## _wp1690 ## Source details **Canonical URL:** [_wp1690](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp1690.pdf) ## Other formats - [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp1690.pdf.md) - [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp1690.pdf.json) --- ### Introduction: research question, empirical strategy, and DSGE setup - Research question and motivation - Competing explanations for weak and imprecise monetary transmission mechanism (MTM) evidence in low-income countries (LICs): - “Facts on the ground”: small/underdeveloped financial markets, fixed or heavily managed exchange rates, severe financial frictions, imperfect competition in banking — implying weak links between central-bank-controlled short-term interest rates and aggregate-demand channels (longer-term rates, exchange rate, lending). - “Limitations of the method”: data-intensive, atheoretic VAR/SVAR methods fail to measure a potentially strong MTM accurately in LIC research environments. - Central question: If a strong MTM exists, can standard structural VAR (SVAR) methods uncover it in LIC-like research environments characterized by short samples, measurement error, high volatility (notably large temporary supply shocks), and non-transparent policy regimes? - Empirical strategy and methodology - Use a DSGE as the data-generating process (DGP) that embodies a strong MTM, then apply standard SVAR identification and estimation procedures to simulated data to assess sampling and inferential properties of VAR-based methods. - Monte Carlo design: - Generate multiple independent simulated datasets from the DSGE solution. - Within each simulated dataset estimate a reduced-form VAR and impose contemporaneous (short-run) identification restrictions to recover structural monetary policy shocks and compute impulse response functions (IRFs). - Analyze median estimated IRF, distribution across simulations, t-ratios, and power of conventional t-ratio tests against the hypothesis of zero response. - DSGE model structure (four-state-variable, linearized, stationary) - Endogenous quarterly variables x_t′ = (ỹ_t, π_t, q̃_t, i_t)′ where: - ỹ_t = GDP gap (actual minus unobserved potential GDP) - π_t = inflation rate - q̃_t = real exchange rate (increase = real appreciation) - i_t = annualized nominal interest rate - Structural shocks vector ε_t′ = (ε_s,t, ε_d,t, ε_x,t, ε_i,t)′ (mutually uncorrelated, i.i.d. in base specification). - Behavioral equations (coefficients preserved exactly): - IS equation: - ỹ_t = 0.5·E_t(ỹ_{t+1}) + 0.5·ỹ_{t-1} − 0.2·(0.5·(i_t − E_t(π_{t+1})/̅r) ) + 0.5·q̃_t + ε_s,t - New Keynesian Phillips curve: - π_t = 0.5·E_t(π_{t+1}) + 0.5·π_{t-1} + 0.15·ỹ_t − 0.15·q̃_t + ε_d,t - Uncovered interest parity: - q̃_t = 0.5·E_t(q̃_{t+1}) + 0.5·q̃_{t-1} + (1/4)·(i_t − E_t(π_{t+1})/̅r^*) + ε_x,t - Taylor-type monetary policy rule: - i_t = 0.5·(r̅ + 1.4·E_t(π_{t+1}) + 0.5·E_t(ỹ_{t+1})) + 0.5·i_{t-1} + ε_i,t - Key modeling and identification choices - Shocks assumed i.i.d. (equation (7)) so distributed-lag dynamics arise from behavioral lags. - Focus on short-run (contemporaneous) identification restrictions in the SVAR tradition (CEE motivation). - DSGE solutions constructed to have exact finite-order VAR representations to eliminate truncation bias. - Researcher estimates reduced-form VAR x_t = A(L) x_{t-1} + u_t with u_t = S ε_t and zero restrictions on S used for identification. - Experimental variations (overview) - Baseline: valid identification, adequate data (Section 4). - Quantify sources of weak transmission (Section 5). - Core Monte Carlo investigations: - Short data samples (Section 6). - Volatility and measurement error (Section 7). - High-frequency supply shocks (Section 8). - Combined effects (Section 9). - Identification caveat (Section 10): mis-specified policy regime examples (e.g., authorities de facto target money while researcher assumes Taylor rule). ### Motivating CEE-recursive structure: definition, economics, and simulation findings - CEE-recursive identification: definition and justification - “CEE-recursive”: system orderable into two or more block-recursive segments with the interest rate in its own diagonal block (weaker than full Cholesky). - Short-run restrictions refer to zero restrictions on contemporaneous structural matrix ܤ ଴; block-triangular structure preserved by inversion. - Motivation: behavioral lags and information assumptions (central bank vs private sector information sets) justify block-recursive zero restrictions. - Two block-recursive identification strategies - CEE-PS (private sector informed) - Interest rate first in recursive ordering and affects all other variables contemporaneously. - Private sector has full information; central bank observes endogenous variables only with a lag. - Rationale: plausible in LICs where central bank has less timely information than private sector. - CEE-CB (central bank informed) - Central bank has full information; private sector does not observe the monetary-policy shock contemporaneously. - Interest rate does not affect other endogenous variables contemporaneously because private sector reacts to forecasted rate based on t−1 information. - Reflects advanced-country VAR practice attributing informational advantage to central bank. - Open-economy simultaneity challenge - Kim and Roubini (2000): interest rate cannot occupy its own diagonal block unless either the central bank does not respond contemporaneously to current exchange rate (CEE-PS) or the exchange rate does not respond contemporaneously to current interest rate (CEE-CB). - Non-recursive short-run restrictions or long-run restrictions are alternatives. - Baseline Monte Carlo experiment (Figure 1; CEE-PS) - Data: 1,000 independent simulated samples, each 40 quarters long. - VAR estimated with four lags (VAR(4)) though true model is VAR(1). - Identification: CEE-PS. - Assumes equal variances for the four structural shocks. - Inference: Bayesian estimation with standard errors computed by a Gibbs Sampler with 1,000 draws; researcher treats t ratios as asymptotically normal and applies 10 percent significance threshold. - Key quantitative simulation findings (baseline) - True model IRFs (Figure 1a): - On impact, a 100 basis point increase in the interest rate leads to a one percent contraction in inflation. - On impact, a 100 basis point increase in the interest rate leads to a reduction in the output gap by around 0.7% of GDP. - Estimation performance under baseline (CEE-PS, 40 years quarterly): - Median estimated IRFs track true IRFs closely; hump-shaped responses for real exchange rate, inflation, and output are recovered. - Estimated IRs for output and inflation show only trivial small-sample attenuation at the median. - For the first few quarters, fully 90 percent or more of point estimates lie on the correct side of zero. - However, distribution of t ratios implies that roughly half of the t statistics fail to reject the null when one end of the population distribution of IRs is close to zero — researcher will tend to reject the null only about half the time. - Alternative information structure (CEE-CB): - Model parameters identical but true impulse responses are much weaker (vertical scales change). - Median estimated IRF tracks true IR closely but 5th and 95th percentiles are more dispersed and there is substantial loss of power. - Low-power experiments: - Scaling down transmission elasticities in IS and PC by 75 percent: - True MTM weakened, especially on real activity. - Median estimated IRs remain close to true IRs; spread of estimated IRs little affected. - Scope for confident inference about MTM cut roughly in half. - Reducing lag parameter in monetary-policy rule by 75 percent (less interest-rate smoothing): - Monetary policy shocks pass through much more weakly into long rates and spending. - Median estimated IRs faithfully reproduce very weak true IRs; virtually no scope to reject the null of zero monetary policy effects. - Overall implication from CEE experiments - With a valid block-recursive identification scheme and sufficient data, structural VARs with short-run restrictions recover the true MTM at the median whether strong or weak. - Population dispersion in estimated IRs is not substantially affected by strength of true MTM. - Weaker true MTM reduces power of tests against the null of no response; with only one data set (even 40 years), a researcher may conclude MTM is missing even when a plausibly weak MTM exists. ### Small samples, volatility, measurement error, HP-filtering, and combined effects - Small sample sizes and implications for VAR inference - Short data samples central constraint in LIC research; quarterly GDP data limited: only fourteen of the seventy low-income countries in IMF databases have any quarterly GDP data, with sample lengths ranging from 1 to 24 years. - Experiment: CEE-PS baseline with 10 years of quarterly data versus 40 years: - Basic shape of true IRs reproduced but median estimated IRs are "discernibly attenuated over the first half-dozen periods" relative to 40-year case. - Widening in population distribution of IR point estimates. - Power of statistical tests (bootstrapped SEs) is 30 to 50 percent smaller with 10 years of data than with 40 years. - Interpretation: short samples produce wide confidence bands — reflect estimation uncertainty, not necessarily on-the-ground instability. - Volatility versus measurement error: differential impacts - True economic volatility leaves VAR-based inference approximately unchanged; measurement error rapidly undermines inference. - Intuition: - In VAR/AR(1) examples scaling up all shock variances tends to cancel out in sampling variances of VAR coefficients; limiting distribution in AR(1) independent of shock variance. - Monte Carlo: doubling variances of all four DSGE shocks has no discernible effect on impulse response distributions or t ratios. - Measurement error experiment: - Added classical measurement error in GDP gap and inflation (but not real exchange rate) by adding white noise with variance equal to 20 percent of variance of structural shocks (section 4 baseline, 40 years quarterly, CEE-PS). - Effects: - Point estimates attenuated toward zero in first two quarters: - GDP gap: estimated effects slightly more than half of true effects in first two quarters; little impact later. - Inflation: larger and more persistent attenuation through first two quarters. - Dispersion of estimated IRs little affected but power of t-ratio tests deteriorates badly during quarters with strongest attenuation bias. - If measurement errors are 100 percent of variance of structural shocks, power of t-ratio tests for output gap and inflation deteriorates to about 20 to 40 percent (results not shown). - Empirical evidence: Ley and Misch find variance of deviations between final and early estimates of annual real GDP is about double in LICs relative to OECD (both excluding resource-rich countries). - High-frequency supply shocks, HP filtering, and measurement error in GDP gap - GDP gap unobservable; common proxy assumes potential GDP follows a slow-moving trend; one-sided HP filtering (quarterly smoothing parameter 1600) is common. - In LICs transitory supply shocks (e.g., droughts, sectoral concentration) may be larger → increased measurement error when potential GDP proxied by slow-moving trend. - Modeling (equations preserved): - Actual output y_t = y_t^n + ỹ_t^ (equation (12)), where y_t^n = natural GDP and ỹ_t^ is model-generated gap. - Natural GDP decomposed y_t^n = y_t^{n,trend} + y_t^{n,transitory}, ∆y_t^{n,trend} = g̅ + ϵ_t^{n,trend}, g̅ = 0.02; y_t^{n,transitory} AR(1) with variance zero outside LICs (equation (13)). - Calibration: variance of ϵ_t^{n,trend} set to be 1/1600th of variance of model-based gap to justify HP smoothing parameter 1600. In LIC environment Var(ϵ_t^{n,transitory}) = Var(ϵ_t^{n,trend}) / (1 − ρ^2). - Experimental procedure: - In each of 1,000 simulation runs researcher observes actual output y_t and applies one-sided HP filter to measure gap ỹ_t^o (HP-cycle). - Even with no high-frequency component in natural GDP, HP filtering induces measurement error because HP-cycle estimator equals true gap plus difference between natural GDP and its HP trend → persistent measurement error. - Results: - Benchmark with no transitory component (Var(y_t^{n,transitory}) = 0): impact on inference confined to GDP responses which show modest initial attenuation; t ratios not strongly affected. Considerable scope remains for qualitatively accurate inference about transmission to output. Inference about inflation even less affected. - Case with transitory supply shocks in natural GDP with variance equal to that of true model-based GDP gap: - HP filter over-smooths GDP series; measurement error exacerbated. - Inference deteriorates: transmission appears weak and unreliable with respect to true GDP gap; slightly worse with persistence in measurement error (e.g., ρ = 0.9 produces similar results). - Combined effects (short samples + measurement error + high-frequency supply shocks) - Combined experiment (strong MTM but 10 years of quarterly data, 20 percent measurement error, i.i.d. shocks to potential output): - VAR estimates substantially biased downwards: median estimated impulse response of output to interest rate shock is about half of true value. - For inflation, median estimated impact effect of a monetary policy contraction is zero. - Uncertainty high; VAR has very little power — only about one third of baseline power — to extract MTM. - Further adjustment: reducing smoothing parameter in reaction function by half produces even stronger attenuation and VAR has only about 20 percent power to reject null. ### Identification challenges in LICs: mis-ordering, money information, and practical remedies - Identification challenges in LIC environments - Correct identification of monetary policy shocks is assumed in baseline; incorrect identification invalidates VAR inference. - Likely more severe in LICs because: - No consensus on behavioral lags and information sets. - Central banks in LICs tend to be far less transparent; policy rule less evident. - Two illustrative identification errors - Error type 1: Researcher imposes CEE-CB when true structure is CEE-PS (interest rate placed too late in recursive ordering). - When data generated by CEE-PS but researcher imposes CEE-CB: - Estimated impulse responses are “weak and unreliable”: essentially zero economically and statistically. - Median estimated IRFs approximate weaker CEE-CB responses despite true CEE-PS responses being much stronger. - Dispersion of estimated IRFs dramatically wider. - Bootstrapped SE tests have essentially no power to reject null even when true effects are extremely powerful. - Error type 2: Authorities use a hybrid rule placing weight on money deviations but researcher ignores money information. - Money demand specification (change in money Δm_t as in source): - Δm_t = a_m (y_t - y*_t) + b_m Δi_t + u^m_t (equation (14) structure). - Hybrid policy rule (Andrle et al. (2013) structure): - λ (i^T_t - i^{T*}_t) + (1-λ) (i^T_t - i^{M*}_t) = ε^p_t (equation (16) structure) where λ defines weight on interest-rate rule (λ=1 → Taylor-type; λ=0 → pure money targeting). - Solving yields implicit interest-rate rule with composite shock term ϵ^m_t capturing money supply and money demand shocks and contemporaneous aggregate shocks affecting interest rate. - Researcher observing x_t = (ĩ_t, y_t, π_t)' will only correctly identify monetary policy shock if λ = 1. For any λ ≠ 1, money growth provides central bank information the researcher cannot decompose, preventing clean identification. - Example: with λ = 0.95 (authorities place only a small weight on money deviations), even this minor deviation: - Strongly attenuates median estimated impulse responses. - Greatly reduces statistical power relative to baseline. - Depending on shock variances and λ, misspecification can even reverse sign of estimated IRFs. - Limits of remedies and identification strategies - In mis-ordered information structure case, experimenting with alternative recursive orderings could help. - In hybrid-rule case, even with a full five-variable vector, neither recursive identification strategy can isolate monetary policy shock cleanly. - Alternative strategies (long-run restrictions, instrumental variables, narrative identification, microdata) might help but require strong, often unavailable, information. - Money-demand specifications in DSGE traditions that include expected inflation and other variables can leave no contemporaneous zero restrictions available to identify monetary shocks. - Implications for VAR power and detection of MTM - Even with proper identification and ample data, VARs sensitive to DGP mis-specification (Sims’s critique). - Key findings: - A weaker MTM is hard for a typical VAR to detect, even with 40 years of pristine data and correct identification: point estimates mildly attenuated but power to reject null of missing MTM is very low. - LIC-specific features — short time series, measurement error, output-gap estimation, volatile data, high-frequency shocks to natural GDP, and reduced interest-rate smoothing — greatly weaken VAR power: - Small samples moderately attenuate median point estimates and raise uncertainty. - Combined effects can almost entirely eliminate VAR power even when true MTM is strong. - Reduced interest-rate smoothing further undermines detectability. - Practical considerations and potential ways forward - Using monthly data: - Ten years of monthly data yield 120 observations versus 40 (effective information increases less than three-fold). - Contemporaneous timing restrictions more plausible; CEE-recursiveness more credible. - Constraint: measurement error likely greater in monthly real-activity measures. - Alternative empirical approaches worth pursuing in LICs: - Country-specific analyses tailored to institutional frameworks. - Identification via long-run restrictions. - Narrative or case-study approaches to identify large monetary policy shocks. - Loan-level or microdata to assess bank-lending channels. - Bayesian methods that impose more economic structure and exploit priors to cope with data scarcity. - Policy implications: - Given uncertainty about MTM, options include passive monetary frameworks (fixed exchange rates or money targeting) or active learning-by-doing. - Textbook money targeting generally impractical: LICs with de jure money targeting often miss targets and adjust subsequent targets rather than force money back to trend. - Exchange rate flexibility may be stabilizing even when MTM uncertain. - Learning and further empirical work are critical complements to monetary regime reform. ### Key quantitative and experimental details (explicit figures and parameters) - Simulation design and numeric experiment settings - Number of simulations: 1,000. - Sample length each: 40 quarters (baseline); alternative experiments use 10 years (40 quarters vs 10 years = 40 vs 40 quarters?—experiment compares 40 years of quarterly data vs 10 years of quarterly data). - VAR estimated with four lags (VAR(4)) though true model is VAR(1). - Gibbs Sampler draws for standard errors: 1,000. - Significance hurdle used by researcher: 10 percent. - Representative quantitative IRF facts (baseline CEE-PS): - A 100 basis point increase in the interest rate leads to a one percent contraction in inflation on impact. - A 100 basis point increase in the interest rate leads to a reduction in the output gap by around 0.7% of GDP on impact. - Parameter and coefficient values preserved in DSGE behavioral equations: - IS: coefficients 0.5 on E_t(ỹ_{t+1}), 0.5 on ỹ_{t-1}, −0.2·(0.5·(...)) on real interest term, 0.5 on q̃_t. - PC: coefficients 0.5 on E_t(π_{t+1}), 0.5 on π_{t-1}, 0.15 on ỹ_t, −0.15 on q̃_t. - UIP: coefficients 0.5 on E_t(q̃_{t+1}), 0.5 on q̃_{t-1}, (1/4) on (i_t − E_t(π_{t+1})/̅r^*). - Taylor rule: i_t = 0.5·(r̅ + 1.4·E_t(π_{t+1}) + 0.5·E_t(ỹ_{t+1})) + 0.5·i_{t-1} + ε_i,t. - Example solution matrices and mappings (preserved exactly as in source for CEE-PS and CEE-CB; structure reported in Appendix A with explicit numeric entries). - HP-filtering and trend calibration - Quarterly one-sided HP smoothing parameter: 1600. - Trend growth parameter g̅ = 0.02. - Variance calibration: Var(ϵ_t^{n,trend}) = Var(model-based gap) / 1600. - In LIC environment Var(ϵ_t^{n,transitory}) = Var(ϵ_t^{n,trend}) / (1 − ρ^2) for AR(1) persistence ρ. - Hybrid money-targeting example - Weight λ on interest-rate rule; example λ = 0.95 demonstrates strong attenuation of estimated IRs even with small deviation from pure Taylor rule. ### Summary of policy relevance and recommended empirical directions - Main diagnostic conclusions - Identification errors (incorrect recursive ordering, neglected money information in hybrid rules) can strongly attenuate or distort estimated MTM even when true MTM is strong. - LIC data environments (short samples, measurement error, output-gap estimation) sharply reduce VAR power to detect MTM; combined effects can render detection effectively impossible. - Practical steps and research directions - Use higher-frequency data (monthly) where available while accounting for increased measurement error in monthly real-activity series. - Pursue microdata (loan-level, bank-level) and narrative identification to assess bank-lending channels and large policy shocks. - Employ Bayesian methods with informative priors and country-specific institutional modeling to mitigate small-sample problems. - Consider long-run restrictions, instrumental-variable approaches, and country-tailored identification strategies rather than blind application of standard short-run recursive SVARs. - Policy implications - Uncertainty about MTM argues for cautious policy design, learning-by-doing, and continued empirical investigation rather than paralysis. - Textbook money targeting generally impractical in LICs; exchange rate flexibility may be stabilizing when MTM is uncertain. *Source: _wp1690 (IMF working paper; sections 1, 3, 6, 10, and Appendix content summarized verbatim as provided)* ### 1. Introduction ........................................................................................................ ### _wp1690 - 1. Introduction ### Research question and motivation - Two competing explanations for weak and imprecise monetary transmission mechanism (MTM) evidence in low-income countries (LICs): - “Facts on the ground”: small/underdeveloped financial markets, fixed or heavily managed exchange rates, severe financial frictions, imperfect competition in banking — implying weak links between central-bank-controlled short-term interest rates and aggregate-demand channels (longer-term rates, exchange rate, lending). - “Limitations of the method”: data-intensive, atheoretic VAR/SVAR methods fail to measure a potentially strong MTM accurately in LIC research environments. - Central question: If a strong MTM exists, can standard structural VAR (SVAR) methods uncover it in LIC-like research environments characterized by short samples, measurement error, high volatility (notably large temporary supply shocks), and non-transparent policy regimes? ### Empirical strategy and methodology - Approach: Use a DSGE as the data-generating process (DGP) that embodies a strong MTM, then apply standard SVAR identification and estimation procedures to simulated data from that DSGE to assess the sampling and inferential properties of VAR-based methods. - Monte Carlo design: - Generate multiple independent simulated datasets from the DSGE solution. - Within each simulated dataset, an empirical researcher estimates a reduced-form VAR and imposes contemporaneous (short-run) identification restrictions to recover structural monetary policy shocks and compute impulse response functions (IRFs). - Analyze the median estimated IRF, distribution of estimated IRFs across simulations, associated t-ratios, and the power of conventional t-ratio tests against the hypothesis of zero response. ### DSGE model structure (four-state-variable, linearized, stationary) - Endogenous quarterly variables x_t′ = (ỹ_t, π_t, q̃_t, i_t)′ where: - ỹ_t = GDP gap (actual minus unobserved potential GDP) - π_t = inflation rate - q̃_t = real exchange rate (increase = real appreciation) - i_t = annualized nominal interest rate - Structural shocks vector ε_t′ = (ε_s,t, ε_d,t, ε_x,t, ε_i,t)′ (mutually uncorrelated, i.i.d. in base specification). - Behavioral equations (coefficients and structure preserved exactly as in the source): - IS equation: - ỹ_t = 0.5·E_t(ỹ_{t+1}) + 0.5·ỹ_{t-1} − 0.2·(0.5·(i_t − E_t(π_{t+1})/̅r) ) + 0.5·q̃_t + ε_s,t - (presented in source as equation (3) with these numeric coefficients) - New Keynesian Phillips curve: - π_t = 0.5·E_t(π_{t+1}) + 0.5·π_{t-1} + 0.15·ỹ_t − 0.15·q̃_t + ε_d,t - (equation (4)) - Uncovered interest parity: - q̃_t = 0.5·E_t(q̃_{t+1}) + 0.5·q̃_{t-1} + (1/4)·(i_t − E_t(π_{t+1})/̅r^*) + ε_x,t - (equation (5)) - Taylor-type monetary policy rule: - i_t = 0.5·(r̅ + 1.4·E_t(π_{t+1}) + 0.5·E_t(ỹ_{t+1})) + 0.5·i_{t-1} + ε_i,t - (equation (6)) ### Key modeling and identification choices - Shocks assumed i.i.d. (equation (7)) rather than AR(1) so distributed-lag dynamics arise from behavioral lags; simplifies DSGE solution and VAR representation. - Focus on short-run (contemporaneous) identification restrictions in the SVAR tradition (Christiano, Eichenbaum and Evans (1999) motivated) that limit contemporaneous interactions among the four variables to identify monetary policy shocks. - The DSGE solution is required to have an (approximately) finite-order VAR representation for VAR methods to have a chance at uncovering MTM features; the authors state their solutions have exact finite-order VAR representations, eliminating truncation bias in experiments. - The researcher estimates a reduced-form VAR: - x_t = A(L) x_{t-1} + u_t (equation (1) in source) - Reduced-form innovations u_t are related to structural shocks by u_t = S ε_t (equation (2) in source), with zero restrictions on elements of S used for identification. ### Experimental variations and issues to be examined - Baseline: valid identification scheme and adequate data — document VAR success in recovering MTM under both strong and weak transmission (Section 4). - Weak transmission sources to be quantified (Section 5), some plausibly related to LIC structural characteristics or to monetary policy regimes. - Core Monte Carlo investigations (Sections 6–9): - Short data samples and their effects on precision (Section 6). - Volatility and measurement error impacts (Section 7). - High-frequency supply shocks and their role in obscuring transmission to output but not necessarily to other variables (Section 8). - Combined effects of these conditions (Section 9). - Identification caveat (Section 10): when the central bank’s operating regime is poorly understood (opacity, scarce research), correct identification is especially challenging and estimates of MTM can be substantially misleading; example: authorities that de facto target money while researcher assumes a Taylor-type rule. ### Intended outcomes and policy relevance - The experiments are designed to discriminate whether weak/uncertain VAR-based evidence on MTM in LICs is driven primarily by actual weak transmission or by method limitations in LIC-like research environments. - If methodological limitations dominate, policymakers and researchers should discount naive VAR evidence and pursue alternative empirical approaches (e.g., bank-level or loan-level microdata) that are more robust to LIC data weaknesses. - The conclusion section (Section 11) will summarize findings and discuss extensions and policy implications based on the Monte Carlo evidence. *Source: _wp1690 - 1. Introduction* ### 3. Motivating CEE-recursive structure ### 3. Motivating CEE-recursive structure ### CEE-recursive identification: definition and justification - Structural simultaneous-equations model (equation (8)) implies reduced-form VAR when ܤ ଴ is invertible, with ܣ ሺ ܮ ሻ ܤൌ ଴ ିଵ ܤ ሺ ܮ ሻ and ܤൌܤ ଴ ିଵ (relationship between structural and reduced-form innovations given by equation (2)). - “Short-run restrictions” refer to restrictions on the elements of ܤ ଴. - Cholesky decomposition imposes full recursiveness (ܤ ଴ lower triangular). Christiano, Eichenbaum and Evans (1999) show that impulse responses to monetary-policy shocks can be recovered under the weaker condition that the system is contemporaneously block-lower-triangular with the interest rate in its own diagonal block. - Any system orderable into two or more block-recursive segments with the interest rate in its own diagonal block is termed “CEE-recursive.” - Matrix inversion preserves block-triangular structure, so zero restrictions can be motivated with reference to ܤ ଴ or ܤ equivalently. - Example: equation (9) illustrates CEE recursiveness in a seven-variable case where “X” denotes unrestricted (nonzero) elements; the interest rate occupies its own diagonal block. ### Economic motivation for block-recursive zero restrictions - Restrictions are typically motivated by: - Behavioral lags: some variables respond to the interest rate only with a lag. - Information assumptions: the monetary authority observes some variables contemporaneously and reacts; other variables are observed by the authority only with a lag or are excluded from the policy reaction function. - Upper block in the example: three-variable system recursively prior to the interest rate and to the third block; monetary authority observes and responds contemporaneously; these variables respond to interest rate only with a lag. - Third block: variables recursively posterior to the interest rate; they are affected immediately by monetary policy but are not observed by the monetary authority contemporaneously or are excluded from the policy reaction contemporaneously. ### DSGE solutions and need for additional restrictions - Under full information, the DSGE solution will generally be highly simultaneous; monetary policy affects all endogenous variables contemporaneously, so the interest rate does not occupy its own diagonal block. - Expectation variables cause any endogenous variable in an agent’s information set to contemporaneously affect all endogenous variables influenced by that agent’s forecasts; with expectations in all equations, full simultaneity results. - To obtain a data-generating process identifiable via short-run restrictions, additional informational asymmetry assumptions are imposed rather than behavioral lags. - Partial and mixed information (different agents having different information sets) are used; models solved via an undetermined coefficients approach (Christiano (2002) variant) yield exact VAR(1) representations with CEE-recursive ܤ matrices. ### Two block-recursive identification strategies - CEE-PS (private sector informed): - Interest rate is first in the recursive ordering and affects all other variables contemporaneously; corresponds to the lower sub-system in equation (9). - Private sector has full information; central bank observes endogenous variables only with a lag. - Monetary policy committee sets systematic policy at beginning of period (based on t-1 information); shocks hit and are observed by private sector at time t, which reacts immediately; central bank can only adjust at next period (next MPC meeting). - Rationale: plausible in LIC contexts where central bank has less access to timely information than private sector. - CEE-CB (central bank informed): - Central bank sets interest rate with full information, but interest rate does not affect other endogenous variables contemporaneously because the private sector does not observe the monetary-policy shock contemporaneously and reacts to its forecast of time-t interest rate based on t-1 information. - Corresponds to alternative sub-system in equation (9) and follows Christiano, Eichenbaum and Evans (2005). - Reflects common advanced-country VAR practice attributing informational advantage to the central bank. ### Open-economy simultaneity challenge - Kim and Roubini (2000): interest rate cannot occupy its own diagonal block unless either - the central bank does not respond contemporaneously to the current exchange rate (CEE-PS), or - the exchange rate does not respond contemporaneously to the current interest rate (CEE-CB). - Otherwise, interest rate and exchange rate are simultaneously determined regardless of block-recursive ordering. - Structural VAR literature handles this via non-recursive short-run restrictions and/or theoretically motivated long-run restrictions; non-recursive identification is noted as a potential extension. ### Empirical experiments and estimation setup (overview of Sections 4–5) - Baseline experiment (Figure 1): - Validly identified CEE-recursive VAR using 40 years of quarterly data. - Assumes equal variances for the four structural shocks. - Information structure: CEE-PS. - Researcher estimates VAR with four lags (VAR(4)) despite true model being VAR(1). - 1,000 data samples generated, each 40 quarters long, from independent simulations of the DSGE solution (independent draws on shock vector ߝ ௧). - For each sample, researcher estimates VAR and imposes CEE-PS identifying restrictions. - Impulse responses focus on the monetary policy shock. - Inference: Bayesian estimation with standard errors computed by a Gibbs Sampler algorithm with 1,000 draws; researcher treats t ratios as asymptotically normal and applies 10 percent significance threshold. ### Key quantitative findings from simulations - True model IRFs (bold line with dots in Figure 1a): - On impact, a 100 basis point increase in the interest rate leads to a one percent contraction in inflation. - On impact, a 100 basis point increase in the interest rate leads to a reduction in the output gap by around 0.7% of GDP. - Simulation experiment details: - Number of simulations: 1,000. - Sample length each: 40 quarters. - VAR estimated with four lags. - Gibbs Sampler draws for standard errors: 1,000. - Significance hurdle used by researcher: 10 percent. - Estimation performance under baseline (CEE-PS, ample high-quality data): - Median estimated IRFs track true IRFs closely; conventional hump-shaped responses for real exchange rate, inflation, and output to a monetary contraction are recovered. - Estimated impulse responses for output and inflation show only trivial small-sample attenuation at the median. - For the first few quarters, fully 90 percent or more of point estimates lie on the correct side of zero. - However, because the researcher has only one data sample, inference is less confident: the distribution of t ratios across simulations implies that when one end of the population distribution of IRs is close to zero, roughly half of the t statistics fail to reject the null. - As a result, the researcher will tend to reject the null only about half the time. - Alternative information structure (CEE-CB, Figure 2): - Model parameters identical, but true impulse responses are much weaker (note change in vertical scales across figures). - Weakening driven by lags that dilute impact of monetary policy in CEE-CB case. - Median estimated IRF still tracks true IR closely, but 5th and 95th percentiles are more dispersed and there is substantial loss of power. - Deterioration in inference reflects smaller true effect sizes. - Low-power experiments (Figures 3 and 4): - Figure 3: uniformly scale down transmission elasticities in IS and Phillips curves by 75 percent (relative to baseline). - True MTM weakened, especially on real activity. - Median estimated IRs continue to correspond closely to true IRs. - No discernible impact on spread of estimated IRs. - Impact on inference: scope for confident inference about MTM is cut roughly in half. - Figure 4: leave transmission elasticities unchanged but reduce the lag parameter in the monetary-policy rule by 75 percent (less interest-rate smoothing). - Monetary policy shocks pass through much more weakly into long rates and spending. - True impulse responses decline slightly more sharply than when transmission elasticities reduced by same proportion; shapes remain virtually identical. - Minimal evidence of bias in impulse responses: median estimated IRs faithfully reproduce very weak true IRs. - Virtually no scope to reject the null hypothesis of zero monetary policy effects. - Overall implication: - Given a valid block-recursive identification scheme and sufficient data, structural VARs with short-run restrictions recover the true MTM at the median whether strong or weak. - Population dispersion in estimated IRs is not substantially affected by the strength of the true MTM. - Therefore, weaker true MTM reduces the power of tests against the null of no response; with only a single data set (even 40 years long), a researcher may conclude the MTM is missing even when a plausibly weak MTM exists. *Source: _wp1690 - 3. Motivating CEE-recursive structure* ### 6. Small sample sizes generate low precision ### 6. Small sample sizes generate low precision ### Small sample sizes and implications for VAR inference - Short data samples are a central constraint in LIC research environments; structural reforms and regime changes mean the current data-generating process often has not been in place for long. - Quarterly data availability is limited: only fourteen of the seventy low-income countries in IMF databases have any quarterly GDP data (listed in the source), with sample lengths ranging from 1 to 24 years. - Experiment: CEE-PS baseline identification with 10 years of quarterly data versus 40 years: - The basic shape of true impulse responses is reproduced, but median estimated impulse responses are "discernibly attenuated over the first half-dozen periods" relative to the 40-year case. - Reduction in sample size produces substantial widening in the population distribution of IR point estimates. - Power of statistical tests for IRs to reject the null of no monetary policy effect (based on bootstrapped standard errors) is 30 to 50 percent smaller with 10 years of data (solid line) than with 40 years of data (bold line with dots). - Interpretation: - Estimation of the strength of the MTM in LICs with VAR methods will generally produce wide confidence bands around estimated IRs when data spans are limited. - Wide confidence bands in short samples should be interpreted as uncertainty about estimates, not as confirmation of on-the-ground instability in policy effects. ### Volatility versus measurement error: differential impacts on VAR inference - Two drivers of data variability considered: true economic volatility and measurement error. - Main finding: true economic volatility leaves VAR-based inference approximately unchanged, while measurement error rapidly undermines inference. - Intuition (stochastic-regressor and AR(1) sketches from the source): - In a stochastic-regressor model y_t = x_t β + u_t, the OLS precision depends on the variance of u_t and the variance of x_t; volatility in the independent variable enhances inference while volatility in the disturbance undermines it. - In a VAR (e.g., x_t = α x_{t-1} + v_t), the variance of x_t is a function of the variance of shocks v_t; scaling up all shock variances tends to cancel out in the sampling variances of VAR coefficients. The limiting distribution in the AR(1) case is independent of the shock variance. - Monte Carlo confirmation: doubling variances of all four shocks in the DSGE model has no discernible effect on population distributions of impulse responses or t ratios (results not shown). - Measurement error effects: - Classical measurement error in GDP gap and inflation (but not real exchange rate) was induced by adding white noise with variance equal to 20 percent of the variance of the structural shocks (section 4 baseline, 40 years quarterly, CEE-PS). - Point estimates show attenuation towards zero in the first two quarters: - GDP gap: estimated effects are slightly more than half of true effects in the first two quarters, little impact in later quarters. - Inflation: larger and more persistent attenuation effects, persisting through the first two quarters. - Dispersion of estimated IRs is little affected, but the power of t-ratio tests deteriorates badly during quarters when attenuation bias is most pronounced. - Comment on magnitude: if measurement errors are 100 percent of the variance of structural shocks, the power of t-ratio tests for output gap and inflation deteriorates to about 20 to 40 percent (results not shown). - Empirical evidence cited: Ley and Misch find the variance of deviations between final and early estimates of annual real GDP is about double in LICs relative to OECD countries (both excluding resource-rich countries). ### High-frequency supply shocks, HP filtering, and measurement error in the GDP gap - The GDP gap is unobservable and typically proxied by assuming potential GDP follows a slow-moving trend; one-sided HP filtering (quarterly smoothing parameter 1600) is a common practice. - Natural GDP includes slow-moving processes and transitory supply-side shocks; in LICs transitory supply shocks (e.g., droughts, sectoral concentration) may be larger and thereby increase measurement error when potential GDP is proxied by a slow-moving trend. - Modeling approach (equations preserved as in source): - Actual output constructed as y_t = y_t^n + ỹ_t^, where ỹ_t^ is the model-generated GDP gap and y_t^n is natural GDP (equation (12)). - Natural GDP decomposed as y_t^n = y_t^{n,trend} + y_t^{n,transitory}, with ∆y_t^{n,trend} = g̅ + ϵ_t^{n,trend}, g̅ = 0.02, and y_t^{n,transitory} an AR(1) with variance zero outside LICs (equation (13)). - Calibration: variance of ϵ_t^{n,trend} set to be 1/1600th of variance of model-based gap to justify HP smoothing parameter of 1600. In the LIC environment the variance of supply shocks is specified as Var(ϵ_t^{n,transitory}) = Var(ϵ_t^{n,trend}) / (1 − ρ^2), where ρ is the AR(1) parameter. - Experimental procedure: - In each of 1,000 simulation runs the researcher observes actual output y_t and applies a one-sided HP filter to measure the gap (researcher’s GDP gap ỹ_t^o is the HP-cycle in actual GDP). - Even with no high-frequency component of natural GDP, this induces measurement error in the GDP gap because the HP-cycle estimator equals the true gap plus the difference between natural GDP and its HP trend—producing persistent measurement error. - Results: - Benchmark case with no transitory component in natural GDP (variance of y_t^{n,transitory} = 0): impact on inference is confined to GDP responses which show modest initial attenuation toward zero; t ratios not very strongly affected. Considerable scope remains for qualitatively accurate inference about transmission to output (impact and early steps). Inference about inflation is even less affected. - Case with transitory supply shocks in natural GDP with variance equal to that of the true model-based GDP gap: - HP filter over-smooths GDP series; measurement error in GDP gap is exacerbated. - Inference deteriorates correspondingly: transmission mechanism appears weak and unreliable with respect to the true GDP gap, slightly more so if there is persistence in the measurement error. - Figure 8 assumes white noise shocks; similar results arise with AR(1) shocks (e.g., ρ = 0.9). ### Combined effects: short samples, measurement error, and high-frequency supply shocks - Combined experiment: strong transmission mechanism, but data series are only 10 years long, there is 20 percent measurement error, and there are i.i.d. shocks to potential output that complicate output-gap estimation. - VAR estimates are substantially biased downwards: median estimated impulse response of output to an interest rate shock is about half of its true value. - For inflation, the median estimated impact effect of a monetary policy contraction is zero. - Uncertainty is high; the VAR has very little power—only about one third of the baseline power—to extract the MTM. - Further adjustment: reducing the smoothing parameter in the reaction function by half (instead of the 75 percent in section 5) produces even stronger attenuation of the true MTM and the VAR has only about 20 percent power to reject the null. *Source: _wp1690 - 6. Small sample sizes generate low precision* ### 10. Identification may be especially tricky in LICs ### 10. Identification may be especially tricky in LICs ### Identification challenges in LIC environments - Correct identification of monetary policy shocks is assumed in the baseline. Incorrect identification invalidates VAR inference and is likely to be a more severe problem in LICs because: - There is no general consensus on behavioral lags and information sets in the LIC environment. - Central banks in LICs tend to be far less transparent than those in high-income countries, making the nature of the monetary policy rule less evident. - As a result, identification of monetary policy shocks is likely to prove far more difficult in LICs than in high-income countries. ### Two illustrative identification errors examined - Error type 1: Researcher places the interest rate too late in the recursive ordering (imposes CEE-CB when true structure is CEE-PS). - When data are generated by CEE-PS but the researcher imposes CEE-CB identification: - The estimated impulse responses are “weak and unreliable”: essentially zero economically and statistically. - The median estimated IRFs approximate the weaker CEE-CB responses despite the true CEE-PS responses being much stronger. - Dispersion of estimated IRFs is dramatically wider than when CEE-CB is correct. - Bootstrapped standard-error-based tests will have essentially no power to reject the null of zero monetary policy effects even when true effects are extremely powerful. - Error type 2: Authorities use a hybrid rule that places weight on money deviations but the researcher ignores the money information. - Money demand specification (as in the source) for change in money Δm_t: - Δm_t = a_m (y_t - y*_t) + b_m Δi_t + u^m_t (equation (14) structure in source) - Interest rate that sets money growth to target i^M_t given by equation (15) in the source. - Hybrid rule (following Andrle et al. (2013)): - λ (i^T_t - i^{T*}_t) + (1-λ) (i^T_t - i^{M*}_t) = ε^p_t (equation (16) structure) - λ defines the weight placed on the interest-rate rule: when λ=1 the rule is a standard Taylor-type rule; when λ=0 policy is pure money targeting. - Solving yields an implicit interest-rate rule (equation (18) structure) where a composite shock term ϵ^m_t (ߝ_{t}^{m} in the source) captures money supply and money demand shocks and contemporaneous aggregate demand and supply shocks affect the interest rate contemporaneously. - The researcher observing the four-variable vector x_t = (ĩ_t, y_t, π_t)' will only correctly identify the monetary policy shock if ൌ1ߣ. For any ൏1ߣ, money growth provides the central bank with information that the researcher cannot decompose, preventing clean identification. - Example: With λ = 0.95 (authorities place only a small weight on money deviations), even this minor deviation: - Strongly attenuates the median estimated impulse responses. - Greatly reduces statistical power relative to the baseline. - Depending on shock variances and λ, misspecification can even reverse the sign of estimated IRFs. ### Limits of remedies and identification strategies - In the first case (alternative information structure), experimenting with alternative recursive orderings could help. - In the hybrid-rule case, even with a full five-variable vector, neither recursive identification strategy can isolate the monetary policy shock cleanly. - Alternative identification strategies (e.g., imposing other restrictions or instrumental-variable approaches) might help but are not trivial: - Money-demand specifications in DSGE traditions can include expected inflation and other variables, leaving no contemporaneous zero restrictions available to identify monetary shocks. - Correct identification would require precise knowledge of a complex policy framework; there is unlikely to be a one-size-fits-all solution. - Overall, incorrect identification is a prime suspect in explaining the “missing MTM.” ### Implications for VAR power and detection of MTM - Even with proper identification and ample high-quality data, VARs are sensitive to data-generating-process mis-specification (Sims’s critique). - Key findings on detection power: - A weaker—but otherwise standard—MTM is hard for a typical VAR to detect, even with 40 years of pristine data and correct identification: point estimates are at most only mildly attenuated, but power to reject the null of a missing MTM is very low. - LIC-specific features—short time series, measurement error, the need to estimate the output gap, volatile data, high-frequency shocks to natural GDP, and reduced interest-rate smoothing—greatly weaken VAR power: - Small samples moderately attenuate median point estimates and raise uncertainty. - Combined, short samples + measurement error + estimated output gap with high-frequency supply shocks almost entirely eliminate VAR power even when the true MTM is strong. - Reduced interest-rate smoothing further undermines detectability. - These conclusions hold under the CEE-PS baseline; qualitatively similar effects arise under CEE-CB, where the true MTM is already weaker and thus easier to hide. ### Practical considerations and potential ways forward - Using monthly data could improve inference because: - Ten years of monthly data yield 120 observations versus 40 (though effective information increases less than three-fold). - Contemporaneous timing restrictions become more plausible in monthly data, making CEE-recursiveness more credible. - Constraint: measurement error is likely greater in monthly real-activity measures. - Alternative empirical approaches worth pursuing in LICs: - Country-specific analyses tailored to institutional frameworks. - Identification via long-run restrictions (e.g., as in Mishra et al. (2014)). - Narrative or case-study approaches to identify large monetary policy shocks. - Loan-level or microdata studies to assess bank-lending channels. - Bayesian methods that impose more economic structure and exploit priors to cope with data scarcity. - Policy implications: - Given uncertainty about the MTM, some argue for passive monetary frameworks (fixed exchange rates or textbook money targeting); others argue for active learning-by-doing and recognize that policy action does not require precise quantitative knowledge—only a view about the sign of monetary effects. - Textbook money targeting is generally impractical: LICs with de jure money targeting often miss targets and adjust subsequent targets rather than force money back to trend. - Exchange rate flexibility may be stabilizing even when MTM is uncertain. - Learning and further empirical work are critical complements to monetary regime reform. ### Key takeaways - Identification errors (incorrect recursive ordering, neglected money information in hybrid rules) can strongly attenuate or distort estimated monetary transmission even when true MTM is strong. - LIC data environments (short samples, measurement error, output-gap estimation) sharply reduce VAR power to detect MTM; combined effects can make detection effectively impossible. - Alternative data frequencies (monthly), richer identification approaches, microdata, Bayesian methods, and careful country-specific modeling offer plausible paths forward—but challenges remain substantial. - Uncertainty about MTM argues for cautious policy design, learning-by-doing, and continued empirical investigation rather than paralysis. *Source: _wp1690 - 10. Identification may be especially tricky in LICs* ### References ### _wp1690 - References ### Bibliography — key works cited - Abuka, Charles; Ronnie K. Alinda; Camelia Minoiu; Jose-Luis Peydro; Andrea F. Presbitero (2015), “Monetary Policy in a Developing Country: Loan Applications and Real Effects”, IMF Working Paper No. 15/270. - Andrle, Michal; Andrew Berg; Enrico Berkes; R. Armando Morales; Rafael Portillo; Jan Vlček (2013), “Money Targeting in a Modern Forecasting and Policy Analysis System: an Application to Kenya”, IMF Working Paper WP/13/239, November. - Andrle, Michal; Andrew Berg; R. Armando Morales; Rafael Portillo; Jan Vlcek (2015), “On the Sources of Inflation in Kenya: A Model-Based Approach”, South African Journal of Economics, Vol 83, Issue 4, December. - Baldini, Alfredo; Jaromir Benes; Andrew Berg; Mai C. Dao; Rafael Portillo (2015), “Monetary Policy in Low-Income Countries in the Face of the Global Crisis: A Structural Analysis”, Pacific Economic Review, Volume 20, Issue 1, pages 149-192. - Batini, Nicoletta and Douglas Laxton (2007), “Under What Conditions Can Inflation Targeting be Adopted? The Experience of Emerging Marketst,” Central Banking, Analysis, and Economic Policies Book Series 11: pp. 467-506. - Berg, Andrew; Rafael Portillo; D. Filiz Unsal (2010), “On the Optimal Adherence to Money Targets in a New-Keynesian Framework: An Application to Low-Income Countries” IMF Working Paper WP/10/134, June. - Berg, Andrew; Luisa Charry; Rafael A. Portillo; Jan Vlcek (2013), “The Monetary Transmission Mechanism in the Tropics: A Narrative Approach” IMF Working Paper WP/13/197, September. - Berg, Andrew; Philippe D. Karam; Douglas Laxton (2006), “A Practical Model-Based Approach to Monetary Policy Analysis” IMF Working Paper WP/06/80, March. - Berg, Andrew; Stephen O’Connell; Catherine Pattillo; Rafael Portillo; Filiz Unsal (2015), “Monetary Policy Issues in Sub-Saharan Africa”, in Monga, Celestin and Justin Yifu Lin, Eds., The Oxford Handbook of Africa and Economics: Volume 2: Policies and Practices, Oxford. - Benes, Mirek; Jaromir Hurnik; David Vavra (2008), “Exchange Rate Management and Inflation Targeting: Modeling the Exchange Rate in Reduced-Form New Keynesian Models,” Czech Journal of Economics and Finance, Vol. 58(03-04), pages 166-194. - Boughton, James M.; George S. Tavlas (1991), “What Have We Learned about Estimating the Demand for Money? A Multicountry Evaluation of Some New Approaches,” IMF Working Papers 91/16. - Christiano, Lawrence J.; Martin Eichenbaum; Charles L. Evans (1999), “Monetary Policy Shocks: What Have We Learned?” In John B. Taylor and Michael Woodford, eds, Handbook of Macroeconomics, Vol 1A (Amsterdam: North Holland). - Christiano, Lawrence J.; Martin Eichenbaum; Charles L. Evans (2005), “Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy” Journal of Political Economy 113(1): February: 1-45. - Faust, Jon; John Rogers (2003), “Monetary Policy’s Role in Exchange Rate Behavior”, Journal of Monetary Economics, Volume 50, Issue 7. October. - Favero, Carlo A. (2001), Applied Macroeconometrics (Oxford: Oxford University Press). - Fernandez-Villaverde, Jesus; Juan Ff. Rubio-Ramirez; Thomas J. Sargent; Mark W. Watson (2005), “ABCs (and Ds) of Understanding VARs” American Economic Review 97(3): 1021-1026. - Hamilton, James D. (1994), Time Series Analysis (Princeton: Princeton University Press). - Leeper, Eric M.; David B. Gordon (1992), “In Search of the Liquidity Effect,” Journal of Monetary Economics, Vol. 29(3), pp. 341-369. - IMF (2015), Evolving Monetary Policy Frameworks in Low-Income and Other Developing Countries, Washington: International Monetary Fund. - Levin, Andrew T. (2014), “The Design and Communication of Systematic Monetary Policy Strategies,” Journal of Economic Dynamics and Control, Vol 49, pp. 52-69. - Li, Bin Grace (2008), “Evaluating Structural Vector Autoregression Models in Monetary Economies”, University of Chicago, Manuscript. - Jerven, Morten (2013), Poor Numbers: How We are Misled by African Development Statistics and What to do about it. Ithaca, N.Y. Cornell University Press. - Kim, Soyoung; Nouriel Roubini (2000), “Exchange Rate Anomalies in the Industrial Countries: A Solution with a Structural VAR Approach” Journal of Monetary Economics 45: 561-586. - Ley, Eduardo; Florian Misch (2014), “Output data revisions in Low-Income Countries”, conference presentation, IMF-DFID conference on Macroeconomic Challenges Facing Low-Income Countries: New Perspective Washington DC (Jan 2014). - Mbowe, Wilfred (2012), “The Bank Lending Channel of Monetary Policy Transmission: Dynamic Bank-Level Panel Data Analysis on Tanzania” Bank of Tanzania, August 3. - Mishra, Prachi; Peter Montiel (2013), “How Effective is Monetary Transmission in Low-Income Countries? A Survey of the Empirical Evidence” Economic Systems. - Mishra, Prachi; Peter Montiel; Peter Pedroni; Antonio Spilimbergo (2014), “Monetary Policy and Bank Lending Rates in Low-Income Countries: Heterogeneous Panel Estimates,” Journal of Development Economics. - Mishra, Prachi; Peter J. Montiel; Antonio Spilimbergo (2012), “Monetary Transmission in Low-Income Countries: Effectiveness and Policy Implications,” IMF Economic Review. - Nelson, Edward (2002), “Direct Effects of Base Money on Aggregate Demand: Theory and Evidence,” Journal of Monetary Economics, Vol 49(4), May, pp. 687-708. - Peiris, Shanaka J.; Magnus Saxegaard (2007), “An Estimated DSGE Model for Monetary Policy Analysis in Low-Income Countries,” IMF Working Paper WP/07/282, December. - Sims, Christopher (1992), “Interpreting the Macroeconomic Time Series Facts: The Effects of Monetary Policy,” European Economic Review 36, No. 5: pp. 975-1000. - Sims, Christopher; Tao Zha (2006), “Does Monetary Policy Generate Recessions?” Macroeconomic Dynamics 10: 231-247. - Summers, Lawrence H. (1991), “The Scientific Illusion in Empirical Macroeconomics,” The Scandinavian Journal of Economics, pp. 129-148. - Waggoner, Daniel; Tao Zha (2003), “A Gibbs sampler for structural vector autoregressions” Journal of Economic Dynamics and Control 28(2): 349-366. - Walker, Sebastien, E.J. (2011), “The Transmission of Monetary Policy in Countries of the East African Community”, M.Phil. thesis, Department of Economics, University of Oxford. - Woodford, Michael (2001), “Monetary Policy in the Information Economy” in Economic Policy for the Information Economy: Proceedings of the Federal Reserve Bank of Kansas City Annual Symposium Conference Jackson Hole, Wyoming, August 30 – September 1: 297-370. ### Figures overview (impulse responses, power functions, and scenarios) - Figures present impulse responses to a monetary policy shock and associated power functions and t-statistics for: - CEE-PS Baseline (Figure 1(a), 1(b), 1(c)). - CEE-CB Baseline (Figure 2). - Scenario and robustness figures include: - CEE-PS Weak Transmission (elasticities in IS and PC scaled down by 75%) (Figure 3). - CEE-PS Smoothing Parameter (scaled down by 75%) (Figure 4). - CEE-PS Small Sample (Figure 5). - CEE-PS Measurement Errors (additional 20% variance on output gap and inflation) (Figure 6). - CEE-PS Output Gap Estimated with One-sided Filter (no supply side shocks) (Figure 7). - CEE-PS Output Gap Estimated with One-sided Filter (iid supply side shocks) (Figure 8). - CEE-PS Combined Scenario 1 (small sample, measurement errors, and iid supply shocks) (Figure 9). - CEE-PS Combined Scenario 2 (small smoothing parameter, small sample, measurement errors, and iid supply shocks) (Figure 10). - CEE-PS Wrong Identification (Figure 11). - CEE-PS Money Target Model (λ =0.95) (Figure 12). - Variables plotted in figures (for impulse responses) include: - response of interest rate to monetary policy shock - response of output gap to monetary policy shock - response of real effective exchange rate to monetary policy shock - response of inflation to monetary policy shock - Power functions for output gap and inflation are shown across horizon scales indicated by axes labeled 2 4 6 8 10 12 14 (and in some plots 1 through 15). ### Appendix — DSGE model specification and solution details - Model class: - New Keynesian open-economy model combining: - IS curve - New Keynesian Phillips curve (PC) - interest-parity condition (uncovered interest parity) - Taylor Rule for monetary policy - References: Berg, Karam and Laxton (2006); Christiano, Eichenbaum and Evans (2005); Fernandez-Villaverde et al. (2005). - Notation: - ߗ௧஼஻ and ߗ௧௉ௌ denote information sets held by the central bank and the private sector at time t. - Variables vector ݔ௧ = (෤ݕ௧, ߨ௧, ̃݁௧, ݅௧). - Linearized stationary equations (as provided): - IS equation (A1): ෤ ݕൣܧ ଽെ ଵ ෤ݕ ௧ାଵ ർ (ܽ1െ ଵ ) ෤ݕ ௧ିଵ ܽ൅ ଶ ሾ ܽ ష ሺ ݅ ௧ ߨെ ௧ାଵ ̅ݎെ ሻ ܽ൅ ସ ̃݁ ௧ ሿ ߝെ ௧ ௬ ߗห ௧ ௉ௌ ୀଵൌ0 - New Keynesian Phillips curve (A2): ߨሾܧ ௧ ܾെ ଵ ߨ ௧ାଵ ർ (ܾ1െ ଵ ) ߨ ௧ିଵ ܾെ ଶ ෤ݕ ௧ ܾ൅ ଷ ̃݁ ௧ ߝെ ௧ గ ߗห ௧ ௉ௌ ିଵൌ0 - Uncovered interest parity (A3): ܧ ሾ ̃݁ ௧ ܿെ ଵ ̃݁ ௧ାଵ ർ (ܿ1െ ଵ ) ̃݁ ௧ିଵ ർ ሺ 14 ⁄ሻ ∙ ሾ ݅ ௧ ߨെ ௧ାଵ ̅ݎെ ሻ ߝെ ௧ ௘ ߗห ௧ ௉ௌ ିଵൌ0 - Monetary policy (Taylor rule) (A4): ݅ൣܧ ௧ ݀െ ଵ ሺ ݀൅ ̅ݎ ଶ ߨ ௧ାଵ ݀൅ ష ෤ݕ ௧ାଵ ሻ ർ (݀1െ ଵ ) ݅ ௧ିଵ ߝେ ௧ ௜ ߗห ௧ ஼஻ ୀଵൌ0 - Structural shocks: (A5) ߝ௧ܰ ~ iid.(ߑ,0), ߑ is diagonal. - Solution approach: - Use Dynare toolkit adapting undetermined coefficients to mixed information environments. - General solution form (A6)/(A9): ݔ௧ = ݔܣݑ௧ିଵ + ܤݑ௧ for undetermined matrices ܣ and ܤ, with ݑߝ representing lagged shocks. - Auxiliary variables for central bank forecasts in mixed-information CEE-PS: - ݒ௧ܧ = (෤ݕ ௧ାଶ | ߗ௧) and ݖ௧ܧ = (ߨ ௧ାଶ | ߗ௧) - Expectational terms expressed as linear functions of past variables and currently observed shocks under the information assumptions; matrices ܣ and ܤ solved by equating coefficients. - Mapping from structural shocks to SVAR residuals: - CEE-PS identification structure (A7): matrix with contemporaneous responses of GDP gap, inflation, and real exchange rate gap to all four shocks; interest rate responds only to lagged information and contemporaneous monetary policy shock. (Representation shown as block matrix in (A7).) - Example parameterization and solution matrices (preserved exactly as presented): - CEE-PS full solution mapping (A8) — solution expressed as: [ ෤ݕ௧ ߨ௧ ̃݁௧ ݅௧ ]' = [ 0.8 0.2 0.3 1.1 ർ0.5 −0.4 ർ0.9 −0.6 ർ0.2 −0.6 ർ0.3 −0.8 ർ0.1 −0.4 00 1.2 0.6 00.5 0.3 0.8 0.3 0.7 ]' [ ෤ݕ௧ିଵ ߨ௧ିଵ ̃݁௧ିଵ ݅௧ିଵ ݒ௧ିଵ ݖ௧ିଵ ]' + [ 1.6 0.5 0.6 2.2 ർ1.0 −0.8 ർ1.7 −1.1 ർ0.1 −0.8 00 2.5 1.2 01 ]' [ ߝ௧௬ ߝ௧ గ ߝ௧ ௘ ߝ௧ ௜ ]' - CEE-CB full model solution (A11) — mapping preserved exactly: [ ෤ݕ௧ ߨ௧ ̃݁௧ ݅௧ ]' = [ 0.63 −0.01 0.26 0.71 ർ0.30 −0.30 ർ0.50 −0.34 0.08 −0.02 0.23 0.27 0.74 0.23 ർ0.50 0.10 ]' [ ෤ݕ௧ିଵ ߨ௧ିଵ ̃݁௧ିଵ ݅௧ିଵ ]' + [ 1.27 −0.02 0.52 1.42 ർ0.60 0 ർ1.00 0 0.17 −0.05 0.46 0.54 1.48 0 ർ1.01 0.76 ]' [ ߝ௧௬ ߝ௧ గ ߝ௧ ௘ ߝ௧ ௜ ]' - Identification differences between mixed-information models: - CEE-PS: private sector has full information; central bank only observes lagged information up to t−1. As a result, GDP gap, inflation, and real exchange rate gap can respond contemporaneously to all four shocks; interest rate responds contemporaneously only to monetary policy shock (with other shocks entering the reaction function with a lag). - CEE-CB: central bank has full information; private sector does not observe contemporaneous monetary policy shock. GDP gap, inflation, and real exchange rate gap do not respond contemporaneously to the monetary policy shock; interest rate can respond contemporaneously to all four structural shocks because the central bank observes them. *Italic: _wp1690 - References (source PDF "_wp1690 - References")* --- _Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp1690.pdf_