Autoregressive Distributed Lag (ARDL) Model

The objective of the paper was to assess the impact of exchange rate movement and the nominal interest rate on infl ation in Ghana and to investigate the Fisher Eff ect and the International Fisher Eff ect scenarios. The study employed an autoregressive distributed lag model and an unrestricted error correction model to estimate the long run and short run relationships between infl ation, exchange rate movement and interest rates. The error correction model was applied due to the fact that the variables were co-integrated. The long run relationships were estimated using the coeffi cients from the autoregressive distributed lag model. The ARDL model was also applied because variables were found to be integrated of diff erent orders. The Fisher Eff ect and International Fisher Eff ect were explained using regression models.

Bayesian inference requires an analyst to set priors. Setting the right prior is crucial for precise forecasts. By using an autoregressive distributed lag model, this paper analyzes how optimal Litterman prior changes when an economy is hit by a recession. The results show that a sharp economic slowdown changes the optimal prior in two directions. First, it changes the structure of the optimal weight prior by setting smaller weight on the lagged dependent variable compared to variables containing more recent information. Second, greater uncertainty brought by a rapid economic downturn requires more space for coefficient variation which is set by the overall tightness parameter. It is shown that the optimal overall tightness parameter may increase to such an extent that Bayesian ADL becomes equivalent to frequentist ADL.

This paper studies quantile regression in an autoregressive dynamic framework with exogenous stationary covariates. Hence, we develop a quantile autoregressive distributed lag model (QADL). We show that these estimators are consistent and asymptotically normal. Inference based on Wald and Kolmogorov-Smirnov tests for general linear restrictions is proposed. An extensive Monte Carlo simulation is con- ducted to evaluate the properties of the estimators. We demonstrate the potential of the QADL model with an application to house price returns in the United King- dom. The results show that house price returns present a heterogeneous autoregressive behavior across the quantiles. The real GDP growth and interest rates also have an asymmetric impact on house prices variations.

the effect of the domestic price realization, linked with exchange rate volatility, on the India’s tea export was timely and relevant. The novelty of this work was in the application of the quantile autoregressive distributed lag model (QADL), recently suggested by Xiao (2009) and Galvao et al. (2009, 2013). While the classical time series models, namely the co-integration and autoregressive distributed lag model, capture the mean relationship between the variables through the conditional mean, the QADL examines the long-run relationship over quantiles through the conditional quantile function along time. The QADL approach would allow us to examine the variation in the India’s tea export across various quantiles along time in re- sponse to the regressors. Also, the QADL results are superior to the results of the standard autoregressive distributed lag model regarding the root mean square error of the fat tail distributions.

Applying cointegration and Granger causality tests, Shawa and Shen (2013) analyse the causality relationship between FDI, export and GDP growth of Tanzania over the period 1980 to 2012. The results of their study indicate that though there exists a long run relationship between the variables in question, no causality was confirmed between GDP and FDI. Only a unidirectional relationship was found between FDI and export with causation running from FDI to export and not otherwise. They suggest more conducive policy framework to attract more FDI in order to boost exports in Tanzania. Applying ARDL model to cointegration and Granger causality test within VECM, Belloumi (2014) examines the dynamic causal relationship between economic growth, foreign direct investment, trade openness, labour, and capital investment in Tunisia for the period of 1970– 2008. The results of ARDL bounds tests indicate that there is along run relationship among the variables when foreign direct investment is the dependent variable. Whereas the variables of interest are not bound together when the other variables are taken as dependent variables. The estimated coefficients of the long run relationship are found significant for capital investment and labour but insignificant for others. According to them, the negative coefficient of labour indicates a growing unemployment problem in the Tunisia. The results of the Granger causality test indicate that there is no significant causal relationship between FDI and economic growth, trade and economic growth.

This study applied the ARDL model to examine the contributions of commercial Banks to GDP growth in Nigeria. To achieve this, annual data covering 1981 to 2015 for loans and advances, savings, lending rates and GDP of Financial Institutions were collected from CBN bulletin. The ADF test revealed that the variables are I(1) except for lending rate which was of I(0) order. The ARDL(1,1,1,2) model revealed that loans and advances, and lending rates are significantly positively related to GDP in Nigeria but savings was not significant in the model, this is in line with work of (Nwachukwu and Odigie 2011).

Alyousef (2014), estimated broad money demand function (M2) in Saudi Arabia, based on ARDL model, and relying on quarterly data for the period (1996-2012). The study used the variables of real income, interest rates, index of financial innovations and stock prices. It’s found that there is a long-run stable relationship between the demand for money and its determinants. Also the results show that all variables have a significant impact on the demand for money in the long and short term, except stock price variable.

This study investigates the effect of the inflation rate in Sudan on stock returns on the Khartoum Stock Exchange. The linear autoregressive distributed lag (ARDL) model was applied to monthly data over the period from September 2003 to December 2019, with the exchange and money supply growth rates, and Murabaha profit margin as control variables. As no previous studies have studied the effect of inflation on stock returns by means of the ARDL approach, this study intends to fill this gap in the current body of literature. The results show that the inflation rate exerts a significantly negative effect on stock returns in both the short and long term, which is crucial to the understanding of all, but especially developing, economies, such as Sudan. First, policymakers must formulate strategies to control inflation and stabilize the stock market; second, any decision-making on short- and long-term investments should take account of these findings.

Mesbah (2014) in his study examined the long-run causal link between remittances and output in Egypt for the period 1977–2012 using the autoregressive distributed lag (ARDL) bounds test for cointegration, also a vector error correction model to estimate the short- and long-run equilibrium dynamics. His result revealed that remittances and GDP are cointegrated, with a statistically significant, positive causality running from remittances to output, while output is found not to be a long-run forcing factor of remittances in Egypt.

Autoregressive Distributed Lag Model (ARDL) model plays a key role when faced with making vital economic decision from past data. Change in economic variables may bring change in other economic variables beyond the time (Kripfganz and Schneider, 2018). This is termed as changes distributed over future periods. This is a model containing the lagged values of the dependent variable, the current and lagged values of the regressors as explanatory variables. The ARDL model uses a combination of endogenous and exogenous variables. It is often necessary for stationary (unit root) test to be conducted to ascertain that no variable is integrated of order 2 i.e. I(2). The ARDL model can be specified if the variables are integrated of different orders. That is, a model having a combination of variables with I(0) i.e. level stationary variables and I(1) i.e. 1 st

The paper modelled both long run and short run effects of government activities on total energy demand in Ghana for the period 1970 to 2011 using Autoregressive Distributed Lag Model (ARDL). The results of the findings indicate significant evidence of cointegration between government activities and total energy demand. The results show that government activities are key explanatory variable in total energy demand. Government activities are recommended as a policy tool to manage energy demand. Further study is worth considering in the area of causality and structural breaks in unit root.

Asymmetric dynamic responses are common in the time series empirical literature. For instance, Beaudry and Koop (1993) show that positive shocks to the U.S. GDP are more persistent than negative shocks. Poterba (1991) and Capozza et al. (2002) among others, present evidence on the asymmetric responses of house prices to income shocks. The occur- rence of these asymmetries call into question the usefulness of models with time invariant structures as means of modeling such series. Quantile regression (QR) is a statistical method for estimating models of conditional quantile functions, which offers a systematic strategy for examining how covariates influence the location, scale, and shape of the entire response dis- tribution, therefore exposing a variety of heterogeneity in response dynamics. Koenker and Xiao (2006) introduced quantile autoregression (QAR) models in which the autoregressive coefficients can be expressed as monotone functions of a single, scalar random variable. QAR models are becoming increasingly popular, and there is a growing literature about estimation of QR models for time series. Engle and Manganelli (2004) propose a quantile autoregres- sive framework to model value-at-risk where the quantiles follow an autoregressive process. Gourieroux and Jasiak (2008) study dynamic additive quantile model. Xiao (2009) proposes QR with cointegrated time series. Recently, Xiao and Koenker (2009) studied conditional quantiles for GARCH models using QR. 1

This study uses the autoregressive distributed lag (ARDL) approach, or bound test of cointegration technique, suggested by Pesaran and Shin (1995); Pesaran and Shin (1999) and extended by Pesaran et al. (2001). Autoregressive Distributed Lag (ARDL) co-integration test is used due to a number of econometric advantages compared to other cointegration procedures, such as, the Granger (1981), Engle and Granger (1987), and Johansen and Juselius (1990). It allows the long and short-run parameters of the model in question to be estimated simultaneously yet evade the problems posed by non-stationary data. In addition, and according to Narayan (2004), the small sample properties of the bounds testing approach are far more superior to that of multivariate cointegration. Also, there is no need to determine the order of the integration among the variables in advance. Other approaches however, do require that variables have the same order of integration (Nkoro and Uko, 2016). Therefore, the model of the study can be expressed as in equation 1:

Regression model analysis and the autoregressive distributed lag (ARDL) model estimates revealed that the financial deepening indicators have no effect on economic growth but their pooled additive effect on economic growth is positive and it is significant under 1% level. The ARDL result showed no evidence of short-run relationship between financial deepening and economic growth but the long-run equilibrium relationship is only significant at 10% level. The result also showed that the system is getting adjusted towards long-run equilibrium at the speed of approximately 500 1 % . This specifies a slow speed of adjustment towards equilibrium. Hence, the government should make more practical policies in financial sector reforms that can boost positive effect of financial deepening on economic growth both in the short-run and long-run.

employed for existence of unit root. In brief, Augmented Dickey-Fuller (ADF) tests indicate that Oil and Gas prices are integrated processes of degree one or I (1) and Coal prices is integrated processes of degree five or I (5). As integration degree of variables are not same the Autoregressive Distributed Lag (ARDL) approach to cointegration adapted to cointegration analysis on Oil, Gas and coal prices. The ARDL model was specified in logarithmic form which coefficients mean as elasticities. The model selection fulfilled by Schwarz Bayesian Criterion (SBC) and so ARDL (2, 0, 0) was selected. Moreover, to confirm the stability of the model, CUSUM and CUSUMSQ tests are also conducted with the results that the estimated model is completely stable.

The impact of oil price changes on selected variables in Nigeria within the period, 1981-2016 had been evaluated in this study. Adopting the ex-post facto research design with annual time series and using The Autoregressive Distributed Lag (ARDL) model; the results revealed that the change in oil price had a positive and significant impact on government revenue and government expenditure, but had no positive and significant impact on the domestic price level. As the world continues to explore alternative energy sources Government must encourage diversifying the economy for improved revenue efficiency and effectiveness.

Finally, we applied the ARDL model approach to cointegration to 5 selected Nigeria macroeconomic series considered and found that the Ination and GDP series have long run relationships with the other macroeconomic series in the annual set of data and a disturbing (instability for GDP and no long run equilibrum for ination) result from the quarterly reported data set. The ARDL models were found to be equivalent to the short term dynamics of the ECM, also the performance of the annual data gave a better and interpretable result and these results follow that of Hassler and Wolters (2006).

The above tests demonstrate that there is a cointegra- tion between the chosen variables. Then we estimate Equation (6) under three measurement criteria of R&D intensity. Autoregressive distributed lag model I is esti- mated on condition that RD/Q is equal to RD/Y; Autore- gressive distributed lag model II is estimated on condi- tion that RD/Q is equal to RD/AL; Autoregressive dis- tributed lag model III is estimated on condition that RD/Q is equal to RD/AHL. The results are as follows:

This paper provides further evidence on the impact of crime on the job market using the time series data over the period 1980-2007 for Argentina. We also address methodological flaws by earlier crime studies by employing autoregressive distributed lag (ARDL) approach to cointegration advocated by Pesaran et al (2001). The results show that unemployment has a statistically positive effect on the crime rate, depending on the model used.

In order to capture both the short-run and long-run relationships between insurance penetration and economic growth, this study employed the autoregressive distributed lag (ARDL) bounds test approach proposed by Pesaran and Shin (1999) and Pesaran et al. (2001). The statistic underlying the procedure is a Wald or F-statistic in a generalized Dickey-Fuller type regression, which is used to test the significance of lagged level variables in a conditional unrestricted equilibrium correction model (Narayan and Narayan, 2004). According to Narayan (2004) this procedure has several advantages over other Contegration approaches such as the Engel and Granger (1987) and Johansen and Juselius (1990). First, the bounds testing procedure is applicable irrespective of whether the underlying regressors are purely I(0), purely I(1) or mutually cointegrated. Second, it is said to perform better for small samples sizes, which is an advantage when working with developing countries data, which are usually short. Third, estimating the long-run and short-run components of the model simultaneously eliminates problems associated with omitted variables and autocorrelations.