economic growth nexus: evidence from Nigeria between 1981-20014 in order to fully account for feedbacks in their results.
3.2.3.5 THE GENERALIZED METHOD MOMENTS
. Lars Peter Hansen in 1982 developed Generalized Methods of Moment as a generalization of the method of moments, which Karl Pearson introduced in 1894.GMM can be described as a statistical methodology that, in its final form, would permit economists to bring out strong conclusions from models that are not completely specified (that is, not all variables, relationships or assumptions are included or succinctly defined). In econometrics and statistics, the generalized method of moments (GMM) is a generic method for estimating parameters in statistical models. Usually,Generalized method of Moments is applied in the context of semi parametric models, where the parameter of interest is finite-dimensional, whereas the full shape of the distribution function of the data may not be known, and therefore maximum likelihood estimation is not applicable. The method invoves the process whereby a certain number of moment conditions were specified for the model. These moment conditions are as a result of the model parameters and the data, such that their expectation is zero at the true values of the parameters. The Generalized Method of Moments restricts some norms of the sample averages of the moment conditions, the GMM estimators are known to be consistent, asymptotically normal, and efficient in the class of all estimators that do not use any extra information aside from that contained in the moment conditions.
GMM is essential because it is capable of presenting econometricians great opportunities to appraise alternative theories and investigate important economic phenomena without fully developing each of their elements. Researchers seldom rely on the most influential explanatory variables and dispense with unnecessary assumptions. GMM also allows you to do something without having to do everything simultaneously, Hansen explains that the Generalized Method of Moments, as the name suggest, can be thought of just as a generalization of the classical MM. A key in the GMM is a set of population moment conditions that are derived from the assumptions of the econometric model.The GMM was not immediately accepted in the field of economics because it is in abstract and mathematically challenging, (Indeed, Hansen’s initial draft was rejected by Econometrica, spurring him to refine and generalize his argument.) Hansen and his colleagues persevered, demonstrating the methodology’s power and range by applying it to exchange rates, asset pricing models and rational expectations theory. All these examples above gradually convinced economists of its utility and, with time, GMM became the gold standard., Hansen was awarded the Nobel Prize in economic sciences for his methodology in 2013, specifically in reference to its ability to evaluate asset pricing models. Generalized Method of Moments (GMM) supplies econometricians and statisticians alike with a computationally convenient method for estimating the parameters of statistical models based on the information in population moment conditions.
Considering the Structure and flexibility of GMM, it has made it very popular in econometrics because competing economic theories often imply that economic variables satisfy different sets of population moment conditions. The exact form or nature of these population moment conditions depends majorly on the context but the generic form of the GMM estimator is the same in each case. The flexibility of GMM denotes that it has been implemented in very different areas spanning macroeconomics, finance, agricultural economics, environmental economics and labour economics. The widespread use of GMM in econometrics has both stimulated and facilitated the growth and acceptance of numerous statistical inference techniques based on GMM estimators. These inference techniques allow researchers, inter alia, to test hypotheses about the parameters of the econometric model and also to test whether the population moment conditions are consistent with the data. In addition, GMM includes many other well-known and acceptable estimators, such as least squares, instrumental variables and maximum likelihood. GMM makes available a convenient framework for taking into account general aspects of estimation and inference in statistics, and, in many ways, is becoming the common language of econometric dialogue. Mirajul and Muhammad (2014) were few of the researchers that employed GMM in their study of the contributions of international trade to economic growth through human capital accumulation: Evidence from nine Asian countries (1972-2012).also Daumal and Ozyurt (2011) examined the impact of international trade flows on economic growth in Brazilian states using dynamic regression with system GMM estimator.
3.2.3.6 AUTOREGRESSIVE DISTRIBUTED LAG (ARDL)
The autoregressive distributed lag (ARDL) model was originally introduced in 1999 by Pesaran and Shin and further extended by Pesaran et al. (2001) and it deals with single cointegration. A distributed lag model is described as a model for time series data in which a regression equation is used to predict current values of a dependent variable based on both the current values of an explanatory variable and the lagged (past period) values of this explanatory variable in statistics and econometrics .Furthermore, it can distinguish dependent and explanatory variables, and allows to test for the existence of relationship between the variables. Finally, with the ARDL it is possible that different variables have differing optimal number of lags.Johansen and Juselius(1990) cointegration procedure cannot be applied when one co-integrating vector exists. Therefore , it become important to adopt Pesaran and Shin (1995) and Pesaran et al (1996) proposed Autoregressive Distributed Lag (ARDL) approach to co-integration or bound procedure for a long run relationship, irrespective of whether the underlying variables are I(0), I(1) or a combination of both. In such situation, the application of ARDL approach to cointegration will produce realistic and well-organized estimates. In contrast to the Johansen and Juselius(1990) cointegration procedure, Autoregressive Distributed Lag (ARDL) approach to cointegration helps in identifying the co integrating vector(s). This means that each of the underlying variables under consideration stands as a single long run relationship equation. When one co integrating vector (i.e the underlying equation) is known, the ARDL model of the co integrating vector is re-parameterized into ECM. The re-parameterized result produces short-run dynamics known as traditional ARDL and long run relationship of the variables of a single model. The re-parameterization is possible because the ARDL is seen as a dynamic single model equation and of the same form with the ECM. Distributed lag Model simply connotes the inclusion of unrestricted lag of the regressors in a regression function. This co integration testing procedure specifically enables us to know whether the underlying variables in the model are co integrated or not, if the endogenous variable is given . EViews provides reliable time-saving tools for estimating and examining the properties of Autoregressive Distributed Lag (ARDL) models. ARDLs are standard least squares regressions that include lags of both the dependent variable and explanatory variables as regressors (Greene, 2008). Although ARDL models have been used in econometrics for many years, they have gained acceptance in recent years as a method of examining cointegrating relationships between variables through the work of Pesaran and Shin (1998, PS(1998)) and Pesaran, Shin and Smith (2001).It was discovered that while it may be possible to use a standard least squares procedure to estimate an ARDL, the specialized ARDL estimator in EViews offers a lot of useful features including model selection and the computation of post-estimation diagnostics. The most convenient way to estimate parameters associated with distributed lags is through the application of Ordinary Least Squares(OLS), by making an assumption of a fixed maximum lag , and by also assuming independent and identically distributed errors, and imposing no structure on the relationship of the coefficients of the lagged explanators with each other. However, multicollinearity among the lagged explanators often develops, leading to high variance of the coefficient estimates. The ARDL is usually applicable for use in Structured estimation.
Structured distributed lag models are of two types, these are finite and infinite. Infinite distributed lags allow the value of the independent variable at a particular time to influence the dependent variable infinitely far into the future, or to put it another way, they allow the current value of the dependent variable to be influenced by values of the independent variable that occurred infinitely long ago; but beyond some lag length the effects taper off toward zero. Finite distributed lags permit for the independent variable at a particular time to affect the dependent variable for only a finite number of periods. The commonest type of structured infinite distributed lag model is the geometric lag, also known as the Koyck lag.The weights (magnitudes of influence) of the lagged independent variable values decline exponentially with the length of the lag in this lag structure; while the shape of the lag structure is thus fully imposed by the choice of this technique, the rate of decline as well as the overall magnitude of effect are determined by the data. Specification of the regression equation is very straightforward: one includes as explanators (right-hand side variables in the regression) the one-period-lagged value of the dependent variable and the current value of the independent variable:
Under Finite distributed lags, the most important structured finite distributed lag model is the Almon lag model. This model allows the data to determine the shape of the lag structure, but the researcher must specify the maximum lag length; an incorrectly specified maximum lag length can alter the shape of the estimated lag structure and also the cumulative effects of the independent variable. The ARDL approach has the immense benefits of not requiring all variables to be I (1) as the Johansen framework and it is still applicable if we have I (0) and I(1) variables in our set. The bounds test method of co-integration has certain econometric advantages in comparison to other methods of co-integration which are the following: • All variables of the model are assumed to be endogenous. • Bounds test method for co-integration is being applied irrespectively the order of integration of the variable. There may be integrated of first order Ι(1) or Ι(0). • The short-run and long-run coefficients of the model are estimated simultaneously. The ARDL methodology is not encumbered with the burden of establishing the order of integration amongst the variables