Brahim Mansouri and Ayad El Baz
2016 / 1 / 16
As it is commonly admitted, econometric models, especially linear macroeconomic as well as microeconomic models, permit to easily forecast future estimates of variables through their past values(1). However, forecasting in such a way faces a variety of challenges and constraints, mainly those tied to economic theory on one hand and quantitative (time-series) data processing on another hand. Indeed, economic forecasting needs deeper theoretical knowledge about determinants of variables to be forecasted, accumulated skills in econometric modeling and know-how about business-cycle factors that may drive significant fluctuations of variables under study.
Since the 1930s, economic forecasting has received much attention from many econometricians. In the 1930s, in his early pioneering works on Netherlands and the USA, Tinbergen used macro-econometric models for purposes of economic analysis and forecasting. For the same goal, Klein and Goldberger, in 1955, elaborated their famous econometric model for the USA economy.
During the recent past three decades, following Sims’s well-known criticism of the Keynesian theory-based structural models, especially the failure of such models to forecast the consequences of the 1970s oil shock, vector Auto-Regressive (VAR) analysis has become the most advantaged econometric tool used to reconstruct dynamic interactions between variables as well as to forecast their future values (see for example, Stock and Watson, 2012). According to Litterman (1986), -var-models are more powerful in economic forecasting than other econometric tools. In particular, -var-models help better to analyze economic policy impact, notably through the simulation of random shocks and the variance decomposition of the forecast-error (Bourbonnais, 2009) .
It is interesting however to note, as Sims (1980) argued, that -var-models remain a-theoretical and, thereby, they don’t exhibit a powerful proof of causality . Therefore, to better deal with issues of economic forecasting, econometricians who are interested in business cycle fluctuations prefer to resort to multivariate-multi-equation models in two different but complementary methodological ways: Standard -var-Models(3) and Structural Multivariate Models, especially Structural -var-(SVAR) and Structural Vector Error Correction models (SVECM)(4). Such structural multivariate models (S-var-and SVECM) have the major characteristics of modeling economic linkages (5) within the framework of a theory-based circular reasoning. Hence, more importantly, these models are seen as powerful in forecast analysis(2).
The remainder of the present summarized research paper is organized as follows. In section 1, we show how economic theory and econometric modeling interact within our research paper. In section 2, we outline the methodology of identification and estimation of the main structural multivariate models (S-var-and SVECM). In section 3, we show why these models are useful to analyze and forecast interactive effects between domestic (mainly fiscal) and external sector variables, especially in the Moroccan case of a small open economy. Finally, section 4 presents preliminary expected results and concludes.
1. THE SYNERGY BETWEEN ECONOMIC THEORY AND ECONOMETRIC MODELING IN THE RESEARCH PAPER:
Our research project is dealing with the issue of such modern structural multivariate models. The paper aims at: i) reconstructing a more comprehensive methodological framework for structural multivariate modeling --;-- and ii) applying this methodology to the forecasting of interactive effects between fiscal and external sector variables in Morocco, with reference to the existing economic theory and formulation of new theoretical hypotheses (6). As well-known worldwide among the econometric profession, to avoid a higher number of restrictions in the process of structural multivariate modeling, estimates and tests, we have selected a restricted number of five variables in line with economic theory predictions. While the selected domestic variables consist of real GDP (in natural logarithm form) and fiscal surplus (as proportion to nominal GDP), the natural logarithm of the real effective exchange rate (7) , real foreign demand (natural logarithm form) and the external current account surplus (in percentage of nominal GDP) are selected as external sector variables (8).
2. THE METHODOLOGY OF STRUCTURAL MULTIVARIATE MODELING FOR FORECASTING PURPOSES: A SIMPLIFIED OUTLINE
To better use structural multivariate models (with multiple equations), notably Structural Vector Auto-Regressive (SVAR) models and Structural Vector Error Correction Models (SVECM), for forecasting purposes, it is important to respect a set of major stages and to apply a rigorous scientific methodology.
In a first stage, the econometrician should scientifically the most appropriate variant of the model in order to better answer the main research questions of the study to undertake. In this framework, it is suitable to rely on theoretical as well as empirical arguments. Moreover, preliminary econometric tests of stationarity and cointegration of the selected variables should be conducted. In a second stage, the issue regarding the identification of the structural model should be tackled before any model estimates. In order to use the structural multivariate model for economic forecasting purposes, the starting point consists of estimating a standard (canonical) VAR. Then, the task will consist of decomposing canonical innovations as a linear combination of structural innovations in order to derive a suitable formulation of the multivariate structural model. These various issues are addressed in what follows below.
PRELIMINARY ECONOMETRIC TESTS:
To the most suitable variant of the multivariate structural model devoted to a reliable economic forecasting, a study of the stochastic characteristics of the concerned time-series should be conducted. This requirement relies on the right idea that the parameters of a canonical -var-model should be estimated with stationary time-series (9). Among the most used tests for stationarity, the well-known tests are the ADF (Augmented Dickey-Fuller--;-- see Dickey and Fuller, 1979, 1981) and PP (Philips-Perron, 1988) tests (10).
If all the studied time-series are integrated of a same order d, they may be cointegrated. The widely used cointegration tests are Engle and Granger (1987) and Johansen (1988, 1991, 1995) tests. Nevertheless, when the number of variables exceeds 2, as in our case study, it is preferable to use the Johansen test.
These two stages of stationarity and cointegration tests allow us to the appropriate variant of our multivariate structural model. If all the variables are integrated of the same order and cointegrated, the model to be estimated will be a SVECM. When there is no cointegration, the structural model to be estimated may be a -var-model with all variables introduced in first differences. However, in this case, the most appropriate model that is useful for forecasting will be a structural -var-(SVAR). Well, our preliminary stationarity and cointegration tests on available data over the period 1970-2014 reveal that all the time-series are integrated of the same order 1 (that is I(1)) and non cointegrated. Then, the appropriate modeling will consist of a S-var-model. Our developments below deal with the identification and estimation issues of such a structural model.
THE PROCESS OF MODEL IDENTIFICATION AND ESTMATION:
Identification is one of the most important and thorniest tasks in structural multivariate analysis in the extent that it is often conducted a-priori and the imposed constraints are difficult to test. Identification consists of estimating the parameters of the structural form through the estimators derived from the reduced form (standard VAR). Nonetheless, in this framework, the number of parameters to be estimated in a structural model is higher than the number of parameters of a standard -var-(11). Therefore, identification of all the parameters of the structural form requires availability of further information and the necessity to impose (n(n-1))/2 restrictions (12) .
Generally, two major identification approaches are commonly used: the Choleski statistical approach and the theory-based approach. The latter frequently requires to imposing short and/or long-term constraints. As far as the S-var-estimation process is concerned, first of all, a “Passage Matrix” (P) permitting to move from the reduced form of the -var-to its structural form should be estimated (13). The estimation of such matrix depends on the adopted identification approach (statistical against theory-based approaches) as well as the nature of constraints to be imposed (short and/or long-run constraints) (14). Moreover, to appreciate the estimation quality of such a structural model, it is interesting to use some batteries of tests such as the Lagrange multiplier test (LM test) for error autocorrelation, the Jarque-Bera error normality test and other tests related to heteroskedasticity and forecast.
3. STRUCTURAL MULTIVARIATE MODELS AS USEFUL TOOLS FOR FORECASTING: WHY AND HOW
Structural multivariate models, especially S-var-models and SVECM, are seen as powerful tools for causality analysis and forecasting. To better gain information channeled through multivariate structural models and to efficiently use it to forecast, for all the variables under study, response --function--s to various structural shocks as identified should be characterized and computed, and a decomposition of the variance of the forecast error should be undertaken. Response --function--s aspire to forecasting the sign as well as the nature (persistent´-or-transitory) of a structural shock on various components of the -var-system at a selected time horizon. Regarding analysis of the variance decomposition, it permits to determine the contribution of each structural shock to the fluctuations in the studied variables at a given time-horizon.
To estimate the two variants of our structural multivariate model, we will resort to an identification approach that is founded on economic theory predictions rather than on a statistical approach like the criticized one adopted in Choleski’s works. Restrictions of exclusion to be imposed are of a long term kind rather than a short term method which is seen to be largely controversial. Such long-run restrictions will be imposed on the long-term matrix to lead to the passage matrix P and, thereby, to formulate two variants of our structural model (SVAR). While the first variant of our S-var-model measures the relative prices as the real effective exchange rate, the second variant considers terms of trade as the alternative proxy for such relative prices.
4. ACHIEVEMENTS AND BEYOND: ADVANCEMENT STAGE AND EXPECTED FINDINGS
Until now, a relatively good literature survey on interactions between fiscal policy and external sector variables has been done, with additional theoretical hypotheses on the under-explored issue regarding the impact of external sector variables on fiscal indicators. The two authors have accumulated significant experience and practice on multivariate structural analysis with good knowledge on computer software packages, especially Eviews and Stata. Data are available mainly from the World Bank (World Development Indicators), the IMF (International Financial Statistics) and the Annuaire Statistique du Maroc (various issues). Data concern six variables since two structural models have to be estimated: the first one incorporates the real exchange rate and the second incorporates the terms of trade as two different measures of relative prices. This means that we work on a set of five variables for each variant of our structural multivariate model. Since the World Bank and IMF data on the real effective exchange rate are available only over the period 1980-2014, we have computed the values of this variable for the whole period (1970-2014), using the well-known weighted geometric mean of bilateral real exchange rates.
Our structural multivariate estimates and tests aspire to deriving useful empirical finding about mutual structural shocks and, more importantly, forecasting changes in variables at a desired time horizon. In this framework, focusing on impulse response and variance decomposition analyses, we expect, in line with the well-known twin deficits hypothesis and Mundel-Fleming model with a regime of relatively fixed exchange rate and imperfect capital mobility, that improvements in fiscal surpluses would contribute significantly to improvements in current account surpluses in the short as well as long terms. This means that negative fiscal shocks would destabilize the balance of payments current account in the short and long runs, suggesting that the shock impact would be persistent. We also expect that negative fiscal shocks would lead to a real exchange rate appreciation in the short as well as long terms in conformity with the Swan-Dornbush hypothesis.
Concerning the impact of external shocks associated with terms of trade and foreign demand, we expect, in line with the Mundell-Fleming model, that they would affect fiscal variables (taxes, expenditures, fiscal surpluses, etc.). Focusing on a decomposition of the variance of the forecast error, we also expect that such external shocks would significantly contribute to fiscal budget fluctuations. More accurately, negative shocks associated with foreign demand and terms of trade would deteriorate fiscal surpluses with the impact being relatively persistent. More importantly, improvements in terms of trade would result in positive shocks which would exert positive effects on budget surpluses thanks to the currently observed moving comparative advantages toward more technology-intensive industry, especially following the implementation of a variety of sectoral strategies in Morocco during the last fifteen years.
(1)- Economic forecasting may be conducted through non-linear models, but with higher risk.
(2)- Standard (canonic) -var-models are not generally founded on economic theory in the sense that they are basically of a statistical nature (see for examples, Candelon ,B and Cudeville, E . (1997), “Politique monétaire et canal du crédit: une estimation empirique sur l’économie française”, Revue d’Economie Politique, 107 (6), nov-dec. PP : 781-807).
(3)- These models refer more accurately to -var-models with reduced form.
(4)- See Malinvaud, E. (2007), “Quelle place donner maintenant à la macroéconomie dans l’enseignement de l’économétrie?”, Revue d’économie politique, Vol.117, p :414.
(5)- Such relationships rely upon economic theory predictions.
(6)- While a widespread economic theory on the impact of domestic variables (especially fiscal variables) on external sector indicators is available, we have devoted much effort to better understanding linkages in the opposite --dir--ection. We are now in a well-advanced stage for formulating and empirically validating (using econometric of nonstationary variables) new theoretical hypotheses in this framework.
(7)- Since the terms of trade may be considered as a good proxy for effective real exchange rate, we have estimated two different structural multivariate models, introducing the real effective exchange rate in a first model and the terms of trade in the second one.
(8)- As in the case of the small open economy of Morocco, economic theory predicts that fiscal policy variables (especially budget surpluses) may affect external sector variables such as current account surpluses and real exchange rates, with some controversies between the Keynesian proposition (Twin Deficits Hypothesis), the monetary approach to the balance of payments, the Mundell-Fleming Model and the Ricardian equivalence theorem. By contrast, theory is still poor in dealing with linkages in the opposite --dir--ection. For instance, --dir--ect and in--dir--ect effects of current account surpluses, foreign demand, real exchange rates and terms of trade have received less attention among economists. Through a rigorous analysis of transmission channels, our rethought of this issue has induced preliminary encouraging and promising results.
(9)- See Mignon, V. (2008), Econométrie : théorie et applications, Edition Economica, Paris. P : 297.
(10)- Other stationarity tests may be used such as Perron and Schmidt-Phillips tests.
(11)- The number of the centered standard -var-parameters is n(n+1)/2+p.n^2, and the number of the associated S-var-model parameters will be (p+1).n^2 , where p refers to the lag order of the canonic VAR, and n represents the number of variables under study in our structural multivariate model.
(12)- The quantity n(n-1)/2 equals the difference between the number of parameters (p+1).n^2 to be estimated in the S-var-model and the number n(n+1)/2+p.n^2 of parameters to be estimated in the canonical (standard) VAR. Formally, one can write: n(n-1)/2=(p+1).n^2-(n(n+1)/2+p.n^2).
(13)- Within this framework, there are other intermediate ways to invert the -var-model in order to rewrite its reduced form in an infinite moving average form and then to re-express it as an infinite structural moving average from.
(14)- When all the variables under study are integrated of the same order d (of order 1 for example), most econometricians agree to use long-run constraints of exclusion in order to identify the structural model. Such constraints lead to the nullity of a certain number of the long-term matrix coefficients. The estimation of the standard -var-and the long-run matrix permits to estimate the passage matrix (P) and to derive the suitable formulation of the structural model.
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