## 1. Production Frontier and Efficiency: A Simple Illustration

## Source details

**Canonical URL:** [1. Production Frontier and Efficiency: A Simple Illustration](https://www.imf.org/-/media/files/publications/wp/2018/wp18183.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/wp/2018/wp18183.pdf.md)
- [Structured JSON version](/-/media/files/publications/wp/2018/wp18183.pdf.json)

---

### Motivation
- Argentina’s per capita output relative to that of advanced economies nearly halved over the past 50 years.
- After the end of the commodity boom of the mid-2000s, divergence with advanced economies increased.
- Yearly labor productivity growth has been close to zero on average since 1980, compared with a 2½ percent average increase in emerging market economies (EMs).
- Argentina has an estimated 10 percent gap in capital intensity compared to the median of EMs.
- As of 2017, Argentina’s employment rate is 67 percent of working-age population, which is 10 percentage points below the median of advanced economies; employment is particularly low for women.
- A simple Solow-type residual shows total factor productivity (TFP) growth averaged essentially zero since 1980 in Argentina; when adjusted for labor and capital utilization, TFP growth averaged ¾ percent per year since 1980 (BCRA, 2017).
- Staff baseline projects only a gradual pick-up of Argentina’s GDP growth over the medium term without significant reform, with limited catching up vis-à-vis advanced economies.

### Framework and Data
- Methodology:
  - Production-function approach following Égert and Gal (2016).
  - TFP proxied by technical efficiency estimated with stochastic frontier analysis (SFA) rather than a Solow-type residual.
- Key decomposition:
  - GDP growth = capital accumulation + labor utilization + total factor productivity/efficiency.
  - In SFA, change in TFP = change in country-specific technical efficiency + technological change common to all countries; the analysis assumes common technological change is zero.
- Empirical strategy:
  - Cross-country reduced-form panel regressions for capital-output ratio and employment rate.
  - Technical efficiency estimated within SFA conditional on structural and macroeconomic variables.
  - Random-effects models with robust standard errors; Hausman test confirmed appropriateness (not reported).
- Sample and data:
  - About 60 advanced and emerging economies (32 EMs including seven Latin American countries; 27 advanced economies) covering 1980–2016 (sample periods vary by variable).
  - Data sources include IMF WEO, Penn World Tables, World Bank WDI, and various sources for structural variables (business regulations, labor market, taxation, trade barriers, governance, education, wealth, energy use, financial development).

### Structural reforms: aggregate simulated impacts and channels
- Overall findings:
  - Structural reforms can significantly affect long-term GDP growth through capital, labor, and especially productivity/efficiency channels.
  - Regulatory changes that promote competition and ease labor market regulations (especially flexible employment forms) matter most for the efficiency channel.
  - Pro-competition regulation also appears to improve labor utilization, together with lower tax rates on income and payroll.
  - Lower entry barriers (cost of starting a business) and trade tariffs are especially important for capital accumulation.
  - For Argentina, policies to promote capital and labor utilization promise larger payoffs given accumulated gaps.
- Aggregate simulated impacts (representative scenarios):
  - An ambitious reform effort that improves the business regulatory environment (closing half the gap with Australia and New Zealand over two decades) would add 1–1½ percent to average annual growth of GDP.
  - Reducing trade tariffs and payroll taxes (closing half the gap with Australia and New Zealand) could each boost average annual real GDP growth by about 0.1 percent.

### Capital deepening (empirical findings and Argentina simulations)
- Channels: product market regulation affects investment via price markups, entry costs, adjustment costs, and rate of return on capital.
- Empirical results:
  - Reducing entry barriers (cost of starting a business) and lowering trade tariffs boost capital deepening.
  - Capital intensity is negatively affected by output volatility and positively affected by availability of private credit and latest technologies.
  - Variables proxying cost of capital (corporate tax rate, real interest rate, relative investment prices) and labor market regulations are not strongly associated with investment in these results.
- Quantitative simulations for Argentina:
  - Cutting the cost of starting a business (proxied by the number of required procedures) to close half the gap relative to the average of Australia and New Zealand would increase Argentina’s capital-output ratio by 0.2 percentage points.
  - Reducing trade tariffs half way to levels in Australia and New Zealand would increase capital-output ratio by less than 0.1 percentage point.
- Selected empirical coefficients (Table A3, dependent variable: ln(K/Y)):
  - Output volatility: -0.63**, -1.23***, -0.60*, -0.77**, -0.76**, -1.37*** (z-statistics shown in source).
  - Cost of starting a business 1/: -0.01**, -0.01***, -0.01**, -0.01**, -0.001*.
  - Trade tariffs: -0.47**, -0.57***, -0.47***, -0.69**.
  - Private credit to GDP: 0.03, 0.05**, 0.04, 0.10**.
  - Availability of latest technologies: 0.02**, 0.02*.
  - Observations: 636, 592, 551, 564, 551, 551; No of countries: 59, 55, 58, 58, 58, 58.

### Employment rate (empirical findings and Argentina simulations)
- Literature: smaller tax wedge on labor, lower unemployment benefits, stronger active labor market policies, and product market deregulation are associated with higher employment.
- Empirical results:
  - Robust positive link between employment rate and pro-competition regulation (PMR).
  - Changes in labor market regulations are not strongly related to overall employment rate.
  - Tax rate changes are statistically important but quantitatively small.
- Quantitative simulations for Argentina:
  - Implementing product market reforms to close half the gap with the average of Australia and New Zealand would increase Argentina’s employment rate from 67 percent to 73 percent.
  - Reducing Argentina’s top marginal income and payroll tax rate from the current 58 percent to 50 percent is associated with an increase in Argentina’s employment rate of about one percentage point.
- Selected empirical coefficients (Table A4, dependent variable: ln(E/WP)):
  - Output gap: 0.01*** across specifications (z-statistics shown in source).
  - PMR: regulatory quality: 0.05*, 0.07***, 0.07***, 0.05***, 0.08***, 0.08***.
  - Share of female in population: -0.04**, -0.03*.
  - Top marginal income & payroll tax rate (τ): -0.001**.
  - Tax rate (τ) * tax compliance: -0.0002**.
  - Observations: 912, 864, 864, 1,140, 602, 612; No of countries: 57, 54, 54, 57, 55, 57.

### Efficiency of factor utilization (TFP / technical efficiency)
- Role of TFP: TFP is generally the main channel through which structural reforms affect growth; pro-competition product market reforms robustly increase TFP growth in many studies.
- Estimation approach and controls:
  - SFA used to estimate technical efficiency and its determinants simultaneously with the production frontier.
  - Controls include change in terms of trade and the output gap.
- Empirical findings:
  - Regulatory changes promoting competition and easing labor market regulations (particularly flexible employment forms) have the largest positive effects on technical efficiency.
  - IMF (2015) and other studies indicate that improvements in business regulations, easing labor market restrictions, and fiscal structural reforms deliver significant productivity gains for EMs.
- Quantified illustrative policy elasticity:
  - A conservative (lower-bound) estimate of the elasticity of technical efficiency with respect to pro-competition regulations suggests Argentina’s efficiency "could increase by over 10 percent if reforms were to close half the gap with Australia and New Zealand."
  - Timing caveat: gains are unlikely to occur quickly and would likely require many years of sustained reform effort.

### Box 1 — Production frontier, illustration for Argentina, and simulation design
- Definition:
  - Production/efficiency frontier: "the greatest level of output that is possible to produce given the factors of production utilized, and the technology adopted."
  - Distance from frontier measures technical inefficiency; θ_{i,t} ∈ (0,1], θ_{i,t} = 1 indicates a country on the efficiency frontier.
- Illustration for Argentina (as of 2016):
  - Given Argentina’s very low level of capital per worker, Argentina was "somewhat behind the production function" but "the distance was not out of line compared to other (more capital-intensive) economies."
  - Estimated efficiency for Argentina has worsened in the last decade, whereas the median of EMs and the full sample remained broadly unchanged.
  - Compared to the average technical efficiency of Australia and New Zealand in 2016, Argentina was "more than 10 percent inefficient."
- Simulation parameters:
  - Output elasticity of capital, α, set to 0.33 in simulations; alternative/implied values cited: 0.57 (Penn World Tables for Argentina) and about 0.61 (Appendix Table A6).
  - Structural policy variables for Argentina are assumed to slowly converge to the average value for Australia and New Zealand, with half the distance covered over a twenty-year period.
- Representative simulation outcomes:
  - Reducing the gap in the cost of starting a business would be associated with additional annual GDP growth of "0.15 percent only through the increase in capital intensity and about one percent through both the capital and efficiency channels."
  - "Illustrative simulations suggest that structural reforms could have substantial effects on long-term GDP growth."

### Policy implications and recommended reform actions
- Core recommendation: "Policies and regulations which would promote investment and capital deepening should be at the core of the structural reform agenda."
- Specific reform directions emphasized:
  - Facilitate firm creation and entry by reducing high costs to start a business and simplifying regulatory procedures.
  - Open the economy to trade by lowering tariffs and promoting technology spillovers.
  - Reduce state involvement where it distorts competition: phase out price controls, rationalize subsidies, reduce regulatory protection of incumbents, and ensure regulatory neutrality.
  - Strengthen competition framework: pass Competition Law and strengthen anti-trust authority.
  - Reduce barriers to investment and improve investment climate (governance, red tape, infrastructure) to increase FDI and technology/management spillovers.
  - Labor market reforms: reduce termination costs and restrictions on temporary/flexible work arrangements; protect workers via unemployment insurance and training rather than strict employment rigidities.
  - Tax reforms: reduce tax wedge on labor and phase out distortionary taxes (e.g., financial transaction tax) to improve labor use and financial intermediation.
- Timing and persistence:
  - Effects require many years of sustained reform effort; examples cited include Australia where reforms unfolded over decades (structural reform process starting in the 1970s and accelerating in the 1980s–1990s).

### Appendix 2 — Stochastic Frontier Analysis (model and selected empirical estimates)
- Model specification (log-linear Cobb-Douglas with inefficiency u_{i,t} = −ln(θ_{i,t})):
  - Frontier: ln Y_{i,t} = β_0 + β_t t + β_L ln L_{i,t} + β_K ln K_{i,t} + v_{i,t} − u_{i,t}
  - Inefficiency model: u_{i,t} = z_0 + γ_z z_{i,t} + w_{i,t}
  - Simultaneous maximum likelihood estimation of frontier parameters and technical efficiency (Battese and Coelli, 1995).
- TFP decomposition (Kumbhakar and Lovell, 2000):
  - ∆TFP = ∆T + ∆TE + (ε−1)[ ε_L/ε ∆x_L + ε_K/ε ∆x_K ]
  - ∆T = β̂_t = dy/dt (technological change); ∆TE = −du/dt (change in technical efficiency); ε_L and ε_K are output elasticities.
- Selected SFA parameter estimates (Table A5 and Table A6 highlights):
  - Table A5 (simple illustration, dependent variable: log real GDP-to-labor ratio; sample 1980–2016):
    - Log capital-labor ratio: 0.54*** (z = 54.75)
    - Time trend: 0.005*** (z = 10.28)
    - Mean inefficiency AE dummy: -1.46*** (z = -6.32)
    - Variance of inefficiency EM dummy: 1.49*** (z = 6.70)
    - Log-likelihood: 104; Observations: 2,082; Number of countries: 59
  - Table A6 (conditional inefficiency effects; multiple specifications):
    - Frontier coefficients (selected): Log labor ≈ 0.25–0.42***; Log capital ≈ 0.50–0.65***; Time trend small and can be negative or positive (examples: -0.004***, 0.005***, 0.01***).
    - Mean inefficiency correlates (selected): PMR: regulatory quality -0.16*** to -0.24***; LMR: CBR_working time positive coefficients up to 0.76***; Log change in terms of trade negative (e.g., -0.54***); Output gap negative (e.g., -0.02***).
    - Variance of inefficiency: EM dummy positive and significant (e.g., 1.85***); political stability negative and significant (e.g., -0.84***).
    - Log-likelihoods and sample sizes vary by specification (examples: Log-likelihood 1,629; Observations 2,082; Number of countries 59).
- Interpretation:
  - Labor and capital coefficients are consistently positive and statistically significant; capital coefficients typically larger than labor coefficients.
  - Better regulatory quality is associated with lower mean inefficiency.
  - Certain labor market regulation measures (working time restrictions) are associated with higher mean inefficiency.
  - Changes in terms of trade and output gap affect both mean and variance of inefficiency.
  - EM status tends to increase the variance of inefficiency; political stability reduces variance.

_Italic: Source: IMF staff estimates (wp18183)._

### 1. Production Frontier and Efficiency: A Simple Illustration _________________________ 9

### 1. Production Frontier and Efficiency: A Simple Illustration

### Motivation
- Argentina’s per capita output relative to that of advanced economies nearly halved over the past 50 years.
- After the end of the commodity boom of the mid-2000s, divergence with advanced economies increased.
- Yearly labor productivity growth has been close to zero on average since 1980, compared with a 2½ percent average increase in emerging market economies (EMs).
- Argentina has an estimated 10 percent gap in capital intensity compared to the median of EMs.
- As of 2017, Argentina’s employment rate is 67 percent of working-age population, which is 10 percentage points below the median of advanced economies; employment is particularly low for women.
- A simple Solow-type residual shows total factor productivity (TFP) growth averaged essentially zero since 1980 in Argentina; when adjusted for labor and capital utilization, TFP growth averaged ¾ percent per year since 1980 (BCRA, 2017).
- Without significant reform, staff baseline projects only a gradual pick-up of Argentina’s GDP growth over the medium term, with limited catching up vis-à-vis advanced economies.

### Framework and Data
- Methodology: production-function approach following Égert and Gal (2016), with TFP proxied by an estimated measure of technical efficiency using stochastic frontier analysis (SFA) rather than a Solow-type residual.
- Key decomposition: GDP growth is analyzed as the sum of separable and independent supply-side components—(i) capital accumulation, (ii) labor utilization, and (iii) total factor productivity/efficiency.
- In the SFA framework, change in TFP = (i) change in country-specific technical efficiency + (ii) technological change common to all countries. The analysis assumes the common technological change is zero.
- Empirical strategy:
  - Cross-country reduced-form panel regressions for capital-output ratio and employment rate, relating them to structural and macroeconomic variables.
  - Technical efficiency estimated within SFA conditional on the same structural and macroeconomic variables.
  - Random-effects models with robust standard errors are used to capture both cross-sectional and within-country variation; appropriateness confirmed by Hausman test (not reported).
- Sample: about 60 advanced and emerging economies (32 EMs including seven Latin American countries; 27 advanced economies) covering 1980–2016 (sample periods vary by variable).
- Data sources: IMF WEO, Penn World Tables, World Bank WDI, and a wide range of sources for structural variables (business regulations, labor market, taxation, trade barriers, governance, education, wealth, energy use, financial development).

### Structural Reforms and Impact on Capital, Labor, and Efficiency

- Overall finding:
  - Structural reforms can have significant impact on long-term GDP growth through all three supply-side channels, with the largest effect generally through the productivity/efficiency channel.
  - Regulatory changes that promote competition and ease labor market regulations (especially flexible forms of employment) matter most for the efficiency channel.
  - Pro-competition regulation also appears to improve labor utilization, together with lower tax rates on income and payroll.
  - Lower entry barriers (cost of starting a business) and trade tariffs are especially important for capital accumulation.
  - For Argentina, policies to promote capital and labor utilization promise larger payoffs given accumulated gaps.

- Aggregate simulated impacts:
  - An ambitious reform effort that improves the business regulatory environment (closing half the gap with Australia and New Zealand over two decades) would add 1–1½ percent to average annual growth of GDP.
  - Reducing trade tariffs and payroll taxes (closing half the gap with Australia and New Zealand) could each boost average annual real GDP growth by about 0.1 percent.

- Capital Deepening
  - Literature and channels: product market regulation affects investment via price markups and entry costs, cost of adjusting/expanding capital stock, and rate of return on capital.
  - Empirical results (this analysis):
    - Reducing entry barriers, especially the cost of starting a business, and lowering trade tariffs boost capital deepening.
    - Capital intensity is negatively affected by output volatility and positively affected by availability of private credit and latest technologies (proxy for trade openness).
    - Variables proxying cost of capital (corporate tax rate, real interest rate, relative investment prices) and labor market regulations are not strongly associated with investment in these results.
  - Quantitative simulation results for Argentina:
    - Cutting the cost of starting a business (proxied by the number of required procedures) to close half the gap relative to the average of Australia and New Zealand would increase Argentina’s capital-output ratio by 0.2 percentage points.
    - Reducing trade tariffs half way to levels in Australia and New Zealand would increase capital-output ratio by less than 0.1 percentage point.

- Employment Rate
  - Literature and channels: smaller tax wedge on labor, lower unemployment benefits, stronger active labor market policies, and product market deregulation are associated with higher employment.
  - Empirical results (this analysis):
    - Robust positive link between employment rate and pro-competition regulation.
    - Changes in labor market regulations are not strongly related to overall employment rate.
    - Tax rate changes are statistically important but quantitatively small.
  - Quantitative simulation results for Argentina:
    - Implementing product market reforms to close half the gap with the average of Australia and New Zealand would increase Argentina’s employment rate from 67 percent to 73 percent.
    - Reducing Argentina’s top marginal income and payroll tax rate from the current 58 percent to 50 percent is associated with an increase in Argentina’s employment rate of about one percentage point.

- Efficiency of Factor Utilization (TFP / Technical Efficiency)
  - Literature: TFP is generally the main channel through which structural reforms affect growth; pro-competition product market reforms robustly increase TFP growth in many studies.
  - This analysis:
    - Uses SFA to estimate technical efficiency and its determinants, allowing simultaneous estimation of efficiency in the production function and its drivers.
    - Controls include change in terms of trade and the output gap.
    - Finds that regulatory changes promoting competition and easing labor market regulations (particularly flexible employment forms) have the largest positive effects on technical efficiency.
    - IMF (2015) and other studies cited indicate that improvements in business regulations, easing labor market restrictions, and fiscal structural reforms deliver significant productivity gains for EMs.

*wp18183 - 1. Production Frontier and Efficiency: A Simple Illustration*

### Box 1. Production Frontier and Efficiency: A Simple Illustration

### Box 1. Production Frontier and Efficiency: A Simple Illustration

### Definition and methodology
- Production/efficiency frontier: "the greatest level of output that is possible to produce given the factors of production utilized, and the technology adopted."
- Distance from frontier measures technical inefficiency; this distance depends on country-specific characteristics.
- Estimation approach: stochastic frontier analysis (SFA) is used so that efficiency is a "structured" variable whose mean and/or variance reflect factors (including structural determinants) explaining the level and volatility of efficiency across countries.
- Model features:
  - Country-specific random shocks capture cyclical variability of efficiency.
  - Common time effects capture impact of global shocks.
  - Simple illustrative specification: output per worker modeled as a function of capital per worker.
  - Heterogeneous and heteroskedastic efficiency model used for frontier estimation.

### Illustration for Argentina (results and magnitudes)
- As of 2016:
  - Given Argentina’s very low level of capital per worker, Argentina was "somewhat behind the production function" but "the distance was not out of line compared to other (more capital-intensive) economies."
  - Estimated efficiency for Argentina has worsened in the last decade, whereas the median of EMs and the full sample of countries remained broadly unchanged.
  - Compared to the average technical efficiency of Australia and New Zealand in 2016, Argentina was "more than 10 percent inefficient."
- Simulation parameters and sensitivity:
  - Output elasticity of capital, α, is set to 0.33 in simulations (noted as the standard value in the literature).
  - Alternative/implied values: 0.57 (implied from recent Penn World Tables values for Argentina) and about 0.61 (estimated in Appendix Table A6).

### Determinants of efficiency (empirical associations)
- Efficiency is strongly associated with product and labor market indicators.
- Results from full SFA (Appendix Table A6) indicate:
  - Regulations promoting competition (combined index of perceived regulatory quality from WB-WGI, 2016) lead to greater efficiency (lower inefficiency in SFA).
  - Less regulated labor markets (especially in terms of working time regulation) lead to greater efficiency.
- Quantified illustrative policy elasticity:
  - Using a conservative (lower-bound) estimate of the elasticity of technical efficiency with respect to the indicator of pro-competition regulations suggests that Argentina’s efficiency "could increase by over 10 percent if reforms were to close half the gap with Australia and New Zealand."
  - Timeliness caveat: "this is unlikely to happen quickly, and would likely require many years of sustained reform effort."
- Additional notes:
  - Measures of human capital were "not found robust" in SFA regressions.
  - Aggregate efficiency masks intersectoral differences; agricultural productivity growth has been "relatively upbeat."

### What is the potential impact of structural reforms on growth? (simulations and channels)
- Framework: combine effects of structural reforms on efficiency (TE), capital (K), and labor (L) using Eq. (1) and estimated elasticities of TE, K, and L with respect to structural variables (z).
- Four policy changes focused on (those with strongest impact in cross-country regressions):
  (i) Product market reforms that make regulation more competition- and private-sector-friendly, particularly reducing costs to start a business (affects TE & K).
  (ii) Labor market reforms easing regulations, particularly facilitating flexible forms of work arrangements (affects TE & L).
  (iii) Eliminating trade tariffs (affects K).
  (iv) Cutting top marginal income and payroll tax rate (affects L).
- Simulation design:
  - Structural policy variables for Argentina are assumed to slowly converge to the average value for Australia and New Zealand, with half the distance covered over a twenty-year period.
- Representative simulation outcomes:
  - Reducing the gap in the cost of starting a business would be associated with additional annual GDP growth of "0.15 percent only through the increase in capital intensity and about one percent through both the capital and efficiency channels."
  - Broader statement: "Illustrative simulations suggest that structural reforms could have substantial effects on long-term GDP growth."

### Policy implications and reform actions (summary)
- Core recommendation: "Policies and regulations which would promote investment and capital deepening should be at the core of the structural reform agenda."
- Specific reform directions highlighted in the source table and text:
  - Facilitate firm creation and entry by reducing high costs to start a business and simplifying regulatory procedures.
  - Open the economy to trade by lowering tariffs and promoting technology spillovers.
  - Reduce state involvement where it distorts competition: phase out price controls, rationalize subsidies, reduce regulatory protection of incumbents, and ensure regulatory neutrality.
  - Strengthen competition framework: pass Competition Law and strengthen anti-trust authority.
  - Reduce barriers to investment and improve investment climate (governance, red tape, infrastructure) to increase FDI and technology/management spillovers.
  - Labor market reforms: reduce termination costs and restrictions on temporary/flexible work arrangements; protect workers via unemployment insurance and training rather than strict employment rigidities.
  - Tax reforms: reduce tax wedge on labor and phase out distortionary taxes (e.g., financial transaction tax) to improve labor use and financial intermediation.
- Timing and persistence: effects require many years of sustained reform effort; examples cited include Australia where reforms unfolded over decades (structural reform process starting in the 1970s and accelerating in the 1980s–1990s).

*Source: IMF staff estimates.*

### Appendix 2. Stochastic Frontier Analysis

### Appendix 2. Stochastic Frontier Analysis

### SFA: Main elements and model specification
- Production representation (Equation (1a)):
  - Y_{i,t} = { f(X_{i,t}, t; β) ∙ exp(v_{i,t}) } ∙ θ_{i,t}(z_{i,t}; γ)
  - θ_{i,t} ∈ (0,1], θ_{i,t} = 1 indicates a country on the efficiency frontier.
  - v_{i,t} captures measurement errors and exogenous shocks; θ_{i,t} captures time-varying technical efficiency conditional on z_{i,t} with parameters γ.
- Log-linear Cobb-Douglas form with inefficiency u_{i,t} = −ln(θ_{i,t}) (Equations (2a) and (3a)):
  - Frontier: ln Y_{i,t} = β_0 + β_t t + β_L ln L_{i,t} + β_K ln K_{i,t} + v_{i,t} − u_{i,t}
  - Inefficiency model: u_{i,t} = z_0 + γ_z z_{i,t} + w_{i,t}
- Estimation approach:
  - Simultaneous maximum likelihood estimation of frontier parameters and technical efficiency (Battese and Coelli, 1995).
- Decomposition of TFP change (Kumbakhar and Lovell, 2000):
  - ∆TFP = ∆T + ∆TE + (ε−1)[ ε_L/ε ∆x_L + ε_K/ε ∆x_K ]
  - ∆T = β̂_t = dy/dt (technological change)
  - ∆TE = −du/dt (change in technical efficiency)
  - ε_L and ε_K are output elasticities with respect to labor and capital; ε = ε_L + ε_K (returns to scale; ε=1 implies constant returns to scale)

### Empirical findings — Regression summaries (selected coefficients and statistics preserved exactly as in source)
- Table A3. Use of Capital (Dependent variable: log of employment rate ln(K/Y))
  - Output volatility coefficients (columns (1)–(6)):
    - -0.63** (z = -1.98)
    - -1.23*** (z = -6.79)
    - -0.60* (z = -1.79)
    - -0.77** (z = -2.37)
    - -0.76** (z = -2.44)
    - -1.37*** (z = -3.25)
  - Cost of starting a business 1/ coefficients:
    - -0.01** (z = -2.15)
    - -0.01*** (z = -2.86)
    - -0.01** (z = -2.53)
    - -0.01** (z = -2.28)
    - -0.001* (z = -1.85)
  - Trade tariffs:
    - -0.47** (z = -2.51)
    - -0.57*** (z = -4.20)
    - -0.47*** (z = -2.78)
    - -0.69** (z = -2.10)
  - Private credit to GDP:
    - 0.03 (z = 1.33)
    - 0.05** (z = 2.05)
    - 0.04 (z = 1.48)
    - 0.10** (z = 2.56)
  - Availability of latest technologies:
    - 0.02** (z = 2.24)
    - 0.02* (z = 1.85)
  - Observations and sample:
    - Observations: 636, 592, 551, 564, 551, 551
    - No of countries: 59, 55, 58, 58, 58, 58
  - R-squared (within): 0.45, 0.45, 0.52, 0.45, 0.45, 0.24

- Table A4. Use of Labor (Dependent variable: log of employment rate ln(E/WP))
  - Output gap (columns (1)–(6)):
    - 0.01*** (z = 9.13)
    - 0.01*** (z = 8.68)
    - 0.01*** (z = 10.04)
    - 0.01*** (z = 9.79)
    - 0.01*** (z = 8.76)
    - 0.01*** (z = 9.00)
  - PMR: regulatory quality:
    - 0.05* (z = 1.82)
    - 0.07*** (z = 2.71)
    - 0.07*** (z = 3.04)
    - 0.05*** (z = 2.68)
    - 0.08*** (z = 4.52)
    - 0.08*** (z = 4.01)
  - Share of female in population:
    - -0.04** (z = -2.32)
    - -0.03* (z = -1.67)
  - Top marginal income & payroll tax rate (τ):
    - -0.001** (z = -2.04)
  - Tax rate (τ) * tax compliance:
    - -0.0002** (z = -2.14)
  - Observations and sample:
    - Observations: 912, 864, 864, 1,140, 602, 612
    - No of countries: 57, 54, 54, 57, 55, 57
  - R-squared (within): 0.33, 0.36, 0.35, x, 0.41, 0.39

### Stochastic Frontier Illustration — parameter estimates and inefficiency correlates
- Table A5. Stochastic Frontier Analysis: A Simple Illustration (Dependent variable: log real GDP-to-labor ratio; sample 1980–2016)
  - Frontier estimates:
    - Log capital-labor ratio: 0.54*** (z = 54.75)
    - Time trend: 0.005*** (z = 10.28)
    - Constant: 1.20*** (z = 24.35)
  - Mean inefficiency:
    - AE dummy: -1.46*** (z = -6.32)
  - Variance of inefficiency:
    - EM dummy: 1.49*** (z = 6.70)
    - Constant: -2.65*** (z = -10.78)
  - Log-likelihood: 104
  - Observations: 2,082
  - Number of countries: 59

- Table A6. Stochastic Frontier Analysis with Conditional Inefficiency Effects (dependent variable: log real GDP; multiple samples and specifications)
  - Frontier: labor and capital coefficients (selected reported values across specifications; z-statistics in parentheses)
    - Log labor: 0.31*** (24.22), 0.33*** (46.58), 0.38*** (30.30), 0.39*** (32.60), 0.38*** (28.17), 0.42*** (22.17), 0.39*** (23.45), 0.42*** (30.38), 0.39*** (21.39), 0.25*** (14.80), 0.25*** (13.15), 0.30*** (30.10)
    - Log capital: 0.65*** (50.40), 0.65*** (85.30), 0.60*** (48.29), 0.60*** (51.09), 0.61*** (45.71), 0.57*** (29.94), 0.59*** (35.67), 0.57*** (40.59), 0.61*** (36.54), 0.50*** (26.45)
    - Time trend: -0.004*** (-3.65), 0.002*** (2.54), 0.003*** (3.02), 0.003*** (3.15), 0.004*** (3.85), 0.005*** (4.14), 0.004*** (4.19), 0.01*** (7.68), 0.003*** (9.92), 0.01*** (7.77)
  - Frontier supplements (selected):
    - Log private capital: 0.45*** (27.86), 0.46*** (26.77)
    - Log public capital: 0.14*** (9.46), 0.10*** (9.37)
    - Log energy use: 0.13*** (9.63), 0.22*** (11.64), 0.12*** (9.61)
  - Mean inefficiency (conditional effects; selected coefficients):
    - PMR: regulatory quality: -0.16*** (-12.99), -0.23*** (-11.29), -0.24*** (-11.30), -0.24*** (-9.94), -0.16*** (-7.54), -0.08*** (-2.61), -0.07** (-1.99), -0.21*** (-5.86), -0.12*** (-7.82), -0.14*** (-5.27), -0.12*** (-7.90)
    - LMR: CBR_total: 0.31*** (7.55), 0.22*** (5.34), 0.18*** (4.08)
    - LMR: CBR_working time: 0.44*** (6.41), 0.50*** (6.01), 0.44*** (5.78), 0.37*** (6.94), 0.43*** (4.77), 0.66*** (13.00), 0.53*** (11.49), 0.76*** (6.45)
    - Log change in terms of trade: -0.54*** (-3.87), -0.53*** (-3.48), -0.63*** (-3.43), -0.61*** (-3.31), -0.88*** (-5.04), -0.91*** (-4.67), -0.66*** (-3.43)
    - Output gap: -0.02*** (-4.19), -0.02*** (-5.63), -0.02*** (-4.62)
    - Cost of starting a business: 0.02*** (6.49)
    - WEF_government effectiveness: -0.15*** (-4.17), -0.20*** (-4.42), 0.00 (0.07)
    - EM dummy: 0.12*** (3.70), 0.06** (2.04), 0.08* (1.77)
    - PMR: WEF_market dominance: -0.05** (-2.33)
    - Mean inefficiency constants: 0.37*** (12.11), 0.19*** (4.03), 0.16*** (2.85), 0.18*** (3.33), 0.21*** (3.34), 0.39*** (14.30), 0.32*** (9.63)
  - Variance of inefficiency (selected):
    - EM dummy: 1.85*** (16.47), 2.35*** (7.19), 2.30*** (7.10), 2.22*** (7.51), 3.22*** (4.04), 2.15*** (6.24), 1.74*** (15.93), 1.54*** (10.00)
    - Log change in terms of trade: -4.64*** (-4.27), -2.91*** (-3.08), -7.98*** (-4.82), -2.31** (-2.33), -6.32*** (-4.78), -6.97*** (-4.44), -6.82*** (-4.41)
    - Political stability: -0.84*** (-7.70), -0.96*** (-7.73)
    - Variance of inefficiency constants: -4.15*** (-50.62), -4.86*** (-14.35), -4.77*** (-14.10), -4.77*** (-15.39), -5.79*** (-7.27), -4.88*** (-13.66), -2.90*** (-27.98), -3.22*** (-24.89), -4.23*** (-55.42), -3.15*** (-17.88), -4.23*** (-37.97)
  - Log-likelihoods and sample sizes (selected columns):
    - Log-likelihood: 1,629; 278; 282; 296; 318; 182; 285; 275; 359; 318; 199; 416
    - Observations: 2,082; 1,040; 1,038; 1,036; 972; 437; 820; 866; 866; 1,013; 451; 1,013
    - Number of countries: 59; 57; 57; 57; 55; 55; 55; 75; 75; 65; 65; 65

### Interpretation of empirical patterns (as reported)
- Frontier production function:
  - Labor and capital coefficients are consistently positive and statistically significant across specifications (coefficients often around 0.3 for labor and 0.5–0.65 for capital).
  - Time trend coefficients are small in magnitude and can be positive or negative depending on the sample/specification (reported values include -0.004*** and positive values such as 0.005*** and 0.01***).
- Inefficiency correlates:
  - Better regulatory quality (PMR: regulatory quality) is associated with lower mean inefficiency (negative and significant coefficients).
  - Certain labor market regulation measures (LMR: CBR_total, CBR_working time) are associated with higher mean inefficiency (positive and significant coefficients).
  - Changes in terms of trade and output gap enter both mean and variance of inefficiency, often with negative coefficients on mean inefficiency and large negative coefficients on variance of inefficiency.
  - EM dummy tends to increase the variance of inefficiency (positive and significant).
  - Political stability is associated with lower variance of inefficiency (negative and significant coefficients).

*Appendix 2. Stochastic Frontier Analysis — IMF Working Paper content as provided*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp18183.pdf_