## Annexes to CHAPTER 3 — Data Sources, Methods, and Empirical Results

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### Data sources and country groupings
- Primary databases:
  - IMF World Economic Outlook database; Penn World Table (PWT) 9.0 database (including capital detail); World Input-Output Database (WIOD) Release 2013 and 2016 (Socio Economic Accounts and World Input-Output tables); EU and World KLEMS databases.
- Additional sources and compilations:
  - International Comparison Program (ICP) 2011; Bureau of Economic Analysis; OECD; Eurostat; US Census Bureau; COMTRADE; Ministry of Finance of Japan; IMF, International Financial Statistics; Haver Analytics; Bloomberg; Caceres and others (2016); World Bank, Global Financial Development Database; Chinn and Ito (2006); CEPII GeoDist Database; Gruss and Kebhajz (2019); International Country Risk Guide; Eora MRIO database; UNCTAD Trade Analysis Information System; WTO Tariff Download Facility; Feenstra and Romalis (2014); Fraser Institute; World Bank, Doing Business Indicators; UNCTAD, World Maritime Review; Calderón, Moral-Benito, and Servén (2015); World Bank, World Development Indicators database; Chapter 3 of the October 2014 World Economic Outlook.
- Authors and support:
  - Weicheng Lian, Natalija Novta, Evgenia Pugacheva, Yannick Timmer, and Petia Topalova (lead), with support from Jilun Xing and Candice Zhao.
- Country groupings:
  - Definitions of advanced economies, emerging market economies, and low-income countries follow the World Economic Outlook’s definition.
- Samples used (selected highlights):
  - Unit-price analysis: China, France, Germany, Japan, United States.
  - Economy-level analysis: Albania, Algeria, Angola, Argentina, Armenia, Australia, Austria, Azerbaijan, The Bahamas, Bahrain, Bangladesh, Belarus, Belgium, Bolivia, Botswana, Brazil, Bulgaria, Burkina Faso, Cameroon, Canada, Chile, China, Colombia, Democratic Republic of the Congo, Republic of Congo, Costa Rica, Croatia, Cyprus, Czech Republic, Côte d'Ivoire, Denmark, Dominican Republic, Ecuador, Egypt, El Salvador, Estonia, Ethiopia, Finland, France, Gabon, The Gambia, Germany, Ghana, Greece, Guatemala, Guinea-Bissau, Haiti, Honduras, Hong Kong SAR, Hungary, Iceland, India, Indonesia, Iran, Iraq, Ireland, Israel, Italy, Jamaica, Japan, Jordan, Kazakhstan, Kenya, Korea, Kuwait, Latvia, Lebanon, Liberia, Lithuania, Madagascar, Malawi, Malaysia, Mali, Malta, Mexico, Moldova, Mongolia, Morocco, Mozambique, Myanmar, Namibia, Netherlands, New Zealand, Nicaragua, Niger, Nigeria, Norway, Oman, Pakistan, Panama, Paraguay, Peru, Philippines, Poland, Portugal, Qatar, Romania, Russia, Saudi Arabia, Senegal, Sierra Leone, Singapore, Slovak Republic, Slovenia, South Africa, Spain, Sri Lanka, Suriname, Sweden, Switzerland, Syria, Tanzania, Thailand, Togo, Trinidad and Tobago, Tunisia, Turkey, Uganda, Ukraine, United Kingdom, United States, Uruguay, Venezuela, Vietnam, Yemen, Zambia, Zimbabwe.
  - Sector-level and other samples detailed in source for sectoral analyses.

### Data definitions and construction of price measures
- Relative price of investment defined relative to the price of consumption.
- Cross-country stylized facts on relative prices use ICP 2011 measures of the price level of machinery and equipment and the price level of consumption for a comparable basket of goods across countries in 2011.
- Evolution of prices over time uses PWT 9.0, which incorporates ICP vintages (1970, 1975, 1980, 1985, 1996, 2005, 2011) and OECD/Eurostat data to derive aggregate investment and consumption price levels.
- Construction to remove international price levels:
  - Relative price of overall investment divided by the relative price of investment in the United States and multiplied by the ratio of the investment price deflator to the consumption deflator for the United States (from the Bureau of Economic Analysis) to cancel out international prices embedded in the PPP-adjusted series (following Restuccia and Urrutia (2001) and Karabarbounis and Neiman (2013)).
- Sector and asset-level deflators:
  - PWT 9.0 capital detail dataset and national accounts consumption deflator used in country-level panel regressions and stylized facts (Figure 3.2).
  - EU and World KLEMS used for sector-level panel regressions on investment in machinery and equipment: relative price = machinery and equipment deflator / country-wide consumption deflator.
  - WIOD Socio Economic Accounts sectoral gross output deflator used for sector-level regressions on drivers of sectoral producer prices.
- Unit-price analysis:
  - Highly disaggregated bilateral trade data: US HS 10-digit, Japan HS 9-digit, France and Germany HS 8-digit, China HS 6-digit.
  - FOB reporting excludes trade costs, focusing on variation due to mark-ups or quality across destinations.
- Real interest rate:
  - Defined as nominal interest rate adjusted for inflation measured by the GDP deflator.

### Indicators and typical sources (selected entries)
- Investment, Consumption, and GDP Prices: International Comparison Program 2011; Penn World Table 9.0; KLEMS; WIOD; Bureau of Economic Analysis.
- Investment-to-GDP Ratios: Penn World Table 9.0, including capital detail and national accounts; KLEMS; WIOD.
- Unit Prices of Exports at the Product Level: US Census Bureau; Eurostat; COMTRADE; Ministry of Finance of Japan.
- Real GDP per Capita in PPP International Dollars: Penn World Table 9.0.
- Nominal Interest Rate: IMF, World Economic Outlook database; IMF, International Financial Statistics; Organisation for Economic Co-operation and Development; Haver Analytics; Bloomberg; Caceres and others (2016).
- Credit-to-GDP Ratio: World Bank, Global Financial Development Database.
- Capital Account Openness: Chinn and Ito (2006).
- Capital Stock (by Asset Type): Penn World Table 9.0, Capital Detail.
- Bilateral Distance: CEPII GeoDist Database.
- Trade Openness: IMF, World Economic Outlook database.
- Export Commodity Price: Gruss and Kebhajz (2019).
- Political Risk Rating: International Country Risk Guide.
- Global Value Chain Participation: Eora MRIO database; IMF staff calculations.
- Tariffs: UNCTAD, Trade Analysis Information System; WTO Tariff Download Facility; Feenstra and Romalis (2014).
- Freedom to Trade Internationally Index: Fraser Institute.
- Cost to Import, Time to Import: World Bank, Doing Business Indicators.
- Liner Shipping Connectivity Index: UNCTAD, World Maritime Review.
- Paved Roads Kilometers per Capita: Calderón, Moral-Benito, and Servén (2015); World Bank, World Development Indicators database; Chapter 3 of the October 2014 World Economic Outlook.

### Stylized facts on relative prices, investment rates, and composition (Annex 3.2)
- Time coverage and construction:
  - PWT 9.0 used for longer time series; ICP vintages include 1970, 1975, 1980, 1985, 1996, 2005, 2011.
  - Relative price defined as investment deflator (for each type of capital good) divided by consumption deflator.
  - Year fixed effects from regressions of log relative prices (including country fixed effects) normalized relative to 1970; shaded areas indicate 95 percent confidence intervals.
- Key empirical patterns:
  - Decline in the price of tradable capital goods (both tangible and intangible) has been widespread; price of structures moved broadly in line with consumption price.
  - For advanced economies and emerging market and developing economies, relative prices of tangible tradable investment goods were on a declining trend since the beginning of the sample, with an acceleration in the pace of decline since the mid-1990s.
  - The acceleration coincided with a pickup in real investment rates in emerging market and developing economies.
- Investment rates and composition:
  - For asset types with larger declines in relative prices (e.g., machinery and equipment and other investment), real investment rates have increased quite significantly across all economies since the 1990s; nominal investment rates changed much less.
  - Dispersion in real investment rates is significantly larger in emerging market and developing economies relative to advanced economies.
  - Real investment rates in tangible tradable capital goods were similar for the median advanced and emerging market and developing economy until the mid-2000s, then diverged: EMDEs’ real investment rates in machinery and equipment (including transport) rose until the global financial crisis and remained relatively robust since; in AEs real investment rates plateaued since the mid-2000s with a dip around the global financial crisis.
  - Real investment rates in structures declined significantly since the global financial crisis in advanced economies while they have steadily increased in emerging market and developing economies.
- Composition in 2014 (PWT 9.0, averages by broad country groups):
  - About 60 percent of gross fixed capital formation in low income countries is accounted for by investment in structures, compared to about 50 percent in advanced economies.
  - Investment in machinery and equipment (including transport) comprises roughly 35 percent of overall investment in all economies.
  - Advanced economies allocate a significantly larger fraction of investment to “other investment” (mostly intellectual property products).

### Unit-price analysis: specification, data, and main empirical findings (Annex 3.3 and Annex Figure 3.3.1)
- Estimation specification (preserved exactly):
  - ln(p*)_{p,x,i,t} = α + β·ln(GDPPC)_{i,t} + α_{p,x,t} + ε_{p,x,i,t}
    - ln(p*)_{p,x,i,t}: log unit value for product p by exporting country x to importing country i in year t.
    - Regressor: ln(GDPPC)_{i,t} (log GDP per capita of importing country i in year t), weighted by FOB value of exports.
    - Fixed effects: product*exporting country*year (α_{p,x,t}).
    - Standard errors clustered at the importing country level.
- Data granularity:
  - US: HS 10-digit exports for 1989–2005 from US Census Bureau.
  - Japan: HS 9-digit product level data for 1988–2017 from the Ministry of Finance.
  - China: HS 6-digit product level data for 1992–2017 from COMTRADE.
  - Germany and France: HS 8-digit export data for 1988–2017 from Eurostat.
- Main findings when pooling Top 5 exporters:
  - Log GDP per Capita coefficient: 0.027 (not statistically distinguishable from zero).
  - Number of Observations: 7,132,542.
  - Number of Unique Products: 812.
  - R2: 0.98.
  - Level of Product Disaggregation: HS 10-digit.
- Heterogeneity across exporters (Log GDP per Capita coefficients and sample details):
  - US: –0.058*** (Number of Observations: 1,607,743; Unique Products: 1,929; R2: 0.78; HS 6-digit).
  - China: –0.157*** (999,810 obs; 674 products; R2: 0.84; HS 8-digit).
  - France: 0.106*** (1,479,250 obs; 2,380 products; R2: 0.92; HS 8-digit).
  - Germany: 0.033** (2,025,791 obs; 2,373 products; R2: 0.94; HS 9-digit).
  - Japan: 0.028 (1,022,125 obs; 1,352 products; R2: 0.80).
- Interpretation:
  - US and Chinese exporters: statistically significant negative correlation between unit values and importer GDP per capita (firms charge importers from poorer countries higher prices for the same product).
  - Germany and France: unit values significantly higher when shipments are sent to countries with higher GDP per capita (consistent with richer importers obtaining higher-quality variants).
  - Pooling exporters hides substantial exporter-specific heterogeneity.

### Broad country-group patterns and robustness (Annex Tables 3.3.2–3.3.3)
- Indicator-variable regressions (Emerging Market Economies; Low Income Countries) — pooled Top 5:
  - Emerging Market Economies: –0.047.
  - Low Income Countries: 0.093.
  - Number of Observations: 7,132,542; Unique Products: 812; R2: 0.98; HS 10-digit.
- Exporter-specific broad-group coefficients (Emerging Market Economies row by exporter):
  - Top 5: –0.047; US: 0.077*; China: 0.236***; France: –0.149**; Germany: –0.037; Japan: –0.062.
- Exporter-specific broad-group coefficients (Low Income Countries row by exporter):
  - Top 5: 0.093; US: 0.239***; China: 0.564***; France: –0.280***; Germany: –0.009; Japan: –0.078.
- Robustness with market-size, remoteness, and distance controls (selected coefficients):
  - Log GDP per Capita coefficients (columns: Top 5; Top 5 with controls; US; China; France; Germany; Japan): 0.027; 0.046; –0.050***; –0.092***; 0.110***; 0.066***; 0.018.
  - Log Remoteness coefficients (where reported): –0.173*; –0.400***; 0.040; –0.010; 0.043; –0.338***.
  - Log Distance coefficients: 0.075***; 0.197***; –0.191***; 0.087**; 0.083***; 0.182***.
  - Log GDP (market size) coefficients: –0.013; –0.047***; –0.070***; 0.023; 0.003; –0.033***.
- Interpretations:
  - Positive correlation of log distance with unit values consistent with Alchian-Allen effect (higher-quality goods survive higher transport costs).
  - Greater remoteness associated with lower unit values (possible lower-quality imports).
  - Larger market size correlated with lower unit values (possible mark-up declining with competition or domestic production presence).

### Trade costs, absolute prices, and productivity decomposition (Annex Tables 3.4.1–3.4.2)
- Trade-cost measures regressions on ln(Absolute Price of Capital Goods) (selected coefficients and stats):
  - Distance: 0.162*** (Number of Observations: 165; R2: 0.14).
  - Connectivity: –0.168*** (119 obs; R2: 0.05).
  - Freedom to Trade: –0.022* (147 obs; R2: 0.04).
  - Tariffs: 0.016* (165 obs; R2: 0.01).
  - Cost to Import: 0.040*** (151 obs; R2: 0.05).
  - Time to Import: 0.030* (151 obs; R2: 0.03).
- Percent-change implications (Coefficient × Standard Deviation):
  - Distance: 0.048***.
  - Connectivity: –0.028***.
  - Freedom to Trade: –0.024*.
  - Tariffs: 0.014*.
  - Cost to Import: 0.027**.
  - Time to Import: 0.020*.
- Decomposition regression results (dependent variable: Relative Price of Capital Goods, log PI/PC):
  - Relative productivity (tradable vs nontradable) coefficients across Trade Barrier columns: –0.467***; –0.467***; –0.499***; –0.352***; –0.396***; –0.314***.
  - Trade Barrier coefficients in same regressions:
    - Distance column: 0.226** (120 obs; R2: 0.28).
    - Connectivity column: –0.322* (93 obs; R2: 0.28).
    - Freedom to Trade column: –0.237*** (116 obs; R2: 0.55).
    - Tariffs column: 0.219*** (121 obs; R2: 0.43).
    - Cost to Import column: 0.285*** (108 obs; R2: 0.42).
    - Time to Import column: 0.408*** (108 obs; R2: 0.58).
- Interpretation:
  - Higher tradable productivity relative to nontradables strongly associated with lower relative capital-goods prices.
  - Trade-cost measures (especially time to import and cost to import) are positively associated with higher relative capital-goods prices; better connectivity or freer trade associated with lower relative prices.

### Sectoral empirical strategy for over-time decomposition (Annex 3.5)
- Conceptual reduced form used:
  - PI/PC = f(aT/aNT, PI*, trade costs), where:
    - PI/PC is the relative price of capital goods.
    - aT/aNT is productivity in tradable goods relative to nontradables.
    - Trade costs include transport costs, tariffs, customs regulation, time and cost of logistics.
- Over-time approach (1995–2011, 40 economies, 33 sectors, WIOD):
  - Two-step empirical strategy:
    1. Estimate elasticity of sectoral producer prices to sectoral labor productivity and exposure to international trade (imports/domestic output), controlling for country-year and country-sector fixed effects.
    2. Combine estimated elasticities with observed changes in relative labor productivity and trade exposure of capital-goods sectors to quantify contributions to the decline in relative prices of machinery and equipment over 2000–11.
  - Instrumental strategy: import tariffs used as instrument for exposure to trade to isolate policy-driven changes in import penetration from price-driven changes in import shares.
  - Adjustment: account for trade’s indirect effect on relative prices via its effect on sectoral labor productivity.

### Regression framework and IV strategy for producer prices and productivity (Chapter 3 regression system)
- Relative producer price equation (notation preserved):
  - ln(푃푖,푗,푡 / 푃̅푖,푡) = 훼푖,푗 + 휇푖,푡 + 훽[ln(푀푖,푗,푡 / 푉퐴푖,푗,푡) − ln(푀̅푖,푡 / 푉퐴̅̅̅̅푖,푡)] + 훾 ln(퐿푃푖,푗,푡 / 퐿푃̅̅̅̅푖,푡) + 휀푖,푗,푡
    - Relative import penetration instrumented by relative import tariff: 휏푖,푗,푡 − 휏̅푖,푡, where sector tariff is constructed from SITC 4-digit bilateral preferential tariff data (Feenstra and Romalis (2014)).
- Relative labor productivity equation:
  - ln(퐿푃푖,푗,푡 / 퐿푃̅̅̅̅푖,푡) = 훼푖,푗^{퐿푃} + 휇푖,푡^{퐿푃} + 훽^{퐿푃}[ln(푀푖,푗,푡 / 푉퐴푖,푗,푡) − ln(푀̅푖,푡 / 푉퐴̅̅̅̅푖,푡)] + 휀푖,푗,푡^{퐿푃}
  - Relative import penetration instrumented by relative import tariff here as well.
- Exogeneity assumption for tariffs:
  - cov(휏푖,푗,푡 − 휏̅푖,푡, 휀푖,푗,푡) = cov(휏푖,푗,푡 − 휏̅푖,푡, 휀푖,푗,푡^{퐿푃}) = 0.

### First-stage, IV, and decomposition results (Annex Tables 3.5.1–3.5.3)
- First-stage and reduced form (Annex Table 3.5.1):
  - Import Tariff coefficient on Relative Import Penetration: −0.014*** (0.003).
  - Import Tariff coefficient on Relative Producer Prices: 0.010*** (0.003).
  - Relative Productivity t−1 coefficient on Relative Producer Prices: 0.003 (column 1) and −0.308*** (column 2) with (0.014) and (0.036) respectively.
  - Number of Observations: 16,077 for both columns.
  - R^2: 0.96 (column 1), 0.62 (column 2).
  - Interpretation: strong first-stage relationship supports using import tariff as instrument; reduced form indicates lower import tariff leads to a decline in producer price after controlling for labor productivity.
- Main IV and productivity results (Annex Table 3.5.2):
  - Relative Import Penetration t−1 (OLS column 1): −0.135*** (0.033).
  - Relative Import Penetration t−1 (various IV columns): −0.568*** (0.146); −0.574*** (0.163); −0.413*** (0.148); −0.964*** (0.374); −0.461** (0.200); −0.458*** (0.177).
  - Relative Productivity t−1: −0.316*** (0.035); −0.328*** (0.032); −0.328*** (0.032); −0.349*** (0.041); −0.274*** (0.034); −0.302*** (0.031); −0.368*** (0.039).
  - Number of Observations varies: 16,077; 12,575; 3,502; 12,321; 15,086.
  - R^2 ranges: 0.40–0.71.
- Labor productivity response to import penetration (Annex Table 3.5.3):
  - Relative Import Penetration t−1 coefficients:
    - OLS: 0.054 (0.049).
    - IV columns show larger positive coefficients: 1.639 (0.000); 1.363*** (0.363); 0.793*** (0.305); 2.403** (1.041); 1.251*** (0.449).
  - Relative Import Penetration for Capital Goods Sectors shows large positive IV coefficients (e.g., 2.771*** (0.564)).
  - Number of Observations across columns: 16,077; 12,575; 3,502; 12,321.
  - R^2: 0.88–0.95.
  - Interpretation: IV estimates indicate a stronger positive effect of import penetration on relative labor productivity than OLS, confirming endogeneity concerns.

### Decomposition of changes in relative producer prices (2000–2011)
- Decomposition uses coefficients from column (3) of Annex Table 3.5.2 and column (4) of Annex Table 3.5.3.
- Change in relative price of investment from 2000 to 2011 decomposed into four components (definitions preserved):
  - (i) Direct effect of deepening trade integration: simple average of 훽 × { change in relative import penetration } across countries and sectors.
  - (ii) Effect of trade integration through higher labor productivity: simple average of 훾 × 훽_{퐿푃} × { change in relative import penetration } across countries and sectors.
  - (iii) Effect of higher labor productivity not due to trade integration: simple average of 훾 × { change in relative labor productivity minus 훽_{퐿푃} × change in relative import penetration } across countries and sectors.
  - (iv) Contributions of other factors (residual term).
- Application quantifies how much of the decline in relative prices of machinery and equipment over 2000–11 can be attributed to direct trade-integration effects, trade-driven productivity gains, other productivity gains, and residuals (numerical decomposition reported in source tables).

### Impact of relative investment prices on aggregate and sectoral investment rates (Annex 3.6 and 3.7)
- Country-level regressions (Annex 3.6):
  - Regression specification:
    - ln(Real M&E Investment / Real GDP)_{i,t} = β · ln(P_{M&E} / P_{GDP})_{i,t} + Controls_{i,t} + μ_i + θ_t + ε_{i,t}
    - P_{M&E} = (I_{Machinery} / I_{M&E}) P_{Machinery} + (I_{Transport} / I_{M&E}) P_{Transport}.
  - Controls include lagged level and growth rate of real GDP per capita (PPP), lagged dependent variable, real interest rates, credit-to-GDP ratio, capital account openness, trade openness, exposure to commodity shocks, institutional quality and political risks, kilometers of paved roads per capita.
  - Estimation approaches: five-year non-overlapping window averages (baseline), annual data robustness checks, IV regressions instrumenting relative price with its lag, system GMM, and IV using other countries’ average relative price.
  - Key country-level findings (selected coefficients preserved):
    - Column 1 (OLS): Log Relative Price coefficient = −0.624*** (0.075).
    - Column 3 (OLS, lagged): −0.221*** (0.079).
    - Column 4 (Annual OLS): −0.092*** (0.030).
    - Main IV estimate (column 5): −0.377*** (0.116).
    - Column 6 (IV, post 1990): −0.292* (0.171).
    - Column 7 (IV, EMDE): −0.491*** (0.161).
    - Column 8 (IV, AE): −0.558*** (0.136).
    - Column 11 (GMM): −0.191** (0.088).
    - Column 12 (IV excluding own): −0.481*** (0.086).
  - Persistence (log investment rate t−1): examples include 0.412*** (0.085) and 0.776*** (0.026) across specifications.
  - First Stage F-Statistics in IV columns: 118.80; 81.81; 64.04; 87.17; 96.87; 169.20; 134.70 reported across columns.
  - Sample and magnitude implication:
    - Based on five-year window average data (column 5) for a sample of 75 countries with data in both periods, between 1990–94 and 2010–14 machinery and equipment investment rates grew by more than 60 percent in EMDEs (increasing from 5 percent to over 8 percent), and a significant portion of that change can be attributed to the decline in relative prices of machinery and equipment.
  - Long-run effect (annual data reported): −0.410*** (0.125) (coefficient divided by (1 – coefficient on lagged dependent variable)).
- Sector-level regressions (Annex 3.7):
  - Data: EU KLEMS and World KLEMS; sample typically 18–19 countries, 15 broad sectors, 1971–2015 (unbalanced panel).
  - Machinery and equipment price construction:
    - P_M&E = (I_IT / I_M&E) P_IT + (I_CT / I_M&E) P_CT + (I_TraEq / I_M&E) P_TraEq + (I_OMach / I_M&E) P_OMach (weights are sector asset shares).
  - Baseline specification (five-year averages):
    - ln(Real M&E In / Real VA)_{i,t,s} = β · ln(P_M&E / P_C)_{i,t,s} + γ · ln(Real M&E In / Real VA)_{i,t-1,s} + μ_{i,t} + θ_{i,s} + ε_{i,t,s}
    - Instrument: lagged log relative price.
  - Main five-year IV results (Annex Table 3.7.2, selected):
    - Column (1) (IV, country-period & country-sector FE): Log Relative Price = –0.326*** (0.078) for Log Real Investment-to-GDP Ratio.
    - Column (5) (IV, period & country-sector FE): Log Relative Price = –0.528*** (0.068) for Log Real Investment-to-GDP Ratio.
    - Column (2) (OLS, Log Real Investment): –0.192** (0.079).
    - Column (6) (OLS, Log Real Investment): –0.444*** (0.071).
    - Effects on Log Value Added: –0.061*** (0.018) and –0.058*** (0.015) in selected OLS columns.
    - Effects on Log Value Added per Worker: smaller and often not statistically significant (examples: –0.016 (0.025); –0.033 (0.021)).
    - Number of observations typically 971; other columns report 1,046, 972, 747 depending on specification.
    - First Stage F-Statistics (five-year IV): examples 645, 643, 729, 729.
  - Annual-frequency robustness (Annex Table 3.7.3):
    - Log Relative Price coefficients (selected): –0.170*** (0.018); –0.264*** (0.018); –0.013*** (0.003); –0.005 (0.004); –0.203*** (0.017); –0.279*** (0.017); –0.011*** (0.003); –0.007* (0.004).
    - Number of observations: 5,629; 6,004; 5,644; 4,430 across specifications.
    - First Stage F-Statistics (annual) very large: e.g., 20,770; 18,595; 26,232; 12,603; 23,442; 20,477; 33,690; 14,700.
  - Key sectoral takeaways:
    - Higher relative prices of machinery and equipment are associated with statistically significant reductions in sectoral investment rates.
    - Negative effects on sectoral value added are small but often significant; effects on value added per worker are smaller and less consistently significant.
    - Results robust to instrumentation with lagged relative prices, alternative fixed effects structures, and both five-year averaged and annual data, with coefficients smaller in magnitude at annual frequency.

### Key policy-relevant implications (synthesized from empirical results)
- Cross-country variation in capital-goods prices is driven by both relative productivity (tradable vs nontradable) and trade-cost measures (notably time-to-import and cost-to-import).
- Reducing logistical trade frictions (time and cost to import) and improving connectivity are empirically associated with lower absolute and relative prices of capital goods.
- Exporter-level pricing behavior varies substantially:
  - Suppliers differ in whether they charge higher prices to poorer importers (US and China in sample) or deliver higher-quality variants to richer importers (France and Germany in sample).
  - Policies that affect supplier market structure, quality provision, and market access can influence the prices facing importing countries differently depending on exporter relationships.
- Measurement and identification cautions:
  - Quality differences within HS codes and the endogeneity between domestic prices and import penetration require fixed effects and instrumental strategies (e.g., tariffs as instruments) to attribute causes to price changes credibly.
- Investment implications:
  - Declines in the relative price of machinery and equipment are robustly associated with higher real investment-to-GDP ratios across specifications and samples.
  - Trade integration affects relative prices both directly (through import penetration) and indirectly (via productivity gains from trade), and both channels contributed to the decline in relative prices of capital goods over 2000–11.

*Source: IMF staff compilation.*

### Annex 3.1. Data Sources and Country Groupings

### Annex 3.1. Data Sources and Country Groupings

### Data sources used
- Primary databases: IMF World Economic Outlook database; Penn World Table (PWT) 9.0 database, including supplemental datasets on national accounts and capital detail; World Input-Output Database (WIOD) Release 2013 and 2016, including both Socio Economic Accounts and World Input-Output tables; EU and World KLEMS databases.
- Additional data and compilation: International Comparison Program (ICP) 2011; Bureau of Economic Analysis; OECD; Eurostat; US Census Bureau; Eurostat; COMTRADE; Ministry of Finance of Japan; IMF, World Economic Outlook database; IMF, International Financial Statistics; Haver Analytics; Bloomberg; Caceres and others (2016); World Bank, Global Financial Development Database; Chinn and Ito (2006); CEPII GeoDist Database; Gruss and Kebhajz (2019); International Country Risk Guide; Eora MRIO database; UNCTAD Trade Analysis Information System; WTO Tariff Download Facility; Feenstra and Romalis (2014); Fraser Institute; World Bank, Doing Business Indicators; UNCTAD, World Maritime Review; Calderón, Moral-Benito, and Servén (2015); World Bank, World Development Indicators database; Chapter 3 of the October 2014 World Economic Outlook.
- Authors and support: Weicheng Lian, Natalija Novta, Evgenia Pugacheva, Yannick Timmer, and Petia Topalova (lead), with support from Jilun Xing and Candice Zhao.

### Data definitions and construction of price measures
- Relative price of investment is defined relative to the price of consumption.
- Cross-country stylized facts on relative prices use ICP 2011 measures of the price level of machinery and equipment and the price level of consumption for a comparable basket of goods across countries in 2011.
- Evolution of prices over time uses PWT 9.0, which incorporates ICP vintages (1970, 1975, 1980, 1985, 1996, 2005, 2011) and OECD/Eurostat data to derive aggregate investment and consumption price levels.
- Construction following Restuccia and Urrutia (2001) and Karabarbounis and Neiman (2013): the relative price of overall investment is divided by the relative price of investment in the United States and then multiplied by the ratio of the investment price deflator to the consumption deflator for the United States (from the Bureau of Economic Analysis) to cancel out international prices embedded in the PPP-adjusted series.
- Country-level panel regressions and stylized facts (Figure 3.2) use PWT 9.0 capital detail dataset (deflators of various types of investment and capital stocks) and PWT 9.0 national accounts consumption deflator.
- Sector-level panel regressions on investment in machinery and equipment use EU and World KLEMS databases; relative price = machinery and equipment deflator / country-wide consumption deflator.
- Sector-level panel regressions on drivers of sectoral producer prices use WIOD Socio Economic Accounts sectoral gross output deflator.
- Unit-price analysis uses highly disaggregated bilateral trade data (US HS 10-digit, Japan HS 9-digit, France and Germany HS 8-digit, China HS 6-digit).
- Real interest rate = nominal interest rate adjusted for inflation measured by the GDP deflator.

### Annex Table 3.1.1 — Indicators and sources (selected entries preserved)
- Investment, Consumption, and GDP Prices: International Comparison Program 2011; Penn World Table 9.0; KLEMS; WIOD; Bureau of Economic Analysis
- Investment-to-GDP Ratios: Penn World Table 9.0, including capital detail and national accounts; KLEMS; WIOD
- Unit Prices of Exports at the Product Level: US Census Bureau; Eurostat; COMTRADE; Ministry of Finance of Japan
- Real GDP per Capita in Purchasing-Power-Parity International Dollars: Penn World Table 9.0
- Nominal Interest Rate: IMF, World Economic Outlook database; IMF, International Financial Statistics; Organisation for Economic Co-operation and Development; Haver Analytics; Bloomberg; Caceres and others (2016)
- Credit-to-GDP Ratio: World Bank, Global Financial Development Database
- Capital Account Openness: Chinn and Ito (2006)
- Capital Stock (by Asset Type): Penn World Table 9.0, Capital Detail
- Bilateral Distance: CEPII GeoDist Database
- Trade Openness: IMF, World Economic Outlook database
- Export Commodity Price: Gruss and Kebhajz (2019)
- Political Risk Rating: International Country Risk Guide
- Global Value Chain Participation: Eora MRIO database; IMF staff calculations
- Tariffs: UNCTAD, Trade Analysis Information System; WTO Tariff Download Facility; Feenstra and Romalis (2014)
- Freedom to Trade Internationally Index: Fraser Institute
- Cost to Import, Time to Import: World Bank, Doing Business Indicators
- Liner Shipping Connectivity Index: UNCTAD, World Maritime Review
- Paved Roads Kilometers per Capita: Calderón, Moral-Benito, and Servén (2015); World Bank, World Development Indicators database; Chapter 3 of the October 2014 World Economic Outlook

### Country groupings and sector definitions
- Definitions of advanced economies, emerging market economies, and low-income countries follow the World Economic Outlook’s definition.
- Tradable capital goods sectors (for this chapter: machinery and equipment and transport equipment) identification:
  - WIOD: sectors 400, 410 and 521 = capital goods producing sectors.
  - Eora MRIO: sectors 9 and 10 = capital goods producing sectors.
  - HS-level trade data: HS codes matched to Broad Economic Categories (BEC); BEC levels 41 (capital goods) and 521 (industrial transport equipment) considered in the analysis.

### Sample of economies used (Annex Table 3.1.2)
- Unit-price analysis: China, France, Germany, Japan, United States
- Economy-level analysis: Albania, Algeria, Angola, Argentina, Armenia, Australia, Austria, Azerbaijan, The Bahamas, Bahrain, Bangladesh, Belarus, Belgium, Bolivia, Botswana, Brazil, Bulgaria, Burkina Faso, Cameroon, Canada, Chile, China, Colombia, Democratic Republic of the Congo, Republic of Congo, Costa Rica, Croatia, Cyprus, Czech Republic, Côte d'Ivoire, Denmark, Dominican Republic, Ecuador, Egypt, El Salvador, Estonia, Ethiopia, Finland, France, Gabon, The Gambia, Germany, Ghana, Greece, Guatemala, Guinea-Bissau, Haiti, Honduras, Hong Kong SAR, Hungary, Iceland, India, Indonesia, Iran, Iraq, Ireland, Israel, Italy, Jamaica, Japan, Jordan, Kazakhstan, Kenya, Korea, Kuwait, Latvia, Lebanon, Liberia, Lithuania, Madagascar, Malawi, Malaysia, Mali, Malta, Mexico, Moldova, Mongolia, Morocco, Mozambique, Myanmar, Namibia, Netherlands, New Zealand, Nicaragua, Niger, Nigeria, Norway, Oman, Pakistan, Panama, Paraguay, Peru, Philippines, Poland, Portugal, Qatar, Romania, Russia, Saudi Arabia, Senegal, Sierra Leone, Singapore, Slovak Republic, Slovenia, South Africa, Spain, Sri Lanka, Suriname, Sweden, Switzerland, Syria, Tanzania, Thailand, Togo, Trinidad and Tobago, Tunisia, Turkey, Uganda, Ukraine, United Kingdom, United States, Uruguay, Venezuela, Vietnam, Yemen, Zambia, Zimbabwe
- Sector-level analysis of drivers of relative producer prices: Australia, Austria, Belgium, Brazil, Bulgaria, Canada, China, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, India, Indonesia, Ireland, Italy, Japan, Korea, Latvia, Lithuania, Luxembourg, Malta, Mexico, Netherlands, Poland, Portugal, Romania, Russia, Slovak Republic, Slovenia, Spain, Sweden, Taiwan Province of China, Turkey, United Kingdom, United States
- Sector-level analysis of relative investment prices and investment rates: Austria, Brazil, Colombia, Czech Republic, Denmark, Finland, France, Germany, Italy, Latvia, Luxembourg, Netherlands, Portugal, Slovak Republic, Slovenia, Spain, Sweden, United Kingdom, United States

### Key personnel and data notes
- Unit-price analysis is based on highly disaggregated bilateral trade data: US export data at the HS 10-digit level, Japanese export data at the HS 9-digit level, French and German export data at the HS 8-digit level, and Chinese export data at the HS 6-digit level.
- The FOB (free-on-board) reporting in export data excludes trade costs, allowing focus on variation due to mark-ups or quality across destinations.
- Real interest rate is derived from nominal interest rate adjusted for inflation as measured by the GDP deflator.

### Stylized facts from Annex 3.2 (evolution and composition)
- Time coverage and data construction:
  - PWT 9.0 used for longer time series; ICP vintages used include 1970, 1975, 1980, 1985, 1996, 2005, 2011.
  - Relative price defined as investment deflator (for each type of capital good) divided by consumption deflator.
  - Year fixed effects from regressions of log relative prices (including country fixed effects) are normalized relative to 1970; shaded areas indicate 95 percent confidence intervals.
- Key patterns:
  - Decline in the price of tradable capital goods (both tangible and intangible) has been widespread; price of structures moved broadly in line with consumption price.
  - For advanced economies and emerging market and developing economies, relative prices of tangible tradable investment goods were on a declining trend since the beginning of the sample, with an acceleration in the pace of decline since the mid-1990s.
  - This acceleration coincided with a pickup in real investment rates in emerging market and developing economies.
- Investment rates and composition:
  - For asset types with larger declines in relative prices (e.g., machinery and equipment and other investment), real investment rates have increased quite significantly across all economies since the 1990s; nominal investment rates changed much less.
  - Dispersion in real investment rates is significantly larger in emerging market and developing economies relative to advanced economies.
  - Real investment rates in tangible tradable capital goods were similar for the median advanced and emerging market and developing economy until the mid-2000s, then diverged: EMDEs’ real investment rates in machinery and equipment (including transport) rose until the global financial crisis and remained relatively robust since; in AEs real investment rates plateaued since the mid-2000s with a dip around the global financial crisis.
  - Real investment rates in structures declined significantly since the global financial crisis in advanced economies while they have steadily increased in emerging market and developing economies.
- Composition in 2014 (PWT 9.0, averages by broad country groups):
  - About 60 percent of gross fixed capital formation in low income countries is accounted for by investment in structures, compared to about 50 percent in advanced economies.
  - Investment in machinery and equipment (including transport) comprises roughly 35 percent of overall investment in all economies.
  - Advanced economies allocate a significantly larger fraction of investment to “other investment” (mostly intellectual property products).

### Unit-price analysis approach (Annex 3.3)
- Motivation: most capital goods produced in a few countries; imported capital goods prices may vary due to mark-ups or trade costs; use export-level FOB values to exclude trade costs.
- Estimation specification (preserved exactly):
  ln(p*)_{p,x,i,t} = α + β·ln(GDPPC)_{i,t} + α_{p,x,t} + ε_{p,x,i,t}
  - ln(p*)_{p,x,i,t}: log unit value for product p by exporting country x to importing country i in year t.
  - Regressor: ln(GDPPC)_{i,t} (log GDP per capita of importing country i in year t), weighted by FOB value of exports.
  - Fixed effects: product*exporting country*year (α_{p,x,t}) to make within product-exporting country comparisons and minimize price differences due to quality.
  - Standard errors clustered at the importing country level.
- Data granularity and sources:
  - US: HS 10-digit exports for 1989–2005 from US Census Bureau (accessed through Peter Schott’s webpage).
  - Japan: HS 9-digit product level data for 1988–2017 from the Ministry of Finance.
  - China: HS 6-digit product level data for 1992–2017 from COMTRADE.
  - Germany and France: HS 8-digit export data for 1988–2017 from Eurostat.
- Identification of capital goods at HS level uses the Broad Economic Categories (BEC) classifications.

*Source: IMF staff compilation.*

### Annex Figure 3.3.1.  Capital Goods Production

### Annex Figure 3.3.1.  Capital Goods Production

### Data and methods
- Sources: Eora MRIO database; ICP 2011; WIOD; and IMF staff calculations.
- Unit-value trade regressions: log unit value of capital goods as dependent variable; regressions include product*exporting country*year fixed effects (Top 5) or product*year fixed effects (individual exporters). Standard errors clustered at the country level.
- Price-index construction (2011): for each importing country i, exporting country x, product p compute uvp,i,x − uvp,x̄ (deviation of log unit value from exporter x’s average across destinations). Aggregate across products and weight by wx,i = US$ value imported by i from x divided by total imports of i from all capital goods exporters in the sample to obtain Pricei.
- Cross-country regressions of absolute and relative capital-goods prices: OLS with heteroskedasticity-robust standard errors. Trade-cost measures used one at a time (distance, UNCTAD liner shipping connectivity, Fraser “Freedom to Trade Internationally”, average applied tariffs on capital goods imports, World Bank “cost-to-import” and “time-to-import”).

### Main empirical findings — unit values and importer income (Annex Table 3.3.1)
- When the five exporting countries are pooled:
  - Log GDP per Capita coefficient: 0.027 (not statistically distinguishable from zero).
  - Number of Observations: 7,132,542.
  - Number of Unique Products: 812.
  - R2: 0.98.
  - Level of Product Disaggregation: HS 10-digit.
- Heterogeneity across exporters (Log GDP per Capita coefficients):
  - US: –0.058*** (Number of Observations: 1,607,743; Unique Products: 1,929; R2: 0.78; HS 6-digit).
  - China: –0.157*** (999,810 obs; 674 products; R2: 0.84; HS 8-digit).
  - France: 0.106*** (1,479,250 obs; 2,380 products; R2: 0.92; HS 8-digit).
  - Germany: 0.033** (2,025,791 obs; 2,373 products; R2: 0.94; HS 9-digit).
  - Japan: 0.028 (1,022,125 obs; 1,352 products; R2: 0.80).
- Interpretation:
  - US and Chinese exporters: statistically significant negative correlation between unit values and importer GDP per capita (firms charge importers from poorer countries higher prices for the same product).
  - Germany and France: unit values significantly higher when shipments are sent to countries with higher GDP per capita (consistent with richer importers obtaining higher-quality variants).
  - Pooling exporters hides substantial exporter-specific heterogeneity.

### Broad country-group results (Annex Table 3.3.2)
- Indicator-variable regressions (Emerging Market Economies; Low Income Countries) — coefficients when all exporters pooled:
  - Emerging Market Economies: –0.047.
  - Low Income Countries: 0.093.
  - Number of Observations: 7,132,542; Unique Products: 812; R2: 0.98; HS 10-digit.
- Exporter-specific patterns:
  - Imports from the US or China: Emerging Market Economies and Low Income Countries appear to pay higher prices than advanced economies (e.g., China → LICs: 0.564***).
  - Imports from France: advanced economies importing from France pay higher prices than poorer countries (France → EMs: –0.149**; France → LICs: –0.280***).
- Coefficients (Emerging Market Economies row by exporter): Top 5: –0.047; US: 0.077*; China: 0.236***; France: –0.149**; Germany: –0.037; Japan: –0.062.
- Coefficients (Low Income Countries row by exporter): Top 5: 0.093; US: 0.239***; China: 0.564***; France: –0.280***; Germany: –0.009; Japan: –0.078.

### Robustness and role of geography/market size (Annex Table 3.3.3)
- Augmented specification controls for market size (log GDP), remoteness (log remoteness), and bilateral distance (log distance).
- Log GDP per Capita coefficients (columns: Top 5; Top 5 with controls; US; China; France; Germany; Japan):
  - 0.027; 0.046; –0.050***; –0.092***; 0.110***; 0.066***; 0.018.
- Log Remoteness coefficients (where reported): –0.173*; –0.400***; 0.040; –0.010; 0.043; –0.338***.
- Log Distance coefficients: 0.075***; 0.197***; –0.191***; 0.087**; 0.083***; 0.182***.
- Log GDP (market size) coefficients: –0.013; –0.047***; –0.070***; 0.023; 0.003; –0.033***.
- Number of Observations (columns): 7,077,421; 7,077,421; 1,603,753; 987,463; 1,466,711; 2,000,981; 1,018,513.
- Number of Unique Products: 812; 812; 1,929; 674; 2,380; 2,373; 1,352.
- R2: 0.98; 0.98; 0.78; 0.84; 0.92; 0.95; 0.81.
- Interpretations:
  - Positive log distance correlation with unit values consistent with Alchian-Allen effect (higher-quality goods survive higher transport costs).
  - Greater remoteness associated with lower unit values (possible lower-quality imports).
  - Larger market size correlated with lower unit values (possible mark-up declining with competition; domestic production presence).

### Trade costs and absolute prices of capital goods (Annex Table 3.4.1)
- Regressions of ln(Absolute Price of Capital Goods) on individual trade-cost measures. Coefficients (Trade Barrier row) and significance:
  - Distance: 0.162*** (Number of Observations: 165; R2: 0.14).
  - Connectivity: –0.168*** (119 obs; R2: 0.05).
  - Freedom to Trade: –0.022* (147 obs; R2: 0.04).
  - Tariffs: 0.016* (165 obs; R2: 0.01).
  - Cost to Import: 0.040*** (151 obs; R2: 0.05).
  - Time to Import: 0.030* (151 obs; R2: 0.03).
- Percent-change implications (Coefficient × Standard Deviation):
  - Distance: 0.048***.
  - Connectivity: –0.028***.
  - Freedom to Trade: –0.024*.
  - Tariffs: 0.014*.
  - Cost to Import: 0.027**.
  - Time to Import: 0.020*.
- Note: robust standard errors in parentheses.

### Decomposition: relative prices explained by productivity and trade costs (Annex Table 3.4.2)
- Dependent variable: Relative Price of Capital Goods (log PI/PC).
- Relative productivity (tradable vs nontradable) coefficient (Trade Barrier columns: Distance, Connectivity, Freedom to Trade, Tariffs, Cost to Import, Time to Import):
  - –0.467***; –0.467***; –0.499***; –0.352***; –0.396***; –0.314*** (robust s.e. reported).
- Trade Barrier coefficient in the same regressions:
  - Distance column: 0.226** (120 obs; R2: 0.28).
  - Connectivity column: –0.322* (93 obs; R2: 0.28).
  - Freedom to Trade column: –0.237*** (116 obs; R2: 0.55).
  - Tariffs column: 0.219*** (121 obs; R2: 0.43).
  - Cost to Import column: 0.285*** (108 obs; R2: 0.42).
  - Time to Import column: 0.408*** (108 obs; R2: 0.58).
- Interpretation:
  - Relative productivity of tradables versus nontradables strongly and negatively associated with the relative price of capital goods (higher tradable productivity → lower relative capital-goods price).
  - Trade-cost measures (especially time to import and cost to import) are positively associated with higher relative capital-goods prices; measures capturing better connectivity or freer trade are associated with lower relative prices.

### Drivers of relative investment prices — conceptual summary and over-time analysis
- Conceptual reduced form: PI/PC = f(aT/aNT, PI*, trade costs), where:
  - PI/PC is the relative price of capital goods.
  - aT/aNT is productivity in tradable goods relative to nontradables.
  - Trade costs include transport costs, tariffs, customs regulation, time and cost of logistics.
- Over-time approach (Annex 3.5) for 1995–2011 (40 economies, 33 sectors, WIOD):
  - Two-step: (1) estimate elasticity of sectoral producer prices to sectoral labor productivity and exposure to international trade (imports/domestic output), controlling for country-year and country-sector fixed effects; (2) combine estimated elasticities with observed changes in relative labor productivity and trade exposure of capital-goods sectors to quantify contributions to the decline in relative prices of machinery and equipment over 2000–11.
  - Instrumental strategy: import tariffs used as instrument for exposure to trade to isolate policy-driven changes in import penetration from price-driven changes.
  - Adjustment: account for trade’s indirect effect on relative prices via its effect on sectoral labor productivity (avoid understating trade’s contribution).

### Key policy-relevant implications drawn from the empirical results
- Cross-country variation in capital-goods prices is driven by both relative productivity (tradable vs nontradable) and trade-cost measures (notably time-to-import and cost-to-import).
- Reducing logistical trade frictions (time and cost to import) and improving connectivity are empirically associated with lower absolute and relative prices of capital goods.
- Exporter-level pricing behavior varies substantially: policies that affect supplier market structure, quality provision, and market access can influence the prices facing importing countries differently depending on their exporter relationships.
- Measurement caution: quality differences within HS codes and the endogeneity between domestic prices and import penetration require careful empirical strategies (fixed effects, instruments) when attributing causes to price changes.

*Source: IMF staff calculations (Annexes, Chapter 3 technical annexes).*

### CHAPTER 3  THE PRICE OF CAPITAL GOODS: A DRIVER OF INVESTMENT UNDER THREAT?

### CHAPTER 3  THE PRICE OF CAPITAL GOODS: A DRIVER OF INVESTMENT UNDER THREAT?

### Regression Framework
- Two separate regressions are estimated to understand relative contributions of global integration and relative productivity growth to the decline in the relative price of machinery and equipment.
- Relative producer price equation (notation preserved):
  - ln(푃푖,푗,푡 / 푃̅푖,푡) = 훼푖,푗 + 휇푖,푡 + 훽[ln(푀푖,푗,푡 / 푉퐴푖,푗,푡) − ln(푀̅푖,푡 / 푉퐴̅̅̅̅푖,푡)] + 훾 ln(퐿푃푖,푗,푡 / 퐿푃̅̅̅̅푖,푡) + 휀푖,푗,푡
  - Definitions:
    - 푃푖,푗,푡 / 푃̅푖,푡: relative price of sector j in country i at time t.
    - 훼푖,푗: country-sector fixed effects.
    - 휇푖,푡: country-year fixed effects.
    - ln(푀푖,푗,푡 / 푉퐴푖,푗,푡) − ln(푀̅푖,푡 / 푉퐴̅̅̅̅푖,푡): relative import penetration (imports of sector j in country i divided by value added of sector j, relative to country average).
    - 퐿푃푖,푗,푡 / 퐿푃̅̅̅̅푖,푡: relative labor productivity (real value-added per employee).
- Relative import penetration is instrumented by relative import tariff (휏푖,푗,푡 − 휏̅푖,푡):
  - Sector tariff: 휏푖,푗,푡 = (∑_{l∈Λ_j} 푚푖,푘,푙,푡 · 휏̂푖,푘,푙,푡) / (∑_{l∈Λ_j} 푚푖,푘,푙,푡)
  - 푚푖,푘,푙,푡: import of country i from country k in sector l at time t.
  - 휏̂푖,푘,푙,푡: tariff imposed on these imports (SITC 4-digit bilateral preferential tariff data compiled by Feenstra and Romalis (2014)).
  - Average tariff: 휏̅푖,푡 = ∑_{j=1}^{J} 휏푖,푗,푡 / J.
- Relative labor productivity equation:
  - ln(퐿푃푖,푗,푡 / 퐿푃̅̅̅̅푖,푡) = 훼푖,푗^{퐿푃} + 휇푖,푡^{퐿푃} + 훽^{퐿푃}[ln(푀푖,푗,푡 / 푉퐴푖,푗,푡) − ln(푀̅푖,푡 / 푉퐴̅̅̅̅푖,푡)] + 휀푖,푗,푡^{퐿푃}
  - Relative import penetration is instrumented by relative import tariff here as well to address reverse causality concerns.
- Exogeneity assumption for tariffs:
  - cov(휏푖,푗,푡 − 휏̅푖,푡, 휀푖,푗,푡) = cov(휏푖,푗,푡 − 휏̅푖,푡, 휀푖,푗,푡^{퐿푃}) = 0.

### First-Stage, Reduced-Form, and Robustness Results (Annex Tables 3.5.1–3.5.3)
- Annex Table 3.5.1 (First-stage and reduced form):
  - Dependent variables: Relative Import Penetration (column 1) and Relative Producer Prices (column 2).
  - Import Tariff coefficient on Relative Import Penetration: −0.014*** (standard error (0.003)).
  - Import Tariff coefficient on Relative Producer Prices: 0.010*** (standard error (0.003)).
  - Relative Productivity t−1 coefficient on Relative Producer Prices: 0.003 (column 1) and −0.308*** (column 2) with (0.014) and (0.036) in parentheses respectively.
  - Number of Observations: 16,077 for both columns.
  - R^2: 0.96 (column 1), 0.62 (column 2).
  - Interpretation: first-stage relationship between import tariff and import penetration is very strong, suggesting import tariff is a good instrument; reduced form suggests lower import tariff leads to a decline in producer price after controlling for labor productivity.
- Annex Table 3.5.2 (Relative Producer Prices, Trade Integration, and Relative Productivity):
  - Dependent Variable: Relative Producer Prices.
  - Key coefficients (selected, with sample/context in table):
    - Relative Import Penetration t−1 (OLS column 1): −0.135*** (0.033).
    - Relative Import Penetration t−1 (IV columns): −0.568*** (0.146), −0.574*** (0.163), −0.413*** (0.148), −0.964*** (0.374), −0.461** (0.200), −0.458*** (0.177).
    - Relative Productivity t−1: −0.316*** (0.035), −0.328*** (0.032), −0.328*** (0.032), −0.349*** (0.041), −0.274*** (0.034), −0.302*** (0.031), −0.368*** (0.039).
  - Number of Observations varies across columns: 16,077; 12,575; 3,502; 12,321; 15,086.
  - R^2 ranges: 0.40–0.71 across columns.
  - Relative Import Penetration for Capital Goods Sectors reported in a row with coefficients (e.g., −0.541* (0.287) in one column).
  - Notes: Relative labor productivity t-2 is used as an instrument for relative labor productivity t-1. Significance levels: *** p < 0.01; ** p < 0.05; * p < 0.1.
- Annex Table 3.5.3 (Labor Productivity and Trade Integration):
  - Dependent Variable: Relative Productivity.
  - Relative Import Penetration t−1 coefficients:
    - OLS column: 0.054 (0.049).
    - IV columns include large positive coefficients: 1.639 (0.000), 1.363*** (0.363), 0.793*** (0.305), 2.403** (1.041), 1.251*** (0.449).
  - Relative Import Penetration for Capital Goods Sectors row shows e.g., 0.108 (0.110), 2.771*** (0.564), 2.758*** (0.624), 2.563*** (1.089), 4.061*** (1.686) across columns.
  - Number of Observations across columns: 16,077; 12,575; 3,502; 12,321.
  - R^2 very high: 0.88–0.95 across columns.
  - Interpretation: IV estimates show a stronger positive effect of import penetration on relative labor productivity than OLS, confirming the need to address endogeneity.

### Decomposing Changes in Relative Producer Prices of Capital Goods Producing Sectors
- Decomposition uses coefficients from column (3) of Annex Table 3.5.2 and column (4) of Annex Table 3.5.3.
- Change in relative price of investment from 2000 to 2011 is decomposed into four components (defined precisely as in source):
  - (i) Direct effect of deepening trade integration:
    - Simple average of 훽 × { [ln(푀푖,푗,2011 / 푉퐴푖,푗,2011) − ln(푀̅푖,2011 / 푉퐴̅̅̅̅푖,2011)] − [ln(푀푖,푗,2000 / 푉퐴푖,푗,2000) − ln(푀̅푖,2000 / 푉퐴̅̅̅̅푖,2000)] } across countries and sectors.
  - (ii) Effect of trade integration through higher labor productivity:
    - Simple average of 훾 × 훽_{퐿푃} × { same bracketed difference as in (i) } across countries and sectors.
  - (iii) Effect of higher labor productivity not due to trade integration:
    - Simple average of 훾 × { [ln(퐿푃푖,푗,2011 / 퐿푃̅̅̅̅푖,2011) − ln(퐿푃푖,푗,2000 / 퐿푃̅̅̅̅푖,2000)] − 훽_{퐿푃} × { same bracketed difference as in (i) } } across countries and sectors.
  - (iv) Contributions of other factors (residual term).

### Empirical Evidence on the Impact of Relative Investment Prices on Investment Rates (Annex 3.6)
- Conceptual basis:
  - A decline in the relative price of investment (from productivity increase in capital-goods sector or decline in capital goods tariffs) raises the optimal steady-state capital stock as a share of output, implying higher real investment-to-GDP ratios to maintain that stock.
- Regression specification (notation preserved):
  - ln(Real M&E Investment / Real GDP)_{i,t} = β · ln(P_{M&E} / P_{GDP})_{i,t} + Controls_{i,t} + μ_i + θ_t + ε_{i,t}
  - P_{M&E} constructed as weighted average of machinery and transport equipment prices:
    - P_{M&E} = (I_{Machinery} / I_{M&E}) P_{Machinery} + (I_{Transport} / I_{M&E}) P_{Transport}.
- Controls include (as listed in source): lagged level and growth rate of real GDP per capita (PPP), lagged dependent variable, real interest rates, credit-to-GDP ratio, capital account openness, trade openness, exposure to commodity shocks (weighted measure), institutional quality and political risks, kilometers of paved roads per capita.
- Estimation approach:
  - Regressions estimated on five-year non-overlapping window averaged data (except column 4 in Annex Table 3.6.1 which uses annual data).
  - Columns 1–4: OLS specifications (baseline, full controls, lagged relative price, annual data).
  - Columns 5–10: IV regressions where relative price is instrumented using its own lag; first-stage F-statistics above 10 across IV specifications.
  - Column 11: system GMM estimator (two-step with Windmeijer correction).
  - Column 12: IV where relative price is instrumented with average relative price of all other countries except own.
- Key empirical findings (Annex Table 3.6.1 — selected coefficients and statistics preserved):
  - Main IV estimate (column 5) — Log Relative Price coefficient: −0.377*** (0.116).
  - OLS and alternative specifications show consistently negative and significant coefficients on log relative price:
    - Column 1 (OLS): −0.624*** (0.075).
    - Column 3 (OLS, lagged): −0.221*** (0.079).
    - Column 4 (Annual OLS): −0.092*** (0.030).
    - Column 6 (IV, post 1990): −0.292* (0.171).
    - Column 7 (IV, EMDE): −0.491*** (0.161).
    - Column 8 (IV, AE): −0.558*** (0.136).
    - Column 11 (GMM): −0.191** (0.088).
    - Column 12 (IV excluding own): −0.481*** (0.086).
  - Log Investment Rate t−1 coefficients (persistence):
    - Column 1: 0.412*** (0.085).
    - Column 3: 0.776*** (0.026).
    - Column 5: 0.378*** (0.086).
  - Log GDP per Capita t−1 coefficients generally negative and significant in many columns (e.g., −0.173** (0.085) in column 2).
  - Trade openness positively correlated with investment rates (e.g., 0.252* (0.134) in column 1; 0.136*** (0.038) in column 3).
  - Institutional quality and political risk positive and significant (e.g., 0.009*** (0.003) in column 1).
  - Log Paved Roads per Capita positive and significant in some columns (e.g., 0.051** (0.021) in column 3).
  - First Stage F-Statistics in IV columns: 118.80; 81.81; 64.04; 87.17; 96.87; 169.20; 134.70 (reported across columns).
  - Number of Observations and Countries:
    - Number of Observations across columns: e.g., 1,688 (col 1), 658 (col 2), 2,944 (col 4), 658 (col 5).
    - Number of Countries: up to 173 (col 1), 127 (cols 2–5), 93 (col 7), 34 (col 8), 108 (col 9).
  - Long-run effect (annual data, dividing coefficient by (1 – coefficient on lagged dependent variable)): −0.410*** (0.125) (reported).
- Interpretation and substantive conclusions:
  - Across all specifications, the coefficient on the relative price of machinery and equipment is significant and negative, indicating that a decline in the relative price of investment is associated with higher real investment rates.
  - The big decline in the relative prices of machinery and equipment over past decades has been a significant contributor to the rise in investment-to-GDP ratios.
  - Based on five-year window average data (column 5) for a sample of 75 countries with data in both periods, between 1990–94 and 2010–14 machinery and equipment investment rates grew by more than 60 percent in EMDEs (increasing from 5 percent to over 8 percent), and a significant portion of that change can be attributed to the decline in relative prices of machinery and equipment.

*Source: IMF staff calculations, Annexes to CHAPTER 3 THE PRICE OF CAPITAL GOODS: A DRIVER OF INVESTMENT UNDER THREAT? (April 2019).*

### Annex 3.7. Empirical Evidence on the Impact of Relative Investment Prices on Investment

### Annex 3.7. Empirical Evidence on the Impact of Relative Investment Prices on Investment

### Data and variable construction
- Data sources: EU KLEMS and World KLEMS.
- Sample: typically 18–19 countries (mostly European, plus United States, United Kingdom, Brazil, and Colombia), 15 broad sectors, period 1971–2015. This is an unbalanced panel.
- Sector coverage (as in source): A: Agriculture, forestry and fishing; B: Mining and quarrying; C: Total manufacturing; D-E: Electricity, gas and water supply; F: Construction; G: Wholesale and retail trade, repair of motor vehicles and motorcycles; H: Transportation and storage; I: Accommodation and food service activities; J: Information and communication; K: Financial and insurance activities; L: Real estate activities; M-N: Professional, scientific, technical, administrative and support service activities; O: Public administration and defense, compulsory social security; P: Education; Q: Health and social work.
- Construction of machinery and equipment price, P_M&E: P_M&E is a weighted average of the prices of four types of capital within Machinery and Equipment: IT (computer hardware), CT (telecommunications equipment), Transport Equipment, and Other machinery and equipment. Weights are shares of each asset type in total machinery and equipment investment of the sector.
  - Equation (as presented):
    P_M&E = (I_IT / I_M&E) P_IT + (I_CT / I_M&E) P_CT + (I_TraEq / I_M&E) P_TraEq + (I_OMach / I_M&E) P_OMach

### Empirical specification
- Baseline specification (five-year non-overlapping averages) mirrors country-level regressions and instruments the log relative price of investment (relative to price of consumption) with its lagged value.
- Regression equation (as presented):
  ln(Real M&E In / Real VA)_{i,t,s} = β · ln(P_M&E / P_C)_{i,t,s} + γ · ln(Real M&E In / Real VA)_{i,t-1,s} + μ_{i,t} + θ_{i,s} + ε_{i,t,s}
- Fixed effects strategies:
  - Baseline: country-period and country-sector fixed effects (period = five-year windows).
  - Alternative: country-sector and 5-year period (or year) fixed effects to avoid absorbing aggregate within-country-period variation.
- Instrument: lagged log relative price of machinery and equipment.
- Frequency: main results use five-year averages; robustness checks use annual data.

### Main empirical findings (five-year averages)
- Regressions include lagged dependent variable and standard errors clustered at the country level.
- Selected coefficient estimates from Annex Table 3.7.2 (dependent variables in columns (1)–(8)):
  - Log Real Investment-to-GDP Ratio:
    - Column (1) (IV, country-period & country-sector FE): Log Relative Price = –0.326*** (0.078)
    - Column (5) (IV, period & country-sector FE): Log Relative Price = –0.528*** (0.068)
  - Log Real Investment:
    - Column (2) (OLS): Log Relative Price = –0.192** (0.079)
    - Column (6) (OLS): Log Relative Price = –0.444*** (0.071)
  - Log Value Added:
    - Column (3) (OLS): Log Relative Price = –0.061*** (0.018)
    - Column (7) (OLS): Log Relative Price = –0.058*** (0.015)
  - Log Value Added per Worker:
    - Column (4) (OLS): Log Relative Price = –0.016 (0.025)
    - Column (8) (OLS): Log Relative Price = –0.033 (0.021)
- Sample sizes and fit statistics (five-year averages):
  - Number of observations: typically 971 for many specifications; other columns report 1,046, 972, 747 depending on dependent variable and specification.
  - R^2 reported as high (examples: 0.94, 0.93, 0.99 across specifications).
  - First Stage F-Statistics reported (examples): 645, 643, 729, 729 (five-year IV specifications).

### Robustness and annual-frequency results
- Annual-frequency regressions (Annex Table 3.7.3) produce smaller magnitude coefficients (consistent with dampened annual changes) but maintain expected signs and statistical significance except for sectoral output per worker.
- Selected annual-frequency coefficient estimates (from Annex Table 3.7.3):
  - Log Relative Price coefficients (columns (1)–(8)):
    - –0.170*** (0.018)
    - –0.264*** (0.018)
    - –0.013*** (0.003)
    - –0.005 (0.004)
    - –0.203*** (0.017)
    - –0.279*** (0.017)
    - –0.011*** (0.003)
    - –0.007* (0.004)
- Annual sample sizes and fit statistics:
  - Number of observations: 5,629; 6,004; 5,644; 4,430 across specifications.
  - R^2 examples: 0.96, 0.99, 0.99, 0.99.
  - First Stage F-Statistics (annual): 20,770; 18,595; 26,232; 12,603; and other large values reported (e.g., 23,442; 20,477; 33,690; 14,700).
- Fixed effects in annual regressions: country-year and country-sector or year and country-sector depending on specification.

### Key takeaways
- Higher relative prices of machinery and equipment are associated with statistically significant reductions in sectoral investment rates (Log Real Investment-to-GDP and Log Real Investment) across multiple specifications.
- Negative effects on sectoral value added are small in magnitude but statistically significant in several specifications; effects on value added per worker are smaller and often not statistically significant.
- Results are robust to instrumentation with lagged relative prices, alternative fixed effects structures, and both five-year averaged and annual data, with coefficients smaller in magnitude at annual frequency.

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_Source: https://www.imf.org/-/media/files/publications/weo/2019/april/english/ch3annex.pdf_