## Monetary policy effectiveness in Kazakhstan: results with a small macro model

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---

### Introduction and motivation
- Central question: how the economy reacts to monetary policy or other macro shocks using structural vector autoregression (SVAR) models following Sims (1980).
- Identification approaches discussed:
  - Parametric restrictions (predominantly zero contemporaneous restrictions) justified by sluggish adjustment or delayed observation.
  - Sign restrictions (“agnostic” identification) that impose only directions of responses rather than exact coefficient values.
- Prior literature:
  - Uhlig (2005) finds contractionary monetary policy shocks show no discernible effect on real GDP.
  - Arias et al. (2019) and external-instrument identification (Gertler and Karadi, 2015) tend to reaffirm short-term GDP effects predicted by models with price rigidities.
- Contribution:
  - Proposes a “quasi-agnostic” identification procedure: an iterative grid search that refines plausible intervals for structural parameters using information from earlier iterations.
  - Results indicate substantially higher acceptance rates and a larger set of economic structures consistent with sign priors.
- Document structure overview:
  - Sections: baseline model; baseline model respecified; agnostic and “quasi-agnostic” sign restrictions; monetary policy effectiveness over time; conclusions.
  - Figures: IRFs and distributions of restricted parameters (Figures 1–6).
  - Tables: lag selection, sign restrictions, and summary statistics for alternative identification procedures.

### Baseline model (three-variable SVAR) — specification and estimation
- Endogenous variables Y = [output gap, π, r]′:
  - Output gap: estimated via Harvey and Jaeger (1993) adapted for mixed-frequency to produce log seasonally adjusted quarterly real GDP at monthly frequency between January 2017 and September 2024; Impavido (2024a) used annual real growth of monthly loans to individuals as proxy for financial-cycle influence.
  - Inflation: seasonally adjusted CPI excluding controlled prices between January 2017 and September 2024.
  - Policy rate: average policy rate used by the Central Bank, consistent across the timeframe.
- SVAR specification:
  - A0 Yt = A1 Yt−1 + A2 Yt−2 + B0 εt
  - A0: lower triangular with ones on diagonal; B0: diagonal with standard errors on diagonal; εt ~ (0, I3); ηt = B0 εt are structural shocks.
- Parameter counting:
  - Total parameters: 27 (6 in A0, 9 in A1, 9 in A2, 3 in B0).
  - Only 24 can be estimated from the underlying VAR → impose three zero contemporaneous restrictions in A0 to make SVAR recursive and exactly identified.
- Lag selection:
  - First LR test that rejects null suggests SVAR order 3; information criteria indicate little loss between lags 2 and 3.
  - Chosen lag = 2 to minimize risk of overfitting.
- Estimation approach:
  - Exactly identified SVAR estimated via 2SLS using instrumental variables (preferred for later flexibility when contemporaneous restrictions differ from zero).

### Baseline IRF findings (original variables)
- Demand shock (one standard deviation):
  - Contemporaneous impact on output gap equal in magnitude to the shock; persistence ~15 periods.
  - Modest positive contemporaneous effect on inflation.
  - Small immediate increase in policy rate, subsequently rising with expanding output gap.
- Supply shock (one standard deviation):
  - Zero contemporaneous impact on output gap (due to zero restriction), rising to ~twenty basis points in about 6–8 periods.
  - Positive contemporaneous response in inflation.
  - Policy rate rises to about twenty-five basis points within 6–8 months before inflationary pressures abate.
- Monetary shock (one standard deviation):
  - Zero contemporaneous impact on output gap and inflation (dictated by zero contemporaneous restrictions).
  - Output gap response accelerates to ~fifteen basis points in a few periods.
  - Inflation response is small and positive.
- Interpretation and concerns:
  - Durable influence of shocks on output gap and interest rates; minimal effects on inflation except for supply shocks.
  - Persistence in output gap attributed to strong habit formation (autoregressive component dominates forward-looking).
  - Persistence in policy rate linked to habit formation in Central Bank reaction function.
  - Limited inflation persistence may reflect strong forward-looking component or high exchange rate pass-through.
  - Price puzzle: monetary shock producing positive inflation response suggests potential misspecification.

### Addressing misspecification — alternative approaches considered
- Four corrective approaches (literature):
  - (i) Add endogenous variables.
  - (ii) Redefine endogenous variables.
  - (iii) Use non-recursive/less strict identification procedures.
  - (iv) Introduce latent variables.
- Trade-offs:
  - (i) and (iv) can resolve puzzles but increase parameter count exponentially and often require state-space/Kalman-filter MLE—beyond this paper’s scope.
  - Paper pursues (ii) and (iii): redefine variables to purge inflation expectations and relax identification via sign restrictions.

### Baseline model respecified (purging inflation expectations) — estimation and results
- Implicit small New Keynesian system estimated via SUR:
  - IS, Phillips, and Policy equations with expectations terms (E_t[·]) and habit/lag components as in equation (3).
- Procedure:
  - Estimate system in (3) via SUR.
  - Subtract estimated expected-inflation components from original endogenous variables to create modified variables (still labeled output gap, inflation, policy rate).
  - Add exogenous controls: COVID dummy and log oil prices in output gap equation.
  - Drop VAR parameters not statistically different from zero.
- Re-specified SVAR with exogenous variables:
  - A0 Yt = A1 Yt−1 + A2 Yt−2 + Γ Xt + B0 εt (equation (4)).
- Estimated structural matrices (equation (5)):
  - Â0 = [ [1 0 0] [−0.021810 1 0] [−0.0770 −0.11961 1] ]
  - B̂0 = [ [0.490200 0 0] [0 0.25900 0] [0 0 0.2988] ]
- Result:
  - IRFs qualitatively similar to baseline; price puzzle resolved, supporting inflation expectations exclusion as a source of previous misspecification.

### Imposing agnostic sign restrictions (SRC procedure) — implementation and findings
- Motivation:
  - Sign restrictions address sensitivity to recursive zero contemporaneous restrictions and ordering.
- SRC implementation (Ouliaris and Pagan (2016) formulation):
  - Random coefficients form: aij = θ/(1−arad(θ)) with θ ~ U(−1,1) (as described in source).
  - Simulate 1,200 combinations of parameters a12^0, a13^0, a23^0 using SRC.
  - For each draw:
    - Estimate B0 and remaining A0 parameters via 2SLS; A1 and A2 via OLS.
    - Compute contemporaneous IRFs IHF_h=0 = Â0^{-1} B̂0 and compare signs to priors in Table 1.
    - Discard IRFs inconsistent with sign priors.
  - Acceptance rate = number of combinations consistent with priors / 1,200.
- Findings (SRC baseline, Figure 3 summary):
  - Monetary shock contemporaneous impact on output gap between zero and thirty basis points.
  - Monetary shock contemporaneous impact on inflation between zero and fifteen basis points, increasing to ~twenty-five basis points after three periods before dissipating.
  - Low acceptance rate indicates model specification can be improved and acceptance depends on sign-restriction method.
  - Sign restrictions solve structural identification but not model identification: each IRF corresponds to a unique structural parameter set; restricting IRFs at multiple horizons narrows plausible models.

### Imposing “quasi-agnostic” sign restrictions — grid-refinement strategy and results
- Problem with SRC(−∞, +∞):
  - Wide parameter range with large standard deviations produces many implausible values → low acceptance rate.
- Quasi-agnostic strategy:
  - Iterative grid search refining plausible parameter intervals based on earlier draws to increase acceptance rates.
- Procedure and rounds:
  - Round 1: SRC(−∞, +∞) with sign restrictions at lag 0, 3, 6; 1,200 simulations; diagnostics for a12^0, a13^0, a23^0.
    - Observations: medians in (0,1); all a13 positive; few successful a12^0 and a23^0 negative and near zero; a23^0 standard deviation very small; a12^0 standard deviation large.
  - Round 2: SRC(0, +∞) (absolute SRC draws) → higher acceptance rates; excludes negative plausible a12^0.
  - Round 3: N(0,1) draws to re-include zero/negative values → broadly comparable to SRC(−∞, +∞).
  - Subsequent rounds: reduce standard deviation of draws and shift means toward earlier estimated means/medians (grid refinement) → acceptance rates increase as draws concentrate around plausible parameter means.
- Example (identification N(0.5,0.25) at time lag six, Figure 5):
  - Many plausible structures where a one standard deviation monetary policy shock:
    - Reduces contemporaneous output gap between zero and twenty-five basis points.
    - Reduces contemporaneous inflation between four and twelve basis points.
  - Output gap response decreases over time; inflation response rises to about eighteen basis points in the first two periods before declining.

### Monetary policy effectiveness over time — time-varying SVAR estimates
- Selected structure yielding strongest inflation response (equation (6)):
  - A0 = [ [1 0.1015 0.6809] [a21^0 1 0.3361] [a31^0 a32^0 1] ] (matrix elements as in source).
- Method:
  - Re-estimate SVAR (equation (4)) with A0 from (6) across six rolling time periods, each extending an additional 12 months starting with sample ending in 2019m12.
- Key empirical results (Figure 6 summary):
  - Contemporaneous impact of a one standard deviation monetary policy shock on output gap:
    - Increased from 8 basis points in 2019 to 17 basis points in 2024.
  - Contemporaneous inflation response to same shock:
    - Increased from 4 basis points in 2019 to 12 basis points in 2024.
  - Temporal dynamics:
    - Early periods (2019–2020): inflation converges back to trend faster than output gap.
    - Later periods (2023–2024): output gap converges faster than inflation.
    - Overall: relatively flat Phillips curve throughout; weak inflation response to output gap beyond immediate impact.
  - Interpretation:
    - Changes suggest evolving relative importance of transmission channels—possible strengthening of the exchange rate channel, and contributions from enhanced central bank credibility, reduced dollarization, and improved communication.

### Key empirical findings and summary statistics (preserved as reported)
- Sample period: January 2017 to September 2024 (monthly series).
- SVAR lag chosen: 2.
- SVAR parameter counts: 27 total; 24 estimable without restrictions.
- Simulations for SRC procedures: 1,200 draws.
- Representative IRF magnitude ranges reported:
  - Monetary shock contemporaneous output-gap impact:
    - Between zero and thirty basis points (SRC baseline).
    - Between zero and twenty-five basis points (quasi-agnostic N(0.5,0.25) at lag six).
  - Monetary shock contemporaneous inflation impact:
    - Between zero and fifteen basis points (SRC baseline).
    - Between four and twelve basis points (quasi-agnostic N(0.5,0.25) at lag six).
    - Inflation rises to about twenty-five basis points after three periods in some specifications before dissipating.
  - Supply shock: output-gap increase to about twenty basis points in about 6–8 periods; policy rate reaches about twenty-five basis points within 6–8 months.
  - Demand shock persistence: output gap persistent for about 15 periods.
- Estimated structural matrices (re-specified SVAR after purging expectations):
  - Â0 = [ [1 0 0] [−0.021810 1 0] [−0.0770 −0.11961 1] ]
  - B̂0 = [ [0.490200 0 0] [0 0.25900 0] [0 0 0.2988] ]
- Time trend in contemporaneous monetary shock impacts:
  - Output gap contemporaneous effect: increased from 8 basis points (2019) to 17 basis points (2024).
  - Inflation contemporaneous effect: increased from 4 basis points (2019) to 12 basis points (2024).

### Acceptance rates, identification diagnostics, and conclusions
- Acceptance rates reported:
  - Contemporaneous sign restrictions on IRFs SRC(−∞, +∞): Acceptance rate of 1.42 percent based on 1,200 simulations and sign restrictions tested up to horizon 0.
  - Period six sign restrictions on IRFs using N(0.5,0.25): Acceptance rate of 13.  50 percent based on 1,200 simulations and sign restrictions tested up to horizon 6.
- Sign restriction priors (Table of sign restrictions for positive structural shocks):
  - Demand Shock: Output gap + ; Inflation + ; Interest rate +.
  - Supply Shock: Output gap - ; Inflation + ; Interest rate +.
  - Monetary Shock: Output gap - ; Inflation - ; Interest rate +.
- Conclusions:
  - Identified shocks exert durable influence on the output gap and interest rates; effects on inflation are minimal except for supply shocks.
  - Evidence consistent with inflation being predominantly imported, a relatively weak interest channel, and a flat Phillips curve.
  - SRC procedure uncovers plausible structures yielding stronger monetary policy responses than the recursive model but yields low acceptance rates, reflecting model misspecification and/or identification limitations.
  - The proposed “quasi-agnostic” grid-refinement strategy can substantially increase acceptance rates and identify a larger set of structures consistent with sign priors.
  - Time-varying estimates indicate a strengthening of contemporaneous monetary-policy effects on output gap and inflation between 2019 and 2024, potentially linked to increased central bank credibility, reduced dollarization, better communication, and a shifting transmission mechanism favoring the exchange rate channel.

*Source: IMF Working Paper No. WP/2025/173, “Monetary policy effectiveness in Kazakhstan: results with a small macro model” — Introduction and Conclusions sections.*

### Introduction ...........................................................................................................

### Introduction

### Document structure and major sections
- Introduction (page 3)
- The baseline model (page 4)
- The baseline model respecified (page 6)
- Imposing agnostic sign restrictions (page 7)
- Imposing “quasi-agnostic” sign restrictions (page 9)
- Monetary policy effectiveness over time (page 10)
- Conclusions (page 10)
- Annex I. Tables and Figures (page 12)
- References (page 18)

### Figures included (titles and numbering)
- Figure 1. Structural impulse responses – baseline model
- Figure 2. Structural impulse responses – baseline model respecified
- Figure 3. Contemporaneous sign restrictions on IRFs using SRC(-∞, +∞)
- Figure 4. Distribution of restricted parameters using alternative identification procedures
- Figure 5. Period six sign restrictions on IRFs using N(0.5,0.25)
- Figure 6. Impact of monetary policy over time

### Tables included (titles and numbering)
- Table 1. Lag selection
- Table 1. Sign restrictions for positive structural shocks
- Table 2. Summary statistics of restricted parameters from SRC(-∞, +∞)
- Table 3. Summary statistics of restricted parameters from SRC(0, +∞)
- Table 4. Summary statistics of restricted parameters from N(0,1)
- Table 5. Summary statistics of restricted parameters from N(0.5,0.5)
- Table 6. Summary statistics of restricted parameters from N(0.5,0.25)

### Themes signaled by section headings
- Model specification and respecification (baseline model; baseline model respecified)
- Identification choices for structural shocks (agnostic sign restrictions; “quasi-agnostic” sign restrictions)
- Analysis of monetary policy effectiveness and its evolution over time
- Presentation of impulse response functions (IRFs) and distributions of restricted parameters
- Use of alternative identification procedures and prior specifications, including SRC(-∞, +∞), SRC(0, +∞), N(0,1), N(0.5,0.5), and N(0.5,0.25)

*IMF WORKING PAPERS Monetary policy effectiveness in Kazakhstan: results with a small macro model — INTERNATIONAL MONETARY FUND*

### Introduction

### Introduction

### Background and motivation
- Central question: how the economy reacts to monetary policy or other macro shocks using structural vector autoregression (SVAR) models following Sims (1980).
- SVARs emphasize dynamic impulse response functions (IRFs) and align with New-Keynesian frameworks that treat structural parameters as central for macro dynamics.
- Identification approaches:
  - Early literature: parametric restrictions (predominantly zero contemporaneous restrictions) justified by sluggish adjustment or delayed observation.
  - More recent: sign restrictions (“agnostic” identification), which impose only directions of responses rather than exact coefficient values.
- Prior findings:
  - Uhlig (2005) finds contractionary monetary policy shocks show no discernible effect on real GDP (consistent with money neutrality).
  - Arias et al. (2019) refinements and external-instrument identification (Gertler and Karadi, 2015) tend to reaffirm short-term GDP effects of monetary policy predicted by models with price rigidities.

### Contribution of this paper
- Proposes a “quasi-agnostic” identification procedure to improve the low acceptance rates typical of agnostic sign-restriction methods.
- The strategy is an iterative grid search that refines plausible intervals for structural parameters using information from earlier iterations.
- Results indicate substantially higher acceptance rates and a larger set of economic structures consistent with sign priors.

### Structure of the paper
- Section I: data overview and baseline small three-variable SVAR for Kazakhstan (output gap, inflation, policy rate).
- Section II: links baseline model to a conventional New-Keynesian framework to address misspecification.
- Section III: critiques unique parametric restrictions and adopts Ouliaris and Pagan (2016) sign-restriction methodology on IRFs at various horizons.
- Section IV: explores alternative “quasi-agnostic” identification procedures to increase acceptance rates.
- Section V: concludes with empirical summary on evolution of monetary policy effectiveness in Kazakhstan.

---

### Baseline model (three-variable SVAR)
- Endogenous variables Y = [output gap, π, r]′ where output gap is estimated via:
  - Harvey and Jaeger (1993) adapted for mixed-frequency to estimate log seasonally adjusted quarterly real GDP at monthly frequency between January 2017 and September 2024.
  - Impavido (2024a) to extract cyclical component using annual real growth of monthly loans to individuals as a proxy for financial-cycle influence.
- Inflation: seasonally adjusted CPI excluding controlled prices between January 2017 and September 2024.
- Policy rate: average policy rate used by the Central Bank, consistent across the timeframe.
- SVAR specification:
  - A0 Yt = A1 Yt−1 + A2 Yt−2 + B0 εt
  - Y = [output gap, π, r]′
  - A0: lower triangular with ones on diagonal; B0: diagonal with standard errors on diagonal; εt ~ (0, I3); ηt = B0 εt are structural shocks.
- Parameter counting:
  - Total parameters: 27 (6 in A0, 9 in A1, 9 in A2, 3 in B0).
  - Only 24 can be estimated from the underlying VAR → impose three zero contemporaneous restrictions in A0 to make SVAR recursive and exactly identified.
- Chosen lag order:
  - Lag selection statistics (FPE, AIC, BIC, HQIC) for SVARs of order 1 through 5.
  - First LR test that rejects null suggests SVAR order 3; information criteria indicate little loss between lags 2 and 3.
  - Chosen lag = 2 to minimize risk of overfitting.
- Estimation approach:
  - Exactly identified SVAR estimated via 2SLS using instrumental variables (preferred for later flexibility when contemporaneous restrictions differ from zero).

### Baseline IRF findings (original variables)
- From the SVAR with A0 as lower-triangular (equation (2)):
  - Demand shock (one standard deviation):
    - Contemporaneous impact on output gap equal in magnitude to the shock; persistence ~15 periods.
    - Modest positive contemporaneous effect on inflation.
    - Small immediate increase in policy rate, subsequently rising with expanding output gap.
  - Supply shock (one standard deviation):
    - Zero contemporaneous impact on output gap (due to zero restriction), rising to ~twenty basis points in about 6–8 periods.
    - Positive contemporaneous response in inflation.
    - Policy rate rises to about twenty-five basis points within 6–8 months before inflationary pressures abate.
  - Monetary shock (one standard deviation):
    - Zero contemporaneous impact on output gap and inflation (dictated by zero contemporaneous restrictions).
    - Output gap response accelerates to ~fifteen basis points in a few periods.
    - Inflation response is small and positive.
- Interpretation:
  - Durable influence of shocks on output gap and interest rates; minimal effects on inflation except for supply shocks.
  - Persistence in output gap attributed to strong habit formation (autoregressive component dominates forward-looking).
  - Persistence in policy rate linked to habit formation in Central Bank reaction function.
  - Limited inflation persistence may reflect strong forward-looking component or high exchange rate pass-through.
  - Consistent with literature: inflation predominantly imported (Hajdenberg 2024), weak interest channel (Zhou 2022), flat Phillips curve (Impavido 2024b).
- Concern: monetary shock producing positive inflation response (price puzzle) suggests potential misspecification.

---

### Addressing misspecification: alternative approaches
- Four corrective approaches discussed (literature):
  (i) Add endogenous variables.
  (ii) Redefine endogenous variables.
  (iii) Use non-recursive/less strict identification procedures.
  (iv) Introduce latent variables.
- Trade-offs:
  - (i) and (iv) can resolve puzzles (e.g., add monetary aggregate or exchange rate) but increase parameter count exponentially, require additional identifying restrictions, and may create new puzzles; estimation often requires state-space/Kalman-filter MLE—beyond this paper’s scope.
  - This paper pursues (ii) and (iii): redefine variables to purge inflation expectations and relax identification via sign restrictions.

### Baseline model respecified (purging inflation expectations)
- Implicit small New Keynesian system (equation (3)):
  - IS: daap_t = γ E_t[daap_{t+1}] + (1−γ) daap_{t−1} − δ (r_t − E_t[π_{t+1}]) + ε_{IID,t}
  - Phillips: π_t = α E_t[π_{t+1}] + (1−α) π_{t−1} + β daap_t + ε_{AI,t}
  - Policy: r_t = φ r_{t−1} + (1−φ)(λ E_t[π_{t+1}] + μ daap_t) + ε_{MP,t}
- Estimation steps:
  - Estimate system in (3) via SUR.
  - Subtract estimated expected-inflation components (multiplied by estimated parameters) from original endogenous variables to create modified variables (still labeled output gap, inflation, policy rate).
  - Add exogenous controls: COVID dummy and log oil prices in output gap equation.
  - Drop VAR parameters not statistically different from zero.
- Re-specified SVAR with exogenous variables (equation (4)):
  - A0 Yt = A1 Yt−1 + A2 Yt−2 + Γ Xt + B0 εt
  - A0 and B0 as in equation (2); A1 and A2 matrices specified; Γ and X defined with COVID dummy and log oil prices.
- Estimated structural matrices (equation (5)):
  - Â0 = [ [1 0 0] [−0.021810 1 0] [−0.0770 −0.11961 1] ] (matrix formatting preserved from source)
  - B̂0 = [ [0.490200 0 0] [0 0.25900 0] [0 0 0.2988] ]
- Results:
  - IRFs qualitatively similar to baseline; price puzzle resolved, supporting inflation expectations exclusion as source of previous misspecification.

---

### Imposing agnostic sign restrictions (SRC procedure)
- Motivation: justify recursive zero contemporaneous restrictions and ordering; with limited structure, many compatible restriction combinations exist—sign restrictions literature addresses selection.
- SRC (generated coefficients) per Ouliaris and Pagan (2016):
  - Random coefficients form: aij = θ/(1−arad(θ)) with θ ~ U(−1,1) (source description as provided).
- Implementation steps:
  - Start with an unrestricted structural matrix A0 having non-zero off-diagonal contemporaneous coefficients as specified.
  - Simulate 1,200 combinations of parameters a12^0, a13^0, a23^0 using SRC.
  - For each draw:
    - Estimate B0 and remaining A0 parameters via 2SLS; A1 and A2 via OLS.
    - Compute contemporaneous IRFs IHF_h=0 = Â0^{-1} B̂0 and compare signs to priors in Table 1 (source).
    - Discard IRFs inconsistent with sign priors.
  - Acceptance rate = number of combinations consistent with priors / total draws (1,200).
- Findings from SRC procedure (Figure 3 summary):
  - Monetary shock (one standard deviation):
    - Contemporaneous impact on output gap between zero and thirty basis points.
    - Contemporaneous impact on inflation between zero and fifteen basis points, increasing to ~twenty-five basis points after three periods before dissipating.
  - Low acceptance rate suggests model specification can be improved, and acceptance depends on sign-restriction method.
  - Sign restrictions solve structural identification but not model identification: each IRF comes from a unique structural parameter set; medians/percentiles may mask multiplicity—restricting IRFs at multiple horizons narrows plausible models.

---

### Imposing “quasi-agnostic” sign restrictions (grid-refinement strategy)
- Problem with SRC(−∞, +∞): generates wide parameter range with large standard deviations, many implausible values → low acceptance rate.
- Quasi-agnostic strategy: iterative grid search refining plausible parameter intervals based on earlier draws to increase acceptance rates.
- Procedure illustrated with Figure 4 and Tables 2–6:
  - First, SRC(−∞, +∞) applied with sign restrictions at lag 0, 3, 6; distributional diagnostics for parameters a12^0, a13^0, a23^0 from 1,200 simulations reported.
  - Observations from first round:
    - Medians of all three parameters lie in (0,1).
    - All a13 parameters are positive.
    - Very few successful a12^0 and a23^0 parameters are negative and near zero.
    - Restricting IRFs at lag six reduces successful negative parameters.
    - Standard deviation of a23^0 is very small (successful values concentrated); standard deviation of a12^0 is large (dispersed).
    - Plausible parameters likely positive; a23^0 concentrated near its mean.
  - Second round: SRC(0, +∞) — use absolute values of SRC draws → higher acceptance rates at all horizons; excludes baseline model and negative plausible a12^0.
  - Third round: draws from N(0,1) to re-include zero/negative values; results broadly comparable to SRC(−∞, +∞).
  - Subsequent rounds: lower standard deviation of draws and shift means toward earlier estimated means/medians (grid refinement) → acceptance rates increase as draws concentrate around plausible parameter means.
- Example results:
  - Using identification procedure N(0.5,0.25) at time lag six (Figure 5):
    - Many plausible structures where a one standard deviation monetary policy shock:
      - Reduces contemporaneous output gap between zero and twenty-five basis points.
      - Reduces contemporaneous inflation between four and twelve basis points.
    - Output gap response decreases over time; inflation response rises to about eighteen basis points in the first two periods before declining.

---

### Monetary policy effectiveness over time (time-varying estimation)
- Selected structure yielding strongest inflation response (equation (6)):
  - A0 = [ [1 0.1015 0.6809] [a21^0 1 0.3361] [a31^0 a32^0 1] ] (matrix elements preserved as in source)
- Method:
  - Re-estimate SVAR (equation (4)) with A0 from (6) across six rolling time periods, each extending an additional 12 months starting with sample ending in 2019m12.
- Key empirical results (Figure 6 summary):
  - Contemporaneous impact of a one standard deviation monetary policy shock on output gap:
    - Increased from eight basis points in 2019 to seventeen basis points in 2024 (more than doubling).
  - Contemporaneous inflation response to same shock:
    - Increased from four basis points in 2019 to twelve basis points in 2024.
  - Temporal variation in output-gap/inflation dynamics:
    - Early periods (2019–2020): inflation converges back to trend faster than output gap.
    - Later periods (2023–2024): output gap converges faster than inflation.
  - Overall interpretation:
    - Relatively flat Phillips curve throughout: weak inflation response to output gap beyond immediate impact.
    - Observed changes suggest evolving relative importance of transmission channels—potential strengthening of the exchange rate channel, and possible contributions from enhanced central bank credibility, reduced dollarization, and improved communication.

---

### Key empirical findings and statistics (preserved as reported)
- Sample period for monthly series: January 2017 to September 2024.
- SVAR lag chosen: 2.
- SVAR parameter counts: 27 total; 24 estimable without restrictions.
- Simulations for SRC procedures: 1,200 draws.
- Examples of IRF magnitudes (reported ranges):
  - Monetary shock contemporaneous output-gap impact: between zero and thirty basis points (SRC baseline); between zero and twenty-five basis points (quasi-agnostic N(0.5,0.25) at lag six).
  - Monetary shock contemporaneous inflation impact: between zero and fifteen basis points (SRC baseline); between four and twelve basis points (quasi-agnostic N(0.5,0.25) at lag six); inflation rises to about twenty-five basis points after three periods in some specifications before dissipating.
  - Supply shock: output-gap increase to about twenty basis points in about 6–8 periods; policy rate reaches about twenty-five basis points within 6–8 months.
  - Demand shock persistence: output gap persistent for about 15 periods.
- Estimated structural matrices (re-specified SVAR after purging expectations):
  - Â0 = [ [1 0 0] [−0.021810 1 0] [−0.0770 −0.11961 1] ]
  - B̂0 = [ [0.490200 0 0] [0 0.25900 0] [0 0 0.2988] ]
- Time trend in contemporaneous monetary shock impacts:
  - Output gap contemporaneous effect: increased from 8 basis points (2019) to 17 basis points (2024).
  - Inflation contemporaneous effect: increased from 4 basis points (2019) to 12 basis points (2024).

*Source: IMF Working Paper — "Monetary policy effectiveness in Kazakhstan: results with a small macro model" (Introduction).*

### Conclusions

### Conclusions

### Key findings from the baseline recursive SVAR
- Identified shocks exert a durable influence on the output gap and interest rates, while their effect on inflation is minimal; with the notable exception of supply shocks, which have a more sustained impact on inflation.
- Results support the priors that:
  - inflation in the country is predominantly imported,
  - the interest channel of monetary policy is relatively weak,
  - inflation exhibits a limited response to the output gap, supporting the notion of a relatively flat Phillips curve.

### Identification strategy and robustness checks
- The structural parameters of a small macro model for Kazakhstan using output gap, inflation, and policy rate are estimated using an exactly identified recursive SVAR.
- The recursive nature of the model cannot be justified with available knowledge of the structure of the economy.
- Short term restrictions are relaxed and sign restrictions are imposed on impulse response functions at different time horizons using the SRC algorithm proposed by Ouliaris and Pagan (2016).
- Results from the SRC procedure suggest there are plausible structures that yield stronger responses to monetary policy shocks than the recursive model; however, the procedure yields very low acceptance rates suggesting either model misspecification, or identification procedure limitations.
- A separate exercise using structural restrictions yielding the median and the minimum contemporaneous inflation response to a monetary policy shock produced comparable results.8
- Part of the impact is due to an increase in the variance of the shocks over time; however, this does not affect the shape of the IRFs that show higher persistence of the inflation response over time.9

### Proposed strategy to improve identification (quasi-agnostic grid search)
- To overcome possible identification procedure limitations, the study proposes a strategy aimed at identifying a greater number of plausible economic structures.
- The proposed strategy is akin to a grid search across progressively refined identification procedures.
- These procedures are designated as “quasi”-agnostic, reflecting their adaptive nature, wherein subsequent methodologies are informed by insights garnered from earlier procedures regarding the likely interval of plausible structural parameters.
- Results suggest this strategy can significantly enhance acceptance rates, revealing a larger set of economic structures consistent with priors on the sign of responses of macro variables to structural shocks.
- The results also leave open the question of the relative importance of possible model misspecification in determining the acceptance rate of any given sign restriction procedure.

### Acceptance rates and simulation details
- Contemporaneous sign restrictions on IRFs SRC(−∞, +∞): Acceptance rate of 1.42 percent based on 1,200 simulations and sign restrictions tested up to horizon 0.
- Period six sign restrictions on IRFs using N(0.5,0.25): Acceptance rate of 13.  50 percent based on 1,200 simulations and sign restrictions tested up to horizon 6.
- The study reports distributional experiments and summary statistics from multiple identification priors and sampling distributions, including SRC(−∞, +∞), SRC(0, +∞), N(0,1), N(0.5,0.5), and N(0.5,0.25), with summary statistics shown for parameters a12, a13, and a23 across horizons Step = 0, Step = 3, and Step = 6.

### Time evolution of monetary policy effectiveness (2019–2024)
- Results suggest a notable enhancement in monetary policy effectiveness over time:
  - The contemporaneous impact of a monetary policy shock on the output gap more than doubling between 2019 and 2024.
  - The inflation response to such shocks has nearly tripled over the same period.
- Possible contributing factors to these changes include:
  - heightened central bank credibility,
  - a decline in dollarization,
  - more effective communication strategies.
- Preliminary findings indicate a potential shift in the relative strength of monetary transmission channels, with the exchange rate channel possibly assuming a more prominent role towards the end of this period.

### Tables and figures noted in the conclusions
- Lag selection statistics reported for horizons 0 through 5 include:
  - Horizon 0: LL = -403.377; FPE = 4.047; AIC = 9.912; HQIC = 9.947; SBIC = 10.000.
  - Horizon 1: LL = -99.710; LR = 607.333; Pval = 0.000; FPE = 0.003; AIC = 2.725; HQIC = 2.866; SBIC = 3.077.
  - Horizon 2: LL = -52.662; LR = 94.097; Pval = 0.000; FPE = 0.001; AIC = 1.797; HQIC = 2.044; SBIC = 2.413.
  - Horizon 3: LL = -42.677; LR = 19.970; Pval = 0.018; FPE = 0.001; AIC = 1.773; HQIC = 2.126; SBIC = 2.653.
  - Horizon 4: LL = -34.222; LR = 16.910; Pval = 0.050; FPE = 0.001; AIC = 1.786; HQIC = 2.245; SBIC = 2.931.
  - Horizon 5: LL = -26.164; LR = 16.116; Pval = 0.064; FPE = 0.001; AIC = 1.809; HQIC = 2.374; SBIC = 3.218.
- Table of sign restrictions for positive structural shocks (Table 2) specifies:
  - Demand Shock: Output gap + ; Inflation + ; Interest rate +.
  - Supply Shock: Output gap - ; Inflation + ; Interest rate +.
  - Monetary Shock: Output gap - ; Inflation - ; Interest rate +.

_Conclusions section, IMF Working Paper No. WP/2025/173, “Monetary policy effectiveness in Kazakhstan: results with a small macro model” — source content._

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_Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025173-source-pdf.pdf_