## Institutions and Growth: a GMM/IV Panel VAR Approach

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### Introduction
- Research question: Do exogenous shocks to institutional quality cause changes in GDP per capita?
- Approach: macroeconometric Panel SVAR estimated with Arellano-Bond's GMM/IV for short panels (N > T), exploiting cross-sectional variation while controlling for time-invariant country characteristics.
- Sample and data window:
  - Panel of 119 countries and 12 years (2000–2012), with final estimation sample of 10 years due to first-differencing and lagged instruments, yielding 1,190 observations.
- Proxy for institutions (baseline): Economic Freedom of the World Index (EFW).
- Identification motivation: institutional quality is assumed to have no contemporaneous effect on GDP per capita, while GDP per capita may contemporaneously affect institutional quality.

### Methodology
- Estimated model:
  - Bi-dimensional Panel SVAR with log GDP per capita (constant 2005 U.S. dollars) and a proxy for institutional quality as endogenous variables.
- Estimation technique:
  - Arellano-Bond GMM/IV applied to first-differenced equations with lagged first differences as instruments to obtain unbiased fixed-effects average coefficients for short panels.
- Identification and recovery:
  - Recover variance-covariance matrix and derive contemporaneous coefficient matrix via triangular decomposition under assumption that structural residuals are uncorrelated.
  - One contemporaneous restriction imposed: institutional quality does not contemporaneously affect GDP per capita.
  - Impulse responses recovered following Lutkepöhl (2007) methodology, truncating impulse horizon to a finite number of periods and calculating structural shocks by multiplying reduced-form responses by the contemporaneous matrix.
- Inference:
  - Standard errors for IRFs calculated nonparametrically via a re-sampling simulation with 1,000 repetitions.

### Data
- Income variable: log of GDP per capita in constant 2005 U.S. dollars (World Bank WDI).
- Institutions proxy (baseline): Fraser Institute's Economic Freedom of the World Index (EFW), composed of five subcomponents: legal system reliability, monetary stability, burden of regulation, size of government, and freedom to trade internationally.
- Rationale for EFW:
  - Significantly correlated with AJR's risk of appropriation index (t-stat > 7) and correlated with other proxies (Economist Intelligence Unit's Democracy Index, Transparency International's CPI).
  - First principal component of EFW, Democracy Index, CPI, and AJR index explains about 70% of total variance.
  - EFW provides continuous annual series between 2000 and 2012 for a wide range of countries.
- Descriptive statistics:
  - Distribution of annual percent changes in the institutions proxy: Mean: 0.4% ; Median: 0.2% ; Std. dev: 3.5%.
  - Example cross-country differences cited: institutional gap between Nicaragua and Costa Rica ≈ 10%; Burundi ≈ 30% below Rwanda.
  - Standard-deviation of reduced-form (structural) shocks: 4.7% (7.5%) for GDP per capita; 4.2% (6.8%) for the institutions proxy.

### Results — Full sample and groups
- Full-sample (N = 119, T = 10) impulse responses:
  - Main finding: on average, a 1 percent temporary shock in institutional quality (EFW) leads to a peak 1.7 percent increase in GDP per capita after six years.
  - The positive effect remains statistically significant up to 10 years after the shock, with uncertainty increasing after year four (wider confidence bands).
  - Panel SVAR is stable: shocks are temporary and series return to deterministic trends in the long run.
- Group heterogeneity — Advanced economies (N = 25) vs Developing countries (N = 94):
  - Advanced economies:
    - Peak response of GDP per capita to a 1 percent shock in institutional quality: 0.35 percent, occurring two years after the shock.
    - Institutional quality returns quickly to trend after shocks on GDP per capita and institutions.
  - Developing countries:
    - Peak statistically significant response of GDP per capita to a 1 percent shock in institutional quality: 2.6 percent.
    - Standard errors substantially larger than in advanced economies, reflecting greater heterogeneity.
- Interpretation:
  - Results are consistent with the institutions hypothesis: exogenous improvements in institutional quality raise income per capita.
  - Different dynamics across country groups suggest diminishing returns to institutional quality improvements.

### Robustness
- Alternative institutions proxy: Transparency International's Corruption Perceptions Index (CPI).
  - Using CPI in place of EFW yields:
    - Peak response of GDP per capita to a 1 percent shock in institutional quality: 1.3 percent.
    - Peak response of institutional quality to a 1 percent shock in GDP per capita: 0.35 percent.
  - Both CPI-based responses fall within the 90 percent confidence interval of the baseline (EFW) model.
- IRF inference detail:
  - Nonparametric re-sampling simulation with 1,000 repetitions used to compute confidence intervals.

### Developing countries — Impulse response specifics (N = 94, T = 10)
- Reported impulse responses (horizon: Years after shock, 0–10):
  - Response of GDP per capita to a 1% shock in institutional quality.
  - Response of institutional quality to a 1% shock in institutional quality.
  - Response of GDP per capita to a 1% shock in GDP per capita.
  - Response of institutional quality to a 1% shock in GDP per capita.
- Confidence information:
  - 90% confidence interval shown for impulse responses where indicated.
- Key interpretation points for developing countries:
  - Exogenous improvements in institutional quality have positive and statistically significant impact on GDP per capita.
  - Model controls for all time-invariant individual characteristics and is claimed not to suffer from endogeneity problems.
  - Different proxies for institutional quality are significantly correlated and yield consistent qualitative responses.
  - Evidence provided for bi-directional causality between institutions and growth.
  - Heterogeneous responses support the view of diminishing returns: countries with higher GDP per capita exhibit smaller percentage payoffs from further institutional improvements, while developing countries have higher payoffs.

### Robustness checks: Peak responses (figures and scales)
- Peak responses reported with 90% confidence intervals based on re-sampling simulation with 1,000 repetitions for:
  - Peak response of GDP per capita to a 1% shock in institutional quality using:
    - Corruption Perception Index
    - Economic Freedom of the World Index
  - Peak response of institutional quality to a 1% shock in GDP per capita using:
    - Corruption Perception Index
    - Economic Freedom of the World Index
- Example numeric axes preserved from source:
  - GDP per capita peak response scale: 0, 0.5, 1, 1.5, 2, 2.5, 3.
  - Institutional quality peak response scale: 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7.
  - Horizon scales shown as integers 0–10 where relevant.

### Appendix — Resampling algorithm (steps)
- Step 1:
  - Draw a random k-dimensional vector, where all elements follow a discrete uniform distribution.
  - The distribution is discrete uniform over {1,…,N}, where N is the number of cross-sections in the sample.
  - Set k to 10 percent of the sample size plus one cross-section (k = 10 percent of sample size + 1) and truncate the result by discarding any decimal points.
- Step 2:
  - Exclude k cross-sections from the original sample, thus restricting the sample to N − k observations.
- Step 3:
  - Re-estimate the model with the restricted sample, collect the matrices of responses, extract individual vectors for each IRF and organize the simulated IRFs into a separate matrix for each m endogenous variable.
- Step 4:
  - After repeating the procedure n times the result will be two distribution matrices D, where m is the number of response variables, h is the response horizon, and n is the number of repetitions of the simulation exercise.
- Step 5:
  - From D take the square root of the second moment of each row to build a vector of standard errors.

### Key numerical findings and specifications (exact values preserved)
- Sample: N = 119 countries; initial panel span 12 years (2000–2012); estimation uses T = 10 years after differencing; total observations used: 1,190.
- Baseline impulse-response result: 1 percent shock in institutional quality → peak 1.7 percent increase in GDP per capita after six years.
- Advanced-economy peak: 0.35 percent after two years (N = 25).
- Developing-country peak: 2.6 percent (N = 94).
- Distribution of annual percent changes in institutions proxy: Mean: 0.4% ; Median: 0.2% ; Std. dev: 3.5% (NT = 1,450 in figure).
- Standard-deviation of reduced-form (structural) shocks:
  - GDP per capita: reduced-form 4.7% ; structural 7.5%.
  - Institutions proxy: reduced-form 4.2% ; structural 6.8%.
- IRF inference: nonparametric re-sampling simulation with 1,000 repetitions.
- Robustness (CPI): GDP per capita peak response to 1% institutional shock = 1.3 percent; institutional response to 1% GDP shock = 0.35 percent.

*Prepared by Carlos Góes (IMF Working Paper WP/15/174).*

### Section 1

### Institutions and Growth: a GMM/IV Panel VAR Approach

### Introduction
- Research question: Do exogenous shocks to institutional quality cause changes in GDP per capita?
- Approach: macroeconometric Panel SVAR estimated with Arellano-Bond's GMM/IV for short panels (N > T), exploiting cross-sectional variation while controlling for time-invariant country characteristics.
- Sample and data window:
  - Panel of 119 countries and 12 years (2000–2012), with final estimation sample of 10 years due to first-differencing and lagged instruments, yielding 1,190 observations.
- Proxy for institutions (baseline): Economic Freedom of the World Index (EFW).
- Motivation for identification: exogenize GDP per capita contemporaneously (institutional quality has no contemporaneous effect on GDP per capita, while GDP per capita may contemporaneously affect institutional quality).

### Methodology
- Estimated model: bi-dimensional Panel SVAR with log GDP per capita (constant 2005 U.S. dollars) and a proxy for institutional quality as endogenous variables.
- Estimation technique: Arellano-Bond GMM/IV applied to first-differenced equations with lagged first differences as instruments to obtain unbiased fixed-effects average coefficients for short panels.
- Identification and recovery:
  - Recover variance-covariance matrix and derive contemporaneous coefficient matrix via triangular decomposition under assumption that structural residuals are uncorrelated.
  - One contemporaneous restriction imposed: institutional quality does not contemporaneously affect GDP per capita.
  - Impulse responses recovered following Lutkepöhl (2007) methodology, truncating impulse horizon to a finite number of periods and calculating structural shocks by multiplying reduced-form responses by the contemporaneous matrix.
- Inference: standard errors for IRFs calculated nonparametrically via a re-sampling simulation with 1,000 repetitions.

### Data
- Income variable: log of GDP per capita in constant 2005 U.S. dollars (World Bank WDI).
- Institutions proxy (baseline): Fraser Institute's Economic Freedom of the World Index (EFW), composed of five subcomponents: legal system reliability, monetary stability, burden of regulation, size of government, and freedom to trade internationally.
- Rationale for EFW:
  - Significantly correlated with AJR's risk of appropriation index (t-stat > 7) and correlated with other proxies (Economist Intelligence Unit's Democracy Index, Transparency International's CPI).
  - First principal component of EFW, Democracy Index, CPI, and AJR index explains about 70% of total variance.
  - EFW provides continuous annual series between 2000 and 2012 for a wide range of countries.
- Descriptive statistics:
  - Distribution of annual percent changes in the institutions proxy: Mean: 0.4% ; Median: 0.2% ; Std. dev: 3.5%.
  - Example cross-country differences cited: institutional gap between Nicaragua and Costa Rica ≈ 10%; Burundi ≈ 30% below Rwanda.
  - Standard-deviation of reduced-form (structural) shocks: 4.7% (7.5%) for GDP per capita; 4.2% (6.8%) for the institutions proxy.

### Results
- Full-sample (N = 119, T = 10) impulse responses:
  - Main finding: on average, a 1 percent temporary shock in institutional quality (EFW) leads to a peak 1.7 percent increase in GDP per capita after six years.
  - The positive effect remains statistically significant up to 10 years after the shock, with uncertainty increasing after year four (wider confidence bands).
  - Panel SVAR is stable: shocks are temporary and series return to deterministic trends in the long run.
- Group heterogeneity — Advanced economies (N = 25) vs Developing countries (N = 94):
  - Advanced economies:
    - Peak response of GDP per capita to a 1 percent shock in institutional quality: 0.35 percent, occurring two years after the shock.
    - Institutional quality returns quickly to trend after shocks on GDP per capita and institutions.
  - Developing countries:
    - Peak statistically significant response of GDP per capita to a 1 percent shock in institutional quality: 2.6 percent.
    - Standard errors substantially larger than in advanced economies, reflecting greater heterogeneity.
- Interpretation:
  - Results are consistent with the institutions hypothesis: exogenous improvements in institutional quality raise income per capita.
  - Different dynamics across country groups suggest diminishing returns to institutional quality improvements.

### Robustness
- Alternative institutions proxy: Transparency International's Corruption Perceptions Index (CPI).
  - Using CPI in place of EFW yields:
    - Peak response of GDP per capita to a 1 percent shock in institutional quality: 1.3 percent (slightly smaller than baseline).
    - Peak response of institutional quality to a 1 percent shock in GDP per capita: 0.35 percent (slightly larger than baseline).
  - Both CPI-based responses fall within the 90 percent confidence interval of the baseline (EFW) model.

### Key numerical findings and specifications (exact values preserved)
- Sample: N = 119 countries; initial panel span 12 years (2000–2012); estimation uses T = 10 years after differencing; total observations used: 1,190.
- Baseline impulse-response result: 1 percent shock in institutional quality → peak 1.7 percent increase in GDP per capita after six years.
- Advanced-economy peak: 0.35 percent after two years (N = 25).
- Developing-country peak: 2.6 percent (N = 94).
- Distribution of annual percent changes in institutions proxy: Mean: 0.4% ; Median: 0.2% ; Std. dev: 3.5% (NT = 1,450 in figure).
- Standard-deviation of reduced-form (structural) shocks:
  - GDP per capita: reduced-form 4.7% ; structural 7.5%.
  - Institutions proxy: reduced-form 4.2% ; structural 6.8%.
- IRF inference: nonparametric re-sampling simulation with 1,000 repetitions.
- Robustness (CPI): GDP per capita peak response to 1% institutional shock = 1.3 percent; institutional response to 1% GDP shock = 0.35 percent.

*Prepared by Carlos Góes (IMF Working Paper WP/15/174).*

### Section 2

### _wp15174 - Section 2

### Impulse response results (Developing Countries)
- Results presented via impulse response functions calculated from GMM/IV Panel VAR (N = 94, T = 10).
- Standard errors from re-sampling simulation with 1,000 repetitions.
- Reported impulse responses:
  - Response of GDP per capita to a 1% shock in institutional quality (horizon: Years after shock, 0–10).
  - Response of institutional quality to a 1% shock in institutional quality (horizon: Years after shock, 0–10).
  - Response of GDP per capita to a 1% shock in GDP per capita (horizon: Years after shock, 0–10).
  - Response of institutional quality to a 1% shock in GDP per capita (horizon: Years after shock, 0–10).
- Confidence information:
  - 90% confidence interval shown for impulse responses where indicated.

### Key findings and interpretation
- Exogenous improvements in institutional quality have positive and statistically significant impact on GDP per capita.
- The model:
  - Controls for all time-invariant individual characteristics typically used as controls in the economic development literature.
  - Does not suffer from endogeneity problems (as claimed in the text).
  - Is robust to using a different proxy for institutions.
- Proxy relationships:
  - Different proxies for institutional quality tend to be significantly correlated.
  - Consistency in the direction of responses using different proxies suggests the qualitative relationship between institutions and growth is similar across proxies.
  - The paper emphasizes that the qualitative result is more important than the magnitude of the responses themselves.
- Evidence for causality:
  - Provides evidence for bi-directional causality between institutions and growth.
- Heterogeneity and diminishing returns:
  - Heterogeneous responses between advanced and developed economies suggest diminishing returns to institutional quality improvements.
  - Countries with higher GDP per capita tend to have higher institutional quality but exhibit smaller payoffs (in percentage increase in GDP per capita) from further institutional improvements.
  - By symmetry, developing countries have higher payoffs when improving institutional quality.

### Robustness checks: Peak responses
- Figures report peak responses and 90% confidence intervals based on re-sampling simulation with 1,000 repetitions for:
  - Peak response of GDP per capita to a 1% shock in institutional quality using:
    - Corruption Perception Index
    - Economic Freedom of the World Index
  - Peak response of institutional quality to a 1% shock in GDP per capita using:
    - Corruption Perception Index
    - Economic Freedom of the World Index
- Reported numeric axes in figures (examples preserved from source):
  - GDP per capita peak response scale: 0, 0.5, 1, 1.5, 2, 2.5, 3.
  - Institutional quality peak response scale: 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7.
  - Horizon scales shown as integers 0–10 where relevant.

### Appendix: Resampling algorithm (steps)
- Step 1:
  - Draw a random k-dimensional vector, where all elements follow a discrete uniform distribution.
  - The distribution is discrete uniform over {1,…,N}, where N is the number of cross-sections in the sample.
  - Set k to 10 percent of the sample size plus one cross-section (k = 10 percent of sample size + 1) and truncate the result by discarding any decimal points.
- Step 2:
  - Exclude k cross-sections from the original sample, thus restricting the sample to N − k observations.
- Step 3:
  - Re-estimate the model with the restricted sample, collect the matrices of responses, extract individual vectors for each IRF and organize the simulated IRFs into a separate matrix for each m endogenous variable.
- Step 4:
  - After repeating the procedure n times the result will be two distribution matrices D, where m is the number of response variables, h is the response horizon, and n is the number of repetitions of the simulation exercise.
- Step 5:
  - From D take the square root of the second moment of each row to build a vector of standard errors.

### References (as listed)
- Acemoglu, Daron, Simon Johnson, and James A. Robinson, 2001, “The Colonial Origins of Comparative Development: An Empirical Investigation,” The American Economic Review, Vol. 91 No. 5.
- Arellano, Manuel and Stephen Bond, 1991, “Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations,” The Review of Economic Studies, Vol. 58 No. 2.
- Canova, Fabio and Matteo Ciccarelli, 2013, “Panel Vector Autoregression: A Survey,” Working Paper 1507, European Central Bank.
- Eldridge, Madeline, 2013, “The Smithian Roots of the Institutions Hypothesis,” George Mason University, Mimeo.
- Gwartney, James, Robert Lawson, and Joshua Hall, 2014, “Economic Freedom of the World: 2014 — Annual Report,” (Vancouver: Fraser Institute).
- Lutkepöhl, Helmut, 2007, “New Introduction to Multiple Time Series Analysis,”( Berlin: Springer).
- Nickel, Stephen, 1981, “Biases in Dynamic Models with Fixed Effects,” Econometrica, Vol. 49. No. 6, pp. 1417–26.
- Sachs, Jeffrey, 2003, “Institutions Don’t Rule: Direct Effects of Geography on Per Capita Income,” NBER Working Paper No. 9490 (Cambridge, Massachusetts: National Bureau of Economic Research).

*Content based on _wp15174 - Section 2*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15174.pdf_