4.1 EMPIRICAL ANALYSIS
4.1.1 Reaction function for Rwanda
Rwanda is a small open economy and it is necessary to examine
how monetary policy reacts to output gap, inflation gap and exchange rate.
To formulate a monetary reaction function for National Bank of
Rwanda the Taylor rule equation was adapted to the context of monetary policy
in Rwanda. Indeed, Osterholm (2003) showed that the Taylor rule could be
estimated where the rule has been used by Central Banks or at least be a close
enough approximation to Central Bank behavior.
The original Taylor rule can be expressed as following:
FFR=f (YG, IG) (1)
Where
FFR= the federal funds rate,
YG= the output gap,
IG= the inflation gap which is (-*), where is the
actual inflation rate and * the target inflation rate.
The present study will follow suit by specifying and
estimating a version of (1). That is, will be determined a variable that seems
to be a plausible indicator of the stance of monetary policy in Rwanda.
Evidence suggests that the short-term interest rate cannot be applied to the
realities of developing countries when taken as an instrument in conducting
monetary policy given the underdeveloped nature of the financial market. It has
been argued that the monetary base is the most appropriate instrument to be
used in developing countries (Sanchez-Fung, 2000).
Because of data availability problems for the monetary base
series of Rwanda, the monetary stock aggregate (M1) will be used as the
instrument policy. Indeed, the monetary stock aggregate (M1) plays an important
role in Rwanda monetary policy since the National Bank of Rwanda assumed its
responsibility to regulate liquidity in the economy and the data of the
monetary base are frequently referred to M1.
In respect of goal variables, inflation and output will be
used. The former variable has emerged from many economists as the real goal of
monetary policy in order to maintain price stability and the latter is
considered as a historically objective of monetary policy in various
countries.
In the context of Rwanda, the strategy used by the Central
Bank is to ensure that liquidity expansion is consistent with target inflation
and GDP growth levels. Thus, the modified version of Taylor's rule to be
estimated can be written as:
Mt= ë0 + ë1 (IGt) +
ë2 (YGt) + t (2)
However, recently, with number of empirical studies related to
the Taylor rule, economists argue that the exchange rate would also be an
essential state variable that has to be included in the model in the case of a
small and open economy (Osterholm, 2003). On this basis, the equation (2) is
extended as follow:
Mt= ë0 + ë1 (IGt) +
ë2 (YGt) + ë3DEXt +
t (3)
Where Mt = monetary stock aggregate (M1),
DEXt = the change in exchange rate in
terms of the Rwandan Francs per US
Dollars,
t = the error term and
ë0, ë1,
ë2, ë3 are constant term and coefficients
respectively to be estimated empirically.
The equation (3) can be seen as a function in which the
monetary stock aggregate (M1) reacts to the inflation gap, output gap and the
change in exchange rate.
The version of the equation (3) to be empirically estimated
can take a dynamic form since there is the lag response of Monetary Authority.
On this basis, the equation (3) is expressed as follows:
Mt= 0 + 1Mt-1 +
2IGt + 3IGt-1 +
4YGt + 5YGt-1 +
6DEXt + 7DEXt-1 + t
(4)
Equation (4) is an autoregressive-distributed lag of order one
[ADL (1, 1)]. This formulation allows one to consider that the forecast value
of M at time t is simply the reaction of monetary authorities to
past and current economic states. Moreover, following Sanchez-Fung (2000: 9)
one should consider that, statistically; equation (4) could help to justify the
problem of wrongly measured data.
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