## _wp15113

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---

### I. INTRODUCTION — context and framing
- China’s GDP has been growing at the average rate of nearly 10 percent per year in the past four decades.
- Post-GFC policy relaxation supported growth; observers described a “goldilocks economy” (JPMorgan, 2009).
- Concerns motivating analysis:
  - Surge in credit-financed investment in response to the GFC pushed credit up to, and even beyond, the point that has typically led to sharp growth slowdowns and banking crises in other countries (Liao and Maliszewski, 2015).
  - A boom in real estate activity linked to growing inventories of unsold houses and rising sectoral leverage.
  - Risk of overinvestment or “malinvestment” with potential sharp correction if demand evaporates.
- Structural concern: Exceptionally high investment rates since the GFC associated by some with “forced savings” (Eckaus, 2014) have reduced investment efficiency and total factor productivity (TFP) growth.
- Central policy question: how much of China’s slowdown is temporary (cyclical) versus long lasting (structural).

### Main contributions and headline results
- Purpose: identify the cyclical position and assess the degree of potential output slowdown in China.
- Headline results:
  - Expect growth to slow in the near-term. Financial cycles play a significant role; the economy is likely near the peak of a powerful cycle since the GFC. An adjustment is likely and needed to bring the economy closer to equilibrium.
  - Potential growth is slowing as China converges to advanced-economy income levels; the pace of convergence depends on structural reforms. With successful reforms, China can follow historical experience of other fast-growing Asian economies.

### Methods overview (methods and model types applied)
- Definitions:
  - Traditional potential output: sustainable level of goods and services without generating inflationary pressures; output gap = actual minus potential.
  - Finance-neutral (termed “sustainable output”): links deviations from sustainable output to credit dynamics and financial cycles.
- Methods applied:
  - Univariate filters: Hodrick-Prescott (HP) filter; band-pass filters (Baxter-King; Christiano-Fitzgerald).
  - Multivariate filters: structural time series linking output fluctuations to inflation; extended models include unemployment (Okun’s law), capacity utilization, inflation expectations.
  - Production function approach: decomposes GDP into labor, capital, and TFP; HP filter applied to labor and TFP inputs; modified version combines growth decomposition with a multivariate filter and adjusts capital by capacity utilization deviations.
  - Finance-neutral measures: include credit gap (deviation of real credit from stochastic trend) and real house price gap; variances of stochastic processes not restricted.

### Empirical results across methods — key findings and exact statistics
- Common finding: secular slowdown in potential growth; methods differ on level of potential growth and sign/size of output gap at end of sample (2013).
- Hodrick-Prescott (univariate):
  - Trend growth at the end of the sample drops to about 8 percent.
  - Produces a negative output gap of about a half percentage point.
- Band-pass filters (Christiano-Fitzgerald; Baxter-King):
  - Produce similar estimates to HP.
- Multivariate filters:
  - Indicate steeper slowdown in potential GDP.
  - Output gaps closer to zero at end of sample; inflation dynamics add significant information.
  - Constructed gaps are relatively small in absolute terms.
- Production function approach:
  - Shows a much lower output gap in 2013 compared with multivariate filters; gap turns persistently negative after the GFC.
  - Capacity utilization deviations drive turning points in the output gap.
  - Current potential output slowdown largely driven by a significant drop in TFP growth, only partly offset by higher contribution from capital.
- Finance-neutral (sustainable output) estimates:
  - Sustainable growth slightly below headline rate in 2013, but deviation from sustainable output is positive and high.
  - Deviations from sustainable output are persistently positive since 2007; distinct increase after 2009 due to post-crisis credit surge.

### Interpretation and economic implications
- Key observations:
  - Potential growth has slowed; even optimistic estimates put potential growth below headline in 2013.
  - Output gaps linked to inflation or capacity utilization are close to zero or negative in 2013, consistent with subdued inflation and falling capacity utilization.
  - Finance-neutral measures point to large positive deviations from sustainable output since 2007, indicating a sizable credit gap sustained by exceptionally strong credit growth after the GFC.
- Reconciliation of divergent results:
  - Traditional output gap largely closed through massive post-GFC stimulus (public and quasi-public investment; loose monetary conditions supporting credit growth, particularly to real estate).
  - Credit-financed investment component of stimulus is likely unsustainable, producing large finance-neutral gaps; a self-propelling real estate cycle (rising asset prices → rising collateral values → low rates) augments adjustment risks.
- Likely adjustment dynamics:
  - Credit-financed development activity likely to drop.
  - Unprofitable projects (including construction-related industries) may be mothballed.
  - Temporary negative swing in traditional output gap as factors are reallocated.
  - Public/quasi-public investment provides a cushion but may be unsustainable long term; removing distortions (e.g., weak social safety net) could raise consumption and interest rates, make some investments unprofitable, and raise public debt burden.
  - Some current investment may not serve future consumption needs if misdirected, risking obsolescence or premature depreciation.
- Policy-relevant conclusions:
  - Cyclical output fluctuations are more connected to the financial cycle than the traditional business cycle, implying slower growth may be needed to address post-GFC imbalances.
  - Output costs of adjustment hinge on flexibility of resource reallocation; structural reforms to open up new activities are important.
  - Historical evidence: liberalizing reforms (for example around WTO accession) aided recovery from previous financial cycles.

### Convergence-path analysis and simulated scenarios — explicit scenarios and numeric benchmarks
- Modeling approach:
  - Model re-estimated on the sample of “Asian Tigers” to construct an upper-bound convergence path (lower barriers to technology diffusion → higher TFP growth).
- Two simulated convergence paths for China:
  - “Low convergence path”: simulated from the full model (sample-wide).
  - “High-convergence path”: simulated from the model estimated on Asian Tigers’ data.
- Empirical relationships:
  - China’s actual growth path is significantly above the low convergence path.
  - Since 1979, China’s actual growth has oscillated around the high-convergence path.
  - Periods identified as “overheated” in the late 2000s; growth remained in overheated territory even after the relative slowdown in 2013.
- Key quantitative findings:
  - Headline growth slowed from the pre-GFC peak of 14 percent to less than 8 percent in 2013.
  - The Asian Tigers–based model predicts growth to fall to about 7½ percent in 2013.
  - China’s per capita income: about 20 percent of the U.S. level (2013).
  - China’s economy size in PPP terms: already equal to three-quarters of the U.S. economy (2013).
  - Korea and Taiwan Province of China sizes in PPP terms in 2013 equivalents when at similar development levels: respectively about 10 percent and 6 percent of U.S. size.
  - Share of labor compensation in income in China of around one half (PWT 8.0 based assumption).

### Productivity, capital, investment patterns, and risks
- Decomposition insights:
  - Fast-growing Asian economies relied heavily on capital accumulation; productivity growth contribution was also significant.
  - China followed a similar pattern, but TFP contribution has been falling off in the post-2009 period.
  - Contribution from capital accumulation has also been declining despite a much higher share of investment in Chinese GDP, indicating declining marginal product of capital.
  - Evidence cited: about half of TFP gains from technological progress have been wiped out by inefficiencies linked to the recent investment drive; rapid credit growth has hindered efficient allocation of capital and productivity growth.
- Risks:
  - Overinvestment and imbalances from post-GFC surge in investment reduce investment efficiency and raise probability of persistent slowdown.
  - Finance-neutral positive gap in 2013 implies correction costs; some losses temporary (reallocation) and some permanent (misallocated capital depreciation).
  - Fiscal limits: further public debt accumulation could undermine sustainability and dampen consumption if tax burdens become excessive; risk of misallocating public investment.
  - Institutional frictions: favored-firm supports and local government behaviors create entry barriers and inefficient public-good allocation; rebuilding incentive systems may be lengthy and bumpy.

### Policy implications and reform potential
- Third Plenum reform blueprint (2013) contains elements necessary to keep China on a convergence path similar to fast-growing Asian economies and to facilitate adjustment after the credit boom.
- Lam and Maliszewski (2015) (as cited): full implementation of the reform package could allow China to sustain long-term growth broadly consistent with fast-growing Asian economies’ experience.
- Historical precedent: past TFP slowdowns were temporary and productivity rebounded after liberalizing reforms (e.g., WTO accession following the 1998 slowdown); current reform round lacks a comparable external anchor, complicating implementation.
- Policy tensions:
  - Need to switch demand driver from investment to consumption while restoring investment efficiency.
  - Maintaining high productivity growth in a domestically oriented growth model will be challenging; export-oriented industries tend to be more efficient and domestic sectors may face weaker competition.
- Reform as first line of defense: full and steadfast implementation of the Third Plenum reform blueprint is presented as the first line of defense against falling into a “middle-income trap.”

### Appendix I. Methodology — concise method inventory and key parameter choices
- Univariate filters:
  - Hodrick-Prescott (HP) filter: smoothness parameter λ set equal to 100 for annual data.
  - Band-pass filters: cycle assumed to last from two to eight years; Baxter-King (BK) and Christiano-Fitzgerald (CF) used.
  - BK: passes fluctuations between six (18 month) and 32 (96 month) quarters; uses leads/lags K = 8 quarters.
  - CF: random walk CF filter; data detrended (linear trend removed); band chosen as eight to 32 quarters.
- Multivariate filters linking output gap to inflation:
  - Unobserved components (state-space) models estimated via Kalman filter; Bayesian regularized maximum likelihood used.
  - Bivariate model: local linear trend for permanent output; cyclical component AR(1); cyclical component linked to inflation via backward-looking Phillips curve.
  - Multivariate model (Benes and N’Diaye, 2010): three gaps—output, unemployment (Okun’s law), capacity utilization; inflation equation links level and change of output gap to inflation; NAIRU evolves with AR processes.
- Multivariate filter with production function:
  - Augments multivariate model by adding Cobb-Douglas production function linking potential output to trend employment and capital adjusted for capacity utilization.
  - TFP A^* follows a stochastic trend with time-varying slope g that follows AR(1).
  - Potential output: y^* = A^* + α log labor^* + (1−α) log k^* (Cobb-Douglas form).
- Multivariate filter to estimate ‘finance-neutral’ output gap:
  - Adds credit gap (real credit deviation from stochastic trend) and housing price gap.
  - Output gap reacts to the credit gap; housing gap linked to credit gap; equilibrium variables follow stochastic trends with time-varying slopes (AR(1)).
  - Footnote: adding housing price gap widens posterior densities due to colinearity with credit gap.
- Production function approach for cross-country analysis:
  - Aggregate Cobb-Douglas: Y_t = A_t K_t^α_t L_t^(1−α_t); input shares α_t from time-varying labor income share.
  - Procedure: derive historical TFP; use HP filter for trend TFP growth and trend capital growth; derive trend labor from working-age population; trend output from trend TFP, labor, capital.
- Data sources noted in methodology:
  - Annual and quarterly GDP and inflation from WEO database; CEIC and Haver Analytics for capacity utilization and unemployment; BIS credit to the private sector; housing prices from CEIC; capital and labor from PWT 8.0.

_Italic: Source — content unit: _wp15113 - conclusion, documenting the fundamental role played by factor accumulation in explaining the (PDF chapter/section)._

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

### _wp15113 - References .............................................................................................................

### Figures and Appendix (as listed)
- Figures:
  - 1. Univariate Filters
  - 2. Multivariate Filters
  - 3. Production Function Filter
  - 4. ‘Finance-Neutral’ Filter
  - 5. Catching Up Process Relative to Fast-Growing Asia
  - 6. GDP Growth and Predicted
  - 7. Contributions to Growth and Investment Shares
  - 8. Contribution to GDP Growth
- Appendix:
  - Methodology

### I. INTRODUCTION — context and framing
- China’s GDP has been growing at the average rate of nearly 10 percent per year in the past four decades.
- The well-timed policy relaxation supported growth in the immediate aftermath of the Global Financial Crisis (GFC).
- Observers described a “goldilocks economy” in China—not too hot to fuel inflation and not too cold to slip into recession (JPMorgan, 2009).
- Concerns that recent deceleration could be a prelude to a deeper growth slowdown (Xie, 2013), driven in part by:
  - A surge in credit-financed investment in response to the GFC that pushed credit up to, and even beyond, the point that has typically led to sharp growth slowdowns and banking crises in other countries (Liao and Maliszewski, 2015).
  - A boom in real estate activity, supporting several sectors but linked to growing inventories of unsold houses and rising leverage in the sector.
  - The risk of overinvestment or “malinvestment” and a potential sharp correction if demand evaporates and leverage proves unsustainable.
- Structural concerns:
  - Exceptionally high investment rates associated by some with “forced savings” (Eckaus, 2014) have grown since the GFC, reducing investment efficiency and total factor productivity (TFP) growth.
- Central policy question: how much of China’s slowdown is temporary (cyclical) versus long lasting (structural).

### Main contributions and headline results (as stated)
- We identify the cyclical position and assess the degree of potential output slowdown in China.
- Main results:
  - We expect growth to slow down in the near-term. Financial cycles in China play a significant role in shaping growth dynamics, and the economy is now likely near the peak of a powerful cycle propelling the economy since the GFC. An adjustment is therefore both likely and needed to bring the economy closer to equilibrium.
  - Potential growth is slowing. This is expected as China makes progress on the long journey of converging to advanced economy income levels. As it moves closer to this technology frontier, growth will continue to slow. However, the pace of convergence, and thus China’s medium-term growth rate, will depend on structural reforms. With success in implementing reforms, China can follow the historical experience of other fast-growing Asian economies.

### Paper organization (method and structure)
- The paper is organized as follows:
  - Start from key themes in the recent literature on China’s growth performance.
  - Discuss and motivate the range of methods to estimate potential output and output gap.
  - Present and discuss results.
  - International comparisons: contrast the performance of fast-growing economies against China’s own.
  - Final section offers broad policy recommendations.

### II. “‘ASIAPHORIA’ MEETS ‘THE MYTH OF ASIA'S MIRACLE’” — literature context
- Historical debate on Asia’s growth performance:
  - Page (1994): found growth performance in fast-growing Asian economies was significantly better compared to other regions, attributing the “Asian Miracle” to factor accumulation combined with efficient allocation reflected in relatively high TFP growth.
  - Krugman (1994), “The Myth of Asia's Miracle”: argued that growth rates were largely input-driven—based on an extraordinary “willingness” to save and sacrifice current consumption for the sake of future production—with little productivity improvement; warned that naive projection of past growth rates would overstate prospects.
  - Young (1995): reached a similar conclusion (text truncated beyond this point in the source).

*Source: _wp15113 - References .............................................................................................................*

### conclusion, documenting the fundamental role played by factor accumulation in explaining the

### _wp15113 - conclusion, documenting the fundamental role played by factor accumulation in explaining the

### Role of factor accumulation versus TFP in East Asia and China
- Postwar growth of Hong Kong SAR, Singapore, South Korea and Taiwan Province of China was fundamentally driven by factor accumulation.
- For China, literature reports wide-ranging estimates of TFP growth and large variation over time:
  - Meta-study (Xu and Xiaohua, 2012): mean reported TFP growth between 1978 and 2009 is about 2 percent, contributing around 20 percent to the GDP growth in this period.
  - Reported average TFP growth rates fluctuate widely: about 1 percent on average in 1985–89 and 1995‒1999; between 4½ and 5 percent in the remainder of the sample.
  - Standard deviation of TFP estimates is very high (from 5 to 10 percent); negative TFP growth values reported in all sub-samples.
  - Zhan, Jiang and Wang (2014): TFP growth of about 1.5 percent in the 1998–2012 sample, with a modest pickup in the last two years of the sample to about 2¼ percent.
  - Wu (2014): alternative GDP series implies negative TFP growth in the 2008–12 period.
- Recent work (Pritchett and Summers, 2014) argues for mean reversion in growth and estimates growth rates in the range of 4–5 percent likely for China at the end of the next decade; they view faster growth as possible but unlikely given historical experience.

### Estimating potential output and output gap — definitions and methodologies
- Traditional potential output: level of goods and services sustainable with existing resources without generating inflationary pressures; output gap = actual minus potential.
- Finance-neutral (termed “sustainable output” and “deviation from sustainable output”) concept: links deviations from sustainable output to credit dynamics and financial cycles (Borio and others, 2014 inspiration, with modifications).
- Methods applied:
  - Univariate filters: Hodrick-Prescott (HP) filter; band-pass filters (Baxter-King; Christiano-Fitzgerald).
  - Multivariate filters: structural time series linking output fluctuations to inflation, extended versions include unemployment (Okun’s law), capacity utilization, inflation expectations.
  - Production function approach: decomposes GDP into labor, capital, and TFP; HP filter applied to labor and TFP inputs in standard implementations; a modified version combines growth decomposition with a multivariate filter and adjusts capital by capacity utilization deviations.
  - Finance-neutral measures: deviations tied to a credit gap (deviation of real credit from stochastic trend) and a real house price gap; credit gap formulation allows deviations from sustainable output to remain positive while credit gap is open; variances of stochastic processes not restricted.

### Empirical results across methods
- Common finding: secular slowdown in potential growth; however, methods differ on level of potential growth and sign/size of output gap at end of sample (2013).
- Hodrick-Prescott (univariate) results:
  - Trend growth at the end of the sample drops to about 8 percent.
  - Produces a negative output gap of about a half percentage point.
  - Band-pass filters (Christiano-Fitzgerald; Baxter-King) produce similar estimates.
- Multivariate filters:
  - Indicate steeper slowdown in potential GDP.
  - Output gaps closer to zero at end of sample; inflation dynamics add significant information (strong disinflation in late 1990s generates negative gap; pickup in inflation around 2007 associated with a positive gap; post-GFC negative inflation associated with negative gap).
  - Using core (nonfood) inflation clarifies link between prices and gap; constructed gaps are relatively small in absolute terms.
- Production function approach:
  - Shows a much lower output gap in 2013 compared with multivariate filters; gap turns persistently negative after the GFC.
  - Capacity utilization deviations (“capacity utilization gap”) drive turning points in the output gap.
  - Growth decomposition: current potential output slowdown largely driven by a significant drop in TFP growth, only partly offset by higher contribution from capital; analogous slowdown observed around Asian crisis with TFP bottoming in 1999.
- Finance-neutral (sustainable output) estimates:
  - Sustainable growth slightly below headline rate in 2013, but deviation from sustainable output is positive and high, reflecting high headline growth rates after the GFC.
  - Deviations from sustainable output show divergent post-GFC dynamics driven by surge in credit and rising housing prices.
  - Deviations from sustainable output are persistently positive since 2007; 2007 peak reflects supportive global environment and loose pre-GFC monetary conditions, with a distinct increase in the gap after 2009 due to post-crisis credit surge.

### Interpretation and economic implications
- Key observations:
  - Potential growth has slowed; even optimistic estimates put potential growth below headline in 2013.
  - Output gaps linked to inflation or capacity utilization are close to zero or negative in 2013, consistent with subdued inflation dynamics and falling capacity utilization.
  - Finance-neutral measures point to large positive deviations from sustainable output since 2007, indicating a sizable credit gap sustained by exceptionally strong credit growth after the GFC.
- Reconciling divergent results:
  - Traditional output gap closed largely through massive post-GFC stimulus (public and quasi-public investment; loose monetary conditions supporting credit growth, particularly to real estate). This absorbed labor market slack and added capacity in construction-related industries.
  - Credit-financed investment component of stimulus is likely unsustainable, producing large finance-neutral gaps. A self-propelling real estate cycle (rising asset prices, rising value of collateral, low rates) creates conditions for an adjustment when expectations or financial conditions change.
  - During adjustment:
    - Credit-financed development activities likely to drop.
    - Unprofitable projects (including in construction-related industries) may be mothballed.
    - Resources will need reallocation; traditional output gap may turn significantly negative as production factors are temporarily unemployed during reallocation.
  - Public and quasi-public investment provides a more stable demand cushion but may be unsustainable longer term; removing distortions (e.g., weak social safety net) could raise consumption and interest rates, potentially making some investments unprofitable and raising public debt burden.
  - Some investment today may not serve future consumption needs if misdirected (infrastructure, housing supply where demand is yet to come), risking obsolescence or premature depreciation.
- Policy-relevant conclusions:
  - Cyclical output fluctuations appear more connected to the financial cycle than the traditional business cycle, implying that a period of slower growth may be needed to address post-GFC imbalances.
  - Output costs of adjustment hinge on flexibility of resource reallocation; structural reforms to open up new activities are important to facilitate reallocation and to arrest slowdown in potential output growth.
  - Historical evidence suggests liberalizing reforms (for example around WTO accession) aided recovery from previous financial cycles.

_Italic: Source — content unit: _wp15113 - conclusion, documenting the fundamental role played by factor accumulation in explaining the (PDF chapter/section)._

### 2009. The convergence path, however, is a function of

### _wp15113 - 2009. The convergence path, however, is a function of

### Convergence-path analysis and simulated scenarios
- Model re-estimated on the sample of “Asian Tigers” to construct an upper-bound convergence path (lower barriers to technology diffusion → higher TFP growth).
- Two simulated convergence paths for China:
  - “Low convergence path”: simulated from the full model (sample-wide).
  - “High-convergence path”: simulated from the model estimated on Asian Tigers’ data.
- Empirical relationship between actual and simulated paths:
  - China’s actual growth path is significantly above the low convergence path.
  - Since 1979, China’s actual growth has oscillated around the high-convergence path.
  - Periods identified as “overheated” in the late 2000s; growth remained in overheated territory even after the relative slowdown in 2013.

### Key quantitative findings on growth dynamics
- Headline growth slowed from the pre-GFC peak of 14 percent to less than 8 percent in 2013.
- The Asian Tigers–based model predicts growth to fall to about 7½ percent in 2013.
- China’s per capita income: about 20 percent of the U.S. level (2013).
- China’s economy size in PPP terms: already equal to three-quarters of the U.S. economy (2013).
- Korea and Taiwan Province of China sizes in PPP terms in 2013 equivalents when at similar development levels: respectively about 10 percent and 6 percent of U.S. size.
- Footnote: share of labor compensation in income in China of around one half (PWT 8.0 based assumption).

### Productivity, capital, and investment patterns
- Decomposition (Hodrick-Prescott filtered) of potential growth components:
  - Fast-growing Asian economies relied heavily on capital accumulation; productivity growth contribution was also significant (notably Japan).
  - China followed a similar pattern, but:
    - TFP contribution has been falling off in the post-2009 period.
    - Contribution from capital accumulation has also been declining despite a much higher share of investment in Chinese GDP, indicating a declining marginal product of capital.
- While China’s capital-to-labor ratio is still much lower than in advanced economies, it is higher than among Asian Tigers at the same development level.
- Evidence cited: about half of TFP gains from technological progress have been wiped out by various inefficiencies linked to the recent investment drive; rapid credit growth has hindered efficient allocation of capital and productivity growth.

### Risks from the current domestically-oriented growth model
- Overinvestment and imbalances:
  - The post-GFC surge in investment has been unsustainable as a source of demand and has reduced investment efficiency.
  - Overinvestment is highlighted as a prominent feature increasing the probability of a persistent growth slowdown.
- Financial-cycle and output-gap implications:
  - Including financial-cycle information points to a relatively large positive “finance-neutral” gap in 2013, reflecting imbalances accumulated since the GFC and exceptionally strong credit growth.
  - The positive “finance-neutral” gap implies correction costs in terms of output; some losses temporary (reallocation of factors) and some permanent (misallocated capital depreciated).
- Fiscal risks:
  - Fiscal policy can stabilize the adjustment but has limits—further public debt accumulation could undermine sustainability and dampen consumption if tax burdens to service debt become excessive.
  - Risk of misallocating public investment to projects that will never be put to use.
- Institutional risks to reform:
  - Current institutional supports for favored firms create a selectively better business climate, raising the risk of a disorderly slowdown when such supports are dismantled.
  - Local government behaviors (support for connected businesses; competition to attract businesses) have benefits but also create entry barriers, inefficient public-good allocation, and potential capture by incumbents.
  - Rebuilding incentive systems to improve efficiency may be a lengthy and bumpy process.

### Reform potential and policy implications
- The Third Plenum reform blueprint (2013) contains elements necessary to keep China on a convergence path similar to fast-growing Asian economies and to facilitate adjustment after the credit boom.
- Lam and Maliszewski (2015) conclusion (as cited): full implementation of the reform package could allow China to sustain long-term growth broadly consistent with fast-growing Asian economies’ experience.
- Historical precedent: past TFP slowdowns were temporary and productivity rebounded after liberalizing reforms (e.g., WTO accession following the 1998 slowdown), but the current reform round lacks a comparable external anchor, making reform implementation more challenging.
- Policy tensions:
  - Need to switch demand driver from investment to consumption while restoring investment efficiency.
  - Maintaining high productivity growth in a domestically oriented growth model will be challenging because export-oriented industries tend to be more efficient and domestic sectors may face weaker competition.

### Conclusions (summary of main findings)
- Potential growth has slowed; even the most optimistic estimates point to a secular slowdown that brought potential growth below the headline rate in 2013.
- The positive “finance-neutral” gap in 2013 signals correction costs tied to imbalances from strong credit growth; adjustment will entail temporary and permanent output costs.
- Traditional output gap estimates linked to inflation or capacity utilization are negative but small in 2013; this small gap masks instability and the risk of stronger deflationary pressures if the unsustainable demand contracts.
- Long-term growth prospects remain strong but subject to risks:
  - Recent slowdown in productivity growth and signs of overinvestment.
  - Institutional quality could become an impediment, raising the risk of falling to growth rates closer to the average of a broader group of emerging market economies.
- Full and steadfast implementation of the Third Plenum reform blueprint is presented as the first line of defense against falling into a “middle-income trap.”

*From: _wp15113 - 2009. The convergence path, however, is a function of*

### Appendix I. Methodology

### Appendix I. Methodology

### A. Univariate Filters
- Hodrick-Prescott (HP) filter
  - Finds trend output (ݕ∗) by minimizing a combination of the gap between actual output and trend output and the rate of change in the trend output.
  - Objective function shown in text; T is the sample size and λ is a smoothness parameter.
  - Following standard practice for annual data, the smoothness parameter is set equal to 100.

- Band-pass filters
  - Concept: take a two-sided weighted moving average to filter out cyclical fluctuations outside a pre-specified frequency band; medium-frequency component interpreted as the business cycle.
  - Standard practice assumes a cycle lasts from two to eight years.
  - Two filters used: Baxter-King (BK) and Christiano-Fitzgerald (CF).

- Baxter-King (BK) band-pass filter
  - Passes components with fluctuations between six (18 month) and 32 (96 month) quarters, removing higher and lower frequencies.
  - Uses specified leads/lags of 8 quarters; filter is a weighted moving average of leads/lags up to 8 quarters.
  - Weights are symmetric for leads and lags and time-invariant.
  - Choosing specified leads/lags (K) results in a loss of K= 8 observations both at the beginning and end of the series; low K gives poor approximation to the ideal filter.

- Christiano-Fitzgerald (CF) filter
  - Random walk CF filter built on same principles as BK.
  - Data must be made stationary before applying CF; text removes the linear trend in real GDP.
  - Band for business cycle chosen as eight to 32 quarters (same as BK).
  - Weights can differ for leads and lags and are time-varying, depending on the data and changing for each observation.
  - CF is a moving average of the full sample and converges in the long run to the optimal filter; in real time applications CF outperforms BK.
  - Footnote: CF also has a version of fixed-length symmetric filter, but moving average weights differ due to different objective function.

- Key methodological trade-offs
  - BK: symmetric approximation, no phase shifts, but requires series trimming (loss of observations).
  - CF: uses whole time series, designed to work on a larger class of series, time-varying weights.

### B. Multivariate Filters Linking Output Gap to Inflationary Pressures
- Estimation approach
  - Use unobserved components (state-space) models estimated via Kalman filter; likelihood constructed for classical or Bayesian methods.
  - Models estimated by a Bayesian regularized maximum likelihood method (Ljung, 1999).
  - Estimates sensitive to choice of priors; robustness checked by estimating the bivariate model with regular maximum likelihood.

- Bivariate model (output and inflation linkage)
  - Decomposition: y_t = y_t^* + y_t^gap (permanent trend y^* and cyclical component).
  - Permanent trend modeled as a local linear trend.
  - Cyclical component assumed stationary, follows AR(1).
  - Cyclical component linked to inflation in a backward-looking Phillips curve.
  - Data: Quarterly GDP and inflation data from WEO database, CEIC, and Haver Analytics.

- Multivariate model (Benes and N’Diaye, 2010)
  - Built around three gaps: output gap (y), unemployment gap (u), capacity utilization gap (c).
  - Identifying equations:
    - Inflation equation: relates level and change of output gap to inflation (full equation in text).
    - Unemployment equation (Okun’s law): links unemployment gap to output gap.
  - Equilibrium variables evolve dynamically with stochastic processes including transitory and persistent shocks.
  - NAIRU (equilibrium unemployment) dynamics include AR processes for persistent shocks.
  - Trend output (y^*) includes time-varying growth rate and depends on changes in the NAIRU; labor share ߠ enters via Cobb-Douglas production function.
  - Output gap equation includes monetary policy influence via output gap and inflation expectations term: includes 4ߨ_t−1^a (inflation expectation).
  - Data: Quarterly GDP and inflation from WEO; inflation expectation from Consensus Economics Forecast; capacity utilization and unemployment from CEIC.

### C. Multivariate Filter with the Addition of a Production Function
- Builds on Barnett and N’Diaye (2013); augments multivariate model by adding Cobb-Douglas–type production function linking potential output to trend employment and capital adjusted for capacity utilization.
- Core equations (output, unemployment, capacity gaps) resemble prior multivariate model; notation and full equations provided in text.
- Labor/input dynamics
  - Labor input depends on unemployment rate combined with population dynamics (n): ∆n_t equation included.
  - Participation rate (p) decomposed into gap and potential participation, both stochastic trends.
  - Labor force defined as population times participation; potential labor force uses potential participation.
  - Potential labor input constructed from first-order expansion of equilibrium unemployment around steady state u_00 (equation shown).
- Capital and productivity dynamics
  - Growth in capital stock (∆k) is stationary AR(1) around steady-state growth ∆k̄.
  - Equilibrium capital input is a function of capital input and equilibrium capacity utilization.
  - Total factor productivity A^* follows a stochastic trend with time-varying slope g; g follows an AR(1).
  - Potential output constructed via Cobb-Douglas: y^* = A^* + α log labor^* + (1−α) log k^* (exact functional form in text).
- Data: Annual GDP and inflation from WEO; capacity utilization and unemployment from CEIC; capital and labor data from PWT 8.0.

### D. Multivariate Filter to Estimate ‘Finance-Neutral’ Output Gap
- Objective: derive a ‘finance-neutral’ output gap by explicitly including financial variables.
- Added gaps: credit gap (ܿ_t^gap) and housing price gap (p_h_t^gap).
- Output gap dynamics
  - Output gap reacts to the credit gap; specification given with AR structure and coefficients (full equation in text).
  - Potential output (y^*) follows stochastic trend with time-varying slope g_t^(y*); dynamics of g shown as AR(1).
- Credit gap dynamics
  - Real credit deviation from stochastic trend (ܿ̅) with time-varying slope g̅_t; dynamics of g̅ shown as AR(1).
- Housing price gap dynamics
  - Housing gap linked to credit gap (excess credit causes deviations of real housing prices from equilibrium).
  - Equilibrium housing prices follow stochastic trends with time-varying slope g_t^(hp); dynamics of g_t^(hp) given as AR(1).
  - Footnote: adding housing price gap as regressor in ‘finance-neutral’ output gap equation significantly widens posterior densities of coefficients—likely due to colinearity between credit and housing price gaps.
- Data: Annual GDP and inflation from WEO; credit data from BIS (credit to the private sector); housing price data from CEIC.

### E. Production Function Approach for Cross-Country Analysis
- Use aggregate Cobb-Douglas production function with input shares α_t estimated from time-varying labor income share.
  - Functional form in text: Y_t = A_t K_t^α_t L_t^(1−α_t) (notation as in source).
- Procedure steps:
  1. Derive historical TFP as output less weighted average of factor inputs; factor weights estimated from average income shares of capital and labor.
  2. Use HP filter to derive trend TFP growth.
  3. Use HP filter to derive trend growth of physical capital stock.
  4. Derive trend labor using working age population.
  5. Trend output derived using trend TFP, trend labor, and physical capital stock.
- Data: Annual data from PWT 8.0.

*Source: _wp15113 - Appendix I. Methodology*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15113.pdf_