Abstract
The previous chapter presented a statistical approach to analyse the relations between time series: starting with univariate models, we asked for relations that might exist between two time series. Subsequently, the approach was extended to situations with more than two time series. Such a procedure where models are developed bottom up to describe relations is hardly compatible with the economic approach of theorising where – at least in principle – all relevant variables of a system are treated jointly. For example, starting out from the general equilibrium theory as the core of economic theory, all quantities and prices in a market are simultaneously determined. This implies that, apart from the starting conditions, everything depends on everything, i.e. there are only endogenous variables. For example, if we consider a single market, supply and demand functions simultaneously determine the equilibrium quantity and price.
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References
The methodology of vector autoregressive processes was first proposed by
CHRISTOPHER A. SIMS, Macroeconomics and Reality, Econometrica 48 (1980), pp. 1 – 48.
This is the main paper for which he got the Nobel Prize in 2011.
KATARINA JUSELIUS, The Cointegrated VAR Model: Methodology and Applications, Oxford University Press, Oxford 2006, chapter 3
with reference on
DAVID HENDRY and JEAN-FRANÇOIS RICHARD, The Econometric Analysis of Economic Time Series (with discussion), International Statistical Review 51 (1983), pp. 111 – 163,
showed that, assuming multivariate normality and time independent first and second moments, the vector autoregressive model is the result of the sequentially decomposition of the joint distribution of the k-dimensional stochastic process X into T conditional distribution functions.
Applications can be found, for example, in
CHRISTOPHER A. SIMS, Comparing Interwar and Postwar Business Cycles: Monetarism Reconsidered, American Economic Review, Papers and Proceedings, 70.2 (1981), pp. 250 – 257; or
CHRISTOPHER A. SIMS, Policy Analysis with Econometric Models, Brookings Papers on Economic Activity 1/1982, pp. 107 – 164.
The presentation in this chapter is mainly based on
HELMUT LÜTKEPOHL, New Introduction to Multiple Time Series Analysis, Springer, Berlin 2005, pp. 13 – 82, 135 – 157.
This textbook offers a comprehensive presentation of this concept and its possibilities. It also shows how confidence intervals can be calculated for impulse response functions (pp. 109ff.). In addition, it compares different criteria to determine the optimal lag length of the VAR (pp. 135ff.). Proficient introductions are given in
GEORGE G. JUDGE, R. CARTER HILL, WILLIAM E. GRIFFITHS, HELMUT LÜTKEPOHL and TSOUNG-CHAO. LEE, Introduction to the Theory and Practice of Econometrics, Wiley, New York 1988, Chapter 18;
WALTER ENDERS, Applied Econometric Time Series, Wiley, Hoboken NJ, 3rd edition 2010, Chapter 5, as well as in
JAMES H. STOCK and MARK W. WATSON, Vector Autoregressions, Journal of Economic Perspectives 15/4 (2001), pp. 101 – 115.
In this article it is assessed how well VAR models have addressed the four macroeconomic tasks: data description, forecasting, structural inference, and policy analysis. A short introduction is also given in
DONALD ROBERTSON and MICHAEL WICKENS, VAR Modeling, in: STEVEN G. HALL (ed.), Applied Economic Forecasting Techniques, Harvester Wheatsheaf, New York 1994, pp. 29 – 47.
Error correction models were first used in an investigation on wages and prices in the United Kingdom carried out by
J. DENIS SARGAN, Wages and Prices in the United Kingdom: A Study in Econometric Methodology, in: P.E. HART, G. MILLS and J.K. WHITAKER (eds.), Econometric Analysis for National Economic Planning, Butterworth, London 1962, pp. 25 – 54.
This concept became popular by a paper about the consumption function in the United Kingdom,
JAMES E.H. DAVIDSON, DAVID F. HENDRY, FRANK SRBA and Y. STEPHEN YEO, Econometric Modelling of the Aggregate Time Series Relationship between Consumers‘ Expenditure and Income in the United Kingdom, Economic Journal 88 (1978), pp. 661 – 692.
The LSE approach, that goes back to J. DENIS SARGAN and DAVID F. HENDRY, is described and confronted with other approaches in
ADRIAN PAGAN, Three Econometric Methodologies: A Critical Appraisal, Journal of Economic Surveys 1 (1987), pp. 3 – 24.
A comprehensive introduction to this approach is presented in a textbook by
DAVID F. HENDRY, Dynamic Econometrics, Oxford University Press, Oxford et al. 1995.
The difference between statistical and econometric approaches to empirically analyse economic problems is discussed, for example, in
CLIVE W.J. GRANGER, Comparing the Methodologies Used by Statisticians and Economists for Research and Modeling, Journal of Socio-Economics 30 (2001), pp. 7 – 14.
For the structural VAR see, for example
GIANNI AMISANO and CARLO GIANNINI, Topics in Structural VAR Econometrics, Springer, Berlin et al., 2nd edition 1997,
JÖRG BREITUNG, RALF BRÜGGEMANN and HELMUT LÜTKEPOHL, Structural Vector Autoregressive Modeling and Impulse Responses, in: H. LÜTKEPOHL and M. KRÄTZIG Applied Time Series Econometrics, Cambridge University Press, Cambridge 2004, pp. 159 – 196.
Different identification schemes for VARs are developed by
OLIVER J. BLANCHARD and DANNY QUAH, The Dynamic Effects of Aggregate Demand and Supply Disturbances, American Economic Review 79 (1989), pp. 655 – 673, and
HARALD UHLIG, What are the Effects of Monetary Policy on Output? Results from an Agnostic Identification Procedure," Journal of Monetary Economics 52 (2005), pp. 381 – 419.
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Kirchgässner, G., Wolters, J., Hassler, U. (2013). Vector Autoregressive Processes. In: Introduction to Modern Time Series Analysis. Springer Texts in Business and Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33436-8_4
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