This chapter briefly describes the methodological framework KGEMM uses. KGEMM is a hybrid model, i.e., it brings together theoretical and empirical coherences at some degree. Put differently, KGEMM nests “theory-driven” and “data-driven” approaches suggested by Hendry (2018), among others, and employed by many modelers in building semi-structural, that is, hybrid macroeconometric models (e.g., see Jelić and Ravnik 2021; Gervais and Gosselin 2014; Bulligan et al. 2017). For this purpose, it uses an equilibrium correction modeling (ECM) framework, in which the long-run relationships follow economic theories, and the short-run relationships are mainly data-driven (see Pagan 2003a, b inter alia). Hara et al. (2009) and Yoshida (1990), among others, note that ECM-based MEMs provide realistic results as their equilibrium correction mechanisms help stabilize long-term projections and capture short-term fluctuations more than other models while Engle et al. (1989) find the forecast performance of ECM more accurate.

KGEMM’s methodological framework for estimating the behavioral equations is based on three pillars: cointegration and ECM, the general-to-specific modeling strategy (Gets) with Autometrics, a machine-learning econometric modeling method (Ericsson 2021), and the encompassing test (Fig. 4.1). This chapter briefs the methodological framework to save space and details of it will be described later in Appendix A.

Fig. 4.1
An illustration depicts K G E M M's methodological framework. A triangle labeled econometric methodology with its edges marked gets with autometrics, cointegration and E C M, and encompassing test.

KGEMM’s methodological framework

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The econometric methods are employed (i) to estimate behavioral equations, which represent behavioral aspects of the economic and energy linkages of Saudi Arabia and (ii) to test the existence of relationships and hypotheses. The following is the “road map” that we use in our empirical estimations and testing.

Because we use annual time series data, the first step is to check the stochastic properties of the data using unit-root tests. For the unit-root analysis, we use the conventional tests, that is, Augmented Dickey–Fuller (ADF) (Dickey and Fuller 1981), Phillips–Perron (PP) (Phillips and Perron 1988), and Kwiatkowski et al. (1992). Additionally, we use unit root tests with structural breaks where it seems reasonable to do so based on the nature of the data. We employ the ADF with a structural break (ADFBP hereafter) developed by Perron (1989), Perron and Vogelsang (1992a, b), and Vogelsang and Perron (1998). We also use the Fourier ADF developed by Enders and Lee (2012a, b) and extended by Furuoka (2017), where there are multiple breaks in a given series and the conventional tests do not produce commonly accepted results. We do not describe these tests here as they are widely used in the literature. Readers interested in these tests can refer to the above-given references as well as Enders (2015), Perron (2006), Zivot and Andrews (1992), and Banerjee (1992).

If the variables are non-stationary, we perform cointegration tests to check whether they are cointegrated. For this purpose, we use Johansen’s (1988) trace and maximum eigenvalue tests, the Pesaran’s bounds test (Pesaran and Shin 1999; Pesaran et al. 2001), Engle and Granger (1987) test, Phillips–Ouliaris test (Phillips and Ouliaris 1990), and variable addition test by Park (1990). If more than two variables are involved in the analyses, which is mostly the case, then we first apply Johansen’s cointegration test since it can reveal the number of cointegrating relationships if there is more than one, while the other tests above assume only one or no cointegrating relationship. We also use Hansen’s (2000) cointegration test, which considers the break in the cointegration relationship. If there is a need to include level shift or trend break dummies in the Johansen cointegration test procedure, then we conduct our analysis in OxMetrics, as this software automatically calculates critical values that account for dummy variables.

If cointegration exists between the variables, then we estimate numerical parameters such as long-run coefficients. For this, we employ the following estimation methods to get robust results. Vector error correction (VEC) maximum likelihood estimation (Johansen 1988; Johansen and Juselius 1990), autoregressive distributed lags (ADL) (Hendry et al. 1984a, b; Pesaran and Shin 1999), fully modified ordinary least squares (FMOLS) (Phillips and Hansen 1990), dynamic ordinary least squares (DOLS) (Saikkonen 1992; Stock and Watson 1993), and canonical cointegration regression (CCR) (Park 1992) methods. After the estimation, we perform post-estimation tests, such as residuals diagnostics for serial correlation, non-normality, heteroscedasticity, parameter stability, misspecification, and other tests where possible.

In the last part of the chain, we employ an ECM to conduct a short-run analysis, that is, estimating short-run coefficients, including the speed of adjustment. We utilize the Gets with Autometrics, following the London School of Economics, or the Hendry, modeling approach (Ericsson 2021). Gets first includes contemporaneous and lagged values of all the relevant variables, based on the related economic theory and evidence of modeler to the specification called the general unrestricted model (GUM). Then it chooses the final specification based on a range of econometric tests for diagnostics, stability, and misspecification. Further details of the Gets can be found in Davidson et al. (1978), Hendry et al. (1984a, b), Ericsson et al. (1990), de Brouwer and Ericsson (1995), and Campos et al. (2005), among others. We usually perform Gets using Autometrics in the OxMetrics software (Doornik 2009; Doornik and Hendry 2018). Autometrics is a cutting-edge machine-learning multi-block search algorithm of modern econometrics. It performs Gets automatically to select a final specification from a GUM using the tests indicated above. One of the advantages of Autometrics is that it can also account for structural breaks and other extraordinary changes observed in data using the impulse indicator saturation technique (e.g., see Doornik 2009; Hendry and Doornik 2009, 2014). Another key advantage of Autometrics is that it addresses the time invariance of the estimated coefficients and hence, super exogeneity properties of variables remained in the final ECM specification can be tested (Castle et al. 2021; Hendry and Santos 2010). These features of Autometrics allows to address the so-called Lucas critique (Ericsson and Irons 1995). It is shown that Autometrics outperforms other model selection methods, such as, Stepwise regression, the least absolute shrinkage and selection operator (LASSO), and the adaptive LASSO (e.g., see Epprecht et al. 2021; Desboulets 2018; Castle et al. 2011 inter alia).

The short-run growth equation is estimated if there is no cointegrating relationship between the variables under consideration. The procedure is the same as in the ECM analysis above, but the equilibrium correction term (ECT) is absent as the variables are not cointegrated. Gets with Autometrics is also applied to growth equations.

We use encompassing tests to compare, choose, and combine different estimated specifications for analysis and forecasting purposes. The encompassing tests compare the predictive ability of alternative specifications and select the best one. Although this is part of our econometric methodology, we have not used this test frequently, primarily because there are not enough previously estimated specifications for Saudi Arabian energy-macroeconomic relations to compare with ours. Details of the tests can be found in Mizon (1984), Mizon and Richard (1986), Harvey et al. (1998), Harvey and Newbold (2000), Ericsson (1992, 1993), Bontemps and Mizon (2008), and Clements and Hendry (2011).

As part of the KGEMM methodology, we also use various tests to validate the estimated behavioral equations and the entire model as a whole (including in-sample and out-of-sample testing for predictive ability). These include post-estimation tests for the residuals of the estimated equations, testing the statistical significance and theoretical consistency of the estimated parameters, as well as in-sample performance test and out-of-sample performance test for the entire model. Detailed discussions of these methods can be found in Fair (1984), Klein et al. (1999), Fair (2004), Bardsen and Nymoen (2008), Clements and Hendry (2011), Hendry and Mizon (2014), Beenstock et al. (1986), Calzolari and Corsi (1977), and Welfe (2011).

The KGEMM model has been built in the EViews software package, as it provides a number of advanced features for building and simulating MEMs compared to other programs. Different stages of the empirical estimations and testing are conducted in EViews and OxMetrics, which includes Autometrics. The final specifications of the equations estimated in OxMetrics are then transferred to EViews to include in the model.

Interested readers can refer to Appendix A for a detailed discussion of KGEMM’s methodological framework and philosophy, including the use of Gets and Autometrics. Appendix A also discusses addressing the endogeneity issue and the Lucas critique using invariance and super exogeneity tests.