J Real Estate Finan Econ (2007) 35:427–448 DOI 10.1007/s11146-007-9080-4

Does Consumption Respond More to Housing Wealth Than to Financial Market Wealth? If So, Why? N. Kundan Kishor

Published online: 9 September 2007 © Springer Science + Business Media, LLC 2007

Abstract This paper uses long-run equilibrium relationship between consumption and different components of wealth to estimate the effect of changes in housing wealth and financial wealth on consumption. By exploiting this longrun property, it has been shown that a dollar increase in housing wealth increases consumption by seven cents, whereas, a corresponding dollar increase in financial wealth increases consumption by only three cents. This difference in the wealth effect arises because transitory shocks dominate variation in financial wealth, whereas permanent shocks account for most of the variation in housing wealth. This paper also shows that the relative importance of permanent component for housing wealth has witnessed an increase over the last thirty years. Therefore, housing wealth effect has also increased over time. Keywords Beveridge–Nelson cycle · Cointegration · Consumption · Kalman filter · State-space model · Wealth effect Introduction There has been a consensus in economic literature and in policymaking about household wealth being one of the determinants of consumption expenditure: for every dollar increase in wealth consumption should increase by 2–10 cents.1 This implies that the U.S. economy should have witnessed a decline in consumption during the last recession as the net worth of household sector 1 Poterba (2000). Some studies like Juster et al. (1999) and Engelhardt (1996) estimate the wealth effect to be even larger than 15 cents but the consensus lies around 2–10 cents.

N. Kundan Kishor (B) University of Wisconsin-Milwaukee, Milwaukee, WI, USA e-mail: [email protected]

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declined by around one thousand billion dollars. On the contrary, it experienced a very robust growth in consumption. The recession of 2001 was unique because both the housing market and the financial market were moving in the opposite direction while the consumption growth was positive for the whole time period. The popular financial press speculated the robust consumption growth to be driven by a very strong housing market as marginal propensity to consume (MPC) out of housing wealth might be higher than the MPC out of financial wealth.2 The effect of housing wealth on consumption has recently attracted widespread attention in the macroeconomic literature. Case et al. (2005) in a recent study using panel data across U.S. states and across OECD countries have shown that changes in housing wealth have a greater effect on consumer spending than changes in stock market wealth. Case (1992) found evidence of a substantial wealth effect during the real estate price boom in the late 1980s using aggregate data for New England. Benjamin et al. (2004)3 have shown that the effect of a dollar increase in real estate wealth on consumption is four times higher than a dollar increase in financial wealth. Ludvig and Slok (2002) in a study on a panel of countries using panel cointegration have shown that the long-run impact of an increase in stock prices and housing prices on consumption is in general higher in countries with a market based financial system than bank based financial system. Campbell and Cocco (2007) use micro level data from U.K. to find out the mechanism through which the house prices affect consumption. They find significant difference in the wealth effect across different population age groups. In a different strand of research, Lettau and Ludvigson (2004) claim that because of the large transitory component of stock market wealth,4 the wealth effect should be much smaller than the usual estimates because consumption does not respond to transitory movements in wealth. They argue that the wealth effect should correspond to only that movement in wealth which is permanent. The paper which is closest in flavor to this paper is by Pichette and Tremblay (2004) where the authors use the same methodology to estimate wealth effect for Canada. This paper uses aggregate macro level flow of funds data to estimate the relative impact of changes in housing market wealth and financial market wealth on consumption. Using the framework of Cochrane (1994) and Lettau and Ludvigson (2001, 2004), I have shown that consumption, after tax labor income, housing wealth and financial wealth move together in the long-run, i.e., they are cointegrated and hence share the common trend. The results show

2 To

be consistent with the model we use financial wealth as a measure of non-housing wealth in our paper. The results do not change if we use stock market wealth instead. See the Appendix for the definition of financial wealth and stock market wealth. 3 They also use Flow of Funds Data from 1952–2001. They define financial wealth = net worth − net real estate wealth. 4 Lettau–Ludvigson’s model has non-durable consumption, labor income and net worth in the cointegrating relationship. They argue that the transitory movement in net worth has been dominated by stock market and hence the net wealth effect reflects the dominance of transitory component of stock market wealth.

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that if there is a deviation from the long-run equilibrium value, then financial wealth adjusts to correct for this short-run disequilibrium error. Using Gonzalo and Ng (2001) methodology this adjustment property of financial wealth has been utilized to find out the relative importance of permanent and transitory components at different forecast horizons for consumption, labor income, housing wealth and financial wealth. It has been shown that the response of consumption to transitory shock is negligible and hence wealth effect should correspond to only those movements in wealth which are permanent. The results show that consumption responds more to housing wealth than to financial market wealth because permanent innovations account for most of the movements in housing market wealth at different forecast horizons whereas almost half of the movements in financial market wealth are generated by transitory shocks. In this framework, the housing wealth effect turns out to be seven cents whereas the corresponding estimate for financial wealth effect is three cents.5 I have also shown that if all the movements in financial wealth and housing wealth were permanent then the wealth effect arising out of these two types of wealth would not be significantly different from each other. Using a time-varying parameter model, it has also been shown that the importance of permanent component in housing wealth has increased over time. The relative share of transitory component at different forecast horizons increased during the 1970s for housing wealth, whereas it decreased during the 1980s and the 1990s. This implies that the impact of a dollar increase in housing wealth today will have a bigger impact on consumption than a dollar increase in housing wealth in 1970s; and hence housing wealth effect has increased over time. The structure of this paper is as follows. Section “Theoretical Background” presents theoretical motivation behind this paper. Section “Comparison of Wealth Effect” outlines the comparison of the wealth effect using econometric methodology. Section “A Time-Varying Parameter Model of Housing Market Deregulation” deals with a time-varying parameter model of housing deregulation. Section “Robustness Analysis” presents the robustness of the proposed model to alternative specifications. Section “Concluding Remarks” presents conclusions.

Theoretical Background This section presents an overview of the theoretical background of our empirical work. It draws heavily, and mainly based, on the model presented in Lettau and Ludvigson (2001, 2004). In this framework, the assumption is that housing enters only into the agent’s budget constraint.6 If Wt is the total wealth at time t, then the budget constraint can be written as: Wt+1 = (1 + Rw,t+1 )(Wt + Yt − Ct ), 5 This

(1)

is qualitatively similar to the estimates obtained in Case et al. (2005). et al. (2005), Benjamin et al. (2004) and Ludvig and Slok (2002) have the same framework. The alternative formulation includes housing in the utility function as well.

6 Case

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where Rw,t is the rate of return on aggregate wealth, Yt is the after tax labor income and Ct is consumption of non durable goods and services. If r≡ log(1 + R), then, taking a first order Taylor approximation of Eq. 1 and solving the resulting difference equation for log wealth forward, imposing transversality condition and taking expectations, Campbell and Mankiw (1991) derive the following expression for consumption-wealth ratio: ct − wt = Et

∞ 

ρwi (rw,t+1 − ct+i ),

(2)

i=1

i.e. the consumption wealth ratio is stationary. ρw is the steady state value of ratio of investment to consumption and ct+i is the rate of growth of consumption between time t and t+i. The intuition behind Eq. 2 is that if there is a deviation from the long-run ratio of consumption and wealth, then this deviation should either predict rate of return on wealth or rate of growth of consumption i.e. either wealth or consumption should adjust to correct for the long-run disequilibrium. However, empirical estimation of Eq. 2 is not feasible because aggregate wealth includes human wealth which is unobservable. I utilize Lettau and Ludvigson’s (2001) framework to handle this issue of unobservability. The total wealth can be thought of as the sum of financial wealth, human wealth and housing wealth: Wt = Ft + Lt + Ht ,

(3)

where Ft is financial wealth, Lt is human wealth and Ht is housing wealth. Since human wealth is unobservable, the assumption made in literature is that permanent human wealth is proportional to current labor income.7 If Y is the current labor income, then, log-linear approximation of Eq. 3 gives us the following relationship: wt ≈ ω ft + θ yt + (1 − ω − θ)ht ,

(4)

small case letters are logarithms of variables and yt is the log of current labor income, ft represents log of financial wealth, and ht is log of housing wealth. ω represents the steady state share of financial wealth in total wealth, θ is the steady state share of labor income in total wealth and (1 − ω − θ) is the steady state share of housing wealth. The return to aggregate wealth can be decomposed as: (1 + Rw,t ) = ω(1 + R f,t ) + θ(1 + R y,t ) + (1 − ω − θ)(1 + Rh,t ),

7 There

(5)

are three ways to rationalize this assumption. First, without imposing any restriction on the functional form of expected or realized returns on human wealth we can get this relationship between current labor income and permanent human wealth if we characterize labor income as annuity value of human wealth. Second, we can specify a Gordon growth model for human capital where expected returns to human capital are constant and labor income follows a random walk. Finally, labor income can be thought of as the dividend on human capital, as in Campbell (1996). See Lettau and Ludvigson (2001) for details.

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where Rw,t , R f,t , R y,t and Rh,t are the returns to aggregate wealth, financial wealth, human wealth and housing wealth. If r≡ log(1 + R), then, substituting for wt and rw,t+1 in Eq. 2, we get: ct − θ yt − ω ft − (1 − ω − θ)ht = Et

∞ 

ρwi {[θr y,t+i + ωr f,t+i + (1 − ω − θ)rh,t+i ] − ct+i } + ηt .

(6)

i=1

The right hand side of Eq. 6 is stationary, therefore, the linear combination of consumption, labor income, financial wealth and housing wealth is stationary; and hence they are cointegrated.

Comparison of Wealth Effect In this paper, non-human wealth has been disaggregated into housing wealth and financial market wealth. In a perfect world where these two assets are perfect substitutes, the MPC out of these two different types of wealth will be equal. But, because of issues like volatility, illiquidity, demographic structure and institutional structure, these propensities might be different. Therefore, Eq. 6 can be written as: ct = β0 + β1 yt + β2 ht + β3 ft + εt ,

(7)

where yt is labor income, ft represents financial market wealth and ht represents house wealth and all variables are in logs. Here ct is log of expenditure on nondurable goods and services.8 Expenditure on housing services has been excluded as housing wealth enters the budget constraint only. Let’s define zt = (1, ct , yt , ht , ft ) . Let z1t be the subset of zt except ct . Hence, z1t = (1, yt , ht , ft ) . Equation 7 represents the long-run relationship among consumption, labor income, financial wealth and housing wealth. The theory implies that the residual should be stationary and consumption, labor income, housing wealth and financial wealth should share a common trend. The estimates β  s are super consistent in this cointegrated framework, and hence there is no regressor endogeneity. Here β2 and β3 represent long-run elasticity of consumption with respect to financial wealth and housing wealth as the variables in Eq. 7 are in logs. These elasticities can be converted into MPC out of financial wealth and housing wealth by using respective consumption-wealth ratios. I first test for cointegration and the number of cointegrating vectors in Eq. 7. The range of data set used spans the period from the first quarter of 1952 to the third quarter of 2002.9 The cointegration test is performed by testing the stationarity of cointegrated residual and performing the Johansen cointegration test. The cointegrating vector has been estimated using Stock–Watson

8 For

robustness check, we also perform the analysis with non-durable goods and services and flow of durable goods expenditure. 9 See Appendix for description of the data set used in the paper.

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Table 1 DOLS estimate of cointegrating vector Coefficient

Value

Std. error

P-value

β1 β2 β3

0.620 0.135 0.372

0.0384 0.0268 0.0206

0.000 0.000 0.000

Standard errors are Newey–West HAC errors

dynamic ordinary least squares (DOLS) and Newey–West heteroscedastic autocorrelation consistent standard errors as there is a significant degree of serial correlation in the residuals if just OLS is used. Six leads and lags have been chosen for the estimation of the cointegrating vector.10 The DOLS equation specification is: ct = β  z1t +

+6 

γ  z1t− j + ut .

(8)

j=−6

As Table 1 shows the coefficient on financial wealth is almost three times bigger than the corresponding coefficient on housing wealth i.e. long-run elasticity of consumption with respect to financial wealth is three times bigger than elasticity of consumption with respect to housing wealth. These elasticities can be converted into corresponding wealth effect by using the respective consumption-wealth ratios. The standard errors are Newey–West HAC errors. In all the cases the null of non stationarity of the residual has been rejected at 5% and 10% significance level.11 The second step is to test the number of cointegrating vectors. For this, I perform the Johansen test for the number of cointegrating relations. Both the trace statistic and the maximum eigenvalue statistic indicate the presence of one cointegrating relationship. Null of no cointegration is rejected whereas the null of one cointegrating relationship is not rejected for the maximum eigenvalue statistic as well as for the trace statistic.12 In the subsequent analysis, one cointegrating vector will be assumed which is also consistent with the theory as well as the Johansen test for number of cointegrating vectors. The estimates of βs in Eq. 8 implies that the long-run elasticity of consumption with respect to financial wealth is three times bigger than the housing wealth. Since the dependent and the explanatory variables are in logarithms, the interpretation of coefficients βs is in terms of elasticities. In order to convert them into the usual wealth effect, these coefficients need to be multiplied by respective consumption-wealth ratios. This turns out to be seven cents for housing wealth and six cents for financial wealth as the consumptionhousing wealth ratio is three times bigger than the consumption-financial

10 The estimates β  s are consistent despite the fact that the explanatory variables and error terms are correlated. This follows from Stock and Watson (1988), as they show that the estimates from cointegrating parameters are√superconsistent i.e. the true parameter converges to the true values at rate T rather than at rate T as in ordinary least squares. 11 Stationary test results can be obtained from the author upon request. 12 The detailed test results are available upon request.

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wealth ratio.13 This implies that one dollar increase in housing wealth will lead to seven cents increase in consumption, and a dollar increase in financial wealth will increase consumption by six cents. But this increase in consumption will take place only if all the movements in housing wealth and financial market wealth affect consumption. If consumption and wealth are cointegrated, then, they share a common trend. Therefore, these βs imply the correlation between the permanent movements in wealth and consumption, not every movement in wealth. They reveal nothing about the relation between consumption and transitory movements in wealth. If most of the movements in financial market wealth are transitory and if transitory movements in financial market wealth have negligible impact on consumption then the final impact of these two measures of wealth will be different than what is implied by these coefficients. Therefore, it is very important to find out whether the movements in financial wealth and housing wealth are dominated by permanent shocks or transitory shocks; and whether consumption responds differently to a permanent shock and a transitory shock. The tools provided by Gonzalo and Granger (1995) and Gonzalo and Ng (2001) enable us to find out the relative importance of permanent and transitory shocks at different forecast horizons using variance decomposition for a cointegrated system.14 For this decomposition, vector error correction model (VECM) associated with cointegrated model needs to be estimated first because the error correction coefficient in VECM provides information about the relative importance of permanent and transitory shocks. The Engle and Granger representation theorem provides a VECM representation of the cointegrated system. The VECM model has the following representation (L)zt = 0 + zt−1 + ut , (9)  p−1 where (L) = In − k=1 k and = αβ  where α = (αc , α y , αh , α f ) . The lag length criteria implies that p=2.15 Therefore, in the VECM representation our model has one lag. The following VECM has been estimated ct = γ10 + γ11 ct−1 + γ12 yt−1 + γ13 ht−1 + γ14  ft−1 + αc β  zt−1 + uct , (10) yt = γ20 + γ21 ct−1 + γ22 yt−1 + γ23 ht−1 + γ24  ft−1 + α y β  zt−1 + u yt , (11) ht = γ30 + γ31 ct−1 + γ32 yt−1 + γ33 ht−1 + γ34  ft−1 + αh β  zt−1 + uht , (12)  ft = γ40 + γ41 ct−1 + γ42 yt−1 + γ43 ht−1 + γ44  ft−1 + αs β  zt−1 + u f t , (13) 13 The

wealth effects for housing wealth and financial wealth are not statistically different from each other. Therefore, marginal propensities to consume out of permanent movements in housing and financial wealth are not statistically different from each other. 14 See King et al. (1991) for details. 15 BIC lag length criterion.

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Table 2 VECM estimation Explanatory variables

ct

yt

ht

 ft

ct−1 yt−1 ht−1  ft−1 β  zt−1

0.177 (0.01) 0.057 (0.22) 0.018 (0.47) 0.035 (0.02) −0.030 (0.08)

0.237 (0.05) −0.076 (0.34) 0.053 (0.20) 0.058 (0.02) −0.017 (0.57)

0.209 (0.33) −0.209 (0.13) 0.278 (0.00) 0.0469 (0.26) −0.014 (0.76)

−0.170 (0.65) −0.211 (0.39) 0.119 (0.35) 0.088 (0.22) 0.215 (0.00)

p-values in parentheses

where β  zt−1 = ct−1 − β0 − β1 yt−1 − β2 ht−1 − β3 ft−1 is the disequilibrium error from the last period. If the α  s are significant, then the current period value of the variables move to correct an error left over from the last period. α y , αh , α f are the corresponding speed of correction for the labor income, housing wealth and financial market wealth. According to Engle–Granger theorem, if there exists a cointegrating relationship then at least one of these α  s must be significant. The above system of equations has been estimated using OLS as they have the same explanatory variables, and hence seemingly unrelated regressions method is equivalent to OLS. The estimation results are shown in Table 2. It shows that the error correction coefficient is significant for financial wealth at all significance levels. Therefore, it’s the financial wealth which does most of the error correction. For the rate of growth of financial wealth only the error correction term is significant whereas for other variables the other explanatory variables are also significant. Therefore, labor income and housing wealth does not move to correct for the disequilibrium error. Variance Decomposition and Wealth Effect The error correction property of the model can be used to get an insight on the importance of permanent and transitory shocks at different forecast horizons for consumption, labor income, housing wealth and financial wealth using Gonzalo–Ng methodology. Structural innovations need to be traced out from the reduced form Wold moving average representation of the VECM model for the variance decomposition. The Granger Representation Theorem provides an explicit link between the VECM form of a cointegrated VAR and the Wold moving average representation. Let zt be cointegrated with r cointegrating vectors captured in the r×n matrix β  , so that βt z is I(0). Suppose zt has the following Wold representation: ∞

zt = μ + (L)ut ,

(14)

where (L) = k=0 k Lk and 0 = In . Here ut is n×1 vector. The Wold representation presented above is akin to a reduced form equation. The problem at hand is to identify innovations distinguished by whether they have permanent or transitory effect. In the model presented above there is one cointegrating vector, so, there are 4–1=3 permanent innovations and one transitory innovation. Let us denote the structural innovations as ηt =(η1t , η2t , η3t , η4t ) ,

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where first three innovations are permanent and the last one is transitory. The permanent and transitory innovations may be identified using the estimated ∧

∧

parameters β and α from the error correction representation. GRT provides us the following conditions α  (1) = 0 and (1)β = 0. Let    α⊥ . (15) G= β Let us assume that D(L) = (L)G−1 . Gonzalo and Ng have shown that the structural innovations can be represented as: ηt = Gut , and the structural residuals are related to zt as: zt = μ + (L)G−1 Gut , = μ + D(L)ηt . The error term ηt is correlated across equations. In order to get the impulse responses and the variance decomposition these structural innovations need to be orthogonalized. Gonzalo and Ng have shown that this can be done by using the Choleski decomposition of the covariance matrix of the structural innovations. If E[ηt ηt ] = η and if there is a matrix H satisfying HH’= η then  H−1 ηt = ηt achieves the permanent and transitory decomposition and the resulting innovations are orthogonalized. The complete permanent-transitory decomposition can be written as: 



zt = μ + D(L)H H −1 ηt = D(L)ηt .

(16)

Here each element of zt has been decomposed into a function of three permanent shocks; and one transitory shock. It can be easily seen that more weight is given to the permanent shock if α is lower implying that the variable participates little in error correction. According to this decomposition, intuitively it makes sense that financial wealth and consumption have large transitory component as both of them participate in error correction. The importance of the permanent shock and the transitory shock can be analyzed quantitatively by taking a look at the variance decomposition of Table 3 Variance decomposition for the case where α y = αh = 0(Restricted) Period

1 2 5 10 ∞

c

y

h

f

P

T

P

T

P

T

P

T

0.75 0.78 0.78 0.78 0.78

0.25 0.22 0.22 0.22 0.22

1 0.998 0.998 0.998 0.998

0 0.002 0.002 0.003 0.003

1 0.996 0.995 0.995 0.995

0 0.004 0.005 0.005 0.005

0.53 0.53 0.53 0.53 0.54

0.47 0.47 0.47 0.47 0.46

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Table 4 Variance decomposition for the case where α y = αh = 0(Unrestricted) Period 1 2 5 10 ∞

c

y

h

f

P

T

P

T

P

T

P

T

0.74 0.77 0.77 0.77 0.77

0.26 0.23 0.23 0.23 0.23

0.97 0.97 0.97 0.968 0.968

0.03 0.03 0.03 0.032 0.032

0.994 0.994 0.994 0.994 0.994

0.006 0.006 0.006 0.006 0.006

0.52 0.52 0.52 0.51 0.51

0.48 0.48 0.48 0.49 0.49

consumption, labor income, housing wealth and financial wealth at different forecast horizons. Table 3 shows the variance decomposition at different horizons for the case where the coefficient of the error correction has been restricted to zero when it is insignificant. Table 4 shows the variance decomposition for unrestricted case where no restriction was placed on the error correction coefficients. The coefficients are restricted to be zero when they are insignificant because as discussed in Podivinsky (1992) these coefficients have poor finite sample properties. Different results can be obtained for the restricted and unrestricted case because the orthogonal complement of a matrix, say z, is not continuous for small perturbations in z. As shown in Table 3, for all forecasting horizons, the forecast errors for consumption, labor income and housing wealth are dominated by permanent shocks. Transitory shocks constitute almost half of the forecast error of financial wealth. Therefore, consumption is a function of only permanent components in yt , ht and ft . This proves our intuitive explanation of large coefficient α for the financial wealth. Around 50% of variations in financial wealth is accounted for by the transitory shocks in both the restricted and the unrestricted case. Here, variance decomposition without any restriction on the coefficient of error correction is called the unrestricted variance decomposition. The variance decomposition with restriction on the coefficient is called the restricted variance decomposition. Looking at Table 4, unrestricted variance decomposition has the same pattern of permanent shocks and transitory shocks across variables. Financial wealth forecast error at infinite horizon is dominated by transitory shocks whereas consumption, labor income and housing wealth are dominated by permanent shocks. The other way to explain the hypothesis that consumption does not contain a significant transitory component is to look at the long-horizon predictability of consumption growth equation. Cointegrating residual should have Table 5 Variance decomposition for housing wealth at different time-periods Period

1970

1990

1995

2003

P

T

P

T

P

T

P

T

1 2 5 10 ∞

0.658 0.667 0.668 0.668 0.67

0.342 0.333 0.332 0.332 0.33

0.44 0.435 0.43 0.43 0.43

0.56 0.565 0.57 0.57 0.57

0.70 0.713 0.714 0.715 0.715

0.30 0.287 0.286 0.285 0.285

0.99 0.985 0.982 0.981 0.98

0.01 0.015 0.018 0.019 0.02

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long-horizon forecasting power for consumption growth if consumption adjusts sluggishly to permanent innovation in housing wealth, financial wealth or labor income. In this case, permanent movements in housing wealth, financial wealth and labor income would not immediately be accompanied by a full adjustment in consumption to its trend level, thereby, generating a transitory component and a temporary deviation in the cointegrating residual from its mean. Table 6 shows the long-horizon predictability results. As can be seen from the table, cointegrating residual is insignificant from zero at all forecasting horizons, and therefore explains a negligible fraction of the variation in consumption at all future horizons. The long-horizon regression

Table 6 Long horizon regression Horizon H H Panel A: h=1 ct+h regressed on 1 4 8 12 Panel B: 1

H h=1

8 12 H h=1

8 12 Panel D: 1 4 8 12

H h=1

 ft+h regressed on

ht

 ft

β  zt

R2

0.06 (0.22) 0.07 (0.61) 0.21 (0.38) 0.40 (0.19)

0.02 (0.47) 0.02 (0.80) −0.12 (0.33) −0.28 (0.10)

0.03 (0.02) 0.13 (0.00) 0.15 (0.00) 0.18 (0.00)

−0.03 (0.09) −0.06 (0.26) −0.01 (0.93) 0.00 (0.99)

0.14

0.24 (0.05) 0.47 (0.06) 0.12 (0.76) 0.17 (0.75)

−0.08 (0.34) 0.05 (0.77) 0.14 (0.54) 0.50 (0.20)

0.05 (0.20) −0.06 (0.53) −0.29 (0.03) −0.43 (0.07)

0.06 (0.02) 0.11 (0.01) 0.05 (0.48) 0.05 (0.59)

−0.02 (0.57) −0.05 (0.44) −0.12 (0.43) −0.17 (0.31)

0.07

0.21 (0.33) 1.18 (0.01) 1.14 (0.25) 1.53 (0.23)

−0.21 (0.13) 0.06 (0.86) −0.01 (0.97) 0.22 (0.75)

0.28 (0.00) 0.61 (0.01) 0.93 (0.03) 1.03 (0.66)

0.05 (0.26) 0.12 (0.33) 0.14 (0.37) 0.04 (0.87)

−0.01 (0.76) 0.09 (0.71) 0.31 (0.40) 0.67 (0.08)

0.08

−0.17 (0.65) −0.35 (0.64) −1.84 (0.05) −0.52 (0.61)

−0.21 (0.39) 0.01 (0.97) 0.73 (0.20) 0.96 (0.17)

0.12 (0.35) −0.17 (0.49) −0.18 (0.59) −0.46 (0.24)

0.09 (0.22) 0.32 (0.06) 0.23 (0.21) 0.39 (0.06)

0.21 (0.00) 0.98 (0.00) 2.02 (0.00) 2.55 (0.00)

ht+h regressed on

4

yt

0.18 (0.01) 0.24 (0.17) 0.01 (0.96) −0.19 (0.55)

yt+h regressed on

4

Panel C: 1

ct

p-values in parentheses and bold numbers are significant at 5% significance level

0.12 0.05 0.05

0.04 0.04 0.03

0.10 0.07 0.07

0.05 0.22 0.42 0.50

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suggests that the only variable for which the cointegrating residual is significant is financial market wealth. Cointegrating residual is a significant predictor of financial wealth growth at all horizons; Furthermore, R2 statistic for the longhorizon regression is also highest for the financial market wealth growth. This implies that financial wealth is mean-reverting and adjusts over long horizons to match the smoothness of consumption, labor income and housing wealth. The quantitative response of consumption to transitory shock has not been shown yet. Figure 1 shows the impulse response of consumption to a unit standard deviation transitory shock. As shown in the figure, the response of consumption to a unit standard deviation transitory wealth shock is insignificant at all forecasting horizons. This reconfirms our earlier result that consumption does not respond to transitory movements in wealth. Standard errors used in calculating the confidence bands of Fig. 1 were computed using the bootstrap procedure described in Gonzalo and Ng paper. What implication does this finding have on the wealth effect? Both restricted and unrestricted variance decomposition show that most of the movements in housing wealth is permanent whereas half of the movements in financial wealth is transitory. Since consumption does not respond significantly to transitory movements in wealth at all forecasting horizons, it should respond to only those movements in wealth which are permanent. If all the movements in housing wealth and financial wealth were permanent, the estimated wealth effects were six cents for financial wealth and seven cents for housing wealth. Statistically, they are not significantly different from each other. Therefore, in a perfect market these two wealth effects are statistically indifferent from each other. But, even the most conservative estimate of the transitory component for the financial wealth implies that 46% of the variation in financial wealth is due to transitory shocks whereas 99% of the movements in housing wealth is permanent. Percentage of financial wealth that is transitory is different from

Fig. 1 Response of consumption to a one standard deviation transitory shock

2

1

0

-1

-2 1

2

3

4 CN

5

6

LB_CN

7

8 UB_CN

9

10

Does Consumption Respond More to Housing Wealth... Fig. 2 Consumption and its trend

439

10.0 9.8 9.6 9.4 9.2 9.0 8.8 8.6 55

60

65

70

75

80

85

90

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00

the VARIATION in financial wealth that is transitory because the measured unit in variation is in squared changes. Calculation of MPC therefore should take into account this difference in the units of measurement. If θ is the percentage variation √in wealth that is transitory, then percentage of wealth that is transitory= √θ+√θ1−θ . For financial wealth θ ≈ 50% , the normalization will leave the relative importance of transitory component unchanged as the percentage of wealth that is transitory will also be 50%. Since MPC out of transitory financial wealth is insignificant and MPC out of permanent financial wealth is six cents, therefore, average MPC out of financial wealth is three cents. Average MPC out of housing wealth is estimated to be seven cents since almost all the movements in housing wealth are permanent. Therefore, the framework adopted in this paper provides us one method of estimating wealth effect arising out of housing wealth and financial market wealth. The response of consumption to a unit dollar change in housing

Fig. 3 Labor income and its trend

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wealth is estimated to be seven cents whereas the corresponding estimate for financial market wealth is three cents. The difference in wealth effect arises in our framework because half of the movements in financial market wealth are transitory whereas most of the movements in housing market wealth are permanent and transitory variation in wealth has no effect on consumer spending. Multivariate Beveridge–Nelson Trend and Cycle The other way to look at the relative importance of permanent and transitory components is to perform multivariate Beveridge–Nelson (BN hereafter) decomposition of non-stationary variables of interest using Engle–Granger theorem. The primary objective is to find out whether multivariate BN decomposition reinforces our result that only financial wealth tend to have significant

Fig. 5 Financial wealth and its trend

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Does Consumption Respond More to Housing Wealth... Fig. 6 Financial wealth cycle

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deviations away from trend. BN methodology decomposes a non-stationary series into a random walk component and a stationary component which is the cycle of the non-stationary series. According to the Engle–Granger theorem the BN decomposition of zt has the following representation: zt = y0 + μt + (1)

t 





ut + ut − u0 ,

(17)

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where   (1) = β⊥ (α⊥ (1)β⊥ )−1 α⊥ , 



(18)



and ut = (L)ut . Where (L)  = (1)+(1-L) (L). The common trend in xt is extracted using TSt = (1) tk=1 ut Using this methodology, consumption, labor income, house wealth and financial wealth have been decomposed into a BN trend and cycle. The practical implementation of this trend-cycle decomposition has been done by using Morley’s (2002) state space technique.16 Appendix shows how to represent the above model into state space format and then how to decompose the variables into a trend and a cycle using above technique. Figures 2 to 6 show the log of consumption, labor income, housing wealth, financial wealth with their respective trend and cycles of consumption and financial wealth. As shown in the figure only financial market wealth tends to have large deviations from its trend. Figure 5 shows the cyclical component of financial market wealth. The cycle of financial wealth follows broadly the pattern as documented in 2004. This gives us interesting insight into the bull and bear market of U.S. stock market. As the figure shows, the U.S. financial wealth was above its trend in

16 Morley’s (2002) methodology provides a simple technique of trend-cycle decomposition of cointegrated variables using state-space method.

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the 1960s, from the mid 1970s to the mid 1980s it was below the trend, and again there was a bull market in post-1997 period. For housing wealth, most of the variations is due to trend as there are very small deviations away from trend. This reinforces the argument that most of the changes in housing wealth are permanent whereas for financial wealth a major portion of the changes is transitory and hence the net effect of housing wealth on consumption is higher.

A Time-Varying Parameter Model of Housing Market Deregulation The U.S. economy has witnessed rapid financial liberalization over the last three decades. The housing market has especially undergone big changes over the last thirty years. Increased competition in the primary mortgage market along with improvements in information processing technology have lowered the explicit financial transaction costs associated with obtaining a mortgage, as reflected in the secular decline in average points and fees on conventional loans. Mortgage refinancing has been at its record high in the last two years because of the institutional changes and lower mortgage rates. There have also been episodes of housing market boom and bust in the last thirty years. Because of the deregulation in the housing market, the housing market is expected to become more efficient and experience less frequency of booms and busts in the housing market over time. This has implications for the error correction coefficient as it tells us about the importance of transitory innovations at different forecast horizons for the housing wealth. Our model shows that the error correction parameter is insignificant for the whole sample but this estimate is an average of all the estimates at different points in time. If the parameter is unstable over time then the average of the estimate will not give us the proper information about that parameter, especially, when there have been big changes in the housing market over time. It is intuitive to think that the impact of housing wealth on consumption should be time varying as the degree of efficiency of housing wealth has increased over time. It would be ideal to allow the β  s in Eq. 7 to vary over time, but, there is no econometric tool to analyze the time variation in a non-stationary framework.17 Therefore, it has been assumed that the long-run relationship between consumption, labor income, housing wealth and financial wealth has remained constant. I assume that short run relationship might have changed due to the deregulation in the housing market. In this section, the parameters of the VECM are allowed to vary over time. The following time-varying parameter model describes the gradual evolution of coefficients in consumption growth equation: ct = γ10t + γ11t ct−1 + γ12t yt−1 + γ13t ht−1 + γ14t  ft−1 + αct β  zt−1 + uct . (19) 17 Hansen (1992) test allows for a single break in the cointegrating relationship. But, we are interested in changes over time, therefore, one break in the cointegrating relationship will not serve our purpose.

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Here, consumption growth equation has been analyzed. The labor income, housing wealth and financial wealth equation will have the same structure. The measurement equation for the state space model is: ⎡ ⎤ γ10t ⎢ γ11t ⎥ ⎢ ⎥ ⎢ γ12t ⎥    ⎢ ⎥. (20) ct = 1 ct−1 yt−1 ht−1  ft−1 β zt−1 ⎢ ⎥ ⎢ γ13t ⎥ ⎣ γ14t ⎦ αct The coefficients follow a random equation is: ⎡ ⎤ ⎡ γ10t 1 0 0 0 ⎢ γ11t ⎥ ⎢ 0 1 0 0 ⎢ ⎥ ⎢ ⎢ γ12t ⎥ ⎢ 0 0 1 0 ⎢ ⎥ ⎢ ⎢ γ13t ⎥ = ⎢ 0 0 0 1 ⎢ ⎥ ⎢ ⎣ γ14t ⎦ ⎣ 0 0 0 0 αct 0 0 0 0

walk process. Therefore, the transition 0 0 0 0 1 0

⎤⎡ ⎤ ⎡ ⎤ 0 γ10t−1 ω11t ⎢ ⎥ ⎢ ⎥ 0⎥ ⎥ ⎢ γ11t−1 ⎥ ⎢ ω12t ⎥ ⎢ γ12t−1 ⎥ ⎢ ω13t ⎥ 0⎥ ⎥⎢ ⎥+⎢ ⎥. ⎥ ⎢ ⎥ ⎢ 0⎥ ⎥ ⎢ γ13t−1 ⎥ ⎢ ω14t ⎥ 0 ⎦ ⎣ γ14t−1 ⎦ ⎣ ω15t ⎦ 1 αct−1 ω16t

(21)

In matrix notation ct = xt−1 t + uct .

(22)

t = F t−1 + ω1t .

(23)

uct  i.i.d.N(0, σc2 ).

(24)

2 ω1t  i.i.d.N(0, σω1 ).

(25)

The Kalman Filter is applied to the above model to make inference on the changing regression coefficients.18 The magnitude of error correction coefficient tells us the importance of transitory innovation in the forecast error variance decomposition. The higher the magnitude of the error correction coefficient, the higher will be the relative importance of transitory innovations in the forecast error variance decomposition. The error correction coefficient for consumption growth and financial wealth growth is stable over time as can be seen from Figs. 7 and 9, except for some volatility in the financial wealth error correction in the 1970s. The figures are plotted with corresponding 90% confidence band. For Engle–Granger representation theorem to hold, at least one of the error-correction coefficients has to be significant for all the time periods. As can be seen from Figs. 7 to 9, this condition holds. The errorcorrection coefficient for consumption growth is insignificant for most of the

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MLE estimation procedure was adopted. See Kim and Nelson (1999) for details.

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time period before 1985. It becomes significant after 1985. The error correction coefficient for housing wealth growth equation is significant till 1980 and then it becomes insignificant except for 1986–1987. The error correction coefficient for financial wealth growth equation is significant for most of the time period. The error correction coefficient of the housing wealth gives us some interesting results. From 1973 to 1981, the error correction coefficient witnessed a large increase. This was also the time when housing wealth increased by 30%. The framework presented in this paper indicates that this increase in housing wealth was not permanent and this was supported by the downfall of the market in the 1980s. Except for an increase during 1985–1986 (abolition of Regulation Q), the error correction term has a declining trend till 1993. The coefficient has become relatively stable and almost insignificant since 1994. This may reflect the increased information processing in the mortgage market and better functioning of the housing market. This argument is consistent with

Fig. 8 Error correction coefficient for housing wealth growth and 90% confidence interval

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Sellon (2002) who has argued that pass through of monetary policy actions to mortgage market has increased substantially since 1994 and the market has become more efficient in processing the information. To quantify this effect, I perform forecast error variance decomposition using the time varying parameter coefficients at four different time period in the whole sample. As shown in Table 5, 35% of the variation in housing wealth was accounted by transitory shocks in 1970, whereas it was 57% in 1990, 30% in 1995 and 2% in 2003. This implies that the relative importance of permanent shock in housing wealth has been increasing over the whole sample period. The time variation in the error correction coefficient has interesting implications for the housing wealth effect. The higher magnitude of error correction coefficient tells us that the relative importance of permanent shocks affecting the housing wealth was lower before 1994. Since the absolute value of error correction coefficient has witnessed a decline over time, therefore, the magnitude of wealth effect arising out of housing wealth should be increasing. This reinforces the argument that the liberalization in the housing market might have led to an increase in the housing wealth effect.

Robustness Analysis The results obtained in this paper are robust to different specification of the model and the use of similar data. The results show the same broad pattern if I include durable goods flow expenditure in non durable goods and services expenditure as a measure of consumption in our model. The results have the same qualitative properties if financial wealth is replaced with stock market wealth which is defined as corporate equities+mutual fund shares+pension fund reserves+life insurance reserves. The pattern of shocks affecting different variables does not change if the ordering of variables in Choleski decomposition is changed. In the time-varying parameter model, the

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results are robust to AR specification of the transition equation. The results in the time-varying parameter model also do not change if coefficients other than α are restricted to remain a constant. Concluding Remarks The objective of this paper is to estimate the relative impact of changes in housing market wealth and financial market wealth on consumption using macro level flow of funds data. It has been shown that on average a dollar increase in housing wealth increases consumption by seven cents whereas the corresponding estimate for financial market wealth effect is three cents. Using Gonzalo and Ng (2001) methodology, it has been shown that the difference in the wealth effect arises from the difference in the relative importance of permanent and transitory innovations at different forecast horizons for both types of wealth. Transitory shocks constitute half of the movements in financial wealth at all horizons whereas permanent shocks dominate housing wealth. Since consumption is shown to respond only to permanent movements, therefore, the average MPC out of housing wealth turns out to be higher than the average MPC out of financial wealth. Using the same framework it has also been shown that BN cycle of financial wealth follows the broad pattern of the business cycles. Using a time-varying parameter model this paper shows that housing wealth effect has increased over time in U.S. as permanent shocks have become more important in forecasting housing wealth at different forecast horizons. This implies that any increase in housing wealth today will have a bigger impact on consumption than the increase in housing wealth twenty years ago. What are the implications of the results obtained in this paper for real-world policymaking? This paper shows the relative impact of financial wealth and housing wealth on aggregate demand via its impact on consumption. The implication of this result is that the policymakers should attach more importance to movements in house prices in forecasting inflation and aggregate demand. Whether or not the policymakers should respond to changes in asset prices is still open to debate. This paper also helps us to understand the behavior of consumption during 2001 recession. One of the explanations of strong consumption growth in presence of declining financial wealth was increasing housing wealth and hence the net impact on consumption was positive as the estimated average MPC out of housing wealth is higher than that of financial wealth. One of the limitations of this paper is that durable goods expenditure has not been modeled explicitly. Although flow of durable goods services has been added to consumption for robustness purposes it does not capture the dynamics of durable goods expenditure. The initial evidence shows that recent surge in housing wealth has also supported the durable goods expenditure. It will be interesting to develop a model which includes durable goods expenditure explicitly as movements in the durable goods expenditure are very important for the business cycle.

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The other limitation is that cointegrating vector is not allowed to vary over time. The econometric tool to analyze a time-varying parameter model in a non-stationary framework has not been developed yet. It will be ideal to deal with the issue of housing market deregulation in a case where the cointegrating coefficients are allowed to vary over time. The results presented in this paper do not claim to have any implication for out of sample predictability of stock returns. Using similar framework, Lettau and Ludvigson have shown that the forecasting performance of this type of model is better than the other competing models in the literature. But, Brennan and Xia (2005) claim that Lettau and Ludvigson’s (2001) results might be spurious as they are using the information from the whole sample to forecast the stock prices within the sample. This is still an open question and might be a productive area for further investigation. Acknowledgements Financial support from Grover and Creta Ensley Foundation is gratefully acknowledged. I am deeply indebted to my supervisor Charles Nelson for his guidance and encouragement. Thoughtful comments from Yu-chin Chen, Evan Koenig, Richard Startz and Eric Zivot are gratefully acknowledged. I am also thankful to Erika Gulyas, Krisztina Nagy, Kisa Watanabe and Bingcheng Yan for helpful comments and suggestions.

Appendix 1. Consumption—The data on consumption has been taken from national income and product accounts of Bureau of Economic Analysis. It includes expenditure on non durable goods and services. Expenditure on housing services has been excluded. It is seasonally adjusted and deflated by chained weighted deflator. The data is in terms of real per capita. Flow of durable goods and services are taken from Federal Reserve Board. 2. Labor income—Labor income in my study is the same as Lettau– Ludvigson’s. After tax labor income has been defined as Wages and Salaries+Transfer Payments+Other labor income-personal contributions for social insurance-taxes. Taxes are defined as [Wages and Salaries/ (Wages and Salaries+Proprietor’s income+rental income+personal dividends+personal income)] times personal tax and non tax payments. The quarterly data are in per capita terms. 3. Housing wealth—Housing wealth is net house wealth of households after adjusting for mortgages. This has also been deflated by chained weighted index and in real per capita terms. The data source is Flow of Funds Account of Federal Reserve Board. 4. Financial wealth—Financial wealth is defined as total financial assetliabilities of households excluding mortgages. This has also been deflated and in real per capita terms. The data source is Flow of Funds Account of Federal Reserve Board. Financial Asset is line 8 of the table B.100 of the Flow of Funds Account and liabilities are line 32. I define stock market wealth as Corporate Equities+Mutual Fund Shares+Pension Fund Reserves+Life Insurance Reserves.

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5. Population—Population data for the U.S. economy has been taken from Bureau of Labor Statistics. 6. Price deflator—This is chained weighted price deflator. The data source is Federal Reserve St. Louis.

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