## _wp1532

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### Key findings on euro area investment dynamics
- Total investment in real terms remains below its pre-crisis level across the euro area.
- Private non-residential investment remains well below its pre-crisis level particularly in stressed countries.
- The decline in investment is larger in stressed economies than in core economies; conditions for SMEs have worsened more than for larger corporations.
- Real GDP in the euro area remains below its pre-crisis level; the output gap is negative and large, and the recovery is more sluggish than in typical recessions.
- The investment-to-GDP ratio in the euro area stands at 4¼ percentage points below the pre-crisis level.
- Evidence from previous financial crises shows that the peak impact on the investment-to-GDP ratio can be 3 to 3½ percentage points three years after the crisis (WEO, 2014).
- Corporate debt financing in the euro area is about 90 percent bank-based.
- Only about one in five recoveries is creditless (IMF, 2014).

### Data coverage, scope, and heterogeneity
- Country coverage for time series regressions: euro area, Germany, France, Italy, Spain, Portugal, Ireland and Greece.
- Regression frequency: quarterly data.
- Regression sample periods: depending on data availability, from the 1990s up to 2012 or 2013.
- Stressed countries defined as debtor countries that experienced high funding costs and financial fragmentation; examples include Greece, Ireland, Italy, Portugal, and Spain.
- Core countries example grouping: Germany, France, Belgium, Netherlands.
- Notes on data availability: Last available data point: DEU = 2012Q4; PRT = 2013Q3. Ireland excluded from May 2011 and Greece from September 2012 in the sample due to lack of data.
- Appendix 1: data sources and definitions; for Ireland and Greece total real investment is used.

### Drivers and mechanisms examined
- Output dynamics (accelerator effects).
- User cost of capital (neoclassical model / real cost of capital).
- Uncertainty, borrowing costs, leverage, and cash flow (the “accelerator +” specification).
- Financial fragmentation, high corporate leverage, and policy uncertainty as contributing factors to weak investment dynamics.
- Credit access and financing costs: lending rates in some countries remain elevated despite the ECB policy rate being effectively at the lower bound; higher bank lending rates raise the cost of capital, especially for smaller firms.
- Credit trends: high non-performing loans and ongoing deleveraging in corporate and banking sectors; credit to the private sector continues to shrink.

### Empirical approach and model specifications
- Preferred approach: country-by-country estimation of aggregate investment equations (time series regressions) to allow heterogeneity in coefficients.
- Three model types used:
  - Accelerator model: links desired changes in capital stock to output growth; empirical specification divides the investment equation by lagged capital stock and includes lags of changes in real GDP (up to 12 lags used); the constant δ can be interpreted as an indirect estimate of the depreciation rate; the current value of GDP growth is excluded to reduce endogeneity.
  - Neoclassical model: incorporates user cost of capital; with Cobb-Douglas technology and output elasticity of capital equal to θ, desired capital stock is set where real cost of capital r_t equals marginal productivity; augmented specifications include financial-constraints proxies.
  - “Accelerator +” model: combines output changes with uncertainty, borrowing costs, leverage, and cash flow variables (output changes, uncertainty, borrowing costs, leverage, and cash flow).
- Investment equation specified as a distributed lag function of changes in the desired capital stock (following Oliner et al., 1995).
- Autocorrelation control: Newey-West standard errors with truncation parameter 3; robustness checks with Prais-Winsten and Cochrane-Orcutt; lags up to 12 used in robustness checks.
- Alternative specifications tested: Tobin’s Q specifications (quarterly interpolations), debt-focused real cost of capital measures, alternative investment series (machinery and equipment).

### Empirical results — summary and quantitative findings
- Accelerator model
  - Tracks investment closely using output changes, particularly for Spain.
  - Implies sizeable underinvestment for most countries during 2010Q2–2013Q4, except Spain.
  - Lags of changes in real GDP are correctly signed and significant (Table A2.1); δ estimates (interpreted as depreciation) reported, e.g., Euro Area δ = 3.43***, Germany δ = 5.99***, Spain δ = 2.76***, Italy δ = 4.29***, Portugal δ = 3.81*** (Newey-West estimates).
  - Adjusted R-squared values in Table A2.1: Euro Area 0.79; Germany 0.82; Spain 0.95; France 0.86; Greece 0.92; Ireland 0.66; Italy 0.75; Portugal 0.82.
- Neoclassical model
  - Real cost of capital is a significant factor; financial constraints held back investment in some countries.
  - Baseline neoclassical model indicates significant underinvestment over the European debt crisis (except Spain).
  - Coefficients on lagged desired changes in capital stock are generally not statistically significant or positive, except for Greece.
  - Augmented neoclassical model: contemporary and lagged financial constraints have significant negative effects on investment in the euro area as a whole, and in Germany, Spain and Portugal.
  - Sample δ estimates (Table A2.2 and A2.3): Euro Area δ ranges (examples) 1.855*** (neoclassical) and 5.394*** (augmented); country δ estimates vary widely (e.g., Greece δ = 13.24*** (Table A2.2)).
  - Model fit: R-squared values in Table A2.2 range from 0.31 (Euro Area) to 0.907 (Greece); augmented model R-squared in Table A2.3: Euro Area 0.628; Germany 0.702; Spain 0.787; Greece 0.921; Italy 0.659; Portugal 0.747.
- Accelerator + model (additional determinants)
  - Additional regressors: real lending rates for NFCs, corporate bond spreads, uncertainty index, corporate leverage, cash flow, and financial constraints.
  - Omitted-variable tests show additional factors are jointly significant at country and euro-area levels (Table A2.5 FLR/LR statistics, all significant at 1% for many countries).
  - Key quantitative findings:
    - High uncertainty reduces investment: a one standard deviation increase in the uncertainty index reduces investment-to-capital ratio by 0.03-0.1.
    - Corporate leverage: in Portugal, Italy, and France, a one percentage point increase in the leverage ratio reduces investment-to-capital ratio by about 0.01–0.04 percentage points.
    - Financial constraints: negatively associated with investment for Italy and Portugal.
    - Cash flow: statistically significant with expected sign for Spain and Germany; Portugal has reverse sign with weaker significance; alternative measures yield mixed results.
    - Corporate bond spreads: statistically significant for Ireland, Spain and, to a lesser degree, Germany.
    - Real lending rates: often insignificant or with reverse signs; significant with expected negative correlation only for Italy. For the euro area, Germany and Spain the real rate coefficients are statistically significant but have the reverse sign.
  - Model performance: works better for stressed countries (particularly Italy and Spain, and to a lesser extent Portugal and the euro area); performs poorly for Germany and France.
  - Accelerator + model reported fit (Table A2.4): R-squared examples — Euro Area 0.88; Germany 0.84; Spain 0.98; France 0.68; Greece 0.94; Ireland 0.93; Italy 0.97; Portugal 0.94.
  - Using estimated coefficients from the Accelerator + model: output changes explain a large share of weak euro-area investment from 2008 onwards; uncertainty, corporate leverage and other factors explain additional shares. For Spain, weak output explains almost all the decline; for Italy and Ireland, additional factors were the main drag.

### The magnitude of missing investment
- Definition: “unexplained investment shortfall” = cumulative sum of residuals from 2010Q2 (inclusive) to the end of the sample (predicted minus actual investment).
- Controlling only for output: cumulative unexplained shortfall in investment is about 3–6 percent of GDP (excluding Spain). Shortfall highest for Italy and Portugal.
- After controlling for additional determinants (uncertainty, corporate leverage, financial fragmentation, etc.): cumulative shortfall declines to about ½–2 percent of GDP.
  - Italy and Portugal: shortfall declines from about 6 percent of GDP to less than 1 percent of GDP.
- Spain: missing investment is around zero across the models due to better overall model fit.
- Data coverage caveats: DEU ends in 2012Q4 and PRT in 2013Q3.

### Implications and policy recommendations
- Macro/structural consequences
  - Weak investment performance has coincided with large output losses and a more sluggish recovery than in typical recessions, implying potential long-term consequences via lower potential output.
  - Improvements in corporate bond and stock markets are likely to benefit mainly larger corporations with better access to capital markets, leaving SMEs more constrained.
  - As companies repair balance sheets and reduce debt, demand for credit remains low, contributing to a prolonged weak investment recovery.
- Policy recommendations
  - Investment expected to pick up as recovery strengthens and uncertainty declines.
  - Complementary policy actions at national and euro-area levels required: demand support, balance sheet repair, completion of the banking union, and structural reforms.
  - Address corporate debt overhang and financial fragmentation to support firms’ access to capital in stressed countries.
  - Future research: firm-level investment analysis (particularly SMEs) to better capture firm-specific determinants such as cash flow, leverage, and Tobin’s Q.

### Selected data and measurement notes (key figures preserved)
- Real cost of capital: as of the latest available data reported in Appendix 1:
  - Lowest real cost of capital is in Germany (5 percent).
  - Highest real cost of capital is in Portugal (12.0 percent).
- Corporate debt financing is about 90 percent bank-based in the euro area.
- Uncertainty index: natural log of uncertainty index * 100; Italy’s index used as a proxy for Spain, Portugal, Ireland and Greece due to lack of data.
- Corporate bond spreads: measured in basis points using average spread of corporate over government bonds with 1 to 5 years maturity (Merill-Lynch indices).
- Financial constraints: percent of correspondents listing financial constraints as factor limiting production (European Commission’s Business and Consumer Survey, quarterly, seasonally adjusted).
- Appendix 2 estimation samples: examples — EA sample includes 1991Q1 - 2013Q4; Germany 1994Q1-2012Q4; Spain and Greece 1995Q1 - 2013Q4; France 1990Q1 - 2013Q4; Ireland 2000Q2 - 2013Q3; Italy 1991Q1 - 2013Q4; Portugal 1998Q2 - 2013Q3.

_Italic: Content drawn from _wp1532 - References (PDF chapter/section)._

### References .............................................................................................................

### _wp1532 - References .............................................................................................................

### Key findings on euro area investment dynamics
- Total investment in real terms remains below its pre-crisis level across the euro area.
- Private non-residential investment remains well below its pre-crisis level particularly in stressed countries.
- The decline in investment is larger in stressed economies than in core economies; conditions for SMEs have worsened more than for larger corporations.
- Real GDP in the euro area remains below its pre-crisis level; the output gap is negative and large, and the recovery is more sluggish than in typical recessions.
- The investment-to-GDP ratio in the euro area stands at 4¼ percentage points below the pre-crisis level.
- Evidence from previous financial crises shows that the peak impact on the investment-to-GDP ratio can be 3 to 3½ percentage points three years after the crisis (WEO, 2014).
- Corporate debt financing in the euro area is about 90 percent bank-based.
- Only about one in five recoveries is creditless (IMF, 2014).

### Data, scope, and heterogeneity
- Country coverage for time series regressions: euro area, Germany, France, Italy, Spain, Portugal, Ireland and Greece.
- Regression frequency: quarterly data.
- Regression sample periods: depending on data availability, from the 1990s up to 2012 or 2013.
- Stressed countries defined as debtor countries that experienced high funding costs and financial fragmentation during the period covered; examples include Greece, Ireland, Italy, Portugal, and Spain.
- Core countries example grouping: Germany, France, Belgium, Netherlands.
- Notes on specific series and data availability: Last available data point: DEU = 2012Q4; PRT = 2013Q3. In the sample, Ireland is excluded from May 2011 and Greece from September 2012 due to lack of data.

### Drivers and mechanisms examined
- Output dynamics (accelerator effects).
- User cost of capital (neoclassical model / real cost of capital).
- Uncertainty, borrowing costs, leverage, and cash flow (the “accelerator +” specification).
- Financial fragmentation, high corporate leverage, and policy uncertainty as contributing factors to weak investment dynamics.
- Credit access and financing costs: lending rates in some countries remain elevated despite the ECB policy rate being effectively at the lower bound; higher bank lending rates raise the cost of capital, especially for smaller firms.
- Credit trends: high non-performing loans and ongoing deleveraging in corporate and banking sectors; credit to the private sector continues to shrink.

### Empirical approach and models
- Preferred approach: country-by-country estimation of aggregate investment equations (time series regressions) to allow heterogeneity in coefficients.
- Three model types used:
  - Accelerator model: links desired changes in capital stock to output growth.
  - Neoclassical model: incorporates user cost of capital; with Cobb-Douglas technology and output elasticity of capital equal to θ, desired capital stock is set where real cost of capital r_t equals marginal productivity.
  - “Accelerator +” model: combines output changes with uncertainty, borrowing costs, leverage, and cash flow variables (output changes, uncertainty, borrowing costs, leverage, and cash flow).
- The investment equation is specified as a distributed lag function of changes in the desired capital stock (following Oliner et al., 1995).
- For the accelerator model the empirical specification divides the investment equation by lagged capital stock and includes lags of changes in real GDP (up to 12 lags used); the constant δ can be interpreted as an indirect estimate of the depreciation rate.
- The current value of GDP growth is excluded from the estimated equation to reduce endogeneity concerns.

### Empirical results (summary)
- The accelerator model, relying only on output changes, tracks investment closely, particularly for Spain, but actual post-crisis investment has remained below its model-implied value for most countries.
- The neoclassical model confirms that real cost of capital is a significant factor and that financial constraints held back investment in some countries; nevertheless, actual post-crisis investment is still below its estimated level for most countries.
- The “accelerator +” model reduces the difference between actual and estimated investment compared with simpler specifications.
- Uncertainty is associated with low investment in most countries.
- Corporate leverage is negatively associated with investment in Italy, Portugal, and France.
- Lags of changes in real GDP in the accelerator specification are correctly signed and significant (Table A2.1 referenced).

### Conceptual and literature context
- Traditional investment models discussed: Tobin’s Q, accelerator, neoclassical, and Euler-equation formulations.
- Tobin’s Q approach models investment using the value of capital in place relative to its purchase price (Tobin, 1969; Hayashi, 1982).
- Accelerator model literature: Clark (1917); Jorgenson (1971).
- Neoclassical model and user cost of capital: Jorgenson (1971); Caballero (1994).
- Bond-market–based Q and credit-risk considerations: Philippon (2009) — Bond Market’s Q is a function of the real risk-free rate, the spread between bond yields and government bonds, leverage, and uncertainty.
- Uncertainty and cash-flow literature: Baum et al. (2010); Bloom (2009); Bloom et al. (2007, 2009); Dixit and Pindyck (1994).
- Empirical work on Europe: Bond et al. (2003); Mizen and Vermeulen (2005); European Investment Bank (EIB, 2013) — EIB finds uncertainty the principal driver of the decline in investment since 2010, with financing constraints a serious concern for only some countries.

### Implications highlighted
- Weak investment performance has coincided with large output losses and a more sluggish recovery than in typical recessions, implying potential long-term consequences via lower potential output.
- Improvements in corporate bond and stock markets are likely to benefit mainly larger corporations with better access to capital markets, leaving SMEs more constrained.
- As companies repair balance sheets and reduce debt, demand for credit remains low, contributing to a prolonged weak investment recovery.

*Source: _wp1532 - References (PDF chapter/section).*

### Appendix 1 presents data sources and definitions. For Ireland and Greece, total real investment is used.

### _wp1532 - Appendix 1 presents data sources and definitions. For Ireland and Greece, total real investment is used.

### Estimation strategy and robustness checks
- Autocorrelation control: Newey-West standard errors with truncation parameter 3.
- Alternative serial-correlation correction: Prais-Winsten estimates and Cochrane-Orcutt estimation produce broadly similar coefficient signs; Prais-Winsten reduces statistical significance of lagged terms for Ireland and Portugal.
- Lag structure: Given data availability, lags up to 12 were also used in robustness checks.
- Alternative investment series and narrower proxies: Different measures of machinery and equipment investment for Ireland and Germany (data up to 2013Q4) produce broadly similar results.
- Tobin’s Q specifications considered: quarterly series interpolated from annual Tobin’s Q; price-to-book ratio; stock prices deflated by GDP deflator. Tobin’s Q model performed weakly at aggregate level.

### A. Accelerator model — findings
- The accelerator model captures broad investment trends but implies sizeable underinvestment for most countries during 2010Q2– 2013Q4, except Spain.
- Spain: model explains variation in investment relatively well.
- Greece and Ireland: model does not adequately explain total investment behavior.
- For most countries, underinvestment becomes smaller towards the end of the sample.
- Baseline residuals are serially correlated; robustness with alternative lag selection and estimators does not alter main conclusions.

### B. Neoclassical model — findings
- Model augments accelerator framework by adjusting desired capital stock for the real cost of capital and adding a proxy for credit rationing (European Commission’s financial constraints survey item).
- Both nominal and real costs of capital are elevated for stressed countries; reduced policy rates lowered borrowing costs in core countries but borrowing costs remained elevated in stressed countries.
- Higher real cost of capital → lower desired capital stock → lower desired investment.
- Baseline neoclassical model indicates significant underinvestment over the European debt crisis (except Spain).
- Coefficients on lagged desired changes in capital stock are generally not statistically significant or positive, except for Greece.
- In the augmented model, contemporary and lagged financial constraints have significant negative effects on investment in the euro area as a whole, and in Germany, Spain and Portugal.
- Results are qualitatively robust to: alternate lag selection strategies; a measure of the real cost of capital focused on debt financing; and using narrower proxies for non-residential investment for Germany and Ireland.
- Intercept terms in crisis-interaction specifications are generally significant; interaction terms show mixed results.

### C. Accelerator + model (additional determinants)
- Additional regressors: real lending rates for non-financial corporations (NFCs), corporate bond spreads, uncertainty (economic policy uncertainty index), corporate leverage, cash flow, and financial constraints.
- Omitted-variable tests show these additional factors are jointly significant at country and euro-area levels.
- Key quantitative and qualitative findings:
  - High uncertainty reduces investment: a one standard deviation increase in the uncertainty index reduces investment-to-capital ratio by 0.03-0.1.
  - Corporate leverage: in Portugal, Italy, and France, a one percentage point increase in the leverage ratio reduces investment-to-capital ratio by about 0.01–0.04 percentage points.
  - Financial constraints: negatively associated with investment for Italy and Portugal.
  - Cash flow: statistically significant with expected sign for Spain and Germany; for Portugal the coefficient has the reverse sign with weaker significance; alternative cash flow-to-sales measures yield mixed results.
  - Corporate bond spreads: statistically significant for Ireland, Spain and, to a lesser degree, Germany.
  - Real lending rates: often insignificant or with reverse signs; significant with expected negative correlation only for Italy. For the euro area, Germany and Spain the real rate coefficients are statistically significant but have the reverse sign.
- Instrumental-variable approach: includes GDP growth, uncertainty, leverage and real lending rates to proxy demand factors; real rates remain positively correlated with investment, suggesting policy-rate response to the cycle is being picked up.
- Model performance: works better for stressed countries (particularly Italy and Spain, and to a lesser extent Portugal and the euro area); performs poorly for Germany and France.
- Using estimated coefficients from the Accelerator + model: output changes explain a large share of weak euro-area investment from 2008 onwards; uncertainty, corporate leverage and other factors explain additional shares. For Spain, weak output explains almost all the decline; for Italy and Ireland, additional factors were the main drag.
- Robustness: alternative investment series for machinery and equipment (Ireland, Germany) and alternative autocorrelation corrections do not alter findings substantially.

### IV. The magnitude of missing investment
- Definition: “unexplained investment shortfall” = cumulative sum of residuals from 2010Q2 (inclusive) to the end of the sample (predicted minus actual investment).
- Controlling only for output: cumulative unexplained shortfall in investment is about 3–6 percent of GDP (excluding Spain). Shortfall highest for Italy and Portugal.
- After controlling for additional determinants (uncertainty, corporate leverage, financial fragmentation, etc.): cumulative shortfall declines to about ½–2 percent of GDP.
  - Italy and Portugal: shortfall declines from about 6 percent of GDP to less than 1 percent of GDP.
- Spain: missing investment is around zero across the models due to better overall model fit.
- Notes: DEU ends in 2012 Q4 and PRT in 2013 Q3 (data coverage caveats).

### V. Conclusion and policy implications
- Drivers of weak investment in the euro area:
  - Output dynamics explain broad trends and much of Spain’s investment movement.
  - For several countries, private non-residential investment remained below levels implied by output since the European debt crisis onset.
  - Financial constraints, high uncertainty and high corporate-sector leverage are important additional impediments—especially for Italy, Portugal, and some stressed countries.
  - The neoclassical model (real cost of capital) is generally not significant except for Greece.
- Policy recommendations and implications:
  - Investment expected to pick up as recovery strengthens and uncertainty declines.
  - Complementary policy actions at national and euro-area levels required: demand support, balance sheet repair, completion of the banking union, and structural reforms.
  - Address corporate debt overhang and financial fragmentation to support firms’ access to capital in stressed countries.
  - Future research: firm-level investment analysis (particularly SMEs) to better capture firm-specific determinants such as cash flow, leverage, and Tobin’s Q.

*Source: IMF staff estimates and calculations.*

### References

### _wp1532 - References

### Key literature cited
- Baker, Scott; Bloom, Nicholas; Davis, Steven, 2013, “Measuring Economic Policy Uncertainty”, Chicago Booth Research Paper No. 13-02.
- Baum, Christopher; Caglayan, Mustafa; and Talavera, Oleksandr, 2010, “On the investment sensitivity of debt under uncertainty”, Economics Letters, Vol. 106, pp. 25–27.
- Bloom, Nick, 2009, “The Impact of Uncertainty Shocks,” Econometrica, Vol. 77, No. 3, pp. 623–85.
- Bloom, Nick; Bond, Stephen; and Van Reenen, John, 2007, “Uncertainty and Investment Dynamics”, Review of Economic Studies, Vol. 74, pp. 391-415.
- Bloom, Nick; Max Floetotto; and Nir Jamovich, 2009, “Really Uncertain Business Cycles” (unpublished; Palo Alto, California: Stanford University).
- Bond, Stephen; Elston, Julie Ann; Mairesse, Jacques; and Mulkay, Benoit, 2003, “Financial Factors and Investment in Belgium, France, Germany, and the United Kingdom: A Comparison Using Company Panel Data” The Review of Economics and Statistics, Vol. 85(1), pp. 153–165.
- Caballero, Ricardo, 1994, “Small Sample Bias and Adjustment Costs,” Review of Economics and Statistics, Vol. 76, No. 1, pp. 52–58.
- Caballero, Ricardo J., 1999, Aggregate Investment, in John B. Taylor and Michael Woodford, eds., Handbook of macroeconomics, Vol 1B, Amsterdam: Elsevier.
- Clark, J.M., 1917, “Business Acceleration and the Law of Demand: A Technical Factor in Economic Cycles,” Journal of Political Economy, Vol. 25, pp. 217–35.
- Dixit, Avinash and Robert Pindyck, 1994, “Investment Under Uncertainty” (Princeton, NJ: Princeton University Press).
- European Investment Bank (EIB), 2013, Investment and Investment Finance in Europe, http://www.eib.org/infocentre/publications/all/investment-and-investment-finance-in-europe.htm
- Hayashi, Fumio, 1982, “Tobin’s Marginal q and Average q: A Neoclassical Interpretation,” Econometrica, Vol. 50, pp. 213–24.
- IMF, Baltic Cluster Report, 2014 Cluster Consultation, Selected Issues, IMF Country Report No. 14/117.
- IMF, Euro Area Policies: 2014 Article IV Consultation-Staff Report, IMF Country Report No. 14/198.
- IMF, Euro Area Policies: Selected Issues; IMF, Country Report No. 14/199; June 26, 2014.
- Jorgenson, D.W., 1971, “Econometric Studies of Investment Behavior: A Survey”, Journal of Economic Literature, Vol. 9, pp. 1111–47.
- Laeven, Luc and Fabián Valencia, 2012, “Systemic Banking Crises Database: An Update”, IMF Working Paper 12/163 (Washington: International Monetary Fund).
- Lee, Jaewoo, and Pau Rabanal, 2010, “Forecasting U.S. Investment”, IMF Working Paper 10/246 (Washington: International Monetary Fund).
- Mizen, Paul and Vermeulen, Philip, 2005, ”Corporate Investment and Cash-Flow Sensitivity: What Drives the Relationship”, ECB Working Paper Series, No. 485 / May 2005.
- Oliner, Stephen, Glenn Rudebusch, and Daniel Sichel, 1995 “New and Old Models of Business Investment: A Comparison of Forecasting Performance,” Journal of Money, Credit, and Banking, Vol. 27, No. 3, pp. 806–26.
- Pérez Ruiz, Esther, 2014, “The Drivers of Business Investment in France: Reasons for Recent Weakness”, France Selected Issues, Country Report No. 14/183.
- Phillippon, Thomas, 2009, “The Bond Market’s Q,” Quarterly Journal of Economics, Vol. 124, No. 3, pp. 1011–56.
- Pina, Alvaro and Abreu, Ildeberta, 2012, “Portugal: Rebalancing the Economy and Returning to Growth Through Job Creation and Better Capital Allocation”, OECD WP 994.
- Regional Economic Outlook (REO): Asia and Pacific, April 2014, “Sustaining the Momentum: Vigilance and Reforms”, Chapter 2: “Corporate Leverage in Asia: A Fault Line?”, (Washington: International Monetary Fund).
- Sharpe, Steven A. and Gustavo A. Suarez, 2014, “The Insensitivity of Investment to Interest Rates: Evidence from a Survey of CFOs”, Finance and Economics Discussion Series, Federal Reserve Board, Washington D.C.
- Tobin, James, 1969, “A General Equilibrium Approach to Monetary Theory,” Journal of Money, Credit and Banking, Vol. 1, pp. 15–29.
- World Economic Outlook (WEO), April 2014, “Recovery Strengthens, Remains Uneven”: Chapter 3: “Perspectives on Global Real Interest Rates”, (Washington: International Monetary Fund).

### Appendix 1 — Data definitions and sources: main variables and measurement
- Real investment:
  - Investment data from Eurostat except Greece and Ireland, where WEO data for total investment is used.
  - Private non-residential investment defined as sum of investment in transport and other machinery and equipment, cultivated assets, and intangible fixed assets.
  - Country-specific series and sources (as labeled in left panel of first text figure):
    - Greece: Gross capital formation, (NSA, millions of chained 2005 euro); source – ELSTAT; Haver code - N174NCC@G10.
    - Ireland: Gross fixed capital formation (SA, millions of chained 2011 euro); source – CSOI; Haver code - S178NFC@G10.
    - Spain: Gross capital formation (SA/WDA, millions of chained 2008 euro); source – INE; Haver code - S184NFBC@G10.
    - Portugal: Gross capital formation (SA, millions of chained 2006 euro); source – INE; Haver code - S182NFBC@G10.
    - Italy: Gross fixed investment (SA/WDA, millions of chained 2005 euro); source – ISTAT; Haver code - S136NFC@G10.
    - Euro Area: Gross capital formation (SA/WDA, millions of chained 2005 euro); source – Eurostat; Haver code - S025NFBC@G10.
    - United Kingdom: Gross fixed capital formation (SA, millions of chained 2010 pounds); source – ONS; Haver code - S112NFC@G10.
    - France: Gross fixed capital formation (SWDA, millions of Chained 2010 euro); source – INSEE; Haver code - FRSNFIC@FRANCE.
    - United States: gross capital formation (SA, billions of chained 2009 dollars); source – BEA; Haver code - S111NFBC@G10.
    - Germany: Gross capital formation (SA/WDA, billions of chained 2005 euro); source – Bundesbank; Haver code - S134NFBC@G10.
- Capital stock:
  - Series from AMECO database.
  - Annual series linearly interpolated so the stock of capital in the last quarter matches the corresponding annual figure.
  - Alternative measures calculated using perpetual inventory method; initial capital stock values from AMECO scaled by applying appropriate investment subcomponent ratios.
  - Depreciation rates assumed constant and equal to average rates implied by the AMECO series.
- Real GDP (quarterly): from the WEO database.
- Real cost of capital:
  - Liabilities of non-financial corporations broken into bank loans, bonds (securities other than shares), and equity; bond financing share less than 10 percent in most periods and countries.
  - Formula uses amounts of bank loans, bonds, and equity in liabilities and prices for each component:
    - For bank loan liabilities: MFI lending rates in a given country for new business at all maturities, denoted .
    - For bond liabilities: yield on the euro area wide corporate bond index, denoted .
    - To price equity liabilities: yield on 10 year government bond, denoted .
  - From the nominal rate, subtract year-on-year change in investment deflator , add estimated depreciation rate  (implied rates based on AMECO series), assumed constant but different across countries , and multiply by the relative price of investment goods to output, .
  - Also construct a measure of real cost of capital for debt financing composed of bond and bank lending.
  - Empirical note: In most countries the real cost of capital has been declining throughout the 2000s; after the crisis Southern European countries diverged from France and Germany.
  - As of the latest available data:
    - Lowest real cost of capital is in Germany (5 percent).
    - Highest real cost of capital is in Portugal (12.0 percent).
  - Volatility of real cost of capital in Greece is driven by volatility of the investment deflator (shorter sample available).
  - Footnote: Alternative approaches to price equity (e.g., dividend growth model) were experimented with but produced counterintuitive country rankings; using a 10-year government bond establishes a sensible lower bound for the cost of equity and, assuming the risk premium is constant, is not expected to affect the results. For the euro area, simple average of the 10-year bond yields in France, Germany, Spain, and Italy is used.
- Financial constraints:
  - From European Commission’s Business and Consumer Survey (quarterly).
  - Seasonally adjusted series for survey of manufacturing industry: percent of correspondents listing financial constraints as the factor limiting production.
- Corporate bond prices:
  - Use average spread of corporate over government bonds with 1 to 5 years maturity for the euro area as a whole for all countries in the sample, proxied by Merill-Lynch indices (Bloomberg).
  - Measured in basis points.
- Real lending rates:
  - Nominal rates for all loan sizes and maturities from the ECB (and IFS for Greece).
  - Deflated by the annualized same-quarter change in the GDP deflator.
- Uncertainty index:
  - Bloom (2009); Baker, Bloom, Davis (2013).
  - Natural log of uncertainty index * 100.
  - Italy’s index used as a proxy for Spain, Portugal, Ireland and Greece due to lack of data.
  - Database downloadable from http://www.policyuncertainty.com/europe_monthly.html.
- Corporate sector leverage:
  - Debt-to-equity ratio from the ECB, defined as ratio of outstanding debt of nonfinancial corporations to outstanding stock of shares (in percent).
- Cash flow-to-sales:
  - From Worldscope.
- IMF’s Corporate vulnerability: percent, median estimate.
- Crisis dummy:
  - crisis =1 from 2008Q3 (used only for robustness checks).

### Figure and visualization notes
- Figure A1.1 and associated panels present nominal and real cost of capital time series for Germany, Spain, France, Greece, Ireland, Italy, Portugal, and the Euro Area.
- Figure legend/source: HaverAnalytics; and IMF staff estimates.
- Axis labels and series in the figure indicate percentage points for cost of capital over the sample period shown.

*Italic: Content drawn from _wp1532 - References (PDF chapter/section).*

### APPENDIX 2. RESULTS

### APPENDIX 2. RESULTS

### Accelerator Model - Total Investments (Newey-West HAC standard error estimates)
- Results are in percent terms.
- Table A2.1 estimates (standard errors in parenthesis). Columns: Euro Area, Germany, Spain, France, Greece, Ireland, Italy, Portugal.
- α-200700** -222248*** -22311*** -90732*** -37403*** -15327 -57655*** -3756
  - (97242.82) (23056.6) (1592.14) (7255.75) (2735.32) (13273.16) (11991.01) (2851.86)
- β1 0.32*** 0.21*** 0.41*** 0.26*** 0.38** 0.75** 0.47*** 0.29***
  - (0.06) (0.06) (0.09) (0.06) (0.17) (0.28) (0.08) (0.08)
- β2 0.21** 0.23*** 0.49*** 0.23*** 0.70*** 0.99** 0.39*** 0.26**
  - (0.1) (0.07) (0.06) (0.05) (0.15) (0.42) (0.09) (0.1)
- β3 0.25*** 0.25*** 0.23*** 0.23*** 1.10*** 0.92** 0.37*** 0.26***
  - (0.06) (0.06) (0.07) (0.05) (0.1) (0.38) (0.07) (0.06)
- β4 0.22*** 0.18*** -0.05 0.20*** 0.71*** 0.76** 0.19** 0.24***
  - (0.07) (0.04) (0.08) (0.05) (0.12) (0.29) (0.08) (0.07)
- β5 0.13* 0.13*** 0.12* 0.20*** 1.04*** 0.37 0.27*** 0.21**
  - (0.07) (0.04) (0.07) (0.05) (0.12) (0.35) (0.09) (0.08)
- β6 0.16*** 0.10** 0.39*** 0.17*** 1.12*** 0.30 0.18*** 0.19**
  - (0.05) (0.04) (0.06) (0.06) (0.16) (0.39) (0.07) (0.08)
- β7 0.17** 0.07 0.09 0.09* 0.82*** 0.28 0.28*** 0.22***
  - (0.07) (0.05) (0.06) (0.06) (0.18) (0.33) (0.07) (0.07)
- β8 0.06 0.09* 0.00 0.12** 0.57** 0.24*** 0.10
  - (0.04) (0.05) (0.05) (0.05) (0.25) (0.07) (0.07)
- β9 0.10** 0.12** 0.05 0.11** 0.55 0.09 0.16**
  - (0.05) (0.06) (0.04) (0.05) (0.34) (0.07) (0.08)
- β10 0.09* 0.07 0.15*** 0.10** 0.71* 0.18*** 0.16*
  - (0.05) (0.05) (0.03) (0.05) (0.39) (0.06) (0.09)
- β11 0.05 0.10* 0.06* 0.08 1.04*** 0.26*** 0.17*
  - (0.04) (0.05) (0.03) (0.05) (0.35) (0.07) (0.09)
- β12 0.18*** 0.20*** 0.75** 0.38*** 0.16*
  - (0.05) (0.06) (0.3) (0.08) (0.08)
- δ 3.43*** 5.99*** 2.76*** 3.98*** 10.65*** 8.92*** 4.29*** 3.81***
  - (0.38) (0.35) (0.05) (0.16) (0.48) (2.75) (0.3) (0.66)
- N 60 76 76 96 75 64 92 62
- Adjusted R-squared 0.79 0.82 0.95 0.86 0.92 0.66 0.75 0.82
- D-W Statistic 0.50 0.38 0.99 0.33 0.69 0.50 0.35 0.80
- S.E. of regression 0.09 0.14 0.06 0.10 0.39 1.52 0.18 0.18
- Notes: * - significant at 10 percent; ** - significant at 5 percent; *** - significant at 1 percent.
- Samples: EA sample includes 1991Q1 - 2013Q4; Germany: 1994Q1-2012Q4; Spain and Greece: 1995Q1 - 2013Q4; France: 1990Q1 - 2013Q4; Ireland: 2000Q2 - 2013Q3; Italy: 1991Q1 - 2013Q4; Portugal: 1998Q2 - 2013Q3.

### Accelerator Model: Private Non-residential Investment/Capital Ratio (Figure A2.1)
- Sources: Eurostat; IMF. World Economic Outlook database; OECD, Analytical database; European Commission, AMICO database; and IMF staff calculations.
- Note: Total investment for Greece and Ireland.
- Chart series (for each country): Actual, Fitted, Residuals (right scale). (Visual time series covering country-specific sample periods shown.)

### Neoclassical Model: Estimates with Newey West Standard Errors (Table A2.2)
- Estimation Period: 1995Q1 - 2013Q4 for most countries. /1
  - 1/ Sample for Germany ends in 2012Q4. Ireland and Portugal 2013Q3. Greek real cost of capital is available from 2001 onwards and Irish real cost of capital is available from 1999 onwards.
- Selected estimates (standard errors in parenthesis). Columns: Euro Area, Germany, Spain, France, Greece, Ireland, Italy, Portugal.
- α 241,396** -205,726*** 34,672*** 22,430 -51,155*** 92,896*** 166,796*** 12,617***
  - (95,654) (49,825) (7,454) (13,375) (10,192) (17,731) (45,868) (1,816)
- β1 -0.142 -0.0623 -0.00878 0.0226 0.244*** -0.0401 -0.000238 0.00587
  - (0.101) (0.135) (0.0109) (0.0203) (0.0637) (0.0417) (0.0825) (0.0386)
- β2 -0.0927 -0.0766 -0.00998 0.00837 0.202** -0.0452 -0.0122 0.0201
  - (0.0942) (0.132) (0.0118) (0.0215) (0.0807) (0.0524) (0.0694) (0.0412)
- β3 -0.00225 -0.0339 -0.00900 0.00535 0.467*** -0.0451 0.0176 -0.0156
  - (0.0772) (0.122) (0.0120) (0.0193) (0.0610) (0.0497) (0.0788) (0.0492)
- β4 -0.0560 0.00871 -0.00996 -0.00782 0.600*** -0.0619 -0.0197 -0.0154
  - (0.0916) (0.0836) (0.0132) (0.0208) (0.0692) (0.0408) (0.0888) (0.0472)
- β5 -0.0952 -0.0102 0.00393 0.757*** -0.0814*** 0.00507 0.00611
  - (0.0937) (0.0133) (0.0267) (0.0788) (0.0256) (0.110) (0.0470)
- β6 0.0392 -0.00869 0.00895 0.909*** -0.0613*** 0.0202 -0.0262
  - (0.0837) (0.0121) (0.0222) (0.104) (0.0209) (0.113) (0.0567)
- β7 0.0710 -0.00514 0.00957 0.976*** -0.0426*** 0.0167 0.00711
  - (0.0707) (0.0108) (0.0195) (0.124) (0.0147) (0.132) (0.0620)
- β8 0.0184 -0.00168 0.0236 0.829*** -0.0319*** 0.0575 0.00266
  - (0.0921) (0.0112) (0.0180) (0.114) (0.00932) (0.140) (0.0599)
- β9 0.0756 0.00284 0.0169 0.704*** -0.0195** 0.0151
  - (0.0973) (0.0123) (0.0173) (0.0946) (0.00939) (0.119)
- β10 0.157 0.0277 0.511*** -0.0180* 0.00667
  - (0.124) (0.0224) (0.0876) (0.00972) (0.127)
- β11 0.0240 0.270*** -0.0129* 0.0365
  - (0.0230) (0.0613) (0.00740) (0.128)
- β12 0.03090 0.154** -0.00697 0.107
  - (0.0309) (0.0611) (0.00585) (0.159)
- δ 1.855*** 5.937*** 1.224*** 2.040*** 13.24*** -12.42*** -0.6960 0.135
  - (0.394) (0.792) (0.268) (0.267) (1.505) (3.869) (1.044) (0.480)
- N 61 64 62 60 29 50 60 62
- R-squared 0.31 0.397 0.511 0.312 0.907 0.69 0.624 0.633
- Adjusted R-squared 0.155 0.345 0.415 0.118 0.827 0.578 0.517 0.570
- S.E. of regression 0.177 0.231 0.211 0.119 0.4851 1.7090 0.2510 0.283
- D-W Statistic 0.234 0.184 0.182 0.231 0.862 0.281 0.156 0.150

### Neoclassical Model Augmented with Financial Constraints (Table A2.3)
- Estimation Period: 1995Q1 - 2013Q4 for most countries. /1 (sample notes as above).
- Selected estimates (standard errors in parenthesis). Columns: Euro Area, Germany, Spain, France, Greece, Ireland, Italy, Portugal.
- α -507,279*** -450,609*** 9,752 6,546 -44,545** 92,896*** 100,171* 24,477***
  - (186,844) (65,147) (6,595) (18,503) (17,547) (17,731) (55,275) (5,235)
- β1 -0.0960 -0.104 -0.00578 0.0222 0.270*** -0.0401 0.0314 -0.141**
  - (0.0750) (0.0889) (0.00419) (0.0179) (0.0846) (0.0417) (0.0894) (0.0516)
- β2 -0.0820 -0.0665 -0.00884* 0.00497 0.244* -0.0452 -0.0220 -0.205***
  - (0.0780) (0.0998) (0.00466) (0.0203) (0.125) (0.0524) (0.0836) (0.0724)
- β3 0.0197 -0.00688 -0.00616 0.00221 0.482*** -0.0451 0.0284 -0.250**
  - (0.0503) (0.0809) (0.00468) (0.0174) (0.0934) (0.0497) (0.0862) (0.0913)
- β4 0.0057 -0.0400 -0.00671 -0.00585 0.591*** -0.0619 0.00272 -0.109
  - (0.0583) (0.0712) (0.00523) (0.0215) (0.104) (0.0408) (0.101) (0.0873)
- β5 -0.0628 -0.00780 0.00159 0.729*** -0.0814*** 0.0256 -0.0608
  - (0.0772) (0.00566) (0.0271) (0.105) (0.0256) (0.106) (0.0449)
- β6 0.0191 -0.00728 0.00753 0.820*** -0.0613*** 0.0352 -0.127**
  - (0.0684) (0.00473) (0.0222) (0.125) (0.0209) (0.117) (0.0582)
- β7 0.0610 -0.00419 0.00722 0.866*** -0.0426*** 0.0458 -0.0978*
  - (0.0636) (0.00399) (0.0186) (0.169) (0.0147) (0.130) (0.0553)
- β8 -0.0186 -0.00121 0.0235 0.714*** -0.0319*** 0.0889 0.0551
  - (0.0844) (0.00472) (0.0169) (0.125) (0.00932) (0.141) (0.0922)
- β9 0.0613 0.00213 0.0171 0.598*** -0.0195** 0.0224
  - (0.0807) (0.00589) (0.0169) (0.120) (0.00939) (0.105)
- β10 0.121 0.0235 0.441*** -0.0180* 0.0471
  - (0.0982) (0.0232) (0.102) (0.00972) (0.124)
- β11 0.0209 0.235*** -0.0129* 0.0579
  - (0.0211) (0.0681) (0.00740) (0.120)
- β12 0.0306 0.139* -0.00697 0.129
  - (0.0296) (0.0685) (0.00585) (0.152)
- γ0 -0.141*** -0.0807*** -0.0681*** -0.00961 -0.0579 -0.0593 -0.0889***
  - (0.0363) (0.0237) (0.0161) (0.00917) (0.0411) (0.0363) (0.0133)
- γ1 -0.0532** -0.0465 -0.0936***
  - (0.0264) (0.0638) (0.0228)
- δ 5.394*** 9.977*** 2.273*** 2.395*** 12.94*** -12.42*** 0.979 -0.343
  - (0.900) (1.073) (0.265) (0.400) (2.215) (3.869) (1.304) (1.123)
- N 61 64 62 60 29 50 60 42
- R-squared 0.628 0.702 0.787 0.330 0.921 0.69 0.659 0.747
- Adjusted R-squared 0.535 0.665 0.740 0.122 0.829 0.578 0.553 0.654
- S.E. of regression 0.131 0.165 0.141 0.119 0.4811 1.7090 0.2420 0.193
- D-W Statistic 0.380 0.376 0.488 0.180 1.017 0.112 0.602 0.767
- Note: Standard errors in parenthesis.

### Neoclassical Model Figures (Figures A2.2 and A2.3)
- Figure A2.2: Neoclassical Model Without Financial Constraints: Private Non-residential Investment to Capital Ratio.
- Figure A2.3: Neoclassical Model with Financial Constraints: Private Non-residential Investment to Capital Ratio.
- For each country (Euro Area, Germany, Spain, France, Greece, Ireland, Italy, Portugal) charts show Actual, Fitted, Residual (rhs) over sample periods (late 1990s–2013).

### Accelerator + Model (Controlling for Output Changes and Financial Constraints) — Table A2.4
- Table A2.4 estimates (standard errors in parenthesis). Columns: Euro Area, Germany, Spain, France, Greece, Ireland, Italy, Portugal.
- α 3.554*** 2.014*** 1.956*** 2.674*** 10.102*** 15.715*** 4.692*** 7.379***
  - (0.577) (0.578) (0.226) (0.443) (1.205) (3.069) (0.382) (0.732)
- β1 -0.0004 -0.001* -0.002*** -0.0004 0.0002 -0.008*** 0.0003 -0.001
  - (0.0005) (0.0004) (0.0003) (0.0005) (0.001) (0.003) (0.0004) (0.001)
- β2 0.089** 0.067** 0.038*** 0.013 -0.012 0.094 -0.07*** 0.06
  - (0.036) (0.025) (0.013) (0.032) (0.031) (0.056) (0.015) (0.036)
- β3 -0.003*** -0.0003 -0.001* 0.0004 -0.012*** -0.027*** -0.003*** 0.0001
  - (0.001) (0.001) (0.0004) (0.0004) (0.002) (0.005) (0.0005) (0.001)
- β4 0.005 -0.003 0.006*** -0.007** 0.01*** 0.033*** -0.005* -0.043***
  - (0.004) (0.002) (0.002) (0.003) (0.003) (0.006) (0.003) (0.013)
- β5 -0.019 0.077** 0.01*** -0.01 -0.065 -0.150 0.018 -0.047*
  - (0.03) (0.036) (0.003) (0.06) (0.053) (0.189) (0.018) (0.025)
- γ1 0.203*** 0.109** 0.293*** -0.115 0.72*** 0.008 0.333*** -0.215*
  - (0.065) (0.045) (0.094) (0.092) (0.216) (0.198) (0.065) (0.117)
- γ2 0.091** 0.165** 0.308** -0.008 0.814*** 0.362 0.194*** -0.277*
  - (0.043) (0.073) (0.115) (0.071) (0.209) (0.225) (0.065) (0.159)
- γ3 0.182*** 0.385*** 0.209*** 0.205*** 1.012*** 0.502** 0.26*** -0.237
  - (0.064) (0.076) (0.076) (0.063) (0.206) (0.231) (0.073) (0.139)
- γ4 0.203*** 0.302*** -0.044 0.205** 0.751*** 0.871*** 0.137** -0.145
  - (0.058) (0.063) (0.076) (0.082) (0.152) (0.228) (0.058) (0.092)
- γ5 0.118* 0.184*** 0.327*** 1.171*** 0.608* 0.138** -0.09
  - (0.061) (0.054) (0.096) (0.142) (0.327) (0.054) (0.074)
- γ6 0.047 0.148 0.345*** 0.965*** 0.445 0.116* -0.147
  - (0.071) (0.091) (0.102) (0.225) (0.32) (0.059) (0.104)
- γ7 0.041 0.115 0.093 0.549*** 0.446 0.132** -0.206*
  - (0.051) (0.09) (0.065) (0.168) (0.315) (0.063) (0.116)
- γ8 0.047 0.199** -0.048 0.493* 0.105 -0.186*
  - (0.073) (0.077) (0.064) (0.263) (0.075) (0.102)
- γ9 0.165*** 0.215** 0.153* 0.185 0.107* 0.099
  - (0.056) (0.1) (0.087) (0.182) (0.058) (0.088)
- γ10 0.218*** 0.176*** 0.340 0.092 0.184**
  - (0.07) (0.057) (0.389) (0.06) (0.065)
- γ11 0.112 0.408 0.107 0.214***
  - (0.08) (0.339) (0.067) (0.065)
- γ12 0.1* 0.131**
  - (0.058) (0.06)
- β6 0.029 0.137*** -0.011 -0.005 -0.005 -0.034*** -0.07***
  - (0.017) (0.024) (0.012) (0.005) (0.022) (0.007) (0.015)
- N 59 55 59 59 44 65 94 60
- R-squared 0.88 0.84 0.98 0.68 0.94 0.93 0.97 0.94
- Adjusted R-sq 0.84 0.76 0.97 0.62 0.92 0.90 0.96 0.89
- S.E. of regression 0.08 0.13 0.05 0.08 0.35 0.86 0.07 0.10
- DW statistic 0.71 0.26 0.55 0.51 0.57 1.09 0.71 1.19

### Accelerator + Model Figures and Contributions
- Figure A2.4: Accelerator + Model (Controlling for Output Changes and Financial Constraints) — plotted Actual, Fitted, Residual (rhs) for each country over sample periods (1999–2013).
- Figure A2.5: Contributions to Change in Investment-to-Capital Ratio (Accelerator + Model, cumulative) — country charts showing decomposition into:
  - Output
  - Other factors 1/
  - Residual
  - 1/ Corporate bond spreads, real lending rates, uncertainty, leverage, cash flow, and financial constraints.

### Significance of Accelerator + Model (Table A2.5)
- Source: IMF staff estimations.
- FLR / LR statistics by country (Full model; Uncertainty and leverage):
  - Euro Area: 8.21*** 39.56*** 9.95*** 21.22***
  - Germany: 6.51*** 34.7*** 7.66*** 17.84***
  - Spain: 21.78*** 75.45*** 19.26*** 36.48***
  - France: 2.98** 15.97*** 7.27*** 14.79***
  - Greece: 18.13*** 63.91*** 41.74*** 58.26***
  - Ireland: 15.44*** 59.71*** 30.01*** 48.58***
  - Italy: 20.21*** 74.35*** 23.8*** 43.97***
  - Portugal: 9.81*** 48.19*** 20.13*** 39.39***
- F = F-statistic; LR = Likelihood ratio. ***, **, and * denote statistical significance at the 1%, 5%, and 10% level, respectively.

*Source: HaverAnalytics; Eurostat and IMF Staff Calculations.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp1532.pdf_