RT Dissertation/Thesis
T1 Essays on Identification of Structural VARMA models
A1 Cabello Pérez, Miguel Ángel
AB Structural vector autoregressive models are widely employed in macro-econometricssince they provide a simple, practical representation of structural theoretical models.For decades, the most preferred framework has been the structural vectorautoregressive models, under the belief that structural economics models arefundamental, which intuitively means that information generated from the history(current and past values) of observable, endogenous variables is equivalent to theinformation constructed from the history of unobservable economic shocks.Under such an assumption, most empirical studies only focus on the identificationchallenges of the contemporaneous effects matrix or the static component of themodel¿the strategies for overcoming this identification problem resort to using externalinformation. Early proposals impose zero or linear restrictions over the matrix ofcontemporaneous effects. Another type of restriction is imposed on the long-run effectsof economic shocks over some outcomes of interests, also known as long-runidentification restrictions, such as the one employed. An alternative strategy is basedon sign restrictions, which only restrain the direction (sign) of the response of someendogenous variable to changes in a single or a subset of economic shocks. Forinstance, it is a consensus to assume that a positive demand shock increases outputand inflation in the short run.On the other hand, a more economic-based identification strategy is the narrativeapproach. This scheme constructs a measure for an unobserved economic shock byanalyzing extensive policy change information. For instance, Romer and Romer (1989)construct a measure of monetary policy shock by analyzing historical records ofFederal Reserve meetings. Recently, an identification strategy that uses externalmeasures as a proxy or instrumental variables for identifying a single shock or a subsetof structural shocks has been introduced.Despite the usefulness of these strategies, they possess essential drawbacks. In thecase of zero, linear or long-run identification restrictions, most of these conditions arenot subject to empirical evaluation unless they are overidentification restrictions. Theirsupport must be done by appealing to economic intuitions, some of which may bearguable. Besides, some of the identification restrictions may be challenging toimplement. For instance, zero long-run restrictions are commonly approximated byrestricting the cumulative response of a shock over a finite time horizon.Regarding identification based on sign restrictions, these can only identify a set ofmodels. Consequently, this strategy entails two sources of variability: sample andmodel uncertainty. Isolating each of these sources of variance is challenging. Finally,regarding the strategy using proxy or instrumental variables, its identification powerdepends on the exogeneity and relevance conditions. Besides, as it is documented byAngelini et al. (2002) when proxy SVARs feature multiple target shocks, it requiresadditional point or sign restrictions. Last but not least, most of these strategies have incommon that they were developed for identifying shocks in a causal (or fundamental)structural VAR model.Besides, the fundamental representation assumption of the structural model may needto be revised, mainly when the econometrician's information set is smaller than theinformation set of the theoretical model. Moreover, it has been documented that thiscase may not be quite an unrealistic situation. Empirically, to deal with possibly non-fundamental structural models is necessary not to impose the location of roots outsidethe complex unit circle but only rule out unit roots in dynamic lag polynomials.Therefore, it is critical to develop methods for estimating structural vectorautoregressive moving-average models, where the location of dynamic lag polynomialroots is unknown and must be determined from data.Nevertheless, distinguishing fundamental from non-fundamental models cannot beaccomplished if the researcher only exploits second-order information, i.e., requiringthat structural shocks are serially and mutually uncorrelated. Because, as has beendocumented in the literature, it is possible to find at least two models, fundamental andnon-fundamental, with serially uncorrelated errors. This issue is what the literature callsthe dynamic identification problem (see Velasco (2022)).Consequently, to overcome this identification problem, higher-order information on theerrors must be exploited. This fact leads to abandoning the Gaussian behaviorassumption regarding the structural shocks and assuming that structural shocks arenon-Gaussian distributed. Otherwise, it is unfeasible to distinguish fundamental fromnon-fundamental models. In recent years, several methodological works haveproposed alternatives for identifying and estimating structural vector autoregressivemoving-average models without imposing the location of roots by exploiting the non-Gaussian behavior of structural shocks. Most of these investigations assumed thatshocks are serial and mutually independent and identified the structural parametersfollowing two approaches. The first strategy is to characterize non-Gaussian behaviorby assuming non-zero third or fourth-order cumulants. This strategy is like a method ofmoments approach. Therefore, for constructing standard errors of the estimates, it isnecessary to impose the finiteness of sixth or eighth-order moments. This assumptionrules out essential types of non-Gaussian behavior.On the other hand, a second approach is to characterize the non-Gaussian behaviorassuming a particular joint density function for the structural shocks and imposing, atleast, non-zero third-order cumulants. This research attempts to fill a gap in theprevious literature by proposing an estimation method that exploits the jointcharacteristic function of pairwise errors. This approach does not require imposing thefiniteness of many higher-order moments or the knowledge of a specific joint densitydistribution of structural shocks. Moreover, the proposed method may be adapted forsituations where structural shocks exhibit higher-order serial dependence while mutualindependence is still assumed.Specifically, the first chapter explains that causal (or fundamental) structural vectorautoregressions models may deliver biased estimates of causal effects of economicshocks when data comes from a non-fundamental structural model. As discussedabove, this paper exploits the joint characteristic function of pairwise model errorsinstead of using specific moments or cumulants or imposing a particular densityfunction for the structural shocks. Thus, our measure dependence is a generalizedautocovariance function of the complex exponential model errors. We summarize theinformation on the autocovariance function using the cumulative spectral distribution,which is the integral of the spectral density function of model errors. We opt for thecumulative spectral function instead of the spectral density because its samplecounterpart does not require a smoothing kernel. Moreover, this feature makes thatweak convergence of estimators occurs at the standard rate.In this line, the contributions of this chapter are twofold. On the one hand, we extend awell-known identification result for SVARMA models with independent shocks to asituation in which disturbances can exhibit a more general serial dependence structure;on the other hand, we propose an estimation procedure that minimizes the distance ofthe generalized cumulative spectral distribution of unrestricted and restricted modelerrors. This procedure does not require imposing a particular joint non-Gaussiandistribution of structural errors, as well as it does not need the existence of a largenumber of higher-order moments. Furthermore, in the case of having seriallydependent shocks, identification (up to sign-permutation) only requires the existence ofsecond-order moments of structural shocks and peculiar characterization of non-Gaussian behavior, consisting of non-linearity of expectations of structural errorsconditional to non-constant linear filters. Regarding the asymptotic properties of ourestimators, in the case of fully independent shocks, the finiteness of third-ordermoments is the only requisite to find the asymptotic distribution of the structuralparameter estimator; in the case of serially dependent structural errors, it is requiredthe finiteness of at least fifth-order moments for finding the asymptotic distribution ofthe estimator.The simulation evidence shows that our method satisfactorily identifies the location ofthe roots with a relatively small sample size. In the case of the bivariate structuralmodel, the rate of correct root location is above 90 percent when structural shocks areasymmetric. In contrast, this rate decays when the errors follow a symmetric non-Gaussian distribution, especially for VARMA models with non-zero AR and MAcomponents. To analyze our method's robustness, we study how well the proposalidentifies the location of roots when structural shocks behave like a multivariateGaussian random element. The rate of correct root location obtained with theMontecarlo experiment is quite close to the theoretical rate when only errors arerequired to be white noise.Finally, we applied our proposal to the dataset analyzed by Blanchard and Quah(1989). This dataset contains only two endogenous variables, GDP growth, andunemployment rate. We select two different specifications. The first case assumes thatthe roots of the AR polynomial lie outside the unit circle, but the location of the roots ofthe MA polynomial is not determined. The second specification is an unrestrictedstructural model, which does not restrict the root location of both the AR and MApolynomials. In both scenarios, the polynomials' overall degree equals one,respectively. The estimation results are the following: for the first restrictedspecification, our proposed method identifies that the roots of the MA polynomial lieoutside the unit circle, i.e., our method identifies that the MA polynomial is invertible.Based on the estimation of the structural model, we compute the estimated causaleffects of both identified shocks (i.e., impulse response functions of each shock). Theanalysis of these causal effects shows that we identify a shock with a non-zero long-run effect and another with zero long-run effect over GDP growth. It is worth mentioningthat identifying these shocks did not require imposing any external identificationrestriction. In the scenario of not restricting the SVARMA model's root location, ourmethod identifies MA roots outside the unit circle but AR roots inside the unit circle. Inother words, our proposal identifies a non-causal but invertible SVARMA model.In the second chapter, we investigate the feasibility of empirically verifying one of thecritical identification assumptions of the statistical strategy for identifying structuralvector autoregressive moving-average models, i.e., the requirement about the non-Gaussian behavior of all shocks in the system. In particular, the statistical identificationof possibly non-fundamental structural vector autoregressive moving-average modelsrequires that shocks satisfy: (i) to be an i.i.d process, (ii) to be mutually independentacross components, and (iii) each shock must be non-Gaussian distributed. Therefore,provided the first two requirements, it is crucial to be able to evaluate the third conditionempirically without requiring estimation of the structural model because this latter maynot be identified, and with a non-zero probability, an attempt to estimate the structuralmodel may deliver an inconsistent one. However, in the literature, few efforts havebeen posed to determine the non-Gaussian dimension in a structural system. Most ofthese investigations assume that the structural model is fundamental, which makes itunfeasible to apply such proposals to more general contexts.Consequently, this research attempts to fill this gap in the literature and proposes amethod for determining the non-Gaussian dimension when the location of polynomialroots is still being determined. In that sense, our proposal is robust to the location ofthe roots of the dynamic polynomials in the model. Therefore, it can be applied tofundamental or non-fundamental contexts.We address the unknown location of roots by relating the non-Gaussian dimension ofstructural errors to the rank of a matrix built from the higher-order spectrum of reduced-form errors. The estimation of the spectral density of the reduced form errors is donenon-parametrically, making the convergence rates of the asymptotic distribution of theestimators to be slower than the standard one. Our estimation approach for the non-Gaussian dimension is a sequential testing procedure. Precisely, we follow theKleibergen and Paap (hereafter KP) approach. The KP -statistic is built from thesingular value decomposition of the interest matrix. The asymptotic distribution of thestatistic is a standard chi-square whose degrees of freedom change depending on thenull hypothesis. Unlike the KP article, our context changes the asymptotic distributionof the test statistic for some particular rank values, specifically under joint Gaussianity.For other null hypotheses, the asymptotic distribution is chi-square, but the degrees offreedom are generally unknown.For this reason, we propose a bootstrap test strategy. This path implies anothersignificant challenge: to impose the null hypothesis in the resampled data. The way forcreating bootstrap samples follows the idea of Nordhausen et al. (2017).The idea is to employ the characteristic vectors associated with zero singular valuesunder each specific null hypothesis. These vectors span the Gaussian dimension.These vectors create a projection matrix over the non-Gaussian dimension, while theGaussian dimension is completed with values drawn from a multivariate standardNormal distribution. The Montecarlo exercises were performed to analyze the size andpower of the bootstrap test to show that our strategy estimates satisfactorily the non-Gaussian dimension. We apply our procedure to two well-known macroeconomicdatasets, such as Blanchard and Quah (1989) and Blanchard and Perotti (2002).Unlike the work of Guay (2021), we can detect at least two non-Gaussian shocks in theBlanchard-Perotti dataset. Meaning that a statistical identification strategy can beapplied to this database, at least assuming that polynomial roots are outside thecomplex unit circle.Finally, the third chapter has explored the conditions under which the combination ofhigher order cumulants identification and sign restrictions may be combined to obtainglobal identification. The statistical identification strategy of causal structural vectorautoregressive models has gained attention recently because it permits theidentification of the causal effects of structural shocks without resorting to externalidentification restrictions. This strategy exploits higher-order information providedstructural errors are mutually independent and non-Gaussian distributed. Thisapproach only identifies the structural model up to the signed permutation, whichimplies a finite set of admissible models. The solution proposed in the literature forselecting a model relies on applying a mechanical procedure. This paper aims to studyan alternative scheme based on imposing economic-motivated sign restrictions overthe causal effects of structural shocks. Only the permutations matter when a single,strict sign restriction is applied to each shock. A sufficient condition for achieving globalidentification is that the matrix of contemporaneous effects has a generalized recursivestructure. Furthermore, when all shocks are either asymmetric or non-mesokurtic, wecan find a relationship between the recursive structure of the contemporaneous effectsmatrix and the rank of the blocks of the matrix version of third or fourth-order cumulantsof reduced-form errors. This result can be seen as an alternative path for determiningthe recursive structure to the standard procedure based on applying Granger'scausality test to each endogenous variable.A weaker sufficient condition for accomplishing point identification of a single shockrequires imposing as many sign restrictions as the number of endogenous variables inthe model and that the system of sign restrictions is sign-solvable. It also explores thenecessary conditions for having a non-empty identified set when only second-ordercumulants and sign restrictions are employed. Although evident, this condition is notconsidered and taken as granted in several empirical works that employ signrestrictions for identifying economic shocks. The condition states that when the Gram-Schmidt algorithm is applied to each tuple of the vectors in the solution set of the signrestrictions intersects the Cartesian product, the identified set is non-empty. Thiscondition holds immediately when only a small set of sign restrictions are imposed overthe shocks and the restrictions are set over the same objects. On the other hand, whenthe model contains more than one Gaussian structural error, identification using higher-order cumulants ensures that the non-Gaussian block remains identified, although theorder is unknown.
AB Structural vector autoregressive models are widely employed in macro-econometricssince they provide a simple, practical representation of structural theoretical models.For decades, the most preferred framework has been the structural vectorautoregressive models, under the belief that structural economics models arefundamental, which intuitively means that information generated from the history(current and past values) of observable, endogenous variables is equivalent to theinformation constructed from the history of unobservable economic shocks.Under such an assumption, most empirical studies only focus on the identificationchallenges of the contemporaneous effects matrix or the static component of themodel¿the strategies for overcoming this identification problem resort to using externalinformation. Early proposals impose zero or linear restrictions over the matrix ofcontemporaneous effects. Another type of restriction is imposed on the long-run effectsof economic shocks over some outcomes of interests, also known as long-runidentification restrictions, such as the one employed. An alternative strategy is basedon sign restrictions, which only restrain the direction (sign) of the response of someendogenous variable to changes in a single or a subset of economic shocks. Forinstance, it is a consensus to assume that a positive demand shock increases outputand inflation in the short run.On the other hand, a more economic-based identification strategy is the narrativeapproach. This scheme constructs a measure for an unobserved economic shock byanalyzing extensive policy change information. For instance, Romer and Romer (1989)construct a measure of monetary policy shock by analyzing historical records ofFederal Reserve meetings. Recently, an identification strategy that uses externalmeasures as a proxy or instrumental variables for identifying a single shock or a subsetof structural shocks has been introduced.Despite the usefulness of these strategies, they possess essential drawbacks. In thecase of zero, linear or long-run identification restrictions, most of these conditions arenot subject to empirical evaluation unless they are overidentification restrictions. Theirsupport must be done by appealing to economic intuitions, some of which may bearguable. Besides, some of the identification restrictions may be challenging toimplement. For instance, zero long-run restrictions are commonly approximated byrestricting the cumulative response of a shock over a finite time horizon.Regarding identification based on sign restrictions, these can only identify a set ofmodels. Consequently, this strategy entails two sources of variability: sample andmodel uncertainty. Isolating each of these sources of variance is challenging. Finally,regarding the strategy using proxy or instrumental variables, its identification powerdepends on the exogeneity and relevance conditions. Besides, as it is documented byAngelini et al. (2002) when proxy SVARs feature multiple target shocks, it requiresadditional point or sign restrictions. Last but not least, most of these strategies have incommon that they were developed for identifying shocks in a causal (or fundamental)structural VAR model.Besides, the fundamental representation assumption of the structural model may needto be revised, mainly when the econometrician's information set is smaller than theinformation set of the theoretical model. Moreover, it has been documented that thiscase may not be quite an unrealistic situation. Empirically, to deal with possibly non-fundamental structural models is necessary not to impose the location of roots outsidethe complex unit circle but only rule out unit roots in dynamic lag polynomials.Therefore, it is critical to develop methods for estimating structural vectorautoregressive moving-average models, where the location of dynamic lag polynomialroots is unknown and must be determined from data.Nevertheless, distinguishing fundamental from non-fundamental models cannot beaccomplished if the researcher only exploits second-order information, i.e., requiringthat structural shocks are serially and mutually uncorrelated. Because, as has beendocumented in the literature, it is possible to find at least two models, fundamental andnon-fundamental, with serially uncorrelated errors. This issue is what the literature callsthe dynamic identification problem (see Velasco (2022)).Consequently, to overcome this identification problem, higher-order information on theerrors must be exploited. This fact leads to abandoning the Gaussian behaviorassumption regarding the structural shocks and assuming that structural shocks arenon-Gaussian distributed. Otherwise, it is unfeasible to distinguish fundamental fromnon-fundamental models. In recent years, several methodological works haveproposed alternatives for identifying and estimating structural vector autoregressivemoving-average models without imposing the location of roots by exploiting the non-Gaussian behavior of structural shocks. Most of these investigations assumed thatshocks are serial and mutually independent and identified the structural parametersfollowing two approaches. The first strategy is to characterize non-Gaussian behaviorby assuming non-zero third or fourth-order cumulants. This strategy is like a method ofmoments approach. Therefore, for constructing standard errors of the estimates, it isnecessary to impose the finiteness of sixth or eighth-order moments. This assumptionrules out essential types of non-Gaussian behavior.On the other hand, a second approach is to characterize the non-Gaussian behaviorassuming a particular joint density function for the structural shocks and imposing, atleast, non-zero third-order cumulants. This research attempts to fill a gap in theprevious literature by proposing an estimation method that exploits the jointcharacteristic function of pairwise errors. This approach does not require imposing thefiniteness of many higher-order moments or the knowledge of a specific joint densitydistribution of structural shocks. Moreover, the proposed method may be adapted forsituations where structural shocks exhibit higher-order serial dependence while mutualindependence is still assumed.Specifically, the first chapter explains that causal (or fundamental) structural vectorautoregressions models may deliver biased estimates of causal effects of economicshocks when data comes from a non-fundamental structural model. As discussedabove, this paper exploits the joint characteristic function of pairwise model errorsinstead of using specific moments or cumulants or imposing a particular densityfunction for the structural shocks. Thus, our measure dependence is a generalizedautocovariance function of the complex exponential model errors. We summarize theinformation on the autocovariance function using the cumulative spectral distribution,which is the integral of the spectral density function of model errors. We opt for thecumulative spectral function instead of the spectral density because its samplecounterpart does not require a smoothing kernel. Moreover, this feature makes thatweak convergence of estimators occurs at the standard rate.In this line, the contributions of this chapter are twofold. On the one hand, we extend awell-known identification result for SVARMA models with independent shocks to asituation in which disturbances can exhibit a more general serial dependence structure;on the other hand, we propose an estimation procedure that minimizes the distance ofthe generalized cumulative spectral distribution of unrestricted and restricted modelerrors. This procedure does not require imposing a particular joint non-Gaussiandistribution of structural errors, as well as it does not need the existence of a largenumber of higher-order moments. Furthermore, in the case of having seriallydependent shocks, identification (up to sign-permutation) only requires the existence ofsecond-order moments of structural shocks and peculiar characterization of non-Gaussian behavior, consisting of non-linearity of expectations of structural errorsconditional to non-constant linear filters. Regarding the asymptotic properties of ourestimators, in the case of fully independent shocks, the finiteness of third-ordermoments is the only requisite to find the asymptotic distribution of the structuralparameter estimator; in the case of serially dependent structural errors, it is requiredthe finiteness of at least fifth-order moments for finding the asymptotic distribution ofthe estimator.The simulation evidence shows that our method satisfactorily identifies the location ofthe roots with a relatively small sample size. In the case of the bivariate structuralmodel, the rate of correct root location is above 90 percent when structural shocks areasymmetric. In contrast, this rate decays when the errors follow a symmetric non-Gaussian distribution, especially for VARMA models with non-zero AR and MAcomponents. To analyze our method's robustness, we study how well the proposalidentifies the location of roots when structural shocks behave like a multivariateGaussian random element. The rate of correct root location obtained with theMontecarlo experiment is quite close to the theoretical rate when only errors arerequired to be white noise.Finally, we applied our proposal to the dataset analyzed by Blanchard and Quah(1989). This dataset contains only two endogenous variables, GDP growth, andunemployment rate. We select two different specifications. The first case assumes thatthe roots of the AR polynomial lie outside the unit circle, but the location of the roots ofthe MA polynomial is not determined. The second specification is an unrestrictedstructural model, which does not restrict the root location of both the AR and MApolynomials. In both scenarios, the polynomials' overall degree equals one,respectively. The estimation results are the following: for the first restrictedspecification, our proposed method identifies that the roots of the MA polynomial lieoutside the unit circle, i.e., our method identifies that the MA polynomial is invertible.Based on the estimation of the structural model, we compute the estimated causaleffects of both identified shocks (i.e., impulse response functions of each shock). Theanalysis of these causal effects shows that we identify a shock with a non-zero long-run effect and another with zero long-run effect over GDP growth. It is worth mentioningthat identifying these shocks did not require imposing any external identificationrestriction. In the scenario of not restricting the SVARMA model's root location, ourmethod identifies MA roots outside the unit circle but AR roots inside the unit circle. Inother words, our proposal identifies a non-causal but invertible SVARMA model.In the second chapter, we investigate the feasibility of empirically verifying one of thecritical identification assumptions of the statistical strategy for identifying structuralvector autoregressive moving-average models, i.e., the requirement about the non-Gaussian behavior of all shocks in the system. In particular, the statistical identificationof possibly non-fundamental structural vector autoregressive moving-average modelsrequires that shocks satisfy: (i) to be an i.i.d process, (ii) to be mutually independentacross components, and (iii) each shock must be non-Gaussian distributed. Therefore,provided the first two requirements, it is crucial to be able to evaluate the third conditionempirically without requiring estimation of the structural model because this latter maynot be identified, and with a non-zero probability, an attempt to estimate the structuralmodel may deliver an inconsistent one. However, in the literature, few efforts havebeen posed to determine the non-Gaussian dimension in a structural system. Most ofthese investigations assume that the structural model is fundamental, which makes itunfeasible to apply such proposals to more general contexts.Consequently, this research attempts to fill this gap in the literature and proposes amethod for determining the non-Gaussian dimension when the location of polynomialroots is still being determined. In that sense, our proposal is robust to the location ofthe roots of the dynamic polynomials in the model. Therefore, it can be applied tofundamental or non-fundamental contexts.We address the unknown location of roots by relating the non-Gaussian dimension ofstructural errors to the rank of a matrix built from the higher-order spectrum of reduced-form errors. The estimation of the spectral density of the reduced form errors is donenon-parametrically, making the convergence rates of the asymptotic distribution of theestimators to be slower than the standard one. Our estimation approach for the non-Gaussian dimension is a sequential testing procedure. Precisely, we follow theKleibergen and Paap (hereafter KP) approach. The KP -statistic is built from thesingular value decomposition of the interest matrix. The asymptotic distribution of thestatistic is a standard chi-square whose degrees of freedom change depending on thenull hypothesis. Unlike the KP article, our context changes the asymptotic distributionof the test statistic for some particular rank values, specifically under joint Gaussianity.For other null hypotheses, the asymptotic distribution is chi-square, but the degrees offreedom are generally unknown.For this reason, we propose a bootstrap test strategy. This path implies anothersignificant challenge: to impose the null hypothesis in the resampled data. The way forcreating bootstrap samples follows the idea of Nordhausen et al. (2017).The idea is to employ the characteristic vectors associated with zero singular valuesunder each specific null hypothesis. These vectors span the Gaussian dimension.These vectors create a projection matrix over the non-Gaussian dimension, while theGaussian dimension is completed with values drawn from a multivariate standardNormal distribution. The Montecarlo exercises were performed to analyze the size andpower of the bootstrap test to show that our strategy estimates satisfactorily the non-Gaussian dimension. We apply our procedure to two well-known macroeconomicdatasets, such as Blanchard and Quah (1989) and Blanchard and Perotti (2002).Unlike the work of Guay (2021), we can detect at least two non-Gaussian shocks in theBlanchard-Perotti dataset. Meaning that a statistical identification strategy can beapplied to this database, at least assuming that polynomial roots are outside thecomplex unit circle.Finally, the third chapter has explored the conditions under which the combination ofhigher order cumulants identification and sign restrictions may be combined to obtainglobal identification. The statistical identification strategy of causal structural vectorautoregressive models has gained attention recently because it permits theidentification of the causal effects of structural shocks without resorting to externalidentification restrictions. This strategy exploits higher-order information providedstructural errors are mutually independent and non-Gaussian distributed. Thisapproach only identifies the structural model up to the signed permutation, whichimplies a finite set of admissible models. The solution proposed in the literature forselecting a model relies on applying a mechanical procedure. This paper aims to studyan alternative scheme based on imposing economic-motivated sign restrictions overthe causal effects of structural shocks. Only the permutations matter when a single,strict sign restriction is applied to each shock. A sufficient condition for achieving globalidentification is that the matrix of contemporaneous effects has a generalized recursivestructure. Furthermore, when all shocks are either asymmetric or non-mesokurtic, wecan find a relationship between the recursive structure of the contemporaneous effectsmatrix and the rank of the blocks of the matrix version of third or fourth-order cumulantsof reduced-form errors. This result can be seen as an alternative path for determiningthe recursive structure to the standard procedure based on applying Granger'scausality test to each endogenous variable.A weaker sufficient condition for accomplishing point identification of a single shockrequires imposing as many sign restrictions as the number of endogenous variables inthe model and that the system of sign restrictions is sign-solvable. It also explores thenecessary conditions for having a non-empty identified set when only second-ordercumulants and sign restrictions are employed. Although evident, this condition is notconsidered and taken as granted in several empirical works that employ signrestrictions for identifying economic shocks. The condition states that when the Gram-Schmidt algorithm is applied to each tuple of the vectors in the solution set of the signrestrictions intersects the Cartesian product, the identified set is non-empty. Thiscondition holds immediately when only a small set of sign restrictions are imposed overthe shocks and the restrictions are set over the same objects. On the other hand, whenthe model contains more than one Gaussian structural error, identification using higher-order cumulants ensures that the non-Gaussian block remains identified, although theorder is unknown.
YR 2023
FD 2023-06
LK https://hdl.handle.net/10016/37733
UL https://hdl.handle.net/10016/37733
LA eng
NO This research has been possible thanks to the financial support from the scholarship MCIN/BES-2017-081997 from the Spanish Agency of Science and Innovation (Ministerio de Ciencia e Innovación).
DS e-Archivo
RD 21 may. 2024