Structural information in recursive VAR orderings

Keating, John W.

doi:10.1016/0165-1889(96)00914-1

Cited by 52 publications

(46 citation statements)

References 14 publications

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“…Equation (12) postulates that each parameter may be affected by the standard error shock of the current term and the lagged terms. While either orthogonalizing the disturbance or preventing the elements of from correlation, Cholesky decomposition takes the squared root of a positive-definite matrix.…”

Section: Impulse Response Functionmentioning

confidence: 99%

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Elucidating the Relationship among EUA Spot Price, Brent Oil Price and Three European Stock Indices

Hu¹,

Hu²,

Chien³

2016

ujaf

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For decades, humans have been consuming large quantities of oil, coal and natural gas. Consequently, people must now take responsibility for having participated in productive activities that have caused the emissions of greenhouse gas (GHG) which has damaged the environment and caused problems associated with abnormal weather. Previous studies investigated the relationships between energy and carbon prices, between oil price and stock index, or between carbon price and macro-economic factors. Few have examined the relationships among EUA spot price, oil price and the stock index in individual nations. Owing to the fact that the European Emissions Trading Scheme (EU ETS) is the world's first carbon market and remains the largest globally, this study, based on the finding of Chevallier (2009) that capital markets are closely related to the commodity markets, examines the long-term equilibrium relationship and causality among European Union Allowance (EUA) spot price, Brent oil price and three European major stock indices from January 1, 2005 to Dec. 31, 2012. The sample period is further divided into three sub-periods of 2005 to 2007 (Phase 1 of the EU ETS), 2008 to 2010 (US subprime loan crisis and the first period of Phase 2 of the EU ETS), and 2011 to 2012 (European debt crisis and the second period of Phase 2 of the EU ETS). Numerous notable findings from the empirical findings are presented. First, EUA spot price, oil price and DAX index are co-integrated with each other during the second sub-period. Although oil price can be adjusted to the long-term equilibrium in German stock market during that period, adjusting EUA spot price to long-term equilibrium is rather difficult. Next, oil price is affected by EUA spot price unilaterally for the full sample period and the third sub-period. Moreover, EUA spot price is unaffected by any factor except itself during the first sub-period, and is affected by three European stock indices for the full sample period, and the third sub-period. Furthermore, the most explanatory power for Brent oil and EUA spot prices arises from themselves, respectively. Finally, the capital markets and commodity markets are closely related during the 2 nd sub-period only.

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Section: Impulse Response Functionmentioning

confidence: 99%

“…According to Keating (1996), Cholesky decompositions can identify the set of a partially recursive structural model. Equation (11) can be transformed through the Wold decomposition Theorem to vector moving average representation (MAR) form as follows:…”

Section: Impulse Response Functionmentioning

confidence: 99%

Elucidating the Relationship among EUA Spot Price, Brent Oil Price and Three European Stock Indices

Hu¹,

Hu²,

Chien³

2016

ujaf

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“…One can also show that two-block versions of the long-run partially recursive structure are necessary for the initial block or the final block of shocks from a long-run recursive ordering to yield structural responses. These results follow from a simple extension of necessary conditions 19 from Section 5 of Keating (1996): Assume the variables are integrated and replace the short-run structural parameter matrix and the short-run identification restrictions with the long-run partially recursive structural parameter matrix and the long-run recursive identification restrictions, respectively.…”

Section: Concluding Commentsmentioning

confidence: 99%

Structural Inference With Long-Run Recursive Empirical Models

Keating

2002

Macroecon. Dynam.

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This paper investigates conditions under which a long-run recursive model can be used to identify a structure. Economists frequently employ this type of empirical model. I define the class of long-run partially recursive structures. If an economic system is a member of this class, then certain long-run recursive empirical models will obtain some of the structural impulse response functions. This sufficient condition for a structure is first shown in a vector autoregression. A well-known example from the literature is used to illustrate this particular class of structures and to present some useful applications of the result. Then the result is shown in models of cointegrated time series. Necessary conditions for a long-run recursive model to identify structure are addressed in the conclusion.

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“…economies in turn provide a natural relative ordering of the two sub-systems that I exploit for structural identification (see Keating, 1996, on block-recursive identification assumptions).…”

Section: Long-run Identificationmentioning

confidence: 99%

Joint Inference and Counterfactual Experimentation for Impulse Response Functions By Local Projections

Jordà

2007

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. This paper provides three measures of the uncertainty associated to an impulse response path: (1) conditional confidence bands which isolate the uncertainty of individual response coefficients given the temporal path experienced up to that point; (2) response percentile bounds} which provide bounds on the universe of permissible paths at a given probability level; and (3) Wald tests of joint significance and joint cumulative significance. These results rely on general assumptions for the joint distribution of the system's impulse responses. Given this distribution, the paper then shows how to construct counterfactual experiments formally; provides a test on the likelihood of observing the counterfactual; and derives the distribution of the system's responses conditional on the counterfactual. The paper then derives the asymptotic joint distribution of structural impulse responses identified by either short-or long-run recursive assumptions and estimated by local projections (Jorda, 2005). An application to a two country system implements all of these new methods. This paper provides three measures of the uncertainty associated to an impulse response path: Terms of use: Documents in(1) conditional confidence bands which isolate the uncertainty of individual response coefficients given the temporal path experienced up to that point; (2) response percentile bounds which provide bounds on the universe of permissible paths at a given probability level; and (3) Wald tests of joint significance and joint cumulative significance. These results rely on general assumptions for the joint distribution of the system's impulse responses. Given this distribution, the paper then shows how to construct counterfactual experiments formally; provides a test on the likelihood of observing the counterfactual; and derives the distribution of the system's responses conditional on the counterfactual. The paper then derives the asymptotic joint distribution of structural impulse responses identified by either short-or long-run recursive assumptions and estimated by local projections (Jordà, 2005). An application to a two country system implements all of these new methods.

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Structural information in recursive VAR orderings

Cited by 52 publications

References 14 publications

Elucidating the Relationship among EUA Spot Price, Brent Oil Price and Three European Stock Indices

Elucidating the Relationship among EUA Spot Price, Brent Oil Price and Three European Stock Indices

Structural Inference With Long-Run Recursive Empirical Models

Joint Inference and Counterfactual Experimentation for Impulse Response Functions By Local Projections

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