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Journal of Business & Economic Statistics
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Kenneth F Wallis
To cite this article: Kenneth F Wallis (2004) Comment, Journal of Business & Economic Statistics, 22:2, 172-175, DOI: 10.1198/073500104000000055
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172 Journal of Business & Economic Statistics, April 2004
so that a better estimator of the var.r/would be
1
The question now is how large is ½. Just as a warning, if ½D:95, then 11C¡½½ D39, and with T D80, there is a serious bias in using the factor.T¡1/¡1. Usually returns are not that predictable from the past, but eq. (69) seems to indicate pre-dictability from macro variables that are usually predictable from the past. Hence the “model-free” estimate should perhaps be used only if the predictability is small.
7. CONCLUSION
I nd the idea behind the GVAR model fascinating and points to a possible path toward a satisfactory answer to the problem of modeling the whole world. But the ideas in the article seem also to point to a number of problems that must be addressed in the future.
Comment
Kenneth F. W
ALLISDepartment of Economics, University of Warwick, Coventry CV4 7AL, U.K. (K.F.Wallis@warwick.ac.uk)
Pesaran, Schuermann, and Wiener have proposed a new ap-proach to global economic modeling in their GVAR model. Their article contains a clear exposition of the modeling princi-ples that they espouse and the theoretical and practical problems that they have had to solve in implementing their approach. In addition to its intellectual contribution, the article represents a heroic data organization and management effort. It concludes with an application in which forecasts generated by an illus-trative GVAR model feed into a credit risk management prob-lem. This comment focuses on some econometric modeling and forecasting questions from a comparative standpoint, to help place the present contribution in a broader context. The com-ment draws on recent comparative research on multicountry models (Mitchell, Sault, Smith, and Wallis 1998; Wallis 2003), together with similar research on models of the U.K. economy (Jacobs and Wallis 2003) that includes the model of Garratt, Lee, Pesaran, and Shin (2000, 2003a) referred to by the authors.
GLOBAL ECONOMIC MODELS
Currently operating global models include the NiGEM model and the IMF’s MULTIMOD (Laxton, Isard, Faruqee, Prasad, and Turtelboom 1998), mentioned by the authors. Other multicountry models that have featured in the compar-ative research referred to earlier, along with these two, are the MSG2 model (see McKibbin and Sachs 1991), forerun-ner of the G-Cubed model (McKibbin and Wilcoxen 1999), and the QUEST model of the European Commission (Roeger and in’t Veld 1997). These models can be taken as typical modern-day representatives of the mainstream structural global modeling tradition to which the present authors seek an alter-native. Like the GVAR model, each of them is constructed, maintained, developed and used by a single research team, un-like Project LINK, mentioned by the authors, which, moreover,
was never a continuously operational system in the same sense. Also like the GVAR model, they contain separate models of national economies of central interest, then aggregate the re-maining economies into various groups. The basic Mark III version of MULTIMOD, for example, contains separate mod-els for each of the G-7 countries—the U.S., Canada, Japan, France, Germany, Italy, and the U.K.—and for an aggregate grouping of 14 smaller industrial countries; the rest of the world is then aggregated into two separate blocks of devel-oping and transition economies. The GVAR model comprises a similar number of submodels, whereas NiGEM and QUEST are more disaggregated.
The mainstream multicountry models were developed from national economy models to facilitate the study of macroeco-nomic interactions among nations, principally the transmis-sion of the effects of economic policy. To this end, explicit modeling of linkages through trade and nancial ows is un-dertaken. Each country model is a structural model in the tradi-tional sense, representing the behavior of households,rms, and the government and the markets in which they interact. Flows cumulate into stocks, and consistent global modeling requires that trade balances and net foreign asset positions sum to 0 at all times. The complete national economy submodels typi-cally have a common theoretical structure, whereas the remain-ing blocks are modeled in much less detail, focusremain-ing on trade and payments in a more reduced-form than structural manner. Whereas some models are engaged in real-time forecasting, others eschew forecasting and concentrate exclusively on pol-icy analysis.
© 2004 American Statistical Association Journal of Business & Economic Statistics April 2004, Vol. 22, No. 2 DOI 10.1198/073500104000000055
In contrast, GVAR is a reduced-form forecasting model with a comparatively small number of variables per country; hence the important international linkages can only be implicit, not explicit. With respect to trade, for example, the dependence of exports and imports on income in the receiving country and relative prices is captured directly in the structural mod-els. In the reduced-form model, however, it is solved out via the national income identity to yield a relationship between do-mestic and foreign GDP, yi and y¤i, which also includes the
price variables. Trade thus makes an implicit contribution to the output equations of the country-specic models. This tribution is acknowledged by the use of trade weights to con-struct the aggregate foreign variables. But linkages through trade remain in the background in GVAR, as do those through nancial ows.
The use of trade weights in aggregation reects common practice in mainstream multicountry models. These are typ-ically nonlinear in variables and are solved by numerical methods, with the various adding-up requirements and global consistency constraints imposed by additional accounting re-lationships. In place of numerical iteration, the link matrix dened in Section 3 of the article is a neat device for achiev-ing a globally consistent solution for the country-specic vari-ables of the GVAR model. This is, of course, facilitated by the model’s linearity.
The conditional or partial VECM form (see Johansen 1995, chap. 8) adopted for the submodels of GVAR, in which foreign variables are treated as weakly exogenous, also reects com-mon practice in mainstream modeling of small open economies. Both assume that the feedback from the domestic economy to the rest of the world is negligible.In contrast, the VECM model of the U.K. economy of Garratt et al. (2000, 2003a) follows the original VAR tradition and abandons an endogenous/exogenous classication of variables (except for the world price of oil), and so treats corresponding domestic and foreign variables in the same way. Much of the early VAR work related to the U.S. economy, treated as a closed economy, and the argument about abandoning a prior exogeneity assumption related principally to policy variables. That argument appears to have been won, even among mainstream macroeconometric models, where pol-icy feedback rules are now the standard specication. Once VAR analysis was extended to small open economies, however, the treatment of foreign variables still seemed open to debate, and the conditionalVECM of GVAR seems to be a more appro-priate specication than the VECM model of the U.K. economy of Garratt et al. in this respect.
Economic theory may contribute to the specication of a model in various ways. There is broader acceptance of a range of long-run or steady-state propositions than of theory-based short-run dynamic specications, but their implementation also varies. At one extreme is MULTIMOD, in which each dynamic equation has an explicit steady-state analog equation. The com-plete system of steady-state analog equations is maintained separately from the system of dynamic equations, to provide an interpretative device for understanding long-run compara-tive statics and to facilitate model handling by providing ter-minal conditions for model-consistent expectations solutions. In other mainstream models there may be no complete system of equations describing the steady state, but instead a set of
propositions describing its properties, such as price level and ination neutrality, intertemporal budget constraints, and long-run sustainability of debt and decit positions. In their VECM model of the U.K. economy, Garratt et al. (2003a) presented a theoretical framework that delivers ve long-run equilib-rium relationships among the variables of the model. The eco-nomic theory says nothing about the statistical characteristics of the variables, but it is then assumed that they are difference-stationary, whereupon these equilibrium relationships become the cointegrating relationships of the error-correction repre-sentation. This is described as long-run structural modeling (Pesaran and Shin 2002), because identifying restrictions on the cointegrating relationships are based on an underlying struc-tural model, whereas a reduced-form VAR describes the short-run dynamics.
The GVAR authors, having selected the variables to be mod-eled, likewise treat them all as integrated of order 1. The coin-tegration rank,r, is estimated from the data and takes values between 2 and 5 in the different submodels. No theoretical interpretation of the cointegrating relationships has yet been developed; instead, an arbitrary just-identifying normalization on the rst r variables is used. Thus little can be said about the long-run properties of the GVAR model, and one suspects that several of them may be implausible. In general, transitory shocks have permanent effects on the individualI.1/variables, which may seem unreasonable in respect of ination and inter-est rates in the current monetary policy environment in many countries. On the other hand, transitory shocks have no perma-nent effect on the cointegrating combinations of variables, and the cointegration of ination and the domestic interest rate in the U.K. VECM (Garratt et al. 2003a) implies that the ex-post real interest rate is invariant to shocks to the variables of the model in the long run, which is more reasonable. The authors report that the U.K. block of GVAR has the same cointegrating rank as the U.K. VECM—5, more than anywhere else—but one suspects that the same restrictions may not hold, neither here nor in other blocks with less cointegration. Another cointegrat-ing relationship in the U.K. VECM corresponds to purchascointegrat-ing power parity—the real exchange rate is invariant to shocks to the variables of the model in the long run—and again this would be a desirable property for the blocks of the GVAR model.
DYNAMIC PROPERTIES
The dynamic properties of large-scale systems are usually summarized by dynamic multipliers or impulse response func-tions, which describe the effects on the endogenous variables over time of a unit shock to an exogenous variable or an equation of the model. These correspond to partial derivatives of the dynamic system and are in widespread use in model com-parisons. The authors’ practice differs in two respects. First, they consider shocks of 1 standard error, rather than 1 unit or 1% of the variable in question; hence the reader interested in the magnitude of multipliers or spillovers has to scale the re-ported responses. It is not clear that interpretability is improved by scaling the shocks in inverse proportion to the goodness of t of the equations of the VECM.
More fundamentally, the authors report generalized impulse response functions (GIRFs; see Pesaran and Shin 1998). GIRFs
174 Journal of Business & Economic Statistics, April 2004
describe dynamic responses to a generalized shock, in which a shock to the equation in question is accompanied by shocks to the other equations of the submodel according to their residual correlations. It is argued that GIRFs describe the effect of “real-istic” shocks, meaning shocks of the type that are typically or at least historically observed, as described by the sample estimate of the error covariance matrix. However, their interpretation as reduced-form partial derivatives is difcult for readers familiar with shock-one-thing-at-a-time exercises, even when they are informed of the components of the generalized shock, which is not always done. It is also difcult to interpret responses to shocks of different composition in different models in compar-ative studies. For these reasons GIRFs have not replaced con-ventional dynamic multipliers in the macro modeling commu-nity. A nal difculty is that a reduced-form VAR in a small number of variables provides few stories about the source of the shock, whether univariate or composite, which may limit its interpretability.
The positive shock to German output reported in Sec-tion 9.7.2 illustrates these points. The source of the output shock could be a scal or monetary policy shock or an increase in productivity, for example. These feature in the recent com-parison of empirical models of the Euro area economy sum-marized by Wallis (2003), and they can be expected to have different second-round effects. However, comparison with these results is hindered by the perturbations to the other German variables in GVAR in proportion to their residual covariance with output. The impulse of 1 standard error corresponds to an increase of .74% in output in the rst quarter, and the com-posite shock or generalized impulse also includes an increase of 2.50% in real equity prices, afallin ination of .12%, and an increase of .21% in the real exchange rate, dened as the DM–US$ rate deated by the German CPI. (These impulses are taken from the quarter 0 column of Table 9. It is inappro-priate to describe them as “the effect of the increase in Ger-many’s output” in the same way as its effect in other regions. The German “impact effects” are components of the general-ized impulse, whereas the effects in other regions are the con-temporaneousresponses to the German shocks, which form part of the weakly exogenousforeign variables in those regions.) In-terpretation of the responses then requires the hybrid nature of the shock to be borne in mind, but this is difcult to do in the absence of information about the dynamic responses to indi-vidual shocks. One surprise among the long-run (quarter 20) results from a European perspective is the difference in ex-change rate responses in France, Germany, and Italy, remem-bering that the sample period saw several realignments of rates within the various phases of the Exchange Rate Mechanism of European Monetary System. (Contemporary forecasting would require adjustment to the model to take into account the nal stage of European Monetary Union and the recent introduction of a common currency among these countries.) Another sur-prise is the difference in output spillovers, with a 1% increase in output in Germany associated with increases between .28% and .37% in other countries of continental Europe, but virtually no change in the U.K. Unfortunately, generalized impulses in a reduced-form VAR tell few stories.
FORECASTING
Emphasis on the forecasting purpose of the model reduces the need for economic analysis and story-telling. It is well es-tablished that the best forecasting model and the best policy analysis model are unlikely to coincide, and that the VAR in differences is a relatively robust forecasting device in the face of endemic structural breaks (see Hendry and Clements 2003 for a recent review). Cointegration restrictions may improve forecasts, unless shifts in their means are the manifestation of structural change. The test of a forecasting model is its out-of-sample track record, and evidence on GVAR’s performance is eagerly awaited. This could include not only point forecasts, but also density forecasts, as the authors note.
Although VARs have become the standard benchmarks used in forecast evaluation, Watson (2003) noted that such small-scale models have had little effect on practical macroeconomic forecasting: “There are several reasons for this, but the most ob-vious is the inherent defect of small models: they include only a small number of variables. Practical forecasters and policy-makers nd it useful to extract information from many more series than are typically included in a VAR.” Whereas the com-plete GVAR model is substantially larger, each of its component blocks, separately estimated, is “typically” sized and contains a typical selection of variables. The nine-variable U.S. VAR of Sims (1993), for example, contains equivalent variables to the seven variables in the U.S. block of GVAR, together with business xed investment and unemployment; the main differ-ence is that Sims includes a more general commodity price index in place of the oil price. The GVAR could thus be re-garded as a natural benchmark for use in global economic fore-cast evaluation.
CONCLUSION
Pesaran et al. have presented a new approach to modeling for forecasting on a global scale. They have further extended a line of development from VAR to VARX to VECM models, and have advanced an elegant yet practical solution to the prob-lem of consistent global closure of their model. The relative simplicity of the model contributes to its tractability, but lim-its the depth of economic analysis that it can sustain compared with the competing structural models. The construction of the model in its present form is already a considerable achieve-ment by the authors, but much further developachieve-ment is needed before the model can support analysis of substantive economic issues, such as those that tantalize the reader of the article’s closing paragraph.
ADDITIONAL REFERENCES
Hendry, D. F., and Clements, M. P. (2003), “Economic Forecasting: Some Lessons From Recent Research,”Economic Modelling, 20, 301–329. Jacobs, J., and Wallis, K. F. (2003), “Comparing SVARs and SEMs: Two
Mod-els of the U.K. Economy,” paper presented at the Tinbergenweek Conference, Erasmus University, Rotterdam, April 2003.
Laxton, D., Isard, P., Faruqee, H., Prasad, E., and Turtelboom, B. (1998), “MULTIMOD Mark III: The Core Dynamic and Steady-State Models,” Oc-casional Paper No.164, International Monetary Fund, Washington, DC.
McKibbin, W. J., and Sachs, J. D. (1991),Global Linkages: Macroeconomic Interdependence and Cooperation in the World Economy, Washington, DC: The Brookings Institution.
McKibbin, W. J., and Wilcoxen, P. J. (1999), “The Theoretical and Empirical Structure of the G-Cubed Model,”Economic Modelling, 16, 123–148. Mitchell, P. R., Sault, J. E., Smith, P. N., and Wallis, K. F. (1998), “Comparing
Global Economic Models,”Economic Modelling, 15, 1–48.
Roeger, W., and in’t Veld, J. (1997), “QUEST II: A Multicountry Business Cycle and Growth Model,” Economic Papers No. 123, European Commis-sion, Brussels.
Sims, C. A. (1993), “A Nine-Variable Probabilistic Macroeconomic Forecast-ing Model,” inBusiness Cycles, Indicators, and Forecasting, eds. J. H. Stock and M. W. Watson, Chicago: University of Chicago Press for NBER, pp. 179–204.
Wallis, K. F. (2003), “Comparing Empirical Models of the Euro Economy,” Economic Modelling, forthcoming.
Watson, M. W. (2003), “Macroeconomic Forecasting Using Many Predictors,” in Advances in Economics and Econometrics: Theory and Applications, Eighth World Congress, Vol. 3, eds. M. Dewatripont, L. P. Hansen, and S. J. Turnovsky, Cambridge, U.K.: Cambridge University Press, pp. 87–114.
Rejoinder
M. Hashem P
ESARANCambridge University and University of Southern California (MHP1@cam.ac.uk)
Til S
CHUERMANNFederal Reserve Bank of New York (til.schuermann@ny.frb.org)
Scott M. W
EINERAlliance Capital Management L.P., New York (scott_weiner@acml.com)
1. INTRODUCTION
We would like to thank all the ve discussants for their gen-erous and constructive comments and the editor, Alastair Hall, for his support and encouragement and for giving us the oppor-tunity to take part in this distinguished forum. Although there is obviously some overlap between the discussants in the issues that they raise, each has brought his distinct expertise and expe-rience to bear on our work on GVAR modeling. The discussants also raise a number of important technical and practical issues that clearly merit further investigation. These include mathe-matical details that underlie the weak exogeniety assumption, the use of small-sample corrections raised by Johansen, the is-sue of allowing for feedback from macroeconomic variables to the trade weights mentioned by Baltagi, Wallis’s desire to see comparative evidence of out-of-sample point and density fore-casts, and Dennis and Lopez’s call for more detailed structural modeling capable of incorporating stock-ow relationships in an explicit manner. Other more general issues raised include structural instability,nonlinearities,dynamic specications, and the interpretation of generalized impulse responses.
2. AN OVERVIEW
National macroeconometric modeling in general and global modeling in particular are subject to a number of important constraints, including the quantity and quality of available time series data, the curse of dimensionality that arises from the numerous between- and within-country channels of interac-tions and transmissions, our knowledge of economic theory and institutions, and the human and computing resources avail-able. The modeling process inevitably involves many trade-offs (for an early discussion, see Pesaran and Smith 1985).
Our modeling objective was to estimate a compact and the-oretically coherent global model capable of generating multi-step-ahead forecasts, whose assumptions could (in principle) be tested. Starting from country-specic macroeconometric mod-els, we were able to deal with the curse of dimensionality by re-lating the country-specic variables to foreign variable indices formed by using trade weights. We allow for the contempora-neous dependence of domestic and foreign variables by treat-ing the latter as weakly exogeneous for estimation purposes, an assumption that we test and do not reject for 59 of the total 62 foreign-specic variables at the 95% level. The U.S. economy is treated differently, both because of its importance in the world economy and because of the fact that we use the U.S. dollar as the numeraire. This also ensures that the remaining 10 coun-tries/regions in the global model can be viewed as “small” open economies. Once estimated, the global model is solved for all of the domestic variables simultaneously. We retain oil prices as the only global exogeneous variable of the model, largely to show that our modeling strategy can cope with such variables, possibly as a proxy for political factors, although it would be straightforward to endogenizeoil prices. For instance, it could be included as an additional endogeneous variable in the U.S. model.
Our modeling approach also has an important bearing on recent developments in the area of panel cointegration. The GVAR structure allows for cointegrating relations to exist between domestic variables, as well as between domestic and foreign variables. As highlighted by Baltagi in his comments, this avoids the criticism of Banerjee et al. (2002) of panel coin-tegration techniques advanced in the literature, which restrict
© 2004 American Statistical Association Journal of Business & Economic Statistics April 2004, Vol. 22, No. 2 DOI 10.1198/073500104000000064
