Consumption-Wealth Ratio and Japanese StockMarket

Kohei Aono, Hitotsubashi UniversityTokuo Iwaisako, Hitotsubashi University

First draft: January 2006

October 5, 2006

Consumption-Wealth Ratio and Japanese Stock Market*

Abstract

We examine if consumption/wealth ratio can explain Japanese stock market data,

following Lettau and Ludvigson (2001a, b). We construct the data series of cayt,

the residuals from the cointegration relationship between consumption and total

wealth of household. Unlike US results, cayt does not predict future Japanese

stock returns. On the other hand, it does help to explain cross-section of Japanese

stock returns of industry portfolios. In US case, cayt comes in as a scaling variable

which explains time-variation of market beta. In Japanese case, the movement of

cayt will be interpreted as the change in the constant terms, hence the changes

of average stock returns. We also propose to improve cayt by taking real estate

wealth into consideration.

JEL Classification: G12, E21, E23, N12.

Keywords: Consumption-wealth ratio; Cointegration; Cross-section of stock re-

turns.

Kohei Aono, Ph.D. student, Graduate School of Economics, Hitotsubashi

University.

Tokuo Iwaisako†, Institute of Economic Research, Hitotsubashi University.

* Acknowledgements: We thank Hitoshi Takehara, the participants of Hitot-

subashi macro lunch and NFA 2006 meeting for their comments. Iwaisako

greatly acknowledges financial assistance from Japan Society for Promotion

of Science 18330067 “Macro-variables and Cross-section of Stock Returns.”

† Corresponding author. E-mail address: iwaisako@ier.hit-u.ac.jp

1

1 Introduction

Consumption-based asset pricing model is among most important bench-

marks in financial economics. Yet, its empirical performance has been a

major disappointment for researchers (see Campbell 2003 for recent survey).

After numerous failed attempts, researchers seem to stop estimating the

Euler equation using aggregate data which was derived from consumption-

based model with “deep structural parameters.”

An obvious alternative research strategy is to use disaggregate consump-

tion data, such as “stockholders vs non-holders” distinction by Mankiw

and Zeldes (1991) and Vissing-Jorgensen (2002). At the same time, some

researchers including Lettau and Ludvigson (2001a, b), Parker and Jul-

liard (2003), and Yogo (2006), have recently started to explore different

aspects of the joint decision of consumption allocation and asset pricing.

Still using aggregate data, they consider less stringent restrictions implied

by consumption-based model than the direct estimation of Euler equations

and obtain some more fruitful empirical results. In particular, Lettau and

Ludvigson (2001a, b) considered the long-run cointegration relationship be-

tween consumption and total financial wealth. They proposed to use the

“cay” variable which is, in essence, consumption-wealth ratio of household

sector, in explaining various aspects of U.S. stock returns. They obtain suc-

cessful results both in predicting aggregate stock return and in explaining

cross-sectional pattern of US stock market.

In this paper, we examine if Lettau and Ludvigson’s framework works

with Japanese data. First, we carefully construct the “cay” variable for

Japan following Lettau and Ludvigson’s manner about US data. Then, we

test if the “cay” variable forecasts future stock returns (Lettau and Ludvig-

son 2001a) and if it helps to explain cross-section of stock returns (Lettau

and Ludvigson 2001b). We find negative answer for the first question, but

positive answer for the second question.

At least two other papers are also examining Lettau and Ludvigson’s

framework with Japanese data. Gao and Huang (2004) examine mostly

2

same topics as we are examining in this paper. However, we are more care-

ful in constructing Japanese consumption and financial wealth data series

so that our definition of variables are more analogous to Lettau and Lud-

vigson’s with US data. This perhaps explains why their empirical results

are very different from ours. Matsuzaki (2003) constructed Japanese con-

sumption and financial wealth data set mostly as we are doing in this paper

(his definition of consumption data is slightly different from ours). He ob-

tained basically the same result for aggregate stock return predictability

with longer data series than ours1. However, he did not examine cross-

sectional pattern. Finally, we attempt to include real estate wealth to the

cointegration relationship in calculating “cay”, which is both paper did not

do.

The remaining of this paper is organized as follows. In section 2, we

summarize the framework proposed by Lettau and Ludvigson. Section 3

discusses about the Japanese data construction. Section 4 presents main

empirical results. Section 5 makes final remarks.

2 Analytical framework

We start our heuristic discussion from Hall’s version of permanent income

hypothesis with forward looking consumers (Hall 1978). Assuming quadratic

utility and infinite horizon, we got the following expression for consumption

level of households.

Ct =i

1 + i

"At +Et

TXs=1

µ1

1 + i

¶−sYt+s

#∀t (1)

Ct = α (At +Ht)

where Ht = EtTXs=1

µ1

1 + i

¶−sYt+s

Equation (1) implies that current consumption of a household should be

the fraction of total financial wealth (At) and the present value of future

1We confirmed his results with our data in the earlier version of ours paper.

3

labor income stream (Ht). Rearranging equation (1), we have a constant

consumption-wealth ratio:

α =Ct

(At +Ht)(2)

We will not claim that Hall’s version of permanent income hypothesis

is an accurate description of individual households’ behavior. Still, we ex-

pect it is a good first approximation of aggregate consumption data. That

is consumption (Ct) and total wealth of household defined as the sum of

financial wealth and human wealth by (At +Ht) would have stable long-run

relationship. Statistically speaking, this means that equation (2) implies

Ct, At, and Ht should be cointegrated.

In a more formal context, Lettau and Ludvigson (2001a,b) use the coin-

tegration among consumption, financial wealth, and human wealth to draw

the implication for stock returns. Their argument starts from the following

very general intertemporal budget constraint:

Wt+1 = (1 +Rw,t+1)(Wt − Ct) (3)

Applying the log-linear approximation proposed by John Campbell (Camp-

bell 1991; Campbell and Shiller 1988) to (3), we get the following relation-

ship:

∆wt+1 ≈ k + rw,t+1 + (1− 1/ρw)(ct − wt) (4)

ρw ≡ (W − C)/W

where lowercase letters are natural logs of the variables in equation (3) and

rw,t+1 = ln(1 +Rw,t+1).

We solve the difference equation (4) forward imposing the “no bubble”

condition limi→∞ρiw(ct+i − wt+i) = 0. After some tedious calculations, weget the following expression for the ex post log consumption-wealth ratio

ct − wt.

ct − wt =∞Xi=1

ρiw(rw,t+1 −∆ct+i) (5)

4

If investors are rational, ex ante expression must hold too.

ct − wt = Et∞Xi=1

ρiw(rw,t+1 −∆ct+i) (6)

As we did in the simpler version in equation (2), we assume the total

wealth of households consist of financial wealth at and human wealth ht (i.e.,

net present value of future labor income stream).

wt ≈ ωat + (1− ω)ht

Hence, we get the following expression for log return using the log linear

approximation:

1 +Rw,t = ωt(1 +Ra,t) + (1− ωt)(1 +Rh,t)

rw,t ≈ ωra,t + (1− ω)rh,t (7)

Substituting this into ex ante budget constraint, we get

ct − ωat − (1− ω)ht = Et

∞Xi=1

ρiw {[ωra,t+i + (1− ω)rh,t+i]−∆ct+i}

Since we cannot observe human wealth ht directly, we assume ht =

κ+ yt + zt and substitute ht by observable current labor income yt.

ct − ωat − (1− ω)yt (8)

= Et

∞Xi=1

ρiw {[ωra,t+i + (1− ω)rh,t+i]−∆ct+i}+ (1− ω)zt

RHS variables of (8) are all stationary, so the sum of LHS should be station-

ary too. This implies we have stationary relationship among LHS variables

{ct, at, yt}, that is, they are cointegrated.

Finally, following Lettau and Ludvigson, we define the “cay” variable as

follows.

cayt ≡ ct − ωat − (1− ω)yt (9)

5

Since ω is not time varying, this is essentially consumption-wealth ratio, in

which total wealth of household defined by the sum of financial and human

wealth. Economic theory implies the long-run consumption-wealth ratio

should be stable, so that cayt should be stationary.

Lettau and Ludvigson estimate cointegration regression (9) to obtain

the time series of cayt. In Lettau and Ludvigson (2001a), they use cayt to

forecast future stock return. In Lettau and Ludvigson (2001b), they showed

cayt explains cross-section of stock returns in US market.

3 Constructing Japanese data

3.1 Data

In this sub section, we summarize Japanese data used in this paper. For

detailed discussions on the data construction, please refer to the data ap-

pendix.

[We prepared a short note for the data construction in Japanese (Aono and

Iwaisako, 2006). In the future revision, English translation of this short note

will be added as the data appendix.]

Our consumption series is household expenditure on nondurables and ser-

vices, excluding shoes and clothing. This definition of consumption follows

US benchmark by Wilcox (1992) as well as Lettau and Ludvigson (2001a,b).

Data series is taken form Japanese Cabinet Office’s Annual Report on Na-

tional Accounts and are seasonally adjusted using E-views’ X-12 command.

Then, the data is converted to log real per capita consumption series de-

noted by ct. Unfortunately, this definition of Japanese consumption data is

available only from 1970 and later.

Financial wealth here is household financial asset measured at the end

of each period. It includes total of all deposits and cash currency, trusts,

securities investment trusts, insurance and securities. Data is taken from the

Bank of Japan’s Flow of Funds Accounts (entries personal stock or household

6

stock) data. Using this measure of financial wealth, we construct log real

per capita financial wealth series at.

Our labor income is after-tax income reported in Annual Report on Na-

tional Accounts tabulated by Japanese Cabinet Office. The log of after-tax

labor income, yt, is also measured in real per capita terms.

3.2 Estimating cointegration relationship

Next, we estimate cointegration regression by dynamic OLS to obtain the

series of cayt. We follow Lettau and Ludvigson(2001a,b) and used dynamic

least squares technique of Stock and Watson (1983) that specifies a single

equation taking the following form:

ct = α+ βaat + βyyt +kX

i=−kba,i∆at−i +

kXi=−k

by,i∆yt−i + ²t (10)

where ∆ denote the first difference operator. We denote the estimated trend

deviation by ˆcay = ct − β̂aat − β̂yyt, where “hats” denote estimated para-

meters.2

Our consumption series “household expenditure on nondurables and ser-

vices, excluding shoes and clothing” only goes back to 1970. So our sample

period in estimating (10) starts from the first quarter of 1970 and ends at

the first quarter of 2004. The following is our full sample estimate.

ct = 3.2565 + 0.3125at + 0.2242yt(17.481) (9.677) (3.745)

(11)

Values in parentheses under the parameter estimates are corresponding t-

statistics.

We also estimate using the sample after the first oil crisis. This sub sam-

ple is the first quarter of 1975 to the first quarter of 2004 and the following

is the sub sample estimate.

ct = 3.011 + 0.2472at + 0.3426yt(4.520) (3.383) (2.108)

(12)

2Following Lettau and Ludvigson(2001), we adopt to k = 8. However, we obtain verysimilar cayt series even we use different number of lags.

7

Sub sample parameter estimates are not very far from the full sample. In

fact, as discussed in the data appendix, we obtain very similar data series for

ˆcay from alternative sample periods. In earlier version, we also considered

potential structural breaks in cointegration relationship using automated

structural break tests such as Gregory and Hansen (1996) and examined

various sub samples. Overall, obtained ˆcay series are very similar to each

other and their predictive abilities for aggregate stock returns are also very

similar. Hence, we concentrate to ˆcayt calculated as residuals of the sub

sample estimation in equation (12) in our following analyses.

3.3 Including real estate wealth

Most important component of Japanese households wealth is, of course, real

estates (Iwaisako 2003; Iwaisako, Mitchell, Piggott 2005). Hence, we also try

to include real estates into the household wealth data. Unfortunately, there

is no quarterly Japanese real estates price data at aggregate level. So we

take two alternative strategies in calculating cayt series including real estate

wealth. The first strategy is to use national real estate wealth valuation in

GDP statistics. Only annual observations exist for this time series. We filled

missing observations by simple spline interpolations. Admittedly, this is very

crude procedure since three out of four observations are interpolations. We

add these values to financial wealth to get the series for log total wealth twt

and then we estimate the cointegration regression as follows:

ct = 1.9813 + 0.1485twt + 0.5768yt(2.459) (1.694) (2.874)

(13)

and tabulate cayt series just we did in the previous subsection.

In the second approach, we use the urban area land price index (Shigaichi-

kakaku-shisu) tabulated by Japan Real Estate Institute3. We choose its

all-purpose nationwide average index lwt and include it in the cointegration

regression as an element independent from financial wealth at.

ct = 2.7859 + 0.2455at + 0.3702yt − 0.0137lwt(3.272) (2.442) (1.673) (−0.479) (14)

3Available from their website: http://www.reinet.or.jp/jreidata/a_shi/index.htm

8

As in equation (12), the sample period for equation (13) and (14) is the first

quarter of 1975 to the first quarter of 2004.

4 Empirical results

In this section, we examine if cayt helps to forecast future stock returns and

if it helps to explain the cross-section of stock returns with the Japanese

data.

4.1 Forecasting future stock returns

While Lettau and Ludvigson (2001a) found cayt predicts future stock re-

turns in the US, we find this is not the case for Japan. The results are

reported in Table 1. In some specifications, cayt seems to predicts future

stock returns. However, if the lagged returns are included in the regres-

sion, its predictive power disappears. Furthermore, the sign of estimated

coefficients of cayt are negative in all specifications. This contradicts with

what economic theory predicts and the empirical evidence for US market.

Overall, we find very little evidence that cayt is useful in predicting future

stock returns in Japanese stock market.

We consider this result is not surprising. From 1987 to the end of 1989,

Japanese stock market had experienced the tremendous boom of historical

magnitude. It was followed by a sharp decline in 1990-1992. Because the

sample contains such a significant one-time event, any study on Japanese

aggregate stock returns including this period faces major empirical difficulty.

Theoretically, the framework proposed by Lettau and Ludvigson imposes

the “no bubble” condition in deriving expression for log consumption-wealth

ratio in equation (4) and (5) from equation (3). This condition rules out

the “bursting bubble” type deviation from the long-run equilibrium. One

way to understand the deviation from long-run cointegration relationship in

late 1980s is that the “no bubble” condition had been actually violated in

this period. Alternatively, we may interpret Japanese bubble in 1980s as a

9

very large one-time deviation which requires much longer time to turn back

to the long-run relationship. Hence, stock return had been predictable, but

only for very long-run, for example, the five-year period.

4.2 Explaining cross-section of stock returns

Next we examine if cayt helps to explain the cross-section Japanese stock

returns. Here, we use 28 industry portfolio returns tabulated by Japan Secu-

rities Research Institute (JSRI). We combined JSRI data with Fama-French

factors (HML and SMB) calculated by Nikkei Media Marketing whose data

construction closely follows the series of works by Keiichi Kubota and Hitoshi

Takehara on Fama-French factors with Japanese data.4 Then, we convert

all asset return and factor data into quarterly basis to implement empirical

analysis along with cayt series.

Following Lettau and Ludvigson (2001b), we used Fama-MacBeth’s two

step approach to examine performances of alternative factors in explaining

cross-section of Japanese stock market. In the first step, quarterly industry

portfolio returns are regressed on alternative sets of factors and conditioning

variables.

ri,t = β0 + Ftβ1,i + Zt−1β2,i i = 1, .., 28.

Then in the second step, average returns are regressed on the betas estimated

in the first step.

E[ri,t] = E[r0,t] + bβiλbβ =hbβ1,i, bβ2,ii (15)

Ft is the vector of factors including following variables:

Rvwt Market portfolioY Gt Labor income growthSMBt Fama-French SMB factorHMLt Fama-French HML factor

4See for example Jagannathan, Kubota and Takehara (1998).

10

Zt−1 includes following conditioning variables:

cayt−1 Consumption-wealth ratiotermt−1 Term premium

In addition, we also included the scaled market factor, cayt−1 · Rvwt, pro-posed in Lettau and Ludvigson (2001b).

We did the horse race among various specifications. Table 2 summarizes

estimates of λs in the second stage regressions. Results of Japanese data

reported in this table exhibit some similarities with and differences from

US results reported in Lettau and Ludvigson (2001b). As we know for US

data, market portfolio Rvwt alone have almost no explanatory power for

the cross-section of stock returns in Japanese data too (Row 1). On the

other hand, Fama-French’s three factor model (Row 5) shows very success-

ful performance. Labor income also has some explanatory power when it is

included with market portfolios as in US results. However, the estimated co-

efficients of labor income growth Y Gt have negative signs, which is puzzling

and contradicts with what theory suggests.

[Table 2 is about here]

We also examine term premium and cayt−1 as conditioning variables.

Term premium is statistically significant when it is used along market port-

folio and/or labor income growth. However, it loses its explanatory power

when included with SMB and HML factors.

The biggest difference between US results by Lettau and Ludvigson and

ours on Japanese data is the role of cayt−1. In US results, cayt−1 is significant

as a scaling variable in the scaled factors models (corresponding to Row 4

in Table 2), but not as a conditioning variable or a risk factor. Table 2

suggest the other way around about Japan. In the Japanese data, cayt−1 is

statistically significant as a conditioning variable.

Why? In Figure 1, Fama-French factors (SMB and HML) and cayt−1

are plotted. From these graphs, cay’s movement is obviously much more

11

persistent than movements of other risk factors, SMB and HML. This sug-

gest cayt−1 should be characterized as a conditioning variable rather than

a risk factor. Our interpretation is that, in Japanese case, while cayt−1

identifies the different phases of market condition, the difference appears as

the regime changes in the constant term E[r0,t]. In U.S. case, Lettau and

Ludvigson (2001b) suggests that cayt−1 identifies the cyclical time variation

of the market beta, i.e., the conditional beta.

In Table 3, we report the results with real estate wealth, the second stage

Fama-MacBeth regression using cayt−1 reported in section 3.4. In part (A) of

Table 3, cayt−1 is tabulated from equation (13), including real estate wealth

to total wealth. On the other hand, in part (B), calculation of cayt−1 is based

on (14) which include log of urban area land price index as an independent

regressor. These results show, on average, significant improve from Table

2’s results: For example, Row 6 in Table 4 (R2 = 48.2; sum of squared

residuals = 2.44), the specification with Fama-French factors plus cayt−1,

corresponds to A1 (R2 = 55.0; ssq = 2.12) and B1 (R2 = 52.8; ssq = 2.22) in

Table 5. Similarly, the specification including term premium, Row 9 in Table

2 (R2 = 48.5; ssq = 2.42) corresponds to A3 (R2 = 56.4; ssq = 2.05) and B3

(R2 = 53.6; ssq = 2.18) in Table 3. Hence, it is safe to say cayt−1 including

real estate wealth explains cross-sectional pattern of Japanese stock market

better than cayt−1 including only financial wealth.

[Table 3 is about here]

Comparison between the case land is included in total asset (A) and the

case separately enters in cointegration (B) in Table 3 is rather difficult. When

scaled factor cayt−1 ·Rvwt is included, performance of the regressions in (B)significantly increase (B2 and B4). However, scaled factor is in anyway,

statistically insignificant. While the authors prefer the results reported in

(B), this is mainly because we are more comfortable with the construction

of cayt−1 series by equation (14).

12

Table 4 and Table 5 report the estimates for the sub sample after the

burst of the bubble, namely 1991:1Q-2003:1Q. Table 4 corresponds to Table

2 and Table 5 corresponds to Table 3. Unlike in Table 2, cayt−1 is statis-

tically insignificant in Table 4. This is consistent with our explanation for

Table 2 that cayt−1 is useful because it captures structural shifts in constant

terms. Also the superiority of cayt−1 including real estate wealth over finan-

cial wealth only cayt−1 disappears in Table 5. Overall, Fama-French factors,

especially HML becomes important in explaining cross-sectional pattern in

the post-bubble sub sample.

[Table 4 and 5 are about here]

5 Concluding Remarks

In this paper, we examine if consumption/wealth ratio (more precisely, the

deviation from its long-run relationship) can explain Japanese stock market

data. Following Lettau and Ludvigson (2001a, b), we carefully construct

the series of cayt, the residuals from cointegration relationship between con-

sumption and total wealth of household. Unlike US results, cayt does not

predict future Japanese stock returns. On the other hand, it provides some

help in explaining cross-section of stock returns of industry portfolios, es-

pecially if we include real estate as a part of total wealth. In US case, cayt

comes in as a scaling variable which explains time-variation of market beta.

In Japanese case, the movement of cayt will be interpreted as the change in

the constant terms, hence the changes of average stock returns.

As we explained in section 4.1, empirical difficulty we or any study on

aggregate Japanese stock return including 1987-1992 observations face is

that the sample contains such a significant one-time boom and bust in stock

market. All sophisticated statistical techniques in this field rely on asymp-

totic and so that they are vulnerable to the existence of rare event and/or

structural break. Lettau and Ludvigson’s analytical framework is no excep-

tion.

13

Theoretically, the biggest advantage of Lettau and Ludvigson’s frame-

work discussed in section 2 is that they allows time-varying investment op-

portunity. However, by imposing the intertemporal budget constraint with

no bubble condition (4), households’ rationality is implicitly assumed. In

particular, rational bubble is ruled out in their framework. A possible expla-

nation for the negative result for return predictability is that there existed

rational bubble in the sample period we considered here, so that no bub-

ble condition was violated at least in ex post sense. Investigating such a

possibility is left for the subject of future research.

14

References

• Campbell, John Y. (1991) “A Variance Decomposition for Stock Re-turns,” Economic Journal, Vol.101, No. 405, pp.157-179.

• Campbell, John Y., (2003) “Consumption-based Asset Pricing,” Chap-ter 13 in G.M. Constantinides, M. Harris and R.M. Stulz eds., Hand-

book of the Economics of Finance, Volume 1, Part 2, Financial Markets

and Asset Pricing, Pages 605-1246, Elsevier B.V.

• Campbell, John Y. and Robert J. Shiller, (1988) “The Dividend-PriceRatio and Expectations of Future Dividends and Discount Factors,”

Review of Financial Studies, Vol.1, No. 3, pp. 195-228.

• Gao, Pengjie and Kevin X. D. Huang (2004) “Aggregate Consumption-Wealth Ratio and the Cross-Section of Stock Returns: Some Interna-

tional Evidence,” FRB of Kansas City Working Paper No. RWP 04-07.

• Gregory, Allan W. and Bruce E. Hansen (1996) “Residual-Based Testsfor Cointegration in Models with Regime Shifts” Journal of Economet-

rics. January 1996; 70(1): 99-126.

• Hall, Robert E. (1978) “Stochastic Implications of Life Cycle-PermanentIncome Hypothesis: Theory and Evidence,” Journal of Political Econ-

omy, LXXXVI: 971-88.

• Iwaisako, Tokuo, (2003) “Household Portfolios in Japan,”NBER work-ing paper #9647, April 2003.

• Iwaisako, Tokuo, Olivia S. Mitchell and John Piggott (2005) “Strate-gic Asset Allocation in Japan: An Empirical Evaluation” Pension Re-

search Council, Wharton School, University of Pensylvania, WP 2005-

1.

• Jagannathan, Ravi, Keichi Kubota, and Hitoshi Takehara (1998) “Re-lationship between labor-income risk and average return: Empirical

evidence from the Japanese stock market,” Journal of Business 71,

319-347.

15

• Lettau, Martin and Sydney Ludvigson, (2001a) “Consumption, Aggre-gate Wealth, and Expected Stock Returns” Journal of Finance. June

2001; 56(3): 815-49.

• – and –, (2001b) “Resurrecting the (C)CAPM: A Cross-Sectional

Test When Risk Premia Are Time-Varying” Journal of Political Econ-

omy. December 2001; 109(6): 1238-87.

• – and –, (2004) “Understanding Trend and Cycle in Asset Values:

Reevaluating the Wealth Effect on Consumption” American Economic

Review. March 2004; 94(1): 276-99.

• Mankiw, N. Gregory and Stephen P. Zeldes (1991) “The Consump-tion of Stockholders and Nonstockholders,” Journal of Financial Eco-

nomics Vol. 29, No. 1 (1991): 97—112.

• Matsuzaki, Arata (2003) Unpublished MA thesis (in Japanese), Grad-uate School of Economics, HitotsubashiUniversity.

• Parker, Jonathan A. and Christian Julliard (2005) “Consumption Riskand the Cross Section of Expected Returns” Journal of Political Econ-

omy. February 2005; 113(1): 185-222.

• Vissing-Jorgensen, Annette (2002) “Limited Asset Market Participa-tion and the Elasticity of Intertemporal Substitution,” Journal of Po-

litical Economy, August 2002; 110(4): 825-853.

• Wilcox, David W., 1992, “The Construction of U.S. ConsumptionData: Some Facts and Their Implications for Empirical Work” Amer-

ican Economic Review. September 1992; 82(4): 922-41

16

Table 1

Forecasting Quarterly Stock Returns

Constant lag ˆcay PDR RREL TRMR̄2

Panel A: Real Returns;1974:1Q-2003:1Q1 0.009 0.316*** 0.03

(1.216) (3.528)2 -0.037** -0.940*** 0.07

(-2.113) (-3.084)3 -0.026 0.258*** -0.671** 0.12

(-1.491) (2.822) (-2.159)Panel B: Excess Returns;1974:1Q-2003:1Q

4 0.001 0.310 0.09(0.081) (3.509)

5 -0.035** -0.694** 0.03(-1.981) (-2.246)

6 -0.024 0.277*** -0.474 0.10(-1.359) (3.071) (-1.544)Panel C: Additional Controls; Excess Returns;1974:1Q-2003:1Q

7 0.047 -1.099*** -0.022 0.09(0.449) (-3.182) (-1.022)

8 0.059 0.235** -0.597* -0.022 -0.575 0.008 0.12(0.713) (2.508) (-1.828) (-1.250) (-0.774) (1.146)

In parentheses are t-statistics.

17

Tab

le 2

Fam

a-M

acB

eth

regr

ess

ions

with E

quity

Only

C

AY:

Full

Sam

ple

Condi

tionin

g V

aria

bles

Fac

tors

Scal

ed

Fac

tor

Sum

of

Const

ant

cay

(-1)

(x100)

term

Rvw

YG

SM

BH

ML

Rvw

・cay

(-1)

R2

Sq.

Resi

d1

0.8

20.8

2-0.0

80.1

4.7

0(

1.0

7)

(1.1

9)

20.9

5-0.1

1-0.2

8*

15.6

3.9

8(

1.0

2)

(1.1

2)

(0.2

7)

31.1

6*

0.7

4*

-0.2

8-0.3

5*

33.8

3.1

2(

0.9

4)

(0.5

0)

(1.0

2)

(0.2

5)

41.0

3*

0.7

4*

-0.3

5*

0.0

034.2

3.1

0(

1.0

0)

(0.5

0)

(0.2

5)

(0.0

6)

52.0

0*

-1.0

4-0.6

1*

-0.4

3*

41.0

2.7

8(

1.0

5)

(1.0

7)

(0.4

1)

(0.3

6)

61.9

7*

0.4

8*

-1.0

1-0.6

7*

-0.4

3*

48.2

2.4

4(

1.0

1)

(0.4

7)

(1.0

3)

(0.4

0)

(0.3

5)

71.3

4*

0.8

4*

0.2

8*

-0.4

8-0.4

8*

39.7

2.8

4(

0.9

5)

(0.5

1)

(0.2

7)

(1.0

4)

(0.3

0)

82.0

6*

0.0

7-1.1

1-0.6

4*

-0.4

3*

42.0

2.7

3(

1.0

8)

(0.2

2)

(1.1

2)

(0.4

2)

(0.3

7)

92.0

0*

0.4

9*

0.0

9-1.0

5-0.6

9*

-0.4

2*

48.5

2.4

2(

1.0

5)

(0.4

9)

(0.2

1)

(1.0

8)

(0.4

1)

(0.3

6)

Note

:Fam

a-M

acB

eth

regr

ess

ions

usi

ng

28 Indu

stry

Port

folio

s: S

econd-

stag

e r

egr

ess

ion

Sam

ple p

eriod: 1978:1

Q-2003:1

Q

Definitio

n o

f va

riab

les

cay

(-1)

Consu

mpt

ion-W

eal

th r

atio

(re

sidu

als

from

coin

tegr

atio

n r

egr

ess

ion)

term

Term

pre

miu

m (10ye

ar J

GB

- C

all ra

te)

Rvw

Val

ue w

eig

hte

d m

arke

t in

dex

YG

Lab

or

incom

e g

row

thSM

BFam

a-Fre

nch S

MB

fac

tor

(retu

rn d

iffe

rence b

etw

een s

ize s

ort

ed

port

folio

s)H

ML

Fam

a-Fre

nch H

ML fac

tor

(retu

rn d

iffe

rence b

etw

een p

ort

folio

s so

rted

by B

ook

to M

arke

t ra

tio)

Tab

le 3

Fam

a-M

acB

eth

regr

ess

ions

with C

AY

inclu

ding

Lan

d: F

ull

Sam

ple

Condi

tionin

g V

aria

bles

Scal

ed

Fac

tor

Sum

of

Const

ant

cay

(-1)

(x100)

term

(x100)

Rvw

SM

BH

ML

Rvw

・cay

(-1)

R2

Sq.

Resi

d(A

)Lan

d in

clu

ded

in T

ota

l A

sset

A1

2.2

4*

0.4

5*

-1.2

5*

-0.6

7*

-0.5

7*

55.0

2.1

2(

0.9

5)

(0.3

5)

(0.9

7)

(0.3

7)

(0.3

4)

A2

1.9

9*

0.5

0*

-1.0

2-0.6

1*

-0.6

8*

0.0

157.9

1.9

8(

1.0

3)

(0.3

6)

(1.0

4)

(0.3

8)

(0.3

9)

(0.0

4)

A3

2.2

3*

0.4

4*

0.1

4-1.2

4*

-0.6

6*

-0.6

4*

56.4

2.0

5(

0.9

6)

(0.3

5)

(0.3

1)

(0.9

8)

(0.3

7)

(0.3

9)

A4

2.0

1*

0.4

9*

0.1

2-1.0

3-0.6

1*

-0.7

3*

0.0

158.8

1.9

4(

1.0

5)

(0.3

6)

(0.3

1)

(1.0

6)

(0.3

8)

(0.4

3)

(0.0

4)

(B)

Lan

d is

sepr

atly

in c

oin

tegr

atio

n r

egr

ess

ion

B1

2.1

5*

0.5

5*

-1.1

8*

-0.7

5*

-0.3

252.8

2.2

2(

0.9

7)

(0.4

2)

(0.9

9)

(0.3

9)

(0.3

5)

B2

1.8

7*

0.6

8*

-0.9

0-0.7

7*

-0.5

6-0.0

261.9

1.7

9(

0.9

3)

(0.4

0)

(0.9

5)

(0.3

6)

(0.3

8)

(0.0

3)

B3

2.1

4*

0.5

1*

0.0

9-1.1

7*

-0.7

3*

-0.3

953.6

2.1

8(

0.9

8)

(0.4

4)

(0.3

3)

(1.0

1)

(0.4

0)

(0.4

2)

B4

1.8

5*

0.6

4*

0.1

1-0.8

7-0.7

5*

-0.6

6*

-0.0

263.2

1.7

3(

0.9

4)

(0.4

1)

(0.3

0)

(0.9

6)

(0.3

7)

(0.4

5)

(0.0

3)

Note

:Fam

a-M

acB

eth

regr

ess

ions

usi

ng

28 Indu

stry

Port

folio

s: S

econd-

stag

e r

egr

ess

ion

Sam

ple p

eriod: 1978:1

Q-2003:1

Q

Definitio

n o

f va

riab

les

cay

(-1)

Consu

mpt

ion-W

eal

th r

atio

(re

sidu

als

from

coin

tegr

atio

n r

egr

ess

ion)

term

Term

pre

miu

m (10ye

ar J

GB

- C

all ra

te)

Rvw

Val

ue w

eig

hte

d m

arke

t in

dex

YG

Lab

or

incom

e g

row

thSM

BFam

a-Fre

nch S

MB

fac

tor

(retu

rn d

iffe

rence b

etw

een s

ize s

ort

ed

port

folio

s)H

ML

Fam

a-Fre

nch H

ML fac

tor

(retu

rn d

iffe

rence b

etw

een p

ort

folio

s so

rted

by B

ook

to M

arke

t ra

tio)

Tab

le 4

Fam

a-M

acB

eth

regr

ess

ions

with E

quity

Only

C

AY:

Post

Bubb

leC

ondi

tionin

g V

aria

bles

Fac

tors

Scal

ed

Fac

tor

Sum

of

Const

ant

cay

(-1)

(x100)

term

Rvw

YG

SM

BH

ML

Rvw

・cay

(-1)

R2

Sq.

Resi

d1

-1.4

10.3

30.5

926.8

7(

1.5

3)

(1.7

1)

2-1.3

30.2

40.0

00.8

626.7

9(

1.7

0)

(1.8

8)

(0.0

1)

3-1.3

6-0.0

90.2

80.0

01.1

226.7

2(

1.7

6)

(0.8

8)

(1.9

5)

(0.0

1)

4-1.3

7-0.0

70.0

0-0.0

10.7

826.8

2(

2.0

9)

(0.8

9)

(0.0

1)

(0.0

9)

50.8

8-1.5

8-0.0

9-2.1

5*

65.3

99.3

5(

1.2

2)

(1.2

2)

(0.8

0)

(0.7

1)

60.7

5-0.1

3-1.4

6*

-0.0

5-2.2

3*

66.0

89.1

7(

1.2

9)

(0.5

8)

(1.2

9)

(0.8

2)

(0.7

3)

7-1.6

4-0.1

60.3

60.6

00.0

012.9

123.5

4(

1.7

2)

(0.0

1)

(0.4

4)

(1.9

1)

(0.0

1)

80.5

70.2

5-1.2

6-0.0

4-2.1

8*

70.3

78.0

1(

1.2

0)

(0.2

5)

(1.2

0)

(0.7

6)

(0.6

7)

90.3

8-0.1

90.2

6-1.0

70.0

1-2.2

5*

71.6

87.6

5(

1.2

7)

(0.5

5)

(0.2

5)

(1.2

7)

(0.7

7)

(0.6

9)

Note

:Fam

a-M

acB

eth

regr

ess

ions

usi

ng

28 Indu

stry

Port

folio

s: S

econd-

stag

e r

egr

ess

ion

Sam

ple p

eriod: 1991:1

Q-2003:1

Q

Definitio

n o

f va

riab

les

cay

(-1)

Consu

mpt

ion-W

eal

th r

atio

(re

sidu

als

from

coin

tegr

atio

n r

egr

ess

ion)

term

Term

pre

miu

m (10ye

ar J

GB

- C

all ra

te)

Rvw

Val

ue w

eig

hte

d m

arke

t in

dex

YG

Lab

or

incom

e g

row

thSM

BFam

a-Fre

nch S

MB

fac

tor

(retu

rn d

iffe

rence b

etw

een s

ize s

ort

ed

port

folio

s)H

ML

Fam

a-Fre

nch H

ML fac

tor

(retu

rn d

iffe

rence b

etw

een p

ort

folio

s so

rted

by B

ook

to M

arke

t ra

tio)

Tab

le 5

Fam

a-M

acB

eth

regr

ess

ions

with C

AY

inclu

ding

Lan

d: P

ost

Bubb

leC

ondi

tionin

g V

aria

bles

Scal

ed

Fac

tor

Sum

of

Const

ant

cay

(-1)

(x100)

term

(x100)

Rvw

SM

BH

ML

Rvw

・cay

(-1)

R2

Sq.

Resi

d(A

)Lan

d in

clu

ded

in T

ota

l A

sset

A1

0.8

3-0.1

0-1.5

2*

-0.0

7-2.2

2*

65.6

9.2

9(

1.2

7)

(0.8

6)

(1.2

7)

(0.8

2)

(0.7

5)

A2

0.3

4-0.0

3-1.0

4-0.0

1-2.4

1*

0.0

067.2

8.8

6(

1.6

0)

(0.8

8)

(1.6

0)

(0.8

3)

(0.8

5)

(0.1

0)

A3

0.4

5-0.1

50.2

6-1.1

30.0

0-2.2

6*

71.2

7.7

8(

1.2

5)

(0.8

1)

(0.2

5)

(1.2

6)

(0.7

8)

(0.7

1)

A4

0.1

3-0.1

00.2

5-0.8

20.0

4-2.3

9*

-0.0

172.0

7.5

7(

1.5

4)

(0.8

3)

(0.2

6)

(1.5

4)

(0.7

9)

(0.8

1)

(0.1

0)

(B)

Lan

d is

sepr

atly

in c

oin

tegr

atio

n r

egr

ess

ion

B1

0.0

6-0.1

7-1.3

4-0.0

3-2.2

2*

67.1

8.9

0(

1.3

1)

(0.4

2)

(1.3

0)

(0.8

1)

(0.7

1)

B2

0.1

2-0.1

3-0.8

6-0.0

3-2.2

5*

-0.0

168.4

8.5

4(

1.7

14

)(

0.4

3)

(1.6

7)

(0.8

1)

(0.7

2)

(0.0

8)

B3

0.3

1-0.2

50.2

6-1.0

20.0

1-2.2

3*

72.1

7.5

4(

1.2

8)

(0.4

0)

(0.2

5)

(1.2

7)

(0.7

6)

(0.6

7)

B4

0.0

5-0.2

20.2

4-0.7

70.0

1-2.2

4*

0.0

072.5

7.4

3(

1.6

4)

(0.4

2)

(0.2

7)

(1.6

0)

(0.7

8)

(0.6

9)

(0.0

8)

Note

:Fam

a-M

acB

eth

regr

ess

ions

usi

ng

28 Indu

stry

Port

folio

s: S

econd-

stag

e r

egr

ess

ion

Sam

ple p

eriod: 1991:1

Q-2003:1

Q

Definitio

n o

f va

riab

les

cay

(-1)

Consu

mpt

ion-W

eal

th r

atio

(re

sidu

als

from

coin

tegr

atio

n r

egr

ess

ion)

term

Term

pre

miu

m (10ye

ar J

GB

- C

all ra

te)

Rvw

Val

ue w

eig

hte

d m

arke

t in

dex

YG

Lab

or

incom

e g

row

thSM

BFam

a-Fre

nch S

MB

fac

tor

(retu

rn d

iffe

rence b

etw

een s

ize s

ort

ed

port

folio

s)H

ML

Fam

a-Fre

nch H

ML fac

tor

(retu

rn d

iffe

rence b

etw

een p

ort

folio

s so

rted

by B

ook

to M

arke

t ra

tio)

Figure 1 Factors for Cross-section Regression

Panel A

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

1977Q4

1979Q4

1981Q4

1983Q4

1985Q4

1987Q4

1989Q4

1991Q4

1993Q4

1995Q4

1997Q4

1999Q4

2001Q4

2003Q4

CAY

Panel B

-30

-25

-20

-15

-10

-5

0

5

10

15

20

1977Q4 1979Q4 1981Q4 1983Q4 1985Q4 1987Q4 1989Q4 1991Q4 1993Q4 1995Q4 1997Q4 1999Q4 2001Q4 2003Q4

SMB

Figure 1 (continued)

Panel C

-25

-20

-15

-10

-5

0

5

10

15

20

25

1977Q4 1979Q4 1981Q4 1983Q4 1985Q4 1987Q4 1989Q4 1991Q4 1993Q4 1995Q4 1997Q4 1999Q4 2001Q4 2003Q4

HML