Monetary Policy in a Markov-Switching VECM: Implications for the Cost of Disinflation in Ghana

Corresponding Author: Richard Kwabi Ayisi Department of Economics, Management and Quantitative Methods (DEMM), University of Milan, Italy Email: ayisi0@gmail.com Abstract: Monetary policy assessment in Ghana has been conducted using vector auto-regression. This however, presumes stability of long run outcomes and particularly ignores monetary policy regime changes that has characterized the economy overtime. This study thus introduced the possibility of switches in the long run equilibrium in co-integrated vector auto-regression by allowing both the covariance and weighting matrix in the error-correction term to switch. The study did not find any significant difference in monetary response in the different states. However, significant difference was obtained for the cost of disinflation across states. Though, disinflation cost has declined as the Bank of Ghana shifts from monetary targeting to inflation-targeting regime, overall cost is still high. This has implication on disinflation policy given the development agenda pursue by the country.


Introduction
Monetary policy has been the main tool used for macroeconomic stabilization in Ghana. Over the years, the monetary framework has undergone important changes regarding implementation (shocks) and policy (regime) framework. The policy regimes involve switches in the policy rule (i.e., from credits to interest rate instruments) to reflect monetary authorities' reaction to target inflation and output. Emerging from a direct control approach, monetary policy has evolved via monetary targeting approach (an indirect approach under the requirement of structural adjustment program) to its current state of inflation targeting.
These evolution processes aim to enhance the impact of monetary actions on the aggregate economy. Though, monetary policy objectives compose of wide range of aggregates (including growth, exchange rate stability, interest rate and among others), its paramount effort is to curtail the high prices that have bedeviled the economy through disinflationary strategies. This is predominantly motivated by the high cost associated with high and volatile prices.
However, following from Okum (1978), there is potential loss in output or employment associated with disinflationary policy. Given that Ghana is a developing country and desires to accelerate growth in its development path, knowledge about the cost of disinflationary policies is worthwhile. This will guide monetary policy implementation because policy makers will be guided by the economic cost of their actions in terms of output loss.
Also, the regime changes can potentially have a large effect on the volatility of money, interest rates, outputs and prices. This study thus investigates monetary shocks by exploring the cost implication of regime changes on the disinflation strategy adopted by Ghana. The investigation is conducted within the periods 1960 to 2013. We conduct this study for Ghana because no literature has been identified on this theme. Secondly, since the focus of the Bank of Ghana is price stability, it is important to understand the economic effect of this policy directions in terms of output loss. This is because a fore knowledge of the economic cost associated with the disinflation policy will aid monetary authorities in implementing monetary policy.
The study adopted the modelling approach based on multivariate Markov-Switching vector error correction model (hereafter MS-VECM). This strategy explicitly allows for regime changes in the variables since Ghana overtime has been characterized by different monetary and policy regime. The regime changes might have potential stochastic effects on both the short and long run dynamic impacts of monetary policy. MS-VECM modelling approach can account for the long run properties in this regard. Existing evidence on the impact of monetary policy in Ghana were based on vector error correction model but the results are mixed (Abradu-Otoo et al., 2003). Hitherto VAR models assume linearity and thus are unable to represent many non-linear dynamic patterns such as asymmetry, amplitude dependence and volatility clustering. For example, GDP growth rates typically fluctuate around a higher level and are more persistent during expansions, but they stay at a relatively lower level and are less persistent during contractions. Given this peculiarity, it would not be reasonable to expect a single, linear model to capture these distinct behaviors.
Also, the underlying linearity assumption implies that the dynamic multipliers obtained from the VAR are invariant about the history of the system, size and sign of the shocks. However, the time-invariance of the parameters and Gaussianity are problematic for the better understanding of monetary policy shocks in Ghana especially regarding the structural shocks that has characterized the economy over the period. For example, as Fig. 2 show, the distribution of GDP and CPI are bimodel. This implies that the single distributional assumption used in hitherto VAR might have probable inference consequences on the estimates and monetary behavior in Ghana. Hence, this paper in its first attempt for Ghana provides an important contribution to the literature in this context.
The study proceeds with section 2 providing a brief literature on monetary policy in Ghana. Section 3 describes the econometric strategy employed. Section 4 presents the results and discussion whiles section 5 concludes the study with some policy recommendations.

Literature Review
The empirical literature directed to verify monetary policy implementation and its effectiveness has grown extensively overtime. Given that monetary policy changes can occur in the implementation of policy (shocks) as well as objectives of policy (regimes), the implementation of policy (shocks) has been typically modelled as vector innovations to a Vector Auto-Regression (VAR) where monetary policy is identified by structural restrictions on the contemporaneous impacts of the variables (Neville and Owyang, 2004;Sims, 1992). The structural VAR literature on monetary policy exists in several studies (Cambazoglu and Karaalp, 2012;Epstein and Heintz, 2006;Luke, 2000;Moscarini and Postel-Vinay, 2010;Bernanke and Mihov, 1998). VAR Models however, assume linearity and thus it is unable to represent many non-linear dynamic patterns such as asymmetry, amplitude dependence and volatility clustering.
Due to these inherent weaknesses in the VAR model, switching monetary policy regimes have gained a lot of attention in recent literature (Boivin and Giannonni, 2002;Hanson, 2002;Ghiani et al., 2014;Thams, 2007). Policy regimes engage switches in the policy rule that mirror changes in the policy maker's reaction to deviations from the target inflation rate and or output growth. Switching monetary policy studies are also able to account for unrelenting adjustments in policy which result from changes in central bank leadership or transparency which also affect the volatility of money, output and interest rates (Clarida et al., 2000;Dennis, 2001;Hanson, 2002). For instance, Dennis (2001) argues that a change in policy maker preferences has shifted after -1979 inflation target from around 7% to a value below 2%.
Other studies have examined both the regime changes (objectives of policy) and policy shocks (policy implementations). To these studies, monetary policy is relevant not only to the policy maker's response to the exogenous economic shocks but also to the contemporaneous effects of the monetary policy innovations (Owyang, 2002;Sims and Zha, 2002). These papers however, failed to address the long-run objectives and impacts of monetary policy. The paper, like Neville and Owyang (2004) incorporates these long-run impacts. Regime switches in the long run relationship through the weighting matrix of the error correction term is also taken care off.
Although a lot of studies have used the Markov Switching in an error correction framework (Clarida et al., 2003;Paap and Van Dijk, 2003;Hanson, 2002 and among others) around the world, Monetary policy studies in Ghana has been based on Vector innovations to a Vector Auto regression (VAR) (Abradu-Otoo et al., 2003;Epstein and Heintz, 2006;Atta-Mensah and Bawumia, 2003). Such studies are unable to represent many non-linear dynamic patterns. Also, these studies ignored monetary policy regime changes that has characterized the Ghanaian economy overtime. This study thus comes handy to address such issues.

Econometric Modelling
The aim of the study is to explore monetary policy implementation in regime switching. Hence the study adopted a vector error-correction model that allows for different states of the economy. The regime switching can either be modelled to allow all or part of the coefficient matrix to switch independently or with the error-correction term. However, this study allows the switch with the error term. This approach thus, assumes a stable long-run relationship i.e., regime invariant co integrating vector whereas the short run dynamics are analyzed in a Markov-Switching framework which allows the error correction to respond to regimes. By this, the study can examine the state dependent responses to monetary policy shocks.
Where: ∆Y t = An n dimensional vector of differenced variables of interest. α = A vector of intercepts. α i = nXn parameter matrices. ω st = The state-dependent long run impact matrices.
The long run state dependent matrix comprises of rXn matrix of co integrating vector β and nXr statedependent weighting matrix t st . Therefore: Given a two state first order Markov process S t ∈{0, 1} with its associated transition kernel P, where P ij = Pr[S t = i| S t-1 = j], then Equation 3.1 can be re-written as: Though, the long run state-dependent matrix can either switch in the co integrating vector, the weighing matrix or both, this study allows only switches in the error-correction term which implies a single set of long run relationship. This means that the correction mechanism depends on the state. By implication, switches in this framework are interpreted as differences in the rate at which the common long run relation is obtained.
Allowing switches only in the error term is predominantly motivated by some potential interpretations. Given a regime-invariant long run relationship between the variables, the state-dependent coefficient assign weights to each relationship which implies that any perturbation to the system could have different long run effects across states (though the long run relationship is unchanged). For example, monetary perturbation has different long run effects depending on the monetary objective (targets). The different effect is because the long run response coefficients (ω st = t st β) is a function of the switching elements (Hamilton 1994, pp. 579-581).
Estimation of Equation 3.2 is through the Gibbs sampling techniques. The procedure determines the co integrating relationships at the initial stage which are used to draw parameter values from the posterior prior. The study used the Bayesian methodology that uses Sims and Zha (2002) prior. This approach uses prior which accounts for non-estimated co integrating vectors. This therefore, does not require any explicit modelling of the co integrating vectors.
To analyze the effect of monetary policy shock, the study adopts the Cholesky ordering which places the policy instrument last in the system ordering. In this three-variable system comprising price, output and policy instrument, the study assumes that monetary authorities observe prices and output before determining the level of the instrument. By this identification, it is assumed that policy does not contemporaneously impact on prices and output.

Data
Annual data ranging between 1964 and 2013 obtained from the World Development Indicator (WDI) were used for the analysis. The variables include consumer price index, gross domestic product at constant local currency unit and broad definition of money (M2). Though the central bank of Ghana in recent times is using interest rate instrument, the study adopted M2 as proxy for policy instruments because the time frame of the study includes periods of monetary targeting regime. To eliminate outliers, all the variables are logged. Figure 1 shows the graph of the series at both level and first differenced. We observe spikes in the plot of the differenced series suggesting structural changes and regime shifts. Thus, we conducted a preliminary exploration analysis to inspect the distribution of the series with some of its lags. This gives first-hand information on whether any of the series contain regimes. Figure 3 and 4 depict non-parametric plots of the series versus their first to fourth lags. The figure reveals a linear approximation for the series. This suggests that a linear approximation for the analysis may not be questionable since the entire series exhibits linear trend with no possibilities of regime shifts. However, the distributional plot for CPI and GDP in Fig. 5 indicates that the series depict bi-modal distribution suggesting the possibilities of regimes (i.e., the evolution process of the series might differ across periods). Following this both regime and non-regime unit root test were conducted on the series. Table 1 shows the test results for both regime and non-regime unit root tests. The non-regime unit root tests were conducted using the ADF test, whiles the regime test is conducted on a unit root null hypothesis against stationary SETAR. The test statistic is compared with the bootstrapped critical value 16.181, 18.4 and 23.01 for 10, 5 and 1% respectively. As Table 1 shows, the results from both tests indicate the presence of unit root in the series.   The study further conducted a formal test to investigate the presence of co integration among the series. The formal test result is provided in Table 2. The test was conducted on two hypotheses. First, a test of no co integration against threshold co integration was conducted. A P-value of 0.93 fails to reject no co integration in the series. The second, a test of linear co integration against threshold co integration, supports the presence of linear co integration given a P-value of 0.44. Though, both tests reject threshold co integration, a test of model fit supports a model with one threshold. A P-value of 0.07 associated with the test statistic in the model fit test of linear VAR versus threshold VAR indicate that at 10% critical level, modelling the data in one threshold regime is superior. Based on this, the study proceeds in a Markov switching approach with one regime.

Result and Discussion
Given the study's objective to investigate monetary shocks in regimes, the study estimated a VECM model with extensions to accommodate states. This follows the exploratory analyses which indicate the presence of cointegration among the variables. The VECM is estimated in the presence of state restrictions following a tractable Markov process. The innovation of monetary shocks is estimated within a simple Cholesky specification ordering the policy variable (i.e., M2) last. Table 3 reports that there is only one co-integrating relationship and provides the weighting matrix for the relation that vary across regimes. The co-integration vector is fixed across regimes.

States
The transition probabilities for each state is reported in Table 4. The probability estimates indicate high level of persistence in each state. The probability of transition from one state to another is approximately the same in the arena of about 12%.

Response to Policy Shocks
The study considered the short run response to a one standard deviation shock to the policy instrument (i.e., money supply). The impulse response function is generated for a horizon up to twelve years. The generated IRF are either conditioned or not conditioned on the state (i.e., when the shock is generated in one state, it is transmitted through that particular state). Figure 6   The graph shows that there are no significant differences in how prices and output respond to the policy instrument. The effect of policy changes on prices and output is very minimal with coefficient ranging the same in both state 1 and state 2. The effect of policy instrument hits prices and output respectively from the 11 months and 8 months onwards in state 1. Similar evidence is found in state 2.

Cost of Disinflation
High inflation has bedeviled the economy of Ghana for long. However, in recent times inflation has showed a downward trend over the past few decades. In comparing the developments in the current monetary regime (inflation-targeting) to the control regimes and the monetary targeting regimes, the inflation rate has been quite stable. It averaged 50.0% per annum during the 1970s, 44.5% during the 1980s and was 27.9% during the 1990s and further down to 16.2% in the early six years of 2000s. Within the period 2009 and 2010, the rate has been stable at single-digit, though the trend has reverted upward in recent years. The favorable downward trend in the inflation rate together with the gains in the general macroeconomic trends raise issues in the short run tradeoff between stability and growth particularly given that Ghana is a developing country and desires to accelerate growth for development purposes. Thus, this study estimated the cost of disinflationary policy for Ghana. The tradeoff between output and inflation has been a popular area of research for years. Though, there are consensus among economists that high inflation is inimical to the economy, disinflationary policies on the other hand result in some short-run costs in terms of loss in output. As identified by (Okun 1978), disinflationary monetary policy result in output or employment loss (See among others Cecchetti and Rich, 2001;Fuhrer, 1994;1995) a one percentage point fall in inflation.
Various methods for estimating the sacrifices ratio has been suggested in the literature (Ball, 1994;Zhang, 2001;Cecchetti and Rich, 2001). To calculate the sacrifice ratio, this study adopted Cecchetti and Rich (2001) VAR approach to access the output cost of disinflationary monetary shock within a single regime. As argued by Neville and Owyang (2004), this modelling approach can measure the cost of disinflation occurring because of switches between regimes.
Following Neville and Owyang (2004), this study posits two distinct disinflationary episodes to include disinflationary periods driven by a policy shock and one driven by change in regime. Aside using the Markov process for the states, the study experimented to investigate the credibility of monetary authorities as policy switched from monetary targeting to inflation targeting framework. The aim is to identify if the credibility is enhanced given that credibility underscore inflation targeting. The estimated sacrifice ratios for both within and across states are reported for both the Markov process and pre-specified regimes in Table 5. As showed in the table, the within-regime sacrifices ratio is estimated to be 1.46 and 1.90 for state 1 and 2 respectively. For the pre-specified, the study estimated the ratios for the periods prior to 2002 and the aftermath representing monetary and inflation targeting regimes respectively. The results indicate that the sacrifice ratio has fallen from 0.59 to 0.43. This has implication for expectation formation hence, credibility from monetary authorities. The results suggest that agents can forecast inflation very well since they are utilizing the same information available to monetary authorities. By this the cost of disinflation becomes minimal.
Generally, the study found a low sacrifice ratio which is in conformity with Kinful (2007) study. Though, the foregoing discussions indicate disinflationary cost has fallen within the inflation targeting period, the overall (pooled sample) sacrifice ratio estimated at 1.42 suggests a cumulative output loss of approximately 15%. This produces a worrying situation given that Ghana is a developing country which desires to accelerate growth for development.

Conclusion and Recommendation
This study examined monetary policy shock in a Markov-switching vector error correction framework. The study assumed a stable long run co-integration relationship, whiles allowing long run variations through switches in the weighing matrix of the error correction term. While as this approach overcomes the linearity assumption in dealing with monetary policy shock, it's theoretical appealing goes to the rational expectation critique of model of this kind.
In investigating monetary impulse, the study found that though, monetary shocks generate different impulse in each state, the monetary response do not differ significantly across regime. The study also analyzed the cost implication of disinflationary policy in Ghana. The estimated sacrifice cost of disinflation differs within and across states. In conformity with studies in the literature, the result indicates that the cost of disinflation is very low though.
The finding of this study has some policy implication for the conduct of monetary policy in Ghana. The sacrifice ratio obtained indicate that monetary policy should be conducted with care in order not to erode output growth given the state of economic development in the country. Further, the study suggests that cost of disinflation is low within inflation targeting period because agents can forecast better due to enhanced credibility. By implication, policy makers should be more transparent and credible in their actions to help minimize associated cost.