# Optimal Economic Uncertainty Index Test

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Published: *Tue, 13 Mar 2018*

**CHAPTER 4**

**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.

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.

**4.2 Data Description**

This study are using the quarterly from quarter one 1994 to quarter four 2012 taken from a variety of sources which is discusses in chapter 3. The gap form data series is generated by:

- The real output gap (): the difference between the logged time series of the current real output and the potential real outputs, which is then multiplied by 100.
- The real interest rate gap (): the difference between the current real interest rate and the potential real interest rates
- The real exchange rate gap ( ): the differences between the logged time series of the current REER and the potential REER
- The inflation gap (): the difference between the current inflation rate and the potential inflation rates.

The potential real output, desired inflation, real interest rate at the potential output and real exchange rate at potential output is generated by using The Hodrick–Prescott (HP) filter with a smoothing parameter (λ) 1600.

**4.3 Empirical Result**

The grid search method calibrates the small structural model using the generalized method of moments (GMM) parameter estimation for the benchmark parameters. The GMM method has been commonly applied to estimate small-scale macroeconomic models (Clarida et al. 1988; Gali and Gertler1999; Smets 2003). The parameters estimated from the small structural model using the GMM method are reported in Table 1.

**Table 1** GMM estimation of the standard macroeconomic reaction function

Dependent variable |
Independent variable(s) |
Parameter |
||

China |
Indonesia |
|||

Selected Asian countries |
||||

0.908***(0.037) |
0.504***(0.056) |
|||

-0.219***(0.041) |
-0.640***(0.074) |
|||

-0.084***(0.016) |
-0.106***(0.029) |
|||

0.074*(0.041) |
0.313***(0.031) |
|||

0.403***(0.101) |
0.285***(0.078) |
|||

-0.047**(0.023) |
-0.098***(0.018) |
|||

1.223***(0.309) |
1.370***(0.500) |
|||

0.575***(0.109) |
0.144*(0.085) |
|||

0.373*(0.214) |
1.188***(0.101) |
|||

-0.141**(0.071) |
-0.081***(0.030) |
|||

**Table 2** continued

Dependent variable |
Independent variable(s) |
Parameter |
||

Thailand |
||||

Selected Asian countries |
||||

0.760***(0.047) |
||||

-1.185***(0.231) |
||||

-0.197***(0.069) |
||||

0.077***(0.015) |
||||

0.335***(0.113) |
||||

-0.023***(0.007) |
||||

1.344***(0.410) |
||||

0.107***(0.037) |
||||

0.656***(0.103) |
||||

-0.112**(0.050) |
||||

*Source* Author’s calculations using EViews software

Standard errors are in parentheses. *, **, and *** denote statistical significance at the 10%, 5%and 1%levels, respectively. The list of instrumental variables for the estimates above includes lagged values of the real output gap, the inflation gap, the real interest rate gap and the real exchange rate gap.

Following Table 3 shows the estimated optimal coefficients of economic uncertainty in the benchmark setting. These coefficients are globally optimal because they depend on all of the state variables. Specifically, optimized economic uncertainties are optimal only in the sense that they represent solutions to the specified constrained optimization problem.

**Table 3** Optimal coefficients, unconditional variances of goal variables, losses (result depend on , and ) and optimized economic uncertainty index for selected Asian countries

Preference |
Selected Asian countries |
||||

, |
|||||

, |
|||||

China |
Indonesia |
Thailand |
|||

2.95 |
2.95 |
2.50 |
|||

0.25 |
0.40 |
0.10 |
|||

0.40 |
1.45 |
1.45 |
|||

1.90 |
2.95 |
2.95 |
|||

1.584 |
1.141 |
1.220 |
|||

1.190 |
1.116 |
1.109 |
|||

2.460 |
1.800 |
1.726 |
|||

3.389 |
2.708 |
2.760 |
|||

: selected Asian countries |
|||||

China |
|||||

Indonesia |
|||||

Thailand |
|||||

*Source* Author’s calculations using RATS econometrics software

* ^{a}*is .

*is the contemporaneous optimal economic uncertainty index;*

^{b}The estimated optimal coefficients of the optimal economic uncertainty index enable to derive the optimal economic uncertainty index over the sample period. This specification includes all related endogenous variables at the optimal level, specifically the real output gap, inflation gap, real exchange rate gap and real interest rate gap. These variables are then weighted using the estimated optimal coefficients and aggregated to find the optimal economic uncertainty index. To find out the validity of the derived indexes as measures of economic uncertainty, four significant economic upheavals that garnered global notoriety are selected as benchmarks for discussion: the Asian financial crisis (July, 1997), the dot-com bubble (March, 2000), the subprime crisis (Quarter 4, 2007) and the global financial crisis (September, 2008). The computed time series of the optimal economic uncertainty index for all of the selected countries are stationary.

**Figure 4.1 Optimal economic uncertainty index for China**

The notations (a, b, c and d) represent four economic upheavals that garnered global notoriety which is a stated for the Asian financial crisis (July, 1997), b stated for the dot-com bubble (March, 2000), c stated for the subprime crisis (Quarter 4, 2007), and d stated for the global financial crisis (September, 2008). The global recession periods (the shaded areas) described by the IMF are 1998, 2001–2003 and 2008–2009. (Source Author’s calculations)

Optimal economic uncertainty index (OEUI) in China has been through different phases of development during the year 1994 to 2012. A higher positive value of OEUI was shown on the Asian crisis and the dot-com bubble. Afterward, a higher MCI higher positive value of OEUI also shown between the subprime crisis and the global financial crisis on year 2008.

**Figure 4.2 Optimal economic uncertainty index for Indonesia**

The notations (a, b, c and d) represent four economic upheavals that garnered global notoriety which is a stated for the Asian financial crisis (July, 1997), b stated for the dot-com bubble (March, 2000), c stated for the subprime crisis (Quarter 4, 2007), and d stated for the global financial crisis (September, 2008). The global recession periods (the shaded areas) described by the IMF are 1998, 2001–2003 and 2008–2009. (Source Author’s calculations)

Figure 4.2 shows the optimal economic uncertainty index (OEUI) for Indonesia. According to figure 4.2, Optimal economic uncertainty index (OEUI) in Indonesia has been through different phases of development during the year 1994 to 2012. It was a sharply drop of MCI during the Asian crisis. Thereafter, a higher OEUI was shown on the dot-com bubble during the year 2000. Anyway, OEUI of Indonesia merely stable during the subprime crisis and the global financial crisis.

**Figure 4.3 Optimal economic uncertainty index for Thailand**

The notations (a, b, c and d) represent four economic upheavals that garnered global notoriety which is a stated for the Asian financial crisis (July, 1997), b stated for the dot-com bubble (March, 2000), c stated for the subprime crisis (Quarter 4, 2007), and d stated for the global financial crisis (September, 2008). The global recession periods (the shaded areas) described by the IMF are 1998, 2001–2003 and 2008–2009. (Source Author’s calculations)

Figure 4.3 shows the optimal economic uncertainty index (OEUI) for Thailand. According to figure 4.3, Optimal economic uncertainty index (OEUI) in Thailand has been through different phases of development during the year 1994 to 2012. It was a rose of OEUI during the Asian crisis. Thereafter, a negatif value of OEUI was shown on the dot-com bubble during the year 2000, the subprime crisis and the global financial crisis.

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