Abstract
This paper evaluates monetary policy trade-offs in low-income countries using a dynamic stochastic general equilibrium model estimated on data for Mozambique, taking into account the sources of major exogenous shocks and the level of financial development. The simulations suggest that an exchange rate peg is significantly less successful than inflation-targeting at stabilizing the real economy due to higher interest rate volatility, as in the literature for industrial countries and emerging markets.
The use of monetary policy for macroeconomic stabilization in low-income countries, particularly sub-Saharan Africa poses a number of challenges that have not been fully analyzed in a literature focusing mainly on the conduct of monetary policy in industrial countries. While a number of studies have analyzed the sources of inflation in developing countries and sub-Saharan Africa (Loungani and Swagel, 2001; Barnichon and Peiris, 2007), only a few papers have analyzed the trade-offs between alternative monetary policy rules in sub-Saharan Africa and low-income countries, in general.1 The vast literature on “the science of monetary policy” is focused on industrial countries and advanced emerging markets (Taylor, 1998; Clarida, Gali, and Gertler, 1999), providing limited insights to the conduct of monetary policy in low-income countries where the characteristics of the economy and monetary policy setting is quite different.
These include the need to coordinate monetary and exchange rate policy with fiscal policy in order to manage large volatile aid inflows and/or government revenues from natural resource exploitation (IMF, 2005a). In particular, economic policy needs to consider the potential adverse effects of such shocks on the tradable sector—the so-called Dutch disease problem2—as well as the traditional objectives of inflation and output stabilization.3 In addition, commercial banks in sub-Saharan Africa are at the center of a formal financial system and for most countries the conduct of monetary policy focuses primarily on the supply of and demand for the monetary base (Adam and others, 2007). As a result, interest rates represent a reliable instrument of monetary policy only in the very few cases where inter-bank money markets and secondary markets for government debt are well developed. Finally, the dominance of commercial banks and information asymmetries are likely to mean that the credit channel is a prominent part of the monetary policy transmission mechanism (Bernanke and Gertler, 1995).
In such an environment, many view the current monetary policy setting in sub-Saharan Africa as an interim stage in a move toward wider adoption of formal inflation targeting practices in which inflation (more precisely, expected inflation) is the intermediate target/goal,4 instead of either some monetary aggregate or the exchange rate, and in which the interest rate rather than base money is the operational target (Adam and others, 2007). Thus, while elements of this debate will necessarily reflect themes in the current literature on monetary policy in emerging market countries (IMF, 2005b), the current policy arrangements in mature stabilizers are inflation-targeting frameworks in the broad sense of having the maintenance of a nominal anchor at their core (Adam and others, 2007). More precisely, they could be described as “lite” inflation targeting regimes as in Stone (2003), in which the monetary authority probably aim to bring inflation into the single-digits and maintain financial stability, including through a relatively interventionist exchange rate policy.5 In this respect, therefore, the relevant policy questions are not wholly those concerned with how, and over what horizon, countries may make the move toward formal inflation targeting; they must also include how best the available instruments of monetary policy be deployed in shock prone mature stabilizers (Adam and others, 2007).
This paper attempts to evaluate monetary policy trade-offs in low-income countries using a dynamic stochastic general equilibrium (DSGE) model estimated on data for Mozambique—a mature stabilizer in sub-Saharan Africa—taking into account the sources of major exogenous shocks, transmission mechanisms, and level of financial development. The central banks of many sub-Saharan African countries conduct monetary policy through a combination of direct instruments (for example, reserve requirements) as well as foreign exchange interventions and open market operations with the private sector that effect the monetary base. Therefore, like Adam and others (2007) and Buffie and others (2004), we analyze the trade-offs of both foreign exchange sales and open market operations in the conduct of monetary policy in Mozambique. We compare three different rules for how the central bank deploys its available instruments. Under the first rule, the central bank stabilizes the exchange rate. The second and third rules assume that the central bank is set to stabilize some measure of inflation around a target. In particular, we consider, firstly, the case where monetary policy seeks to stabilize consumer price index (CPI) inflation, secondly, a policy that stabilizes inflation in nontraded goods. To our knowledge this is a first attempt at estimating a DSGE model for sub-Saharan Africa excluding South Africa. More generally, we hope to provide a benchmark DSGE model incorporating features of sub-Saharan Africa and low-income countries that could serve as a starting point for monetary policy analysis.
In line with the existing literature on the welfare implications of monetary policy, our model is solved using recent methods in computational economics that makes it feasible to compute higher-order approximations to the equilibrium conditions in dynamic general equilibrium models. We also consider the best response, in terms of minimizing macroeconomic volatility, of alternative monetary policy rules in response to foreign aid and numerous other exogenous shocks that are important in sub-Saharan Africa, motivated by the interest of central bankers there. To preview our results, both nontradable and CPI inflation targeting performs better than an exchange rate peg, in line with the findings of standard new open-economy macroeconomics models.
I. The DSGE Model
This paper develops a macroeconomic model for monetary policy analysis in sub-Saharan Africa using data for Mozambique. As compared with previous empirical analysis of the Mozambican economy, or for that matter most sub-Saharan African countries, we conduct our analysis within the context of a microfounded DSGE model. DSGE models have several benefits that make them attractive for the analysis of macroeconomic policy:
They are structural in the sense each equation has an economic interpretation. Policy interventions and their transmission mechanism can therefore be clearly identified, thereby facilitating a discussion of alternative policies.
They are microfounded in the sense that they are explicitly derived from the optimizing behavior of households and firms in the economy. They thus describe the behavior of the agents in the economy in terms of parameters that are structural in the sense that one would not expect them to change as the result of changes in economic policy, thereby validating the analysis of alternative policies.
They are stochastic in the sense that they explicitly discuss how random shocks, such as an aid shock or a shock to fiscal policy, affect the economy.
They are forward-looking in the sense that agents optimize from rational, or model consistent, forecasts about the future evolution of the economy.
These characteristics make DSGE models particularly attractive for the purpose of analyzing the effect of alternative macroeconomic policies, for example the appropriate policy response to an aid shock, which helps explain its widespread use among central banks and other policy institutions in Organization for Economic Cooperation and Development countries. This paper represents the first attempt at constructing such a model for Mozambique.
A traditional weakness of DSGE models has been the difficulty in parameterizing them using economic data. This problem is particularly severe in developing countries, such as Mozambique, where data series are short or, in many cases, lacking. In order to overcome this problem, research often resort to calibrating the parameters of the model using information from previous studies or characteristics, such as the volatility of the data. The difficulty of explicitly relating the model to the data seriously undermines its use as a tool for policy analysis.
In order to overcome the problem of the parameterizing the data, this paper makes use of recent advances in Bayesian econometrics. Within this framework, the Kalman filter is used to allow inferences about the unobserved variables in the model and prior empirical or theoretical knowledge about the parameters of interest is used to increase the efficiency of the estimation, thereby overcoming the problem of short data series. These Bayesian inferences have been successfully applied to the estimation of DSGE models by, inter alia, Juillard and others (2004), Smets and Wouters (2003 and 2005), Lubik and Schorfheide (2006), and Saxegaard (2006b). As far as we are aware, this paper represents the first attempt at estimation of a DSGE model using Bayesian methods on data for a country in sub-Saharan Africa other than South Africa.
The use of Bayesian inference has a number of benefits that are worth highlighting. Firstly, this approach allows us to incorporate prior empirical or theoretical knowledge about our parameters of interest. Thus, if it is known that a parameter, such as the discount rate, must lie between zero and one, it seems that this information would be a useful addition to our estimation procedure. More generally, the incorporation of prior information allows us to formalize the use of information about parameters from prior studies.
It should be noted, however, that the impact of prior information on the estimation procedure is one of the main criticisms of Bayesian methods. However, Fernández-Villaverde and Rubio-Ramírez (2004) show that asymptotically the parameter point estimates converge to their true values and thus that the importance of the prior disappears as the sample grows. In small samples such as ours, the same authors provide compelling evidence for the strong performance of Bayesian methods.
Secondly, Bayesian inference provides a natural framework for parameterizing and evaluating simple macroeconomic models, such as ours, which are likely to be fundamentally misspecified. As pointed out by Fernández-Villaverde and Rubio-Ramírez (2004) and Schorfheide (2000), the inference problem is not to determine whether the model is “true” or the “true” value of a particular parameter, but rather to determine which set of parameter values maximize the ability of the model to summarize the features of the data.
Finally, Bayesian methods provide a simple framework for comparing and choosing between different misspecified models that may not be nested, on the basis of the probability that the model assigns to having observed the data (the marginal likelihood of the data, given the model). Geweke (1998) shows that this is directly related to the predictive performance of the model and is thus a natural benchmark for assessing the usefulness of economic models for policy analysis and forecasting.
Structure of the Model
The model is based on the open-economy DSGE model outlined in Kollmann (2002) and Saxegaard (2006a). The augmented model features an explicit treatment of the conduct of monetary policy in sub-Saharan Africa as in Adam and others (2007) by assuming that the monetary authority affects the money supply through the sale of foreign exchange and bond transactions, although the bonds are bought by the banking sector instead of consumers as in Agénor and Montiel (2007a and 2007b) and Peiris (2002). The model incorporates credit frictions by assuming that firms have to borrow at a premium over deposit rates to finance part of the inputs in the production process as in Atta-Mensah and Dib (2003). The premium, in turn, is inversely related to the ratio of firms’ assets (the value of their beginning-of-period physical capital stock times the price of the domestic good) over their liabilities, which consist of beginning-of-period borrowing as in Agénor and Montiel (2007a and 2007b). Learning by doing is incorporated as in Prati and Tressel (2006) by assuming that productivity is a function of the size of the tradable sector and public investment expenditure.
The basic structure of the model consists of perfectly competitive firms that produce a final nontradable good that is consumed by a representative household and the fiscal authorities, in addition to being used for investment. The inputs used in the production of the final good are either produced domestically or imported by monopolistically competitive intermediate goods firms.6 The domestically produced goods, which are produced using capital, labor, and borrowing from a financial intermediary as inputs, are sold either in the domestic market or exported overseas. For simplicity we assume that the capital account is closed. The markets for capital, labor, and commercial bank loans are competitive. The model is completed with a description of the fiscal and monetary authorities.
In order to provide a rationale for monetary and fiscal stabilization policy, four sources of inefficiency are included in the model: (1) mono-polistically competitive product markets; (2) sluggish price adjustment in the domestic economy using the specification of Rotemberg (1982); (3) capital adjustment costs and investment adjustment costs using the specification of Christiano, Eichenbaum, and Evans (2005); and (4) adjustment costs in commercial bank reserves and an interest rate spread that depends on the net worth of companies as described above. This framework captures many of the rigidities that previous studies have found are important to describe the dynamics in the data and serves as a useful starting point for developing a DSGE model for Mozambique.
Household Behavior
The objective of the consumer is to maximize the expected value of the discounted sum of period utility functions:
where Ct is consumption, Lt is labor supply,
where
where δ is the rate of depreciation and ψt is an adjustment cost function that is a function of the ratio of investment to capital:
where ϕ1,ϕ2>0 and
The consumer’s problem can thus be written as:
where λt and ωt are Lagrange multipliers.
The relevant first-order conditions for consumption, labor, money, and deposits are:
The first-order conditions for capital and investment are, respectively:
where
Final Goods Production
Final good producers produce a good Ft by aggregating over a continuum of domestically and imported intermediate goods, indexed by sϵ[0,1]. The aggregating technology is given by the constant elasticity of substitution (CES) aggregate:
for some elasticity of substitution ϑ > 1.
for i = d, m. Profit maximization implies the standard demand functions for intermediate goods:
with an associated cost-minimizing price index.
Intermediate Goods Production
Following Prati and Tressel (2006), we incorporate learning by doing in the production function as well as credit constraints following Atta-Mensah and Dib (2003). The credit constraints are incorporated by assuming that intermediate good firms use an intermediate good input, ϑt, that is funded by borrowing from a financial intermediary. Following Atta-Mensah and Dib (2003), we assume that firms borrow to pay for intermediate goods inputs as opposed to wages or capital because it is equivalent to using the loan as a variable in the production function and it generates more dynamics in the model.
The production technology is Cobb-Douglas:
where θt represents productivity that we assume is affected by both the size of the tradable sector and the amount of government expenditure on capital goods:
where we allow productivity to follow a stochastic autoregressive process and where
The problem facing the firm is to minimize costs subject to satisfying demand:
where we assume for the moment that the firm takes prices as given. The first-order condition for Kt, Lt and
Nominal marginal costs can be written as the ratio of the nominal wage to the marginal product of labor:
We assume that each domestic firm sells it output both on the domestic and export market so that
where
Price-Setting by Intermediate Goods Producers
Intermediate goods producers face quadratic adjustment costs in setting prices measured in terms of the intermediate good and given by:
Hence, we assume that the cost of price adjustment is related to the change in inflation relative to the past observed inflation rate. Juillard and others (2004) argues that this allows for more realistic inflation dynamics in the model with a backward-looking term in the solved out Phillips curve.
The optimal price-setting equation for the nontradable price can then be written as:
which reduces to the well-known results that prices are set as a markup over marginal cost if prices are flexible. For simplicity, we assume that the law of one price holds in the export market so that
Financial Intermediary
The financial sector is assumed to convert deposits from households into loans to intermediate goods firms and the public sector and bank reserves similar to Agénor and Montiel (2007a and 2007b):
Thus, for a given level of bank reserves, an increase in the amount of deposits at the financial intermediary reduces the amount of money in circulation and thus the utility from liquidity services.
Deposits are assumed to earn the same rate of interest as the interest on government bonds. Lending to intermediate good firms earns an interest that is a markup over the interest rate on deposits where the markup is a function g(.) of firms’ beginning of period net worth (the value of their capital stock over their liabilities) as in Agénor and Montiel (2007a and 2007b):
The Public Sector
The central bank’s balance sheet is:
where et is the nominal exchange rate, Zt are international reserves, and Bt+1 are government securities held by the central bank maturing next period. We assume for simplicity that no interest is earned on international reserves. Under the assumption that profits of the central bank are transferred to the fiscal agent, the public sector’s budget constraint takes the form:
where At is aid and
The consolidated budget constraint is then:
where
Fiscal and Monetary Policy Rules
In our model the fiscal and monetary authorities have access to four different instruments of which three can be used independently. The fiscal agent controls government spending, taxation, and net domestic borrowing, whereas the monetary authority controls the level of international reserves.
We analyze fiscal policy rules of the form:
where ω and ι determine the fraction of aid used to reduce taxes and increase expenditure and thus increase the primary fiscal deficit (before grants). A ω less than one unambiguously lowers the primary deficit after grants. If ω equals zero, the primary deficit after grants falls by the amount of aid. If ω is between zero and one so that part of the aid is spent, ι determines the allocation of that spending between the private and the public sector. If ι equals zero the increased spending is carried out by the government whereas if ι is one the increased spending is done by the private sector. We assume the fiscal regime remains unchanged and foreign aid, which is very large in many sub-Saharan Africa countries (IMF, 2005a), is fully spent, unless otherwise stated.7
The effect of a shock to aid on international reserves and the monetary base will depend on the actions of the central bank. We follow Adam and others (2007) and Peiris (2002) in our specification of the policy rules for the central bank. Foreign exchange rate intervention is governed by:
where z1 governs the authorities commitment to a constant level of reserves and z2 determines the commitment to an absorb as you spend scenario whereby the sale of foreign exchange is conducted in line with government spending increases financed by the aid inflows. z3 governs the commitment to a crawling peg where the crawl is determined by the steady-state inflation differential (π—π*) between at home and the rest of the world. Finally, z4 determines the extent to which the sale of foreign exchange reserves is used to achieve a given target of the inflation rate π.
Any foreign exchange rate intervention will have an impact on the monetary base and the exchange rate with possible implications for inflation and output volatility. The authorities have the option of conducting open-market operations on a temporary basis. Thus we have:
where b1 governs the extent to which bond operations are used to sterilize the impact of foreign exchange interventions on the monetary base; b2 determines the commitment to the inflation target; b3 governs the effect of output gap considerations in the conduct of monetary policy; and b4 > 0 entails that all bond operations are unwound over time.
Market Clearing and Aggregation
In general equilibrium, supply equals demand in the intermediate and final goods market at posted prices:
The model can alternatively be closed using the balance of payments identity:
Stochastic Shocks
A number of stochastic shocks are included in the model in order to ensure that the model is not stochastically singular and in order to be better able to reproduce the dynamics in the data. In particular, the number of exogenous shocks must be at least as large as the number of observed variables in order to estimate the model using classical Maximum Likelihood or Bayesian methods. Our model includes 14 structural shocks: two preferences shocks to the marginal utility of consumption and labor
II. Empirical Findings
The model described above was estimated on quarterly data for Mozambique covering the period 1996:Q1–2005:Q4 on 18 key macroeconomic variables: GDP, consumption, exports, imports, the real exchange rate, inflation, export price inflation, import price inflation, M2, currency in circulation, deposit rates, lending rates, foreign currency reserves, government bonds, commercial bank reserves, aid, government spending, and lending to the private sector. This vastly exceeds the number of observed variables included in recent papers that use Bayesian techniques to estimate DSGE models, such as Juillard and others (2004) and Saxegaard (2006b). The remaining endogenous variables in the model are assumed to be unobserved.
Prior to estimation, the macroeconomic variables were transformed into real per capita measures. Following the approach in Juillard and others (2004) we remove a time trend in the data on the key macro variables using the Hodrick-Prescott filter. In addition, we remove seasonal effects in the series in which these are evident using the X12arima filter and transform all variables to mean zero variables.
Following Juillard and others (2004) and Saxegaard (2006b), our estimation strategy involves fixing the parameters that determine the steady-state of the model, based either on findings from previous studies, notably Tarp and others (2002), or in order to replicate features in the data, and then estimating the parameters that determine the dynamic properties of the model. The calibrated parameters values and calibrated steady-state ratios are summarized in Appendix Table A1.
As mentioned previously, estimation of the model by Bayesian methods allows the incorporation of prior empirical or theoretical knowledge through the specification of a prior distribution for the parameters to be estimated. Our choice of prior distributions is guided both by theoretical restrictions imposed on some of the parameters as well as empirical evidence. In instances where the literature and theory provide little or no guidance, diffuse priors are chosen. The choice of priors together with the resulting parameter estimates (posterior distribution) is summarized in Appendix Table A2.8 Overall, the Bayesian estimation methodology yields plausible parameter estimates for the model, which are broadly in line with the results from previous studies. A comparison of the one-step-ahead forecasts with the actual data (Appendix Figure A1) reveals that the model is able to replicate fairly well the movements in the data.
III. Monetary Policy Rules in a Shock-Prone Economy
The discussion in the previous section suggests that the model appears to be able to deliver reasonable parameter estimates when estimated using Bayesian estimation techniques. In this section, we explore the impact of alternative shocks under three alternative monetary policy rules. First, we analyze the effect of a persistent (autocorrelation coefficient of 0.8) shock to technology before turning our attention to analyze the effect of a similarly persistent aid shock that raises aid by 2 percent of steady-state GDP. With the exception of the policy rules and the assumption that all aid is spent by the government, the parameterization of the model is that resulting from the estimation results discussed above. The response of the system is analyzed under the assumption that the authorities aim to stabilize either CPI inflation (b2 = z4 = 10), nontradable inflation (same but with nontradable inflation), or the rate of depreciation (equal to the long-run inflation differential between Mozambique and the rest of the world) of the nominal exchange rate (z3 = 10).
Figure 1 show the impulse responses associated with an unanticipated shock to technology. Not surprisingly, the impulse response functions resemble those reported in Saxegaard (2006a), although differences do exist mainly due to the assumption of a closed capital account and flexible import and export prices. In particular, under all policy rules output rises in response to the improvement in production technology. As is standard in new-Keynesian models (Galí, 1999), labor falls as a result of the interaction between sticky prices and technological change. Technological change induces a decline in marginal costs across all firms. However, due to the assumption of price adjustment costs, firms do not fully adjust prices. Hence, although the aggregate price level will fall, aggregate demand will increase less than proportionally to the increase in productivity and thus firms will react by reducing employment.
Unanticipated Shock to Technology
Citation: IMF Staff Papers 2010, 001; 10.5089/9781589069114.024.A008
The extent to which employment falls will depend on the response of monetary policy. Clearly, the fact that aggregate demand does not rise proportionally to the increase in productivity means that there will be downward pressure on nontradable prices. As a result, under nontradable (PID) inflation targeting, the government increases the supply of base money with the result that interest rates fall. This is less true in the case of CPI inflation targeting due to the effect of imported inflation. It is even less true under exchange rate targeting in which the interest rate only falls due to nominal rigidities.
The differences in the response of monetary policy translates directly into the behavior of inflation, which increases under PID inflation targeting due to the expansionary monetary policy but falls under exchange rate targeting as monetary policy does not offset the effect of declining marginal cost on firm behavior. This in turn implies that the improvement in competitiveness arising from the technology shock occurs through a decline in prices under exchange rate targeting and through nominal exchange rate depreciation under PID and CPI inflation targeting.
Due to the importance of aid shocks in low-income countries we also analyze the impulse responses following an unanticipated shock to aid in Figure 2. The response of the economy to an unanticipated aid shock under different assumptions about foreign exchange sales (absorption) and bond sales (sterilization) has been analyzed extensively in Clément and Peiris (2007). The aid, which is fully spent by the government, leads to an increase in the demand for nontradable goods as well as imports. As a result of the former, there is an increase in labor as well as GDP, while the increased demand for imports leads to a deterioration in the trade balance. Under both CPI and nontradable inflation targeting, the authorities react to the increasing pressure on prices by contracting base money with the result that interest rates rise sharply. This is less true under exchange rate targeting in which the authorities contract base money only to the extent necessary to counter the pressure on the exchange rate caused by the deterioration in the trade balance. As a result, inflation volatility is higher under exchange rate targeting than under inflation targeting. Interestingly, this also translates into higher real exchange rate volatility when the monetary authorities stabilize the path of the nominal exchange rate. It is worth pointing out the fact that under inflation targeting—in which part of the increase in base money is sterilized—interest rates remain high due to the persistent increase in the stock of government bonds. The persistent increase in inflation under inflation targeting reflects an increase in marginal costs reflecting the higher interest rates associated with sterilization.
Unanticipated Shock to Aid
Citation: IMF Staff Papers 2010, 001; 10.5089/9781589069114.024.A008
We now proceed to an overall evaluation of the three monetary policy regimes. In particular, we investigate whether stabilizing inflation or the nominal exchange rate might provide a better recipe for macroeconomic policy in a shock-prone economy, in which the economy is subject to a wider array of shocks, in terms of macroeconomic volatility and traditional welfare-based measures.9
Table 1 shows standard deviations of key macroeconomic variables for CPI inflation targeting, nontradable inflation targeting, and the crawling exchange rate peg. Contrary to the discussion above, we use the estimated value for the share of aid that is spent and the distribution of this expenditure between the public and the private sector, as well as the estimated persistence and standard deviations of the structural shocks. The results confirm the well-known result that because of higher interest rate volatility the exchange rate peg is significantly less successful than inflation targeting at stabilizing the real economy, although the differences are relatively small.10 Not surprisingly, the exchange rate peg also implies significantly higher CPI inflation volatility that, despite of lower nominal exchange rate volatility, leads to higher real exchange rate volatility.
Standard Deviations of Macroeconomic Variables
Standard Deviations of Macroeconomic Variables
| GDP | Consumption | Net Exports | CPI Inflation | Nominal Exchange Rate | Real Exchange Rate | Interest Rate | Welfare | |
|---|---|---|---|---|---|---|---|---|
| CPI inflation targeting | 0.4822 | 0.3023 | 0.0438 | 0.0049 | 0.0424 | 0.0518 | 0.0369 | −7.2561 |
| Nontradable price inflation targeting | 0.4842 | 0.3025 | 0.0425 | 0.0103 | 0.0382 | 0.0510 | 0.0355 | −7.2578 |
| Crawling exchange rate peg | 0.4892 | 0.3033 | 0.0541 | 0.0391 | 0.0072 | 0.0521 | 0.0410 | −7.2861 |
Standard Deviations of Macroeconomic Variables
| GDP | Consumption | Net Exports | CPI Inflation | Nominal Exchange Rate | Real Exchange Rate | Interest Rate | Welfare | |
|---|---|---|---|---|---|---|---|---|
| CPI inflation targeting | 0.4822 | 0.3023 | 0.0438 | 0.0049 | 0.0424 | 0.0518 | 0.0369 | −7.2561 |
| Nontradable price inflation targeting | 0.4842 | 0.3025 | 0.0425 | 0.0103 | 0.0382 | 0.0510 | 0.0355 | −7.2578 |
| Crawling exchange rate peg | 0.4892 | 0.3033 | 0.0541 | 0.0391 | 0.0072 | 0.0521 | 0.0410 | −7.2861 |
With the exception of the difference in CPI inflation volatility, the two inflation targeting rules perform relatively similarly in terms of macroeconomic volatility, a fact that may be related to the openness of the economy. In terms of overall welfare, there is some evidence that CPI inflation targeting outperforms nontradable inflation targeting, although the differences are small relative to the differences between inflation and exchange rate targeting.11
IV. Conclusions
A key contribution of this paper has been to consider the best response, in terms of minimizing macroeconomic volatility and traditional welfare-based measures, of alternative monetary policy rules in response to aid and numerous other exogenous shocks in an estimated DSGE model for a sub-Saharan Africa country. To our knowledge this is a first attempt at estimating a DSGE model for sub-Saharan Africa that provides a benchmark DSGE model incorporating characteristics of sub-Saharan African and low-income countries that could serve as a starting point for macroeconomic policy analysis.
Sub-Saharan Africa countries like Mozambique are prone to numerous exogenous shocks and our simulations suggests that a exchange rate peg is significantly less successful than inflation targeting at stabilizing the real economy because of higher interest rate volatility, although the differences are relatively small. Importantly, the exchange rate peg also implies significantly higher CPI inflation volatility that, despite of lower nominal exchange rate volatility, leads to higher real exchange rate volatility. This finding is of interest to sub-Saharan Africa central bankers, as there does not seem to be any gains from targeting the nominal exchange rate in terms of minimizing real exchange rate volatility and thus the performance of the tradable goods sector, including in the presence of aid and terms of trade shocks. “Lite” inflation targeting regimes with an appropriate combination of foreign exchange interventions and open market operations may thus be more suitable for countries in sub-Saharan Africa during a gradual transition to a fully fledged inflation targeting framework as conditions permit.
Appendix
Calibration
Calibration
| Parameter | Value | Description |
|---|---|---|
| ϑ | 1.5 | Home elasticity of substitution |
| η | 3.5 | Foreign elasticity of substitution |
| ψ—1 | 1.5 | Inverse of Frisch elasticity |
| ε | 2 | Inverse of elasticity of money supply |
| αd | 0.731 | Share of nontradables in consumer price index (CPI) |
| v/(v—1) | 1.09 | Markup factor for intermediary goods |
| ς | 0.15 | Cost share of borrowing |
| α | 0.41 | Cost share of capital |
| δ | 0.025 | Quarterly depreciation rate of capital |
| β | (1.093/1.123)1/4 | Quarterly subjective discount rate |
| uγ | 0.5 | Steady-state learning by doing |
| u μ | 0.3 | Steady-state share of government investment expenditure |
| π | (1.093)1/4 | Steady-state CPI inflation |
| π* | (1.059)1/4 | Steady-state foreign inflation |
| i + 1 | (1.123)1/4 | Steady-state domestic interest rate |
| i* + 1 | (1.117)1/4 | Steady-state foreign interest rate |
| (MC)/(M0 + D) | 0.22 | Currency-to-M2 ratio |
| (M0 + D)/Y | 0.7 | M2-to-GDP ratio |
| T/Y | 0.15 | Steady-state-tax-to-GDP ratio |
| A/Y | 0.15 | Steady-state-aid-to-GDP ratio |
| Z | 4.6 months of imports | Steady-state level of foreign currency reserves |
Calibration
| Parameter | Value | Description |
|---|---|---|
| ϑ | 1.5 | Home elasticity of substitution |
| η | 3.5 | Foreign elasticity of substitution |
| ψ—1 | 1.5 | Inverse of Frisch elasticity |
| ε | 2 | Inverse of elasticity of money supply |
| αd | 0.731 | Share of nontradables in consumer price index (CPI) |
| v/(v—1) | 1.09 | Markup factor for intermediary goods |
| ς | 0.15 | Cost share of borrowing |
| α | 0.41 | Cost share of capital |
| δ | 0.025 | Quarterly depreciation rate of capital |
| β | (1.093/1.123)1/4 | Quarterly subjective discount rate |
| uγ | 0.5 | Steady-state learning by doing |
| u μ | 0.3 | Steady-state share of government investment expenditure |
| π | (1.093)1/4 | Steady-state CPI inflation |
| π* | (1.059)1/4 | Steady-state foreign inflation |
| i + 1 | (1.123)1/4 | Steady-state domestic interest rate |
| i* + 1 | (1.117)1/4 | Steady-state foreign interest rate |
| (MC)/(M0 + D) | 0.22 | Currency-to-M2 ratio |
| (M0 + D)/Y | 0.7 | M2-to-GDP ratio |
| T/Y | 0.15 | Steady-state-tax-to-GDP ratio |
| A/Y | 0.15 | Steady-state-aid-to-GDP ratio |
| Z | 4.6 months of imports | Steady-state level of foreign currency reserves |
Estimation results
Estimation results
| Parameter | Description | Prior | Posterior | ||||
|---|---|---|---|---|---|---|---|
| Density | Mean | Standard deviation | Mean | 90 percent interval | |||
| Φ | Cost of nontradable goods price adjustment | Normal | 100.000 | 10.000 | 86.8394 | 101.4355 | 117.1080 |
| b | Habit persistence | Beta | 0.400 | 0.100 | 0.2534 | 0.3833 | 0.5036 |
| Φ1 | Capital-stock adjustment costs | Normal | 1.000 | 0.100 | 0.9078 | 1.0412 | 1.1971 |
| Φ2 | Investment-level adjustment costs | Normal | 80.000 | 10.000 | 60.6232 | 76.5648 | 90.0185 |
| ω | Share of aid spent | Normal | 1.000 | 0.100 | 0.9647 | 1.1450 | 1.3188 |
| ι | Share of aid spent by public sector | Normal | 1.000 | 0.100 | 1.0438 | 1.1920 | 1.2892 |
|
|
Commercial-bank-reserve smoothing (bonds) | Gamma | 0.200 | 0.100 | 0.0797 | 0.1440 | 0.2190 |
|
|
Commercial-bank-reserve smoothing (lending) | Gamma | 0.200 | 0.100 | 0.1036 | 0.1592 | 0.2119 |
|
|
Commercial-bank-reserve smoothing (deposits) | Gamma | 0.200 | 0.100 | 0.0424 | 0.1012 | 0.1510 |
| η | Interest-rate-spread markup factor | Normal | 10.000 | 1.000 | 8.1881 | 9.7740 | 11.5823 |
| z1 | International reserves stabilization | Normal | 0.001 | 0.100 | -0.0121 | 0.7730 | 0.1737 |
| z2 | Exchange rate stabilization | Normal | 0.500 | 0.100 | 0.1816 | 0.3193 | 0.4713 |
| z3 | Absorption | Normal | 0.500 | 0.100 | 0.6741 | 0.7971 | 0.9065 |
| b1 | International reserves sterilization | Normal | 0.500 | 0.100 | 0.2949 | 0.4751 | 0.6245 |
| b2 | Inflation stabilization | Normal | 0.500 | 0.100 | 0.3079 | 0.4630 | 0.6291 |
| b3 | Output stabilization | Normal | 0.500 | 0.100 | 0.0570 | 0.1634 | 0.2490 |
| b4 | Bond stabilization | Normal | 0.001 | 0.100 | 0.0950 | 0.1991 | 0.2953 |
| ρY | Technology shock persistence | Beta | 0.800 | 0.100 | 0.5890 | 0.7430 | 0.9471 |
| ρπ* | Foreign inflation shock persistence | Beta | 0.800 | 0.100 | 0.5928 | 0.6951 | 0.7942 |
| ρL | Labor supply shock persistence | Beta | 0.800 | 0.100 | 0.6305 | 0.7691 | 0.9216 |
| ρC | Consumption shock persistence | Beta | 0.800 | 0.100 | 0.5092 | 0.6596 | 0.8185 |
| ρ* | Aid shock persistence | Beta | 0.800 | 0.100 | 0.6551 | 0.7735 | 0.9077 |
| ρi* | Foreign interest rate shock persistence | Beta | 0.800 | 0.100 | 0.6581 | 0.8025 | 0.9579 |
| ρμ | Government investment shock persistence | Beta | 0.800 | 0.100 | 0.4929 | 0.5852 | 0.6816 |
| ργ | Learning-by-doing shock persistence | Beta | 0.800 | 0.100 | 0.6418 | 0.7723 | 0.9313 |
| ρI | Investment shock persistence | Beta | 0.800 | 0.100 | 0.6375 | 0.7671 | 0.9349 |
| ρi | Interest rate spread shock persistence | Beta | 0.800 | 0.100 | 0.2398 | 0.3930 | 0.5251 |
| ρB | Bond shock persistence | Beta | 0.800 | 0.100 | 0.6558 | 0.7740 | 0.9040 |
| ρto t | Terms of trade shock persistence | Beta | 0.800 | 0.100 | 0.4902 | 0.6486 | 0.7749 |
| ρZ | International reserves shock persistence | Beta | 0.800 | 0.100 | 0.7996 | 0.8725 | 0.9606 |
| uY | Size of technology shock | Invgamma | 0.002 | Inf | 0.0048 | 0.0048 | 0.0248 |
| uμ* | Size of foreign inflation shock | Invgamma | 0.002 | Inf | 0.0166 | 0.0084 | 0.0281 |
| uL | Size of labor supply shock | Invgamma | 0.100 | Inf | 0.0273 | 0.0209 | 0.0746 |
| uC | Size of consumption shock | Invgamma | 0.200 | Inf | 0.0611 | 0.0529 | 0.1012 |
| uA | Size of aid shock | Invgamma | 0.100 | Inf | 0.0196 | 0.0122 | 0.0329 |
| uμ | Size of government investment shock | Invgamma | 0.050 | Inf | 0.0016 | 0.0118 | 0.0023 |
| uγ | Size of learning-by-doing shock | Invgamma | 0.100 | Inf | 0.0132 | 0.0257 | 0.0431 |
| uB | Size of bond shock | Invgamma | 0.050 | Inf | 0.0241 | 0.0102 | 0.0873 |
| uI | Size of investment shock | Invgamma | 5.000 | Inf | 0.0136 | 0.0257 | 0.0248 |
| ui | Size of interest rate spread shock | Invgamma | 10.000 | Inf | 15.6567 | 2.4793 | 24.7542 |
| utot | Size of terms of trade shock | Invgamma | 0.050 | Inf | 2.8191 | 0.0130 | 4.9487 |
| uZ | Size of international reserves shock | Invgamma | 0.050 | Inf | 0.0145 | 0.0062 | 0.0268 |
| ui* | Size of foreign interest rate shock | Invgamma | 0.050 | Inf | 0.0065 | 0.0164 | 0.0105 |
| uv | Size of price markup shock | Invgamma | 10.000 | Inf | 0.0121 | 1.6522 | 0.049 |
Estimation results
| Parameter | Description | Prior | Posterior | ||||
|---|---|---|---|---|---|---|---|
| Density | Mean | Standard deviation | Mean | 90 percent interval | |||
| Φ | Cost of nontradable goods price adjustment | Normal | 100.000 | 10.000 | 86.8394 | 101.4355 | 117.1080 |
| b | Habit persistence | Beta | 0.400 | 0.100 | 0.2534 | 0.3833 | 0.5036 |
| Φ1 | Capital-stock adjustment costs | Normal | 1.000 | 0.100 | 0.9078 | 1.0412 | 1.1971 |
| Φ2 | Investment-level adjustment costs | Normal | 80.000 | 10.000 | 60.6232 | 76.5648 | 90.0185 |
| ω | Share of aid spent | Normal | 1.000 | 0.100 | 0.9647 | 1.1450 | 1.3188 |
| ι | Share of aid spent by public sector | Normal | 1.000 | 0.100 | 1.0438 | 1.1920 | 1.2892 |
|
|
Commercial-bank-reserve smoothing (bonds) | Gamma | 0.200 | 0.100 | 0.0797 | 0.1440 | 0.2190 |
|
|
Commercial-bank-reserve smoothing (lending) | Gamma | 0.200 | 0.100 | 0.1036 | 0.1592 | 0.2119 |
|
|
Commercial-bank-reserve smoothing (deposits) | Gamma | 0.200 | 0.100 | 0.0424 | 0.1012 | 0.1510 |
| η | Interest-rate-spread markup factor | Normal | 10.000 | 1.000 | 8.1881 | 9.7740 | 11.5823 |
| z1 | International reserves stabilization | Normal | 0.001 | 0.100 | -0.0121 | 0.7730 | 0.1737 |
| z2 | Exchange rate stabilization | Normal | 0.500 | 0.100 | 0.1816 | 0.3193 | 0.4713 |
| z3 | Absorption | Normal | 0.500 | 0.100 | 0.6741 | 0.7971 | 0.9065 |
| b1 | International reserves sterilization | Normal | 0.500 | 0.100 | 0.2949 | 0.4751 | 0.6245 |
| b2 | Inflation stabilization | Normal | 0.500 | 0.100 | 0.3079 | 0.4630 | 0.6291 |
| b3 | Output stabilization | Normal | 0.500 | 0.100 | 0.0570 | 0.1634 | 0.2490 |
| b4 | Bond stabilization | Normal | 0.001 | 0.100 | 0.0950 | 0.1991 | 0.2953 |
| ρY | Technology shock persistence | Beta | 0.800 | 0.100 | 0.5890 | 0.7430 | 0.9471 |
| ρπ* | Foreign inflation shock persistence | Beta | 0.800 | 0.100 | 0.5928 | 0.6951 | 0.7942 |
| ρL | Labor supply shock persistence | Beta | 0.800 | 0.100 | 0.6305 | 0.7691 | 0.9216 |
| ρC | Consumption shock persistence | Beta | 0.800 | 0.100 | 0.5092 | 0.6596 | 0.8185 |
| ρ* | Aid shock persistence | Beta | 0.800 | 0.100 | 0.6551 | 0.7735 | 0.9077 |
| ρi* | Foreign interest rate shock persistence | Beta | 0.800 | 0.100 | 0.6581 | 0.8025 | 0.9579 |
| ρμ | Government investment shock persistence | Beta | 0.800 | 0.100 | 0.4929 | 0.5852 | 0.6816 |
| ργ | Learning-by-doing shock persistence | Beta | 0.800 | 0.100 | 0.6418 | 0.7723 | 0.9313 |
| ρI | Investment shock persistence | Beta | 0.800 | 0.100 | 0.6375 | 0.7671 | 0.9349 |
| ρi | Interest rate spread shock persistence | Beta | 0.800 | 0.100 | 0.2398 | 0.3930 | 0.5251 |
| ρB | Bond shock persistence | Beta | 0.800 | 0.100 | 0.6558 | 0.7740 | 0.9040 |
| ρto t | Terms of trade shock persistence | Beta | 0.800 | 0.100 | 0.4902 | 0.6486 | 0.7749 |
| ρZ | International reserves shock persistence | Beta | 0.800 | 0.100 | 0.7996 | 0.8725 | 0.9606 |
| uY | Size of technology shock | Invgamma | 0.002 | Inf | 0.0048 | 0.0048 | 0.0248 |
| uμ* | Size of foreign inflation shock | Invgamma | 0.002 | Inf | 0.0166 | 0.0084 | 0.0281 |
| uL | Size of labor supply shock | Invgamma | 0.100 | Inf | 0.0273 | 0.0209 | 0.0746 |
| uC | Size of consumption shock | Invgamma | 0.200 | Inf | 0.0611 | 0.0529 | 0.1012 |
| uA | Size of aid shock | Invgamma | 0.100 | Inf | 0.0196 | 0.0122 | 0.0329 |
| uμ | Size of government investment shock | Invgamma | 0.050 | Inf | 0.0016 | 0.0118 | 0.0023 |
| uγ | Size of learning-by-doing shock | Invgamma | 0.100 | Inf | 0.0132 | 0.0257 | 0.0431 |
| uB | Size of bond shock | Invgamma | 0.050 | Inf | 0.0241 | 0.0102 | 0.0873 |
| uI | Size of investment shock | Invgamma | 5.000 | Inf | 0.0136 | 0.0257 | 0.0248 |
| ui | Size of interest rate spread shock | Invgamma | 10.000 | Inf | 15.6567 | 2.4793 | 24.7542 |
| utot | Size of terms of trade shock | Invgamma | 0.050 | Inf | 2.8191 | 0.0130 | 4.9487 |
| uZ | Size of international reserves shock | Invgamma | 0.050 | Inf | 0.0145 | 0.0062 | 0.0268 |
| ui* | Size of foreign interest rate shock | Invgamma | 0.050 | Inf | 0.0065 | 0.0164 | 0.0105 |
| uv | Size of price markup shock | Invgamma | 10.000 | Inf | 0.0121 | 1.6522 | 0.049 |
Actual and One-Step-Ahead Forecasts
Citation: IMF Staff Papers 2010, 001; 10.5089/9781589069114.024.A008
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Shanaka J. Peiris is a senior economist with the IMF’s Monetary and Capital Markets Department. Magnus Saxegaard is an economist with the IMF’s Asia and Pacific Department. The authors thank Andrew Berg, Doug Laxton, Jean A. P. Clément, Michel Juillard, Catherine Pattillo, Steven O’Connell, Manrique Saenz, Tsidi Tsikata, Reza Vaez-Zadeh, and participants in seminars in the IMF’s African Department and Small Modeling Group.
This partly reflects the preoccupation with the need for fiscal control and effective nominal anchors to bring down inflation from very high levels, which have now been largely achieved in a group of poststabilization countries dubbed “mature stabilizers” (IMF, 2006; and Clément and Peiris, 2007).
A key issue in sub-Saharan Africa concerns the impact of spending scaled-up foreign aid on the real exchange rate, exports, and competitiveness, which according to Rajan and Subramanian (2005) explains the weak link between aid inflows and growth in developing countries. Similar assertions have been made regarding the poor growth performance of natural resource rich economies (Sachs and Warner, 1995).
Pallage and Robe (2003) estimate the median welfare cost of business cycles in developing countries between 10 and 30 times that of the United States.
It is now widely accepted that the primary role of monetary policy is to maintain price stability (Batini and Yates, 2003; IMF, 2005b). This is often thought to correspond to an annual rate of inflation in the low single digits in industrial countries (Bernanke and others, 1999) and single-digit levels in low-income countries (Fischer, 1993; Ghosh and Phillips, 1998).
Further, “lite” inflation targeting regimes employ less market-oriented monetary targets and instruments are relatively nontransparent in the operation and objectives of monetary policy owing to shallow financial markets.
The product market as modeled in this paper is equivalent to a more realistic model with monopolistically competitive final goods firms. The approach adopted in this paper is common in the literature because it allows the model to be somewhat simplified.
For example, aid inflows ranging between 10 and 20 percent of GDP have been mostly spent in Mozambique (Clément and Peiris, 2007), requiring a monetary policy response to maintain macroeconomic stability in the face of large aid-financed liquidity injections.
The estimation is carried out using the software package DYNARE (Juillard and others, 2004), which utilizes Chris Sims’ CSMINWEL routine to maximize the likelihood of the model and the Metropolis-Hasting algorithm with two separate chains of 100,000 draws each so as to eliminate the importance of the steady-state.
It is well known (see, inter alia, Schmitt-Grohé and Uribe, 2004, and Saxegaard, 2006b) that up to a first-order approximation, monetary policy is neutral in the sense that the policy rules we consider imply the same (nonstochastic) steady-state for the economy. We therefore follow the literature in evaluating welfare using a second-order approximation to the model in which the expected variability of the economy will have an effect on welfare.
It should be noted, however, that the costs of interest rate volatility on the real economy may be lower in low-income countries compared to more developed economies due to a weak interest rate channel.
The similarity between CPI and nontradable inflation targeting is consistent with findings in Kollman (2002) and Saxegaard (2006b).
