___ ____ ____ ____ ____(R) /__ / ____/ / ____/ ___/ / /___/ / /___/ Statistics/Data Analysis Title svarih -- Structural vector autoregressive models, identified through heteroskedasticity Syntax svarih method depvarlist [if] [in] [, options] method description ------------------------------------------------------------------------- bacchiocchi Bacchiocchi (2011) method and model bfanelli Bacchiocchi/Fanelli (2012) method and model llutkepohl Lanne/Lütkepohl (2008) method and model ------------------------------------------------------------------------- For the detailed syntax and description of these estimation methods, see svarih bac, svarih bfa and svarih llu. Description svarih implements several identification methods and models for structural vector autoregressions that are based on identification through heteroskedasticity. For a detailed exposition of these estimation methods, see their respective help files. Abbreviations, definitions, notation The following list contains abbreviations, definitions, and notation that are used throughout this help file, the help files for svarih methods, and for dsimih and dsimih subcommands. Definitions: volatility regime/state period of time within which the structural / reduced-form covariance matrix does not change. regime variable categorical numeric variable that identifies volatility regimes regime matrix matrix that pins down the volatile shocks for each volatility state Abbreviations: IH identification through heteroskedasticity IH-BAC IH, Bacchiocchi (2011) method IH-BFA IH, Bacchiocchi/Fanelli (2012) method IH-LLU IH, Lanne/Lütkepohl (2008) method (S)VAR (structural) vector autoregression SIRF structural impulse response function SFEVD structural forecast-error variance decomposition Remarks Remarks are presented under the following headings: Structural VAR IH models Variants of IH models Notation Help file access Structural VAR IH models Structural VAR estimation has a long tradition in economics. Various methods have been proposed to identify the parameters of a structural VAR simultaneous equations model, the most prominent ones being short-run (exclusion/equality) restrictions, long-run restrictions, and sign restrictions. Kilian (2011) provides an excellent overview of the identification methods that have been advanced. Identification through short-run and long-run restrictions have been implemented in official Stata through the svar command. svarih, by contrast, uses identification methods that are based on heteroskedasticity in the data. It posits the existence of different "regimes". This means that the covariance matrix of the structural (as well as the reduced-form) shocks varies over time but remains constant within a certain time span ("regime"). In practice, this often translates into defining a "baseline" regime and one or several "volatility" regimes that deviate from the baseline. Each regime can occur multiple times. The sequence of regimes is unrestricted. There can be gaps in the data. Apart from the existence of different error covariance matrices, the model employed fully corresponds to the standard structural VAR model. In particular, this means that the A-matrix and/or the B-matrix (in AB-model notation; see [TS] svar (manual) and svar (online)), if they are present in the respective SVAR-IH model, contain constant coefficients. IH models achieve identification through positing a priori knowledge about the changing nature of structural shocks, i.e. different volatility regimes. The applicability of IH models thus depends on the plausibility of such assumptions. The advantage of these identification methods is that apart from normalization restrictions no or fewer constraints on the parameters to be estimated are necessary, or that constraints can be imposed in a more flexible way. Since IH models assume different states of volatility, you have to supply the estimation command with information regarding the different volatility periods. All svarih methods take a variable as input that identifies the regimes. svarih bacchiocchi additionally needs a matrix that tells the estimation routine which shocks have modified volatility during each volatility regime. After estimation, you can use dsimih to create SIRFs and SFEVDs. predict generates prediced values, residuals, shocks, and historical decompositions. For these and other postestimation tools, see svarih postestimation. Variants of IH models The seminal contribution in the IH SVAR literature is Rigobon (2003). It consists of an A-model where shock volatility regimes are defined exogenously. To account for correlatedness of the structural shocks, common shocks can be added to the model. There is no asymptotic framework. Standard errors are obtained through a bootstrap. Lanne and Lütkepohl (2008) converted the model to a B-model and added an asymptotic ML framework. Lanne and Lütkepohl (2010) set up a similar B-model that models the residuals as following a mixture normal distribution. Lanne et al. (2010) add Markov-switching properties to a B-model so that regimes are determined endogenously. Bacchiocchi (2011) provides an AB-model ML framework that also allows for different shock propagation in different regimes. Finally, Bacchiocchi and Fanelli (2012) tackle the issue of simultaneous changes in volatility and B-matrix elements. For a survey of these and similar methods, see Lütkepohl (2012). Notation The usage of conflicting notation for VAR and SVAR related model parameters in different publications is an obstacle in understanding and comparing the different methods. To facilitate the understanding of the differenet IH methods and how they compare to the standard svar methods, the notation of svarih leans heavily on the Stata time-series manual entries of var and svar. Notation matters in some instances for command options and for returned e()-values but mostly for the accompanying PDF document on methods and formulas. Help file access The help files for the subcommands of svarih are available under their minimum abbreviated form. For example, type "help svarih bac" instead of "help svarih bacchiocchi". Likewise, the other estimation subcommand help files are accessible under "svarih bfa" and "svarih llu". Help for the postestimation option "svarih, cmat" is available under "help svarih cmat". Help for the utility svarih examples which generate example estimates can be accessed by "help svarih examples". A PDF document called svarihMethodsAndFormulas.pdf that details methods and formulas used in svarih and dsimih is part of the svarih package. During package installation the PDF file is copied into the same directory as svarih.ado. To find the directory where both files are located, you can type . findfile svarih.ado , all Author Daniel C. Schneider, Goethe University Frankfurt, dan_schneider@outlook.com Citation svarih is not an official Stata command. It is a free contribution to the research community, like a paper. Please cite it as such: Schneider, Daniel C. (2014): svarih: Stata Module to Estimate and Analyze Structural VAR Models Based on Selected Methods of Identification through Heteroskedasticity. Downloadable from http://www.dan-schneider.net/stata. Acknowledgements The code of official Stata's svar has served as a point of reference throughout the development of svarih. Any remaining errors in svarih are mine. DISCLAIMER THE SVARIH STATA PACKAGE (THE "SOFTWARE") COMES AS-IS. NO WARRANTIES, EXPRESS OR IMPLIED, ARE GIVEN. ANY CONSEQUENTIAL DAMAGE DUE TO THE USE OF THE SOFTWARE IS THE SOLE RESPONSIBILITY OF THE USER. References Bacchiocchi, E. (2011): Identification in Structural VAR Models with Different Volatility Regimes. Universita Degli Studi di Milano, Working Paper No.2011-39. Bacchiocchi, E. and L. Fanelli (2012): Identification in Structural Vector Autoregressive Models with Structural Changes. Universita Degli Studi di Milano, Working Paper No.2012-16. Kilian, L. 2011. Structural Vector Autoregressions. Working Paper, University of Michigan. Lanne, M. and H. Lütkepohl (2008): Identifying Monetary Policy Shocks via Changes in Volatility. Journal of Money, Credit and Banking, 40 (6), 1131-1149. Lanne, M. and H. Lütkepohl (2010): Structural Vector Autoregressions with Nonnormal Residuals. Journal of Business and Economic Statistics, 28, 159-168. Lanne, M., Lütkepohl, H. and K. Maciejowska (2010): Structural Vector Autoregressions with Markov Switching. Journal of Economic Dynamics and Control, 34, 121-131. Lütkepohl, H. (2012): Identifying Structural Vector Autoregressions via Changes in Volatility. DIW Discussion Papers No.1259. Rigobon, R. (2003). Identification through Heteroskedasticity. The Review of Economics and Statistics 85(4): 777-792. Also see Help: [TS] svar, svarih bac, svarih bfa, svarih llu, svarih postestimation, svarih cmat, dsimih