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# Modeling and forecasting inflation in Rwanda (1995-2009)

par Ferdinand GAKUBA
Kigali Independent University - Degree in economics 2009

## 2.2. Conceptual framework

Inflation is thought to be an outcome of various economic factors. In Rwanda context we choice the factors from supply side that come from cost-push or mark up relationships; the demand side factors that may cause the demand pull inflation; monetary factors ; and foreign factors like exchange rate effects. In order to capture the various determinants of inflation we will combine the methodology developed in Brouwer and Neil R. Ericsson (1998) and Juselius(1992). The mark up model has a

resence in economics generally; see Duesenberry 93).

2.2.1. LONG- RUN RELATIONSHIPS 2.2.1.1. Mark up

We Investigate a mark up relationships following Brouwer and Ericsson(1998) for Australia inflation. In the long-run the domestic general price level in Rwanda is a mark up(cost- push) characterized by unit labor cost , import prices and oil prices index which we will find by segmenting variables a priori based on some sense of economic theory. Assuming linear homogeneity the long-run relation of the domestic consumer price level to its determinants is;

CPI = log (13) +p*UCL +6* IP +ip*PP (1)

Where CPI is consumer price index, UCL is the unit labor cost of out put, IP is import price in domestic currency, PP is petroleum price index in national currency, 3-1 correspond to a mark up .the equation assumes that linear homogeneity hold in long-run. The value of 3-1 is the retail mark up over cost and both the mark up and cost may vary over the cycle.

In formula, (1) is express in log- linear form:

cpi = log (13) +p*ulc +6* ip +(p*pp (2)

Where logarithms of variables are denoted by italic letters the log- linear form is used in the error correction model below. Linear homogeneity implies the following testable hypothesis.

p+ 6+ (p=1 (3)

This is unit homogeneity in all prices. Under that assumption, (2) can be rewritten as

à = log (13) +p (ulc-cpi) +6 (ip-cpi) +cp(pp-cpi) (4)

The equation (4) links real prices in the labour, foreign goods(import prices) and oil
prices index using this representation its will allow as to interpret the empirical error

 ` ` multiple markets influencing prices; Juselius (1992)

2.2.1.2 Money supply determinants

As we already define the mark up, we turn to monetary determinant of inflation In order to measure the excess money that eventually leads to inflationary pressures, we need to examine the long run relationship between broad money supply(M2), CPI inflation, Nominal GDP, exchange rate expressed in USD, landing interest rate in banking system. The estimated VAR corresponds to Juselius (1992) and Sekine (2001).? The functional structure of their model is given as;

Money supply (M2) = F(nwr, ngdp, cpi, tdc, echusd ) 5)

Changes in the price level (CPI) are modeled as being positively related to the changes in broard money stock (m2), exchange rate expressed in USA dollar (echusd), lending rate (tdc), domestic wage rate expressed as percentage changes for salaries (nwr), and negatively related to changes in productivity expressed as nominal GDP (ngdp)40.

Some authors have argued that in an open economy, and especially in a developing country, the money demand equation needs to be augmented with the exchange rate41. That is why; our excess money supply function above has the following functional form;

M2= a + ngdp +nwr +cpi+ tdc+ echusd +vt (6)

Where nwr is the nominal wage constucted and echusd is the nominal exchange rate measured in terms of RWF in USA dollar. The interest rate and the exchange rate are in levels. If long-run money supply is stable, then the error term in the above equation will be stationary. The long-run equilibrium level of board money can be estimated by a long-run cointegrating relationship to see if its has cointegrating vector.

40 BROWER, G.and ERICSSON ,N.R.(1995), Modeling inflation in Australia, Reserve Bank of Australia, Research discussion Paper No 9510, Page 21

This section describes the data available and considers some of their basic properties. Our sample period runs through the first quarterly of 1995 to second quarterly of 2009. There is single indicator of price movements in Rwanda Two different price indices are published in Rwanda: the Consumer Price Index (CPI), and Producer Price Index (PPI). The movements in primary articles are dominated by supply shocks, and the prices of fuel and energy are administered. The central banks of Rwanda focus on core inflation that excludes food and energy42. To take care of the issue of supply shocks and administered price controls, we focus on the import price and oil price index calculated by Laspeyres formula see appendix 1. We use the data from BNR to evolution of money supply the quarterly data are available. Since real GDP data are available only at an annual frequency, we use Eviews to get the estimated quarterly data for nominal GDP. The interest rates in Rwanda were administered prior to financial liberalization this imposes a problem in the selection of an appropriate interest rate as an opportunity cost of holding money. Moosa (1992) uses the call money rate as a measure of the opportunity cost of holding money. The problem with using call money rate as an opportunity cost of holding real money balance is that it is highly volatile and is affected more by the weekly funding demands of commercial banks43. Depending on availability of data we use the bank rate as opportunity cost of holding real money balance (in banking system). The bank rate is the rate at which the NBR lends liquidity to banks, broad money growth, and exchange rate has been obtained from the NBR website unit labor cost was calculated by having the gross salaries for all employees in central administration, local administration, the voluntaries insured, public institutions, government projects, mixed sector and private sector this sum was corrected by adding 5% of contribution for employers as social contribution to pension and divided it by nominal GDP (see appendix1).

41 Morling, S . (1997), Modeling inflation in Fiji, Working paper , Reserve Bank of Fiji, No 23, page 13

42 See economic Bulletin of BNR of second quarterly 2008

els

2.3.1. Mark up

A situation is said to be an inflationary situation when, either the prices of goods and services or money supply rise. Friedman mentioned inflation as `always a monetary phenomenon'. But most of the economists today, do not agree that money supply alone is the cause of inflation. So other factors which drive inflation in developing countries could be expressed as mark up.

2.3.1.1 Integration

Before modeling the CPI, it is useful to determine the orders of integration for the variables considered. Table 1 lists fourth-order augmented Dickey- Fuller (1981) (ADF) statistics for the CPI, unit labour costs, import prices, and petrol prices index. Under standard optimizing behaviour, the mark-up itself should be stationary. The deviation from unity of the estimated largest root appears in parentheses below each Dickey-Fuller statistic: this deviation should be approximately zero if the series has a unit root. Unit root tests are given for the original variables (all in logs), for their changes, and for the changes of the changes. This permits testing whether a given series is I(0), I(1),or I(2), albeit in a pair wise fashion for adjacent orders of integration44. Where k is the number of lags on the dependent variable, augmented Dickey-Fuller statistic ADF, and (in parentheses) the estimated coefficient on the lagged variable. That coefficient should be zero under the null hypothesis that is I(1). For a null order of I(2) (I(3)), the same pairs of values are reported, but from regressions where replace in the equation above. Thus, these ADF statistics are testing a null hypothesis of a unit root in {1% and 5%) against an alternative of a stationary root in {1% and 5%). The sample is 1995(1)-2009(2) for all.

43 Mishkin, F. S. (1992), Is the Fisher effect for real: A reexamination of the relationship between Inflation and Interest rates , Journal of Monetary Economics 30: Page 185- 215

44 For k~0 if the notation I (k) indicates that a variable must be differenced k times to make it stationary. That is, if CPI is I(k), then {dcpi) is I(1).

 Null order cpi ulc ip opi I(0) 1.30** -3.31* -5.27* -2.67** ` ` ( o.o4) (0.32) (-0.67) (-0.23) I(1) -4.23 -4.12 -10.11 -5.19 ` ` (0.12) (0.58) (0.18) (0.17) I(2) -4.90 -5.11 -17.66 -6.87 ` ` ` ` (0.11) (0.11) (0.16) (0.25)

g for a Unit Root in all Time Series45

Empirically, all variables appear to be integrated of order one. Unit labour costs,CPI and petrol prices appear to be I(1), whereas the import prices appear to be also I(1) if inferences are made on the Dickey-Fuller statistics alone. Thus, all four price series are treated below as if they are I(1), while recognizing that some caveats may apply. Specifically, it may be valuable to investigate the cointegration properties of the series.

2.3.1.2. Cointegration

Cointegration analysis helps clarify the long-run relationships between integrated variables. Johansen's (1988, 1991) procedure is maximum likelihood for finite-order vector auto regressions (VARs) and is easily calculated for such systems, so it is used here. Empirically, the lag order of the VARs is not known a priori, so some testing of lag order may be fruitful in order to ensure reasonable power of the Johansen procedure.

Beginning with a fourth-order VAR in CPI,ULC,IP and OPI that includes a constant term (see appendix 7) shows that it is statistically acceptable to simplify to a first-order VAR. Table 2 reports the standard statistics and estimates for Johansen's procedure applied to this first-order VAR. The maximal eigenvalue and trace eigenvalue statistics (Amax and Atrace) strongly reject the null of no cointegration in

45Here and elsewhere in this paper, asterisks * and ** denote rejection at the 5% and 1% critical values. The critical values for this table are calculated from MacKinnon (1996). The values in parentheses are the estimated coefficient on the lagged variables. That coefficient should be zero under the null hypothesis that k is I(1). For a null order of I(2) (I(3)), the same pairs of values are reported,

 ` ` ng relationship, and little evidence exists for more

Table 2: Cointegration analysis in the mark-up model

 Ho=rank=p A A max 95% CV A trace 95% CV p=0 0.0174 27.43 24.15 47.30 40.17 p~1 0.0082 0.047 3.76 0.047 3.76

In Johansen cointegration procedure, the Amax statistic tests the null hypothesis that the cointegration rank is equal to p, against the alternative of p+1 cointegration vectors. The Atrace statistic tests the null of cointegration of rank p, against a general alternative. In both tests if a computed test statistic exceeds the critical value, the null is rejected. In the present case, the results indicate presence of cointegration between oil prices and CPI at 1 and 5 percent critical levels. The values of the Amax and Atrace statistics are such that the null hypothesis of no cointegration can be soundly rejected. The Johansen Atrace statistics supports existence of one cointegrating vector, while various tests on residuals properties imply congruent VAR.

The estimated coefficient on oil price shows that if the world oil price increases by 1 percent, the CPI will rise by 0.277 percent. This is small number but it is statistically significant. Speed of adjustment coefficients that measure the degree to which the variable in question responds to the deviation from the long-run equilibrium relationship, indicate weak exogeneity of oil prices. Weak exogeneity stands for the fact that a given variable does not respond to the discrepancy from the long-run equilibrium relationship.

The mark up is views to be caused by three factors in Rwanda as using OLS the resultants are as follows; and the model proved to be satisfactory.

Method: Least Squares

Date: 11/04/09 Time: 10:21

 Variable Coefficie nt Std. Error t-Statistic Prob. LULC 0.573163 0.064287 8.915645 0.0000 LIP 0.178627 0.027577 6.477289 0.0000 LOPC 0.277785 0.096332 2.883627 0.0056 R-squared 0.658918 Mean dependent var ` ` 0.027192 Adjusted R-squared 0.646285 S.D. dependent var ` ` 0.273971 S.E. of regression 0.162941 Akaike info criterion ` ` -0.739659 Sum squared resid 1.433691 Schwarz criterion ` ` -0.632130 Log likelihood 24.08028 Hannan-Quinn criter. ` ` -0.697869 Durbin-Watson stat 0.340532 ` ` ` ` ` `

Assuming one cointegrating vector and linear homogeneity, the derived long run markup relationship becomes:

From the above empirical model of Inflation mark -up the estimated equation using OLS methods is as follows; the low Durbin Watson is due to the big number of variables estimated as founded by Mankiw in His book Economic Principles (1998).

LIPC = 0.573*LULC + 0.178626*LIP + 0.27778*LOPC (7)

For the obove estimated equation the mark up is;

Lmarkup =LCPI -0.57* LULC - 0.178*LIP-0.27 LOPC

The share of unit labor cost in total unit cost (0.57) seems reasonable considering
that Rwanda economy is highly dominated by service sector. Share of unit labour
costs in total unit cost is higher than in Australia (- 0.43), but much lower than Japan

on, 1998; Sekine, 2002). Relatively small share of

ue to high import dependency of Rwanda economy and with a large value of oil price mean how much Rwanda spend on pretroleum product due to oil shocks and fluctuation.

2.3.2 Excess money supply

The next long -run relationship is monetary conditions. Beginning with Friedman and Schwartz (1963), many researchers have examined whether inflation is a monetary phenomenon. For instance advocates of the p star approach (Hellman, Porter and Small, 1991) examine inflationary effects of excess money in terms of difference between actual money velocity and its long-run value (together with the output gap). Also Juselius (1992) finds excess money in terms of cointegartion vector which represents the long-run money demand as one source of inflation. In this case following Juselius we have a vector of five variables: price (CPI), money (M2), income (nominal GDP), exchange rate and interest rates ( in banking system). We estimated the VAR corresponds to Juselius (1992) and Sekine (2001).Table 3, Table 4 and Table 5 summarize residual properties and a system cointegrating analysis of the VAR. The Johansen test supports existence of one cointegrating vector. There are indications of autocorrelation in the residuals (indicated by AR test), but otherwise the VAR seems satisfactory. The occurrence of autocorrelation can be attributed to estimated GDP series. All diagnostic tests are satisfactory.

Table 4: Properties of VAR residuals

 tests LM2 lpibc ltcusd ltdc lipc normality 1.88 I68 2.77 13.30 7.46 ARCH test 0.24 0.38 0.25 0.162 0.182 AR 2.43 6.78 3.10 1.92 2.36 Jarque - Bera 1.88 12.00 174.00 2.72 14. 93 Chi- Sq 0.78 7.73 6.76 0.01 1.82 Lm2 0.004 0.023 0.132 0.25 0.12 Lipc 0.003 0.001 -0.0015 -0.0037 0.0029 lpibc 0.016 0.0129 -0.008 0.0123 0.0081 ltcusd 0.005 0.062 -0.0077 -0.0011 -0.0018 ltdc -0.024 0.0031 -0.036 0.0053 -0.0103 ` ` t coefficients

Table 6: Properties of cointegration vector

 Eigenvalues 0.361 0.305 0.215 0.119 0.081 Hypotheses r=0 r~1 r~2 r~3 r~4 Amax 24.21 19.65 13.11 6.89 4.58 Atrace 68.46 44.25 24.59 11.48 4.58

Table 5 reports, in bold, the eigenvalues statistically different from zero on the basis of the trace and the maximum eigenvalue tests. The critical values are taken from Mackinnon- Haug Michelis(1999). The trace test points out the existence of two long-run relationships. The maximum eigenvalue test suggests a cointegration rank equal to three (at the 10% significance level), while its version corrected for the number of degrees of freedom indicates a rank equal to two (at the 5% significance level). According to Johansen (1992) the maximum eigenvalue test may produce an incoherent testing strategy, therefore the trace test results are preferred and the cointegration rank r is set equal to two.

LM2 = 0.093*LPIBC + 0.308*LTCUSD _ 0.174*LTDC + 1.75*LIPC

From above resultants;

Lexcess_money = LM2-0.093*LPIBC - 0.308*LTCUSD + 0.174*LTDC - 1.75*LIPC

This model will be useful to calculating the long run relationship of inflation and the variables coefficients are satisfactory and prevailing the insight on inflation behavior.