**3. Theoretical review and methodology**

The study is based on Mundell-Fleming model (MFM) developed by [29, 30]. The model is based on the extension of IS-LM model. The traditional IS-LM model describes an economy under autarky (i.e., closed economy) but MFM describes an open economy. It designates the relationship between output (short run), nominal exchange rate and interest rate in an economy. Thus, Mundell-Fleming model is adopted in this study since Nigeria is attributed to an open economy. In that, Nigeria is small to influence the world market in terms of world prices and interest rate and then assumed to have a perfect capital mobility.

#### **3.1 Model specification**

The overall model to capture the broad objective of the study which is to examine the asymmetric relationship between exchange rate volatility and macroeconomic variables in Nigeria is stated in the equation below:

$$Y\_t = f\left(ERV\_t^\*\right) \tag{1}$$

where '*Y*' is output and 'ERV' is exchange rate volatility.

The macroeconomic theory in relation to Mundell-Fleming framework implies that income, interest rate, exchange rate, price, net export and similar variables can be implicitly related.

$$Y\_t = f(\text{ERV}\_t, Z\_t) \tag{2}$$

where '*Yt*' is output, '*ERVt*' is exchange rate volatility; *Zt* is vector of macroeconomic variables.

The explicit equation of the above is presented below as:

*Exchange Rate Volatility and Macroeconomic Performance in Nigeria DOI: http://dx.doi.org/10.5772/intechopen.100444*

$$Y = f(i, e, P, \text{NX}) \tag{3}$$

where 'i' is interest rate, 'e' is exchange rate, 'P' is price and 'NX' is Net Export.

Also, macroeconomic theory behind the Mundell-Fleming framework makes us believe that income, interest rate, exchange rate, price, net export variables can be implicitly related as follows:

The Mundell-Fleming Model

$$Y = \mathbf{C}(Y - t(Y)),\\r - E(\pi) + I(r - E(\pi), Y\_{t-1}) + G + \text{NX}(\varepsilon, Y, Y^\*)\tag{4}$$

where *Yt* = Output; *Ct* = Consumption; *It* = Investment; *Rt* = Interest rate; *int* = Inflation rate; *Gt* = Government spending; *TBt* = Trade balance; *Et* = Exchange rate.

Therefore, the model formation of this study is illustrated below as:

$$Y = f(i, R, E, \text{NX}) \tag{5}$$

where 'i' is inflation rate; 'R' is interest rate; 'E' is Exchange Rate and NX is 'Net Export'.

#### **3.2 Estimation of heteroskedasticity using non-linear GARCH model**

The confirmation of the presence of ARCH in the model as presented in **Table 1** enabled the study to proceed to non-linear GARCH. The ARCH model comprises of two parts: the mean equation and the variance equation as proposed by [31]. The mean equation can be mathematically specified as:

$$Y\_t = \alpha + \boldsymbol{\beta}^! X\_t + \mu\_t \tag{6}$$

where *Yt* is the vector of variables; *α* represents the constant term. *β*! is the vector of unknown parameter; *Xt* represents the vector of unknown variable; then *μ<sup>t</sup>* is the random error term.

The variance equation is presented as:

$$h\_t = \chi\_0 + \sum\_{i=1}^{q} \chi\_1 \mu\_{t-i}^2 \tag{7}$$

ARCH model is majorly a moving average (MA) and the variance is mainly responding to errors. It does not capture the autoregressive (AR) part of the model. This prompted the use of more comprehensive models like GARCH propounded by [32].

Consequently, the GARCH model also lack some important features. It cannot explain the effect of events and news which exhibit asymmetric effect on exchange rates. However, investors react in different ways to incidence of good and bad news in the financial market, wherein bad news leads to higher volatility. But the non-linear


**Table 1.** *ARCH test.*

GARCH (EGARCH) model is proficient in capturing events, news and incidence that lead to asymmetric impact and this gives preference to use EGARCH which is believed to be superior in accounting for asymmetric and non-linear effects [33].

The aim of achieving a robust result resulted in the consideration of EGARCH model for this study. To begin with, exchange rate returns was generated through the log of difference of exchange rate which is mathematically specified as:

$$d\log\left(\text{EXR}\_{t} - \text{EXR}\_{t-1}\right) \tag{8}$$

The EGARCH model as propounded by Nelson (1991) is specified in a general form as:

$$\log \left( h\_t \right) = \gamma\_0 + \sum\_{i=1}^p \beta\_i |\frac{\mu\_{t-i}}{\sqrt{h\_{t-i}}}| + \sum\_{i=1}^q \gamma\_i \frac{\mu\_{t-i}}{\sqrt{h\_{t-i}}} + \sum\_{i=1}^m a\_i \log \left( h\_{t-1} \right) \tag{9}$$

where *γ*<sup>0</sup> is constant term, *β<sup>i</sup>* is a measure of ARCH effect, *γ*<sup>1</sup> is the leverage effect, *α<sup>i</sup>* is the GARCH effect, positive value of *μ<sup>t</sup>*�*<sup>i</sup>* with total effect as 1 þ *γ<sup>i</sup>* ð Þ∣*μ<sup>t</sup>*�*<sup>i</sup>* denotes good news, negative value of *μ<sup>t</sup>*�*<sup>i</sup>* with total effect as 1 � *γ<sup>i</sup>* ð Þ∣*μ<sup>t</sup>*�*<sup>i</sup>* denotes bad news. In this case, good news is assumed to have a greater effect on volatility compared to bad news. There is asymmetry if *γ<sup>i</sup>* 6¼ 0 and symmetry when *γ<sup>i</sup>* ¼ 0.

#### **3.3 Source of data and variable selection**

This research employed secondary (quarterly) data spanning from 1986Q1– 2019Q4. The data was sourced from CBN Statistical Bulletin (2018; 2019; 2020) and International Financial Statistics (2019) editions. The macroeconomic variables used in the study are trade balance, industrial output and inflation while interest rate was used as control variable in the model.
