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Structural VAR and Finance

Structural VAR and Finance. Abstract In this paper, I discuss VAR (vector autoregression) framework, which is widely used in finance and economics to examine dynamic relations among variables. I also discuss the identification of VAR model (structural VAR) using several examples from finance.

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Structural VAR and Finance

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  1. Structural VAR and Finance Abstract In this paper, I discuss VAR (vector autoregression) framework, which is widely used in finance and economics to examine dynamic relations among variables. I also discuss the identification of VAR model (structural VAR) using several examples from finance. Bong Soo Lee

  2. I. Introduction/Motivations - Dynamic effects in a multivariate system • The effect of financial news on stock prices (or returns) [r, y, , d, c  P (or sr)] ex. Chen, Roll, Ross (JB, 1986) • Analysis of policy effects (Ms, G) on stock market - Relative importance APT (DY, TP, , IPG, Ms, TOT, EX RATE, oil price,…) CECF (NAV or USMR) Second board market returns (e.g., NASDAQ, KOSPI, KOSDAQ)

  3. Empirical tool: VAR (vector autoregression) framework - Identification issue: under-identified VAR • Cholesky identification: Ordering issue • Permanent/temporary shocks (components), • substitution/complement shocks, • positive/negative shocks. - Theroleof theory

  4. II. VAR (vector autoregression) framework • Dynamic effects (impulse responses) a. VAR (vector autoregressive representation)

  5. b. MAR (moving average representation)

  6. C. Orthonormalized MAR

  7. - Examples: • The effect of financial news on stock prices (or returns) [r, y, , d, c  P (or sr)], ex. Chen, Roll, Ross (JB, 1986) • Analysis of policy effects (Ms, G) on stock market • Stylized facts (dynamic relation) • Transmission mechanism (ex. Volatility, …)

  8. 2. Forecast error decompositions --- relative importance.

  9. - Applications • relative importance • exogeneity of (policy) variables • causal relations - examples: • APT (DY, TP, , IPG, Ms, TOT, EX RATE, oil price,…) • CECF (NAV or USMR) [Lee and Hong (JIMF, 2002)] • Second board market returns (e.g., NASDAQ, KOSPI, KOSDAQ) [Lee, Rui, and Wang (JFR, 2003)]

  10. Identification: Under-identified system of VAR Note: Dynamic effects and relative importance are based on the orthonormalized MAR coefficients C(L).

  11. Question: Given estimates of A(L) and , how to identify C(L)? Clue (match):

  12. Identification 1. Cholesky decomposition • Cholesky decomposition imposes a certain ordering c120 = 0 • [2nd variable does not affect the first variable contemporaneously] • u2 has no contemporaneous effect on X1. • Place an exogenous variable first [e.g., policy variable (Ms, G,…)]

  13. Note : trivariate case • in general, the ordering of variables in VAR matters

  14. Identification 2. Permanent/temporary restriction [Blanchard & Quah (1989)]

  15. - Applications: • Permanent earnings hypothesis of dividend [ Lee (RFS, 1996)]. • Stock market responds more strongly to permanent earnings [Lee (JFQA, 1995)]. • Permanent, temporary, and non-fundamental components of stock prices [Lee (JFQA, 1998)]. • Stock returns and inflation [Hess and Lee (RFS, 1999)] • Payout policy (Flexibility Hypothesis): Dividends are related to permanent earnings, and share repurchases are related to transitory earnings [Lee and Rui (JFQA, 2007)].

  16. Application 2.1 Dynamic dividend behavior [Lee (RFS, 1996)]

  17. Model 1. Dividends are proportional to the permanent component of earnings: • Characterized by the restriction that C12(L) = C21(L) = 0. Implications: • Temporary changes in earnings do not affect dividend (changes). • Permanent changes in earnings do not affect the spread.

  18. Model 2. Dividends are proportional to a present discounted value of future expected earnings:

  19. Earnings and dividends respond proportionately to transitory changes in earnings so their net effect on the spread is zero. • This requires dividends to respond to the transitory changes in earnings. • Against the permanent earnings hypothesis (PEH).

  20. Application 2.2 Permanent & temporary components in stock prices [Lee (JFQA, 1995)] Proposition: The stock price valuation model (PV model) is characterized by the restriction c12(1)=0 on the following bivariate model:

  21. Comparison w/ Fama & French (1988). (i) F/F assume that log stock price is the sum of r.w. and an AR(1) process. Lee (1995) does not restrict the permanent component to be a r.w. and the temporary component to be an AR (1) process. The data determines the two components. (ii) In F/F, price is not related to dividends. In Lee, price components are due to dividend components, and they are related by the stock price valuation model. (iii) F/F model predicts ARMA (1,1) model of stock returns.  US data implies ARMA (2,2) model.

  22. Application 2.3 Permanent, temporary, and non-fundamental components of stock prices: Lee (JFQA, 1998) - Use log-linear models • Model.

  23. Proposition 1. Models of earnings, dividends, and prices in case 1 are characterized by the restrictions

  24. Proposition 2. Models in case 2 are characterized by the restrictions

  25. Proposition 3 . Models in case 3 are characterized by the restrictions

  26. Application 2.4 Stock returns and inflation with supply and demand disturbances: Hess and Lee (1999, RFS) • Theoretical model is characterized by the restriction

  27. - Motivation and observation: srt and t are negatively correlated in post-war period, but positively correlated in pre-war period. - Findings and our results: • Supply components of srt and t are negatively correlated, whereas demand components are positively correlated. • Supply component (shock)------permanent • Demand component (shock)------temporary • Supply shock is more important in post-war period, but demand shock is more important in pre-war period.

  28. Application 2.5 Flexibility Hypothesis (Temporary Cash Flow): • Lee and Rui (JFQA, 2007) Dividends: ongoing commitment, to distribute permanent cash flows, Share repurchases: to pay out temporary cash flows, thus preserve financial flexibility relative to dividends - Jagannathan et al. (2000), Guay and Harford (2000), Lie (2000) et al. (2000) • = permanent shock and = temporary (or stationary) shock.

  29. - Identification: . • H0: RP are not related to the permanent component of earnings, . • H0: RP are not related to the temporary component of earnings, . • H0: Div are not related to the permanent component of earnings, . • H0: Div are not related to the temporary component of earnings, .

  30. Identification 3. Substitutes and complements • zt = [X1t, X2t]' = C(L) t, or restriction on the substitution disturbance, ts : the coefficients in C12(L) and C22(L) add up to zero: k c12k + k c22k = C12(L)|L=1 + C22(L)|L=1 = C12(1) + C22(1) = 0, where Cij(L)|L=1 = Cij(1) = k cijk represents the cumulative effect of the j-th disturbance on the i-th variable over time. • Examples: • payout policy: dividends versus share repurchases • stocks and bonds: correlations vary • Banking sector versus stock market in economic development

  31. Application 3.1 The Substitution Hypothesis : Lee and Rui (JFQA, 2007) • Grullon and Michaely (2002): corporations have been substituting share repurchases for dividends. • Jagannathan et al. (2000): repurchases seem to serve the complementary role of paying out short-term cash flows and not appear to be replacing dividends. • the following bivariate moving average representation (BMAR): , = the complement shock, = the substitution shock; • Identification of Substitution and Complement Effects

  32. Application 3.2 Correlation Coefficients between Stock and Bond Returns Table 1. Correlation Coefficients between Stock and Bond Returns Panel A. Based on Monthly Real Returns Period Canada  Germany  Japan   U.K. U.S.  86-99 23.94%*** 23.61%*** 10.68% 39.36% *** 25.67%*** 00-07 -6.13% -45.31%*** -30.95%***-20.39%** -35.90%*** 86-07 15.91%*** 1.44% 4.90% 27.12%*** 4.00% Q: How to understand different corr. across countries and over time?(Hong, Kim, & Lee (2009, WP))

  33. zt = [Rt, Qt]' = C(L) t, or where Rt = stock return; Qt = bond returns; t is a 2 x 1 vector consisting of ty and ts ; ty = income effect shock; ts = substitution effect shock • Identifying restriction:

  34. Identification 4. Positive and negative shocks / components zt = [X1t, X2t]' = C(L) t, or Restrictions: c110 + c120 = 0 • Examples: 1. stock returns and volatility 2. stock returns and inflation: to identify two sources of shocks: Lee (2009, JBF)

  35. - Observation: • Between stock returns and inflation, we observe + and -correlation in pre-war and post-war period, respectively. - Interpretation: • both +/- shocks to inflation have positive effect on SR. • AD shock drives a + correlation between inflation and SR, while AS shock drives a – correlation; • + inflation shock that reflects AD is more important in pre-war period, and - inflation shock that reflects AS is more important in post-war period. • we observe + correlation between stock returns and inflation in pre-war period, and – correlation in post-war period. • Not easily compatible with ‘the inflation (money) illusion hypothesis’ that anticipates only negative correlation.

  36. III. Concluding Remarks -VAR: dynamic effects & relative importance -VAR: under-identified -To achieve identification: introduce restrictions from theory and test implications (hypotheses) -Examples • permanent/temporary • Substitutes/complements • Positive/negative

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