英语论文网

Empirical Finance:Analysis of non-stationary processes II: Estimating and testing long-run relationships in systems of equations
Module Leader: Dr Stuart Fraser
stuart.fraser@wbs.ac.uk
代写留学生论文Room D1.18 (Social Studies)Warwick Business School 2
Today
1. Key problems with Engle-Granger 2 Step Estimator.
2. VAR and VECM models.
3. ‘Johansen’: A systems approach to testing for cointegration.
Seminar 8: Testing PPP using Johansen
Warwick Business School 3
Problems with EG 2 step: 1. Presence of multiple cointegratingrelationships.A key problem with EG 2 step is that it can only identify a single cointegratingrelationship.Single equation OLS is used to estimate the long-run (Step 1).However with n variables there can be up to n-1cointegratingrelationships (see Appendix 1):If EG 2 Step is used in this context we may end up estimating some unidentified linear combinationof all the cointegratingrelationships.1−≤nr‘r’is standard notation for the number of cointegratingrelationshipsNeed at least one I(1) linear combinationwhich corresponds to the common stochastic trend(s):n-r≥1If r=n then all the variables must be individually I(0) (see Appendix 1). ⇒with n>2 there can be multiple cointegratingrelationships (r>1)
Warwick Business School 4
Example: Testing the Expectations Hypothesis of the term structure (see Brooks 7.12 and lecture 7).A test of the EH could be based on testing for cointegrationamongst pairs of yieldsof different maturities.However, a more comprehensive (and powerful) test could be based on a vector of yieldsfrom across the maturity spectrumNormalizing the spreads on the one period spot rate, EH implies there are n-1 (linearly independent) spreads which are I(0): ()()()()1,1~1,1~1001010100112CIyCIRRRtntttβ′⇒⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛−−−MKMMKK()()njCIRRjtt,,2 ,1,1~K=−(). theare ) of (rows of columns Thematrix. 1an is vectors ingcointegratβββ′−×nnIn matrix form ⇒()()()()()1,1~,,2,CIRRnjRRktjtjttjt−⇒=+Τ+=KεThe EH (+rational expectations)implies the yield spreads arecointegrated.Warwick Business School 5
Problems with EG 2 step: 2. EG 2 step is an inefficient estimator On one level the distinction between exogenous and endogenous variables is unimportant with cointegratedvariables.–Super-consistency still holds even if X is endogenous:So in effect it doesn’t matter which variable (Y or X) we make the ‘dependent variable’:ββεββ⎯→⎯+=ΣΣ−−piiixTxTˆˆ211With cointegratedvariables super-consistency still holdsin the long run equation even if X is endogenous. Why? Because the sample variance of X tends to ∞(X is I(1)).This is in sharp contrast to the CLRM where Y and X are assumed to be I(0). In that case endogeneityimplies the OLS estimator is inconsistent (see Lecture 4).***ttttttYXXYεβμεβμ++=++=Either regression will yield super-consistent estimates of the long run parameters.For example, with PPP we ‘normalized’the relationshipon log(S) (log nominal exchange rate). However we might just as well have normalized on log(P) or log(P*).Warwick Business School 6
Problems with EG 2 step: inefficiencyHowever this also means we can write an ECM for X. Starting from the ADL for X……the corresponding ECM for X is:Therefore Y and X form a systemof本论文由英语论文网提供整理，提供论文代写，英语论文代写，代写论文，代写英语论文，代写留学生论文，代写英文论文，留学生论文代写相关核心关键词搜索。