METHODOLOGY AND EMPERICAL RESULT OF OPTIMAL ECONOMIC UNCERTAINTY INDEX

4.0 Introduction

This chapter discussed about the methodology, data analysis and the results obtained from different tests for Optimal Economic Uncertainty Index. The generalized method of moments (GMM) parameter is using to estimate the benchmark parameters for the small structural model following by the grid search method. Lastly this chapter will closing by a conclusion.

4.1 Model Specification of OEUI

The optimal economic uncertainty index is using the small structural model which is described by Svensson (2000 as the basic idea of contemporaneous model of the economic uncertainty. The equations of small structural model is written in logarithmic form which are represent the inputs for the small structural model except the real interest rate gap, the inflation gap and the economic uncertainty index. All of the variables in this model are presenting in gap form by using potential value or equilibrium value as a benchmark to calculated the deviations of the actual value from the potential values.  is the real output gap,  is the inflation gap,  is the real exchange rate gap,  is the real interest rate gap. The equations can be written as below:

 (2)

 (3)

 (4)

 (5)

 (6)

Equation 2 is an IS curve which is explain the relationship of aggregates output, real interest rate and real exchange rate and the Equation 3 is presenting an open economy Phillips curve which is explain the relation of unemployment and inflation to derive the aggregate supply curve. Following equation 4 is a reduced form of the exchange rate which is determines the real exchange rate gap and captures the concept that a higher real interest rate gap. And Equation 5 is a monetary policy reaction function.

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Equation 6 is a contemporaneous economic uncertainty function. This function assumes describes the relation of economic uncertainty with the shocks of macro variables and policy variables which is output gap, inflation gap, exchange rate gap and interest rate gap. The positive signs on  and  indicate that the output gap mitigation and the inflation reduction could reduce economic uncertainty. However the negative signs on  and  indicate that the central bank increasing the exchange rate and the interest rate to reduce economic uncertainty.

The origin of the theoretic model of the optimal economic uncertainty index assumes that the central bank minimize the discounted expected loss subject to the small structural model by using a set of inflation, output gap and interest rate values. Below is the model of central bank’s period loss function which is assumed to be quadratic for the inflation gap, the output gap and the interest rate gap.

 (7)

,  and  stand for the weights attached to the stabilization of the real output gap, the inflation gap and the real interest rate gap. In addition, as the discount factor β of the loss function of structural Eq.1 approaches unity, it can be shown that the loss becomes proportional to the expected unconditional value of the period loss function as below where is  and  represent the unconditional variance of the real output gap and the inflation gap, respectively.

 (8)

The variance in the monetary policy instrument is often put in the loss function of the central bank. The unconditional variance of the real interest rate gap ( ) is mainly to prevent an unrealistic situation of high interest rate volatility. ,  and  are the weights attributed to the stabilization of the real output gap, the inflation gap and the real interest rate gap, respectively.