Consumption adjustment to real interest rates: Intertemporal substitution revisited

ELSEVIER

Journal of Economic Dynamics and Control 22 (1998) 293-320

Consumption adjustment to real interest rates: Intertemporal substitution revisited Joon-Ho Hahm**“yb aKorea Development Institute, P.O. Box 113, Cheong Ryang, Seoul 130-012. South Korea bDepartment of Economics, University of California, Santa Barbara, CA 93106, USA Received 17 June 1996; accepted 1 January 1997

Abstract

This paper investigates the degree of elasticity of intertemporal substitution in consumption using post-war US aggregate data. Previous findings suggest that the elasticity of substitution is unlikely to be much above 0.1 and may well be zero. In contrast, I find

strong evidence that there is a statistically significant positive response of consumption growth to changes in expected real interest rates. The elasticity estimates cluster around 0.3. Previous weak results are attributed to either the inappropriate choice of instruments or the use of an inadequate measure of consumption. This finding is robust to considerations of the time aggregation bias, different sample periods, and alternative formulations of the permanent income consumption model which include ‘rule-of-sum’ consumers and borrowing constraints. For example, if the Campbell and Mankiw model is adopted as an approximate description of US aggregate time series in consumption, income and real interest rates, the implied elasticity of intertemporal substitution for permanent income consumers could be as high as 0.8, which implies that the coefficient of relative risk aversion is around 1.25. Keywords: Consumption and Relative risk aversion JEL class$cation: E21; D91

saving;

Intertemporal

substitution;

Real interest

rate;

*Corresponding address: Korea Development Institute, P.O. Box: 113, Cheong Ryang, Seoul 130-012, South Korea. I am grateful to Henning Bohn, Douglas Steigerwald, Charles Stuart, Linda Tesar and Steve Trejo for their useful comments. Any errors and misinterpretation are mine alone. 016%1889/98/.$19.00 0 1998 Elsevier Science B.V. All rights reserved PI1 SO165-1889(97)00053-5

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1. Introduction

One important source of adjustment in consumption-savings allocation is the movement in expected real interest rates. The magnitude of the elasticity of intertemporal substitution in consumption has received serious attention from many macroeconomists since the emergence of intertemporal optimization approach as a dominant framework in macroeconomic modeling. The degree of intertemporal substitution in consumption has also been at the heart of a long debate in the finance literature, due to its potential link with the attitude toward risk, and its implications on equilibrium asset pricing. In the present paper, I investigate the degree of elasticity of intertemporal substitution in consumption. Contrary to recent findings that there has not been any important response of consumption to changes in real interest rates in the US, I find strong and systematic evidence that the elasticity of intertemporal substitution in consumption is indeed significantly positive and well above zero, though not greater than one. Previous weak results are attributed to either the inappropriate choice of instruments or the use of an inadequate measure of consumption. Using nondurables consumption data, Hall (1988) argued that the elasticity of intertemporal substitution is unlikely to be much above 0.1 and may well be zero. His conclusion does not seem to be warranted due to the inappropriate choice of instruments, more specifically, due to the use of unusually short lagged instruments in his quarterly regression. More careful choice of instruments and using longer lags effectively reverse his finding. Indeed, I find that the elasticity of intertemporal substitution is precisely estimated and the magnitude is around 0.3 for nondurables consumption. For nondurable and services consumption, Campbell and Mankiw (1989, 1990, 1991) showed that the elasticity of intertemporal substitution is basically zero especially when income growth is added to the regression. However, as argued below, due to the housing component of services consumption, the use of nondurable and services consumption may yield a highly misleading conclusion when one attempts to draw inferences about the magnitude of intertemporal substitution. Using the nondurable and services consumption excluding housing services I find again a precisely estimated and significantly positive coefficient of the real interest rate, which is robust to the inclusion of income growth rate in the regression. This suggests that there has been a significant response of consumption to changes in the real interest rate in the post-war US. I also explicitly test the underlying models. The simple stochastic real interest rate version of the permanent income hypothesis is rejected although the coefficient of the real interest rate is precisely estimated. However, an alternative model proposed by Campbell and Mankiw (1989, 1990, 1991) postulating the presence of both forward-looking and rule of thumb consumers is not readily rejected. For both nondurables, and nondurable and services excluding housing, I show that the permanent income consumers indeed adjust

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their consumption allocations in response to changing real interest rates. If the Campbell and Mankiw model is adopted as an approximate description of US aggregate time series in consumption, income and real interest rates, the implied elasticity of intertemporal substitution for permanent income consumers could be as high as 0.8 for nondurables, and 0.5 for nondurable and services excluding housing. For a diagnostic purpose, I also investigate the model using an alternative specification where the two components of the real interest rate are included as separate regressors. The estimation results support the conclusion above and indicate that both the nominal interest rate and inflation are related with consumption growth only through the real interest rate channel as predicted by the model. This paper is organized as follows: In Section 2, I provide a simple theoretical framework used for estimating the elasticity of intertemporal substitution. A brief review of existing evidence on the magnitude of the parameter in various permanent income consumption models is also provided in Section 2. Section 3 discusses the estimation methodology with a brief description of the data. The main empirical evidence for nondurables consumption, and results on various other considerations are reported in Section 4. In this section, I also report the evidence on nondurable and services consumption comparing with the existing evidence. Section 5 summarizes and concludes. Finally in the appendix, I consider another variant of the permanent income consumption model with borrowing constraints, and show that my results are robust to the inclusion of expected future income as well as expected current income. 2. Intertemporal

substitution

2. I. The permanent

in consumption

income hypothesis

under uncertain

real returns

Assume an infinitely lived representative consumer who maximizes expected life-time utility, and has additively time-separable preferences. She is allowed to buy and sell assets in capital markets. The consumer’s problem is to maximize

Er f (1 + 4-’ U(G+,) s=o

subject to the sequence of asset evolution equation,’ W

ffl

=

(1

+

rr+

1) W,

+

Yt

-

G)

(2)

‘This asset evolution equation implicitly assumes that there is only a single asset in the capital market. Since I focus on the consumption-savings decision rather than portfolio choice problem among alternative assets, it would be more convenient to work with this simplifying assumption without losing any essential insight. However for any asset, as long as the representative consumer holds that asset, the Euler equation below will be a valid necessary condition. See Hansen and Singleton (1983) for consideration of multiple assets.

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and some terminal condition to avoid infinite borrowing. U( ) is the one-period utility function, 6 denotes the constant rate of time preference, and E, is the conditional expectations operator based on the information set available at t. C,, Y,, and W, are period-r consumption, labor income, and asset, respectively, and rl+ 1 is the uncertain real rate of return on any asset between t and t + 1. The first order necessary condition implied by the above optimization problem is, V’(G) = (1 + 6)-i Ml

+ rt+ 1) U’(C,+ 111,

(3)

where V’( ) denotes the first derivative. If the real rate of return is constant, consumers smooth expected marginal utilities over time, and this implies Hall’s (1978) famous result that marginal utilities of consumption should follow a random walk with drift. This simplest version of the modern permanent income hypothesis (PIH) has been rigorously analyzed and widely rejected.’ When real asset returns are stochastic, the above PIH model predicts that consumers revise their optimal intertemporal consumption plan in response to the changing relative price of future consumption in terms of today’s consumption. This theoretical framework has received serious attention from both the macroeconomics and finance literatures due to its implications on the optimal consumption-savings behavior and equilibrium asset pricing.3 To see the relationship between consumption path and real asset return more clearly, assume that the representative consumer has a constant relative risk aversion period utility with Arrow-Pratt measure of relative risk aversion y: U(C,) = c: - ‘/( 1 - y),

y > 0.

(4)

Under CRRA utility and the assumption of joint log-normality between consumption growth and asset returns, 4 the Euler equation (3) can be transformed to the following log-linear form,’ E, Ac,+r = - Sir + y/2 a2 + l/y E, rr+ i >

(5)

‘Various consumption puzzles have emerged from the rejections; among others, see Flavin (1981) for excess sensitivity of consumption to current income, and Deaton (1987) for excess smoothness. “In the present paper, I focus on the consumption behavior in response to changing expected real asset returns. For the related asset pricing models, see the consumption-based capital asset pricing models due to Rubinstein (1976), Lucas (1978), Breeden (1979), and Brock (1982). 4Various authors have exploited the assumption of CRRA utility with joint log-normality of consumption growth and asset returns. See Grossman and Shiller (1981), Hansen and Singleton (1983), among others. %ee Hansen and Singleton (1983) for exact derivations. Also essentially the same consumption growth equation could be obtained using a Taylor series approximation as in Mankiw (1981).

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where AC, + I is the consumption growth rate from period t to t + 1 (that is, ln(C,+ i/C,)), rr2 is the constant conditional variance of AC,+ 1 - l/y Y,+i, which in turn, depends on conditional variances of consumption growth rate and real rate of return and their covariance.6 Also, the approximations ln(l + 6) = 6 and ln(1 + rJ = rt were used. The ex post relationship of Eq. (5) assuming rational expectation is Ac,+i = CY + B rt+1 + %+1,

(6)

where

TV= - S/y + y/2 o’, /l = l/y, u,+r = (Ac,+~ - l/y rt+ r) - E,(Ac~+~ l/r~t+~), and hut+1 = 0. The PIH under stochastic real returns implies that any variable in the current information set should not be correlated with consumption growth beyond its predictive power for the consumer’s real rate of return. The coefficient fl is the elasticity of intertemporal substitution and represents the degree to which consumers defer current consumption in response to a higher expected real return. In Table 1, I summarize some of the previous estimates of p in this simple form of the permanent income model. Although this summary is far from exhaustive, it is indicative of the previous findings on the magnitude of the elasticity. Since I will use the treasury bill as the appropriate choice of asset, I focus on the estimates where treasury bill returns were used. Two important observations emerge from the table. First, as strongly argued by Hall (1988), the correction of time aggregation bias seems to be crucial at least for the nondurable consumption case. ’ Hansen and Singleton (1983) found large and significant estimates for the elasticity. However, Hall (1988) found that /? is not statistically different from zero when appropriate econometric methods are used to account for the time aggregation bias, effectively reversing the previous authors’ findings.* He concluded that earlier evidence of significant

6Following the literature, I assume constant conditional variances of consumption growth, real asset returns, and their covariance. If the underlying conditional variances are time varying, there will be an additional source of the consumption growth fluctuations due to precautionary savings motive. However, concrete evidence has not yet been established on the possible role of changing second moments. For some empirical explorations, see Carroll (1992), and Hahm (1993). 7Christiano et al. (1991) argued that continuous time versions of the PIH model hold much better in the US. If consumption is a continuous time random walk, the time-average of it as in our data would show spurious first order serial correlations. This result is originally due to Working (1960). ‘Hall (1988) argued that the coefficient of real rate of return in the consumption growth equation should be interpreted as the intertemporal elasticity of substitution and not the reciprocal of the relative risk aversion. With the assumption of additively time-separable utility, expected utility maximization implies that the degree of intertemporal substitution is inversely related with the coefficient of relative risk aversion. Thus under standard expected utility framework, his near zero intertemporal elasticity would imply infinite relative risk aversion, which is not empirically plausible. Nonexpected utility framework as in Kreps and Porteus (1978) would lead to the separation of those two coefficients avoiding this difficulty. See Epstein and Zin (1989), and Weil (1990).

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Table 1 The elasticity of intertemporal substitution in US aggregate consumption: model and using treasury bill returns” C

Sample

Mankiw (1981)

NDS

48: l-80:4 (Q)

Hansen & Singletonb (1983)

ND ND NDS NDS

59:2-78:12(M) 59:2-78:12(M) 59:2-78:12(M) 59:2-78:12(M)

Mankiw (1985)

NDS NDS

50-81(4th Q) 50-8 l(4th Q)

Hall (1988)

ND ND ND ND ND

2440, 50-83 (A) 59: 10-78: 12(M) 59: 10-83: 12(M) 59: 10-83: 12(M) post-war(Q)

ND

post-war(Q)

Campbell & NDS Mankiw NDS (1989) NDS NDS NDS NDS NDS NDS

53: 1-86:4(Q) 53: l-86:4 (Q) 53:1-86:4(Q) 53:1-86:4(Q) 53:1-86:4(Q) 53: 1-86:4(Q) 53: 1-86:4(Q) 53:1-86:4(Q)

under the simple PIH

Time agg. considered

Instruments

0.252*

No

r{l to 2)

6.0976**

5.3191:; 1.0741** 0.7758**

No No No No

dc{l to dc{ 1 to dc{l to dc{ 1 to

0.41 0.33

No No

r{l) r{ 1 to 2}, log C{ 1 to 2)

-0.40** 0.98** 0.48** -0.03 0.34**

Yes No No Yes

0.10

Yes

r(2), dc{2), i{2) r{ 1 to 6}, dc{ 1 to 3) r{ 1 to 6}, dc{l to 3) r{ 2 to 6}, dc(2 to 3) r{ 1 to 2}, inf{l to 2}, dc{l to 2) r{2}, inf{2}, dc(2)

Estimate

0.270** 0.281** -0.707 0.992** 1.263** 1.213** 0.204* 0.150

No

Yes Yes Yes Yes Yes

Yes Yes Yes

2}, r{l to 4}, r{ 1 to 2}, r{l to 4}, r{ 1 to

2) 4) 2) 4)

r(2 to 4) r{2 to 6)

dc{2 to 4) dc{2 to 6) di{2 to 4) di{2 to 6) r(2 to 4}, dc{2 to 4) r{2 to 4}, dc{2 to 4}, di{2 to 4)

‘Under the column headed by consumption (C), ND denotes nondurables, and NDS denotes nondurable and services as a measure of consumption. Frequency A, Q, M denote annual, quarterly, and monthly, respectively. 4th Q denotes sampling of 4th quarter data for each year. ** and * denote t-values are greater than 1.960, and 1.645, respectively. For the instrument sets, following notations are used; number of lags are in the { }, r: real interest rate, dc: consumption growth rate, i: nominai 3-month treasury bill rate, di: the first difference in the 3 month T-bill rate, inf: inflation rate, C: level of consumption. bHansen and Singleton (1983) originally report the estimates of relative risk aversion coefficient. I report the implied elasticity of intertemporal substitution here.

and large elasticity of intertemporal substitution comes from the inappropriate estimation method. Indeed, in Hall’s case, consideration of time aggregation bias yields either implausible negative value or insignificant estimates. The second important point to make is that even though the /I coefficient is statistically significant in some cases, the underlying model is always rejected,

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making the interpretation of the coefficient difficult.’ Mankiw (1981, 1985) rejected the simple PIH model by finding lagged income growth significant when added in the consumption growth equation. Hansen and Singleton (1983) found the strongest rejection of the overidentifying restriction for the T-bill return case. Campbell and Mankiw (1989) obtained some significant estimates for nondurable and services consumption. However, the coefficient of the real interest rate was always insignificant when the current income growth rate was added to the consumption growth equation. Moreover, the income growth rate was always significant, suggesting the rejection of the simple real rate version of the PIH. 2.2. Alternative

PIH models and the elasticity

of intertemporal

substitution

Rejections of the stochastic real return version of the PIH have led to considerations of alternative models. In the present paper, I only discuss the alternative PIH models relevant to the discussion of intertemporal substitution. In Table 2, I summarize two important alternative PIH models which report the elasticity of intertemporal substitution. Mankiw et al. (1985) considered nonseparability of consumption with leisure. For both nondurables, and nondurable and services consumption, they found some large values of the coefficient. However, these estimates were never significant and the overidentifying restrictions were strongly rejected. Campbell and Mankiw (1989, 1990, 1991), in a series of papers, proposed an alternative model as a valid time-series characterization of the post-war US aggregate consumption, income, and interest rates. In their model, a fraction of the consumers is current income (rule of thumb) consumers due to myopia or liquidity constraints, and the remaining consumers are permanent income consumers.” Specifically, they considered the following equation, &+1

=p++et+1

+AdY,+1

+E,+l,

(7)

where /1is the fraction of aggregate income received by the current income (rule of thumb) consumers, p is (1 - 1)x, and 6’is now (1 - 1) times the elasticity of intertemporal substitution /I. Ef+l is again orthogonal to the variables in the current information set. As can be seen in Table 2, for each and every instrument set, they fail to reject that the coefficient of the real interest rate is zero in Eq. (7). Note that the time aggregation bias was properly handled by always using instruments lagged at

‘Hall (1988) did not explicitly test the model. “‘Antzoulatos(l994) show that under borrowing constraints, consumption growth will depend on expected future income as well as current income. In the appendix below, I also estimate the variant of the permanent income consumption model under borrowing constraints.

Sample

ND ND NDS

Post-war (Q) Post-war (Q) Post-war (Q)

0.008 0.014

53:1-894 (Q) 53:1-85:4 (Q)

NDS

NDSd

dc(2 to 4}, r{2 to 4) di(2 to 4), r{2 to 4) dy{2 to 41, dc(2 to 4}, r{2 to 4) log C/Y(2) dy{2 to 4}, dc{2 to 4}, r(2 to 4) log C/Y{21

Not rejected Not rejected Not rejected Not rejected

dy{2 to 4}, r(2 to 4) dc(2 to 4}, r{2 to 4} di(2 to 41, r{2 to 4)

C{ 1,2}, i{ 1,2), LIl,2}, P{1,2), W{ l,2) C(W), i{O,l}, Wl), P(W), W(O.1) C{1,2}, i{l,2}, L{1,2}, P{1,2}, W{1,2}

Instruments

Not rejected Not rejected Not rejected

Rejected Rejected Rejected

Overidentifying restriction

din this specification, they added additional lag of income growth rate to capture the slow adjustment of current income consumers.

‘In their original papers, they report the coefficient of real interest rates, which is (1 - A)times the estimate of elasticity of intertemporal substitution. Since their estimated fraction of current income consumers (A)is approximately 0.5 and always significant, here I multiply the coefficients by two for consistency with other results.

“Under the column headed by consumption (C), ND denotes nondurables, and NDS denotes nondurable and services as a measure of consumption. Frequency Q denotes quarterly. All coefficient estimates reported in this table are not significant at the 10% level. For the instrument sets, following notations are used; number of lags are in the { }, r: real interest rate, dc: consumption growth rate, dy: income growth rate, di: first difference in the 3 month T-bill rate, C: level of consumption, Y: level of disposable income, P: price, L: leisure, W: nominal wage. bI report reciprocals of a estimates in concave utility case in their Table 2. In all cases, they fail to reject the separability, thus l/oc would be a relevant measure of elasticity of intertemporal substitution.

0.098 - 0.044

53:1-85~4 (Q) 53:1-85:4 (Q)

NDS NDS

Campbell and Mankiw (1990) Campbell and Mankiw (1991)

0.160 0.178 0.032

3.891 2.661 6.803

Estimate

53:1-864 (Q) 53: l-86:4 (Q) 53:1-86:4 (Q)

NDS NDS NDS

Campbell and Mankiw (1989)

2. PIH & rule of thumb consumers combined’

Mankiw, Rotemberg and Summe& (1985)

1. Nonseparability of consumption with leisure

C

Table 2 The elasticity of intertemporal substitution in U.S. aggregate consumption: under alternative PIH model and using treasury bill returns

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least twice. Moreover, in every case they failed to reject the overidentifying restrictions. They concluded, ‘forward-looking consumers do not adjust their consumption growth in response to interest rates, so their intertemporal elasticity of substitution in consumption must be close to zero.“’ As surveyed in this section, the magnitude of intertemporal substitution seems to be low and statistically fragile, especially when the income growth rate is added to the specification. This conclusion however, is not warranted as I show in the following sections.

3. Data description and estimation 3.1. Measure

of consumption,

methodology

income and real asset returns

For the empirical analysis in this paper, I use quarterly data. Consumption and disposable income series were obtained from the constant dollar (billions of 1987 $) series in the US national income and product account (NIPA), and deflators are corresponding series from the same source. All consumption, income, and deflators are seasonally adjusted. Real per capita measures were computed using total population series including armed forces overseas, which is also from the NIPA. As a measure of the nominal asset return, I used 3-month treasury bill returns (discount basis) as in Hall (1988).” The after-tax real interest rate was computed assuming a marginal tax rate of 30% on the nominal interest rate as in Mankiw (1985) and Campbell and Mankiw (1989,199O). In the later empirical section, I also consider the possibility of measurement errors arising from assuming constant marginal tax rates. The sample period is from 1953 : 1 to 1994: 4.13 However, to check for robustness, I also report results for Campbell and Mankiw’s (1990, 1991) sample period, 1953 : l-1985 : 4. In the upper panel of Table 3, I show some statistical properties of nondurables versus nondurable and services combined measure of consumption. Inflation and real interest rates were computed using the corresponding implicit

“Campbell

and Mankiw (1989, p. 186).

‘*Another asset category often used in the literature is stock returns. However, as argued in Mankiw and Zeldes (1991), more than two-thirds of food consumption is accounted for by non-stockholders, and thus stock returns may not be an appropriate choice in our representative agent framework. I reproduced the empirical results using stock returns, and found that the qualitative results were similar to the treasury bill case, although the coefficient estimates were a little bit smaller. IsBlinder and Deaton (1985), Campbell (1987), Campbell and Deaton (1989), and Campbell and Mankiw (1989, 1990, 1991) used the sample period from 1953: 1 avoiding the Korean War period. Actual estimation in the following empirical section covers 1953 : l-1994: 3 period since computing growth rates loses one data point.

F

- 0.2208 0.2878 0.4201

iY inf 3.205 1.169 5.654

0.134

1.964 (3.682)

0.025 0.324 0.001

Marginal significance level

3.137 (3.684) 4.219 (2.675)

Avg. (std.)

inf

- 0.292

- 0.333

p(dc, inf )

5.507 (2.966)

avg. (std.)

i

‘OLS regression of dependent variable on its own lags 2-4, and on consumption growth rates lagged 24. Consumption growth rate is from real per capita nondurable comsumption, and after tax ex post real interest rate was computed using nondurable consumption deflator. F value is from the restriction that coefficients of lagged consumption growth rates are jointly zero.

“Definitions of variables are the following; dc: quarterly real per capita consumption growth rate (% p.a.), irk quarterly inflation rate estimated from corresponding consumption deflator (% p.a.), dy: quarterly real per capita income growth rate (% p.a.), i: nominal return on 3-month treasury bills (% p.a.), r: after tax ex post 3-month real interest rate assuming marginal tax rate of 0.3 (% p.a.).

Sum of coeff. of dc{24}

Dependent variable

0.502

0.263

0.497

1.018 (2.850) 1.840 (1.963) 0.118 (3.219) -0.363 (1.934)

Avg. (std.)

Avg. (std.)

p(dc.dY)

Avg. (std.) p(dc, r)

dY

r

dc

B. Bivariate granger causality analysisb

NDS

ND

Measure of consumption

Table 3 Data description: quarterly, 1953 : 1-1994: 3 A. Basic statistics’

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price deflator. As one can see from the averages and standard deviations, both the consumption growth rate and the after-tax real interest rate computed using nondurable consumption and its deflator show more volatility relative to their combined counterparts. The more volatile real return is driven by more volatile inflation for nondurables. Note that both inflation and the real interest rate show higher correlation with consumption growth in nondurables relative to the case of nondurable and services. As previously noted, Campbell and Mankiw focused on the combined measure of nondurable and services consumption. In this paper, as in Hall (1988), I mainly focus on nondurables as a measure of consumption. If nondurable and services components are not perfect substitutes, there could be some important loss of information by aggregating those two components. Even if those two components are additively separable in preferences, the nonconstancy of the relative price between those two may cause serious problems in using the combined measure. In addition, when one attempts to draw inferences about the magnitude of the intertemporal substitution, using the combined measure becomes particularly problematic due to the inclusion of housing services. For homeowners, the consumption of housing services is measured from the imputed market rent for the equivalent housing. This imputed rent of a home owner is counted both as her consumption expenditure as well as income, providing another source of the high correlation between consumption and income. For both homeowners and renters, it would be prohibitively costly to intertemporally substitute their housing consumption in response to frequently changing real interest rates. Even for renters, frequent moving is very costly due to adjustment cost. Homeowners can probably add or reduce existing housing stock, but this is also costly due to the possible irreversibility. Indeed the consumption growth of housing services is much smoother relative to other components of consumption. For the sample period, the average growth rate of the consumption in housing services is 2.288% p.a. with standard deviation of 1.639. The housing services also account for a nonnegligible share of total consumption. During the sample period, the average share of housing services is 29% of total services consumption, and 16.5% of total nondurable and services consumption. This suggests that using the nondurable and services consumption could be misleading due to the housing component. Thus, I focus on the nondurables consumption as a more appropriate measure for estimating the elasticity of intertemporal substitution. In a later empirical section, I provide additional evidence in favor of this conjecture by explicitly considering the nondurable and services consumption excluding housing services. In the second panel in Table 3, I report results of simple bivariate Grangercausality tests for the pair of nondurable consumption growth, and after-tax ex post real interest rate, disposable income and inflation, respectively. Interestingly, in the case of nondurable consumption and using its deflator, the consumption growth Granger-causes real interest rates. This implies that the

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consumption growth rate has important additional information about future real interest rates, suggesting a strong possibility that consumers are forecasting future real returns and incorporating that forecast into current consumption behavior. Note that for nondurables, the evidence of Granger-causality from consumption growth to income growth is much weaker compared to the nondurable and services case.14 Finally, nondurable consumption growth Granger-causes inflation showing that consumers are actually increasing consumption anticipating future increases in inflation. This is consistent with intertemporal substitution if the real interest rate and inflation are negatively associated as in the post-war USI 3.2. Instrumental variables methods I use instrumental variables methods to estimate Eqs. (6) and (7) due to contemporaneous correlations between the disturbance term and the regressors (ex post real interest rate and income growth rate). The use of instrumental variables method is also important to avoid spurious correlations between consumption growth rates and real interest rates arising from possible measurement errors in inflations. As noted in Section 2.1, consideration of time aggregation bias plays a critical role in drawing inferences about the magnitude of intertemporal elasticity of substitution. As in Hall (1988), and Campbell and Mankiw (1989, 1990, 1991), I always use instruments lagged twice or more to avoid spurious rejections of the model due to the first-order autocorrelation in the disturbance from using time-averaged variables. As noted in Campbell and Mankiw (1991), this choice of instruments also avoids the problem of a firstorder moving average in the disturbance due to the partial durability of some nondurable goods such as clothing and shoes. Also, to avoid possible inconsistency in the variance-covariance matrix due to any remaining serial correlation, I use serial correlation and heteroskedasticity consistent standard errors proposed by Hansen (1982), White (1980), and Newey and West (1987). However, I also report non-corrected standard errors to check the sensitivity of the results. The choice of instruments plays a critical role particularly in testing the overidentifying restrictions. The various sets of instruments that I employ are summarized in Table 4. For comparison with previous nondurable and services results, I chose the first three instrument sets from Campbell and Mankiw where “‘Campbell and Mankiw (1991) give evidence that consumption income growth in the case of nondurable and services.

growth does Granger-cause

“The literature on the Fisher hypothesis found a wide rejection of the ex-ante real interest rate constancy, which I do not survey here. In addition, Huizinga and Mishkin (1986) give strong evidence that expected real interest rates are negatively associated with expected inflations in the post-war US.

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Table 4 Instrument sets for IV estimation of nondurable consumption growth equation Instruments”

Adjusted R2 (marginal significance levelb) dc

1. dc{Z to 41, r{2 to 4) 2. dif2 to 4}, r(2 to 4) 3. dy(2 to 4}, dc(2 to 4} r{2 to 4}, logC/Y{2} 4. dy(2 to 4}, dc(2 to 4)

di{2 to 4}, inf(2 to 4) logC/Y{2) 5. dy(2 to 4}, dc(2 to 4) sr(2 to 4}, inf(2 to 4) logC/Y{2) 6. dc.,{2 to 4}, r{2 to 4) 7. dy{2 to 4}, dc,,{2 to 4) r{2 to 4}, log C.,lY{2}

dy

0.061 (0.005) 0.065 (0.003) 0.041 (0.036)

o.ocs (0.058) - 0.004 (0.409) - 0.004 (0.059)

0.070 (0.000)

0.006 (0.025)

0.047 (0.010)

- 0.015 (0.089)

0.080 (0.001) 0.077 (0.001)

0.032 (0.004) 0.041 (0.000)

r 0.3 J 7 (0.000) 0.289 (0.000) 0.324 (0.000)

0.189 (0.000)

0.182 (0.000)

0.298 (0.000) 0.3 17 (O.c@O)

‘sr is quarterly before-tax nominal stock return and computed from S&P composite common stock index and its dividend yield series. C., is the level of consumption from nondurable and services combined. dc,, denotes real per capita nondurable and services consumption growth rate. See previous tables for the definition of other variables. bAdjusted RZ statistics are from the regressions of consumption growth, income growth, and real interest rate on the instruments. Marginal significance level is associated with the chi-square statistic on the hypothesis that instruments in the regression are jointly zero. All test statistics are heteroskedasticity and serial correlation consistent.

model specification includes the real interest rate.16 The fourth and fifth instrument sets include inflation and a nominal return variable (the first difference in the 3-month T-bill rate and three month stock returns, respectively) instead of the real interest rate in the third instrument set. The nominal stock return series was computed from the S & P composite common stock price index and its dividend yield. The adjusted R2 statistics from the first stage regressions on instruments show reasonably high values for consumption growth rates and the real interest rates. Note, however, that for the first five instrument sets, even if instruments show decent significance in the income growth regression, the adjusted R2 is not large relative to the adjusted R2 for the real interest rate. As noted in Nelson and Startz (1990), this might raise some difficulty in the instrumental variables estimation which includes income growth as a

16First two instrument sets are from Campbell and Mankiw’s (1990) Table 6. Third instrument set is from Campbell and Mankiw’s (1991) Table 3.

306

J.-H. Hahm / Journal of Economic

Dynamics and Conirol22

(1998) 293-320

regressor. Campbell and Mankiw show that the lagged nondurable and services consumption growth and the error-correction term are good instruments for the income growth rate. Thus as the last two instrument sets, I replace the consumption growth and error-correction terms in the first and third instrument sets with nondurable and services counterparts. The adjusted R2 rises to 0.032 and 0.041 and instruments are jointly significant at the 1% level. in the income growth regression.

4. Empirical evidence 4.1. Main regression results for nondurable consumption Table 5 summarizes estimation results on the elasticity of intertemporal substitution in both the simple and alternative PIH models using the nondurable consumption and its deflator. First, consider the simple stochastic real rate version of the PIH model (model (a)) where the real interest rate is the only regressor.” In the first column headed ‘model test’, I report the adjusted R2 from the regression of residuals from the instrumental variables regression on the instruments to provide a diagnostic check for the restriction that instruments have significant explanatory power for consumption growth only through the included regressors. Results of more exact tests of the overidentifying restrictions are provided in the parenthesis below the adjusted R2 statistic, and this is the marginal significance level from the Wald test of joint significance of instruments when added to the above instrumental variables regression. la For every instrument set, the coefficient of real interest rate p is always positive and significant at the conventional significance level. This finding is robust to the use of serial correlation and heteroskedasticity unadjusted standard errors in the second parentheses. The magnitude of the intertemporal elasticity of substitution ranges from 0.2357 to 0.4144 with the average value of 0.3061 implying the relative risk aversion coefficient of 3.2669. This contradicts Hall’s (1988) finding that the elasticity is never larger than 0.2 and may well be zero. Not only are the estimates above 0.2 but they are also precisely estimated. It is problematic however, that in 5 out of 7 cases the overidentifying restriction of the model is rejected at the 10% level. Thus the simple version of the permanent income hypothesis is rejected.

“Constant term is always included in both the instrument set and the actual IV regressions. I do not report estimates for constant terms to save space. ‘*As noted in Campbell and Mankiw (1990, 1991), this will be the valid test of overidentifying restrictions under possible serial correlations and heteroskedasticity in residuals.

0.028 (0.039) 0.030 (0.087) 0.008 (0.157) 0.035 (0.018) 0.009 (0.212) 0.064 (0.003) 0.048 (0.007)

1

0.2878** (0.l309)(0.11440) 0.3074** (0.1356)(0.1189) 0.2763** (0.1218)(0.1103) 0.3466*** (0.1277)(0.1336) 0.4144*** (0.1333)(0.1370) 0.2357* (0.1413)(0.1169) 0.2746** (0.1282)(0.1112) avg B = 0.3061

P

(a) ~Ic,+~=cc+~r,+,+u,+,

(ES)

L 0.8059*** (0.2841)(0.3065) 0.9593*** (0.3331)(0.3813) 0.6653*** (0.2446)(0.2395) 0.7554*** (0.1816)(0.2068) 0.6290*** (0.2132)(0.2185) 0.7836*** (0.2040)(0.2358) 0.6762*** (0.1786)(0.1812) avg I = 0.7535

0.013 (0.080) 0.001 (0.082) 0.005 (0.118) - 0.015 (0.427) 0.016 (0.059) 0.009 (0.092)

Model test

Model (b)

(b) d~,+,=a+Idy,+~+u,+,

-

-

-

-

-

-

-

0

+Idy,+,

+&,+I

0.2466** 0.010 (0.1086)(0.1173) (0.306) 0.010 0.2344** (0.213) (0.1167)(0.1319) 0.024 0.2398** (0.624) (0.0976)(0.1055) 0.037 0.2654** (0.1187)(0.1351) (0.667) 0.029 0.3511*** (0.522) (0.1262)(0.1291) 0.017 0.2423** (0.422) (0.1133)(0.1253) 0.021 0.2243** (0.371) (0.0999) (0.1079) avg 0 = 0.2577

Model test

Model (c)

(c) AC,+, =p+fer,+,

0.7145** (0.3020)(0.2973) 0.8016*** (0.2974)(0.3584) 0.5919** (0.2522)(0.2352) 0.6826*** (0.1881)(0.2053) 0.5001** (0.2288)(0.2 199) 0.7912*** (0.2117)(0.2416) 0.6264*** (0.1788)(0.1795) avg 1 = 0.6726

I

“First column IV set denotes instrument set number (see Table 4 for instrument sets). Under the column ‘mode1 test’, I report adjusted R2 statistics from the regression of residuals from the instrumental variables regression on the instruments. Marginal significance levels from the Wald test ofjoint significance of instruments when added in the above instrumental variables regression are reported in the parentheses below adjusted R’, and this is a valid test of overidentifying restrictions under possible serial correlations and heteroskedasticity in residuals (see Campbell and Mankiw, 1990, 1991). I report the serial correlation and heteroskedasticity consistent standard errors in the first parenthesis below the coefficient estimate. In the second parenthesis below the coefficient estimate, usual unadjusted standard errors are reported for comparison. *, **, *** next to the coefficient estimate denotes it is significant at the lo%, 5%, and 1% level, respectively, and this is from the marginal significance level using standard errors in the first parenthesis. Average in the last line reports average values of the coefficient estimates across different instrument sets.

7

6

5

4

3

2

Model test

IV set

Model (a)

Regression results:’

Modelspecifications:

Table 5 IV estimation: PIH and alternative model: nondurable consumption, quarterly, 1953:1-19943

308

J.-H. Hahm /Journal

of Economic Dynamics and Control 22 (1998) 293-320

The next column, under model (b), shows the Campbell and Mankiw’s alternative model without the real interest rate. The income growth rate is always positive and significant, and ranges from 0.6290 to 0.9593 with the average of 0.7535. Thus when nondurables consumption is used, the fraction of current income consumers is larger than the Campbell and Mankiw’s estimate of 0.5 obtained using nondurable and services. However, again in 5 out of 7 cases the overidentifying restriction is rejected at the 10% level, suggesting the possible role of real interest rates for nondurables consumption. To check the quality of the instrumental variables estimation, in Figs. 1 and 2, I show plots of expected consumption growth versus expected real interest rate, and expected consumption growth versus expected income growth rate. These are fitted values from regressions on the instruments in the first instrument set, and show a reasonably strong association.ig In the next specification (model (c)), I report results for the real interest rate version of the Campbell and Mankiw’s alternative model applied to nondurable consumption. Contrary to their results for nondurable and services in Table 2, the real interest rate is always significant even in the presence of a significant income growth rate. The estimated coefficient on the real interest rate is slightly lower than before with an average value of 0.2577. However, in this model, the elasticity of intertemporal substitution for the permanent income consumers is the coefficient of real interest rate divided by one minus the fraction of current income consumers. If we take the average value of 1,0.6726 as the fraction of current income consumers, the implied elasticity of intertemporal substitution is 0.7871, which is larger than in model (a). Again under the expected utility maximization framework, this could be interpreted as the relative risk aversion coefficient of 1.2705. Note that the overidentifying restriction of this alternative model is not rejected in any case, and the adjusted R2 in the regression of residuals from instrumental variables estimation on instruments is always negative. This suggests that the Campbell and Mankiw’s alternative model augmented with intertemporally substituting permanent income consumers, is also a reasonable approximation of the underlying behavior of post-war US nondurable consumption. 4.2. Decomposition

of the real interest rate

As noted previously, the assumption of a constant marginal tax rate could be invalid. If marginal tax rates were significantly time-varying, the after-tax real interest rate would be subject to measurement errors. One indirect diagnostic check is to decompose the real interest rate into the after-tax nominal return and

I91 checked plots for other instrument sets and found that the fits are more or less the same. I do not report them to save space.

J.-H. Hahm /Journal

of Economic Dynamics and Control 22 (1998) 293-320 19S3:1-/99~:3

3.6

fff@tJlhsrfmt

309

set //

,p

u

2.4 -L

I .2

0.0 0

-2.4

0

0

q

-1.6

-6.4

3.2

Expected Real Interest Rote (X p.0.) Fig. 1. Expected consumption

growth and expected real interest rate.

/9&3:/ -i994:3 /frlxn l+lenwf

set /)

3.6

w

-2.4

Li

' -0.8

0 2.4 0.8 Expected Income Growth (% p.0.)

4.0

Fig. 2. Expected consumption growth and expected income growth.

inflation. If the nominal return is measurement error driven, it should have large standard errors while inflation term is not significantly affected. In addition, this yields an alternative way of testing the underlying model. Consider the following equation:

310

J.-H. Hahm / Journal of Economic Dynamics

and Control 22 (1998) 293-320

where, r is the marginal tax rate assumed at 0.3, i, is the 3-month nominal interest rate observed at t, and inf,, I is the inflation rate from t to t + 1. If the assumption of constant tax rate is not a major mis-specification, the coefficients of after-tax nominal interest rate and inflation should be of similar magnitude with the opposite sign. I test explicitly the hypothesis of Ho : 8r + f& = 0 for a diagnostic check of the model. Table 6 summarizes results on this specification. for nondurable consumption. First, the coefficient of after-tax nominal interest rate has in general large standard errors and significant only in one case, while inflation is relatively precisely estimated and significant at the usual significance level as conjectured. This indicates that measurement error might play a role for the nominal returns. However, the hypothesis that the sum of the two coefficients is zero is never rejected, indicating that this may not be a significant problem and the overall significance of inflation comes from the real interest rate channel as the PIH model predicts. Note that those two coefficients are jointly significant at the 10% level in 5 out of 7 cases. Again the overidentifying restriction is not rejected in all cases corroborating the findings in the previous section. 4.3. Subsample regression results Finally, to check the robustness from a different dimension, I reestimated previous nondurables regressions for Campbell and Mankiw’s (1990, 1991) sample period of 1953:1-1985:4. The results are reported in Table 7. The evidence is similar in that the real interest rate is always significant even in the presence of income growth rate. Income growth rates are now significant only in 4 out of 7 cases. Note however, that the overidentifying restrictions are rejected in 5 cases for model (a). In model (b) which includes the two components of the real interest rate as separate regressors, the coefficient of inflation is again always negative and significant in 5 cases. The hypothesis that coefficients of two components sum to zero is never rejected, while the nominal interest rate and inflation are jointly significant in 4 cases. The results of overidentifying restrictions test improve slightly, and now in 4 cases, the restriction is rejected. This suggests that possibly other variables may explain the residual behavior of nondurable consumption growth rate in this subsample period. However, the overall evidence of significant elasticity of intertemporal substitution remains robust to the consideration of this subsample period. 4.4. Comparison with Hall (1988) As noted in Section 2.1 and in Table 1, Hall (1988) found low and insignificant estimates for the elasticity of intertemporal substitution for nondurable

- 0.010 (0.245) - 0.004 (0.552) - 0.025 (0.483) - 0.037 (0.729) - 0.028 (0.410) - 0.018 (0.487) - 0.036 (0.688)

Model test

-r)i,+&inf,+,

0.2367 (1.1139)(0.9911) - 0.2186 (0.7014)(0.7215) 0.2546 (0.1709)(0.2001) 0.2649 (0.1985)(0.2427) 0.3253 (0.2003)(0.2211) 0.2978 (1.4329)(1.3271) 0.4441** (0.2214)(0.2555)

AC,+, =p+f,(l

+E,+~

- 0.2460* (0.1279)(0.1321) - 0.2088* (0.1132)(0.1218) - 0.2403** (0.0985)(0.1066) - 0.2653** (0.1234)(0.1431) - 0.3452*** (0.1274)(0.1348) - 0.2462* (0.1423)(0.1587) - 0.2443** (0.1150)(0.1221)

+/ldy,+I

0.7120: (0.4025)(0.3857) 0.5251 (0.5314)(0.5355) 0.6012** (0.27 18)(0.2603) 0.6824*** (0.2116)(0.2315) 0.4870** (0.2423)(0.2370) 0.8099* (0.4696)(0.5095) 0.7632*** (0.2276)(0.2448)

a

(0.993) (0.075) (0.523) (0.107) (0.914) (0.051) (0.998) (0.082) (0.878) (0.019) (0.969) (0.103) (0.224) (0.080)

Marg. sig. Hi: 8, + ez = 0 Hi; e, = e2 = 0

“First column IV set denotes instrument set number (see Table 4 for instrument sets). Under the column ‘model test’, I report adjusted R2 statistics from the regression of residuals from the instrumental variables regression on the instruments. Marginal significance levels from the Wald test ofjoint significance of instruments when added in the above instrumental variables regression are reported in the parentheses below adjusted R2, and this is a valid test of overidentifying restrictions under possible serial correlations and heteroskedasticity in residuals (see Campbell and Mankiw, 1990,199l). I report the serial correlation and heteroskedasticity consistent standard errors in the first parenthesis below the coefficient estimate. In the second parenthesis below the coefficient estimate, usual unadjusted standard errors are reported for comparison. *, *+, *+* next to the coefficient estimate denotes it is significant at the lo%, 5%, and 1% level, respectively, and this is from the marginal significance level using standard errors in the first parenthesis. In the first parenthesis of the last column, I report marginal significance level from the asymptotic chi-square test that sum of coefficients of after-tax nominal interest rate and inflation is zero. In the second parenthesis, I report marginal significance level from the chi-square test of joint significance of those two components.

7

6

5

4

3

2

1

IV set

Regression results:”

Modelspecification:

Table 6 IV Estimation: decomposition of real interest rate nondurable consumption, quarterly, 1953 : 1-1994: 3

w

0.043 (0.062)

0.058

1

2

0.033 (0.002)

- 0.013 (0.488)

0.041 (0.117)

0.051 (0.001)

4

5

6

7

0.2359** (0.1059) (0.1043) 0.1931* (0.1016) (0.1153) 0.2423** (0.1116) (0.1070) 0.3067*** (0.0985) (0.1164) 0.4171*** (0.1273) (0.1287) o-2012** (0.0950) (0.1052) 0.1945** (0.0992) (0.1016)

e

0.3231 (0.2522) (0.2651) 0.5727*** (0.1832) (0.2437) 0.1598 (0.2257) (0.2115) 0.3504** (0.1665) (0.1682) 0.1953 (0.2028) (0.2044) 0.5190*** (0.1984) (0.2182) 0.3930** (0.1654) (0.1652)

1

(0.~)

0.050

- 0.024 (0.657)

- 0.015 (0.333)

0.033 (0.002)

0.014 (0.045)

- 0.030 (0.329)

0.037 (0.030)

Model test

Model (b)

, + .q+1 0~) A~,+~=~+B~(l-r)i,+e~mf,+,+Idy,+~+~,+~

(a) AC,+, = p + Ore+, + 1 dy,,

‘For detailed explanation of the table, see Tables 5 and 6.

0.015 (0.012)

3

(O.f@O)

Model test

IV set

Model (a)

Regression results:’

Model specifications:

- 0.1454 (1.0411) (1.2697) - 1.8475 (2.9670) (2.1082) 0.2779* (0.1647) (0.1621) 0.2991’ (0.1592) (0.1665) 0.4623** (0.2018) (0.1852) - 1.6567 (3.4887) (3.8127) 0.2170 (0.1617) (0.1831)

6,

IV estimation: subsample period: nondurable consumption, quarterly, 1953 : 1-1985 : 4

Table 7

- 0.2268** (0.1074) (0.1116) - 0.1483 (0.2950) (0.2402) - 0.2417** (0.1136) (0.1077) - 0.3066*** (0.0985) (0.1168) - 0.4202*** (0.1298) (0.1302) - 0.1388 (0.2964) (0.2331) - 0.1950* (0.1000) (0.1025)

e2

0.4053** (0.1806) (0.1860)

(1.6823)

0.1754 (0.4529) (0.5611) - 0.4700 (1.5733) (1.1808) 0.1692 (0.2242) (0.2153) 0.3473** (0.1671) (0.1757) 0.2050 (0.2026) (0.2084) - 0.2778 (1.4834)

1

(0.856) (0.149)

(0.589) (0.574)

(0.766)

(0.950) (0.008)

(0.778) (0.094)

(0.486) (0.597)

(0.714) (0.08 1)

Marg. sig. H,,: 0, + & = 0 Ho: fI1 = t$ = 0

J.-H. Hahm / Journal of Economic Dynamics and Control 22 (1998) 293-320

313

consumption when time aggregation bias is corrected.20 Since I have found significant elasticities for nondurable consumption under appropriate treatment of time aggregation, those two sets of different results must be explained. The main difference comes from the instrument set. Here I reestimate the simple PIH model using Hall’s instruments in his quarterly regression. For the subsample period of 1953: l-1985:4, using his instrument set (ex-post real interest rate, inflation, and consumption growth rate all lagged twice) gives the following regression result, Ac,+i = constant + 0.1194 rt+ 1 + u,+ 1, (0.1420) where, the serial correlation and heteroskedasticity consistent standard error is in the parenthesis. The estimate of intertemporal substitution coefficient is similar to the Hall’s estimate in Table 1 and insignificant with the marginal significance level of 0.400. When I use my instruments (from instrument set 4) for the same data, the regression result is: AC,+1 = constant + 0.3869 rt+l + ut+ 1. (0.1227) Note that the elasticity measure rises more than three times in magnitude and becomes significant with the marginal significance level 0.002, suggesting that the main difference in the results comes from the choice of instruments. Compared with Hall’s instruments, the instrument sets used in the present analyses always include longer lags and some other information such as lagged income growth rates and the error-correction term. More specifically, I found that the third lag in ex post real interest rate is an important instrument in that it always has significant explanatory power for both consumption growth and real interest rates. When components of real interest rates are used as instruments, the third lag of inflation captures the significant explanatory power for both consumption growth and real interest rates. Also the lagged error-correction term seems to have additional common explanatory power for both variables, especially in the subsample period. Finally, another difference may be that I am not using the Hayashi-Sims estimator unlike Hall.” Applying the Hay ashi-Sims estimator and again using “Hall (1988) actually used Hayashi-Sims (1983) estimator in addition to using the twice lagged instruments, and also explicitly aggregated consumption growth-real interest rate relationship assuming monthly relationship is the correct one. *‘Hayashi and Sims (1983) proposed an estimator to correct for the possible inconsistency problem in an instrumental variables regression under serially correlated residuals and endogenous instruments. For detailed application of the Hayashi-Sims estimator in the current setting, see Hall (1988).

314

J.-H. Hahm /Journal of Economic Dynamics and Control 22 (1998) 293-320

my instrument set no. 4 yields: Ac,+~ = constant + 0.3657 I~+l + u,+ ,. (0.1457) The coefficient is again similar in magnitude to the one without the HayashiSims estimator, and remains significant with the marginal significance level 0.013. To summarize, at least for Hall’s quarterly regressions, the use of insufficient instruments especially omitting longer lags yielded misleading results. 4.5. Evidence

on

nondurable and services consumption

Until now, I have focused on nondurables consumption, One other frequently analyzed measure of consumption is nondurables and services. While I found strong evidence for nondurables, Campbell and Mankiw (1989, 1990, 1991) found no significant response of consumption to changes in real interest rates using nondurable and services. In this section, I explore a possible source of the two sharply different sets of results. As discussed in Section 3.1, one strongly possible source of the discrepancy is the housing service. In Table 8, I compare results on two different measures of consumption; total nondurable and services, and nondurable and services excluding the housing service. The upper panel in Table 8A summarizes regression results using the total nondurable and services consumption and its deflator. Again I report the instrumental variables estimation results on the two previously considered specifications which include the income growth rate.z2 The result on model (a) is consistent with the Campbell and Mankiw, and the real interest rate is always insignificant while the income growth rate is strongly significant. The coefficient of the income growth rate is similar in magnitude to the Campbell and Mankiw’s estimate of 0.5 even for this longer data set. In model (b) where I decompose the real interest rate, the nominal interest rate and inflation are not jointly significant in all cases. Now consider the possible role of housing services. In the lower panel of Table SA, I report regression results using the nondurable and services consumption excluding housing services. To compute the corresponding real interest rate and inflations I used the nondurable consumption deflator.23 Note that as conjectured, excluding the housing service dramatically changes results. In

221 report regression results for three instrument sets; no. 3, 4 and 5 in Table 4. For other instrument sets, I obtained basically the same results and I do not report them to save space. 231n principle, an implicit price deflator for the nondurable and services consumption excluding housing services could be constructed. When this constructed deflator was used, for the three instrument sets in Table 8, the coefficient estimate of the real interest rate was 0.1875, 0.3336 and 0.4110, respectively, and the last two estimates were statistically significant at the 5% level.

0

0.1965** (0.0887) (0.0864)

0.2896*** (0.1118) (0.1119)

- 0.033 (0.591)

- 0.043 (0.392)

3

4

& services excluding

0.2490 (0.1903) (0.1915)

- 0.036 (0.720)

5

b. Nondurable

0.2227 (0.1905) (0.1996)

- 0.039 (0.557)

4

0.0893 (0.1108) (0.1132)

- 0.039 (0.859)

3

housing

& services consumption:

Model test

a. Nondurable

IV set

and services consumption,

0.4989*** (0.1286) (0.1388)

0.4681*** (0.1527) (0.1518) - 0.054 (0.535)

- 0.045 (0.829)

- 0.034 (0.621)

0.4254*** (0.1289) (0.1314)

(0.910)

- 0.044

Model test

- 0.038 (0.999)

service:

: l-1994: 3

- 0.3256** (0.1283) (0.1289)

0.4350** (0.2137) (0.2134)

- 0.2070 (0.2588) (0.2410)

0.1736 (0.3605) (0.3311)

- 0.2064** (0.0979) (0.0939)

- 0.2094 (0.3131) (0.2914)

0.1965 (0.4501) (0.4165)

0.3421** (0.1682) (0.1623)

- 0.0959 (0.1177) (0.1207)

82

0.1710 (0.1873) (0.1867)

61

(b) Ac,+,=~+6,(l-r)i,+f$inf,+,+Idy,+,+~,+~

1953

Model (b)

quarterly,

0.4799*** (0.1037) (0.1166)

0.4512*** (0.1283) (0.1304)

1

(a) A~,+~=~+er,+,+Idy,+,+~,+,

nondurable

Model (a)

AIVEstimation:”

IV Estimation:

Table 8

(0.410) (0.040)

0.5646*** (0.1655) (0.1700)

(0.795) (0.374)

0.4076*** (0.1424) (0.1435)

(0.262) (0.081)

(0.935) (0.468)

0.4723*** (0.1478) (0.1462)

0.5470*** (0.1874) (0.1792)

(0.541) (0.649)

Marg. sig H,,: 0, + & = 0 Ho: 0i = ~9~= 0

0.5024*** (0.1659) (0.1648)

I

$ 3 k B

B a \

Model test

e

1

- 0.040 (0.569)

0.3191*** (0.1119) (0.1122)

0.4362*** (0.1577) (0.1565)

- 0.050 (0.776)

0.4601** (0.2184) (0.2055)

01

- 0.3548*** (0.1366) (0.1276)

02

0.095 (0.000) 0.174(0.000) 0.044(0.000)

0.056 (0.004) 0.317(0.000) 0.030(0.001)

dc r dy

0.074 (0.000) 0.167(0.001) 0.014 (0.002)

IV5

(0.434) (0.034)

Marg. sig Ha: 01 + 19~= 0 ~a: e1 = ez = 0

bNumbers in the parenthesis are marginal significance levels from the chi-square test ofjoint significance of instruments in the first stage regression.

‘For detailed explanation of the table, see Tables 5 and 6.

IV4

IV3

Variable

0.4910*** (0.1857) (0.1800)

I

+Idy,+i+~,+r

B. Adjusted R2 from first stage regressions on instruments: nondurable & services excluding housing service?

5

Model test

Model (b)

(a) AC,+, = p + Or,, 1 + I dy,+ I + E,+1 (W A~,+~=~+8~(l-t)i,+e~inf,+,

b. Nondurable & services excluding housing service:

IV set

Model (a)

A. IV Estimation:”

Table 8 Continued

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317

model (a), the coefficient of the real interest rate is now strongly significant and positive even in the presence of the income growth rate. The average value of the coefficient estimates of the real interest rate is now 0.2684, which is similar to the average value 0.2577 for nondurables consumption in Table 5. The coefficient estimates for income growth rates are a little bit lower than in nondurables case, and the average is 0.4677. The implied elasticity of intertemporal substitution for permanent income consumers computed from the two average values is 0.5042. This suggests that the coefficient of relative risk aversion is around 2, which is again plausible. The result on model (b) also strongly supports the existence of non-negligible intertemporal substitution. The nominal interest rate and inflation are both jointly and individually significant for every instrument set. Moreover, I fail to reject the hypothesis that the sum of the two coefficients is zero in every case. Note that the overidentifying restrictions are never rejected for both models. Finally, in Table 8B, I report the adjusted R* statistics from the first stage regressions of endogenous variables on the instruments to check the quality of the instrumental variables estimator for the case of nondurable and services consumption excluding the housing service. In the parenthesis I also report the marginal significance level from the chi-square test of joint significance of instruments in the first stage regression. Note that for all three endogenous variables, the instruments are always jointly significant and the adjusted R* statistics are reasonably high. This indicates that the coefficient estimates reported here should not be subject to problems arising from a poor quality of instruments. Overall evidence in this section strongly supports the claim that consumers are indeed intertemporally substituting consumption in response to the changing expected real interest rate. Campbell and Mankiw’s failure to find this important channel of consumption adjustment seems to be due to the inclusion of the housing service, which is highly problematic when one is to estimate the elasticity of intertemporal substitution.

5. Concluding remarks In the present paper, I provided strong and systematic evidence that the elasticity of intertemporal substitution is indeed positive in the post-war US. For nondurables consumption, the precisely estimated values of the elasticity of intertemporal substitution cluster around 0.3. However, the simple stochastic real interest rate version of the PIH is rejected. When the model is modified to include current income consumers as in Campbell and Mankiw, the actual elasticity of intertemporal substitution for permanent income consumers could be as high as 0.8 for nondurables, and 0.5 for nondurables and services excluding housing. This implies that the coefficient of relative risk aversion is in the range between 1.25 and 2.

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Previous failures to find the significant response of consumption to real interest rates can be attributed to either the use of inappropriate instruments or the use of an inadequate measure of consumption. More careful choice of instruments and excluding the problematic housing services effectively reverse the previous conclusion. Future research should focus on the responsiveness of consumer durables expenditure to the real interest rate. Mankiw (1985) found that consumer durables expenditure is far more sensitive to real interest rates than expenditures on nondurables and services. Indeed, possible presence of non-negligible adjustment cost or irreversibility in adjusting the durable stock complicates the precise estimation of the real interest rate effect. However, given the large volatility of consumer durable expenditure over the business cycle, the real interest rate channel should deserve further investigations.

Appendix In this appendix, I consider a variant of the permanent income consumption model under borrowing constraints. Antzoulatos (1994) shows that under borrowing constraints, consumption growth depends not only on expected current income but also on expected future incomes, and hence, the Campbell and Mankiw model is possibly a misspecification if the borrowing constraint is binding. More specifically, the following regression model was estimated, &+1

= p + or,+1 +

A~Y,+1

+

12

dY,+z

+

~f+l~

(A.11

where both A1 and AZare positive under binding borrowing constraints due to the positive Lagrange multiplier. Using the US total per capita consumption measure which includes durable expenditure, the author reported instrumental variables estimation results that both A1 and & are significantly positive while the coefficient of real interest rate is essentially zero. Since my finding of significantly positive coefficient of real interest rates could be due to the omission of future income growth rate (Ay,+J, I reestimate the regression model (A.l) using the more appropriate measure of consumption, that is, nondurables consumption, or nondurable and services consumption excluding housing service. For the identical sample period of 1953 : 1-1989: 4 as in Antzoulatos, and using my instrument set number 4 in Table 4, I obtained a dramatically different result, which effectively reverses the author’s conclusion. Consider the following regression results: NDS AC,+ 1 = constant + 0.2837 I~+1 + 0.23834~~~+1 + 0.17874~,+~ f %+1 (0.0919) (0.1663) (0.1121)

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ND only AC,+1 = constant + 0.3102r,+ 1 + 0.4176Ay,+ 1 + O.l752Ay,+, + Et+1 (0.1832) (0.1543) (0.1235) NDS excluding AC,+ 1 = constant + 0.3017 r-y+l + 0.3327Ay,+ 1 (0.1358)

housing service

(0.1337)

+ O.l099Ay,+, + E,+1 (0.1265) where, the serial correlation and heteroskedasticity consistent standard errors are in the parentheses. For nondurable and services consumption (NDS) which include housing service, the coefficient of real interest rate is not significantly different from zero as found in Antzoulatos. Note that using nondurable and services consumption instead of total consumption, gives less significant coefficient of AY,+~. Furthermore, if we focus on nondurables consumption (ND), or nondurable and services consumption excluding housing service, the coefficient of real interest rate becomes significantly positive at the 5% level. Note also that the coefficient of Ay, +z becomes insignificant in both cases. To summarize, the finding of Antzoulatos may be misleading due to the inappropriate choice of consumption measure, and the main result of the present paper - the significant real interest rate effect on consumption, is robust to the consideration of alternative consumption model under borrowing constraints.

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