Asian Journal of Economics and Empirical Research ISSN(E) : 2409-2622 ISSN(P) : 2518-010X Vol. 3, No. 1, 84-93, 2016 http://asianonlinejournals.com/index.php/AJEER 84 Modelling Economic Growth Function in Nigeria: An ARDL Approach Chinwuba Okafor1  Ibrahim Shaibu2 1 Department of Accounting, University of Benin, Benin City 2 Department of Business Administration, University of Benin, Benin City ( Corresponding Author) Abstract The objectives of the study were to identify the significant variables that underlie economic growth in Nigeria, ascertain the stability of the economic growth model in Nigeria over the sample period, and examine the forecasting performance of the linear dynamic model. This study applies a linear dynamic model based on Pesaran et al. (2001) multivariate autoregressive distributed lag (ARDL) modelling technique to analyze the short-run and long-run dynamics of economic growth in Nigeria over the sample period between 1986 and 2013 using quarterly data. The empirical results show that economic growth in Nigeria finds explanation in adaptive expectations. The main determining variables of economic growth in Nigeria in the short-run and long-run are expected economic growth, population and trade openness. To achieve sustainable economic growth, it is suggested that government policies directed at improving the performance of the economy should largely consider the short-run and long- run behaviour of these variables and the policies should be pursued with high degree of transparency. Keywords: Adaptive expectation, ARDL, Co-integration, Dynamic model, First difference, Gross capital, Growth, NEEDS, Openness, Parsimonious model. Contents 1. Introduction ......................................................................................................................................................................... 85 2. Theoretical Framework and ARDL Specification .............................................................................................................. 85 3. Empirical Literature on the Determinants of Economic Growth ...................................................................................... 86 4. Pre-estimation Analysis ....................................................................................................................................................... 87 5. Estimation, Diagnostics and Interpretation of ARDL Model ............................................................................................ 89 6. Discussion of Findings, Conclusion and Recommendations ............................................................................................... 91 References ................................................................................................................................................................................ 92 Citation | Chinwuba Okafor; Ibrahim Shaibu (2016). Modelling Economic Growth Function in Nigeria: An ARDL Approach. Asian Journal of Economics and Empirical Research, 3(1): 84-93. DOI: 10.20448/journal.501/2016.3.1/501.1.84.93 ISSN (E): ISSN (P): 2409-2622 2518-010X Licensed: This work is licensed under a Creative Commons Attribution 3.0 License Contribution/Acknowledgement: All authors contributed to the conception and design of the study. Funding: This study received no specific financial support Competing Interests: The authors declare that they have no conflict of interests. Transparency: The authors confirm that the manuscript is an honest, accurate, and transparent account of the study was reported; that no vital features of the study have been omitted; and that any discrepancies from the study as planned have been explained Ethical: History: This study follows all ethical practices during writing. Received: 13 November 2015/ Revised: 23 December 2015/ Accepted: 17 February 2016/ Published: 13 May 2016 Publisher: Asian Online Journal Publishing Group http://creativecommons.org/licenses/by/3.0/ http://crossmark.crossref.org/dialog/?doi=10.20448/journal.501/2016.3.1/501.1.84.93 https://orcid.org/orcid-search/quick-search?searchQuery=Chinwuba Okafor https://orcid.org/orcid-search/quick-search?searchQuery=Ibrahim Shaibu http://search.crossref.org/?q=10.20448/journal.501/2016.3.1/501.1.84.93 http://crossmark.crossref.org/dialog/?doi=10.20448/journal.501/2016.3.1/501.1.84.93 https://orcid.org/orcid-search/quick-search?searchQuery=Chinwuba Okafor https://orcid.org/orcid-search/quick-search?searchQuery=Ibrahim Shaibu http://search.crossref.org/?q=10.20448/journal.501/2016.3.1/501.1.84.93 http://crossmark.crossref.org/dialog/?doi=10.20448/journal.501/2016.3.1/501.1.84.93 https://orcid.org/orcid-search/quick-search?searchQuery=Chinwuba Okafor https://orcid.org/orcid-search/quick-search?searchQuery=Ibrahim Shaibu http://search.crossref.org/?q=10.20448/journal.501/2016.3.1/501.1.84.93 http://crossmark.crossref.org/dialog/?doi=10.20448/journal.501/2016.3.1/501.1.84.93 https://orcid.org/orcid-search/quick-search?searchQuery=Chinwuba Okafor https://orcid.org/orcid-search/quick-search?searchQuery=Ibrahim Shaibu http://search.crossref.org/?q=10.20448/journal.501/2016.3.1/501.1.84.93 Asian Journal of Economics and Empirical Research, 2016, 3(1): 84-93 85 1. Introduction Nigeria, like any other nation, has a key policy objective of promoting a sustainable economic growth process that could improve the living standard of the people. Nigerian is recognized globally as a country with great potentials required for achieving this broad objective of sustainable economic growth. However available statistics indicate that the country has been struggling to grow (Omoke, 2010). Given the limited resources available to support development and reforms, it is not possible to tackle all possible constraints and therefore the country as a matter of necessity must prioritize. Understanding the determining variables of economic growth in Nigeria is prerequisite to identifying critical areas that need reforms. This is useful in order to direct the available resources to the most binding determining factors. Previous efforts at planning and economic reforms such as the Structural Adjustment Programme (SAP) (1986) the National Economic Empowerment Development Strategy (NEEDS) (2003-2007) and the United Nations (UN)- sponsored National Millennium Goals for Nigeria (NMGN) (2000-2015), appear not to have accelerated the pace of economic growth to the desired threshold. This is evidenced in the adverse inflationary trend, undulating foreign exchange rates, the fall and rise of gross domestic product, unfavourable balance of payments as well as increasing unemployment rates. One reason adduced for the failure of these policy measures is the relatively weak scientific effort at explaining the dynamics of economic growth in Nigeria. As a result, policy making has relied upon macroeconomic forecasts that are not anchored on scientific models that track major economic indices (Adenikinju et al., 2009). The application of economic models in explaining the dynamics of economic growth will enable economic decision makers to exercise their judgmental analyses in a much more structured and quantified manner and to develop a more adequate understanding of macroeconomic time line. This study attempted to do this by identifying and estimating a linear dynamic model based on Pesaran et al. (2001) multivariate autoregressive distributed lag (ARDL) approach. 2. Theoretical Framework and ARDL Specification The starting point of conventional economic growth theorization is the neoclassical model developed by Solow (1956) and Swan (1956) which involved a series of equations showing the relationship between labour-time, capital goods, output, and investment. This model was the first attempt to model long-run growth analytically. This model assumes that countries use their resources efficiently and that there are constant returns to scale, diminishing marginal productivity of capital, exogenously determined technical progress and substitutability between capital and labour. According to this view, the role of technological change is very important. The role of technological progress as a key driver of long-run economic growth proposed by Solow-Swan has been put to scrutiny by some economists, who accept constant and increasing returns to capital (Romer, 1990; Grossman and Helpman, 1991). Unsatisfied with Solow-Swan explanation, they worked to "endogenize" technology. Some studies (Azege, 2004; Adebiyi, 2006; Bello and Adeniyi, 2010; Ighodaro and Oriakhi, 2010; Omoke, 2010; Adediran, 2012; Alani and Isola, 2012) have investigated the factors underlying economic growth. Using differing conceptual and methodological viewpoints, these studies have placed emphasis on different sets of explanatory parameters and offered various insights to the sources of economic growth. A major issue with growth modeling is the determination of the variables to include in the analysis which has resulted to well over ninety (90) different variables have being proposed as potential growth determinants (Petrakos et al., 2007; Ristanović, 2010) each of which has some ex ante plausibility. This issue results because of the open-endedness of growth theories whereby the validity of one causal theory does not imply the falsity of another. To deal with the issue of open-endedness, some researchers such as Levine and Renelt (1992) have proposed ways to deal with the robustness of variables in growth regressions by identifying a set of potential control variables for inclusion. Inclusion of a variable in the final choice requires that its associated coefficient proves to be robust with respect to the inclusion of other variables. A coefficient is robust if the sign of its OLS stays constant across a set of regressions representing different possible combinations of other variables. The bulk of modern empirical work on growth has focused on growth regressions of the type pioneered by Barro (1991). A generic form for growth regression is: i i i ig X Z     (1) Where ig is real per capita growth in economy i over a given period of time. Xi represents variables whose presence is suggested by Solow’s growth model: a constant, initial income and a set of country-specific savings and population growth controls. The Solow’s model is often treated as a baseline from which to build up more elaborate growth models, hence these variables tend to be common across studies. Zi, in contrast, consists of variables chosen to capture additional growth determinants that a researcher believes are important and so generally differ across analysis. Starting from the key macroeconomic relation, with an aim to considering the impact that relevant economic variables have on economic growth (proxied by GDP), Equation (1) is augmented by the influence of exchange rate (EXCRT), financial deepening (FIND), foreign direct investment (FDI), government expenditure (GOVEXP), gross capital formation (GCF), human capital (HCAP), inflation (INFN), interest rate (INTR), oil price (OILP), population growth (POP) and trade openness (TOPEN).   2t t t t t t t t t t t t tGDP EXCRT FDI FIND GOVEXP GCF HCAP INF INTR OILP TOPEN POP u            The autoregressive distributed lag (ARDL) model deals with single equation modelling and was introduced by Pesaran et al. (2001). The autoregressive distributed lag (ARDL) approach is a co-integration technique for determining long-run and short-run relationships among variables under study simultaneously. Following Pesaran et al. (2001) the ARDL representation of Equation (2) is formulated and specified as follows: http://en.wikipedia.org/wiki/Efficiency_(economics) http://en.wikipedia.org/wiki/Technological_change Asian Journal of Economics and Empirical Research, 2016, 3(1): 84-93 86 0 1 2 3 4 5 1 0 0 0 0 6 7 8 9 10 0 0 0 0 0 n n n n n t i t i i t i i t i i t i i t i i i i i i n k n n n i t i i t i i t i i t i i t i i i i i i RGDP RGDP EXCRT FDI FIND GOVEXP GCF HCAP INFN INTRT OILP                                                                11 12 1 1 2 1 3 1 4 1 0 0 5 1 6 1 7 1 8 1 9 1 10 1 11 1 12 1 + n n i t i i t i t t t t i i t t t t t t t t t TOPEN POP GDP EXRT FIND FODI GEXP GCF HCAP INF INTR OILP POP TOPEN                                                  (3) where : RGDP Real gross domestic product, EXRT Exchange rate, FIND Financial deepeni   ng, FODI Foreign direct investment, GOVEXP Government expenditure, GCF Gross capital formation, HCAP Human capital, INFN Inflation, INTRT Interest rate,       0 OILP Oil price, POP Population, TOPEN Trade openness   denotes the first difference operator, is the drift component, and is the residual. t       The left-hand side is the economic growth proxied by the gross domestic product (GDP). The expressions with the summation sign 1 12( )  on the right-hand side represent the short-run dynamics of the model. The first until twelve expressions 1 12( )  on the right-hand side correspond to the long-run relationship of the model. Therefore, apriori expectations of the coefficients are: 1 3 4 5 6 7 10 11 12 2 8 9, , , , , , , , 0., , , 0.             3. Empirical Literature on the Determinants of Economic Growth Economic growth has long been considered an important goal of economic policy. Economic growth is most frequently expressed in terms of increase in gross domestic product (GDP), a measure of the economy’s total output of goods and services. The issue of economic growth has received considerable attention from scholars. Despite this growth in research efforts, the choice of a modelling framework has remained inconclusive both at the theoretical and empirical levels in Nigeria. A literature survey on the relationship between the selected variables and economic growth in Nigeria has been outlined in this session (see Table 1). Table-1. Determinants of Economic Growth: Literature Survey Variable Study Sample Period Country Estimation Technique Main Result Exchange Rate Anthony et al. (2012). 1975-2008 Nigeria OLS technique A long run relationship Dada and Oyeranti (2012). 1970-2009 Nigeria Simultaneous equations model No strong relationship Shehu and Youtang (2012). 1970-2009 Nigeria Significant effects Financial Deepening Abur et al. (2013). 1990-2011 Nigeria Co-integration and causality Positive impact Azege (2004). Nigeria Moderate positive Nzotta and Okereke (2009). 1986-2007 Nigeria 2SLS No impact Foreign Direct Investment Akinlo (2004). 1970-2001 Nigeria ECM Not significant Ayanwale (2007). 1970-2002 Nigeria 2SLS Not significant Bello and Adeniyi (2010). 1970-2006 Nigeria ARDL No long run relationship Egwakhide (2012). 1980-2009 Nigeria VECM Lag effect Government Expenditure Abu and Abdullahi (2010). Nigeria Disaggregated analysis Mixed Ighodaro and Oriakhi (2010). 1960-2007 Nigeria Cointegration test and granger causality test Negative impact Okoro (2013). Nigeria OLS Long run Positive impact Gross Capital Formation Adekunle and Aderemi (2012). Nigeria Negative relationship Ejiogu et al. (2013). 1981-2011 Nigeria OLS technique No causality Ugwuegbe and Uruakpa (2013). Nigeria OLS technique Positive and significant impact Alani and Isola (2012). Nigeria Growth account model Significant relationship Human Capital development Anaduaka and Eigbiremolen (2014). 1999-2012 Nigeria Augmented Solow model Positive impact Ismail et al. (2010). 1970-2008 Nigeria VECM Significant impact Inflation Aminu and Anono (2012). 1970-2010 Nigeria Granger causality test GDP causes inflation Bassey and Onwioduokit (2011). 1970- 2006 Nigeria OLS Negative & insignificant Asian Journal of Economics and Empirical Research, 2016, 3(1): 84-93 87 relationship Omoke (2010). 1970-2005 Nigeria Granger causality test No co-integrating relationship Interest Rate Chete (2006). Nigeria Long run relationship Obamuyi (2009). 1970-2006 Nigeria ECM Significant effect Obansa et al. (2013). 1970-2010 Nigeria VAR technique Positive relationship Oil Price Odularu (2007). 1970-2005 Nigeria OLS No significant effect Olomola and Adejumo (2006). 1970-2003 Nigeria Regression analysis No significant effect Oriakhi and Iyoha (2013). 1970-2010 Nigeria VAR Positive impact Population Adediran (2012). 1981- 2007 Nigeria Trend analysis Positive impact Onwuka (2005). 1980-2003 Nigeria Negative impact Trade Openness Adebiyi (2006). Nigeria VAR Positive effect Seetanah et al. (2012). 1990-2009 Selected African countries Panel Vector Autoregressive model (PVAR) Positive effect Source: Authors’ Computations From the array of empirical literature review, we found that there is no general consensus between economic growth and each of the various macroeconomic determinants. We also found that there have been few dynamic models estimated on the basis of quarterly data in explaining economic growth dynamics in Nigeria. 4. Pre-estimation Analysis Before estimation, the graphs of the time series under study are plotted, descriptive statistics are displayed, unit root test for the variables are performed, and co-integration analysis is done on the variables. The figures below show the line graphs of the historical performance of the variables used in this study. Figure-1. Variables at Levels Source: Authors’ Computations Figure 1 shows the multiple graphs of the series at their level form 0 40 80 120 160 200 1990 1995 2000 2005 2010 EXCRT -100,000 0 100,000 200,000 300,000 400,000 500,000 1990 1995 2000 2005 2010 FDI 2 4 6 8 10 1990 1995 2000 2005 2010 FIND 0 10,000 20,000 30,000 40,000 50,000 1990 1995 2000 2005 2010 GCF 0 400,000 800,000 1,200,000 1,600,000 1990 1995 2000 2005 2010 GOVEXP 20 24 28 32 36 1990 1995 2000 2005 2010 HCAP -20 0 20 40 60 80 100 1990 1995 2000 2005 2010 INFN 8 12 16 20 24 28 32 36 1990 1995 2000 2005 2010 INTRT 0 20 40 60 80 100 120 1990 1995 2000 2005 2010 OILP 20,000,000 30,000,000 40,000,000 50,000,000 60,000,000 1990 1995 2000 2005 2010 POP 50,000 100,000 150,000 200,000 250,000 300,000 1990 1995 2000 2005 2010 RGDP 0 5 10 15 20 1990 1995 2000 2005 2010 TROPEN Asian Journal of Economics and Empirical Research, 2016, 3(1): 84-93 88 Figure-2. Logarithm of Variables Source: Authors’ Computations The graphs show that there is little evidence to suspect the presence of structural break or outlier in the twelve variables but the graphs of logarithmic series display a more stable variance than the changes in the original series. 4.1. Descriptive Statistics The descriptive statistics of the transformed variables were also conducted. Table 2 below provides a full descriptive statistics of the macroeconomic variables used for the research work. Table-2. Descriptive Statistics of Variables in Nigeria (1986-2013) Returns Mean Median Std. Dev. Skewness Kurtosis Jarque-Bera Observations EXCRT 76.87 98.10 60.62 -0.003 1.22 14.75 (0.00) 112 FDI 81516.29 28619.66 103537.6 1.47 4.56 51.93 (0.00) 112 FIND 4.83 4.28 2.19 0.90 2.49 16.35 (0.00) 112 HCAP 27.77 26.62 4.22 0.46 1.70 11.83 (0.00) 112 INFN 21.61 13.00 20.54 1.44 4.02 43.71 (0.00) 112 INTRT 19.34 18.64 4.28 0.74 5.07 30.21 (0.00) 112 LGCF 9.22 9.18 0.79 -1.22 6.57 87.12 (0.00) 112 LGGOVEXP 11.74 12.21 1.77 -0.45 1.96 8.85 (0.00) 112 LPOP 17.26 17.24 0.23 0.52 2.60 5.82 (0.00) 112 LRGDP 11.63 11.52 0.38 0.56 2.36 7.69 (0.00) 112 OILP 39.13 23.15 33.02 1.20 2.99 26.84 (0.00) 112 TROPEN 2.62 0.62 5.22 2.24 6.27 144.12 (0.00) 112 Source: Authors’ Computations The table shows the mean, standard deviation, skewness, kurtosis, and normality of the variables. The mean of the variables shows their average values from 1986 to 2013. The standard deviation shows that there is some dispersion in all the variables. Lastly, skewness, kurtosis and Jarque-Bera (JB) statistics showed that all the variables are normally distributed at 1% level of significance. 0 40 80 120 160 200 1990 1995 2000 2005 2010 EXCRT -100,000 0 100,000 200,000 300,000 400,000 500,000 1990 1995 2000 2005 2010 FDI 2 4 6 8 10 1990 1995 2000 2005 2010 FIND 20 24 28 32 36 1990 1995 2000 2005 2010 HCAP -20 0 20 40 60 80 100 1990 1995 2000 2005 2010 INFN 8 12 16 20 24 28 32 36 1990 1995 2000 2005 2010 INTRT 5 6 7 8 9 10 11 1990 1995 2000 2005 2010 LGCF 8 10 12 14 16 1990 1995 2000 2005 2010 LGOVEXP 16.8 17.0 17.2 17.4 17.6 17.8 18.0 1990 1995 2000 2005 2010 LPOP 10.8 11.2 11.6 12.0 12.4 12.8 1990 1995 2000 2005 2010 LRGDP 0 20 40 60 80 100 120 1990 1995 2000 2005 2010 OILP 0 5 10 15 20 1990 1995 2000 2005 2010 TROPEN Asian Journal of Economics and Empirical Research, 2016, 3(1): 84-93 89 The absence of outliers, especially real gross domestic product (LRGDP), indicates that we can model economic growth in Nigeria without having extreme large or small values that deviate from the historical real gross domestic product (RGDP) series. The descriptive statistics show that the variables have some variations and using them in the models will require identifying their stationarity properties. 4.2. Unit Root Tests for the Variables The use of ARDL models does not impose pre-testing of variables for unit root problems. However, unit root tests are conducted in this study to find out if there are mixtures in the order of integration of our variables. The order of integration of the time series was investigated by applying the Augmented Dickey and Fuller (1979) test. The Augmented Dickey-Fuller (ADF) unit root test results for the time series variables are presented in Table 3 below. Table-3. Unit Root Test Results Variable ADF Test Statistic 95% Critical ADF Value Order of Integration Remark D(EXCRT) -9.49* -2.888 I (1) Stationary D(FDI ) -11.04* -2.888 I (1) Stationary D(FIND) -4.93* -2.888 I (1) Stationary D(HCAP) -3.51* -2.888 I (1) Stationary D(INFN) -7.14* -2.888 I (1) Stationary D(INTRT) -9.79* -2.888 I (1) Stationary D(LGCF) -9.92* -2.888 I (1) Stationary D(LGOVEXP) -6.73* -2.888 I (1) Stationary D(LPOP) -5.02* -2.888 I (1) Stationary D(LRGDP) -31.16* -2.888 I (1) Stationary D(OILP) -9.94* -2.888 I (1) Stationary D(TOPEN) -11.08* -2.888 I (1) Stationary Source: Authors’ Computations Note: * = 1percent significance; ** = 5 percent significance. In the results shown in Table 3 above, the ADF test statistic for each of the variables are greater than the respective critical values. Thus, we accept the hypothesis of unit roots in each of the time series. In our final evaluation all the variables became stationary after first difference. Hence, they are integrated of order I (1). Once all the series are non-stationary in the level, one can estimate an econometric model only if they are co-integrated. Thus co-integration tests can be applied for all variables. 4.3. Co-Integration Test The two popular co-integration tests in applied time series modelling are the Engel and Granger (1987) co- integration test and the Johansen and Juselius (1990) co-integration test. The Engel & Granger co-integration test is adopted in cases of single equation models while the Johansen and Juselius co-integration test is used for system equation models. The autoregressive distributed lag (ARDL) model is based on single equation modelling (Pesaran et al., 2001). This therefore implies that Engel & Granger co-integration method is used in the co-integration test. Using the Engel and Granger two-stage technique, the co-integration test result for the research model is presented in Table 4 below. Table-4. Engel & Granger Residual Based Co-Integration Test SERIES ADF 5% CRITICAL VALUE ORDER OF INTEGRATION REMARK RESIDUAL -5.88 -2.888 I (0) Co-integrated Source: Authors’ Computations. The results in Table 3 show that there is co-integration among economic growth proxied by real gross domestic product (RGDP), exchange rate (EXCRT), financial deepening (FIND), foreign direct investment (FDI), government expenditure (GOVEXP), gross capital formation (GCF), human capital formation (HCAP), inflation (INF), interest rate (INTRT), oil price (OILP), trade openness (TOPEN), and population growth (POP). Since the ADF test value for the residual is greater than the critical value, it is said to be stationary. Thus, the time series are co-integrated, implying that a long-run stable relationship exists among the variables used in this study. This means that any short- run deviation in their relationships would return to equilibrium in the long-run. 5. Estimation, Diagnostics and Interpretation of ARDL Model The autoregressive distributed lag (ARDL) is a technique that allows us to simultaneously estimate the short-run and long-run coefficients of our model. In order to examine the long-run and short-run relationships between economic growth and its focus variables, the parametized version of ARDL model (Pesaran et al., 2001) with lag four is estimated. The diagnostic tests like Breusch-Godfrey serial correlation LM test, the ARCH test for heteroscedasticity, Jarque-Bera test for normality of the residual term, are performed on the model. Finally, the model is used to forecast inflation in Nigeria over the sample period and the forecast performance evaluated. 5.1. The Parsimonious Autoregressive Distributed Lag (ARDL) Estimates Following Hendry (1995) general to specific modelling approach, exchange rate, foreign direct investment and price of crude oil were deleted from the parametized model because of their insignificant coefficients to arrive at the parsimonious model. The parsimonious model equation can be formed as: Asian Journal of Economics and Empirical Research, 2016, 3(1): 84-93 90 1 4 4 1( ) 24.4 0.30 0.73 0.03 0.02 0.001 ( 4.5) (4.5) (10.6) ( 1.8) ( 2.0) t t t t t tLRGDP LRGDP LRGDP FIND HCAP INTRT                   2 3 4 -1 -2 ( 0.95) 0.0003 0.001 0.0009 0.0004 0.02 ( 0.17) ( 0.8) (0.5) t t t t tINTRT INTRT INTRT LGCF LGCF              -1 -2 -3 1 (0.04) ( 1.44) 0.07 0.03 0.08 2.4 1.27 (1.5) (0.55) t t t t tGOVEXP GOVEXP GOVEXP LPOP LPOP            2 -1 -2 -3 4 (1.6) (2.8) (2.1) 0.32 0.03 0.02 0.02 0.01 (0.6) t t t t tLPOP TOPEN TOPEN TOPEN TOPEN           07 -1 -1 1 -1 -1 -1 (4.2) (3.9) (3.8) (2.7) 0.62 1.50 0.0048 0.03 0.09 E t t t t t tLRGDP FDI INFN INTRT LGCF LGOEXP       -1 -1 ( 5.1) (1.6) (-1.7) (2.7) (3.5) (-3.8) 1.87 0.03 (4.7) (4.3) t tLPOP TOPEN    4 5.2. Estimated ARDL (4, 0, 4, 4, 2, 3, 2, 4) Diagnostics After the estimation of the empirical ARDL (4, 0, 4, 4, 2, 3, 2, 4) model, there are a variety of diagnostic and stability tests which enhance the credibility of the model. The model was tested for autocorrelation (Breusch-Godfrey serial correlation LM test), for heteroskedasticity (White test), for normality (Jarque-Bera test), and for specification error/omitted variables (Ramsey RESET test). The results of the respective diagnostic test are presented in Table 5. Table-5. ARDL (4, 0, 4, 4, 2, 3, 2, 4) Diagnostic Tests TEST F-STATISTIC P-VALUE Serial Correlation: Breusch-Godfrey serial correlation LM test 5.75 0.00 Autoregressive conditional Heteroskedasticity: White test. 0.31 0.59 Normality: Jarque-Bera test. 441.24 0.00 Specification Error: Ramsey RESET test 16.64 0.00 Source: Authors’ Computations From the results reported in Table 5 the diagnostics indicate that the residuals are serially uncorrelated, homoskedastic, normally distributed based on Breusch-Godfrey serial correlation LM test, ARCH LM test, and Jarque-Bera test respectively. This means that the model is valid and can be used for policy recommendations without re-specification. The model is well specified on the basis of the Ramsey RESET test. The existence of a stable and predictable relationship is considered a necessary condition for the formulation of economic policy strategies. Instability of a model could result from inadequate modelling of the short-run dynamics characterizing departures from the long-run relationship. Hence, it is important to include the short-run dynamics for constancy of long-run parameters. In view of this we apply the CUSUM-of-squares (CUSUM-SQ) test, which Brown et al. (1975) developed. If the plot of CUSUM-SQ statistic stays within 5% significance level, then the estimated coefficients are said to be stable. A graphical presentation of this test for our ARDL model is provided in Figure 3 below. Figure-3. Cumulative sum (CUSUM) of recursive residuals plot Source: Authors’ Computations The result in Figure 3 clearly indicates that the model has been relatively stable apart from between 1999 and 2004. We are therefore safe to conclude that ARDL economic growth function is stable and economic growth can be used as a target variable. 5.3. Forecast and Forecast Evaluation for ARDL (4, 0, 4, 4, 2, 3, 2, 4) Model In the next step, forecast of Nigerian inflation series using ARDL (4, 0, 4, 4, 2, 3, 2, 4) model is conducted. Smaller values of the coefficients are preferred. The duration of the forecasts is from 1986Q1 to 2013Q4. The forecasts are plotted in Figure 4. -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 CUSUM of Squares 5% Significance Asian Journal of Economics and Empirical Research, 2016, 3(1): 84-93 91 Figure-4. Forecast of economic growth by ARDL (4, 0, 4, 4, 2, 3, 2, 4) Model Source: Authors’ Computations In Figure 4 some forecasting measurements such as root mean squared error (RMSE), mean absolute error (MAE), and Theil inequality coefficient are shown. Their coefficient values from ARDL (4, 0, 4, 4, 2, 3, 2, 4) model are tabulated in Table 6. The results show that the model is relevant for forecasting economic growth in. Table-6. Forecasting Performance of ARDL (4, 0, 4, 4, 2, 3, 2, 4) Forecast Performance Coefficient RMSE 0.08 MAE 0.05 Theil Inequality Coeff. 0.00 Source: Authors’ Computations From Table 6 we can conclude that ARDL (4, 0, 4, 4, 2, 3, 2, 4) model performs very well. In other words, ARDL (4, 0, 4, 4, 2, 3, 2, 4) model can be applied in explaining economic growth dynamics in Nigeria over the sample period. 6. Discussion of Findings, Conclusion and Recommendations The study empirically examines the economic dynamics in Nigeria using the autoregressive distributed lag (ARDL) framework using quarterly time series data that cover the period from the first quarter of 1986 to the fourth quarter of 2013 (1986Q1-2013Q4). The data were sourced from the publications of the Central bank of Nigeria (CBN) and the National Bureau of Statistics (NBS). By considering recent empirical studies in the context of economic growth, an empirical multivariate autoregressive distributed-lag model is constructed which emphasizes the effect of eleven (11) variables on economic growth. The study estimates a parsimonious ARDL model. Diagnostic tests for serial correlation (Breusch-Godfrey serial correlation LM test), heteroskedasticity (ARCH test), normality (Jarque-Bera test), specification error (Ramsey RESET test), and CUSUM-of-squares test were performed on the estimated model. In-sample forecast of economic growth dynamics using the estimated ARDL (4, 0, 4, 4, 2, 3, 2, 4) model was conducted. Some forecasting measurements such as root mean squared error (RMSE), mean absolute error (MAE), mean absolute percent error (MAPE), and Theil inequality coefficient (TIC) were computed. The empirical results from the parsimonious ARDL (4, 0, 4, 4, 2, 3, 2, 4) model is reported in Table 7 below. Table-7. The Parsimonious ARDL (4, 0, 4, 4, 2, 3, 2, 4) Result Dependent Variable: D(LRGDP) Short-run Dynamics Independent Variable Coefficient Probability Constant -24.37 (-4.47)* 0.0000 Independent Variables First difference log of real gross domestic product with one-period lag 0.30 (4.53)* 0.0000 First difference log of real gross domestic product with four-period lag 0.73 (10.59)* 0.0000 First difference of financial deepening -0.03 (-1.78)*** 0.0784 First difference log of real gross domestic product with four-period lag -0.02 (-2.02)** 0.0469 First difference log of population 2.4 (2.75)* 0.0073 First difference log of population with one-period lag 1.27 (2.06)** 0.0431 First difference of trade openness with one-period lag 0.03 (4.19)* 0.0001 First difference of trade openness with two-period lag 0.02 (3.93)* 0.0002 First difference of trade openness with three-period lag 0.02 (3.76)* 0.0003 First difference of trade openness with four-period lag 0.01 (2.75)* 0.0075 10.8 11.2 11.6 12.0 12.4 12.8 13.2 88 90 92 94 96 98 00 02 04 06 08 10 12 LRGDPF ± 2 S.E. Forecast: LRGDPF Actual: LRGDP Forecast sample: 1986Q1 2013Q4 Adjusted sample: 1987Q2 2013Q4 Included observations: 107 Root Mean Squared Error 0.077462 Mean Absolute Error 0.053713 Mean Abs. Percent Error 0.450060 Theil Inequality Coefficient 0.003322 Bias Proportion 0.000206 Variance Proportion 0.012260 Covariance Proportion 0.987533 Asian Journal of Economics and Empirical Research, 2016, 3(1): 84-93 92 Long-Run Dynamics Log of real gross domestic product -0.6 (-5.12)* 0.0000 Inflation -0.0004 (-1.77)** 0.0804 Interest rate 0.004 (2.68)* 0.0090 Log of gross capital formation 0.03 (3.53)* 0.0007 Log of government expenditure -0.09 (-3.77)* 0.0003 Log of population 1.87 (4.66)* 0.0000 Trade openness -0.03 (-4.26)* 0.0001 R-squared 0.933064 Adjusted R-squared 0.909036 F-statistic 38.83198 Prob(F-statistic) 0.000000 Source: Authors’ Computations T-statistics are in parenthesis; *, and ** imply significant at 1% and 5% confidence level respectively. Table 7 presents the results of short-run and long-run coefficients of the estimated parsimonious model. The coefficient of determination ( = 0.93) of the estimated model shows that about 93% of the variation in economic growth of Nigeria is jointly explained and accounted for by the independent variables in the estimated ARDL (4, 0, 4, 4, 2, 3, 2, 4) model. This when adjusted for degree of freedom based on the adjusted coefficient of determination (Adjusted R-bar squared = 0.91) shows that the ARDL (4, 0, 4, 4, 2, 3, 2, 4) model has about 91% explanatory power with respect to variations in economic growth of Nigeria. This implies that the ARDL model has a satisfactory goodness of fit. The F-test which is used to determine the overall statistical significance of a regression model shows that the overall regression is statistically significant at 1% level. This therefore means that the overall ARDL (4, 0, 4, 4, 2, 3, 2, 4) model (that is, the short and long run coefficients of the entire explanatory variables as they relate to the dependent variable) is statistically different from zero. The findings were discussed with the research objectives. As shown in Table 7 in the short run, the first quarter lag and fourth quarter lag of gross domestic product are statistically significant at 1% with positive impact. This means that the economic growth function follows the adaptive expectation theory. The current level of financial deepening has a negative impact and significant at 10%. This result is not consistent with extant literature (Azege, 2004; Nzotta and Okereke, 2009; Abur et al., 2013). The fourth quarter lag of human capital has a negative and significant impact at 5%. This result is not consistent with extant literature (Ismail et al., 2010; Anaduaka and Eigbiremolen, 2014). The current level of population has a positive impact and significant at 1% and the first quarter lag of population has a positive impact and significant at 5%. These results are consistent with Adediran (2012) but not consistent with Onwuka (2005). The first quarter, second quarter, third quarter and the fourth quarter lags of trade openness have positive impacts and significant at 1%. These results are consistent with Adebiyi (2006) and Seetanah et al. (2012). In the long-run, expected gross domestic product has a negative impact on economic growth at 1%. This also means that the economic growth function follows the adaptive expectation theory. Government expenditure has a negative impact on economic growth at 1%. This result is consistent with the results of Ighodaro and Oriakhi (2010) and but not consistent with the result of Okoro (2013). Inflation has a negative impact on economic growth at 10%. This result is consistent with the results of Bassey and Onwioduokit (2011) but not consistent with the result of Omoke (2010). Trade openness has a negative impact on economic growth at 1% population on economic growth at 1%. This is not consistent with the results of Adebiyi (2006) and Seetanah et al. (2012). Interest rate has a positive impact on economic growth at 1%. This result is consistent with the results of Chete (2006); Obamuyi (2009) and Obansa et al. (2013). Gross capital formation has a positive impact on economic growth at 1%. This result is consistent with the result Ugwuegbe and Uruakpa (2013) but not consistent with the result of Adekunle and Aderemi (2012). Population growth has a positive impact on economic growth at 1%. This result is consistent with the result Adediran (2012) but not consistent with Onwuka (2005). This study has empirically attempted to investigate the relationship between economic growth and the selected explanatory variables by employing the ARDL modelling technique. The study found that ARDL (4, 0, 4, 4, 2, 3, 2, 4) model can provide information both on the short-run and on the long-run behaviour of economic growth in Nigeria. The empirical results showed that the main determining variables of economic growth in Nigeria in the short-run and long-run are expected economic growth, population and trade openness. To achieve sustainable economic growth, it is recommended that government policies directed at improving the performance of the economy should largely consider the short-run and long-run behaviour of these variables and the policies should be pursued with high degree of transparency. References Abu, N. and U. Abdullahi, 2010. Government expenditure and economic growth in Nigeria, 1970-2008: A disaggregated analysis. Business and Economics Journal, 4: 2-4. Abur, C.C., M.A. Chiawa and J.T. Torruam, 2013. Financial deepening and economic growth in Nigeria: An application of cointegration and causality analysis. 3rd International Conference on Intelligent Computational Systems (ICICS, 2013) Singapore, 20-26. Adebiyi, M.A., 2006. Inflation targeting: Can we establish a stable and predictable policy instrument between inflation and monetary policy instruments in Nigeria and Ghana. Available from http://www.google.com.ng [Accessed May 1st 2014]. http://www.google.com.ng/ Asian Journal of Economics and Empirical Research, 2016, 3(1): 84-93 93 Adediran, O.A., 2012. Effect of population on economic development in Nigeria: A qualitative assessment. International Journal of Physical and Social Sciences, 2(5): 1-14. Adekunle, K.A. and A.K. Aderemi, 2012. Domestic investment, capital formation and population growth in Nigeria. Developing Country Studies, 2(7): 37-46. Adenikinju, A., D. Busari and S. Olofin, 2009. Applied econometrics and macroeconometric modelling in Nigeria. Ibadan: Ibadan University Press. Akinlo, A.E., 2004. Foreign direct investment and growth in Nigeria: An empirical investigation. Journal of Policy Modelling, 26(3): 627- 639. Alani, R.A. and A.W. Isola, 2012. Human capital development and economic growth: Empirical evidence from Nigeria. Asian Economic and Financial Review, 2(7): 813-827. Aminu, U. and A.Z. Anono, 2012. Effect of inflation on the growth and development of the Nigerian economy (An Empirical Analysis). International Journal of Business and Social Sciences, 3(10): 183-191. Anaduaka, S.U. and G.O. Eigbiremolen, 2014. Human capital development and economic growth: The Nigeria experience. International Journal of Academic Research in Business and Social Sciences, 4(4): 25-35. Anthony, I.I., L.M. Olatunji and P.C. Uzomba, 2012. An analysis of interest and exchange rates effect on the Nigerian economy: 1975– 2008. Asian Economic and Financial Review, 2(6): 648-657. Ayanwale, A.B., 2007. FDI and economic growth: Evidence from Nigeria. African Economic Research Consortium Research Paper, No. 65. Azege, M., 2004. The impact of financial intermediation on economic growth: The Nigerian perspective. Available from SSRN 607144. Barro, R.J., 1991. Economic growth in a cross section of countries. Quarterly Journal of Economics, 106(2): 407-443. Bassey, G.E. and E.A. Onwioduokit, 2011. An analysis of the threshold effects of inflation on economic growth in Nigeria. WAIFEM Review, 8(2). Bello, A. and O. Adeniyi, 2010. FDI and the environment in developing economies: Evidence from Nigeria. Environmental Research Journal, 4(4): 291-297. Brown, R.L., J. Durbin and J.M. Evans, 1975. Techniques for testing constancy of regression relationship over time. Journal of the Royal Statistical Society, Series B(Methodological): 149-192. Chete, L.N., 2006. The determinants of Interest rate in Nigeria. Ibadan, Nigeria: A Monograph Publication of Nigerian Institute of Social and Economic Research NISER. Dada, E.A. and O.A. Oyeranti, 2012. Exchange rate and macroeconomic aggregates in Nigeria. Journal of Economics and Sustainable Development, 3(2): 93-10. Dickey, D.A. and W.A. Fuller, 1979. Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74(366a): 427-431. Egwakhide, C.I., 2012. The impact of foreign direct investment on Nigeria’s economic growth; 1980-2009: Evidence from the Johansen’s cointegration approach. International Journal of Business and Social Science, 3(6): 122-134. Ejiogu, U., A.I. Okezie and C. Nwosu, 2013. Causal relationship between Nigeria government budget allocation to the education sector and economic growth. Discourse Journal of Education Research, 1(8): 54-64. Engel, R.F. and C.W.J. Granger, 1987. Co-integration and error correction: Representation, estimation and testing. Econometrica, 55(2): 251- 276. Grossman, G. and E. Helpman, 1991. Innovation and growth in the global economy. Cambridge, Mass: MIT Press. Hendry, D.F., 1995. Dynamic econometrics. Oxford: Oxford University Press. Ighodaro, C.A.U. and D.E. Oriakhi, 2010. Does the relationship between government expenditure and economic growth follow Wagner’s law in Nigeria? Annals of the University of Petroşani, Economics, 10(2): 185-198. Ismail, R., O.J. Sankay and A.H. Shaari, 2010. The impact of human capital development on the economic growth of Nigeria. Prosiding Perkem V, Jilid, 1: 63 – 72. Johansen, S. and K. Juselius, 1990. Maximum likelihood estimation and inference on cointegration with application to the demand for money. Oxford Bulletin of Economics and Statistics, 52(2): 169-210. Levine, R. and D. Renelt, 1992. A sensitivity analysis of cross-country growth regressions. American Economic Review, 82: 942-963. Nzotta, S.M. and E.J. Okereke, 2009. Financial deepening and economic development of Nigeria: An empirical investigation. African Journal of Accounting, Economics, Finance and Banking Research, 5(5): 52-66. Obamuyi, T.M., 2009. An investigation of the relationship between interest rate and economic growth in Nigeria, 1970-2006. International Journal of Business Management, 1(1): 006-010. Obansa, S.A.J., O.K.D. Okoroafor, O.O. Aluko and E. Millicent, 2013. Perceived relationship between exchange rate, interest rate and economic growth in Nigeria: 1970-2010. American Journal of Humanities and Social Sciences, 1(3): 116-124. Odularu, O.G., 2007. Crude oil and the Nigerian economic performance. Oil and Gas Business. Okoro, A.S., 2013. Impact of monetary policy on Nigeria economic growth. Prime Journal of Social Science, 2(2): 195-199. Olomola, P.A. and A.V. Adejumo, 2006. Oil price shocks and macroeconomic activities in Nigeria. International Research Journal of Finance and Economics, 3(1): 28-34. Omoke, P.C., 2010. Inflation and economic growth in Nigeria. Journal of Sustainable Development, 3(2): 159-166. Onwuka, C.E., 2005. Another look at the impact of Nigeria’s growing population on the country’s development. African Population Studies, 21(1): 1-18. Oriakhi, D.E. and D.O. Iyoha, 2013. Oil price volatility and its consequences on the growth of the Nigerian economy: An examination (1970- 2010). Asian Economic and Financial Review, 3(5): 683-702. Pesaran, M.H., Y. Shin and R.J. Smith, 2001. Bounds testing approaches to the analysis of level relationships. Journal of Applied Econometrics, 16(3): 289-326. Petrakos, G., P. Arvanitidis and S. Pavleas, 2007. Determinants of economic growth: The experts’ view. Dynamic Regions in a Knowledge Driven Global Economy Lessons and Policy Implications for the EU. Ristanović, V., 2010. Macroeconomic determinants of economic growth and world economic financial crisis. Facta Universitatis Series: Economics and Organization, 7(1): 17 - 33. Romer, P., 1990. Endogenous technological change. Journal of Political Economy, 98(5): 71- 102. Seetanah, B., J. Matadeen and J. Matadeen, 2012. Trade openness and economic performance: An African perspective. International Conference on Intelligent Computational Systems ICITI. Shehu, A.A. and Z. Youtang, 2012. Exchange rate volatility, trade flows and economic growth in a small open economy. International Review of Business Research Papers, 8(2): 118 – 131. Solow, R., 1956. A contribution to the theory of economic growth. Quarterly Journal of Economics, 70: 65-94. Swan, T.W., 1956. Economic growth and capital accumulation. Economic Record, 32(2): 334–361. DOI http://dx.doi.org/10.2307/1884513. Ugwuegbe, S.U. and P.C. Uruakpa, 2013. The impact of capital formation on the growth of Nigerian economy. Research Journal of Finance and Accounting, 4(9): 36-42. 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