Journal Issue

Republic of Madagascar: Selected Issues and Statistical Appendix

International Monetary Fund
Published Date:
September 2005
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II. Determinants of Inflation in Madagascar1

A. Introduction

1. Madagascar’s exchange rate and inflation has been volatile in recent years, underlining the economy’s vulnerability to shocks and policy slippages. Inflation (consumer price index (CPI)) surged from -0.8 percent at end-December 2003 to 27 percent at end-December 2004, compared with an original target of 5 percent. During the same period, the nominal exchange rate depreciated by about 40 percent against the euro, and broad money (M3) grew by 23 percent, exceeding an original target of 12 percent. This chapter applies cointegration analysis and error-correction modeling to study the determinants of inflation in Madagascar. It finds inflation inertia, which may reflect weak financial intermediation and ineffective monetary policy transmission mechanism. Exchange rate pass-through and broad money growth (a policy variable) are also found to be significant determinants of inflation. However, the return to price stability is found to be a slow process, even in a relatively tight monetary policy environment.

2. This chapter is organized as follows. Section II provides selected stylized facts concerning money and prices in Madagascar. Section III specifies the model used in the empirical work. Data issues and results from cointegration tests are discussed in Section IV. Section V presents the results from estimating the single equation error-correction model for inflation and evaluates its statistical properties, and systems estimation and impulse response analysis are conducted in Section VI.

B. Background

3. A combination of policy inconsistencies, adverse weather conditions (cyclones), terms of trade shocks, and political crises have contributed to swings in the exchange rate and bouts of inflation with varying intensity and duration since 1970. Madagascar left the franc zone in 1973 and experienced a first burst of inflation in 1974 (Figure 1). This inflation experience was short-lived, in part because the Malagasy franc remained pegged to the French franc, which dampened inflationary expectations. A second and more protracted burst of inflation occurred in the early 1980s, following years of large net bank financing of fiscal deficits, high money growth, and persistent terms of trade shocks (Figures 2, 3, and 4). Madagascar abandoned its currency peg with the French franc in 1982 and instituted a crawling peg system from 1982 to 1994, accompanied by frequent step devaluations, notably in 1987. Over the period 1986–88, Madagascar implemented structural reforms supported by the IMF’s Structural Adjustment Facility (SAF), including the removal of all impediments to exports (example, licenses and prior authorizations) and import restrictions. A floating exchange rate regime was adopted in 1994, along with the establishment of an interbank foreign exchange market (MID), based on an auction system. In 2004, the auction system was replaced by a continuous MID.

Chapter I. Figure 1.Madagascar: Nominal Effective Exchange Rate (NEER) and Inflation, 1970–2004

Note: Calculated as 12-month percentage change in quarterly CPI and NEER.

Chapter I. Figure 2.Madagascar: Net Bank Credit to Government and Inflation, 1970–2004

Note: Calculated as 12-month change in quarterly data.

Chapter I. Figure 3.Madagascar: Broad Money Growth and Inflation, 1970–2004

Note: Both variables calculated as 12-month percentage change in the quarterly series.

Chapter I. Figure 4.Madagascar: Terms of Trade Shocks and Inflation, 1970–2004

Note: Calculated as 12-month percentage change in quarterly data (terms of trade 1970=100).

4. Inflation displayed strong correlation with exchange rate movements during periods characterized by high inflation. During the period 1987–2004, Madagascar experienced three large exchange rate depreciations: in June 1987, in May 1994 (following the introduction of a floating exchange rate regime), and in the first half of 2004 (following tax and tariff exemptions of capital goods and selected other imports effective since September 2003). Following the 1987 and 2004 depreciation episodes, inflation soared against a background of moderate inflation; however, inflation had already started to accelerate before the 1994 depreciation.

5. Inflation also showed some correlation with trends in velocity (Figure 5). During 1982–83, the public adjusted, with a lag, to rising inflation and a more flexible exchange rate regime by reducing their real money balances. Thereafter, velocity trended downward, as financial sector reforms deepened2 and cash holdings (in real terms) began to build up. This downward trend, which lasted from 1984 through 2004, was interrupted temporarily by the inflationary bubbles of 1987 and 1994. With currency substitution allowed in 1994, however, the response of velocity of M3 to inflation remained subdued.

Chapter I. Figure 5.Madagascar: Velocity and Inflation, 1970–2004 1/

(Velocity, 1970=100)

1/ Velocity is calculated as y.P/M3, where y is real GDP, P is the CPI, and M3 is broad money stock.

6. The demand for real money balances fell in 2004, despite a tightening of monetary policy. Following a sharp economic slump in 2002 (Figure 6), the central bank lowered the reserve requirement ratio on two occasions—in October 2002 and in January 2003—with a view to accelerating GDP growth. With the exchange rate depreciating sharply and inflationary pressures intensifying in 2004, however, the central bank took successive monetary tightening measures, including three consecutive increases of the reserve requirement ratio. These measures led to an increase in interest rates on treasury bills across the board and absorbed the excess liquidity that had accumulated in the banking system to a point that commercial banks were compelled to borrow from the central bank at higher costs. However, interest rates on deposits remained relatively stable, reflecting, in part, the unwillingness of commercial banks to roll over their stock of treasury bill holdings. Meanwhile, inflation increased sharply, following the adjustment in the exchange rate in the first half of the year. This has led to negative deposit rates in real terms. Consequently, the stock of treasury bills held by the public increased, further weakening demand for real money balances.

Chapter I. Figure 6.Madagascar: Real GDP Growth and Inflation, 1970–2004

(Annual percentage change)

C. Model Specification

7. The specification of the inflation equation is a traditional extension of a monetary disequilibrium model to an open economy.3 It is derived from a theoretical model describing a small economy that has both a tradable goods sector and a nontradable goods sector. The overall price level in logs (LCPIt) is a weighted average of tradable prices (LCPItT), and nontradable prices (LCPItN):

Where λis the weight of nontradable prices in the price index. The price of tradable goods is determined in the world market, with their price in the domestic economy being a function of the foreign currency price expressed in foreign currency terms (LFCPIt), and the exchange rate expressed in foreign currency per national currency, (LNEERt):

8. The price of nontradables is determined by disequilibrium in the domestic money market, such that inflation (DLCPI) is obtained as

where LMt is the outstanding stock of money, LMtd is the demand for real money balances, and φ is a scale factor representing the relationship between economywide demand and the demand for nontradable goods. The demand for real money balances is assumed to be determined by real income (LRGDPt), foreign interest rates (FINT), and the expected depreciation of the exchange rate (DLNEER). Consequently, inflation in the nontradables sector can be written as:

9. An increase in the outstanding money stock is expected to result in higher inflation; an increase in real income is expected to increase the demand for money for transaction purposes and, in turn, lead to a decline in inflation; an increase in the opportunity cost of holding money, by reducing the demand for money balances, will result in an increase in inflation; and a depreciation will stoke inflationary expectations.

10. Assuming price homogeneity and a stable money demand function, which are confirmed by the data, the inflation equation can be estimated as follows:4


corresponds to a measure of disequilibrium in the money market.

D. Data, Unit Root Tests, And Cointegration Analysis


11. The empirical analysis is conducted using quarterly data from 1982:Q1 to 2004:Q2.5 All variables are in logarithms, except interest rates. Figure 7 plots the individual time series. Due to a lack of a reliable data series of a lower denomination of the money stock, the monetary aggregate used in this study is M3, defined as currency outside the banking system plus demand deposits, time and savings deposits, and foreign currency deposits. M3 is the intermediate target for monetary policy in Madagascar. Alternative financial assets are lacking; indeed, owing to financial controls imposed until the mid-1990s, the only time series of domestic interest rates available is the base rate (taux directeur) of the central bank. However, this interest rate shows very little variation over the sample period. The yields on 10-year government bonds in France are used as foreign interest rates.6 Foreign prices are the CPI (US$, 2000=100) weighted by trade imports from advanced economies. The exchange rate is the nominal effective exchanged rate, defined as foreign currency per unit of local currency. As real GDP (RGDP) is available only in annual frequency, end-of-period values are converted into quarterly data. Furthermore, four dummy variables (dum87Q3, dum94Q1, dum02Q2 and dum02Q3) are used to capture (i) the sharp depreciation of the exchange rate in the third quarter of 1987; (ii) the switch from a crawling peg regime to a flexible exchange rate regime and financial sector reforms initiated in 1994; and (iii) the impact of the political crisis in the second and third quarters of 2002. These four variables enter the dynamic inflation equation.

Chapter I. Figure 7.Madagascar: Prices, Income, Money, Exchange Rate, and Foreign Interest Rates, 1982–2004

E. Unit Root Tests

12. To avoid spurious regression results, the integrating properties of the variables are investigated using the augmented Dickey-Fuller (ADF) unit root tests (Table 1). The lag length in the ADF regression is selected using the Schwarz information criterion. The ADF tests include a constant term. All variables are found to be nonstationary in levels, but stationary in their first differences (that is, they are I (1)).

Chapter I. Table 1.Madagascar: Augmented Dickey-Fuller (ADF) Statistics for Unit Root Tests
VariablesADF StatisticsADF statistics
LagsIn levelsLagsIn first
LCPI0-1.3050-7.845 **
LRGDP5-0.2404-3.524 **
LM300.2300-9.603 **
LNEER0-0.6540-7.006 **
LFCPI6-1.7725-3.524 **
FINT4-2.1813-5.418 **
Note: The estimation period is 1982:Q1–2004:Q2 for all variables. Lags indicate the order of each variable, using the Schwarz info criterion. The ADF statistics are testing a null hypothesis of a unit root in each variable against an alternative of a stationary root. Each regression is run with a constant term. (**) denote rejection at the 5 percent and 10 percent critical values, respectively.

F. Cointegration Analysis

13. After determining the order of integration of the variables, the Johansen procedure is used to test for cointegration among the I (1) variables of Equation 5. The trace eigenvalue statistics reject the null hypothesis of no cointegrating vector in favor of one cointegrating vector at the 1 percent level (Table 2). The price level is expected to be positively related to the money stock and foreign interest rates, but negatively related to real income. The restricted, stable long-run relationship between the price level, the money stock, real income, and foreign interest rates is estimated as

Chapter I. Table 2.Madagascar: Cointegration Analysis
Null hypothesis onr = 0r ≤ 1r = ≤ 2r = ≤ 3
rank = r0.280.180.11
λ trace54.84**26.519.920.30
95 percent critical value 
Standardized eigenvectors
Standardized adjustment coefficient
Statistics for testing the significance of a given variable
χ2 (1)9.6**11.1**3.10.7
Note: The estimation period is 1982Q1–2004:Q2.The VAR includes five lags on each variable and centered seasonal dummies.

14. Even though the coefficients are of the right signs, real income and foreign interest rates are not significantly different from zero. This may be due to the fact that GDP is a relatively poor proxy for transaction demand and quarterly GDP was generated from annual data using the cubic spline method.

15. Various misspecification tests of the unrestricted vector autoregression (VAR) underlying Equation (7) are reported in Table 3. These include portmanteau, ARCH 1–4, normality, and heteroscedasticity tests, which reveal some problems, including the rejection at 1 percent critical value of normality for LCPI and LRGDP. It is, however, shown that this is not a problem for the Johansen procedure used in this paper.7

Chapter I. Table 3.Properties of VAR Residuals
Normality test:χ2(2)22.39**2.6714.34**2.77
ARCH 1–4 test: F (4,56)0.560.692.81*1.57
Heteroskedasticity test: F (40,16)0.490.420.380.36
Note: The portmanteau statistic is a degrees-of-freedom corrected version of the Box and Pierce statistic for each variable and for the system as a whole. See Doornik and Hendry (1997) for details. Normality denotes the results of the Doornik-Hanson test for each variable and for the system as a whole. It checks whether the residuals are normally distributed. ARCH (autoregressive conditional heteroscedasticity) denotes the results of the LM (Lagrange multiplier) tests for autocorrelated squared residuals.

16. Having established the existence of a stable long-run relationship for the price level, an error-correction representation of inflation, Equation (5), is estimated in Section V.

G. Determinants of Inflation

17. The error-correction term that captures deviations from the long-run price level is estimated in Section IV. In this section, the error-correction model for inflation is constructed by including the first difference of the error-correction term along with four lags of all the variables in the system. Thus, Equation (5) is estimated, using the ordinary least squares (OLS) estimator, as

where k=4 is the lag structure; ECMpis the error-correction term obtained from Equation (6); and CSeasonals are centered seasonal dummy variables used in the regression.

18. The econometric results of Equation (7) are presented in Table 4 below. The error-correction term enters negatively and significantly, implying that if inflation is 1 percent below its equilibrium level in one quarter, inflation will increase by 0.06 percent in the following quarter. The magnitude of the coefficient of the error-correction term indicates that the adjustment process toward long-run equilibrium of domestic prices is quite slow. All the significant stationary variables that capture the short-run dynamics on inflation also have the expected signs in the parsimonious equation (see column 2 of Table 4). More interestingly, inflation inertia and lagged depreciation are among the dynamic factors that determine inflation in Madagascar. In addition, broad money growth has a short-run positive inflationary effect with no lags. As shown in Figure 8, the estimated Equation (7) fits quite well the quarterly inflation over the period 1982:Q1 to 2004:Q2.

Chapter I. Table 4.Madagascar: Coefficient Estimates of the Error-Correction Inflation Equation
Constant0.27**0.21**DLNEER (-3)-0.07*
DLCPI (-1)0.16*0.29**DLNEER (-4)-0.04
DLCPI (-2)0.080.17**DLFCPI0.17
DLCPI (-3)0.03DLFCPI (-1)0.32
DLCPI (-4)0.14DLFCPI (-2)-0.86
ECM (-1)-0.08**-0.06**DLFCPI (-3)0.95
DLRGDP-0.04DLFCPI (-4)-0.7*
DLRGDP (-1)-0.62DFINT-0.002
DLRGDP (-2)0.60.37**DFINT (-1)0.01
DLRGDP (-3)0.62DFINT (-2)0.01
DLRGDP (-4)-0.23DFINT (-3)-0.01*
DLM30.110.11**DFINT (-4)0.01
DLNEER (-1)-0.11**-0.12**Cseasonal (-1)-0.02*-0.05**
DLNEER (-2)-0.05Cseasonal (-2)0.01
Notes: 1. t-statistics are in parentheses. 2. (**) indicates significant at 5 percent level; (*) indicates significant at 10 percent level. 3. Diagnostic tests of the restricted model: testing for error auto regressive (AR 1–5) test F (5,68)=1.1584 [0.3387]; Auto regressive conditional heteroscedasticity (ARCH 1–4) test F (4,65) = 1.0067 [0.4106]; Normality test χ2(2) = 0.41931 [0.8109]; heteroscedasticity test F (17,55) = 0.90981 [0.5665]; and RESET test F (1,72) = 0.45876 [0.5004].

Chapter I. Figure 8.Madagascar: Actual and Fitted Inflation, 1983–2004

Diagnostic tests

19. A battery of tests was conducted to evaluate the statistical properties of the model. The results for the single-equation parsimonious model are presented in the notes to Table 4. Error autocorrelation, ARCH errors, Normality, heteroscedasticity, and RESET errors are rejected. Overall, the residuals seem to be well behaved.

20. Furthermore, the model is estimated recursively from 1986 to 2004 to examine its stability. The recursive estimates of the coefficients that are significant in the estimated inflation equation are presented in Figure 9. The first seven plots are of the coefficient estimates at each point in the sample together with their approximate 95 percent confidence intervals (±2SEshown on either side). The estimates are relatively constant over the sample once past the initial estimates. The eighth plot is of the 1-step ahead residuals (forecast errors), with an approximately 95 percent confidence interval; the confidence bands are again reasonably constant. The final plot of the break-point Chow test shows that constancy is not rejected over the sample period.

Chapter I. Figure 9.Madagascar: Stability Tests of the Restricted Inflation Equation

H. Impulse Response Analysis

Systems estimation

21. The objective of this section is to trace the effect of standard errors originating from variables of the system on other endogenous variables through the dynamic structure of the VAR. To utilize all the information contained in the data, the full system is estimated using the full information maximum likelihood (FIML) estimator. Table 5 presents the results of the FIML estimation for the three variables of interest: domestic prices, money, and the exchange rate. For brevity, the insignificant regressors are omitted from Table 5.

Chapter I. Table 5.Madagascar: FIML Estimates of the Error-Correction System
DLCPI (-2)0.15*0.34**-0.78**
DLCPI (-4)-0.33**
ECM (-1)-0.08**0.34**
DLRGDP (-1)-0.64*
DLRGDP (-3)0.84*
DLNEER (-1)-0.13**-0.16**
DLNEER (-3)-0.07**
DLNEER (-3)-0.08**
DLFCPI (-1)0.61*
DLFCPI (-2)-1.06*
DLFCPI (-4)-0.67*
DFINT (-2)0.03**
DFINT (-3)-0.02**
DFINT (-4)0.01*
Notes: 1. t-statistics are in parentheses. 2. (**) indicates significant at 5 percent level; (*) indicates significant at 10 percent level. 3. Diagnostic tests: testing for error auto regressive (EGE-AR) 1–5 test F (180,108)=1.3150 [0.0602]; Normality test χ2(12)=53.537 [0.0000]**; heteroscedasticity test χ2 (1134)=1110.1[0.6883].

22. The inflation equation is essentially the same as in the OLS estimation discussed above. The money equation shows that broad money growth depends mainly on lagged inflation, but also on lagged exchange rate, lagged foreign interest rates, and its own lag. An increase in inflation two quarters ago has a positive impact on money, while inflation four quarters ago has a negative impact on money. However, the net impact is positive. The inflation error-correction term is not significant in the money equation. Notice that the impact of an exchange rate depreciation on inflation is much more than that on nominal money growth, which implies that a depreciation causes real money growth to fall. Regarding the exchange rate equation, Table 7 suggests that higher domestic inflation leads to exchange rate depreciation, while money growth leads to exchange rate appreciation, which is counterintuitive. Moreover, the error-correction term for inflation is positively correlated with changes in the exchange rate, indicating that excess supply in the money market leads to an appreciation of the currency.

Impulse response

23. This subsection examines the impact of different shocks on the variables in the model and analyzes the lagged structure of the responses. Each initial shock is assumed to be one standard error shock. The impulse response and cumulative impulse response results are presented in Figure 10 and Figure 11, respectively. The focus is on DLCPI, DLM3, DLFCPI, and DLNEER variables.

Chapter I. Figure 10.Madagascar: Impulse Response in the Full Model

Chapter I. Figure 11.Madagascar: Cumulative Impulse Response in the Full Model

24. As Figure 11 shows, a positive shock on domestic prices leads, as expected, to a cumulative depreciation of the nominal exchange rate. The impact of inflation on money, after being positive in the first quarter, dissipates thereafter; this implies that nominal balances fall after a price shock, and so real money balances fall.

25. A shock to nominal money growth briefly leads to a fall in inflation, although this impact fades quickly and becomes inflationary thereafter. This outcome, along with the higher-than-proportionate cumulative increase in nominal money, suggests that the real money stock increases permanently. In addition, following a positive monetary shock, the nominal exchange rate depreciates immediately, but this impact dissipates and becomes cumulatively positive over time. Contrary to expectations, Figure 11 also shows that foreign inflation affects domestic inflation negatively, but domestic money growth positively.

26. A standard error shock to the change in the nominal exchange rate, such as an appreciation (a positive shock), leads immediately to lower inflation, and its impact fades over 10 quarters. The cumulative impact on money growth is positive and larger than the fall in inflation, which suggests that an appreciation of the exchange rate increases real money growth over time.


Prepared by Koffie Nassar.

Along with the introduction of the MID in 1994, the banking sector was liberalized and foreign exchange deposit accounts allowed. Treasury bills were introduced in 1997.

See for example Khan and Knight (1991), Moser (1995), Toujas-Bernate (1996), and Callen and Chang (1999) for similar specification.

See Appendix I for the derivation of this equation.

The data are from the International Financial Statistics.

The rate of return on French treasury bonds is expected to be relevant, given the close relationship of Madagascar’s business community with France since independence in 1960.

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