## _wp0655 - 5. Standard deviation of efficiency indexes across all provinces, 1978-98

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---

### Major findings on provincial productivity dynamics
- All provinces recorded increases in labor productivity between 1978 and 1998.
- The average annual growth rate of labor productivity for all provinces was 7.4 percent between 1978 and 1998.
- Coastal provinces such as Fujian, Guangdong, and Zhejiang experienced labor productivity growth of about 10 percent per year.
- Landlocked provinces such as Heilongjiang, Gansu, and Qinghai experienced labor productivity growth of only 4-5 percent per year.
- In 1978, Liaoning and Shanghai had efficiency indexes of 1, implying they lay on the estimated technology frontier in 1978; the nonparametric approach excluded 26 provinces from the technology frontier in 1978.
- Pattern of developments:
  - Several coastal provinces that were initially less productive (Fujian, Guangdong, Zhejiang ranked 17th, 12th, and 16th in 1978) surpassed previously more productive landlocked provinces (Qinghai and Gansu ranked 8th and 10th in 1978).
  - By 1998 Fujian, Guangdong, and Zhejiang ranked 8th, 5th, and 7th while Qinghai and Gansu ranked 22nd and 25th.

### Methodology and theoretical framework
- Technique used: Data Envelopment Analysis (DEA) with inputs (capital and labor) and output (GDP).
- Production technology assumption: constant returns to scale (CRS), which implies transformed frontier f_t(k_t)=y_t with f_t exhibiting non-increasing returns to scale (NIRS).
- Frontier construction: the production set F_t is the smallest convex set enveloping all available input-output data up to time t; weights θ_iτ satisfy t ∑_{τ=1}^I ∑_{i=1} θ_iτ ≤ 1 to impose NIRS and free disposal.
- Efficiency measure: output-based (Farrell) efficiency function E_t(k_t,y_t)=min{λ : (k_t,y_t/λ)′ ∈ P_t}; province efficiency index λ_i^t is computed by solving the specified linear programming problem (minimize λ_i^t subject to linear constraints using all observations up to t).
- Decomposition identity (geometric mean of two representations following Caves et al. (1982), Färe et al. (1994), Kumar and Russell (2002)):
  - g_y = g_eff + g_tech + g_cap
  - g_eff: average annual growth rate of the efficiency index
  - g_tech: average annual growth rate of technical progress
  - g_cap: average annual growth rate of potential outputs due to change in capital intensity
- Key methodological choices and motivations:
  - Use of all historical observations up to t (following Diewert (1980)) to prevent technological regress observed when using only contemporaneous observations.
  - Nonparametric, data-driven frontier avoids assuming Hicks-neutral technical change and avoids assuming competitive markets.
  - DEA allows separation of efficiency change and technological progress and identifies relative performance against a common benchmark across provinces.
- Caveats: the constructed frontier is relative to the best technology observed in the sample and may lie below the true frontier; efficiency indexes therefore represent lower bounds on true inefficiencies; measurement errors are not modeled.

### Quantitative decomposition results (aggregate and cross-province patterns)
- On average across provinces, capital deepening accounted for about 70 percent of total labor productivity growth between 1978 and 1998.
- On average across provinces, efficiency gains accounted for about 15 percent of total labor productivity growth.
- On average across provinces, technological improvements accounted for about 15 percent of total labor productivity growth.
- Cross-provincial dispersion:
  - In most coastal, northeastern, and southeastern provinces, capital deepening accounted for more than 75 percent of productivity growth.
  - In most western and northern provinces, capital deepening accounted for less than 70 percent of productivity growth.
  - Improvement in efficiency was higher in initially less advanced provinces than in richer ones, indicating catching up toward the technology frontier by less advanced provinces.
  - Relatively more productive provinces benefited more from technological progress than less developed provinces.

### Sample and frontier observations
- 28 observations available in 1978; 588 observations available in 1998 (28 for each year over 21 years).
- Shanghai had an efficiency index of 1.
- The 1998 frontier is shaped by the input-output combinations of Zhejiang in 1985, Fujian in 1993, Shanghai in 1984, and Shanghai in 1993, 1994, and 1998.
- Production activities were generally closer to the frontier in 1998 than in 1978.
- Average efficiency index across provinces:
  - 1978: 0.636
  - 1998: 0.746
- Standard deviation of efficiency indexes across provinces:
  - 1978: 0.198
  - 1998: 0.128
- Interpretation: Trends suggest convergence in both the mean (β-convergence) and the standard deviation (σ-convergence) of efficiency indexes across provinces.

### Time-paths and cross-sectional dispersion
- Selected provinces (Beijing, Fujian, Guandong, Ningxia, Yunnan): except for Beijing, efficiency indexes trended upward between 1978 and 1998.
- Standard deviation of efficiency indexes across provinces declined sharply until the end of the 1980s and then remained broadly constant in the 1990s.
- Most of the reduction in dispersion is explained by improvement in efficiency indexes in landlocked provinces; coastal provinces were already close to the technology frontier in 1978 and remained close.
- Convergence in efficiency indexes likely contributed to convergence in per capita income across provinces in the 1980s.

### Decomposition of labor productivity growth (1978–1998)
- Average productivity growth: 7.4 percent.
- Contribution of capital deepening: 5.2 percentage points (about 70 percent of countrywide productivity growth).
- Heterogeneity across provinces:
  - Contribution of capital deepening to average annual labor productivity growth in Fujian, Jiangsu, Zhejiang: 8-9 percentage points.
  - Contribution of capital deepening in Gansu, Ningxia, Qinghai: less than 3.5 percentage points.
  - In almost all coastal provinces capital deepening accounted for at least 75 percent of labor productivity growth.
- Role of FDI:
  - FDI inflows contributed 1.6 percentage points to average annual GDP growth in provinces with SEZs and open cities during 1990-97.
  - FDI inflows contributed 0.2 percentage points to average annual GDP growth in other provinces.
  - Through impact on total factor productivity, Zebregs (2003) estimated FDI contributed 2.5 percentage points per year to overall GDP growth during the 1990s.

### Regression evidence on components and initial productivity
- Absolute β-convergence in efficiency across provinces:
  - Regression g_i^λ = β_0 + β_1 ln(λ_i1978) + ε_i yields β_1 = −0.028 with standard error 0.004 (statistically significant).
- Relation between initial labor productivity and growth of components:
  - Growth rate of efficiency regressed on initial labor productivity: β = −0.010 with standard error 0.003 (negative and significant).
  - Change in technology regressed on initial productivity: coefficient = 0.016 with standard error 0.002 (positive and significant).
  - Growth rate of capital deepening regressed on initial (log) labor productivity: coefficient = −0.009 with standard error 0.003 (negative and significant).
  - Regression of growth rate of productivity growth on initial (log) productivity level: coefficient = −0.004, not statistically significant (0.005).

### Interpretation of technological progress and FDI
- Technological progress generally largest in initially more productive provinces, consistent with technological diffusion theories.
- Technological progress in coastal provinces was not noticeably higher than in other provinces despite large FDI inflows.
- Possible explanations:
  - Early FDI (1980s) concentrated in low-tech export-processing sectors and aimed to exploit low-cost labor, yielding limited technology transfer or spillovers.
  - Shift in the 1990s toward European, Japanese, and U.S. multinationals seeking local production may alter this pattern; separate decompositions for the 1980s and 1990s could clarify.

### Conclusions and implications
- Capital deepening was the dominant source of labor productivity growth in China’s provinces between 1978 and 1998.
- Efficiency improved between 1978 and 1998, particularly in initially least productive (often agricultural) provinces — likely reflecting economic reforms and labor reallocation from farming and state-owned enterprises to more productive non-state industries.
- Evidence of:
  - No absolute convergence in labor productivity across provinces.
  - Absolute convergence in efficiency.
  - Evidence of absolute convergence in capital deepening (this result may be sensitive to sample period).
- Observation that by 1998 some initially poorer coastal provinces had surpassed several initially richer landlocked provinces points to conditional convergence in capital deepening.
- Future research planned: more rigorous econometric analysis of determinants of provincial productivity growth to better understand effects of geography, preferential policies, openness, and other structural factors on capital deepening, efficiency gains, and technological progress.

### Data appendix — key data construction notes
- Sample: 28 provinces between 1978 and 1998 (Hainan and Tibet Autonomous Region were excluded for lack of data on value-added and fixed-capital investment).
- Value added and investment data: provincial yearbook of China.
- Labor data: Young (2000) compiled from provincial yearbooks, A Compilation of Historical Statistics (State Statistical Bureau, 1990), and Hsueh, Li and Liu (1993).
- DEA-based frontier construction used all observed input-output combinations at the province level up to date t.
- Adjustments:
  - Qinghai and Ningxia investment-to-GDP ratios over 1978–98 appeared implausibly high; assumed their investment-to-output ratios equal the average of Shaanxi, Gansu, and Xinjiang.
- Capital accumulation identity:
  - K_{t+1} = I_t + (1−δ)K_t, K_0 > 0
  - Depreciation rate δ assumed 5 percent.
  - Initial capital stock computed by K_0 = I_0 / (g + δ), where g (annual growth rate of capital stocks before 1978) assumed 5 percent.
- Investment data available from 1952 but pre-1978 data judged low and volatile and incomplete for Guangdong and Jiangxi; analysis restricted to 1978–1998 investment data for comparability.

*Source: _wp0655 - 5. Standard deviation of efficiency indexes across all provinces, 1978-98; excerpts from IMF working paper content unit _wp0655.*

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

### References

### Tables
- 1. Capital intensity, labor productivity, and efficiency, 1978-98 ..................................................................12
- 2. Decomposition of labor productivity growth, 1978-98 .........................................................................16

### Figures
- 1. Decomposition of output per worker ...............................................................................................8
- 2. Production set and frontier, 1978..................................................................................................13
- 3. Production set and frontier, 1998..................................................................................................13
- 4. Selected provinces: Efficiency index, 1978-98 .............................................................................14

*Source: _wp0655 - References; https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2006/_wp0655.pdf*

### 5. Standard deviation of efficiency indexes across all provinces, 1978-98 ...........................15

### 5. Standard deviation of efficiency indexes across all provinces, 1978-98

### Major findings on provincial productivity dynamics
- All provinces recorded increases in labor productivity between 1978 and 1998.
- The average annual growth rate of labor productivity for all provinces was 7.4 percent between 1978 and 1998.
- Coastal provinces such as Fujian, Guangdong, and Zhejiang experienced labor productivity growth of about 10 percent per year.
- Landlocked provinces such as Heilongjiang, Gansu, and Qinghai experienced labor productivity growth of only 4-5 percent per year.
- In 1978, Liaoning and Shanghai had efficiency indexes of 1, implying they lay on the estimated technology frontier in 1978; the nonparametric approach excluded 26 provinces from the technology frontier in 1978.
- The pattern of developments: several coastal provinces that were initially less productive (e.g., Fujian, Guangdong, Zhejiang ranked 17th, 12th, and 16th in 1978) surpassed previously more productive landlocked provinces (e.g., Qinghai and Gansu ranked 8th and 10th in 1978; by 1998 Fujian, Guangdong, and Zhejiang ranked 8th, 5th, and 7th while Qinghai and Gansu ranked 22nd and 25th).

### Methodology and theoretical framework
- Technique used: Data Envelopment Analysis (DEA) with inputs (capital and labor) and output (GDP).
- Production technology assumption: constant returns to scale (CRS), which implies transformed frontier f_t(k_t)=y_t with f_t exhibiting non-increasing returns to scale (NIRS).
- Frontier construction: the production set F_t is the smallest convex set enveloping all available input-output data up to time t; weights θ_iτ satisfy t ∑_{τ=1}^I ∑_{i=1} θ_iτ ≤ 1 to impose NIRS and free disposal.
- Efficiency measure: output-based (Farrell) efficiency function E_t(k_t,y_t)=min{λ : (k_t,y_t/λ)′ ∈ P_t}; province efficiency index λ_i^t is computed by solving the specified linear programming problem (minimize λ_i^t subject to linear constraints using all observations up to t).
- Decomposition of labor productivity growth: using the geometric mean of two representations (following Caves et al. (1982), Färe et al. (1994), Kumar and Russell (2002)), the identity g_y = g_eff + g_tech + g_cap decomposes average annual growth rate of output per worker into:
  - g_eff: average annual growth rate of the efficiency index,
  - g_tech: average annual growth rate of technical progress,
  - g_cap: average annual growth rate of potential outputs due to change in capital intensity.
- Key methodological choices and motivations:
  - Use of all historical observations up to t (following Diewert (1980)) to prevent technological regress observed when using only contemporaneous observations.
  - Nonparametric, data-driven frontier avoids assuming Hicks-neutral technical change and avoids assuming competitive markets (important because market regulation in China may be extensive).
  - DEA allows separation of efficiency change and technological progress and identifies relative performance against a common benchmark across provinces.
- Caveats noted: the constructed frontier is relative to the best technology observed in the sample and may lie below the true frontier; efficiency indexes therefore represent lower bounds on true inefficiencies; measurement errors are not modeled (stochastic frontier approaches exist but impose additional functional-form restrictions).

### Quantitative decomposition results (aggregate and cross-province patterns)
- On average across provinces, capital deepening accounted for about 70 percent of total labor productivity growth between 1978 and 1998.
- On average across provinces, efficiency gains accounted for about 15 percent of total labor productivity growth.
- On average across provinces, technological improvements accounted for about 15 percent of total labor productivity growth.
- Cross-provincial dispersion:
  - In most coastal, northeastern, and southeastern provinces, capital deepening accounted for more than 75 percent of productivity growth.
  - In most western and northern provinces, capital deepening accounted for less than 70 percent of productivity growth.
  - Improvement in efficiency was higher in initially less advanced provinces than in richer ones, indicating catching up toward the technology frontier by less advanced provinces.
  - Relatively more productive provinces benefited more from technological progress than less developed provinces.

### Data and sample
- Sample: 28 provinces between 1978 and 1998 (Hainan and Tibet Autonomous Region were excluded for lack of data on value-added and fixed-capital investment).
- Data sources:
  - Value added and investment data: provincial yearbook of China.
  - Labor data: Young (2000) compiled from provincial yearbooks, A Compilation of Historical Statistics (State Statistical Bureau, 1990), and Hsueh, Li and Liu (1993).
- Additional empirical notes:
  - The DEA-based frontier construction used all observed input-output combinations at the province level up to date t.
  - The authors followed Kumar and Russell (2002) for the decomposition approach but modified the frontier construction to include all prior observations to prevent regression in estimated technology.

*Source: _wp0655 - 5. Standard deviation of efficiency indexes across all provinces, 1978-98*

### 1998. In 1978 we had only 28 observations. Consequently, we only used these 28 observations in solving

### _wp0655 - 1998. In 1978 we had only 28 observations. Consequently, we only used these 28 observations in solving

### Sample and frontier observations
- 28 observations available in 1978; 588 observations available in 1998 (28 for each year over 21 years).
- Shanghai had an efficiency index of 1.
- The 1998 frontier is shaped by the input-output combinations of Zhejiang in 1985, Fujian in 1993, Shanghai in 1984, and Shanghai in 1993, 1994, and 1998.
- Production activities were generally closer to the frontier in 1998 than in 1978.
- Average efficiency index across provinces:
  - 1978: 0.636
  - 1998: 0.746
- Standard deviation of efficiency indexes across provinces:
  - 1978: 0.198
  - 1998: 0.128
- Interpretation: Trends suggest convergence in both the mean (β-convergence) and the standard deviation (σ-convergence) of efficiency indexes across provinces.

### Time-paths and cross-sectional dispersion
- Selected provinces (Beijing, Fujian, Guandong, Ningxia, Yunnan): except for Beijing, efficiency indexes trended upward between 1978 and 1998.
- Standard deviation of efficiency indexes across provinces declined sharply until the end of the 1980s and then remained broadly constant in the 1990s.
- Most of the reduction in dispersion is explained by improvement in efficiency indexes in landlocked provinces; coastal provinces were already close to the technology frontier in 1978 and remained close over the next two decades.
- Convergence in efficiency indexes likely contributed to convergence in per capita income across provinces in the 1980s.

### Decomposition of labor productivity growth (1978–1998)
- Average productivity growth: 7.4 percent.
- Contribution of capital deepening: 5.2 percentage points (about 70 percent of countrywide productivity growth).
- Heterogeneity across provinces:
  - Contribution of capital deepening to average annual labor productivity growth in Fujian, Jiangsu, Zhejiang: 8-9 percentage points.
  - Contribution of capital deepening in Gansu, Ningxia, Qinghai: less than 3.5 percentage points.
  - In almost all coastal provinces capital deepening accounted for at least 75 percent of labor productivity growth.
- Role of FDI:
  - FDI inflows contributed 1.6 percentage points to average annual GDP growth in provinces with SEZs and open cities during 1990-97.
  - FDI inflows contributed 0.2 percentage points to average annual GDP growth in other provinces.
  - Through impact on total factor productivity, Zebregs (2003) estimated FDI contributed 2.5 percentage points per year to overall GDP growth during the 1990s.

### Regression evidence on components and initial productivity
- Absolute β-convergence in efficiency across provinces:
  - Regression g_i^λ = β_0 + β_1 ln(λ_i1978) + ε_i yields β_1 = −0.028 with standard error 0.004 (statistically significant).
- Relation between initial labor productivity and growth of components:
  - Growth rate of efficiency regressed on initial labor productivity: β = −0.010 with standard error 0.003 (negative and significant) — improvement in efficiency higher in initially less advanced provinces.
  - Change in technology regressed on initial productivity: coefficient = 0.016 with standard error 0.002 (positive and significant) — technological progress larger in initially more productive provinces.
  - Growth rate of capital deepening regressed on initial (log) labor productivity: coefficient = −0.009 with standard error 0.003 (negative and significant) — capital deepening higher in initially less developed provinces.
  - Regression of growth rate of productivity growth on initial (log) productivity level: coefficient = −0.004, not statistically significant (0.005).

### Interpretation of technological progress and FDI
- Technological progress generally largest in initially more productive provinces, consistent with technological diffusion theories.
- Technological progress in coastal provinces was not noticeably higher than in other provinces despite large FDI inflows.
- Possible explanations:
  - Early FDI (1980s) concentrated in low-tech export-processing sectors and aimed to exploit low-cost labor, yielding limited technology transfer or spillovers.
  - Shift in the 1990s toward European, Japanese, and U.S. multinationals seeking local production may alter this pattern; separate decompositions for the 1980s and 1990s could clarify.

### Conclusions and implications
- Capital deepening was the dominant source of labor productivity growth in China’s provinces between 1978 and 1998.
- Efficiency improved between 1978 and 1998, particularly in initially least productive (often agricultural) provinces — likely reflecting economic reforms and labor reallocation from farming and state-owned enterprises to more productive non-state industries.
- Evidence of:
  - No absolute convergence in labor productivity across provinces.
  - Absolute convergence in efficiency.
  - Evidence of absolute convergence in capital deepening (this result may be sensitive to sample period).
- Observation that by 1998 some initially poorer coastal provinces had surpassed several initially richer landlocked provinces points to conditional convergence in capital deepening.
- Future research planned: more rigorous econometric analysis of determinants of provincial productivity growth to better understand effects of geography, preferential policies, openness, and other structural factors on capital deepening, efficiency gains, and technological progress.

### Data appendix — key data construction notes
- Provincial GDP data: from various issues of the Statistical Yearbook of China.
- Labor data: used a dataset compiled by Young (2000) rather than the reported Statistical Yearbook of China labor series due to large swings and omission of migration effects.
- Investment data: from provincial yearbooks; available from 1952 but pre-1978 data judged low and volatile and incomplete for Guangdong and Jiangxi, so analysis restricted to 1978–1998 investment data for comparability.
- Adjustments: Qinghai and Ningxia investment-to-GDP ratios over 1978–98 appeared implausibly high; assumed their investment-to-output ratios equal the average of Shaanxi, Gansu, and Xinjiang to correct potential measurement errors.
- Capital accumulation identity:
  - K_{t+1} = I_t + (1−δ)K_t, K_0 > 0
  - Depreciation rate δ assumed 5 percent.
  - Initial capital stock computed by K_0 = I_0 / (g + δ), where g (annual growth rate of capital stocks before 1978) assumed 5 percent.

*Source: IMF working paper content unit _wp0655 (excerpts provided).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2006/_wp0655.pdf_