## _wp12277

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### I. Key findings on China’s investment stance and dynamics
- Predicted investment norm for China over the last thirty years: between 33-43 percent of GDP.
- Actual investment in China over the same period: between 35-49 percent of GDP.
- Estimated current over-investment (model-based): around 10 percent of GDP higher than suggested by fundamentals.
- Neoclassical steady-state over-investment range (2007-11, alternative assumptions): between 12 and 20 percent of GDP relative to steady-state desirable value.
- China (2005-9) comparative metrics (5-year lead-up to crisis comparisons):
  - i-i* (average): 4.3
  - i-i* (cumulative): 21.6
  - Number of years i>i*: 5
  - Credit/GDP (annual percent change): 5.6
  - Real cost of capital (annual average): 1.5
  - Real GDP per capita (annual percent change): 10.8
- Investment-to-GDP is already close to 50 percent; marginal contribution of additional investment to growth has been falling and would need investment to contribute 60-70 percent of growth to sustain the same amount of growth absent other improvements.

### II. Econometric evidence from the cross-country panel (sample and methodology)
- Sample: dynamic panel of 36 economies; unbalanced; period 1955-2009.
- Observations by estimation columns: 892, 892, 892, 892, 718, 718.
- Estimation strategy: first-differences GMM with lagged instruments, time dummies, tests for no higher-order serial correlation and Hansen test for instrument validity.
- Main dependent variable: investment-to-GDP ratio (first-differenced).
- Explanatory variables (selected): lagged dependent variable; real per capita GDP growth; growth in credit (% of GDP); real interest rate; real GDP per capita (US$); age dependency ratio (population over 65 to 15-64); uncertainty (sd of 3-year rolling real GDP growth); reserves-to-GDP.
- Specification tests (selected): m2 test values by column: 0.201, 0.241, 0.239, 0.266, 0.250, 0.23; Hansen test reported as 1.000 across columns (and 0.000 in one column).

### III. Principal regression estimates (preferred specification highlights; preserve exact coefficients)
- Investment persistence (lagged dependent variable coefficients across columns): 0.652**, 0.628**, 0.630**, 0.615**, 0.652**, 0.664**.
- Growth effect (real per capita GDP growth coefficients across columns): 0.372**, 0.339**, 0.350**, 0.329**, 0.364**, 0.390**.
- Cost of capital (real interest rate coefficients where present): -0.043**, -0.041**.
- Credit availability (growth in credit, annual percent of GDP, coefficients where present): 0.033**, 0.030**, 0.023*, 0.032*, 0.031*.
- Level of development (real per capita GDP (US$) coefficients where present): 0.0002*, 0.0003*, 0.0002*, 0.0002*.
- Demographics (age dependency ratio coefficients where present): -0.560*, -0.696*, -0.612*, -0.622**.
- Uncertainty (sd of 3-year real GDP growth coefficients where present): -0.271**, -0.200**, -0.203**.
- Note on interpretation: first-differences estimation implies annual changes in some variables (e.g., demographics) are tiny; impacts in levels may be larger.

### IV. Over-investment and crisis probability (probit results)
- Probit selected coefficients and standard errors:
  - Real interest rate: -0.016** (0.003) in both specifications (1) and (2).
  - Real per capita GDP growth: -0.015** (0.011) in both (1) and (2).
  - Growth in credit (annual percent of GDP): -0.001 (0.003) in (1); -0.002 (0.003) in (2) — not significant.
  - Current account (percent of GDP): -0.022** (0.008) in (1); -0.026** (0.008) in (2).
  - Over-investment (percent of GDP): 0.031** (0.013) in (2).
- Sample and period for probit: 36 economies; 752 observations; 1955-2009.
- Interpretation and mechanical application to China:
  - Cross-country estimate: over-investment by 1 percent of GDP increases crisis probability by 0.03 percentage points (0.031**).
  - Applying coefficients mechanically to China’s estimated over-investment implies probability of a crisis would rise from 8 percent in 2005 to around 20 percent today (indicative; subject to parameter uncertainty and China-specific differences).

### V. Distinctive features of China’s investment model and financing implications
- China finances high investment largely from domestic savings (self-reliant model).
- High savings are argued to be arbitrarily high due to remaining financial sector controls that transfer subsidies from households and SMEs to large corporates.
- Unlike other emerging markets where excess investment often shows up as bank stress or foreign exchange crises, in China cost distortions may be absorbed as hidden transfers within the financial/intermediary system; weak links in implicit subsidy arrangements could capture or trigger macroeconomic costs.

### VI. Hidden costs and approximate magnitudes (stylized two-tier allocation)
- Stylized allocation: credit first to large corporations (LCs) at benchmark rates; remaining credit to SMEs largely through nonbank channels where SMEs face kinked demand and higher funding costs.
- Components of transfers/losses described:
  - A: Transfer from depositors (households) to corporates (profit margin enjoyed by LCs).
  - C: Transfer from depositors to banks (profit transfer).
  - E: Additional cost to SMEs from higher funding costs outside banking system.
  - F: Deadweight loss (identification problem prevents precise estimate).
- Rough quantitative approximations for China (using ASEAN-4, Hong Kong SAR, Korea as proxies and midpoint adjustments):
  - Resource transfer from households to large corporates (average of mid-points over last 10 years): about 4 percent of GDP.
  - Additional cost to SMEs: averaged about 0.2 percent of GDP, rising to 0.8 percent of GDP in 2011.
  - Resource transfer from households to banks on average was negative: difference in bank spreads between China and the average Asian economies was -0.5 percent in nominal terms and -0.3 percent in real terms (adjusted for inflation differentials).
  - Deadweight loss: not estimated due to identification issues.

### VII. Policy implications and recommendations
- Objective: engineer a gradual reduction in investment toward a path that maximizes social welfare.
- Norm-based guidance: cross-country regression suggests lowering China’s investment by 10 percentage points of GDP over time would bring it to levels consistent with fundamentals.
- Reforms to accompany lower investment to preserve growth and stability:
  - raise productivity and efficiency;
  - ensure fruits of growth are shared more equitably across economic agents, especially ordinary households.
- Rationale: returning to more “normal” investment levels need not compromise growth if accompanied by productivity-enhancing and distributional reforms; international experience indicates such reforms are prerequisites for sustainable growth.

### VIII. Data and methodological appendices (high-level)
- Neoclassical steady-state formula used: i* = k*(g + d)/(1 + g).
- Capital stock: perpetual inventory method; investment data from Penn World Tables (1950‒80) and IMF WEO (1980 onwards); initial capital stock assumption set at steady-state in 1950 (alternatives tested).
- k* determined as maximum average capital-output ratio over long windows (15- and 20-year periods) between 1950 and 2011; sample average capital-output ratio around 2½ during 1950-2011.
- Depreciation rates tested: 5 percent, 7 percent, and 10 percent. Results shown use 7 percent (robust to alternatives).
- Potential growth (g) scenarios: (i) maximum long-run growth (capped at 5), or (ii) medium-term WEO projections (around 8 percent, higher for China); results rely on latter but are generally robust.

*IMF Working Paper excerpt: _wp12277 - References (IMF staff working paper).*

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

### _wp12277 - References

### I. Introduction — role and risks of high investment
- High investment is strongly associated with economic take-offs in non-resource rich countries; Asia exemplifies how high investment facilitated rapid economic growth.
- During 1970-2010, the correlation between a 5 year moving average investment-to-GDP ratio and economic growth was around 0.83 in developing Asia; the correlation was 0.74 for advanced economies (the G7 example).
- Despite generally high savings rates, several Asian countries resorted to foreign financing to sustain even higher investment ratios, which often preceded banking or foreign exchange crises.
- Overly cheap financing (mispricing), frequently involving currency and maturity mismatches obscured by implicit guarantees or lack of information, enabled excessive investment in property and manufacturing, later triggering crises.
- This paper compares China’s current investment level against comparator economies using up-to-date panel data selected to match China’s features and development phase.

### II. Literature review — mixed macro and stronger micro evidence of over-investment
- Macro studies:
  - Bai and others (2006): returns to capital fell during the 1990s but remain relatively high → investment not excessive.
  - Lu and others (2008): corporate profitability rising after 1990s → similar conclusion.
  - Dong and others (2006): marginal product of capital relatively high in last two decades but China may be on a dynamically inefficient path; investment has consistently exceeded the share of capital income in GDP since the early 1990s.
  - Rawski (2002): low investment returns and widespread excess capacity across many sectors during the 1990s.
  - Barnett and Brooks (2006): rise in capital-to-output ratio and fall in marginal product of capital during 1990-2005.
  - Qin and Song (2009): pervasive over-investment using a profit-maximizing capital spending calculation.
- Micro studies:
  - Ding and others (2010): using 10,000 firms (2000-07) find evidence of over-investment across firm types.
  - Liu and Siu (2006): SOEs implicated in over-investment because their implied cost of capital is artificially low.
  - Dollar and Wei (2007): using 12,000 firms in 120 cities (2002-04), SOEs have lower marginal returns but receive biased capital allocation; correcting the bias could lower China’s investment rate by as much as 8 percentage points without adverse growth effects.
  - Hsieh and Klenow (2009): equalizing marginal products to U.S. levels could raise manufacturing TFP by 30-50 percent.
  - Geng and N’Diaye (2012): investment propped up by low interest rates and an undervalued currency.
- Common limitations in literature:
  - Strong assumptions, measurement error risk, focus on China only (indigenous approach), unrepresentative samples, short time periods, limited coverage of post-2005 surge in investment.

### III. Neoclassical model approach — Golden Rule and China’s position
- Golden Rule steady-state investment formula: i* = k*(g +d)/(1 + g).
- Relative to the Golden Rule, China is currently over-investing.
- Historical pattern:
  - China under-invested in the 1970s and to a lesser extent in the 1980s; investment picked up especially after 2000.
  - By 2005, China’s capital-to-output ratio was close to its long-run level; theoretically investment should have fallen toward steady-state.
  - During 2007-11, China raised investment further to counter the global crisis.
- Over-investment estimate:
  - Depending on assumptions, during 2007-11 China may have been over-investing by between 12 and 20 percent of GDP relative to its steady-state desirable value.
- Limitations of the neoclassical steady-state approach:
  - Does not capture structural changes (e.g., shifts away from capital-intensive growth) or changes in investment efficiency over time.
  - No a priori reason that a fast-growing, catch-up economy should have lower capital-to-output ratio or investment rate than long-run levels; TFP and other factors matter.
- Comparative observations:
  - China’s capital-to-output ratio has risen relative to other emerging markets over two decades but remains within the average cross-country range on simple metrics.
  - China stands out for the pace of its growth.
  - China has moved to an extreme outlier position in the relationship between investment rates and capital-to-output ratios since the 1990s, suggestive of potential over-investment.
  - Unless TFP surges and export performance improves, the contribution of investment to growth would need to reach 60-70 percent to support the same amount of growth.
  - Elevated investment that earns declining marginal returns risks creating hidden deadweight and domestic financing strains.

### IV. Theoretical framework of optimal investment — welfare optimization and determinants
- Welfare optimization framework:
  - Investment should maximize social welfare through inter-temporal consumption choices; investment is endogenous to consumption preferences and influenced by depreciation, marginal product of capital, and cost of capital.
  - A representative welfare function is given generally as (1) and parameterized as (2) in the source; parameters σ, ρ, γ, and η are all [0, 1].
  - Typical budget constraint expressed as (3), with k = capital stock, i = interest rate, π = inflation, and δ = depreciation.
  - First-order condition equates marginal product of capital to the cost of capital (real interest rate adjusted for other model variables), as summarized in (4).
- Mechanics and implications:
  - Preference shifts toward future consumption imply more investment and less consumption today.
  - Under usual concavity of marginal product of capital, higher investment leads to a lower marginal product of capital.
  - A lower real interest rate is associated with a lower marginal product of capital and higher investment.
- Other determinants discussed:
  - Cross-country differences in capital productivity can reflect availability of other production factors (e.g., large new labor entries shift production function upwards).
  - Higher savings (ceteris paribus) reduce real interest rates (Solow mechanism), implying higher investment and lower marginal product of capital.
  - Strong export-led demand expansion can justify high investment during market expansion, with firms operating at low long-run average cost and continued profitable entries.
- Welfare perspective:
  - Assessing appropriateness of investment size requires more than comparing marginal product of capital; multiple variables and inter-temporal welfare trade-offs must be considered.

*Source: _wp12277 - References*

### 17.      Under a welfare maximizing state, inter temporal consumption preference will

### 17.      Under a welfare maximizing state, inter temporal consumption preference will

### Measuring inter-temporal consumption preference and defining an investment norm
- The relative time preference is not directly observable.
- Indirect measurement approach: assume the average level of consumption, or investment, of a relatively large sample of countries approximates the inter-temporal preference.
- Define an optimal investment level, or “norm”, as the level that would maximize social or household welfare.
- Based on Section IV, the investment norm is determined by economic fundamentals including the real interest rate and the depreciation rate and can be estimated from regressions linking cross-country investment rates over time to a set of fundamentals.

### Data, sample, and estimation strategy
- Sample: dynamic panel for 36 economies over the period 1955-2009; panel is unbalanced.
- One innovation: starting period for each economy calibrated to capture its economic take-off (and associated elevated levels of investment) to avoid downward bias in the investment norm.
- Sample composition: emerging market economies, as well as Japan and Taiwan Province of China; around one-third are Asian economies.
- Empirical strategy: allows for changes in preferences over time but imposes a “normal” preference for inter-temporal consumption across emerging markets relative to fundamentals.
- Estimation details:
  - Dependent variable: investment-to-GDP ratio (first-differenced).
  - Estimation method: first-differences using GMM to control for fixed effects, account for lagged dependent variable, measurement error, and potential endogeneity (instruments are lagged values of regressors).
  - Includes time dummies (covering the Asian crisis and the latest global financial crisis).
  - Tests: no higher-order serial correlation in residuals and Hansen test for instrument validity.

### Explanatory variables included (motivated by theoretical model)
- Lagged dependent variable.
- Savings-to-GDP and credit-to-GDP measures (availability of financing).
- Real lending rates (cost of capital).
- Exports-to-GDP (external contributions to investment).
- Real growth rates (proxy for return to capital).
- Level of real GDP (level of economic development).
- Age dependency ratios (demographics).
- Macroeconomic uncertainty: standard deviation of three-year rolling windows of real GDP growth.
- Reserves-to-GDP (to measure need to save against volatile capital flows).

### Regression results and principal findings (preferred specification: column 5 of Table 1)
- Investment persistence:
  - Lagged dependent variable coefficients (by column): 0.652**, 0.628**, 0.630**, 0.615**, 0.652**, 0.664** (robust t-statistics in parentheses).
- Growth effect:
  - Real per capita GDP growth coefficients (by column): 0.372**, 0.339**, 0.350**, 0.329**, 0.364**, 0.390**.
  - Including exports does not yield a significant coefficient (column 6), implying globalization affects investment primarily via stronger overall economic growth.
- Cost of capital:
  - Real interest rate coefficients (in columns where present): -0.043**, -0.041**.
  - Higher real interest rates reduce investment.
- Credit availability:
  - Growth in credit (annual percent of GDP) coefficients (where present): 0.033**, 0.030**, 0.023*, 0.032*, 0.031*.
  - Change in credit renders savings-to-GDP insignificant when both are tried.
- Level of development:
  - Real per capita GDP (US$) coefficients (where present): 0.0002*, 0.0003*, 0.0002*, 0.0002*.
  - Squared per capita GDP term was not significant.
- Demographics:
  - Age dependency ratio (population over 65 to population aged 15-64) coefficients (where present): -0.560*, -0.696*, -0.612*, -0.622**.
  - Aging reduces investment, possibly via slower growth and lower returns to capital.
- Uncertainty:
  - Uncertainty (standard deviation of three-year rolling window of real GDP growth) coefficients (where present): -0.271**, -0.200**, -0.203**.
  - Macroeconomic uncertainty leads to lower investment; volatility of growth captures this effect better than changes in reserves.
- Specification tests (selected):
  - m2 test (no second-order serial correlation in residuals): reported values by column: 0.201, 0.241, 0.239, 0.266, 0.250, 0.23.
  - Hansen test (instrument validity): 1.000 across columns (and 0.000 in one column per table).
- Sample size and period:
  - Number of economies: 36.
  - Number of observations (by column): 892, 892, 892, 892, 718, 718.
  - Time period: 1955-2009.
- Notes on interpretation:
  - Estimation in first-differences means annual changes in demographic variables are very small; actual impacts of variables on investment may be larger in levels.
  - Excluding the demographic variable increases predicted investment in China by 1 percent of GDP in 2009 (illustrative).

### China: predicted norm, observed investment, and over-investment
- Model prediction for China:
  - Predicted investment norm over the last thirty years ranged between 33-43 percent of GDP.
  - Actual investment fluctuated between 35-49 percent of GDP.
  - Using parameter estimates, investment in China may currently be around 10 percent of GDP higher than suggested by fundamentals (Figure 7).
  - Deviations were usually not significant prior to 2000 and typically closed over a 5-year horizon, but the current deviation is larger and more persistent.
- Cumulative and average deviations and related indicators (Table 3, 5-year lead-up to crisis comparisons):
  - Indonesia: i-i* (average) 1.6; i-i* (cumulative) 7.9; Number of years i>i* 4; Credit/GDP (annual percent change) 6.0; Real cost of capital (annual average) 9.2; Real GDP per capita (annual percent change) 5.3.
  - Japan: i-i* (average) 1.0; i-i* (cumulative) 4.9; Number of years i>i* 2; Credit/GDP (annual percent change) 2.9; Real cost of capital (annual average) 3.7; Real GDP per capita (annual percent change) 4.1.
  - Malaysia: i-i* (average) 2.1; i-i* (cumulative) 10.6; Number of years i>i* 4; Credit/GDP (annual percent change) 8.1; Real cost of capital (annual average) 5.7; Real GDP per capita (annual percent change) 6.2.
  - Philippines: i-i* (average) -2.4; i-i* (cumulative) -12.1; Number of years i>i* 1; Credit/GDP (annual percent change) 2.2; Real cost of capital (annual average) 6.9; Real GDP per capita (annual percent change) 2.3.
  - Thailand: i-i* (average) 1.7; i-i* (cumulative) 8.3; Number of years i>i* 4; Credit/GDP (annual percent change) 11.0; Real cost of capital (annual average) 7.7; Real GDP per capita (annual percent change) 5.1.
  - China (2005-9): i-i* (average) 4.3; i-i* (cumulative) 21.6; Number of years i>i* 5; Credit/GDP (annual percent change) 5.6; Real cost of capital (annual average) 1.5; Real GDP per capita (annual percent change) 10.8.

### Over-investment and crisis probability (probit results, Table 2)
- Probit model findings (selected coefficients and significance):
  - Real interest rate: -0.016** (standard error 0.003) in both (1) and (2).
  - Real per capita GDP growth: -0.015** (standard error 0.011) in both (1) and (2).
  - Growth in credit (annual percent of GDP): -0.001 (0.003) in (1); -0.002 (0.003) in (2) — not significant.
  - Current account (percent of GDP): -0.022** (0.008) in (1); -0.026** (0.008) in (2).
  - Over-investment (percent of GDP): 0.031** (0.013) in (2).
- Sample and period:
  - Number of economies: 36.
  - Number of observations: 752.
  - Time period: 1955-2009.
- Interpretation:
  - On average, other things being equal, over-investment by 1 percent of GDP as measured in the cross-country regression leads to a 0.03 percentage point increase in the probability of an economy encountering a crisis.
  - Mechanically applying probit coefficients to China’s estimated over-investment: probability of a crisis would rise from 8 percent in 2005 to around 20 percent today (these numbers are indicative and subject to parameter uncertainty and differences in China’s investment model).

### Distinctive features of China’s investment model and implications for crisis triggers
- Distinguishing factor: China’s self-reliance on domestic resources for investment, driven by high savings.
- High savings are argued to be arbitrarily high due to remaining financial sector controls that effectively transfer subsidies from households and SMEs to large corporates.
- In other countries, excess investment costs often show up via bank stress or foreign exchange crises; in China, weak links in the implicit subsidy system could capture or trigger the cost of over-investment.

### Estimating hidden costs: resource transfers, higher SME costs, and deadweight loss
- Stylized two-stage allocation: credit initially allocated to large corporations (LCs) at around the benchmark rate; remaining credit allocated to SMEs largely through the nonbank financial sector; SMEs face a kinked demand curve for credit.
- Components of transfers and losses (Figure 10):
  - A: Transfer of resources from depositors (households) to corporates (profit margin enjoyed by LCs from benchmark lending).
  - C: Transfer of resources from depositors to banks (profit transfer).
  - E: Additional cost to SMEs due to higher funding costs outside the banking system.
  - F: Deadweight loss (identification problem complicates precise estimate).
- Rough quantitative approximations for China:
  - Proxy for market-clearing rate (ieq) and competitive spread (P”) used: average values of ASEAN-4, Hong Kong SAR, and Korea.
  - Adjustments for country differences when estimating A: by real GDP growth differences (upper bound) and by inflation differences (lower bound).
  - The average of the mid-points of these ranges over the last 10 years was about 4 percent of GDP for the estimated resource transfer from households to large corporates (Figure 11).
  - Additional cost to SMEs averaged about 0.2 percent of GDP, rising to 0.8 percent of GDP in 2011, reflecting tightened liquidity conditions.
  - The resource transfer from households to banks on average was negative:
    - Difference in bank spreads between China and the average of the Asian economies was -0.5 percent in nominal terms, and -0.3 percent in real terms (adjusted for inflation differentials).
  - Failed to calculate an estimate of deadweight loss due to the usual identification problem.

### Conclusion (implications summarized)
- The econometric evidence suggests China has been over-investing relative to fundamentals, with estimated over-investment around 10 percent of GDP currently.
- Over-investment raises the probability of crises in the cross-country evidence, but China’s high-savings, self-reliant investment model and implicit subsidy arrangements alter how the costs and triggers of a crisis might materialize.
- Hidden costs from the regulated two-tier financial sector—resource transfers to large corporates (about 4 percent of GDP on mid-point average), additional SME costs (0.2 percent of GDP on average, up to 0.8 percent in 2011), and ambiguous deadweight loss—are economically significant and concentrate the burden on households via the financial sector.

*Source: WEO, WDI, and Fund staff calculations (excerpt from IMF staff working paper).*

### 31.      There is little doubt that China’s extraordinary economic performance over the

### There is little doubt that China’s extraordinary economic performance over the past three decades is in large part attributable to investment

### Investment’s contribution and limits
- China’s capital-to-output ratio is still in the range of those of other emerging market economies while its growth rate has far outpaced others over the last two decades.
- The marginal contribution of an extra unit of investment to growth has been falling, necessitating ever larger increases in investment to generate an equal amount of growth.
- Investment-to-GDP is already close to 50 percent, suggesting the current growth model may have run its course.

### Evidence that China is over-investing
- Measured against a norm estimated from a panel data on a large number of countries, China is over-investing.
- The deviation accumulating over the last decade is larger and more persistent than the estimated over-investment in other Asian economies leading up to the Asian crisis.
- The latest divergence was the result of the 2009 measures used to contain the spillover from the global financial crisis.
- The government is accelerating efforts to reorient the economy, moderating investment growth while promoting consumption.

### Financing risks and distributional costs
- While an external crisis appears unlikely when assessed against dependency on external funding, potential strains from financing high investment still exist and could be quite large.
- Assuming conditions that prevailed in other emerging market economies during their pre- and post-crisis periods also apply to China, the probability of a crisis in China would mechanically be about one in five.
- Because of differences in the modality of financing of investment, an external crisis of the kind experienced by many other emerging market economies appears very unlikely to occur in China.
- Costs are present but distributed to other sectors of the economy as a hidden and implicit transfer of resources:
  - Households bear a large burden of the financing of over-investment, estimated at close to 4 percent of GDP per year.
  - SMEs are paying a higher price of capital because of the funding priority given to larger corporations.

### Policy challenge and recommended direction
- The challenge is to engineer a gradual reduction in investment to a path that would maximize social welfare.
- Since the optimal path is not identifiable, a norm estimated using a large sample of emerging markets could provide guidance.
- Based on cross-country regressions, lowering China’s investment by 10 percentage points of GDP over time would bring it to levels consistent with fundamentals.
- Returning to a more “normal” level of investment should not compromise growth and macroeconomic stability and should be accompanied by reforms that:
  - raise productivity and efficiency;
  - ensure that the fruits of growth are shared more equitably across different economic agents, in particular ordinary Chinese households.
- International experience indicates these reforms are prerequisites for sustainable growth.

### Data appendix — Implementing the Neo-Classical Approach (methodology and key parameter choices)
- Neo-classical model formula: steady-state level of investment (i*) is given by: i* = k*(g +d)/(1 + g), based on estimates of:
  - steady-state capital-output ratio (k*),
  - depreciation rate (d),
  - rate of potential output growth (g).
- Capital stock:
  - Derived from the standard perpetual inventory method.
  - Data on gross fixed real investment during 1950‒80 from Penn World Tables, and from 1980 onwards from the IMF World Economic Outlook (WEO) database.
  - Initial estimate of capital stock assumes the country is at steady-state capital-output ratio in 1950, using averages of k, g, and d over 1950–60.
  - Alternative assumptions (e.g., setting it equal to 10 times the initial level of investment) show the guess at the initial capital stock becomes relatively unimportant decades later.
- k*:
  - For a given depreciation rate, k* is found as the maximum value of the capital-output ratio on average over long (15- and 20-year periods) between 1950 and 2011.
  - The average capital-output ratio for the countries in the sample was around 2½ during 1950-2011 and for industrial countries it was similar during 1970-2011.
- d (depreciation rates tested):
  - 5 percent, 7 percent, and 10 percent.
  - Results shown in the text are for a 7 percent depreciation rate, but results were robust to alternatives.
- g (potential growth assumptions):
  - Two sets: using the maximum growth rate over long periods between 1950 and 2011 for each country (capped at 5); or using medium-term projections for growth from the latest WEO database (around 8 percent, higher for China).
  - Results shown in the text rely on the latter, but were generally robust.
  - Since these growth rates are higher in the case of China, they present a stricter test of over-investment since i* is larger.

### Cross-country investment regressions (model and sample)
- Aggregate-level panel regression specification used where I/GDP is the investment-to-GDP ratio and Z is a vector of additional variables including:
  - lagged dependent variable,
  - real per capita GDP growth,
  - uncertainty (measured as the standard deviation of three-year rolling windows of real GDP),
  - growth in credit as a percent of GDP,
  - real GDP per capita in US dollar terms,
  - the age dependency ratio (population aged over 65 to the working-age population),
  - the real interest rate.
- Data sources:
  - I/GDP, real per capita GDP growth, uncertainty from the WEO;
  - growth in credit as percent of GDP, real GDP per capita in US dollars, age dependency ratio, and real interest rate from the World Bank World Development Indicators database.
- Sample: unbalanced, covering the period 1955-2009, including the following emerging market economies (starting year in parentheses): Albania (1993); Algeria (1994); Argentina (1970); Armenia (1995); Belarus (1995); Bolivia (1979); Brazil (1970); Bulgaria (1991); Chile (1970); China (1982); Colombia (1970); Croatia (1994); Czech Republic (1997); Egypt (1970); Hungary (1989); India (1970); Indonesia (1971); Iran (2004); Israel (1980); Japan (1955); Korea (1963); Malaysia (1970); Mexico (1971); Morocco (1978); Pakistan (2004); Peru (1986); Philippines (1970); Poland (1991); Romania (1994); South Africa (1964); Sri Lanka (1978); Taiwan Province of China (1965); Thailand (1970); Turkey (1973); Venezuela (1984); and Vietnam (1993).

*IMF Working Paper section text (excerpt).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12277.pdf_