## 1. Monthly Frequency of Price Changes and Per Capita GDP Relative to the U.S.

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---

### Research question and empirical strategy
- Test hypothesis: monetary policy frameworks are irrelevant for propagation of external shocks in Low-Income Countries (LICs) — i.e., test money neutrality in LICs.
- Two empirical strategies:
  - Panel analysis (reduced-form approach à la Jorda (2005)) on a cross-country panel of 79 LICs over 1990–2015.
  - Event study (difference-in-difference) for 28 Sub-Saharan African (SSA) LICs around the surprise devaluation of the CFA franc in early 1994.
- External shocks analyzed (constructed as forecast errors using World Economic Outlook forecasts):
  - Unanticipated changes in world GDP (“world GDP shock”).
  - Shifts in the terms of trade.
  - Fluctuations in the price of oil.
- Monetary policy framework indicator:
  - Binary annual indicator based on IMF AREAER classification.
  - Two groups: (a) frameworks that rely primarily on the exchange rate as the nominal anchor; (b) frameworks that use money- or inflation-targeting to foster price stability.
- Empirical implementation:
  - Regress output growth at various horizons on the interaction between the shock and the monetary policy framework dummy.
  - Controls include wars, external demand (when testing terms of trade and oil shocks), and country characteristics to address endogenous regime choice.
  - Robustness checks, alternative classifications, and subsamples (including the poorest LICs) are used.

### Sample facts and classifications
- Sample coverage:
  - 79 LICs over 1990–2015 (composition of the LIC group changes over time).
  - Panel composition over time: 79 LICs in 1990; 60 LICs in 2015.
- AREAER-based classification:
  - About one-third of observations: framework focused on targeting money or inflation.
  - About two-thirds of observations: framework focused on exchange rate stability.
- Event study sample:
  - 28 SSA LICs: 10 LICs in the CFA zone (devalued in early 1994) and 18 SSA LICs in a control group (did not devalue).

### Main empirical findings
- Overarching result:
  - Overwhelming rejection of the money neutrality hypothesis for LICs based on both empirical strategies.
- Effects by framework:
  - Countries with monetary policy frameworks that target the exchange rate as the nominal anchor exhibit statistically larger real domestic output growth responses to surprises in world GDP, terms of trade shifts, and oil price fluctuations compared with money- and inflation-targeting countries.
- Event study (1994 CFA franc devaluation):
  - Real GDP growth rates in the CFA zone were statistically higher than those in the control group during the two-year period after the 1994 devaluation.
- Robustness:
  - Results hold across various specifications, control variables, and subsamples, including the poorest LICs.
- Micro evidence on price adjustment:
  - Monthly frequency of price changes tends to be higher in countries with lower per capita income.
  - New Keynesian models calibrated for LICs have often assumed a low frequency of price changes (25 percent), which may be inappropriate given observed high frequency of price adjustment in many LICs.
- Interpretation and caveats:
  - Findings indicate money non-neutrality in LICs without imposing a particular structure of nominal rigidities.
  - The empirical reduced-form approach cannot identify structural sources of non-neutrality.
  - Potential structural explanations include informational frictions (incomplete knowledge about the economy; misperceptions of central bank goals/operations) rather than classic staggered price-setting.

### External demand (world GDP) shocks — identification, intuition, and primary results
- Identification and normalization:
  - External demand shock measure: difference between actual and WEO forecast of country-specific world GDP growth (forecast at t-1 for realization at t); interpreted as the unanticipated shock to world GDP growth (one-year and two-year ahead forecast error realized at year t).
  - Forecast errors of world GDP vary from -3.6 to +1.9 percent; the standard deviation is 1.1 percent.
  - Empirical test: effect of a 1 percent shock to world GDP on domestic output growth, across monetary policy frameworks.
- Economic intuition:
  - Positive unanticipated external demand shock raises aggregate demand, money demand, and prices; under fixed nominal exchange rates central bank offsets by lowering interest rates to maintain parity, amplifying aggregate demand; under flexible exchange rates nominal exchange rate adjusts instead and may dampen aggregate demand change.
- Key panel regression findings (79 countries, 1,578 observations):
  - In response to an unanticipated positive one-percent shock to world GDP:
    - Positive effect on domestic output growth (by about 0.5 percentage points) only in frameworks maintaining price stability through fixed exchange rates.
    - Effect is highly statistically significant (mostly at 1 percent level) in the year when the shock occurs (horizon 0), and also in the subsequent year.
    - Statistically significant difference between effects in exchange-rate-targeting frameworks versus monetary or inflation targeting frameworks.
- Poorest LICs subsample:
  - Subsample definitions: countries below median GDP per capita in 1990, using two medians: US$800 (cross-sample median) and US$540.7 (cross-country median for 1990). Country must remain in category for at least a year.
  - About sixty percent of sample are in the first subsample (below US$800).
  - For LICs below median, impact in rigid exchange-rate frameworks is stronger than entire LIC sample: up to sixty percent stronger in horizon 1 and the difference between frameworks almost doubles in horizon 0.
- Robustness and sensitivity:
  - Results robust to different outlier treatments and inclusion of controls one at a time: trade openness, capital openness (inflows+outflows/GDP; Ito's index), financial depth (bank assets/GDP; credit to private sector/GDP), and fiscal policy (overall central government balance as percent of GDP).
  - Introducing controls can weaken some results: impact at horizon 0 can become insignificant while remaining significant at horizon 1; financial depth lowers the shock impact at horizon 1.
  - Broader conclusion: evidence that even in inflation- or monetary-targeting frameworks prices adjust relatively slowly, allowing the exchange rate to act as a shock absorber.

### Terms-of-trade shocks
- Identification and normalization:
  - Shock defined as difference between actual country terms of trade and its forecast at horizon k.
  - Standard normalization: 10 percent unanticipated change (forecast-error SD of terms of trade about 15 percent).
- Key empirical findings (Table 3; 76 countries, 1,484 observations / 1,504 observations reported):
  - In response to an unanticipated ten-percent improvement in terms of trade:
    - Positive effect on domestic output growth (about 0.20 percentage points) mainly in frameworks maintaining price stability through rigid exchange rates.
    - Statistically significant at 5 percent in the year of the shock (horizon 0) and at 10 percent in the subsequent year.
    - Highly statistically significant difference between rigid exchange-rate frameworks and monetary/inflation targeting (1 percent at 1-year horizon).
- Robustness and interactions:
  - Eliminating outliers and adding controls generally strengthens precision and significance.
  - Interaction with fiscal policy: inclusion of fiscal policy can prevent isolating the monetary policy framework’s role for terms-of-trade shocks in some specifications.

### Oil price shocks
- Identification and normalization:
  - Shock defined as unanticipated difference between forecasted and actual oil price at one-year horizon.
  - Forecast error of oil price in sample varies between -60 and +40 percent; median forecast error is 12 percent.
- Key empirical findings:
  - For oil-importing LICs: impact of an unanticipated ten percent oil price shock does not differ across monetary policy frameworks (results not reported but available on request).
  - For big oil exporters (crude oil production exceeding 5% of nominal GDP in at least one year in sample):
    - In response to an unanticipated ten-percent increase in global oil prices:
      - Positive effect on domestic output growth (by about 0.45 percentage points in the year of the shock and higher in the subsequent year) only in frameworks maintaining price stability through rigid exchange rates.
      - Statistically significant effects at 1 percent level, especially one year after the shock.
      - Statistically significant difference between rigid exchange-rate frameworks and monetary/inflation targeting frameworks at 1 percent in the year after the shock.
    - Sample of big oil exporters: Angola, Cameroon, Chad, Rep. of Congo, Ghana, Mauritania, Nigeria, Sudan, Yemen (9 countries, 183 observations).
  - Robustness: effects remain at 1 and 5 percent significance when controlling for outliers and other controls, especially in year following shock.
- Policy implication highlighted:
  - Big oil exporters using a fixed exchange rate as nominal anchor experience very volatile domestic output growth — large gains when oil prices increase and large losses when they plunge.
  - Policy advice: good demand management, consistent policy mix, adjustment strategies, strong built-in automatic stabilizers and safety nets, and nominal wage flexibility are needed if LICs choose a rigid exchange-rate framework to achieve price stability.

### Event study: 1994 CFA franc devaluation (difference-in-differences)
- Background:
  - CFA zone: 14 countries in two currency unions (WAEMU and CEMAC); CFA fixed to French franc since 1980 and to euro since 1999.
  - By late 1993 the CFA overvaluation averaged 30 percent; devaluation of the CFA franc by 50 percent occurred on January 1, 1994.
- Method and samples:
  - Difference-in-differences comparing 10 CFA zone African LICs with 18 control-group African LICs; measure difference in average real GDP growth between 1994–1995 and 1992–1993 (two-year windows); results demeaned over 1990–2015 sample.
  - CFA sample (10 countries): Benin, Burkina Faso, Cameroon, CAR, Chad, Cote d’Ivoire, Mali, Niger, Senegal, Togo.
  - Control group (18 countries) listed in Table 6 (examples: Burundi, Cabo Verde, Ghana, Nigeria, Tanzania, Uganda, Zambia).
  - Baseline regression: dependent = change in two-year real GDP growth rate (1994-1995 vs 1992-1993), demeaned; independent: constant, CFA zone dummy, battle-related deaths; regressions estimated by Panel Least Squares.
- Main event-study results (two-year window):
  - Real GDP growth on average improved by 5 percent after the devaluation in the CFA zone, while control group growth remained relatively unchanged.
  - Statistical significance and robustness:
    - Result is statistically significant and robust at 5 percent (Table 6).
    - Estimated impact on real growth of the devaluation in CFA zone is between 2¾ and 5½ percent once different outliers are excluded.
    - The average growth in CFA zone was about 4 percent after devaluation; difference between before and after 1994 two-year windows was about 5 percent and statistically significant (at 10 percent in one specification).
  - Example regression coefficients (sensitivity rows from Table 6):
    - Baseline: 5.21** (standard deviation 2.06) for CFA; control group -0.23 (1.23); p-value 0.07.
    - Excluding CFA outlier with very high 1994 growth (Togo): CFA 2.81** (1.13); control -0.23 (1.23); p-value 0.06.
    - Other sensitivity exclusions report CFA effects of 5.32**, 5.52** with corresponding SDs reported.
  - Distributional evidence: Figure 3 shows similar pre-devaluation distributions across groups but markedly different post-1994 distributions (difference = 4.98 reported in figure annotation).

### Conclusions, modeling implications, and policy recommendations
- Overarching empirical conclusion:
  - Strong and robust evidence that the effect on domestic output growth of unanticipated external shocks depends on the monetary policy framework used in LICs.
  - LICs using exchange-rate targeting to achieve price stability exhibit statistically larger responses in real domestic output growth to external shocks than LICs using inflation or monetary targeting.
  - Results hold across specifications, controls, subsamples, and for the poorest LICs, indicating presence of nominal rigidities and informational frictions even in low-income settings.
- Modeling implications:
  - Findings reject monetary neutrality in LICs and indicate that monetary policy frameworks matter empirically.
  - The source and size of nominal rigidities need further study to assess shock impacts and appropriate policy responses as LICs modernize monetary frameworks.
  - Model calibrations for LICs should be reassessed given evidence of high frequency of price adjustment and heterogeneity across LICs; New Keynesian assumptions of low frequency of price changes (25 percent) may be inappropriate for many LICs.
- Policy recommendations and considerations:
  - The choice of nominal anchor and the design of the monetary policy framework influence shock transmission; frameworks matter for insulation from external shocks.
  - Ongoing reforms in LICs to strengthen monetary policy frameworks while allowing greater exchange rate flexibility are likely to matter for macroeconomic management.
  - Specific policy measures emphasized:
    - Good demand management and consistent policy mix.
    - Adjustment strategies and strong built-in automatic stabilizers and safety nets for commodity-dependent LICs.
    - Liquidity management and sterilization tools for countries with fixed exchange rates (to dampen transmission from external shocks).
    - Nominal wage flexibility to restore competitiveness in commodity-rich LICs using rigid exchange-rate frameworks.
  - Research priorities:
    - Clarify sources and magnitudes of nominal rigidities and informational frictions in LICs to better inform model choice and policy design.
    - Reassess model calibration for LICs given evidence of high frequency of price adjustment and heterogeneity across LICs.

*Source: wpiea2020139-print-pdf — 1. Monthly Frequency of Price Changes and Per Capita GDP Relative to the U.S.; Appendix V; Appendix I—Estimation.*

### 1. Monthly Frequency of Price Changes and Per Capita GDP Relative to the U.S.

### 1. Monthly Frequency of Price Changes and Per Capita GDP Relative to the U.S.

### Research question and empirical strategy
- Test the hypothesis that monetary policy frameworks are irrelevant for propagation of external shocks in Low-Income Countries (LICs) — i.e., test money neutrality in LICs.
- Two complementary empirical strategies:
  - Panel analysis (reduced-form approach à la Jorda (2005)) on a cross-country panel of 79 LICs over the period 1990–2015.
  - Event study (difference-in-difference) for 28 Sub-Saharan African (SSA) LICs around the surprise devaluation of the CFA franc in early 1994.
- External shocks analyzed (constructed as forecast errors using World Economic Outlook forecasts):
  - Unanticipated changes in world GDP (“world GDP shock”).
  - Shifts in the terms of trade.
  - Fluctuations in the price of oil.
- Monetary policy framework indicator:
  - Binary annual indicator based on IMF AREAER classification.
  - Two groups: (a) frameworks that rely primarily on the exchange rate as the nominal anchor; (b) frameworks that use money- or inflation-targeting to foster price stability.
- Empirical implementation:
  - Regress output growth at various horizons on the interaction between the shock and the monetary policy framework dummy.
  - Controls include wars, external demand (when testing terms of trade and oil shocks), and country characteristics to address endogenous regime choice.
  - Robustness checks, alternative classifications, and subsamples (including the poorest LICs) are used.

### Key sample facts and classifications
- Sample: 79 LICs over 1990–2015 (the composition of the LIC group changes over time).
- Panel composition over time:
  - 79 LICs in 1990.
  - 60 LICs in 2015.
- AREAER-based classification:
  - About one-third of observations: framework focused on targeting money or inflation.
  - About two-thirds of observations: framework focused on exchange rate stability.
- Event study sample:
  - 28 SSA LICs: 10 LICs in the CFA zone (devalued in early 1994) and 18 SSA LICs in a control group (did not devalue).

### Main findings
- Overwhelming rejection of the money neutrality hypothesis for LICs based on both empirical strategies.
- For countries with monetary policy frameworks that target the exchange rate as the nominal anchor:
  - Surprises in world GDP, terms of trade shifts, and oil price fluctuations have a statistically larger real domestic output growth response compared with money- and inflation-targeting countries.
- Event study result:
  - Real GDP growth rates in the CFA zone were statistically higher than those in the control group during the two-year period after the 1994 devaluation.
- Robustness:
  - Results hold across various specifications, control variables, and subsamples, including the poorest LICs.
- Micro evidence on price adjustment:
  - Monthly frequency of price changes tends to be higher in countries with lower per capita income.
  - New Keynesian models calibrated for LICs have often assumed a low frequency of price changes (25 percent), which may be inappropriate given observed high frequency of price adjustment in many LICs.
- Interpretation and caveats:
  - Findings indicate money non-neutrality in LICs without imposing a particular structure of nominal rigidities.
  - The empirical reduced-form approach cannot identify the structural sources of non-neutrality.
  - Potential structural explanations include informational frictions (incomplete knowledge about the economy; misperceptions of central bank goals/operations) rather than classic staggered price-setting.

### Policy implications and recommendations
- The monetary policy framework matters for how external shocks affect growth in LICs; choice of nominal anchor and the design of the framework influence shock transmission.
- Ongoing reforms in LICs to strengthen monetary policy frameworks while allowing greater exchange rate flexibility are likely to matter for macroeconomic management.
- A well-designed monetary policy framework (beyond mere choice of anchor) can help insulate domestic economies from external shocks.
- Research priorities:
  - Clarify the sources and magnitudes of nominal rigidities and informational frictions in LICs to better inform model choice and policy design.
  - Reassess model calibration for LICs given evidence of high frequency of price adjustment and heterogeneity across LICs.

*Source: wpiea2020139-print-pdf — 1. Monthly Frequency of Price Changes and Per Capita GDP Relative to the U.S.*

### Appendix V. As the theory would predict, we observe that countries using exchange rate as

### Appendix V. As the theory would predict, we observe that countries using exchange rate as an intermediate target to achieve price stability tend to be more open to trade

### External demand shocks: identification, intuition, and primary results
- Identification and normalization
  - External demand shock measure: difference between actual and WEO forecast of country-specific world GDP growth (forecast at t-1 for realization at t); interpreted as the unanticipated shock to world GDP growth (one-year and two-year ahead forecast error realized at year t).
  - Forecast errors of world GDP vary from -3.6 to +1.9 percent; the standard deviation is 1.1 percent.
  - Empirical test: effect of a 1 percent shock to world GDP on domestic output growth, across monetary policy frameworks (exchange-rate-based vs inflation/monetary targeting).
- Economic intuition
  - Positive unanticipated external demand shock raises aggregate demand, money demand, and prices; under fixed nominal exchange rates the central bank offsets by lowering interest rates to maintain parity, amplifying aggregate demand; under flexible exchange rates nominal exchange rate adjusts instead and may dampen aggregate demand change.
- Key empirical findings (Panel regressions; 79 countries, 1578 observations)
  - In response to an unanticipated positive one-percent shock to world GDP:
    - Positive effect on domestic output growth (by about 0.5 percentage points) only in frameworks maintaining price stability through fixed exchange rates.
    - Effect is highly statistically significant (mostly at 1 percent level) in the year when the shock occurs (horizon 0), and also in the subsequent year.
    - Statistically significant difference between effects in exchange-rate-targeting frameworks versus monetary or inflation targeting frameworks.
  - Results hold when focusing on poorest LICs (subsamples):
    - Subsample definitions: countries below median GDP per capita in 1990, using two medians: US$800 (cross-sample median) and US$540.7 (cross-country median for 1990). Country must remain in category for at least a year.
    - About sixty percent of sample are in the first subsample (below US$800).
    - For LICs below median, impact in rigid exchange-rate frameworks is stronger than entire LIC sample: up to sixty percent stronger in horizon 1 and the difference between frameworks almost doubles in horizon 0.
- Robustness and sensitivity
  - Results robust to different outlier treatments and inclusion of control variables (one at a time): trade openness, capital openness (inflows+outflows/GDP; Ito's index), financial depth (bank assets/GDP; credit to private sector/GDP), and fiscal policy (overall central government balance as percent of GDP).
  - Introducing controls weakens some results: impact at horizon 0 can become insignificant while remaining significant at horizon 1; financial depth lowers the shock impact at horizon 1.
  - Broader conclusion: evidence that even in inflation- or monetary-targeting frameworks prices adjust relatively slowly, allowing the exchange rate to act as a shock absorber.

### Terms-of-trade shocks
- Identification and normalization
  - Shock defined as difference between actual country terms of trade and its forecast at horizon k.
  - Standard normalization for this shock: 10 percent unanticipated change (forecast-error SD of terms of trade about 15 percent).
- Key empirical findings (Table 3; 76 countries, 1484 observations / 1504 observations reported)
  - In response to an unanticipated ten-percent improvement in terms of trade:
    - Positive effect on domestic output growth (about 0.20 percentage points) mainly in frameworks maintaining price stability through rigid exchange rates.
    - Statistically significant at 5 percent in the year of the shock (horizon 0) and at 10 percent in the subsequent year.
    - Highly statistically significant difference between rigid exchange-rate frameworks and monetary/inflation targeting (1 percent at 1-year horizon).
- Robustness and interactions
  - Eliminating outliers and adding controls generally strengthens precision and significance.
  - Interaction with fiscal policy: inclusion of fiscal policy can prevent isolating the monetary policy framework’s role for terms-of-trade shocks in some specifications (final row of Table 3 shows fiscal policy inclusion does not allow pinpointing the monetary framework’s role).

### Oil price shocks
- Identification and normalization
  - Shock defined as unanticipated difference between forecasted and actual oil price at one-year horizon.
  - Forecast error of oil price in sample varies between -60 and +40 percent; median forecast error is 12 percent.
- Key empirical findings
  - For oil-importing LICs: impact of an unanticipated ten percent oil price shock does not differ across monetary policy frameworks (results not reported but available on request).
  - For big oil exporters (crude oil production exceeding 5% of nominal GDP in at least one year in sample):
    - In response to an unanticipated ten-percent increase in global oil prices:
      - Positive effect on domestic output growth (by about 0.45 percentage points in the year of the shock and higher in the subsequent year) only in frameworks maintaining price stability through rigid exchange rates.
      - Statistically significant effects at 1 percent level, especially one year after the shock.
      - Statistically significant difference between rigid exchange-rate frameworks and monetary/inflation targeting frameworks at 1 percent in the year after the shock.
    - Sample of big oil exporters: Angola, Cameroon, Chad, Rep. of Congo, Ghana, Mauritania, Nigeria, Sudan, Yemen (9 countries, 183 observations).
  - Robustness: effects remain at 1 and 5 percent significance when controlling for outliers and other controls, especially in year following shock.
- Policy implication highlighted
  - Big oil exporters using a fixed exchange rate as nominal anchor experience very volatile domestic output growth — large gains when oil prices increase and large losses when they plunge.
  - Policy advice: good demand management, consistent policy mix, adjustment strategies, strong built-in automatic stabilizers and safety nets, and nominal wage flexibility are needed if LICs choose a rigid exchange-rate framework to achieve price stability.

### Event study: 1994 CFA franc devaluation
- Background
  - CFA zone: 14 countries in two currency unions (WAEMU and CEMAC); CFA fixed to French franc since 1980 and to euro since 1999.
  - Many CFA countries are major commodity exporters (examples provided).
  - By late 1993 the CFA overvaluation averaged 30 percent; devaluation of the CFA franc by 50 percent occurred on January 1, 1994.
- Method and samples
  - Difference-in-differences comparing 10 CFA zone African LICs with 18 control-group African LICs; measure difference in average real GDP growth between 1994–1995 and 1992–1993 (two-year windows); results demeaned over 1990–2015 sample.
  - CFA sample (10 countries): Benin, Burkina Faso, Cameroon, CAR, Chad, Cote d’Ivoire, Mali, Niger, Senegal, Togo.
  - Control group (18 countries) listed in Table 6 (e.g., Burundi, Cabo Verde, Ghana, Nigeria, Tanzania, Uganda, Zambia).
  - Baseline regression: dependent = change in two-year real GDP growth rate (1994-1995 vs 1992-1993), demeaned; independent: constant, CFA zone dummy, battle-related deaths; regressions estimated by Panel Least Squares.
- Main event-study results (two-year window)
  - Real GDP growth on average improved by 5 percent after the devaluation in the CFA zone, while control group growth remained relatively unchanged.
  - Statistical significance and robustness:
    - Result is statistically significant and robust at 5 percent (Table 6).
    - Estimated impact on real growth of the devaluation in CFA zone is between 2¾ and 5½ percent once different outliers are excluded.
    - The average growth in CFA zone was about 4 percent after devaluation; difference between before and after 1994 two-year windows was about 5 percent and statistically significant (at 10 percent in one specification).
  - Example regression coefficients (Table 6 sensitivity rows):
    - Baseline: 5.21** (standard deviation 2.06) for CFA; control group -0.23 (1.23); p-value 0.07.
    - Excluding CFA outlier with very high 1994 growth (Togo): CFA 2.81** (1.13); control -0.23 (1.23); p-value 0.06.
    - Other sensitivity exclusions report CFA effects of 5.32**, 5.52** with corresponding SDs reported.
  - Distributional evidence: Figure 3 shows similar pre-devaluation distributions across groups but markedly different post-1994 distributions (difference = 4.98 reported in figure annotation).

### Conclusions and policy implications
- Overarching empirical conclusion
  - Strong and robust evidence that the effect on domestic output growth of unanticipated external shocks depends on the monetary policy framework used in LICs.
  - LICs using exchange-rate targeting to achieve price stability exhibit statistically larger responses in real domestic output growth to external shocks than LICs using inflation or monetary targeting.
  - Results hold across specifications, controls, subsamples, and for the poorest LICs, indicating presence of nominal rigidities (price stickiness, informational frictions, etc.) even in low-income settings.
- Implications for modeling and policy
  - Findings reject monetary neutrality in LICs and indicate that monetary policy frameworks matter empirically.
  - The source and size of nominal rigidities need further study to assess shock impacts and appropriate policy responses as LICs modernize monetary frameworks.
  - Best-practice building blocks for successful monetary policy frameworks in LICs are similar to those for advanced economies and emerging markets; systematic and transparent frameworks may be especially important in contexts such as the COVID-19 pandemic.
- Specific policy recommendations and considerations emphasized in text
  - Good demand management and consistent policy mix.
  - Adjustment strategies and strong built-in automatic stabilizers and safety nets for commodity-dependent LICs.
  - Importance of liquidity management and sterilization tools for countries with fixed exchange rates (to dampen transmission from external shocks).
  - Nominal wage flexibility as part of adjustments to restore competitiveness in commodity-rich LICs using rigid exchange-rate frameworks.

*Source: Appendix V, wpiea2020139-print-pdf.*

### APPENDIX I—ESTIMATION

### APPENDIX I—ESTIMATION

### Estimation approach
- Use of a parsimonious, single equation model as a flexible alternative to VARs for estimating impulse-response functions, following Jordà (2005).
- Motivation: suited to capture nonlinearities in dynamic responses; avoids dynamic restrictions embedded in VAR specifications.
- Limitation: ignores interaction with other variables, which could obscure the true source of shocks if omitted from the regression.

### Core specification
- The estimated equation (for country i, horizon k) is:
  y_i,t+k – y_i,t = α_i^k + γ_t^k + β_k * θ_1 * FE(x_i,t) * MP_ER_i,t + β_k * θ_2 * FE(x_i,t) * (1-MP_ER_i,t) + φ z_i,t + e_i,t^k
- Definitions:
  - y_i,t+k – y_i,t: percent change in real GDP growth y_i,t (measured in logs) observed between times t and t+k.
  - α_i^k and γ_t^k: country and time fixed-effects, respectively.
  - FE(x_i,t): forecast error (i.e., shock) in exogenous driver variable x_i,t.
  - MP_ER_i,t: vector of binary indicators of the monetary policy framework (equals 1, if exchange rate targeting, or 0, if money or inflation targeting).
  - z_i,t: vector of controls.
- Estimation is performed with annual data from LICs for intervals k = 1, 2 years.
- Parameter β_k allows construction of impulse responses (IRF) for the effect of a shock to x_i,t on y_i,t over horizon k.

### Hypothesis testing and interpretation
- Wald tests used to assess statistical difference between the effect of x_i,t on y_i,t across monetary policy frameworks: test whether θ_1 ≠ θ_2.
- Baseline hypothesis tested: the monetary policy framework does not have a differentiated impact of the shock on growth. This is tested by checking whether θ_1 = 0, θ_2 = 0 and θ_1 - θ_2 = 0.
- Reported results in tables: β_k θ_1, β_k θ_2 and β_k (θ_1 - θ_2), respectively, to interpret impacts of a certain shock on domestic output growth according to the monetary policy framework (e.g., β_k θ_1 for exchange rate targeting).

### Forecasts and forecast errors
- Use WEO forecasts to compute forecast errors because the WEO covers the entire global economy and reflects rigorous analysis and expert judgment of Fund staff.
- Rationale against mechanically generated forecasts (e.g., VAR-based): such forecasts would rely on specific technical assumptions (e.g., linearity or stationarity).
- Forecast horizon considerations: forecast error variance increases rapidly with the forecast horizon; using a longer forecast horizon would add unnecessary noise and diminish prospects of statistically significant or economically meaningful results.

### Controls, autocorrelation, and standard errors
- Note (footnote): Introducing lagged domestic GDP growth as a control would reduce autocorrelation in the error term but would make it more difficult to disentangle the difference in the impact of the shock relative to the monetary policy framework.
- To account for the possibility of autocorrelation in residuals, robust standard errors are used.

*Source: APPENDIX I—ESTIMATION (wpiea2020139-print-pdf)*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020139-print-pdf.pdf_