Finite-Sample Simulation-Based Inference in VAR Models with Applications to Order Selection and Causality Testing
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- Vector autoregression
- VAR
- money and income
- interest rate
- inflation
- [JEL:C32] Mathematical and Quantitative Methods - Econometric Methods: Multiple; Simultaneous Equation Models; Multiple Variables; Endogenous Regressors - Time-Series Models
- [JEL:C12] Mathematical and Quantitative Methods - Econometric and Statistical Methods: General - Hypothesis Testing
- [JEL:C15] Mathematical and Quantitative Methods - Econometric and Statistical Methods: General - Statistical Simulation Methods; Monte Carlo Methods; Bootstrap Methods
- [JEL:E4] Macroeconomics and Monetary Economics - Money and Interest Rates
- [JEL:E5] Macroeconomics and Monetary Economics - Monetary Policy, Central Banking, and the Supply of Money and Credit
- [JEL:C32] Mathématiques et méthodes quantitatives - Méthodes en économétrie; modèles à équations multiples et simultanées - Modèles de séries chronologiques
- [JEL:C12] Mathématiques et méthodes quantitatives - Économétrie et méthodes statistiques; généralités - Tests d'hypothèses
- exact test
- [JEL:C15] Mathématiques et méthodes quantitatives - Économétrie et méthodes statistiques; généralités - Méthodes de simulation statistique: la méthode Monte Carlo
- [JEL:E4] Macroéconomie et économie monétaire - Monnaie et taux d'intérêt
- [JEL:E5] Macroéconomie et économie monétaire - Politique monétaire, banque centrale, masse monétaire et crédit
- Monte Carlo test
- maximized Monte Carlo test
- bootstrap
- Granger causality
- order selection
- nonstationary model
- macroeconomics
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Abstract
Statistical tests in vector autoregressive (VAR) models are typically based on large-sample approximations, involving the use of asymptotic distributions or bootstrap techniques. After documenting that such methods can be very misleading even with fairly large samples, especially when the number of lags or the number of equations is not small, we propose a general simulation-based technique that allows one to control completely the level of tests in parametric VAR models. In particular, we show that maximized Monte Carlo tests [Dufour (2002)] can provide provably exact tests for such models, whether they are stationary or integrated. Applications to order selection and causality testing are considered as special cases. The technique developed is applied to quarterly and monthly VAR models of the U.S. economy, comprising income, money, interest rates and prices, over the period 1965-1996.