In this study we make use of three variables of Brazil, that is, rate of currency exchange, the use of renewable energy, as well as the rate of inflation for a period 1990 to 2019. Use of renewable energy refers to the power sources which are not harmful and hazardous to the environment. They are environment friendly and have the capability of being used over and over again, hence cannot be depleted, unlike fossil fuels sources of energy that are hazardous to the environment and can be depleted. Sources of renewable energy include those sources such as; water, wind, tidal, waves and solar among many others. Rate of exchange is the price at which one currency is sold against another currency in the foreign exchange market. In this study the exchange rate employed is expressed as Brazilian Real per one United States dollar (Real/Dollar) and a rise in the rate of currency exchange indicates a depreciation in the Brazilian Real whereas a drop in the currency shows an appreciation. Inflation rate is referred to as a general rise in the price of goods and services and the Consumer Price Indicator (CPI) of Brazil, in this study is used to proxy inflation rate.
In order to analyze the causal link of use of renewable energy, rate of inflation and rate of currency exchange of Brazil, dynamic Autoregressive Distributive Lag (ARDL) model is employed. The ARDL approach was pioneered by Pesaran, Shin and Smith (1997; 1999; 2001). Before, it was not possible to run levels relationship with variables that are integrated of different orders, rather variables were supposed to be stationary to be specified in the traditional Ordinary Least Square (OLS) model or to be integrated of the same order one, I (1), in order to be specified in cointegration regressions such as Fully Modified Ordinary Least Square (FMOLS) or Dynamic Ordinary Least Square (DOLS) or in a Vector Error Correction Mechanism (VECM) (Pesaran, et al., 2001; Keele and DeBoef, 2008). However, the ARDL approach allows for variables that are integrated of different orders, I (0) and I (1) or that are not mutually cointegrated to be specified in a levels’ relationship, Pesaran, et al. (2001); Keele and DeBoef (2008). It follows that, inasmuch as I (0) and I (1) variables can be specified by employing the ARDL method, I (2) variables cannot be specified; hence unit root test should be employed to check if all variables are I (0) and I (1) (Pesaran, et al., 2001; Smolovic, et al., 2020; Salim & Rafiq, 2020). Thus, in this paper we test for stationarity by employing Augmented Dickey Fuller (ADF) test, that was pioneered by Dickey and Fuller (1979) and Phillips Peron (PP) test, that was pioneered by Phillips and Peron (1988). Various studies have recommended the ADF and PP tests of unit root as the best and appropriate methods (see, Granger, 1986).
The ARDL model is a univariate method that is based on F-statistics and t-statistics to test for the existence of levels relationship of variables irregardless of them being I (0), I (1), Pesaran, et al., (2001). The null hypothesis of the model is that there is no levels relationship irregardless of the fact that the regressions are I (0), I (1), Pesaran, et al., (2001). When the F-statistics and t-statistics values of the ARDL bounds test, approach is greater than the I (0) and I (1) bounds, then levels relationship exists and we can specify the short-run ARDL model and the Equilibrium Correction Mechanism (ECM), Pesaran, et al., (2001). The ECM examines the long-run association and equilibrium among variables and the rate of adjustment to longrun equilibrium (see, for example, Granger, 1986; Engle & Granger, 1987; Pesaran, et al., 2001). When the F-statics and t-statistics values is less than the I(1) and I(0) then we can only specify the short-run ARDL model, Pesaran, et al., (2001). However, when the F-statistics and t-statistics lies in between the I (0) and I (1) bounds then inference is inconclusive and the dilemma can be overcome by examining the integration order and cointegration of variables, Pesaran, et al., (2001).
Equations 1 and 2 below are the statistical representation of the short-run and long-run ARDL model respectively (see, for example, Pesaran, et al., 1999; Pesaran, et al., 1997; Pesaran, et al., 2001). The long-run ARDL model contains the error correction term (ECT) of the ECM model plus short-run coefficients of the regressors. The ARDL model in this study is employed in such a way that all variables are employed as dependent variables, in turns, to examine how each variable is impacted by other variables, Pesaran, et al., (2001). \({ER}_{t}\) represents the rate of exchange value of Brazil currency; \({lnRE}_{t}\) is the log value of use of renewable energy sources of Brazil; \({INF}_{t}\) is the rate of inflation of Brazil; \({ECT}_{t-1}\) stands for the ECM's error correction term; \(\varDelta\) represents the operator of the first difference; \({\beta }_{0}\) ; \({\beta }_{1i}\) ; \({\beta }_{2i}\) ; \({\beta }_{3i}\) are the coefficients of the short- and long-run ARDL model, and \({\beta }_{4i}\) is the ECT’s coefficient whereas et is the error term.
To test the robustness, validity and reliability of the results of this model, Breusch-Godfrey test of serial correlation, Jarque-Bera normality test, and Breusch-Pagan-Godfrey test of heteroskedasticity is employed. If the null hypothesis is not rejected, then we conclude that the residuals of the models are free from serial correlation, are homogeneous and normally distributed. Moreover, CUSUM stability test is also employed to test model stability.