4. Methodology and Econometric Strategy
4.1. General Methodological Framework
The objective of this study is to analyze the propagation of monetary policy shocks in a banking-dominant emerging economy, with a focus on the timing of adjustments between financial valuations, balance sheet variables, and inflation. The analysis does not aim to identify a specific structural channel but to characterize the relative dynamics between these different dimensions of the financial system.
Macro-financial interactions being intrinsically dynamic and interdependent, a single-equation approach appears insufficient to capture the simultaneous effects between expectations, asset prices, credit decisions, and macroeconomic variables. In this context, the use of a reduced-form vector autoregressive (VAR) model (Sims, 1980; Lütkepohl, 2005) allows for the modeling of these interdependencies without imposing a priori causal structure, while capturing the short-term dynamics at the heart of this study.
The identification of monetary shocks relies on a recursive Cholesky decomposition, interpreted as an intra-period sequencing hypothesis, in which some variables can react more quickly than others within the same period. This approach allows for the introduction of a temporal structure consistent with the analysis, without attributing a strict causal interpretation to the estimated relationships.
However, this identification strategy relies on a strong hypothesis of variable hierarchy, which may influence the empirical results. In particular, the chosen order can condition the interpretation of impulse response functions, which limits the robustness of the conclusions when the actual temporal structure between variables remains uncertain. This limitation is particularly important in the context of this study, where the temporal hierarchy between variables is precisely the subject of the analysis.
In this context, generalized impulse response functions (GIRFs) are also utilized. Unlike the recursive approach, these functions are invariant to the order of ranking of the variables and thus allow for verifying the robustness of the observed dynamics. The joint use of Cholesky-type IRFs and GIRFs thus allows distinguishing results dependent on a specific identification structure from those that reflect more robust empirical regularities.
The analysis is complemented by the Forecast Error Variance Decomposition (FEVD), which allows for the evaluation of the relative contribution of different shocks to the dynamics of each variable. This approach offers a complementary reading of the transmission mechanisms by highlighting the relative importance of the sources of fluctuations.
Finally, the stability of the model is examined using Chow-type structural break tests. The eventual identification of breaks allows for the verification of the robustness of the estimated relationships and, if necessary, the integration of indicator variables to account for regime changes.
This methodological framework seeks to examine the dynamic interactions among financial, banking, and macroeconomic variables from a short-term viewpoint, highlighting the variations in timing of the observed adjustments.
4.2. Data
The empirical analysis is based on monthly macro-financial data covering the period from January 2018 to December 2024, totaling 83 observations. This period corresponds to the longest interval for which a coherent and continuous set of data could be established for all variables, based on official institutional sources, notably Bank Al-Maghrib and the Casablanca Stock Exchange.
The use of a monthly frequency is central to this study, as the objective is to examine the timing of short-term adjustments between the variables. This frequency allows capturing the sequence of reactions between financial valuations, balance sheet variables, and inflation, providing sufficient temporal resolution to observe differentiated adjustments without introducing excessive complexity associated with a higher frequency.
The study period includes the years 2020 and 2021, marked by macro-financial disruptions related to the COVID-19 crisis. Rather than segmenting the sample into sub-periods, the analysis relies on a unified framework to preserve the coherence of the VAR model and maintain a sufficient number of observations for estimation. Segmentation would have reduced the sample size and compromised the robustness of dynamic analyses, particularly impulse response functions and variance decompositions.
In this perspective, the COVID-19 episode is treated as part of the macrofinancial environment in which the interactions between variables take place, rather than as a distinct regime. This approach allows for the analysis of monetary transmission within a context that integrates heterogeneous economic conditions, without imposing a structural break a priori.
In general, this choice of data and frequency is meant to make sure that the analysis is empirically consistent while also letting us look at the short-term dynamics that are at the heart of this study’s problem.
4.3. Variable Selection
The VAR model is based on a set of selected endogenous variables in order to capture the main dimensions of short-term monetary transmission in a bank-dominated financial system. The specification aims to articulate, within a unified framework, the interactions between financial valuations, balance sheet variables, and inflation in line with the study’s objective focused on the timing of adjustments.
Bank credit to the non-financial sector is retained as an indicator of real economy financing. By focusing on non-financial borrowers, this variable allows for the isolation of credit flows directly related to productive activity, excluding interbank operations. It constitutes a standard measure of the credit channel, widely used in the literature (Bernanke & Gertler, 1995; Stiglitz & Weiss, 1981).
The holdings in Treasury bonds are introduced to capture the portfolio reallocations made within the bank’s balance sheet. In banking-dominant systems, sovereign securities represent an allocation characterized by high liquidity, favorable prudential treatment, and low capital intensity. Their inclusion allows for understanding the substitutions between risky assets and safe assets in response to monetary conditions (Tobin, 1969; Acharya & Steffen, 2015; Ongena et al., 2019).
The joint introduction of credit and Treasury bonds thus allows for the characterization of the allocative dimension of the bank balance sheet. While credit involves an informational assessment and risk-bearing, sovereign debt constitutes a more liquid and less regulatory-constrained alternative.
The policy rate is introduced as a monetary policy instrument, allowing for the capture of policy innovations without imposing an explicit structural hypothesis on the central bank’s reaction function, in accordance with the standard VAR approach (Sims, 1980; Christiano et al., 2005).
The MASI banking index is integrated as a market indicator, allowing for the capture of the informational dimension of transmission. Stock valuations aggregate expectations related to profitability, financing conditions, and balance sheet risks. In the context of informational efficiency (Fama, 1991), they can quickly reflect monetary policy signals through adjustments in expectations (Bernanke & Kuttner, 2005; Nakamura & Steinsson, 2018).
Finally, inflation is introduced to incorporate the macroeconomic dimension of transmission. It reflects the diffusion of monetary effects through aggregate demand, financial conditions, and expectations (Clarida et al., 1999; Galí, 2008; Woodford, 2003). Given nominal rigidities, its dynamics are generally more gradual, making it a relevant indicator of the final stage of transmission.
Overall, this choice of variables allows for structuring the analysis around three complementary levels: (i) an informational dimension captured by stock market valuations, (ii) an allocative dimension reflected in balance sheet variables, and (iii) a macroeconomic dimension represented by inflation.
This structuring constitutes the central analytical framework of the study and allows for examining the differences in timing in responses to monetary policy shocks.
4.4. Time-Series Properties
The time series employed in this study exhibit heterogeneous statistical properties and are transformed to ensure stationarity, following standard econometric practice in VAR modeling (Granger & Newbold, 1974; Sims, 1980; Hamilton, 1994; Lütkepohl, 2005).
Macroeconomic balance-sheet aggregates observed at monthly frequency typically display strong persistence and stochastic trends. This is the case for bank credit to the non-financial sector (CREDIT-NFS) and banks’ holdings of Treasury securities (TBILLS), which are measured in levels and represent cumulative stock positions. Both variables are therefore expressed in first logarithmic differences:
The central bank policy rate (PR_t), although bounded, also exhibits persistence at the monthly frequency and is transformed in first differences:
The MASI Banking Index (MASI-B) is expressed in first logarithmic differences:
Inflation (INF_t) is introduced as a macroeconomic variable reflecting price dynamics. Consistent with standard practice in macro-financial VAR models, inflation is expressed in logarithmic differences, allowing for a stationary representation of its dynamics:
Unit root tests confirm that all transformed variables are stationary at conventional significance levels. The VAR model is therefore estimated using stationary first-difference representations of the variables.
4.5. VAR Model Spécification
Given the stationarity of the transformed variables, the empirical analysis relies on a Vector Autoregressive (VAR) framework specified in stationary form. The VAR approach provides a flexible representation of the joint dynamics among macro-financial variables, allowing for feedback effects and endogenous interactions without imposing a priori structural restrictions on causal relationships.
The vector of endogenous variables is defined as:
where:
measures changes in the monetary policy stance of Bank Al-Maghrib;
reflects short-term adjustments in banks’ holdings of sovereign Treasury securities;
captures short-term changes in bank credit to the non-financial private sector;
represents monthly returns of banking sector equities;
denotes changes in inflation dynamics.
The general VAR model of order
is given by:
where
is a vector of intercepts,
are coefficient matrices to be estimated, and
is a vector of reduced-form innovations assumed to be serially uncorrelated with constant variance.
All variables are treated as endogenous, reflecting the joint determination of monetary policy, financial market valuations, portfolio allocation, credit supply, and inflation within a system characterized by short-run feedback mechanisms.
The ordering of variables in the VAR is consistent with the timing assumptions underlying the identification strategy discussed in the subsequent section.
4.6. Pre-Estimation Diagnostics and Model Adequacy
4.6.1. Unit Root Tests
Prior to estimating the VAR model, the time-series properties of all variables are examined using Augmented Dickey–Fuller (ADF) and Phillips–Perron (PP) unit root tests in order to determine their order of integration.
Ensuring stationarity is a standard requirement in VAR analysis, as non-stationary series may generate spurious results and invalidate inference (Lütkepohl, 2005). The tests are conducted under specifications including intercept terms, consistent with the statistical characteristics of the data.
4.6.2. Structural Stability: Chow Breakpoint Test
The stability of the relationships among variables over the sample period is examined using the Chow breakpoint test. This test allows for the detection of structural changes at specified breakpoints by comparing the fit of the model across sub-periods.
In the present study, particular attention is given to the COVID-19 period and its aftermath, which constitute major macro-financial disruptions likely to affect monetary transmission dynamics. Breakpoints are therefore selected around key dates associated with the onset of the pandemic and the subsequent post-COVID adjustment phase.
This approach provides a useful framework for assessing whether the relationships between variables remain stable or exhibit structural shifts in response to these events. When structural breaks are identified, they can be accounted for through the inclusion of appropriate dummy variables in the VAR specification.
4.6.3. Multicollinearity Test
Potential multicollinearity among the explanatory variables is assessed prior to estimation. High multicollinearity may affect the precision and stability of coefficient estimates and complicate the interpretation of dynamic interactions.
The analysis relies on standard diagnostic measures, including correlation matrices and variance inflation factors (VIF), to evaluate the degree of linear dependence among variables. This step ensures that the variables included in the VAR system do not exhibit excessive collinearity that could undermine the reliability of the estimated relationships.
4.7. VAR Specification and Lag Order Selection
In order to determine the appropriate number of lags, several information criteria are used, notably the Akaike Information Criterion (AIC), the Schwarz Criterion (BIC), and the Hannan-Quinn Criterion (HQ). These criteria allow for a trade-off between the quality of fit and the parsimony of the model by penalizing the introduction of additional parameters.
The final choice of the number of lags is based on a combination of these criteria while taking into account the economic coherence of the model and the stability of the estimates. This approach ensures a balanced specification, suitable for the analysis of short-term dynamics.
4.8. Post-Estimation Diagnostic Tests
After estimating the VAR model, a series of diagnostic tests are conducted to verify the statistical validity of the model and the robustness of the results.
First, the absence of autocorrelation of the residuals is examined using the Lagrange multiplier (LM) test. This test allows us to verify if the model’s innovations are independent over time, a necessary condition to ensure the validity of the inferences.
Next, the normality of the residuals is assessed using the Jarque-Bera test. Although normality is not a strict condition for VAR estimation, it is a useful element for interpreting impulse response functions and variance decompositions.
The homoscedasticity of the residuals is also tested to verify the constancy of the error variance. The presence of heteroscedasticity could affect the accuracy of the estimates and the reliability of the confidence intervals.
Furthermore, the stability of the model is examined through the roots of the characteristic polynomial. A VAR is considered stable when all the roots are located inside the unit circle. This condition guarantees the validity of impulse response functions and variance decompositions.
Overall, these tests ensure that the estimated model meets the necessary conditions for a reliable interpretation of the observed dynamics.
4.9. Dynamic Analysis: IRFs and FEVDs
The dynamic behavior of the VAR system is analyzed using impulse response functions (IRFs) and forecast error variance decompositions (FEVDs). IRFs trace the temporal response of each endogenous variable to a one-standard-deviation innovation, while FEVDs quantify the relative contribution of each shock to forecast error variance at different horizons (Sims, 1980; Lütkepohl, 2005).
Identification of innovations relies on a Cholesky decomposition of the variance–covariance matrix of reduced-form residuals. This approach imposes a recursive contemporaneous ordering of variables and yields orthogonal shocks, facilitating interpretation. The resulting IRFs and FEVDs are therefore interpreted as conditional dynamic responses, rather than as structural causal effects.
Statistical inference is conducted using bootstrap confidence intervals, which are well suited to finite samples and macro-financial environments characterized by potentially non-Gaussian innovations (Kilian, 1998).
4.10. Robustness to Identification: Generalized Impulse Response Functions
To assess the sensitivity of the results to the recursive identification implied by the Cholesky decomposition, generalized impulse response functions (GIRFs) are computed following Pesaran and Shin (1998). Unlike orthogonalized IRFs, GIRFs do not require orthogonality of shocks and are invariant to the ordering of variables in the VAR system.
Confidence intervals for the GIRFs are obtained using Monte Carlo simulations. This robustness exercise allows verification that the qualitative dynamic patterns identified in the baseline analysis are not driven by the specific identifying assumptions and remain stable when these constraints are relaxed.