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 1

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 (  M s,  G) on stock market - Relative importance APT (DY, TP, , IPG, M s, TOT, EX  RATE, oil price,…) CECF (NAV or USMR) Second board market returns (e.g., NASDAQ, KOSPI, KOSDAQ) 2

-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. - The role of theory 3

II. VAR (vector autoregression) framework 1.Dynamic effects (impulse responses) a. VAR (vector autoregressive representation) 4

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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 (  M s,  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, M s, 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

3.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

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Identification 1. Cholesky decomposition Cholesky decomposition imposes a certain ordering c 12 0 = 0 [2 nd variable does not affect the first variable contemporaneously] 1. u 2 has no contemporaneous effect on X Place an exogenous variable first [e.g., policy variable (M s, G,…)] 14

Note : trivariate case in general, the ordering of variables in VAR matters 15

Identification 2. Permanent/temporary restriction [Blanchard & Quah (1989)] 16

- 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)]. 17

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Application 2.1 Dynamic dividend behavior [Lee (RFS, 1996)] 19

Model 1. Dividends are proportional to the permanent component of earnings:  Characterized by the restriction that C 12 (L) = C 21 (L) = 0. Implications: Temporary changes in earnings do not affect dividend (changes). Permanent changes in earnings do not affect the spread. 20

Model 2. Dividends are proportional to a present discounted value of future expected earnings: 21

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). 22

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 c 12 (1)=0 on the following bivariate model: 23

-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. 24

Application 2.3 Permanent, temporary, and non- fundamental components of stock prices: Lee (JFQA, 1998) - Use log-linear models Model. 25

Proposition 1. Models of earnings, dividends, and prices in case 1 are characterized by the restrictions 26

Proposition 2. Models in case 2 are characterized by the restrictions 27

Proposition 3. Models in case 3 are characterized by the restrictions 28

Application 2.4 Stock returns and inflation with supply and demand disturbances: Hess and Lee (1999, RFS) Theoretical model is characterized by the restriction 29

- Motivation and observation: sr t and  t are negatively correlated in post-war period, but positively correlated in pre-war period. -Findings and our results: Supply components of sr t 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. 30

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. 31

-Identification:. H 0 : RP are not related to the permanent component of earnings,. H 0 : RP are not related to the temporary component of earnings,. H 0 : Div are not related to the permanent component of earnings,. H 0 : Div are not related to the temporary component of earnings,. 32

Identification 3. Substitutes and complements z t = [X 1t, X 2t ]' = C(L)  t, or restriction on the substitution disturbance,  t s : the coefficients in C 12 (L) and C 22 (L) add up to zero:  k c 12 k +  k c 22 k = C 12 (L)| L=1 + C 22 (L)| L=1 = C 12 (1) + C 22 (1) = 0, where C ij (L)| L=1 = C ij (1) =  k c ij k 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 33

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 34

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 %*** 23.61%*** 10.68% 39.36% *** 25.67%*** % %*** %***-20.39%** %*** %*** 1.44% 4.90% 27.12%*** 4.00% Q: How to understand different corr. across countries and over time? (Hong, Kim, & Lee (2009, WP)) 35

z t = [R t, Q t ]' = C(L)  t, or where R t = stock return; Q t = bond returns;  t is a 2 x 1 vector consisting of  t y and  t s ;  t y = income effect shock;  t s = substitution effect shock Identifying restriction: 36

Identification 4. Positive and negative shocks / components z t = [X 1t, X 2t ]' = C(L)  t, or Restrictions: c c 12 0 = 0 Examples: 1. stock returns and volatility 2. stock returns and inflation: to identify two sources of shocks: Lee (2009, JBF) 37

Application 4.1 Stock returns and volatility 38

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Application 4.2 Stock returns and inflation 40

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- 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. 42

III. Concluding Remarks -VAR: dynamic effects & relative importance -VAR: under-identified -To achieve identification: introduce restrictions from theory and test implications (hypotheses) -Examples (i)permanent/temporary (ii)Substitutes/complements (iii)Positive/negative 43