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 costpush 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 longrun 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 longrun 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, 31 correspond to a mark up .the
equation assumes that linear homogeneity hold in longrun. The value of
31 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 (ulccpi) +6 (ipcpi) +cp(ppcpi) (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 rate^{41}. 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 longrun money supply is stable, then the error term in the
above equation will be stationary. The longrun equilibrium level of board
money can be estimated by a longrun 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 energy^{42}. 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 banks^{43}.
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 fourthorder
augmented Dickey Fuller (1981) (ADF) statistics for the CPI, unit labour
costs, import prices, and petrol prices index. Under standard optimizing
behaviour, the markup itself should be stationary. The deviation from unity of
the estimated largest root appears in parentheses below each DickeyFuller
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 integration^{44}. Where k is the number of lags on
the dependent variable, augmented DickeyFuller 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
Series^{45}
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
DickeyFuller 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 longrun
relationships between integrated variables. Johansen's (1988, 1991) procedure
is maximum likelihood for finiteorder 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 fourthorder 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 firstorder VAR. Table 2 reports the standard
statistics and estimates for Johansen's procedure applied to this firstorder
VAR. The maximal eigenvalue and trace eigenvalue statistics (Amax and Atrace)
strongly reject the null of no cointegration in
^{45}Here 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 markup
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 longrun 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 longrun 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
Sample (adjusted): 1995Q2 2009Q2
Included observations: 57 after adjustments
Variable

Coefficie
nt Std. Error

tStatistic

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

Rsquared

0.658918

Mean dependent var


0.027192

Adjusted Rsquared

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

HannanQuinn criter.


0.697869

DurbinWatson 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*LIP0.27 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
longrun value (together with the output gap). Also Juselius (1992) finds
excess money in terms of cointegartion vector which represents the longrun
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 longrun 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 = LM20.093*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.
