.35.
  - 2012 Importers: Observations 2,566; TFP 0.166; Size 1.11; Import ratio 0.38.
- Table 3b (import/survival status):
  - All firms: 8,232 firms, 36,310 observations.
  - Importers: 1,718 firms, 7,057 observations.
  - Survivors: 5,256 firms, 27,605 observations.
  - Quitters: 2,976 firms, 8,705 observations.
  - Switchers: 3,771 firms, 20,773 observations.

### Methodology notes (Olley-Pakes specifics)
- Olley-Pakes addresses endogeneity from correlation between unobserved productivity ߱_{it} and inputs, and sample selection due to exit.
- Key assumptions and steps:
  - Unobserved productivity ߱_{it} follows a first-order Markov process.
  - Investment demand function i_{it} = i_t(k_{it}, ߱_{it}) is monotonically increasing in productivity and invertible.
  - Productivity can be expressed as ߱_{it} = h_t(k_{it}, i_{it}).
  - Estimation steps:
    - First step: estimate variable inputs coefficients using a polynomial approximation of capital and investment to control for state variables.
    - Second step: determine exit probability threshold to correct for sample selection.
    - Third step: estimate coefficient on the state variable using nonlinear least squares.

### Main conclusions and policy implications
- Confirmed firm-level stylized facts for Korea:
  - The ratio of imported inputs in total inputs is pro-cyclical.
  - Use of imported inputs increases firm productivity.
  - Larger firms are more likely to use imported inputs.
- Quantitative conclusion:
  - Firm-level import decisions explain a non-trivial fraction of aggregate productivity fluctuations in Korea during 2006–2012, particularly amplifying downturns when import intensity falls among large firms.
- Policy-relevant implication:
  - Results suggest a potential link between the global productivity slowdown and the global trade slowdown via the imported inputs channel; quantifying this channel is a relevant topic for future research.

*Source: _wp16162 - Appendix Tables (IMF working paper content provided).*

### 2012. Main findings of this paper suggest a possible link between the recent global

### _wp16162 - 2012. Main findings of this paper suggest a possible link between the recent global

### Main themes
- Possible link between the recent global productivity slowdown and the global trade slowdown.
- JEL Classification Numbers: E3, F1, F4, O4
- Keywords: Firm-level imports, Productivity pro-cyclicality, Aggregate TFP growth
- Authors’ E-Mail Addresses: jahn@imf.org, mjchoi@bok.or.kr

### Acknowledgements and affiliations
- The authors are grateful to Woon Gyu Choi, Sunyoung Jung, Geun-Young Kim, Kyungmin Kim, Seungwon Kim, Jearang Lee, Jin-Su Park, Seryoung Park, Wook Sohn, and participants in the seminar at the Bank of Korea for their helpful comments.
- Author affiliations:
  - Economist, Research Department, International Monetary Fund, 700 19th st. NW, Washington, DC 20431.
  - Economist, Economic Research Institute, The Bank of Korea, 39 Namdaemun-Ro, Jung-Gu Seoul, Korea.

### Structure of the paper (Contents)
- I. Introduction (Page 3)
- II. Data (Page 5)
- III. Model and Empirical Strategy (Page 6)
- IV. Results (Page 8)
  - A. Production Function Estimation with O-P Methodology (Page 8)
  - B. Aggregate-level TFP Accounting (Page 9)
  - C. Industry-level TFP Accounting (Page 10)
- V. Conclusion (Page 12)
- References (Page 13)

### Figures listed
- 1. Pro-cyclicality of TFP and Imports (Page 16)
- 2. Import Growth by End-Use Category (Page 16)
- 3. Distribution of TFP and Firm Size (Importer vs. Non-Importer) (Page 17)

### Tables listed
- 1. OLS Estimation Results for Production Function (Page 18)
- 2. Summary Statistics for TFP, Firm Size and Import Ratio (Page 19)
- 3a. Average TFP and Firm Size (Importer vs. Non-importer) (Page 20)
- 3b. Descriptive Statistics by import/survival status (Page 20)
- 4. Estimation Results for Production Function with Import Ratio (Page 21)
- 5. Estimation Results for Industry-level Production Function with Import Ratio (Page 22)
- 6. Aggregate TFP Growth and Contribution of Imported Inputs (%) (Page 22)
- 7. Decomposition of Aggregate TFP Growth Associated with Imported Inputs (%) (Page 23)
- 8. TFP Growth and Contribution of Imported Inputs by Industry (%) (Page 24)
- 9. Industry-level Decomposition of TFP Growth associated with Imported Inputs (%) (Page 25)
- 10. Regression Results: Industry-level Decomposition of TFP Growth Associated with Imported Inputs (Page 26)
- 11. Regression Results: Industry-level Decomposition of TFP Growth associated with Imported Inputs (Page 27)

### Key methodological note
- Production function estimation uses O-P Methodology (Olley-Pakes implicit from abbreviation O-P in table headings).

### Core finding (as stated)
- Main findings of this paper suggest a possible link between the recent global productivity slowdown and the global trade slowdown.

*IMF Working Paper _wp16162 - 2012. Main findings of this paper suggest a possible link between the recent global*

### Appendix Tables

### Appendix Tables

### Data and Sample
- Main data source: Survey of Business Activities (SBA) from Statistics Korea (KOSTAT).
- Sample period: 2006 to 2012.
- Sample coverage: manufacturing sector limited to 22 industry categories (24 two-digit KSIC codes 10–33 with industries 12 and 18 excluded).
- Panel: unbalanced panel including 36,310 observations of 8,232 firms.
- Firms covered: all firms with 50 or more employees and 300 million won or greater capital.
- Price deflators:
  - Revenue deflated with sector-level Producer Price Index (PPI) compiled by the Bank of Korea.
  - Capital and investment deflated with domestic PPI for capital goods.
  - Domestic and imported inputs deflated by sector-level effective PPI and Imported Inputs Price Index, respectively, constructed following Amiti and Konings (2007).
- Import intensity: import ratio calculated as real imported inputs divided by real total inputs.
- Summary statistics highlights:
  - Importing firms are larger and more productive than non-importing firms.
  - Importers import one third of their input materials on average.
  - Firms that imported continuously have an average import ratio about 0.4.

### Empirical Framework and Estimation
- Production function specification: Cobb-Douglas with log output as function of log labor (l), log capital (k), log intermediate inputs (m), and TFP.
- TFP decomposition: TFP broken into a component due to imported inputs (function of import ratio f) and a residual TFP from other sources.
- Endogeneity concerns addressed:
  - Simultaneity bias between inputs and unobservable productivity shocks.
  - Sample selection bias from exit decisions correlated with productivity.
- Estimation methodology:
  - Olley-Pakes (O-P) semiparametric approach extended to include import intensity as a state variable (following Kasahara and Rodrigue (2008) and Halpern et al. (2011, 2015)).
  - O-P uses investment (and import ratio) as proxies to control for unobservable productivity inverting the investment function.
- Aggregation and decomposition:
  - Aggregate TFP computed as output-share-weighted sum of firm-level TFP.
  - Decomposition of aggregate TFP growth into:
    - Change in unweighted average TFP across firms.
    - Change in covariance between firm output share and firm TFP (efficiency/resource allocation term).
  - Further decomposition of covariance into intra-firm efficiency (within-firm TFP changes keeping shares constant, includes exit effect) and inter-firm efficiency (resource reallocation across firms, includes entry effect).

### Key Estimation Results
- Production function estimates:
  - OLS, within-group, and O-P compared.
  - Import ratio coefficient:
    - Positive and statistically significant across estimators.
    - O-P coefficient for import ratio is significantly positive and larger than OLS estimate (O-P controls for simultaneity and selection biases).
  - Labor coefficients: OLS and within estimators tend to be upwardly biased relative to O-P.
  - Capital coefficients: OLS and within estimators tend to be downwardly biased relative to O-P.
  - Industry-specific O-P estimates (16 industries with >100 firms): import ratio coefficient positive and significant in most industries, magnitudes vary between 0.14 and 0.36.
- Robustness checks (summary):
  - O-P results remain positive and significant after including export ratio and R&D.
  - Lagged import ratio (1-year lag) also shows positive dynamic effects on productivity with smaller magnitude.

### Aggregate-level TFP Accounting: Role of Imported Inputs
- Manufacturing aggregate TFP growth (2006–2012): generally positive except during the Global Financial Crisis (GFC).
- 2008–2009 (GFC) aggregate TFP:
  - Aggregate TFP declined by 8.7 percent (column (a) Table 6).
  - 2.9 percent of the decrease is attributed to shrinkage of import intensity (column (b) Table 6) — about one third of the drop.
- Import-related TFP decomposition (2008–2009):
  - Growth of aggregate TFP explained by imported inputs dropped by 31 percent (column (a) Table 7).
  - Decomposition of the -31 percent:
    - Unweighted average TFP growth due to imported inputs: 1 percent (column (b)).
    - Covariance term: -32 percent (column (c)).
  - Covariance decomposition:
    - Intra-firm efficiency: -39 percent (column (d)).
    - Inter-firm efficiency: 7 percent (column (e)).
  - Interpretation: the large negative import-related TFP shock during the GFC was driven overwhelmingly by intra-firm declines in import intensity among relatively larger firms; the skewed concentration of importing activity in larger firms amplified aggregate TFP losses.

### Industry-level TFP Accounting and Heterogeneity
- Industry selection: nine industries with more than 500 firms reported (selected industry codes and descriptions preserved as in source).
- Industry-level findings (Table 8 and Table 9 highlights):
  - Several industries experienced sharp TFP drops in 2009 ranging approximately from 2 percent to 21 percent.
  - Industries 22 (Rubber and Plastic Products), 24 (Basic Metal Products), 25 (Fabricated Metal Products, Except Machinery and Furniture), and 29 (Other Machinery and Equipment) had large TFP drops in 2009; contribution of import ratio to these drops ranged about 0.6 percent to 6 percent.
  - Industry 28 (Electrical equipment) experienced a TFP decrease tied to import ratio and a 16 percent TFP drop in the following year with about half attributed to import ratio.
  - Industry-level decompositions mirror aggregate patterns: most industries’ import-related TFP declines in 2009 were dominated by negative covariance (efficiency) effects, and within that, primarily by intra-firm efficiency loss rather than inter-firm reallocation.
- Cross-sector accounting regressions (Tables 10 and 11):
  - Regression of industry TFP growth on components shows:
    - On average, TFP due to imported inputs explains about 20 percent of variation in industry TFP growth across sectors and time; other factors account for about 80 percent.
    - Covariance term explains around 87 percent of variation in TFP growth due to imported inputs.
    - Over the full sample, intra- and inter-firm efficiency improvements explain roughly equal shares of covariance variation on average, but during turbulent periods (GFC) intra-firm efficiency dominates fluctuations.

### Main Conclusions and Implications
- Confirmed stylized facts for Korea at the firm level:
  - The ratio of imported inputs in total inputs is pro-cyclical.
  - Use of imported inputs increases firm productivity.
  - Larger firms are more likely to use imported inputs.
- Quantitative conclusion:
  - Firm-level import decisions explain a non-trivial fraction of aggregate productivity fluctuations in Korea during 2006–2012, particularly amplifying downturns when import intensity falls among large firms.
- Policy-relevant implication:
  - Findings suggest a potential link between the global productivity slowdown and the global trade slowdown via the imported inputs channel; quantifying this channel is a relevant topic for future research.

*Source: _wp16162 - Appendix Tables (IMF working paper content provided).*

### REFERENCES

### REFERENCES

### Key empirical estimates (production function)
- Table 1 OLS estimation results for production function (Dependent variable: log (total real revenue)):
  - Column (1) (OLS, no fixed effects):
    - Labor: 0.467*** (standard error: -0.006)
    - Capital: 0.171*** (standard error: -0.004)
    - Materials: 0.431*** (standard error: -0.005)
    - Constant: 2.500*** (standard error: -0.022)
    - Observations: 36,310
    - R-squared: 0.864
  - Column (2) (sector-year fixed effects):
    - Labor: 0.499*** (-0.006)
    - Capital: 0.157*** (-0.004)
    - Materials: 0.413*** (-0.005)
    - Constant: 2.512*** (-0.031)
    - Observations: 36,310
    - R-squared: 0.880
  - Column (3) (firm fixed effects):
    - Labor: 0.414*** (-0.021)
    - Capital: 0.165*** (-0.014)
    - Materials: 0.146*** (-0.012)
    - Constant: 5.613*** (-0.198)
    - Observations: 36,310
    - R-squared: 0.966
  - Column (4) (sector-year and firm fixed effects):
    - Labor: 0.410*** (-0.018)
    - Capital: 0.095*** (-0.008)
    - Materials: 0.139*** (-0.010)
    - Constant: 6.205*** (-0.151)
    - Observations: 36,310
    - R-squared: 0.973

- Table 4 estimation results for production function with import ratio (Dependent variable: log (total real revenue)):
  - Column (1) OLS:
    - Labor: 0.459*** (-0.006)
    - Capital: 0.170*** (-0.004)
    - Materials: 0.429*** (-0.005)
    - Imported inputs ratio: 0.233*** (-0.011)
    - Observations: 36,310
    - R-squared: 0.866
  - Column (2) sector-year FE:
    - Labor: 0.492*** (-0.006)
    - Capital: 0.155*** (-0.004)
    - Materials: 0.411*** (-0.005)
    - Imported inputs ratio: 0.217*** (-0.011)
    - Observations: 36,310
    - R-squared: 0.883
  - Column (3) firm FE:
    - Labor: 0.411*** (-0.021)
    - Capital: 0.163*** (-0.014)
    - Materials: 0.150*** (-0.012)
    - Imported inputs ratio: 0.100*** (-0.012)
    - Observations: 36,310
    - R-squared: 0.967
  - Column (4) sector-year and firm FE:
    - Labor: 0.408*** (-0.018)
    - Capital: 0.095*** (-0.008)
    - Materials: 0.142*** (-0.010)
    - Imported inputs ratio: 0.075*** (-0.010)
    - Observations: 36,310
    - R-squared: 0.973
  - Column (5) Olley-Pakes:
    - Labor: 0.092*** (-0.013)
    - Capital: 0.264*** (-0.017)
    - Materials: 0.389*** (-0.009)
    - Imported inputs ratio: 0.422*** (-0.007)
    - # of firms: 8,232
    - Observations: 36,310

### Robustness checks (Olley-Pakes with additional state variables)
- Table A3 Olley-Pakes results (Dependent variable: log (total real revenue)):
  - Column (1) (capital and import ratio as state variables):
    - Labor: 0.092*** (0.01)
    - Capital: 0.264*** (0.02)
    - Materials: 0.389*** (0.01)
    - Imported inputs ratio: 0.422*** (0.01)
    - # of firms: 8,232
    - Observations: 36,310
  - Column (2) (adds export ratio):
    - Labor: 0.391*** (0.01)
    - Capital: 0.092*** (0.01)
    - Materials: 0.423*** (0.01)
    - Imported inputs ratio: 0.270*** (0.01)
    - Export ratio: -0.066*** (0.01)
    - # of firms: 8,232
    - Observations: 36,310
  - Column (3) (adds R&D):
    - Labor: 0.399*** (0.01)
    - Capital: 0.094*** (0.01)
    - Materials: 0.410*** (0.01)
    - Imported inputs ratio: 0.260*** (0.02)
    - R&D: 0.015*** (0.00)
    - # of firms: 8,232
    - Observations: 36,310
  - Column (4) (lagged imported inputs ratio):
    - Labor: 0.407*** (0.01)
    - Capital: 0.092*** (0.02)
    - Materials: 0.410*** (0.01)
    - Imported inputs ratio (t-1): 0.066*** (0.02)
    - # of firms: 7,077
    - Observations: 6,956

### Aggregate TFP growth and contribution of imported inputs
- Table 6 (Aggregate TFP Growth and Contribution of Imported Inputs (%)):
  - 2007:
    - Growth of aggregate TFP (a): 0.59
    - Contribution of imported inputs (b): -2.02
    - Excluding contribution of imported inputs (c): 2.60
  - 2008:
    - (a): 5.49
    - (b): 4.00
    - (c): 1.49
  - 2009:
    - (a): -8.66
    - (b): -2.87
    - (c): -5.79
  - 2010:
    - (a): 12.28
    - (b): 0.26
    - (c): 12.01
  - 2011:
    - (a): 1.52
    - (b): 0.81
    - (c): 0.71
  - 2012:
    - (a): 6.13
    - (b): 0.22
    - (c): 5.91

- Notes: Growth of aggregate TFP in column (a) is the sum of contributions from imported inputs in column (b) and all others in column (c). Specific calculation formulas are reported in the table.

### Decomposition of aggregate TFP growth associated with imported inputs
- Table 7 (Decomposition of Aggregate TFP Growth associated with Imported Inputs (%)):
  - 2007:
    - TFP growth due to imported inputs (a): -25.97
    - Contribution of unweighted average (b): 3.92
    - Contribution of covariance term (c): -29.88
    - Intra-firm efficiency (d): -30.97
    - Inter-firm efficiency (e): 1.09
  - 2008:
    - (a): 69.93; (b): 3.38; (c): 66.55; (d): 60.78; (e): 5.77
  - 2009:
    - (a): -31.11; (b): 1.09; (c): -32.20; (d): -39.31; (e): 7.10
  - 2010:
    - (a): 3.78; (b): 14.03; (c): -10.25; (d): -12.80; (e): 2.55
  - 2011:
    - (a): 12.57; (b): -6.72; (c): 19.29; (d): 10.28; (e): 9.01
  - 2012:
    - (a): 3.10; (b): 4.94; (c): -1.84; (d): -10.16; (e): 8.32

- Notes: Column (a) is sum of (b) unweighted average contribution and (c) covariance term; (c) is decomposed into (d) intra-firm efficiency improvement and (e) inter-firm efficiency improvement. Specific calculation formulas are provided in the table.

### Industry-level results (selected highlights)
- Table 8 (TFP Growth and Contribution of Imported Inputs by Industry (%)) reports sector-year (industry codes 10, 20, 22, 24, 25, 26, 28, 29, 30) values of:
  - Growth of sector-level TFP (a), Contribution of imported inputs (b), Excluding contribution of imported inputs (c) for years 2007–2012. Examples:
    - Industry 10, 2007: (a) -2.39; (b) 0.02; (c) -2.40
    - Industry 10, 2010: (a) 14.76; (b) 3.03; (c) 11.73
    - Industry 28, 2008: (a) 38.03; (b) 20.20; (c) 17.83
    - Industry 26, 2012: (a) 11.17; (b) 0.94; (c) 10.23

- Table 9 (Industry-level Decomposition of TFP Growth Associated with Imported Inputs (%)) reports for each industry-year the decomposition into:
  - (a) TFP growth due to imported inputs, (b) Contribution of unweighted average, (c) Contribution of covariance term = (d) intra-firm efficiency + (e) inter-firm efficiency.
  - Examples:
    - Industry 10, 2008: (a) 46.93; (b) 4.39; (c) 42.53; (d) 16.89; (e) 25.65
    - Industry 24, 2008: (a) 144.36; (b) 4.95; (c) 139.41; (d) 139.92; (e) -0.51
    - Industry 28, 2008: (a) 372.89; (b) 28.40; (c) 344.48; (d) -14.12; (e) 358.60

- Table 10 and Table 11 present regression results at industry level:
  - Table 10 (dependent variable: contribution of imported inputs or excluding contribution):
    - Coefficients on (TFP growth)st: 0.195*** and 0.805*** in different specifications; Adj R squared up to 0.967.
    - Including a 2009/2010 dummy and interaction does not change coefficient sums (they sum to 1 across reported columns).
  - Table 11 (decomposition regressions):
    - Coefficients for (TFP growth due to imported inputs)st vary across columns (e.g., 0.134***, 0.866***, 0.455***, 0.411***, 0.563***), with Adj R squared values ranging from 0.339 to 0.900.

### Data and sample summaries
- Table 2 summary statistics (TFP, Firm Size, Import ratio) — Importer vs. Non-importer:
  - Mean TFP: Importer 0.18; Non-importer -0.17
  - Mean Size: Importer 0.88; Non-importer 0.08
  - Mean Import ratio: Importer 0.35; Non-importer 0.08
  - Median TFP: Importer 0.11; Non-importer -0.24
  - Median Size: Importer 0.71; Non-importer 9.93
  - S.D. TFP: 0.77 (importer) and 0.69 (non-importer)
  - Observations: Importer 17,521; Non-importer 18,789
- Table 3a Average TFP and Firm Size (Importer vs. Non-importer) by year (2006–2012):
  - Example rows:
    - 2006: Importer Observations 2,309; TFP 0.134; Size 0.71; Import ratio 0.35. Non-importer Observations 3,300; TFP -0.175; Size 0.11.
    - 2012: Importer Observations 2,566; TFP 0.166; Size 1.11; Import ratio 0.38. Non-importer Observations 2,690; TFP -0.141; Size 0.10.
- Table 3b Descriptive statistics by import/survival status (sample period 2006-2012):
  - All firms: 8,232 firms, 36,310 observations
  - Importers: 1,718 firms, 7,057 observations
  - Survivors: 5,256 firms, 27,605 observations
  - Quitters: 2,976 firms, 8,705 observations
  - Switchers: 3,771 firms, 20,773 observations
  - Non-importers: -2,743 firms, 8,480 observations (as presented in table)

- Table A2 Industry-level summary statistics (selected lines):
  - Total mean (Revenue, Worker, Capital, Inputs, Import Ratio): 10.61, 4.93, 9.30, 9.78, 0.17; S.D.: 1.30, 0.86, 1.48, 1.64, 0.28; Obs.: 36,310
  - Industry 10 mean: 10.67, 5.08, 9.35, 9.92, import ratio 0.15; Obs. 2,330
  - Industry 19 mean: 13.06, 5.65, 11.26, 12.43, import ratio 0.35; Obs. 77
  - Industry 28 mean: 10.63, 4.87, 8.99, 9.93, import ratio 0.16; Obs. 2,269
  - Industry 30 mean: 10.73, 5.04, 9.55, 10.05, import ratio 0.09; Obs. 4,401

### Methodology notes (Olley-Pakes)
- Olley-Pakes methodology addresses endogeneity from correlation between unobserved productivity shock (߱_{it}) and inputs, and sample selection due to exit.
- Assumptions and steps highlighted:
  - Unobserved productivity ߱_{it} follows a first-order Markov process.
  - Capital accumulates through firms' dynamic investment process; investment demand function i_{it} = i_t(k_{it}, ߱_{it}) is monotonically increasing in productivity and thus invertible (Pakes (1994)).
  - Productivity can be expressed as function of capital and investment: ߱_{it} = h_t(k_{it}, i_{it}).
  - Estimation steps:
    - First step: estimate variable inputs coefficients using a polynomial approximation of capital and investment to control for state variables.
    - Second step: determine exit probability threshold to correct for sample selection.
    - Third step: estimate coefficient on the state variable using nonlinear least squares.

*Italic: Source: _wp16162 - REFERENCES (IMF PDF)._

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp16162.pdf_