**3.6 Model specification**

Chen [36] did note that volatility in the rate of exchange volatility might be either for the description of a regime that is tranquil regime, and this rests how descriptive the adopted policy tools are (e.g. interest rate) utilized as a tool of stabilization instruments as follows:

Model 1

$$\mathbf{Err} = f \text{ (MPR, M2)}$$

$$\mathbf{Err} = \mathbf{MPR} + \mathbf{M2} + \mathbf{u}\_{\text{t}} \tag{1}$$

Model 2

$$\mathbf{Err} = f \text{ (TBR, LQR, EXR)}$$

$$\mathbf{Err} = \mathbf{TBR}\_t + \mathbf{LQR} + \mathbf{EXR} + \mathbf{u}\_t \tag{2}$$

#### **3.7 Method of data analysis**

Experience has shown in Nigeria that the monetary authority uses either the quantitative or qualitative measures of stabilizing the macroeconomic activities. But most often, money supply, interest rate, and inflation are the major quantitative measures employed by the Central Bank in maintaining a close watch of monetary balances in Nigeria. However, the exchange rate deepening experienced in the past prompted the monetary authority to strengthen the stock of money reserves to decelerate exchange rate volatility and watch the overall economy performance closely in terms of productivity. Based on the above argument, the empirical model for analyzing the effect of monetary policy shocks on generated exchange rate volatility series in Nigeria by considering the most employed monetary tools in formulating the error correction model is as follows:

Model 1

$$\mathbf{Err}\_{\mathbf{t}} = \mathbf{d}\_0 + \mathbf{d}\_1 \mathbf{M} \mathbf{P} \mathbf{R}\_{\mathbf{t}} + \mathbf{d}\_2 \mathbf{M} \mathbf{2}\_{\mathbf{t}} + + \mathbf{u}\_{\mathbf{t}} \tag{3}$$

Model 2

$$\mathbf{Err}\_{\mathbf{t}} = \mathbf{d}\_{\mathbf{0}} + \mathbf{d}\_{\mathbf{t}} \mathbf{TBR\_{\mathbf{t}}} + \mathbf{d}\_{\mathbf{2}} \mathbf{LQR\_{\mathbf{t}}} + \mathbf{d}\_{\mathbf{3}} \mathbf{EXR} + \mathbf{u\_{t}} \tag{4}$$

Here erv represents volatility in the rate of exchange, which is generated from the nominal rate of exchange of Nigeria's domestic currency the naira as measured in value against the US dollar by adopting the approach trough the standard deviation; mpr is the proxy for the nominal rate of interest, the monetary policy rate, which is the rate at which the Central Bank lends to the bank; ms is the broad money supply; tbr is the treasury bills rate; rsq is the reserve requirement; lqr is the liquidity ratio; and u represents the error term, and it describes the Markov models depiction transition from one regime to another. The dynamics linking monetary policy to volatility in the rate exchange for the Nigeria economy in the short run via the error correction mechanism model is investigated.

Since estimated regression results do not provide an answer to which variables cause changes in the other while ignoring the impact interaction. In terms of data requirement and sources, the paper uses a time-series data on the nominal exchange rate of naira vis-a-vis US dollar, minimum policy rate as a proxy for the interest rate, money supply, inflation rate, reserve requirement.

#### **4. Presentation of data/results**

#### **4.1 Empirical analysis**

This section elaborates on the empirical results and the analysis.

#### *4.1.1 Unit root tests*

The test for unit root reveals information on the stationarity properties of variables. The variables were tested at levels and their first differences. The results are given in **Tables 1** and **2** respectively.

The unit root test result for the variables at level are shown in **Table 1**, the ADF test statistic for exchange rate (t = 0.29, p > 0.05) is insignificant at the 5% level. From the foregoing, a unit root at the 5% significance level for the null hypothesis cannot be rejected. The rate of exchange is thus not stationary at level. Similarly, liquidity ratio (t = �1.79, p > 0.05), monetary policy rate (t = �1.55, p > 0.05), money supply (t = �2.46, p > 0.05), and Treasury bill rate (t = �2.41, p > 0.05) are nonstationary at levels. These variables were all tested determine their stationarity at their first differences.

#### *Exchange Rate Volatility and Monetary Policy Shocks DOI: http://dx.doi.org/10.5772/intechopen.99606*


#### **Table 1.**

*(augmented dickey-fuller unit root tests at levels (augmented Dickey-Fuller regression has an intercept as an addition, but not a linear trend).*


*Note: Note: D denotes first difference of the variable. Source: Results Extract from E views 11.0.*

#### **Table 2.**

*(augmented dickey-fuller unit root tests at first differences (augmented Dickey-Fuller regressions include an intercept but not a linear trend).*

The results for the unit root test at first difference are given in **Table 2**; the findings indicate that at the 5% level of significance both the independent and dependent variables are all significant at first difference. This is because the ADF test statistics are all greater than the 5% critical values in absolute terms. Thus, we fail to accept the null hypothesis of a unit root at the 5% level.

#### *4.1.2 Cointegration tests*

Following the establishment of the time-series data's properties, the study carried out the multivariate Johansen cointegration test. The test was conducted for the two sets of the VEC models. The findings from the tests for exchange rate volatility, monetary policy rate, and money supply are reported in **Tables 3** and **4**, and those of exchange rate volatility, treasury bill rate, liquidity ratio, and exchange rate are presented in **Tables 5** and **6**.

As shown in **Tables 3** and **4**, the cointegration test based on the trace and maximum eigen statistics indicate that there is one cointegrating equation among exchange rate volatility, monetary policy rate, and money supply within significance level of the 5% level. The findings indicate that there exists a long run relationship among: exchange rate volatility, monetary policy rate, and money supply. Similarly, from **Tables 5** and **6**, the cointegration test based on the trace and maximum eigen statistics indicates that there is one cointegrating equation among exchange rate volatility, Treasury bill rate, liquidity ratio, and exchange rate at the 5% level. This shows that exchange rate volatility, Treasury bill rate, liquidity ratio, and exchange rate have a common long-run trend.


*Trace test indicates 1 cointegrating eqn(s) at the 0.05 level. \**

*denotes rejection of the hypothesis at the 0.05 level.*

*\*\*MacKinnon-Haug-Michelis [37] p-values.*

*Source: Results Extract from Eviews 11.0.*

#### **Table 3.**

*Unrestricted cointegration rank test (trace).*


*Max-Eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level. \* denotes rejection of the hypothesis at the 0.05 level.*

*\*\*MacKinnon-Haug-Michelis [37] p-values.*

*Source: Results Extract from Eviews11.0.*

#### **Table 4.**

*Unrestricted cointegration rank test (maximum eigenvalue).*


*Trace test indicates 1 cointegrating eqn(s) at the 0.05 level.*

*\* denotes rejection of the hypothesis at the 0.05 level.*

*\*\*MacKinnon-Haug-Michelis [37] p-values.*

*Source: Results Extract from Eviews11.0.*

#### **Table 5.**

*Unrestricted cointegration rank test (trace).*


*Max-Eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level. \**

*denotes rejection of the hypothesis at the 0.05 level.*

*\*\*MacKinnon-Haug-Michelis [37] p-values.*

*Source: Results Extract from Eviews11.0.*

#### **Table 6.**

*Unrestricted cointegration rank test (maximum eigenvalue).*

#### *4.1.3 Analysis of the estimated vector error correction models*

The results of the first estimated VEC model are reported in **Table 7**.

The coefficient of determination (*R*<sup>2</sup> ) for exchange rate volatility short-run equation is approximately 0.26. This indicates that the regressors in the equation account for about 26% of the systematic variations in volatility of the rate of exchange on the short-run basis. Similarly, the adjusted *R*<sup>2</sup> shows all the independent variables in the first model account for about 21% of the systematic variations in exchange rate volatility in the short run. Thus, the overall goodness of fit of the exchange rate volatility short-run model is low.

From the exchange rate volatility short-run equation, its one-month previous volatility rate has a negative significant effect on its current rate, but its two-month previous volatility rate has an insignificant impact on its current rate in the short term. The two previous values of monetary policy rate have no significant effects on exchange rate volatility in the short run. However, the one-month lagged value of money supply has a negative significant effect on exchange rate volatility in the short run. The foregoing leads to a rejection of the acceptance of the null hypothesis that the monetary policy rate has no significant effect on the volatility in the exchange rate in Nigeria, whereas the null hypothesis on money supply not having a significant nexus with the volatility in the exchange rate is rejected as money supply has a significant impact on exchange rate volatility in Nigeria.

The results of the second estimated VEC model are reported in **Table 8**.

The coefficient of determination (*R*<sup>2</sup> ) for exchange rate volatility short-run equation is approximately 0.26. This indicates that the regressors in the equation account for about 26% of the systematic variations in exchange rate volatility in the short term. Similarly, the adjusted *R*<sup>2</sup> accounts for about 21% systematic variations in exchange rate volatility in the short run. Thus, the overall goodness of fit of the exchange rate volatility short-run model is low.

From the exchange rate volatility short-run equation, its one-month previous volatility rate has a negative significant effect on its current rate, but its two-month previous volatility rate has an insignificant impact on its current rate in the short term. The two previous values of monetary policy rate have no significant effects on exchange rate volatility in the short run. However, the one-month lagged value of money supply has a negative significant effect on exchange rate volatility in the short run.

The results of the second estimated VEC model are reported in **Table 9**.

The coefficient of determination (*R*<sup>2</sup> ) for exchange rate volatility short-run equation is approximately 0.92. This indicates that the regressors in the equation account for about 92% of the systematic variations in exchange rate volatility in the short term. Similarly, the adjusted *R*<sup>2</sup> indicates that all the independent variables in the second model account for about 91% systematic variations in exchange rate volatility in the short run. The F-statistic (F = 139.33, p < 0.05) indicates the overall exchange rate volatility short-run model is significant at the 5% level.

From the exchange rate volatility short-run equation, its one-month previous volatility rate has a negative significant effect on its current rate while its twomonth previous volatility rate has a positive significant impact on its current rate in the short term.

The two previous values of Treasury bill rate have no significant effect on exchange rate volatility in the short run. Also, the two lagged values of liquidity ratio have no significant effect on exchange rate volatility in the short run. However, the two lagged values of exchange rate have positive significant effects on


*Notes: Standard errors are in ()and t-statistics are in [].*
