## wpiea2024182

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---

### Executive Summary
- The financial cycle in Kazakhstan has a small but significant contribution to the business cycle.
- Dominant transmission channels:
  - consumption (credit to individuals), and
  - construction (housing prices),
  - rather than investment (long-term credit and corporate credit).
- Financial shocks:
  - persistent and amplifying impact on the business cycle.
  - impact is similar during both expansion and contraction phases (symmetric impact).
- Policy implications:
  - Relevance of using macroprudential policy to manage the financial cycle and preserve financial stability.
  - Use of macroeconomic policies to manage the business cycle and preserve macroeconomic stability.
  - Need for symmetric calibration of macroprudential policy given symmetric impact of financial shocks in expansions and contractions.
- Methodological caution:
  - Chosen approach significantly reduces the confidence interval around cyclical component estimates, but end-sample (real-time) estimates retain inherent limitations.
  - Policymakers should not rely exclusively on real-time estimates for policy setting; consider a range of indicators and analyses.

### A. Motivation and Introduction
- Objective:
  - Examine the role of financial cycle proxies in refining estimates of the business cycle in Kazakhstan.
  - Support macro-financial integration in IMF surveillance using a parsimonious estimation approach that does not require detailed structural modeling.
- Reasons financial sector fluctuations expected to have a small impact:
  - Kazakhstan is an upper middle-income open economy with a large extractive industry largely financed by foreign direct investment (FDI) with marginal intermediation through the domestic financial system.
  - Economy exports primarily oil and raw materials and imports higher value-added goods.
  - Banking sector characteristics:
    - Total financial assets: 47 percent of GDP.
    - Credit penetration: 25 percent of GDP, mainly local currency loans to individuals (mortgage and other retail loans).
    - LC and FX loans to corporates less important; primarily used for working capital and some investments.
    - Banks funded primarily by deposits in LC; deposit dollarization remains at 25 percent of total deposits (decreasing).
  - State footprint:
    - Large infrastructure investments financed by SOEs and FX debt issuance, bypassing domestic banks.
    - Pervasive credit subsidies and significant dollarization weaken interest rate channel of monetary policy.
  - Banking sector risk profile:
    - Highly capitalized; average capital adequacy ratio exceeded 19 percent at end-2023.
    - Some liquidity and FX imbalances; monetary data report a long foreign currency position of about 11 percent of capital (largely closed via off-balance sheet items).

### B. Select Literature Survey
- Broad findings:
  - Credit and asset price cycles typically procyclical and tend to peak before the business cycle.
  - With financial frictions, shocks can have persistent and amplifying effects via borrower-lender agency costs, financial accelerator (convex cost of capital), and fire-sales depressing collateral.
  - Financial busts can cause severe recessions through liquidity mismatches, spirals, and margin calls.
  - Less tradable, more labor-intensive, externally financed sectors are more sensitive to the credit cycle.
- Two empirical strands:
  - Structural literature: structural/semi-structural GE models identifying channels (collateral constraints, credit spreads, financial accelerator); example DSGE application for Kazakhstan.
  - Parsimonious literature: extends filters or adds auxiliary equations/external indicators to improve output gap estimation; credit-cycle proxies and unemployment contain significant information for real-time output gap estimates.

### C. Empirical Framework
- Strategy:
  - Parsimonious estimation approach leveraging financial cycle proxies to refine business cycle estimates without detailed structural modeling.
- Baseline:
  - Hodrick and Prescott (HP) filter in state-space form with λ = 1600 for quarterly data (Ravn and Uhlig (2002)).
  - Static HP: state-space Kalman filter on second-order difference (notation in source) yields static HP trend τ_t and cycle c_t = y_t − τ_t.
- Augmented (dynamic) HP:
  - Include AR(1) for the cycle: (y_t − τ_t) = β(y_{t−1} − τ_{t−1}) + ε_{2,t} and exogenous financial-cycle variables.
  - Use Impavido (2024) formulation estimated by maximum likelihood with Kalman Filter; constraints: (1 − β)^2 δ λ σ_ε1^2 = σ_ε2^2 and λ = 1600 where δ scales cyclicality.
  - Estimates using this are denoted “dynamic” HP filter estimates.
- Methodological distinctions:
  - Correct for small-sample bias from AR process.
  - Estimate β outside the state-space model (as in Berger et al. (2015)).
  - State-space representation allows restrictions on variance-covariance of residuals.
  - Propose formal test for stability in means of exogenous variables.
  - Use Kalman filter to estimate β to ensure same sample used for γ and β estimation.
  - Use lower threshold to estimate δ to better match cyclicality between (3) and (2).

### D. Data, Estimation Strategy, and Results
- Endogenous variable:
  - Log of quarterly real GDP.
- Financial-cycle proxy variables (all demeaned and detrended; cyclical components included):
  - Headline inflation: one- and four-quarter difference of log CPI. Expected positive with cycle.
  - Real interest rates: annual real lending rate on Tenge loans to individuals and non-financial corporates. Expected negative with cycle.
  - Short-term real credit: one- and four-quarter difference in log of short-term banking sector loans deflated by CPI. Expected positive (consumption).
  - Long-term real credit: one- and four-quarter difference in log of long-term banking sector loans deflated by CPI. Expected positive (investment).
  - Total real credit: one- and four-quarter difference in log sum of short- and long-term loans deflated by CPI.
  - Real credit to individuals: one- and four-quarter difference in log of loans to individuals deflated by CPI. Expected positive (consumption).
  - Real credit to nonfinancial corporates: one- and four-quarter difference in log of loans to corporates deflated by CPI. Expected positive (investment).
  - House price inflation: one- and four-quarter difference in log of house price index. Expected positive with cycle.
- Estimation approach:
  - Estimate equation (3) repeatedly including each proxy separately; assess statistical significance of γ̂ via Wald statistic w and p-value χ(1).
  - Select candidate explanatory variables based on Wald statistics.
- Key empirical findings:
  - Real interest rates:
    - Fail to reject null for real lending rates to individuals.
    - Reject null for real lending rates to corporates but only at a seven percent confidence level.
    - Context: during 2021-23 ex-ante real policy rate drifted into negative territory (especially in late 2022) while inflation surged above 20 percent.
    - Interpretation: interest rate channel is weak; pass-through low and stronger for corporates than individuals.
  - Headline inflation:
    - Fail to reject null that annual headline inflation contains no information about the cycle.
    - Reject it for quarterly inflation but only at a high six-seven percent confidence level and with the wrong sign.
    - Interpretation: inflation does not contain meaningful information about the business cycle and/or Phillips curve is rather flat; inflation mostly externally determined.
    - Supported by observation that unemployment barely moves during recessions.
  - Housing price inflation:
    - Fail to reject null for quarterly house price inflation; reject for annual house price inflation.
    - Interpretation: house prices behave procyclically and tend to peak before the output gap peaks; relevance linked to large share of construction in supply GDP.
  - Short- and long-term real credit:
    - Long-term real credit has a larger and more significant contribution than short-term credit, driving total credit’s behavior.
    - Fail to reject null at five percent confidence level for quarterly growth but reject it for annual growth — implying procyclicality relative to the business cycle.
  - Real credit to individuals and corporates:
    - Credit to individuals is highly correlated with the business cycle and contains the largest information among variables.
    - Context and magnitudes: in 2021, credit to individuals accounted for about 13 percent of GDP, or 54 percent of the credit portfolio.
    - Contribution of credit to individuals has been increasing since 2022 due to a boom in loans to individuals while share of credit to non-financial corporates has been decreasing.
  - Variable selection:
    - Six variables selected as best candidates based on Wald statistics: short-term credit, long-term credit, total credit, credit to individuals, credit to non-financial corporates, and house prices.

### Structural Breaks and Non-linearities
- Stability checks:
  - Visual inspection of recursive means starting from an initial five-year period; initial instability around GFC ignored.
  - CUSUM test (Brown et al. (1975)) applied to test parameter/mean stability.
- CUSUM findings:
  - Only for ST credit fail to reject absence of structural breaks at 95 percent confidence level.
  - For all other variables, structural break exists in the mean primarily around the GFC.
  - Mean of house price series strongly trended before 2011; stable after 2011.
- Accounting for structural breaks:
  - Interact exogenous variables with recession dummies: d08 (2008q3-q4), d15 (2015q1-q2), d16 (2016q1-q2), d20 (2020q2-q3).
  - Deviations indicate GFC and COVID-19 recessions are largest sources of non-linearities.
- Conditioning tests:
  - Differences before/after floating of Tenge (dIT); differences during positive vs negative output gap periods (dpos).
  - Findings:
    - Flexible exchange rate adoption might have affected business cycle but not contribution of financial proxies.
    - Financial cycle does not impact business cycle differently in positive or negative output gap periods → supports symmetric calibration of macroprudential policies.

### Static (HP) versus Dynamic Cycle Estimates
- Comparison:
  - Static HP (equation (2)) vs six dynamic estimates (equation (3)) including each of six exogenous variables with interaction dummies for GFC and COVID-19.
- Period-specific findings:
  - 1999-2007:
    - Dynamic estimates notably higher than static HP.
    - Real GDP grew on average by about 10 percent per year.
    - Real credit and house prices grew on average by about 39 percent per year (real credit reached 67 percent annual growth rate in 2007q2).
  - 2008-19:
    - Dynamic estimates notably lower than static HP.
    - Real GDP grew on average by 4 percent per year.
    - House prices grew on average by 5 percent per year.
    - Real credit contracted on average by 2 percent per year.
    - Period characterized by GFC in 2008, financial crisis in 2014, floating of the Tenge and adoption of inflation targeting in 2015, three recessions, high nonperforming loans, and slow bank balance sheet cleanup.
  - 2020-23:
    - Dynamic estimates notably higher than static HP.
    - Real GDP grew on average 2 percent per year.
    - House prices grew on average by 14 percent.
    - Real credit grew on average by 6 percent.
    - Period characterized by the COVID-19 global pandemic.
- Mechanism and confidence:
  - Static HP fails to capture amplifying impact of financial cycle (over/underestimates potential GDP depending on proxy deviations).
  - Dynamic estimates capture amplifying effect; produce much narrower 95 percent confidence intervals than static HP.
  - Confidence intervals constructed using RMSE of one-step-ahead Kalman filter forecast; both methods show end-sample widening but (3) yields considerably narrower intervals.

### Role of Cyclical vs Structural Factors around COVID-19
- Financial cycle did not contribute to 2020 recession (demand shock from closures/restrictions).
- Factors keeping financial proxies above trend during 2020-23:
  - Cyclical:
    - Monetary policy remained loose especially in 2022 and first half of 2023.
    - Authorities subsidized local currency deposits limiting switch to FX deposits.
    - Pension fund contributors allowed to use cash balances to purchase houses.
    - Large influx of Russian citizens contributing to high house prices after invasion of Ukraine.
  - Structural:
    - Increasing state footprint since 2014 weakened link between business and financial cycles.

### Weak Exogeneity and Causality
- Identification and tests:
  - Use lagged values of ξ_t in (3); results qualitatively similar.
  - Granger-causality tests (Table 7):
    - Always reject null that exogenous variable does not Granger cause the business cycle.
    - Always fail to reject that the cycle does not Granger cause the exogenous variable.
    - Note: Granger causality tests strict, not weak, exogeneity.

### Contemporaneous and Historical Contributions of Financial Cycle Proxies
- Contemporaneous contributions:
  - Calculated as 후ො훏.
  - Procyclicality, persistence, and amplifying effects evident, especially around GFC.
  - During COVID-19 recession, financial proxies did not amplify recession; in 2023 ST credit and housing prices had negative or trivial contributions as they were growing at or below trend.
- Historical decomposition (Appendix II):
  - Initial-condition component (β̂1(y1|τ̂1)) practically zero around 2003; AR(1) parameter β̂ = 0.672 indicating short memory.
  - Historical contributions:
    - ST and LT credit procyclical: peak before recessions and revert to means before business cycle.
    - LT credit has largest amplifying effect during expansions and contractions.
    - ST credit has largest contribution during recessions (matures earlier; banks stop rollovers).
    - Unexplained component particularly large around COVID-19.
    - In 2023, historical contribution of LT credit about two percentage points of potential GDP while ST credit had reverted to its mean.

### Main Conclusions and Policy Implications
- Main conclusions:
  - Financial cycle plays a small but meaningful role in Kazakhstan’s business cycle, mainly via household credit and housing prices.
  - Financial shocks are persistent and amplify business fluctuations, with similar effects in expansions and contractions.
  - Headline inflation contains no information about the business cycle (flat Phillips curve); inflation primarily imported.
  - Real interest rates contain limited information:
    - Rates on loans to individuals contain no information.
    - Rates on loans to corporates have a small impact (different from zero only with a high p-value) → interest rate channel works primarily through credit to corporates.
- Policy implications:
  - Macroprudential policy has a significant role in managing Kazakhstan’s economic cycle while preserving financial stability; complements macroeconomic policies.
  - Preserve significant buffers in bank balance sheets and implement balance sheet repair swiftly.
  - Symmetric calibration of macroprudential tools appropriate given symmetric impacts across phases.
  - Exercise caution in relying exclusively on real-time filter estimates for policy; use multiple indicators and analyses.

### Methodological Contributions
- Formal test for stability of the mean of exogenous variables to limit low-frequency cycles being captured in trend estimates.
- Provides self-contained statistical software simplifying estimation strategy.
- Parsimonious approach:
  - Reduces confidence interval around cyclical component estimates.
  - Does not require detailed structural modeling of economy or financial frictions.
  - Still requires caution for policy use.

### Appendix II — Derivation of the Historical Decomposition (key steps)
- Autonomous first-order difference equation solution (A.1–A.2):
  - y_{t+1} = a y_t + b; forward-iteration yields y_t = a^t (y_0 − ȳ) + ȳ for a ≠ 1.
- Non-autonomous first-order difference equation solution (A.3–A.4):
  - y_{t+1} = a_{t+1} y_t + b_{t+1}; forward-iteration yields y_t = (∏_{i=1}^t a_i) y_0 + ∑_{j=1}^t (∏_{i=j+1}^t a_i) b_j.
- Observation equation as partial non-autonomous difference equation (A.5):
  - (y_t − τ_t) = β (y_{t-1} − τ_{t-1}) + 후훏_t + ε_{s,t}.
- Historical decomposition (A.6–A.8):
  - (y_t − τ_t) = β^t (y_0 − τ_0) + ∑_{j=1}^t β^{t-j} 후훏_j + ∑_{j=1}^t β^{t-j} ε_{s,j}.
  - Decomposition components:
    - Initial-condition (neutral cycle): β^t (y_0 − τ_0).
    - Exogenous contributions: ∑ β^{t-j} 후훏_j.
    - Unexplained residual: ∑ β^{t-j} ε_{s,j}.

*IMF Working Paper: Executive Summary contained in source document.*

### Executive Summary ......................................................................................................

### wpiea2024182 - Executive Summary ......................................................................................................

### Executive Summary
- The financial cycle in Kazakhstan has a small but significant contribution to the business cycle.
- The impact of the financial cycle on business fluctuations primarily occurs through:
  - consumption (credit to individuals), and
  - construction (housing prices),
  rather than through investment (long-term credit and corporate credit).
- Financial shocks have a persistent and amplifying impact on the business cycle.
- The impact of financial shocks is similar during both expansion and contraction phases of the economy (symmetric impact).
- Policy implications highlighted:
  - Relevance of using macroprudential policy to manage the financial cycle and preserve financial stability.
  - Use of macroeconomic policies to manage the business cycle and preserve macroeconomic stability.
  - Need for symmetric calibration of macroprudential policy given symmetric impact of financial shocks in expansions and contractions.
- Methodological caution:
  - The chosen approach significantly reduces the confidence interval around cyclical component estimates, but end-sample (real-time) estimates retain inherent limitations.
  - Policymakers should not rely exclusively on real-time estimates for policy setting; consider a range of indicators and analyses.

### A. Motivation and Introduction
- Objective:
  - Examine the role of financial cycle proxies in refining estimates of the business cycle in Kazakhstan.
  - Support macro-financial integration in IMF surveillance using a parsimonious estimation approach that does not require detailed structural modeling.
- Reasons why financial sector fluctuations are expected to have a small impact on the business cycle in Kazakhstan:
  - Kazakhstan is an upper middle-income open economy with a large extractive industry largely financed by foreign direct investment (FDI) with marginal intermediation through the domestic financial system.
  - The country produces and exports primarily oil and raw materials and imports higher value-added goods.
  - The banking sector is relatively small with traditional funding and business models:
    - Total financial assets amount to 47 percent of GDP.
    - Credit penetration accounts for only 25 percent of GDP, mainly local currency (LC) loans to individuals (mortgage and other retail loans).
    - LC and foreign exchange (FX) loans to corporates are less important and primarily used for working capital and some investments.
    - Banks are primarily funded by deposits in LC; deposit dollarization, which has been decreasing, remains at 25 percent of total deposits.
  - The state retains a large footprint:
    - Large infrastructure investments tend to be financed by SOEs and funded by issuance of FX debt securities, bypassing the domestic banking sector.
    - Pervasive credit subsidies and significant dollarization weaken the interest rate channel of monetary policy.
  - Banking sector risk profile:
    - Highly capitalized; average capital adequacy ratio exceeded 19 percent at end-2023.
    - Some liquidity imbalances and FX imbalances suggest financial frictions have a limited amplifying impact on the business cycle.
    - Monetary data report a long foreign currency position of about 11 percent of capital for the sector; that position is largely closed through off-balance sheet items (e.g., derivatives), so banks comply with prevailing regulation in this area.
- Importance of assessing financial cycle impact:
  - Refine assessment of monetary and fiscal policy stances.
  - Support macroprudential policy as an integral countercyclical tool.
  - Gauge the strength of the interest channel of monetary policy transmission.
  - Inform calibration of macroprudential policy tools.

### B. Select Literature Survey
- Broad findings from theoretical and empirical literature:
  - Credit and asset price cycles are typically procyclical relative to the business cycle and tend to peak before the business cycle, contributing to mean reversion.
  - With financial frictions, shocks can have persistent and amplifying effects on the business cycle:
    - Persistence can arise from linear changes in borrower-lender agency costs linked to borrower net-worth changes affecting lending and investment.
    - Amplification can occur via convex increases in the cost of capital (financial accelerator) or fire sales of collateral depressing collateral values.
  - Financial busts can have severe economic consequences, with mechanisms like liquidity mismatches, spirals, and margin calls contributing to deep recessions and long-lived crises.
  - Sectors that are less tradable, more labor-intensive, and more dependent on external finance are more sensitive to the credit cycle.
- Two empirical strands:
  - Structural literature:
    - Uses structural and semi-structural general equilibrium models to identify channels (e.g., collateral constraints linked to house values, credit spreads, lending spreads, default and liquidity risks, decline of risk premia, financial accelerator).
    - Example application to Kazakhstan: DSGE estimate identifying borrowing constraints associated with housing and entrepreneurs’ capital as amplifying channels.
  - Parsimonious literature:
    - Focuses on empirically measuring the impact of the financial cycle on the business cycle without detailed channel identification.
    - Approaches extend filters (HP) or add auxiliary equations (Phillips curve, Okun’s law) or external indicators (prices, unemployment, credit) to improve output gap estimation and policy calibration.
    - Studies find that credit-cycle proxies and unemployment contain significant information to produce robust real-time output gap estimates.

### C. Empirical Framework
- Strategy:
  - Use a parsimonious estimation approach that leverages financial cycle proxies to refine business cycle estimates.
  - The approach does not require detailed knowledge of the economy’s structure or of specific financial frictions.
- Rationale:
  - Provide a practical tool for surveillance and policy calibration that integrates macro-financial information into cyclical estimation.

### D. Data, Estimation Strategy, and Results
- Data (summary of salient data-related facts reported):
  - Total financial assets: 47 percent of GDP.
  - Credit penetration: 25 percent of GDP.
  - Deposit dollarization: 25 percent of total deposits (decreasing).
  - Average capital adequacy ratio: exceeded 19 percent at end-2023.
  - Long foreign currency position: about 11 percent of capital (largely closed via off-balance sheet items).
- Empirical strategy and results (high-level findings reported):
  - Financial cycle proxies provide information that helps refine business cycle (cyclical component of GDP) estimates.
  - The financial cycle’s contribution to the business cycle is small but significant.
  - The dominant transmission channels identified are credit to individuals and housing prices, not long-term or corporate credit.
  - Financial shocks are persistent and amplifying, with symmetric effects across expansions and contractions.
- Structural breaks and other non-linearities:
  - The paper discusses structural breaks and non-linearities as part of robustness checks and interpretation of results (details in main text and appendices).
- Static and dynamic cycle estimates:
  - The methodological approach reduces confidence intervals around cyclical component estimates relative to unconstrained filters, while acknowledging end-sample uncertainty.
- Contemporaneous and historical contribution of financial cycle proxies:
  - Analysis distinguishes contemporaneous contributions and historical decompositions for short- and long-term credit, and for credit to individuals and housing; results indicate stronger roles for short-term/retail channels.

### E. Conclusions
- Main conclusions:
  - Financial cycle plays a small but meaningful role in Kazakhstan’s business cycle, mainly via household credit and housing prices.
  - Financial shocks are persistent and amplify business fluctuations, with similar effects in expansions and contractions.
  - Macroprudential policy is relevant and should be integrated with macroeconomic policy to preserve financial and macroeconomic stability.
  - Symmetric calibration of macroprudential tools is appropriate given symmetric impacts of financial shocks across phases.
  - Methodological improvements help narrow uncertainty in cyclical estimates, but policymakers should treat real-time end-sample estimates cautiously and use multiple indicators.

*IMF Working Paper: Executive Summary contained in source document.*

### introduction.

### introduction.

### C. Empirical Framework
- Objective:
  - Improve on the HP filter estimates of the Kazakhstan business cycle.
  - Remain parsimonious to facilitate applicability across countries/situations.
- Baseline: Hodrick and Prescott (HP) filter in state-space representation.
  - Given T observations of log GDP y, HP separates y_t into trend τ_t and cycle c_t = y_t − τ_t by minimizing problem (1) with smoothing parameter λ.
  - λ is set at 1600 for quarterly data following Ravn and Uhlig (2002).
  - The HP penalty constrains the estimated variance ratio σ_ε1^2/σ_ε2^2 (notation in source).
- State-space representation and Kalman filter:
  - The second-order difference formulation is recast into two first-order linear equations (2).
  - Using the Kalman filter on (2) with 1600 = λ = σ_ε2^2/σ_ε1^2 yields the static HP trend τ_t and cycle c_t = y_t − τ_t.
  - The paper denotes estimates using (2) as “static” HP filter estimates.
- Augmented (dynamic) HP filter:
  - Augment (2) to include an AR(1) process for the cycle (y_t − τ_t) = β(y_{t−1} − τ_{t−1}) + ε_{2,t} in the observation equation and exogenous variables containing financial-cycle information.
  - Formal estimation uses Impavido (2024) formulation in (3), estimated by maximum likelihood using the Kalman Filter.
  - Constraints in (3): (1 − β)^2 δ λ σ_ε1^2 = σ_ε2^2 and λ = 1600, where δ scales cyclicality to preserve the static HP filter’s assumed cyclicality.
  - Estimates using (3) are denoted “dynamic” HP filter estimates.
- Methodological distinctions from related literature:
  - Correct for small-sample bias introduced by the AR process for the business cycle.
  - Estimate the autoregressive parameter β outside the state-space model (as in Berger et al. (2015)), not via Bayesian methods (difference from Borio et al. (2013, 2014)).
  - Use a state-space representation allowing restrictions on the variance-covariance matrix of residuals rather than on parameters.
  - Propose a formal test for stability in the means of exogenous variables (novel relative to cited papers).
  - Use the Kalman filter to estimate β to ensure the same sample is used for estimating financial-cycle impact γ and β.
  - Use a lower threshold to estimate δ to increase the match in cyclicality between (3) and (2).

### D. Data, Estimation Strategy, and Results
- Endogenous variable:
  - Log of quarterly real GDP.
- Financial-cycle proxy variables (all demeaned and detrended; cyclical components of proxies also included):
  - Headline inflation: one- and four-quarter difference of log CPI. Expected sign: positive with the cycle.
  - Real interest rates: annual real lending rate on Tenge loans to individuals and non-financial corporates. Expected sign: negative with the cycle.
  - Short-term real credit: one- and four-quarter difference in log of short-term banking sector loans deflated by CPI. Expected: positive with the cycle (consumption).
  - Long-term real credit: one- and four-quarter difference in log of long-term banking sector loans deflated by CPI. Expected: positive with the cycle (investment).
  - Total real credit: one- and four-quarter difference in log sum of short- and long-term loans deflated by CPI. Expected: positive with the cycle.
  - Real credit to individuals: one- and four-quarter difference in log of loans to individuals deflated by CPI. Expected: positive with the cycle (consumption).
  - Real credit to nonfinancial corporates: one- and four-quarter difference in log of loans to corporates deflated by CPI. Expected: positive with the cycle (investment).
  - House price inflation: one- and four-quarter difference in log of house price index. Expected: positive with the cycle.
- Estimation approach:
  - Estimate equation (3) repeatedly including each proxy separately; assess statistical significance of γ̂ via Wald statistic w and p-value χ(1).
  - Select candidate explanatory variables based on Wald statistics in Table 3.
- Key empirical findings (preserve reported numeric detail and qualitative interpretation):
  - Real interest rates:
    - Fail to reject the null for real lending rates to individuals.
    - Reject the null for real lending rates to corporates but only at a seven percent confidence level.
    - Context: during 2021-23 ex-ante real policy rate drifted into negative territory (especially in late 2022) while inflation surged above 20 percent.
    - Interpretation: the interest rate channel in Kazakhstan is weak; pass-through from policy to lending rates is low and stronger for corporates than individuals.
  - Headline inflation:
    - Fail to reject the null that annual headline inflation contains no information about the cycle.
    - Reject it for quarterly inflation but only at a high six-seven percent confidence level and with the wrong sign.
    - Interpretation: inflation does not contain meaningful information about the business cycle and/or the Phillips curve in Kazakhstan is rather flat; inflation is mostly externally determined.
    - Supported by observation that unemployment barely moves during recessions.
  - Housing price inflation:
    - Fail to reject the null for quarterly house price inflation; reject for annual house price inflation.
    - Interpretation: house prices behave procyclically and tend to peak before the output gap peaks; relevance linked to large share of construction in supply GDP.
  - Short- and long-term real credit:
    - Long-term real credit has a larger and more significant contribution than short-term credit, driving total credit’s behavior.
    - Fail to reject the null at five percent confidence level for quarterly growth but reject it for annual growth — implying procyclicality relative to the business cycle.
  - Real credit to individuals and corporates:
    - Credit to individuals is highly correlated with the business cycle and contains the largest information among variables.
    - Context and magnitudes: in 2021, credit to individuals accounted for about 13 percent of GDP, or 54 percent of the credit portfolio.
    - Contribution of credit to individuals has been increasing since 2022 due to a boom in loans to individuals while the share of credit to non-financial corporates has been decreasing.
  - Variable selection:
    - Six variables selected as best candidates to explain the business cycle based on Wald statistics: short-term credit, long-term credit, total credit, credit to individuals, credit to non-financial corporates, and house prices.

### Structural breaks and other non-linearities
- Cautionary approach:
  - Check for stability in variable means and other non-linearities.
- Stability check implemented:
  - Visual inspection of Figure 2 plotting each variable together with its recursive mean obtained by extending the sample successively by one observation starting from an initial period of five years of observations.
  - Rationale: initial five-year period long enough to obtain a meaningful starting estimate of the underlying mean and let it stabilize.
  - Visual inspection suggests means are stable if the initial instability around the global financial crisis (GFC) is ignored.

*IMF Working Paper — introduction.*

### conclusion can be drawn from Figure 3 that plots the recursive γො obtained from estimating (3) by

### wpiea2024182 - conclusion can be drawn from Figure 3 that plots the recursive γො obtained from estimating (3) by

### Formal testing of parameter/mean stability
- Method:
  - CUSUM test for parameter stability proposed by Brown et al. (1975).
  - Regress each exogenous variable on a constant and test 퐻0 ∶ β1 = β.
  - CUSUM statistic constructed using recursive OLS residuals and the one-step-ahead standardized forecast error.
  - Inference based on path crossing a theoretical Brownian motion boundary at given probability; linear approximation for 95 percent confidence level used in Figure 4.
- Findings:
  - Only for ST credit do we fail to reject the null of absence of structural breaks at the 95 percent confidence level.
  - For all other variables, a structural break exists in the mean primarily around the GFC.
  - The mean of the house price series is strongly trended especially before 2011; it appears quite stable after 2011.

### Accounting for structural breaks and non-linearities
- Approach:
  - Interact exogenous variables with four recession dummies:
    - d08: 2008q3-q4 (onset of GFC)
    - d15: 2015q1-q2 (soon after the 2014 financial crisis)
    - d16: 2016q1-q2 (soon after the floating of the Tenge in 2015)
    - d20: 2020q2-q3 (onset of COVID-19)
  - Table 4 reports estimated average contributions (γො) and deviations for these four recessions.
- Findings:
  - Deviations indicate recessions during the GFC and COVID-19 are the largest source of non-linearities.

### Conditioning tests: exchange rate regime and output gap phases
- Tests performed:
  - Differences before and after the floating of the Tenge (dIT).
  - Differences during positive versus negative output gap periods (dpos).
- Findings:
  - Adoption of the flexible exchange rate regime might have affected the business cycle but not the contribution of financial cycle proxies.
  - Rationale: banks in Kazakhstan are not funded from abroad and are required to close net open FX positions by regulation, minimizing balance sheet FX effects.
  - Financial cycle does not seem to impact the business cycle differently in positive or negative output gap periods → supports symmetric calibration of macroprudential policies.

### Static (HP) versus dynamic cycle estimates (equation (2) vs (3))
- Method:
  - Static HP business cycle estimate (equation (2)) compared with six dynamic cycle estimates (equation (3)) where each of six exogenous variables is successively included with interaction dummies for GFC and COVID-19.
- Key period findings (Figure 6):
  - 1999-2007:
    - Dynamic estimates notably higher than static HP estimates.
    - Real GDP grew on average by about 10 percent per year.
    - Real credit and house prices grew on average by about 39 percent per year (real credit reached 67 percent annual growth rate in 2007q2).
  - 2008-19:
    - Dynamic estimates notably lower than static HP estimates.
    - Real GDP grew on average by 4 percent per year.
    - House prices grew on average by 5 percent per year.
    - Real credit contracted on average by 2 percent per year.
    - Period characterized by GFC in 2008, financial crisis in 2014, floating of the Tenge and adoption of inflation targeting in 2015, three recessions, high nonperforming loans, and slow bank balance sheet cleanup.
  - 2020-23:
    - Dynamic estimates notably higher than static HP estimates.
    - Real GDP grew on average 2 percent per year.
    - House prices grew on average by 14 percent.
    - Real credit grew on average by 6 percent.
    - Period characterized by the COVID-19 global pandemic.
- Mechanism:
  - Static HP filter fails to capture amplifying impact of financial cycle:
    - When financial proxies are above trend → HP overestimates potential GDP → output gaps lower.
    - When financial proxies below trend → HP underestimates extent financial sector is holding back economy → optimistic output gap estimates.
  - Dynamic estimates capture amplifying effect and better reflect sustainability of growth.
- Confidence intervals (Figure 7):
  - Cycle estimated with (3) has much narrower 95 percent confidence interval than HP filter.
  - Confidence intervals constructed using RMSE of one-step-ahead forecast from Kalman filter.
  - Both methods show end-sample widening, but (3) yields considerably narrower intervals — accounting for autocorrelation and financial cycle reduces imprecision.

### Role of cyclical vs structural factors around COVID-19
- Financial cycle did not contribute to the 2020 recession (demand shock driven by closures and restrictions).
- Factors keeping financial cycle proxies above trend during 2020-23:
  - Cyclical:
    - Monetary policy remained loose especially in 2022 and first half of 2023.
    - Authorities subsidized local currency deposits, limiting depositors’ switch into FX deposits.
    - Pension fund contributors allowed to use cash balances to purchase houses.
    - Large influx of Russian citizens contributing to high house prices after invasion of Ukraine.
  - Structural:
    - Increasing state footprint in the economy and financial sector since the 2014 financial crisis progressively weakened link between business and financial cycles.

### Weak exogeneity and causality
- Identification strategy and tests:
  - Assumptions:
    - Variables contain information about contemporaneous state of business cycle but react to past/expected values or are exogenous to the business cycle.
  - Robustness:
    - Use lagged values of 휉t in (3); results qualitatively similar to Table 3.
    - Test whether cycle Granger-causes exogenous variables (Table 7).
- Findings:
  - Always reject the null that the exogenous variable does not Granger cause the business cycle.
  - Always fail to reject that the cycle does not Granger cause the exogenous variable.
  - Note: Granger causality tests strict, not weak, exogeneity.

### Contemporaneous and historical contributions of financial cycle proxies
- Contemporaneous contributions (Figure 8):
  - Calculated as 후ො훏.
  - Procyclicality, persistence, and amplifying effects are evident, especially around GFC.
  - During COVID-19 recession, financial proxies did not amplify recession; in 2023 ST credit and housing prices had negative or trivial contributions as they were growing at or below trend.
- Historical contributions (Figure 9; Appendix II for calculation details):
  - Initial condition component (β̂1(y1|τ̂1)) is practically zero around 2003, consistent with low estimated AR(1) parameter (β̂ = 0.672) indicating short memory.
  - Historical contributions of ST and LT credit:
    - Display clearly procyclical behavior: peak before recessions and revert to means before the business cycle.
    - LT credit has largest amplifying effect during expansions and contractions.
    - ST credit has largest contribution during recessions (ST credit matures earlier, banks can stop rollovers to improve balance sheets).
  - Unexplained component particularly large around COVID-19.
  - In 2023, historical contribution of LT credit was around two percentage points of potential GDP while ST credit had reverted to its mean.

### Main conclusions and policy implications
- Main findings:
  - The financial cycle in Kazakhstan has a small but significant contribution to the business cycle.
  - Banking sector credit to individuals and housing prices contribute on average more to the business cycle than long-term credit and credit to corporates.
  - Financial cycle affects business cycle more through consumption and construction than through investment.
  - Headline inflation contains no information about the business cycle (flat Phillips curve); inflation is primarily imported.
  - Real interest rates contain limited information about the business cycle:
    - Rates on loans to individuals contain no information about the cycle.
    - Rates on loans to corporates have a small impact (different from zero only with a high p-value) → interest rate channel works primarily through credit to corporates.
  - Financial cycle displays procyclicality and persistence and has an amplifying effect; exception: financial cycle supported growth during 2020q2-q3.
- Policy implications:
  - Macroprudential policy has a significant role in managing Kazakhstan’s economic cycle while preserving financial stability, complementing macroeconomic policies.
  - Importance of preserving significant buffers in bank balance sheets and implementing balance sheet repair swiftly.
  - Because impact of financial cycle appears similar in expansions and contractions, macroprudential policy should be calibrated symmetrically across phases.
  - Caution advised in relying exclusively on real-time filter estimates for policy due to end-sample imprecision; policymakers should consider multiple indicators and analyses.

### Methodological contributions
- Paper proposes a formal test for stability of the mean of exogenous variables to limit low-frequency cycles being captured in trend estimates.
- Provides self-contained statistical software that simplifies the estimation strategy.
- Parsimonious approach:
  - Reduces confidence interval around estimates of cyclical component.
  - Does not require detailed structural modeling of economy or financial frictions.
  - Contrasts with complex structural approaches but still requires caution for policy use.

*IMF WORKING PAPERS — Financial and business cycles: shall we dance?; INTERNATIONAL MONETARY FUND*

### Appendix II. Derivation of the Historical

### Appendix II. Derivation of the Historical Decomposition

### Autonomous first-order difference equation: general form and solution
- General form:
  - 푦_{t+1} = a 푦_t + b, for t = 0,1,⋯  (A.1)
- Forward-iteration solution (for a ≠ 1):
  - Initial condition: 푦_0 = 푦_0
  - 푦_1 = a 푦_0 + b
  - 푦_2 = a (a 푦_0 + b) + b
  - 푦_3 = a (a (a 푦_0 + b) + b) + b
  - ⋯
  - 푦_t = a^t 푦_0 + ∑_{j=0}^{t-1} a^j b = a^t (푦_0 - 푦̄) + 푦̄  (A.2)
    - where 푦̄ is the steady state value of 푦.

### Non-autonomous first-order difference equation: general form and solution
- General form:
  - 푦_{t+1} = a_{t+1} 푦_t + b_{t+1}, for t = 0,1,⋯  (A.3)
- Forward-iteration solution:
  - 푦_0 = 푦_0
  - 푦_1 = a_1 푦_0 + b_1
  - 푦_2 = a_2 (a_1 푦_0 + b_1) + b_2
  - 푦_3 = a_3 (a_2 (a_1 푦_0 + b_1) + b_2) + b_3
  - ⋯
  - 푦_t = (∏_{i=1}^t a_i) 푦_0 + ∑_{j=1}^t (∏_{i=j+1}^t a_i) b_j  (A.4)

### Observation equation as a “partial” non-autonomous difference equation
- Observation equation (notation from main text):
  - 푦_t = (1 - β) ∑_{τ=τ_0}^{t} τ_{t} τ_{t-1} + (β 후) ∑_{?} + ε_{s,t}  [original shows structure in (A.5) with variable intercepts and constant autoregressive parameter]
  - Equivalent form shown in text:
    - (푦_t - τ_t) = β (푦_{t-1} - τ_{t-1}) + 후훏_t + ε_{s,t}  (A.5)
- Interpretation:
  - The equation has a constant autoregressive coefficient (β) and time-varying intercepts (the exogenous terms 후훏_t and the error ε_{s,t}), making it a partial non-autonomous difference equation.

### Combining solutions: deriving the historical decomposition
- Start from the non-autonomous solution (A.4) and set a_i = a ∀ i:
  - 푦_t = a^t 푦_0 + ∑_{j=0}^{t-1} a^{t-1-j} b_j  (A.6)
  - Alternate expressions in the text:
    - 푦_t = a_t 푦_0 + ∑ a^{t-j} b_j + b_t
    - 푦_t = a_t 푦_0 + ∑ a^{t-j-1} b_j
- Substitute the observation equation intercepts and errors into (A.6) to express deviations around trends:
  - (푦_t - 휏_t) = β_t (푦_0 - 휏_0) + ∑_{j=1}^t β^{t-j} 후훏_j + ∑_{j=1}^t β^{t-j} ε_{s,j}  (A.7)
- Rearranged decomposition (labelled components in text):
  - (푦_t - τ_t) =
    - Neutral cycle component:
      - β_t (푦_0 - τ_0)  (Initial condition)
    - Exogenous component(s):
      - ∑ β^{t-j} 후훏_j  (Exogenous component(s) as of s)
    - Unexplained residual:
      - ∑ β^{t-j} ε_{s,j}  (Unexplained residual)  (A.8)

### Key structural points from the derivation
- The solution of the observation equation is a linear combination of:
  - An initial-condition term scaled by powers of the autoregressive coefficient (β).
  - A weighted sum of exogenous/intercept terms (후훏_t) where weights are powers of β.
  - A weighted sum of residuals (ε_{s,t}) where weights are powers of β.
- This provides a historical decomposition into:
  - Initial-condition (neutral cycle) contribution.
  - Exogenous-component contributions across time.
  - Unexplained (residual) contributions across time.

*IMF Working Paper — Appendix II, “Derivation of the Historical Decomposition”*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024182.pdf_