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Working Paper No 2009/12
APRIL 2009
Money and exchange rate channels for food and non
food inflation: a cointegrated VAR for Zambia
Elva Bova*
Abstract
This paper uses a cointegrated VAR to detect how sensitive Zambian food and non food inflation
is to changes in the money supply and in the exchange rate. It finds that the monetary
transmission mechanism is weak and effective only for non-food prices, while the exchange rate
channel is stronger, especially for food prices. Estimates also indicate that the exchange rate is
very sensitive to changes in copper prices. The study suggests, then, that foreign exchange
intervention to avoid real appreciations and safeguard competitiveness may not be too
inflationary. This is also in the case when the money supply is not sterilised.
KEY WORDS
Exchange rate, Inflation, Monetary policy, cointegrated VAR
* Elva Bova is a Doctoral student of the NCCR individual project on “Primary Commodities” and a PhD candidate in the Economics
Department of the School of Oriental and African Studies, University of London.
NCCR TRADE WORKING PAPERS are preliminary documents posted on the NCCR Trade Regulation website (<www.nccr-trade.org>) and
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1. Introduction
Due to the recent copper boom the Zambian economy has been exposed to a sudden and
significant increase in foreign exchange. This has accrued mainly to the mining companies and
large part has been spent into the copper industry for mines expansion and investments. The
spending effect associated with the boom has determined a nominal appreciation of the
Zambian Kwacha, exacerbated by inflows of foreign capital in the form of aid and of portfolio
flows. Moreover, the concession of debt relief in 2005 has released additional foreign exchange
in to the economy. As illustrated in different studies (Cali and te Welde, 2007; Fynn, and
Haggblade, 2006; Weeks et al 2007; Weeks, 2008; Exports Board of Zambia, 2007) the nominal
appreciation in 2005 has dramatically damaged some non traditional exports, such as tobacco,
cotton and horticultural products, production of which fell sharply in 2006.
While exporters demanded a more managed exchange rate, the response of the central bank
has been to let the currency float, as prescribed by their inflation-focused monetary framework.
This, framework maintains price stability as the main objective, to be achieved through a
monetary target, and it calls for flexibility in the exchange rate with very limited foreign
exchange interventions.
With this focus, foreign exchange intervention to avoid a nominal appreciation during a
boom should be avoided, since, when sterilisation of the money supply is not possible, the
accumulation of international reserves may be inflationary. Also, with a focus on external
competitiveness, an increase in inflation resulting from intervention may, in turn, cause a real
appreciation of the currency, simply because domestic goods will become more expensive in
the international market. Thus, even under a more managed exchange rate, a boom may
damage a country’s competitiveness, through an increase in inflation. Therefore the correct
policy would be to let the currency float, since floating would at least avoid an increase in
inflation.
In this study we examine whether, in Zambia, a real appreciation would have similarly
followed under a more managed exchange rate regime. In this vein, we test for the
effectiveness of the monetary transmission mechanism and the exchange rate channel, since
these are the mechanisms through which accumulation of foreign exchange may increase
domestic prices. To test for effectiveness, we use a cointegrated VAR to examine how sensitive
Zambian inflation is to changes in the money supply and in the exchange rate. Since almost 60
per cent of the Zambian CPI is made of food prices, we distinguish between effects on food
and on non food prices. The model also includes the copper price and oil price, as exogenous
variables, to investigate, firstly, to what extent the Zambian Kwacha responds to changes in
the copper price, and, secondly, how much the exchange rate pass through is connected to the
oil price.
The paper is organised as follows. The next section presents the theoretical background,
while section III offers a brief review of the empirical literature. The unrestricted VAR is
described in section IV, while section V illustrates the long and short run restrictions and
examines the results. Section VI offers a conclusion and some policy implications.
2. Theoretical background
As postulated by the “Dutch disease” literature, a commodity boom may cause
a real exchange rate appreciation with significant damage for the non traditional
exports. In the traditional model this impact emerges out of two main effects: a
spending effect and a resource switching effect (Corden, 1984; Corden and Neary,
1982; Neary and Van Wijnbergen, 1984). In both cases real exchange rate
appreciation is determined by changes in relative prices, that is a relative increase
in the price of non tradable goods with respect to the price of tradable goods 1.
This is consistent with a definition of the real exchange rate as the ratio of prices
of non tradable goods over prices of tradable goods, which can be considered as a
proxy for competitiveness in a small open economy. This first specification of the
Dutch disease effects 2 tends, however, to ignore the implications a particular
exchange rate regime has on the effects of a boom. This is because one of the
main assumptions of the model is of an economy with no money.
In this study we rely, then, on a rather marginal specification of the Dutch disease dynamics,
put forward by Edwards in 1989 to examine the impact of the coffee boom in Columbia. This
alternative framework distinguishes the impacts a boom may have on a country’s
competitiveness in the light of the exchange rate regime.
The assumption of a small open economy bears implications for price movements, since while prices of non tradables are set
according to demand and supply adjustments in the local market, prices of tradable goods are set in the international
market and they do not change with changes in the aggregate demand.
2 We consider “Dutch disease dynamics and models” to be all those that refer to the negative impact a commodity boom or a
resource discovery may have on one country’s non traditional exports.
1
Under a flexible regime, in fact, an increase in foreign exchange will appreciate
the currency in nominal terms, which will be passed on to a real appreciation.
Exports will become more expensive, which will damage the country’s external
position. On the other hand, under a fixed exchange rate regime, the central bank
will need to accumulate foreign exchange in its international reserves so as to
keep the parity. To do so it will need to increase the money supply. However, in
many developing countries with shallow financial markets 3 , the increase in
money supply cannot be sterilised and may become inflationary. Inflation, in
turn, will appreciate the real exchange rate, since the price of local goods will be
higher in the international market 4 . Hence, under either a flexible or a fixed
exchange rate a surge in the foreign exchange will appreciate the real exchange
rate, which implies that neither arrangement is better than the other; however, a
float would at least avoid an increase in inflation.
Whenever the monetary transmission mechanism is weak, however, then there is reason to
believe that the real appreciation and consequent loss in competitiveness will be more likely
under a float. This may be of relevance in developing countries where there are several
reasons why an increase in the money supply may not result in an increase in domestic prices.
Firstly, where the economy is largely a cash economy, any increase in the money supply
within the interbank market may be rather marginal compared with the amount of cash
circulating into the economy. If this is the case, then, an increase in the money supply may not
spur aggregate demand (Saxegaard, 2006). Secondly, if an increase in the money supply does
raise aggregate demand, then it may be that this increase does not affect domestic prices. This
may be for two main reasons. One is the large food component typical of developing
countries’ CPI. Food prices are, in fact, income inelastic, for an increase in demand would be
redirected to other goods; therefore a surge in the money supply will not raise the domestic
CPI. The other is the fact that the economy does not operate at full capacity. Therefore, an
Sterilisation is costly because usually conducted through open market operations, and since government bonds and treasury
bills are the main components of the financial market any change in their volume may sharply affect the interest rate. If
the interest rate increases too much the government may find itself in an unsustainable domestic debt.
4 The same is true in the case of exports denominated in foreign currency. This is because although their price will not increase
and export earnings will be the same in foreign currency, the exporter will face increasing production costs. Similarly
under a float, while the earnings in dollars will be the same their corresponding value in local currency declines under a
nominal appreciation, and the exporter will face lower earnings but the same level of costs.
3
increase in aggregate demand may effectively spur output and prices will remain stable.
However, if absorptive capacity is limited in the economy, then prices may increase after all.
However, despite the weak monetary transmission mechanism, foreign exchange
interventions may still impact on inflation through the exchange rate channel. This is because
in developing countries a large share of goods are imported and their prices are sensitive to
changes in the nominal exchange rate. When a central bank conducts foreign exchange
interventions to offset a nominal appreciation, it basically cancels out the impact the nominal
appreciation would have had on imported prices, namely a reduction of these prices. Thus,
with foreign exchange intervention inflation may actually increase, or at least it may not
decrease.
In the case of the Zambian economy, it may be that for one or more of the reasons mentioned
above, the monetary transmission mechanism is weak. If this is the case, then a more managed
float would probably perform better than a float, in as much as it would better safeguard the
non traditional exports during the boom.
For this analysis we consider that foreign exchange intervention may impact on inflation
through the release of unsterilised money supply (monetary transmission mechanism) and
through an increase in the CPI imported component (exchange rate pass-through). As a matter
of fact, prices of imported goods will not increase but their level would be higher then the one
during a nominal appreciation. Thus we examine whether and to what extent prices of food
and non food are sensitive to changes in the money supply and then we consider the extent of
the exchange rate pass-through.
3. Empirical literature
To understand how sensitive domestic prices are to changes in the exchange rate and in the
money supply we draw on the existing literature on the monetary transmission mechanism in
developing countries. The issue of the efficacy of the monetary transmission mechanism has
recently been studied with the purpose of detecting whether the link between the money
supply and inflation is strong in developing countries. The literature provides mixed evidence
with respect to the monetary transmission mechanism in African countries. A seminal study
by Canetti and Greene (1992) did not find a common pattern in African countries as far as the
causes of inflation are concerned; in some cases the exchange rate channel seems to be more
effective, in others the money supply growth has the longer term impact.
As far as Zambia is concerned, there have been different studies on the effectiveness of the
monetary transmission mechanism, most of them focusing on the consequences of the
exchange rate liberalisation of the early 1990s. A study by Mwenda in 1993 looked at the
impact on the effectiveness of monetary policy of switching to indirect monetary policy
instruments, with a special focus on growth and variability in broad money and in inflation.
The study finds out that the move to indirect instruments for policy has indeed reduced the
variability in broad money and inflation. A further study by Adam (1999) found that the
variance of currency demand has increased in Zambia since the end of the 1980s. It also
observed that stabilisation policy based on controlling reserve money is likely to have an
imprecise link to inflation in the short and medium term, which is shown by the fact that
short-run forecast variance around the money demand is relatively high.
A more comprehensive study, by Simatele (2004), examined how the effectiveness of the
monetary transmission mechanism to the macro-economy has changed with the liberalisation
reform, using two different models for the period prior and the period after the boom. The
analysis adopted a VAR using the Choleski decomposition to impose restrictions, thus, relying
on the assumption that policy does not respond contemporaneously to macro-shocks and that
this may be due to information lags. Through impulse responses and variance decompositions
the study illustrates that the potency of monetary policy has increased with the reforms, since
prices are more responsive to monetary policy shocks. The study also illustrates that the
exchange rate seems to be an important variable in the explanation of prices in Zambia.
Probably the most relevant study on the issue, at least for our analysis, is the one by Mutoti
(2006). The author tries to investigate short and long term dynamics and transmission
mechanisms of post-liberalised Zambia. He does this through a cointegrated VAR, in which
restrictions are imposed according to a priori information on the relationships between the
variables (Christiano et al., 1994; Leeper et al., 1996). The model is framed in an IS-LM-AS
theoretical structure and considers the domestic and foreign (South African) interest rate,
money supply (as broad money), output, domestic and foreign prices and the nominal
exchange rate Kwacha to the South African Rand. Running the model for the years 1992-2003
Mutoti found that there is a stable money demand relationship, implying that money growth
has a predictable impact on the economic activity and also that money demand is sensitive to
the interest rate; inflation appears to be associated with excess demand and disequilibrium in
the exchange rate. From the impulse responses to a money supply shocks it appears that
domestic prices react strongly only in the first period, suggesting that the link between money
supply and inflation may be weak. As expressed in Mutoti (2006:18) “(this may give) rise to
situations where getting the monetary target does not produce the desired inflation outcome
and where money fails to produce reliable signals of the stance of monetary policy. Since food
price has the largest share in CPI and the dominant role of exchange rate in inflation dynamics
established, sustaining lower inflation in Zambia requires policies meant at boosting domestic
food supply and stabilising exchange rate”.
Further to this conclusion, this study analyses the transmission mechanism on the price of
food and non food. Similarly to Mutoti, we use a cointegrated VAR, yet we consider money
supply and exchange rate as the policy variables and include copper and oil prices.
4. The unrestricted VAR
To formulate a cointegrated VAR for Zambia we consider the following unrestricted
structure:
xt = П1xt-1 + П2xt-2 + Θyt-1 + ΦDt + εt;
(t=1…..T)
(1)
εt ~ Np (0, Σ),
(2)
Where xt is a k x 1 vector which includes the following endogenous variables:
M3 = log M3sea – log CPIz,
(3)
ER = log CPIz – log CPIus –NEus-z
(4)
∆CPI fz,
(5)
∆CPI nfz
(6)
Where M3 is defined as the logarithm of the seasonally adjusted real broad money (M3),
deflated by the Zambian headline CPI. ER is the log of the real bilateral exchange rate ZMKUS Dollar5. ∆CPI fz, and ∆CPI nfz are, respectively, the rate of change in the food and non food
Zambian CPI. For the exogenous variables, yt-1, we use the log of real copper prices, obtained
as the nominal market value price of copper in US$ per metric ton divided by the Zambian
CPI and the logarithm of the real price of oil, obtained as the oil price in US$ per barrel
divided by the Zambian CPI. The data on the Zambian economy are from Bank of Zambia,
5
This specification of the exchange rate is not the real rate we have assumed in the study, which refers instead to prices of
tradable and non tradable goods and it is more a measure of competitiveness of the economy with respect to the
international market.
while the data on copper and oil prices are from the International Financial Statistics database
of the IMF.
The model uses a sample of monthly data from April 1996 to April 2008, which
corresponds to a period of macroeconomic adjustment subsequent to the adoption of several
liberalisation reforms. It also covers the period of the copper boom which starts in
approximately 2004. A deterministic trend has been added to the model, which proves to be
significant for food and non food inflation and we also account for a break in the trend in
December 2005, corresponding to a change in the rate of growth of the money supply. From
tests for lag determination reported in annex A the VAR is significant for two lags, which is
confirmed by the fact that the autocorrelation in the residuals disappears when accepting two
lags (annex A).6 To assess whether the VAR assumptions are accepted we first conduct a visual
inspection of the data and their time-series properties.
Real money supply (M3)
Exchange rate, ZMK to US$
9.0
8.50
8.25
Figure 1:8.8 The endogenous variables
8.00
8.6
7.75
8.4
7.50
Real money supply (M3)
9.0
8.2
8.8
8.0
7.00
8.25
6.75
8.00
8.6
7.8
1994
1996
1998
2000
2002
2004
2006
8.4
Exchange rate, ZMK to US$
7.25
8.50
6.50
7.75
2008
1994
1996
1998
2000
2002
2004
2006
2008
2006
2008
7.50
Food inflation
48
8.0
40
7.8
1994
Non food inflation
7.25
56
8.2
55
7.00
50
6.75
45
6.50
32
1996
1998
2000
2002
2004
2006
2008
1994
40
1996
35
1998
2000
2002
2004
2006
2008
24
56
16
48
40
32
-8
30
Food inflation
55
25
8
50
20
0
45
15
40
10
1994
1996
1998
2000
2002
2004
2006
2008
35
Non food inflation
1994
1996
1998
2000
2002
2004
24
30
16
25
8
20
0
15
-8
10
1994
1996
1998
2000
2002
2004
2006
2008
1994
1996
1998
2000
2002
2004
2006
2008
Source: Bank of Zambia data
The graphs in figure 1 suggest that the series of the endogenous variables display a non
stationary behaviour, which may indicate the presence of a unit root in all of them. The non
stationarity of the series is however tested within the VAR structure, through the rank test and
However, the test comparing two different models tends to accept more a three lag system. This
result may, hence, indicate that the variables react with different lags, which is totally understood in
the case of monetary variables.
6
the standard Dickey Fuller test for unit root is not applied, since its validity is questioned in a
multivariate context (Juselius, 2006).
To account for the presence of outliers in the residuals of some of the variables the
unrestricted VAR is corrected for blip transitory dummies associated to shocks in non food
inflation, and for permanent dummies which are related to money and exchange rate’s
behaviour7. As discussed in Juselius (2006), the presence of dummy variables in a VAR has a
different meaning and implication than in the case of univariate time series analysis. This is
because, while the dummy variables eliminate the outlier from a single variable they do not
eliminate the impact this outlier has on the relationships among and between variables.
From the residuals analysis in table 1 the model is accepted and correctly
specified. According to the LM test for the model with two lags, there is no
autocorrelation in the residuals with a rather high p-value of 0.295, although
the Ljung Box test does not reject autocorrelation. Normality is not rejected
with a p-value of 0.06, and a much higher p-value for the individual series,
except for non food inflation where normality is not rejected at 5 per cent
confidence level. ARCH residuals are not rejected for multivariate test, but
they are rejected with high p-values for the individual series, except for the
exchange rate where the p-value is 0.077. Kurtosis and skeweness estimates do
not deviate too much from their normal values, of 3 and zero.
Table 1: residual analysis
Multivariate tests
Tests for Autocorrelation
Ljung-Box(37):
ChiSqr(560) = 674.636 [0.000]
LM(1):
ChiSqr(16)
=
39.811 [0.001]
LM(2):
ChiSqr(16)
=
18.501 [0.295]
Test for Normality:
ChiSqr(8)
=
14.927 [0.061]
Univariate Tests
Std.Dev
M3
ΔCPI
f
z
ΔCPInf
ER
z
Skewness Kurtosis
ARCH(2)
Normality
R-Squared
0.021
-0.097
3.111
2.727 [0.256]
0.721 [0.697]
0.510
0.009
0.241
2.823
0.735 [0.692]
1.684 [0.431]
0.755
0.006
0.434
2.853
3.735 [0.155]
6.306 [0.043]
0.735
0.024
-0.101
3.720
5.131 [0.077]
4.872 [0.088]
0.612
Source: Rats estimation
7
The dummies have been included for December 2000, where both exchange rate and money supply present some outliers in
the residuals, for December 2005, which corresponds to the sharp appreciation of the Kwacha; for April 2004, December
1998 and June 1997 which reflect outliers in food and non food inflation.
Test for Constancy of the Log-Likelihood
5
X(t)
R 1(t)
5% C .V. (1.36 = Index )
4
The Log Likelihood test, reported in figure 2, accepts constancy for the parameters of the
adjusted 3series (Rt). Yet, for the unadjusted series X(t) there could be some irregularity at the
beginning2 of the series since the line of X(t) lies above the confidence level set by the 5 per cent
critical value represented by the black line.
1
0
Figure
2: Test2000
for Constancy
2001
2002
2003
2004
2005
2006
2007
Test for Constancy of the Log-Likelihood
5
X(t)
R 1(t)
5% C .V. (1.36 = Index )
4
3
2
1
0
2000
2001
2002
2003
2004
2005
2006
2007
Source: RATS estimation
To assess the existence of cointegrating relationships and their number we first rely on
graphical evidence on the β vectors (annex B). The graphs seem to indicate the existence of
three long term cointegrating relationships between the variables. A similar result seems to be
suggested by the root of the companion matrix as reported in annex B. Estimates from the
Johansen test or rank test are also consistent with a rank level of three, as resulting from the
asymptotic tables in table 2.8
Table 2: The Trace test
I(1)-ANALYSIS
p-r r Eig.Value
Trace
Trace*
Frac95 P-Value P-Value*
4
0
0.506 191.011 181.954 63.659
0.000
0.000
3
1
0.279
90.130
86.714 42.770
0.000
0.000
2
2
0.204
43.341
41.043 25.731
0.000
0.000
1
3
0.072
10.671
10.052 12.448
0.101
0.127
WARNING: Critical/P-values correspond to the 'Basic Model'.
WARNING: The Bartlett Corrections correspond to the 'Basic Model'.
Source: RATS estimation
8
The results of Trace test are derived from the Bartlett corrected series, which applies when the number of observations is
relatively small.
5. The long run and short run structure
To obtain a cointegrated VAR from an unrestricted one, we need to impose some
restrictions on the basis of the economic theory we want to demonstrate and then check for
their significance.
For the long run structure we consider the following beta vector:
Xt = (M3, Ex, ΔCPI nfz, ΔCPIf , Cop, T(2005:12), Trend)z
(7)
Where a trend and a break in the trend T(2005:12) are included, and impose the following
identifying restrictions:
R1 = ( 1, 1, 0, 1, 0, 0, 0), to capture the relationship between the money supply, the
exchange rate and the copper price;
R2 = ( 0, 1, 1, 0, 0, 1, 1), to capture the relationship among the exchange rate, food inflation,
the trend and its break;
R3 = ( 1, 0, 1, 0, 1, 0, 1), to capture the relationship among the money supply, non food
inflation, copper price and the trend.
Interestingly, the real oil price disappears from the cointegrated VAR. This is because,
although significant in the unrestricted VAR, the oil prices result not to be significantly related
to any variable within the restricted structure. This comes as a surprise, and the explanation is
given by the fact that oil prices in Zambia are set by the Ministry of Energy and do not reflect
the international oil price (the one used here) 9.
Out of these restrictions we obtain the following long run structure for the cointegrated
VAR, which is accepted with a p-value of 0.879 (table 3).
Table 3: Long run structure
Beta(1)
M3
0.225
Ex
CPIf
CPInf
1.000 0.000 0.000
COP
-0.377
T(2005:12)
0.000
TREND
-0.007
9 This is also confirmed by a study by Weeks (2007), where he detects a diverging trend
between domestic and international oil prices during the copper boom.
Beta(2)
Beta(3)
(2.107)
0.000
(.NA)
0.020
(4.632)
(.NA) (.NA) (.NA) (-12.009)
0.195
1.000 0.000
0.000
(6.010) (.NA) (.NA)
(.NA)
0.000
0.000 1.000
0.000
(.NA) (.NA)
(.NA)
(.NA)
TEST OF RESTRICTED MODEL:
(.NA)
(-8.803)
0.009
-0.016
(9.418) (-119.363)
0.000
0.000
(.NA)
(.NA)
CHISQR(7) = 3.748[0.879]
t-values in paranthesis
Source: RATS estimation
The first long run vector (Beta 1) captures how the money supply, the exchange rate and
the price of copper change jointly in the long run, when a linear trend is included. We choose
to normalise for the exchange rate since this allows capturing directly how the copper price is
related to the exchange rate. The money supply and exchange rate relationship indicates that
when the money supply increases by 0.2 per cent then the exchange rate depreciates by 1 per
cent. This result indicates how when real money increases the exchange rate depreciates, since
the domestic currency loses its value with respect to the foreign exchange; and vice versa.
The vector also reveals another interesting result. As already mentioned, the price of
copper is exogenous by definition and it appears to be significantly related to both the
exchange rate and the money supply. When the price of copper goes up by 0.3 per cent then
the exchange rate appreciates by 1 per cent and the money supply goes down by 0.2 per cent.
We explain the relationship between the copper price and the exchange rate in the sense of the
Kwacha being a commodity currency. A commodity currency identifies an exchange rate
which exhibits a long run relationship with the main exported commodity, and this has clearly
implications for policy (Chen and Rogoff, 2002; Cashin and Cespedes, 2004).
The second long run vector (Beta 2) captures instead changes in food prices and in the
nominal exchange rate when a linear broken trend is included. When imposing the restrictions,
we found no significant relationship between the money supply and food prices, thus the
money supply was not included. This finding could have suggested food inflation is not
sensitive to changes in the money supply, as is plausible, since changes in food prices are more
associated with changes in supply conditions such as weather and production costs. On the
other hand, these prices exhibit a significant long run relationship with the exchange rate with
a coefficient equal to 0.2 per cent. The reason for this is that food in Zambia is largely imported
from abroad, especially wheat and rice.
The third beta vector attempts to identify the determinants of non food inflation. Money
supply appears to be the only variable that significantly affects non food inflation with a
highly significant coefficient of 0.02 per cent. The exchange rate proves not to be significant.
The reason may be in the fact that non food inflation refers to housing, medical care and
communication in addition to traditional imported goods and services like fuel, clothing and
footwear. Yet, as mentioned, fuel, which is usually the largest component, has a price
behaviour which is not sensitive to the exchange rate since it is managed by the Ministry of
Energy. On the contrary, the positive relationship between non food inflation and the money
supply can confirm the existence of absorptive capacity bottlenecks, maybe in the service
sectors, since the assumption of full employment does not hold in the Zambian context.
Checking for the identifying conditions, the structure satisfies the rank conditions and one
of the relationships is just identified while the other two are over identified (table 4).
Table 4: Ranking conditions
R(i.j)
R(i.jk)
(1.2): 2
(1.23): 3
(1.3): 1*
(2.1): 2
(2.13): 3
(2.3): 2
(3.1): 2
(3.12): 4
(3.2): 3
*
: rank condition just satisfied,
** : rank condition violated.
Source: RATS estimation
As far as the parameters constancy in the restricted model are concerned, we report in
figure 3 a test with recursive estimates.
Figure 3: Test for Constancy
LR-test of Restrictions
1.4
X(t)
1.2
R 1(t)
5% C .V. (14.1 = Index )
1.0
0.8
0.6
0.4
0.2
0.0
2000
2001
2002
2003
2004
2005
2006
2007
Source: RATS estimation
The test shows that at least for the adjusted series the constancy of parameters is respected.
Short run identification restrictions
In modeling the cointegrated VAR we do not only aim at detecting long run relationships
among the variables, but also at trying to see how the individual series adjust with respect to
this equilibrium. This allows understanding short run dynamics in food and non food prices.
To obtain a short run structure we run the VAR in its error correcting form, where the
variables are balanced, since they are all I(0) and refer to lagged values or to differences.
ΔXt = αβ’Xt-1 +ГΔXt-1 +μt + φDt + εt:
(8)
In the model the Г matrix includes the parameters for the adjustments to the long run
equilibrium, whereas αβ refers to the coefficients of the short run adjustment of the variable
with respect to itself and to the other individual variables at time t-1. We first then obtain the
coefficients for these relationships through simultaneous equations and then through a general
to specific approach we exclude all insignificant coefficients from the model. Finally, we obtain
the following short run structure for the VAR:
Table 5: Short run structure
ER_1
DCPIf_1
M3
ER
0.155032
0.249244
(0.0218)
(0.0004)
-0.5693
(0.0003)
DCPIf
DCPInf
-0.05144
(0.0069)
0.517224
0.116361
(0.000)
(0.0082)
M3_1
-0.29389
(0.0001)
ECM1_1
-0.06708
-0.16889
(0.0543)
(0.0000)
ECM2_1
-0.16968
(0.0000)
ECM3_1
-0.79821
(0.0000)
Dcop
0.146941
(0.0000)
p-values in parenteses
LR test of over-identifying restrictions: Chi^2(43) = 61.645 [0.0613]
Source: Oxmetrics estimation
The identification for the short run structure reported in table 5 is accepted with a p-value
of 0.06. On the basis of the estimates we can assess that in the short run changes in the broad
money are very sensitive to changes in food inflation at time t-1 with a coefficient of -0.57, and
this may capture the Bank of Zambia’s policy function: when food inflation increases by 1 per
cent, the money supply is contracted by 0.6 per cent with a one month lag. Changes in the
money supply are also sensitive to the exchange rate with a 0.15 coefficient, and this could be
due to the fact that the exchange rate affects food inflation in the long run. Finally, the series of
broad money adjusts very slowly (0.12%) to the first cointegrating relationship, but does not
adjust to the other two (it is excluded from one of them). As for the exchange rate, this adjusts
in the short run to changes in the money supply (-0.3), to changes in the first cointegrating
relation (-0.16) and in the price of copper (0.14), In the case of food inflation, estimates indicate
that it has a large autoregressive component, since it adjusts mostly to its previous values (0.5).
However, it is also sensitive to deviations from its long run relationship with the exchange rate
(-0.169). Non food inflation, by contrast, is found to adjust quite fast to deviations from its long
run equilibrium with the money supply (-0.79) and is slightly sensitive to its previous values
(0.11). It also adjusts very slowly to changes in the exchange rate (-0.05).
6. Conclusion
On the grounds that a float has been detrimental for the Zambian non traditional exports
this paper considers what could have been the impact of a more managed exchange rate. Since
the main deterrent for adopting such an arrangement is the fear of an increase in inflation that
may, in turn, appreciate the real exchange rate and damage exports, the paper tests the impact
of a managed float on food and non food inflation.
In line with the empirical literature, we adopt a cointegrated VAR to test for the price
sensitivity to changes in the money supply and changes in the value of the currency. This is
because foreign exchange intervention may determine an increase in domestic prices either
through the usual monetary transmission mechanism or through the exchange rate passthrough.
From the cointegrated VAR it emerges that, while non food prices tend to be more
sensitive to changes in the money supply, non food inflation is clearly more related to changes
in the value of the exchange rate. An effective exchange rate pass-through on food prices is
explained by the fact that food imports are almost 20 per cent of total imports. Overall, the two
effects appear to be weak since they display small coefficients, with the pass-through effect
slightly larger than the monetary transmission mechanism.
Furthermore the model indicates that the exchange rate exhibits a significant long run
relationship with the copper price, indicating that the Zambian Kwacha is a commodity
currency. Also, the oil price does not appear to be significant in the VAR model, which has
been explained in the light of the fact that the local oil price in Zambia differs from the
international one, since it is managed by the Ministry of Energy.
To conclude, the study seems to suggest that a more managed float in Zambia would have
not been as detrimental as a float with respect to the non traditional exports. This is because,
had the Bank of Zambia tried to curb the appreciation, the increase in inflation would have not
been so high, and consequently the real exchange rate appreciation would have not been as
high as under a float.
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Annex A
Test for Lag length determination
Effective Sample: 1996:03 to 2008:03
MODEL SUMMARY
Model
k
T
Regr Log-Lik
SC
H-Q
LM(1) LM(k)
VAR(5) 5 145
35 2419.248 -28.564 -30.270 0.218 0.438
VAR(4) 4 145
29 2400.514 -29.129 -30.543 0.067 0.809
VAR(3) 3 145
23 2390.012 -29.808 -30.929 0.339 0.689
VAR(2) 2 145
17 2376.348 -30.443 -31.272 0.169 0.128
VAR(1) 1 145
11 2311.576 -30.374 -30.910 0.000 0.000
Lag Reduction Tests:
VAR(4) << VAR(5)
:
ChiSqr(24) =
VAR(3) << VAR(5)
:
ChiSqr(48) =
58.473 [0.143]
VAR(3) << VAR(4)
:
ChiSqr(24) =
21.005 [0.638]
VAR(2) << VAR(5)
:
ChiSqr(72) =
85.802 [0.127]
VAR(2) << VAR(4)
:
ChiSqr(48) =
48.333 [0.459]
VAR(2) << VAR(3)
:
ChiSqr(24) =
27.329 [0.289]
VAR(1) << VAR(5)
:
ChiSqr(96) = 215.344 [0.000]
VAR(1) << VAR(4)
:
ChiSqr(72) = 177.876
[0.000]
Beta1'*Z1(t)
5
VAR(1) << VAR(3)
:
ChiSqr(48) = 156.871 [0.000]
4
3
<< VAR(2)
: ChiSqr(24) = 129.542 [0.000]
2
1
0
Schwarz
Criterion
-1
-2
Hannan-Quinn
Criterion
-3
LM-Test
for autocorrelation of order k
-4
1996
1997
1998
1999
2000
2001
2002
VAR(1)
SC
:
H-Q
:
37.468 [0.039]
LM(k):
2003
2004
2005
2006
2007
2008
2003
2004
2005
2006
2007
2008
Beta1'*R1(t)
4
Annex B
3
Graphs on the
cointegrating relations
2
1
0
-1
Beta1'*Z1(t)
-2
5
4
3
2
1
0
-1
-2
-3
-4
-3
1996
1996
1997
1997
1998
1998
1999
1999
2000
2000
2001
2001
2002
2002
2003
2004
2005
2006
2007
2008
2003
2004
2005
2006
2007
2008
Beta1'*R1(t)
4
3
2
1
0
-1
-2
-3
1996
1997
1998
1999
2000
2001
2002
Beta3'*Z1(t)
4.8
3.6
2.4
1.2
0.0
-1.2
-2.4
-3.6
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2003
2004
2005
2006
2007
2008
2003
2004
2005
2006
2007
2008
2004
2005
2006
2007
2008
Beta3'*R1(t)
3.6
2.4
1.2
0.0
-1.2
-2.4
1996
1997
1998
1999
2000
2001
2002
Beta4'*Z1(t)
4
3
2
1
0
-1
-2
-3
1996
1997
1998
1999
2000
2001
2002
Beta4'*R1(t)
2.4
1.6
0.8
-0.0
-0.8
-1.6
-2.4
1996
1997
1998
The companion matrix
1999
2000
2001
2002
2003
Roots of the Companion Matrix
1.0
1.0
Rank(PI)=4
1.0
Rank(PI)=3
0.5
0.5
0.5
0.0
0.0
0.0
-0.5
-0.5
-0.5
-1.0
-1.0
-1.0
1.0
-0.5
0.0
0.5
1.0
Rank(PI)=1
0.5
0.5
0.0
0.0
-0.5
-0.5
-1.0
-1.0
-1.0
1.0
-0.5
0.0
0.5
1.0
-0.5
0.0
0.5
1.0
Rank(PI)=0
-1.0
-1.0
-0.5
0.0
0.5
1.0
Rank(PI)=2
-1.0
The Roots of the COMPANION MATRIX // Model: H(0)
Real Imaginary Modulus Argument
Root1 1.000
0.000
1.000
0.000
Root2 1.000
-0.000
1.000
-0.000
Root3 1.000
0.000
1.000
0.000
Root4 1.000
0.000
1.000
0.000
Root5 0.376
0.000
0.376
0.000
Root6 -0.291
0.000
0.291
3.142
Root7 0.047
0.059
0.075
0.899
Root8 0.047
-0.059
0.075
-0.899
The Roots of the COMPANION MATRIX // Model: H(1)
Real Imaginary Modulus Argument
Root1 1.000
0.000
1.000
0.000
Root2 1.000
-0.000
1.000
-0.000
Root3 1.000
0.000
1.000
0.000
Root4 0.168
0.320
0.362
1.089
Root5 0.168
-0.320
0.362
-1.089
Root6 0.247
0.176
0.303
0.617
Root7 0.247
-0.176
0.303
-0.617
Root8 -0.169
0.000
0.169
3.142
The Roots of the COMPANION MATRIX // Model: H(2)
Real Imaginary Modulus Argument
Root1 1.000
0.000
1.000
0.000
Root2 1.000
-0.000
1.000
-0.000
Root3 0.665
-0.000
0.665
-0.000
Root4 0.201
0.347
0.401
1.047
Root5 0.201
-0.347
0.401
-1.047
Root6 0.352
0.000
0.352
0.000
Root7 0.226
-0.000
0.226
-0.000
Root8 -0.153
-0.000
0.153
-3.142
The Roots of the COMPANION MATRIX // Model: H(3)
Real Imaginary Modulus Argument
Root1 1.000
0.000
1.000
0.000
Root2 0.804
-0.000
0.804
-0.000
Root3 0.614
-0.286
0.677
-0.436
-1.0
-0.5
0.0
0.5
1.0
Root4 0.614
Root5 0.224
Root6 0.224
Root7 -0.064
Root8 -0.064
0.286
-0.365
0.365
-0.094
0.094
0.677
0.428
0.428
0.114
0.114
0.436
-1.021
1.021
-2.170
2.170
The Roots of the COMPANION MATRIX // Model: H(4)
Real Imaginary Modulus Argument
Root1 0.915
-0.026
0.915
-0.028
Root2 0.915
0.026
0.915
0.028
Root3 0.599
-0.300
0.670
-0.464
Root4 0.599
0.300
0.670
0.464
Root5 0.220
0.375
0.434
1.041
Root6 0.220
-0.375
0.434
-1.041
Root7 -0.080
-0.134
0.156
-2.111
Root8 -0.080
0.134
0.156
2.111