Bubbles, fundamentals, and investment: A multiple equation testing strategy

JOURNALOF

Monetary ELSEVIER

Journal of Monetary Economics 38 (1996) 47-76

ECONOMICS

Bubbles, fundamentals, and investment: A multiple equation testing strategy Robert S. Chirinko *'"'b, Huntley Schaller c aDepartment of Economics, Emory University, Atlanta, GA 30322-2240, USA b Federal Reserve Bank of Kansas City, Kansas City, MO 64198, USA c Department of Economics, Carleton University, Ottawa, Ont. K IA 5B6, Canada

(Received June 1994; final version received March 1996)

Abstract D r a m a t i c fluctuations in the stock m a r k e t raise questions a b o u t whether actual asset prices c o r r e s p o n d to the expected present value of future cash flow a n d whether deviations from this f u n d a m e n t a l price can affect real investment spending. Even if there are deviations from f u n d a m e n t a l price, they m a y not distort real b e h a v i o r if firms ignore these deviations in m a k i n g their investment decisions. O n the o t h e r h a n d , overvaluation of equities could provide firms with a relatively cheap source of finance a n d might therefore influence investment. To evaluate these issues, this p a p e r introduces a new e c o n o m e t r i c testing strategy, a n d assesses the existence of stock m a r k e t bubbles a n d the sensitivity of i n v e s t m e n t spending to bubbles. We estimate the Q a n d Euler equations in a s i m u l t a n e o u s equations model a n d exploit the idea that these equations reflect different

*Corresponding author. We would like to acknowledge useful comments from an anonymous referee, F. Black, O. Blanchard, H. Dezhbakhsh, S. Durlauf, J. Eberly, M. Galeotti, L. Hansen, J. Huizinga, M. Ogaki, J. Poterba, D. Scharfstein, F. Schiantarelli, R. Shiller, and T. Whited, as well as seminar participants at Carleton University, the Econometric Society, the Federal Reserve Banks of Atlanta, Cleveland, St. Louis, and Kansas City, the University of Illinois, the NBER Working Group on Behavioral Economics and Finance, the Northern Finance Association, Rutgers University, the SEDC summer conference, and UCLA. J.R. Dempsey provided timely computational support, and Yongduk Pak excellent research assistance. We would like to thank O. Blanchard, C. Rhee, and L. Summers for letting us use their data; C. Rhee deserves special mention for explaining the construction of their data and providing us with related data not used in their paper. The second author would like to thank the Social Sciences and Humanities Research Council (Canada) for financial support and the Operations Research Center at MIT for providing a pleasant environment in which to conduct this research. All errors, omissions, and conclusions remain the sole responsibility of the authors. The views expressed herein do not necessarily reflect those of the Federal Reserve Bank of Kansas City nor the Federal Reserve System. 0304-3932/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved PII S 0 3 0 4 - 3 9 3 2 ( 9 6 ) 0 1267-6

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information about the stock market and investment spending. Based on U.S. data for 1911-1987, our formal statistical tests indicate that bubbles exist but real investment decisions are based on fundamentals. A variety of robustness checks and three types of collateral evidence corroborate this interpretation. Key words: Real-financial interactions; Investment; Stock market; Testing J E L classification: E44; C32; E22

I. Introduction Events such as the 1987 stock market crash have raised doubts about the traditional assumption that stock markets are efficient in the sense that actual prices correspond to fundamental prices. If actual prices deviate from fundamentals, this would have serious economic implications. First, like taxes and subsidies, such deviations would create wedges which could distort both intertemporal investment decisions and cross-sectional capital allocations. Second, deviations from fundamentals m a y raise the level of risk in asset markets. Finally, the sharp movements in asset prices associated with bubbles may contribute to macroeconomic fluctuations, as some economists believe occurred with the October 1929 Wall Street crash and the Great Depression. Concern about bubbles and their effect on the aggregate economy appears to play a role in monetary policy. As Friedman and Schwartz (1963, pp. 253-270) document, stock market speculation 'became the focal point of Federal Reserve policy' in the late 1920s in the U.S. More recently, the Economist (April 30, 1994, p. 27) reports that 'the F e d . . . hoped, at least initially, that raising shortterm rates might prick what it saw as a speculative bubble in the stock market. The fear of causing too loud a pop is a reason why the arguments of some Fed governors, such as Lawrence Lindsey, in favour of one big increase in rates were rejected in favour of several smaller ones'. Dealing with speculative bubbles appears to be a consideration in monetary policy in other countries as well. 1 Even if there are bubbles in the stock market, they may not lead to distortions of real behaviour. In contrast to other areas of macroeconomics, there is relatively little empirical evidence on whether bubbles exist and, if they do, whether they affect the real economy. A small number of recent papers have examined the link between investment and stock market bubbles by decomposing

1For example, the Washington Post (April 20, 1992, p. A12) reports that 'in late 1989, a toughminded new governor, Yasushi Mieno, was named to head the Bank of Japan and he quickly made clear his intentions to end the rampant speculation' by forcing up interest rates.

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the valuation of the firm's capital into fundamental and nonfundamental components. These papers have used various proxies for the fundamental component in investment equations, but have found it difficult to draw firm conclusions. 2 The innovative feature of this paper is that we combine the Q and Euler investment equations in order to develop a richer set of specification tests. This multiple equation testing strategy provides an alternative framework for addressing the relationship between the stock market and investment. By exploiting information from the firm's optimization problem, we are able to distinguish hypotheses of economic interest without making strong parametric assumptions about fundamentals and bubbles. The Q equation is derived by solving forward a first-order difference equation to obtain the shadow value of capital as the expected present value of the future stream of marginal products of capital. The fundamental value of a stock is the expected present value of the firm's future cash flow. Assuming that stock market prices correspond to fundamental values, Hayashi (1982) shows that stock prices can be used to capture the shadow value of capital, which is not directly observable. If stock prices do not correspond to fundamentals, then the observed Q will consist of the true shadow value of capital plus an additional term which we refer to as a 'bubble') As a result, the Q equation will fail our specification test if there are bubbles in the stock market. The Euler equation is a period-to-period arbitrage condition for the firm's investment spending with the following feasible perturbation interpretation: holding the capital stock constant in all other periods, a firm will choose the timing of its investment between two subsequent periods in order to equate the marginal costs and benefits across the periods. Even if there are bubbles in the stock market, the Euler equation may remain valid. However, bubbles in the stock market can affect the firm's discount rate. As Fischer and Merton (1984) point out, if a firm's stock is overvalued, the firm effectively has access to relatively cheap finance by issuing new shares. Thus, overvaluation of its shares may imply that the discount rate the firm uses in making investment decisions is lower than the market interest rate for loans. Because the Euler equation balances costs and benefits across periods, it is sensitive to the discount rate.

2 See Blanchard, Rhee, and Summers (1993), Galeotti and Schiantarelli (1994), Morck, Shleifer, and Vishny (1990), and Rhee and Rhee (1991). 3 We want to make it clear that we use the term 'bubble' as a more succinct phrase than 'deviations of stock market prices from the expected present value of future cash flow'. These deviations could arise for m a n y reasons, such as fads, noise trading, investor sentiment, etc., as described, for example, by De Long, Shleifer, Summers, and W a l d m a n ~1990), Shiller (1984), and Summers (1986). We do not restrict our attention to what are sometimes called 'rational bubbles', as discussed, for example, by Tirole (1982, 1985). Similarly, we use 'inefficient' interchangeably with 'the presence of a bubble' without taking a stand on the existence of arbitrage profits.

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If bubbles exist and if they affect the discount rate used to assess investment projects, there will be an additional term in the Euler equation which reflects the bubble and the Euler equation will fail our statistical test. If both the Q and Euler equations are correctly specified, then variables in the firm's information set in period t - 1 should be uncorrelated with the regression error terms. On the other hand, if either equation is misspecified, an orthogonality test will reject the overidentifying restrictions. In our econometric work, we use a test proposed by Eichenbaum, Hansen, and Singleton (1988) to help us determine which equations (Q, Euler, both, or neither) are suspect. The tests allow us to distinguish three interesting cases. If there are no bubbles in the stock market, both the Q and Euler equations will pass the test. If there are bubbles in the stock market but they do not affect investment, the Q equation will fail but the Euler equation will pass. If bubbles exist and affect investment, both the Q and Euler equations will fail. Using U.S. data for the period 1911-1987, we find that the Q equation fails, but the Euler equation passes. This is consistent with the existence of stock market bubbles which do not affect investment. Interestingly, the results are generally the same for the periods before and after World War II. Any econometric test is based on certain maintained hypotheses. In this study, the most important concern technology and market structure. In our main tests (the 'base case'), we assume constant returns to scale in production, competitive output markets, and smoothly functioning debt markets. We then relax all of these assumptions and repeat our specification tests. In addition, we introduce a variance ratio statistic and other robustness tests which provide checks on alternative sources of misspecification (such as serial correlation of adjustment cost shocks). We also examine three types of collateral evidence. First, we look at the correlation between the Q and Euler residuals and a measure of stock market bubbles. As noted above, if stock market bubbles exist, then the Q residual will contain a component which is correlated with the bubble. Similarly, if bubbles exist and affect the discount rate (and thus investment), then the Euler residual will contain a component which is correlated with the bubble. Second, we use the residuals from the Q equation to calculate a statistic which gives an approximate measure of the proportion of the variance of Q which is accounted for by bubbles. Third, we examine plots of the Q and Euler residuals in the periods around 1929 and 1987. If there are stock market bubbles, the Q residuals should rise as the bubble grows and fall when the bubble collapses. If bubbles exist and reduce the cost of capital (thus raising the discount factor), then the Euler residuals should fall as the bubble grows and rise when it collapses. The collateral evidence tends to support our main finding, namely that there are bubbles in the stock market but they do not seem to affect investment.

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Our paper is organized as follows. Section 2 provides intuition for the testing strategy. Section 3 derives the Q and Euler equations under the assumption that the stock market is efficient. Section 4 examines what happens if there are bubbles in the stock market. Section 5 describes the details of the econometric specification and data. Section 6 presents the results of the formal specification tests. Section 7 relaxes the technology and market structure assumptions, considers other potential sources of misspecification (e.g., serial correlation of shocks), and provides informal collateral evidence which helps to sharpen our interpretation of the specification tests. A summary and conclusion are offered in Section 8.

2. Intuition for the testing strategy It may be helpful to provide some intuition for the economic interpretation of the specification tests. The usual Q investment equation (derived in Section 3) has the form: Q* -

[l,/K,] = e?,

V t,

where Q* is fundamental Q, C~ is the derivative of the adjustment cost function with respect to investment without the stochastic adjustment cost shock, I is investment, K is the capital stock, and e Q is the regression error. If there are bubbles in the stock market, we cannot observe the true Q*; instead, we see Q - - Q * + B, where B is the bubble. In order to express the Q investment equation in terms of observables, we need to add B to both sides of the equation. The result is that the Q equation error term (u% will contain the bubble: u? = e? + 8,.

Since the nonfundamental component of the stock price is partly predictable, Bt will not be orthogonal to variables in the period t - 1 information set. This will lead the Q equation to fail the specification test. The general form of the Euler equation is [FK., -- C r . , ] - (p[ + C'~,,) + R * ( p I + ,

+ Ci.t+l)

=

etc,

Vt,

where F~ is the marginal product of capital, CK is the reduction in adjustment costs due to an additional unit of capital, p/is the relative price of investment, R* is the market-based discount factor, and eE is the regression error. The first and second terms represent the marginal benefit of having an additional unit of capital available today, and the marginal cost of buying and installing the capital today, respectively. The third term represents the present value of the savings to the firm from not needing to buy or install the capital tomorrow. If bubbles exist and affect investment by changing the cost of capital (to say, R* +f(B), wheref(B) is some positive and increasing function of the bubble),

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then the Euler equation error term (uE) will be:

u~t = err --f(Bt)(p[+I + C',,t+l). The presence off(B) would lead the Euler equation to fail the specification test.

3. The Q and Euler equations when there are no bubbles We assume that the firm chooses inputs to maximize the discounted sum of expected cash flows. Initially, we assume that the firm is a price-taker in both its input and output markets and is further constrained by production, adjustment cost, and accumulation technologies. Output (Yt) is determined by labour (Lt) and capital (Kt), and the production technology is Y, = F (Lt, Kt). Capital is quasi-fixed, and hence net increments to the capital stock are subject to adjustment costs. These are assumed separable from production, and are represented by C (It, Kt:a,), which is positive in investment (It), negative in Kt, valued by the price of foregone output, and affected negatively by a stochastic shock (a,). The stock of existing capital is accumulated as a weighted sum of past investments. If the weights follow a declining geometric pattern, then the accumulation technology is given by the familiar transition equation for capital, K, = It + (1 -- 6)Kt-1, where 6 is the depreciation rate. The firm faces a terminal condition on the shadow value of its capital stock. The price of output is numeraire, and the relative prices of labour and capital are represented by wt and p[, respectively. These considerations lead to the following optimization problem for the firm: max {I,+j,L,÷j}

(1)

× [F(Kt+j, Lt+j) - C(I,+j, Kt+i, at+j) - wt+jLt+~ - plt+jlt+~J}, subject to

Kt+j = (1

-

t$)Kt+j_ 1 +

It+j,

lim Et {(J~_[ilo

j , o~

1

~ 2*+~Kt+j~ = 0,

1 + r,+~}

)

(2) where rt+s is the market interest rate, 2"÷~ is the contemporaneous (i.e., period t + j) shadow value of capital, Et {. } is the expectations operator (conditional on the information set at the beginning of period t), and I]~ xs ---- 1, for k = - 1. We solve the firm's optimization problem using the Discrete Maximum Principle,

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53

and the Lagrangian is E f ® /j-1

1

)

[F(Kt+j, Lt+j)

C ( I , + j , K t + j , at+j)

/

-

Wt+jLt+j-- pt+jI,+ I 3+

}

2"+3[(1 - 6)K,+ 3 ~ + lt__ 3 - K,+3] ] , Vt.

(3) The first-order condition for capital is 0L~,

--=[FK,,--CK,t]--2*+Et[R*2*+1] =0, Vt,

(4)

where R* = (1 - di)/(1 + r,). Eq. (4) is a difference equation which can be solved forward, subject to a terminal condition, to obtain the following expression for the shadow value of capital: 2* = Et ~

R*÷s

[ F K . , , , j -- CK,t..j],

(5)

Vt.

j=O

The first-order condition for investment is t3~t_

[CLt+p[] +2"=0.

V t.

(6)

By substituting the first-order condition for investment into the first-order condition for capital and assuming that C t ( I , , K , : a t ) can be separated into components representing marginal adjustment costs (C't ( I , K,)) and the stochastic cost shock (at), we obtain the Euler equation for capital: p

*

I

t

[ f r.~ - CK.t] -- (p[ + Cx,t) + g t (Pt+l Jr- C1,t--1) = eft,

Vt,

(7)

where ef represents expectation errors and adjustment cost shocks. We now turn to the Q equation, which can be obtained following the well-known derivation of Hayashi (1982), who shows that, under stock market efficiency and other conditions, 4 the unobserved shadow price of capital can be equated to the value of the firm as determined by financial markets (V*), per unit of capital, 5 2* = V * / ( 1 -- , ~ ) K t _ , .

(8)

4 Hayashi's other conditions are that markets are competitive and technologies are linear homogeneous. Subsequent work (reported below) has shown how these assumptions can be relaxed. In addition, capital must be homogeneous (i.e., putty-putty) and must depreciate geometrically. 5To obtain (8), use Euler's Theorem for Homogeneous Functions to rewrite F(L,,K~) and C (I~, Kt:a,) in terms of their partial derivatives; use (4) and (6) to eliminate (Fr. t - CK,,) and C],tg u s e the transition equation for capital to eliminate It; solve the resulting difference equation forward; and impose the terminal condition.

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Combining (6) and (8), we obtain the following Q equation: Q* - c},, = e?,

(9)

where Q* =

( v * - p[ (1 - ~) K , _ ,)

(1

-

6) K t -

,

(lo)

1

e~ equals the adjustment cost shock, and Q* is the difference between the financial market and replacement values of the firm per unit of capital.

4. Q and Euler equations when the stock market is inefficient Our formal testing strategy is based on the orthogonality conditions between the instrumental variables (Zt) and the regression errors from the Euler and Q equations, u~ and u~, respectively. Since (7) and (9) contain endogenous variables dated t and t + 1, instrumental variables must be used to obtain consistent parameter estimates. Under rational expectations, no bubbles, and a correctly specified modell variables in the information set at time t - 1 will be orthogonal to the period t errors. However, if there are bubbles in financial markets, then the orthogonality conditions for either the Euler or the Q equation, or both, may be rejected. This section relates financial market efficiency and investment behaviour to the orthogonality properties of the Euler and Q equations. 6 A generic way of allowing for rational bubbles, fads, and other such departures from the present value model is to define a bubble as the deviation of actual stock market value V~ from fundamental value V* (normalized by the capital stock): B, - ( V t - - V*)/(1 - 6 ) K ,

~.

(11)

It is important to note that (11) does not rely on any particular parametrization of the bubbles process, and thus avoids a major concern with previous tests of stock market bubbles. Our testing strategy will detect departures from fundamentals due to exploding or bursting rational bubbles that eliminate arbitrage profits in the stock market or fads, noise traders, or other such phenomenon that do not eliminate arbitrage possibilities.

6The analysis in Section 4 is based on the assumption that firms rely on their own expectations about future cash flow. An alternativeapproach examinedin AppendixA is that firms rely directly on the stock market in making their investment decisions, regardless of whether or not the stock market is efficient.

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Bubbles in the stock market can affect the firm's discount rate. As Fischer and Merton (1984) point out, if a firm's stock is overvalued, the firm effectively has access to relatively cheap finance by issuing new shares. Morck, Shleifer, and Vishny (1990) call this the 'financing' hypothesis. 7 Thus, overvaluation of its shares may imply that the discount rate the firm uses in making investment decisions is lower than the market interest rate for loans. A general way of representing this effect is to allow the discount factor to depend on the degree of overvaluation, so that Rt = R* +f(Bt), where we choose the letter ' f ' for this function as a mnemonic for the 'financing' mechanism. The function f(B,) is a positive and an increasing function of Bt since a larger bubble reduces the cost of capital and thus increases the discount factor. 8 This financing mechanism can be either active or inactive and, in conjunction with bubbles in the stock market, leads to two distinct cases that have implications for the regression errors in the Euler and Q equations. The first case is the one originally considered by Fisher and Merton. If bubbles exist and affect investment through the discount rate, then we need to replace R* in (7) by R* +f(Bt). By rearranging the terms involving B,, we obtain the following expression for the Euler regression error: u,

=

, , -f(Bt)(Pt+l + C1a+l).

e,

(12)

Thus, if bubbles influence investment through the discount rate, the error term in the Euler equation will be correlated with variables in the information set at t - 1. A number of recent studies show that stock market prices are partially predictable and 'have typically suggested half-lives of several years' for the predictable component (Poterba and Summers, 1988, p. 48). Thus, variables in the information set in period t - 1 may be correlated with any bubbles in stock market prices, and the Euler equation will fail. We now turn to the implications of an active financing mechanism for the Q equation. To derive these implications, replace R* by (R* +f(Bt)) in (5): ~c

)~ = E, ~

j-1

~I (R*+~ +f(B,+s))[F~.t+j - CK.,.jJ

j=O s=O

= Et ~ I ] ( R * ) [ F r , , + j - C~,,+j] + Et ~ j

0

= 2* + )~(Bt),

I~(Bt)[FK,,+j-- CK.,+i]

j--O

(13}

7 Loughran and Ritter (1995) provide evidence that firms are overvalued at the time they issue equity and suggest that firms time their offerings to take advantage of swings in investor sentiment. 8 For example, if the firm's cost of funds was 10% and a bubble (Bf) effectively reduces this cost to 5%, the discount factor would rise from 0.91 to 0.95 a n d f ( B , ) would rise from 0 to 0.04.

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where I~ (R*) = I]~-Jo R*+~ and 1-I(B,) represents all the terms in i ~ =( Ro1 , ÷ s -

+

f ( B , +~)) which involve f ( B t +,). Thus, when bubbles exist and affect financing,

2 consists of two components: 2* (which corresponds to the efficient stock market case) and a new term, 2~ (Bt) (where we assume that the second sum in (13) converges). To derive the Q equation, we combine (13) and (6) to obtain C,,t + p[ = 2* + 2,~ (B,).

(14)

Using (8), (9), (10), and (14), we obtain the following Q equation: Qt - c'~,, = e? + Bt - zB (Bt) = u ? ,

(15)

where actual Q (which is observable) is the sum of 'fundamental' Q (Q*), as defined in (10), and the deviation from fundamentals: Bt = Qt - Q . . 9 The error term in the Q equation includes Bt if the financing mechanism is active, and thus both the Q and Euler equations fail the specification tests.l° The second case is the one in which bubbles exist but do not affect the discount rate and therefore do not affect investment. 11 Blanchard, Rhee, and Summers (1993) outline three reasons why bubbles may exist without influencing the firm's investment behaviour. First, the firms may issue new shares to take advantage of the overvaluation but invest the proceeds in financial assets rather than physical capital. Second, the overvaluation may be affected by the firm's actions (such as issuing new shares), and the firm may therefore be reluctant to base the discount rate it uses in making investment decisions on an ephemeral financing opportunity. Third, issuing new shares may involve transfers from new to existing shareholders, and managers who plan to remain with the firm may be reluctant to engage in this transfer. In addition, since taxes discriminate against equity finance, the tax wedge may be sufficiently large that debt remains the marginal source of finance even if shares are overvalued. If bubbles exist but, for any of the above reasons, do not influence investment, then the financing mechanism is inactive, the discount factor is R*, and the Euler equation will be the same as that derived in Section 3 under the assumption of stock market efficiency and will pass the specification test. Even if bubbles do not affect the discount rate, however, the Q equation, will tend to fail. To see why, inspect the Q equation in Section 3, particularly Eq. (10)

9Note that this definition of B t is consistentwith (11)becausep[ (1 - 6) Kr_ 1is subtracted from both Vt and V*. 10If B = 2B(B),then the terms involvingB would disappear from uQ, and the Q equation would pass the specification test. However, there does not seem to be any economic motivation for this knife-edge case and, in general, it therefore appears that, if the financing mechanismis active, both the Q and Euler equations will fail the specification tests. 11This is the case discussed by Bosworth (1975), who characterizedthe stock market as a 'sideshow'.

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which defines Q* in terms of the efficient market value of the firm V*. If the stock market is inefficient, the actual market value does not coincide with V*; as a result, we observe Qt = Q* + Bt, rather than Q*. In order to express the Q equation in terms of observables, we need to add Bt to both sides of (9), and the regression error becomes u~ = e,e + B,. When the Q equation is estimated, the presence of B, implies that the error term is not orthogonal to variables in the information set at time t - 1. The situation described in the previous paragraph illustrates the difference between our work and previous studies. Blanchard, Rhee, and Summers (1993) and Galeotti and Schiantarelli (1994) decompose the actual stock market price into fundamental and nonfundamental components (i.e., Q* and B) and then estimate the coefficients on the components to determine their significance and relative importance. In contrast, we take a nonparametric approach, treating Bt as part of the error term and applying specification tests. To summarize our formal testing strategy, we assess the possible misspecifications with the J test proposed by Hansen (1982) and the related MESH test proposed by Eichenbaum, Hansen, and Singleton (1988). 12 The J test is used to evaluate the two-equation system, and a significant J statistic indicates that some part of the system is misspecified. In turn, the MESH test can be used to identify the equation leading to the failure of the J test. The MESH statistic equals the difference between the criteria for the overall system (valid under the null hypothesis) and the equations valid under the alternative hypothesis, 13 and is distributed ~2 with degrees of freedom equal to the number of orthogonality conditions introduced in the 'suspect' equation (i.e., the number of instruments less the number of parameters that appear only in the 'suspect' equation). A significant MESH statistic reveals that the misspecification in the econometric system is traceable to the equation valid only under the null.14 The interpretation of the specification tests of the Q and Euler equations are summarized in Table 1.

5. Specifications and data This section discusses the parametric specifications and data needed to translate the model in Section 4 into a testable econometric system. The Euler L2See their Appendix C for further discussion of the MESH statistic, which they label the C r statistic. As noted there, this test has many parallels to the Q L R statistic developed by Gallant and Jorgenson (1979). See Newey and West (1987) for an extension to the case of non-iid errors. 13 The two estimates forming the MESH statistic are both computed with elements of the weighting matrix for the overall system (i.e., the equations valid under the null). 14 The MESH tests for misspecification are related to H a u s m a n specification tests, which have been previously used by West (1987) to test for stock market bubbles.

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Table 1 Summary of hypotheses about the stock market and investment and their implications for the Q and Euler equations Q

Euler

Efficient stock market (no bubbles)

Pass

Pass

Inefficient stock market (bubbles) Active financing mechanism (bubbles affect investment) Inactive financing mechanism (bubbles do not affect investment)

Fail Fail

Fail Pass

This table is intended to provide a convenient summary of the analysis; a more precise statement of the hypotheses is available in the text.

and Q equations rely on two technological relations, marginal adjustment costs (16), and the net marginal product of capital (17). In the base model, these relations are homogeneous of degree zero and are parameterized by the following second-order Taylor expansions: 2

C~,, --- ~ ctj i[ + v~'c ,

(16)

j=o 2

V~,, - C~,, - Z fl~Y[ + 7jil + v~wk,

(17)

j=O

where it is the investment-capital ratio, Yt is the output-capital ratio, and v~'c and v7 p* are white noise approximation errors. We use annual data for the U.S. nonfinancial corporate sector for the period 1911 to 1987 (after accounting for all leads and lags). 15 We choose this long sample since it includes some of the most frequently discussed periods of possible bubbles. Table 2 presents summary statistics, and Figs. 1-3 plot the investment-capital ratio, Q, and the output-capital ratio. There is some evidence of a level shift in the investment-capital and output-capital ratios around the time of World War II. Also, the volatilities in the series are markedly reduced. The coefficients of variation fall by 74%, 67%, and 40% for the investment-capital ratio, Q, and the output-capital ratio, respectively. Such a shift may be due to structural change or differences in data definition. ~6 In either case, estimating the Q and

15 The data are described in a data appendix available from the authors. For the Liquidity Model (Table 5), data are available for 1916-1987. 16 For example, the 90% increase in the output-capital ratio between 1938 and 1944 may be partly due to the increase in government-owned but privately-operated capital that contributes to the flow of private output but is not included in the stock of private capital (Gordon, 1969).

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Table 2 Summary statistics (means and standard deviations) Full sample 1911-1938 1948 1987 Q

- 0.215 (0.239)

1911 1938

1948 1987

0.121 (0.262)

- 0.282 (0.199)

I/K

0.0670 (0.0158)

0.0533 (0.0156)

0.0766 (0.00584)

Y/K

0.522 (0.0794)

0.440 (0.0456)

0.579 (0.0363)

Y-growth

0.0283 (0.0527)

0.0196 (0.0758)

0.0343 (0.0264)

LIQ

0.0161 (0.0243)

0.00335 (0.0335)

0.0234 (0.0123)

M2-growth

0.0603 (0.0594)

0.0480 (0.0825)

0.0688 (0.0341)

0.0221

(0.0165)

0.0262 (0.0184)

0.0193 (0.0146)

0.983 (0.0548)

0.979 (0.0818)

0.986 (0.0225)

SYC 1/(1 + r)

IlK is the investment~capital ratio; Y/K is the output-capital ratio; Y-growth and M2-growth are the annual percentage growth rates of GN P and M2, respectively; LIQ is liquidity; S YC is the slope of the yield curve; and r is the interest rate. The variable LIQ is only available starting in t916. Detailed data definitions are in a data appendix available from the authors. E u l e r e q u a t i o n s o v e r the full s a m p l e c o u l d l e a d to s p u r i o u s e v i d e n c e of misspecification. W e t h e r e f o r e split the s a m p l e i n t o a p r e - W o r l d W a r II p e r i o d (1911-38) a n d a p o s t - w a r p e r i o d (1948-87). 17

6. Specification tests of the base model T a b l e 3 p r e s e n t s e s t i m a t e s of the b a s e specification. W e b e g i n by d i s c u s s i n g the results for t h e s h o r t i n s t r u m e n t set. is W h e n we e s t i m a t e the Q a n d E u l e r

17 Parameter stability over these two subsamples is decidedly rejected. The subsamples are the same as used by Blanchard, Rhee, and Summers (1993), who also reject the hypothesis of parameter stability using the same data but a different econometric specification. t s Tauchen (1986) provides Monte Carlo evidence on the potential problems with excessively long instrument sets in this context.

R.S. Chirinko, I-L Schaller / Journal of Monetary Economics 38 (1996) 47-76

60 0.09 0.08 0.07 0,06 0.05

0,04 0.03 0,02 0.01

0 to

Fig. 1. Investment/capitalratio, 1911-1987.

0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6

Fig. 2. Q ratio, 1911 1987. equations as a system, there is substantial evidence against the orthogonality conditions. For the period before World War II, the p-value is 0.029; for the period after World War II, it is 0.001. The Eichenbaum, Hansen, and Singleton (1988) test points to the Q equation as the culprit. For the 1911-38 period, the p-value is 0.020; for the 1948-87 period, it is 0.000. There is little evidence that

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61

0.9

0,8

0.7

/

/

0.6

J 0.5

0,4

0.3

0,2

Fig. 3. Output/capital ratio, 1911 1987 Table 3 Base model, NL3SLS Short instruments

Long instruments

Specification tests

1911-38 (1)

1948-87 (2)

1911 38 (3)

1948 87 (4)

Test system (p-value)

20.071 (0.029)

29.981 (0.001)

33.334 (0.007)

35.992 (0.003)

Test Q (p-value)

19.644 (0.020)

29.964 10.000)

30.863 (0.002)

35.535 (O.O00t

Test Euler (p-value)

2.219 (0.696)

5.745 (0.219)

8.775 (0.269)

9.994 (0.189)

Variance ratio BR

6.107 0.652

6.500 0.631

13.939 0.930

12.517 0.726

Nonlinear three-stage least squares estimates: Test system is the Hansen (1982) test statistic of overidentifying restrictions; Test Q and Test Euler are the test statistics of Eichenbaum, Hansen, and Singleton (1988) for the validity of the Q and Euler equations, respectively. See the text for further discussion of these statistics. The variance ratio is V [uQ]/V [ur], where u Q and u E are the Q and Euler residuals, respectively; the interpretation of the variance ratio is discussed in Section 7.2. BR is the bubble ratio statistic defined in Section 7.3; it provides a lower bound estimate of the proportion of the variance of Q attributable to the bubble component. The short list of instruments includes a constant, time, time squared, the first lag of Q, the investment~zapital ratio, the output~capital ratio, and the discount factor, and the second lag of the forward differences in the price of investment and the investment-~capital ratio (where the forward difference is weighted by (1 - 6)/(1 + r,)). The long list of instruments includes the above plus the second lags of Q, the investment-capital ratio, and the output~apital ratio.

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Table 4 Base model, GMM

Specification tests Test system

(p-value) Test Q

(p-value) Test Euler

(p-value) Variance ratio BR

Condition number

Short instruments

Long instruments

1911-38 (1)

1948 87 (2)

1911 38 (3)

1948 87 (4)

17.262 (0.069)

18.910 (0.041)

21.619 (0.156)

25.522 (0.061)

16.531 (0.057)

18.886 (0.026)

17.399 (0.135)

24.751 (0.016)

2.840 (0.585)

2.722 (0.605)

4.401 (0.733)

8.193 (0.316)

7.038 0.658 13

5.051 0.634 14

13.076 0.929 15

7.892 0.697 16

Generalized Method of Moments estimates. See the footnote to Table 3 for information about the statistics and instruments. The condition number is the ratio of the largest to the smallest eigenvalues for the covariance matrix, expressed as 10x, where x is the number reported in the table. A matrix is ill-conditioned if the condition number is large relative to the inverse of the precision of the algorithm, equal to 1012 in the case of the program used here.

the o r t h o g o n a l i t y c o n d i t i o n s associated with the Euler e q u a t i o n are p r o b l e m atic. The c o r r e s p o n d i n g p-values are 0.696 a n d 0.219, respectively. The results are qualitatively similar with the long i n s t r u m e n t set. T h e system is rejected at high levels of significance for b o t h periods. In b o t h cases, there is strong evidence that the Q e q u a t i o n fails a n d little evidence against the Euler equation. Table 4 presents a similar set of estimates for the base specification; it differs from T a b l e 3 because we allow here for c o n d i t i o n a l heteroscedasticity. These G M M results are similar to those in T a b l e 3. There is m u c h stronger evidence that the Q e q u a t i o n fails t h a n that the Euler e q u a t i o n fails. (In fact, the p-value for the Euler e q u a t i o n is n o lower t h a n 0.3.) 19 The e c o n o m i c i m p l i c a t i o n of the specification tests in Tables 3 a n d 4 is that the U.S. data c o r r e s p o n d to the case in which there are b u b b l e s in the stock market, b u t the financing m e c h a n i s m is inactive. I n other words, there is

19While GMM estimates allow for a more general pattern of heteroscedasticity than the NL3SLS estimates in Table 3, this generality is obtained by having to estimate the covariance matrix of orthogonality conditions used to form the GMM weighting matrix. Due to its size relative to the variability in the available data, this covariance matrix is nearly singular, as indicated by the condition numbers reported at the bottom of Table 4. Thus, while the robustness of results across Tables 3 and 4 is comforting, our preferred estimates are those based on NL3SLS in Table 3.

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63

evidence that stock market prices deviate from fundamentals, but that these deviations do not affect investment. This interpretation is consistent with Blanchard, Rhee, and Summers (1993) and Morck, Shleifer, and Vishny (1990), both of which mildly favour the view that investment is driven by fundamentals, z° Since our testing strategy does not rely on a particular decomposition of the stock market value into fundamentals and bubbles, our results are complementary to previous work.

7. Additional evidence 7.1. Relaxing assumptions about technology and market structure

The specification analyzed in Section 6 is based on the maintained assumptions of constant returns to scale, competitive output markets, and frictionless capital markets. The impact of relaxing these assumptions is explored in this subsection. 21 Nonconstant returns to scale and imperfect competition can be incorporated into the Q equation by quasi-forward differencing the terms in the Q equation and adding the term ~Yt/Kt, where the parameter ~ reflects returns to scale and market demand elasticities (see the derivation in Chirinko and Fazzari, 1988). 22 In this expanded model, the marginal product of capital is now interpreted as a marginal revenue product, and a CES production function implies that the marginal product of capital now includes the level of output. Estimates of this expanded model are presented in the first two columns of Table 5. (Owing to the additional parameters, the long instruments are the only set that identifies the model.) For either sample period, the evidence again points to the Q equation as suspect. We also loosen the base specification by allowing for liquidity constraints, which are modeled by assuming that the interest cost on external funds is sensitive to balance sheet variables and that, when procuring external funds, firms incur flotation costs reflecting either transactions costs or information problems similar to those affecting the interest cost. For the Q model, the effects

2oIn contrast, Galeotti and Schiantarelli (1994) find that nonfundamentals also seem to affect investment, but to a lesser degree than fundamentals. zi It should be noted that our specificationtests could also be sensitive to the maintained assumptions that delivery lags and time-to-build do not affect the firm. Prior studies analyzing these technologies have usually relied on Marginal Q investment models, and an empiricallysatisfactory specification using Average Q appears unavailable (see Chirinko, 1993, Sect. III.D, for further discussion and references). 22A potential problem with allowing for nonconstant returns to scale and imperfectcompetition is that quasi-forward differencing could remove a large portion of the bubble, thus decreasing the power of our tests.

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Table 5 Alternative models, NL3SLS, long instruments

Specification tests Test system

(p-value) Test Q

(p-value) Test Euler

(p-value)

Imp. compt./Non-CRTS

Liquidity constraints

1911-38 (I)

1948-87 (2)

1911-38 (3)

1948 87 (4)

24.773 (0.074)

20.216 (0.211)

24.760 (0.074)

24.252 (0.084)

24.730 (0.016)

19.210 (0.084)

24.409 (0.018)

24.236 (0.019)

12.578 (0.083)

3.063 (0.879)

7.928 (0.339)

2.919 (0.892)

18.386 0.807

1.539 0.570

Variance ratio

12.875

10.806

BR

*

*

See the footnote to Table 3 for information about the statistics and instruments. For the Imperfect Competition/Non-CRTS Model, the terms in the Q equation (9) are quasi-forward differenced, i.e., Xf - X, ÷ x/( 1 + rt +1) then ( Yt/Kt is added; the net marginal product of capital approximation (17) entering the Euler equation now contains ~/j Y~ (j = 1, 2). For the Liquidity Model, marginal flotation costs enter the Q equation (see the derivation in Chirinko and Schaller, 1995, Sect. 3), and are represented as a second-order Taylor expansion in the flow of outside finance relative to the capital stock (or),that is, ~bjof (j = 1,2); for the Euler equation, the net marginal product of capital approximation reflects the dependence of marginal flotation costs on perturbations in the capital stock, and now contains ~b~o,j (j = 1, 2). * Quasi-forward differencing precludes calculation of the BR statistic.

of m o s t of these l i q u i d i t y c o n s t r a i n t s are capitalized into Q, except for m a r g i n a l flotation costs. These costs are a function of the flow of e x t e r n a l finance relative to the c a p i t a l stock, a n d also enter the Euler equation. The results for the liquidity m o d e l are p r e s e n t e d in c o l u m n s (3) a n d (4) of T a b l e 5. The system of Q a n d E u l e r e q u a t i o n s is rejected, a n d the M E S H tests a g a i n p o i n t to the Q e q u a t i o n as the source of the rejection. 7.2. Serially correlated adjustment cost shocks

S o m e p r e v i o u s research (e.g., Blundell, Bond, Devereux, a n d Schiantarelli, 1992) has suggested t h a t the shocks to the a d j u s t m e n t cost function (at) m i g h t be positively serially correlated. M o r e generally, a variety of forms of misspecific a t i o n m i g h t lead to s o m e t h i n g resembling serial c o r r e l a t i o n of at. In this subsection, we e x a m i n e w h e t h e r this c o u l d a c c o u n t for the rejection of the Q equation. (See A p p e n d i x B for the d e r i v a t i o n s of the tests r e p o r t e d in this subsection.)

R.S. Chirinko, 11. Schaller / Journal of Monetary Economics 38 (1996) 47-76 Table 6 Estimated autocorrelations ofu~:

u~ = /~j u E t-j + rh

Short instruments

/~x

/32

Long instruments

1911 38 (1)

1948 87 (2)

1911 38 (3)

- 0.310 ( - 1.642)

- 0.033 (-0.2(t0)

-- 0.317 (-1.654)

0.047 (0.286)

0.204 1.029)

- 0.256 ( - 1.611)

-- 0.064 ( - 0.317)

- 0.215 ( - 1.332)

0.172 (0.858)

0.078 (0.465)

0.207 (1.020)

0.093 (0.549)

--

(/33

65

1948 87 (4)

The Euler residuals uE are from estimates of the Base Model but with the discount factor held constant at 0.884. The results are robust to this restriction, which follows from the derivation in Appendix B. Numbers in parentheses are t-statistics.

Our variance ratio test is derived from the structure of the Q and Euler error terms, and is robust to either an AR(1) or MA(1) processes for at. Intuitively, this robustness is obtained because both u~ and u~ contain at. The variance ratio statistic, V R =- V [uQ]/V [uE], is based on the relatively weak assumptions that either: 1) adjustment cost shocks are not excessively serially correlated (p <_ 0.45) or 2) the variance of adjustment cost shocks is less than the variance of expectation errors. If there is no bubble, then VR < 1; on the other hand, if there is a bubble that varies substantially, VR _> 1. This reversal occurs because, when the financing mechanism is inactive (as the tests reported above suggest), u~ contains a bubble term but uff does not. In Tables 3-5, eleven of the twelve variance ratios exceed 5.0. If at is MA(1), it is straightforward to show that the orthogonality tests reported in Section 5 will be valid with instruments in the information set at t - 2. For the post-war period with either the short or long instrument set (now dated t - 2) or the earlier period with the long instruments (also dated t - 2), the Q equation is more strongly rejected than the Euler equation. A third approach is based on the fact that, if the financing mechanism is inactive, then the bubble will not appear in u,e and it is therefore possible to use u~ to draw inferences about the serial correlation properties of at. For example, if a t = p a t _ 1 +st,

p~O,

(18)

then the autocorrelation coefficients/~j of u~ will be of the form/~j = pJX, where X is a function of variances, R* and p, and is always nonnegative. Hence, the/~'s are always nonnegative. The estimates of/~j in Table 6 generate two key results.

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Table 7 Correlation of the residuals with bubbles and other macroeconomic variables Bubble

S YC

Y-yrowth

M2-growth

0.725 - 0.325

- 0.145 - 0.068

0.271 - 0.116

0.187 0.031

0.730 - 0.151

- 0.126 0.064

0.261 - 0.025

0.198 0.400

0.772 0.093

0.016 - 0.116

0.198 0.241

0.032 0.046

0.823 0.089

- 0.066 - 0.190

0.241 0.342

0.028 - 0.009

Short; 1911 38 uQ(Q) uE(Euler)

Short; 1948 87 uQ(Q) u~ (Euler)

Long; 1911-38 uq(Q) uE(Euler)

Long; 1948 87 uQ(Q) u~ (Euler)

The construction of the bubble measure is described in Appendix C. S Y C is the slope of the yield curve; Y-yrowth and M2-growth are the annual percentage growth rates of GNP and M2, respectively. The critical value for the correlation coefficientat the 5% level is 0.37 for the 1911-1938 period and 0.31 for the 1948-87 period.

First, m o s t of the coefficients are small a n d statistically insignificant.23 Serial correlated Euler residuals are n o t a m a j o r feature of o u r empirical results a n d hence serial correlation in the a d j u s t m e n t costs shocks does n o t a p p e a r to be q u a n t i t a t i v e l y i m p o r t a n t . Second, in all four estimates, f12 is negative, a direct c o n t r a d i c t i o n of the AR(1) model. I n sum, these results offer little s u p p o r t for the presence of serial correlation in the a d j u s t m e n t cost shock, a n d speak especially strongly against the AR specification of a,. 7.3. C o l l a t e r a l e v i d e n c e

We begin by c o n s t r u c t i n g a measure of stock m a r k e t b u b b l e s (described in A p p e n d i x C) which can be m o t i v a t e d either in terms of stochastic b u b b l e s or noise traders. I n T a b l e 7, we correlate the residuals from the Q a n d Euler e q u a t i o n s from each specification with the b u b b l e measure. F o r the earlier period, the correlations between the Q residuals a n d the b u b b l e m e a s u r e are 0.725 a n d 0.772 for the short a n d long i n s t r u m e n t sets, respectively; for the later period, the correlations are 0.730 a n d 0.823. This high correlation is precisely

23Note that the statistical significanceof the estimated fl's does not translate directly into a statement about the statistical significanceof p because of the structure of the error terms.

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67

what we would expect if there are bubbles in the stock market. In contrast, the correlation of the Euler residuals with the bubble measure is relatively small and statistically insignificant, offering little support for an active financing mechanism. To check the possibility that the bubble measure is simply a proxy for an omitted variable, we calculate the correlation of the Q and Euler residuals with three other macroeconomic variables - the slope of the yield curve ( S Y C ) and the growth rates of real G N P (Y-growth) and M2 (M2-growth). As shown in Table 7, none of these variables is as strongly correlated with the Q residuals as the bubble measure. Several are more strongly correlated with the Euler residuals. The second piece of collateral evidence quantifies the variance in Q attributable to the bubble component. Absent a specific parameterization of the bubbles process, we cannot measure the variance exactly, but we can derive an approximate relationship. 24 We begin by projecting the residuals from the Q equation on the instruments (Zt), u,O = e ~ + B t = Z t o ~ + v,,

e?±Zt,

a,2

var(Zr~).

(19)

The assumption that e ° is orthogonal to the instruments is consistent with the model. The variance of the portion of u °- which is correlated with the instrumerits is defined as a,.2 If u~ does not contain a bubble, then au2 = 0 since e~ is orthogonal to the instruments by assumption. If B, exists and is perfectly correlated with Z,, then a 2 = a2. In general, the correlation will be imperfect so 0-u2 ~.~ 0 - 2 and 0-u2is a lower bound on the variance of the bubble. 25 With the variance of the fitted value computed from (19), we can calculate the bubble ratio statistic: B R = a,/02 o. 2 As shown in Table 3, for the short instrument list, B R is 65% and 63% for the earlier and latter parts of the sample, respectively; other tables show a similarly large BR. z6 Therefore, bubbles appear to account for a sizeable proportion of the variation in Q. The final piece of collateral evidence is time plots of the residuals. In Fig. 4, we graph the Q and Euler residuals for the period 1926 32. The Q residual rises

2~ O u r approach is closely related to that used by Durlauf and Hall (1990) in deriving their noise ratio statistic. 25 This inequality can be established formally by the Cauchy Schwarz inequality, ~rzz8 < cr~ a z. Thus, o 2 ~ var(Z,&)

=

~20"2

~

2

2

2 2 2 GZ~B/ffZ

2 fiB"

2~ It is interesting to compare these statistics with the results of Cutler, Poterba, and Summers (1989, Table 2), who analyzed the extent to which macroeconomic variables explain the real value-weighted return on NYSE stocks. They find that only about 10-20% of the variation of returns can be explained by current and lagged macroeconomic variables, using annual data over the period 1871-1986.

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68

0.5 0.4 0.3 0.2 0.1 0 -0.1

-0.2 -0.3 -0.4 -O.S 1926

1927

1928

1929

1930

1931

1932

Fig. 4. Residuals from the Q and Euler equations, short instrument list, 1926-1932.

0.4

0.3

0,2

0.1

0

-0.1

-0.2

-0,3

1981

1982

1983

1984

1985

1986

1987

Fig. 5. Residuals from the Q a n d Euler equations, short i n s t r u m e n t list, 1981-1987.

substantially in 1928 and, especially, in 1929. Interestingly, it falls to a very low value in 1932, a time when one might have expected on a priori grounds that the stock market was undervalued. The Euler residuals are relatively small and s h o w no comparable pattern. A similar picture appears in the 1980's, as s h o w n in Fig. 5.

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69

From a slightly negative value, the Q residuals rise to a peak in 1987. In contrast, the Euler residuals are stable from 1985 to 1987.

8. Summary and conclusion Some economists now believe that there may be bubbles in the stock market, but the evidence is far from conclusive. Even if bubbles exist, they may not lead to major allocational distortions or macroeconomic disruptions. Unfortunately, several recent empirical papers have found it difficult to determine whether bubbles (if they exist) affect such real variables as investment spending. In this paper, we introduce a multiple equation testing strategy which brings more information to bear on the question of bubbles, fundamentals, and investment. The key empirical results can be summarized briefly. The system specification test rejects the standard investment model. The rejection stems mainly from the Q equation, which depends on the assumption that stock market prices do not deviate from fundamentals. Our analysis suggests that the Euler equation will fail only if firms exploit the overvaluation of their shares, so that their discount rate and investment decisions are affected. The fact that the Euler equation is not rejected in our data suggests that apparent deviations from fundamental price do not affect investment. Relaxing our maintained hypotheses concerning technology and market structure has little effect on our qualitative results. In addition, we consider three additional robustness checks (including a variance ratio statistic) which allow for misspecification which takes the form of apparent serial correlation of adjustment cost shocks. To check the interpretation of the specification tests, we examine the correlation of the Q and Euler equation residuals with a measure of stock market bubbles. We find that the Q residuals are significantly correlated with the bubble measure, but the Euler residuals are not. The correlation of the Q residuals with the bubble measure is stronger than their correlation with other macroeconomic variables. In contrast, the Euler residuals are frequently more strongly correlated with other macroeconomic variables than with the bubble measure. We also examine the pattern of Q and Euler residuals around the time of the 1929 and 1987 stock market crashes. If there are bubbles in the stock market, the Q residuals should rise as the bubble grows. We find a pattern of rising Q residuals leading up to both crashes. If bubbles affect investment by lowering the cost of capital, the Euler residuals should fall as the bubble grows. We find no pattern in the Euler residuals around either the 1929 or 1987 crashes. Thus, for the United States, both the multiple equation specification tests and the collateral evidence seem most consistent with a situation in which stock market bubbles exist but do not influence investment spending.

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Appendix A

Firms rely on the stock market

In this subsection we consider the possibility that firms rely directly on the stock market in making their investment decisions, regardless of whether or not the stock market is efficient. Morck, Shleifer, and Vishny (1990) provide a nice summary of this view, which they refer to as the 'active informant' hypothesis (p. 164): that stock market prices predict investment because they convey to managers information useful in making investment d e c i s i o n s . . . Even if the stock market sends an inaccurate signal, the information may still be used and so the stock return will influence investment. Under the active informant hypothesis, investment is related to actual Q, regardless of whether or not actual stock market prices V, correspond to fundamental price V*: Q, - c},, = e?.

(A.1)

Under certain assumptions about the rationality of stock market participants, it is possible to derive the Euler equation under the active informant hypothesis and thus determine whether it will pass the specification tests. 27 In deriving the Euler equation, the usual approach is to start from the firm's optimization problem and use equations such as (4) and (6) to derive an equation like (7). Under the assumption that firms rely on the stock market, this is not appropriate since we begin by assuming that managers base their investment decisions on the stock market value of the firm, regardless of whether the stock market represents the present value of expected future earnings. So instead of using the firm's optimization problem to derive the Euler equation, we start with (A.1), and make assumptions about the stochastic process for the stock market value. Specifically, suppose we assume that stock market participants display period-to-period rationality 28 of the following form: Vt (1 --

6)Kt-1

- R * E t { V , + a / ( 1 - 6 ) K t } + ( F I ~ , t - CK,t),

(A.2)

27We thank Olivier Blanchard for suggesting the following analysis. 28Rational bubbles followa condition like (A.2);in fact, they are referred to as 'rational' because the bubble component grows at a rate corresponding to the discount factor. A condition like (A.2)does not necessarily hold for fads. In general, the distinction between rational bubbles and fads is not relevant to our approach, since either form of stock market inefficiencycan lead to a divergence between actual and fundamental price. Our use of the term bubbles (without the adjective'rational') is intended to be generic, including all deviations of actual from fundamental price.

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71

and, in contrast to (A.1), define actual Q using the actual stock market value: Qt = (Vt - p[ (1 - 6) K,_ ,)/(1 - 6) K,_ ,.

(A.3)

Substituting for Qt in (A.1) with (A.3), using (A.2) to eliminate (Vt/(1-6)K,_ 1), and using (A.1) and (A.3) advanced one period to eliminate (V,+ t/(1 - 6) Kt), we obtain an Euler equation identical to (7), which was derived under the assumption of an efficient stock market. The analysis in this subsection suggests that, under the assumptions that firms rely on the stock market (A.1) and that stock market values are constrained by the period-to-period rationality condition (A.2), u~ = e~, u? = e,Q, both the Euler and Q equations should pass our specification tests.

Appendix B The variance ratio and autocorrelation tests

This appendix derives the two tests discussed in Section 7.2. Variance ratio test

The formal model implies that, in the absence of bubbles, the errors for the Q and Euler equations (u,Q and uff, respectively) are as follows: u~ = - a,,

(B.1)

u~ = ~:f+l + R ' a , + 1 -- a,,

(B.2)

where a, is the adjustment cost shock, e,+ 1 is the serially uncorrelated expectation error, and R* is the stochastic discount factor. 29 The relation between the variances of the Q and Euler equations can be evaluated in terms of a specific serially correlated process. Suppose at is AR(I), at=pat

i + s,,

(B.3)

where ,st is an innovation. With M [.] and V [.] as the mean and variance operators, respectively, and K equal to the ratio of the variance of the expectation error to the variance of the adjustment cost shock (i.e., ~: = V [ e ] / V [ a ] ) , we

29 Eqs. (B.1) and (B.2) omit the approximation errors introduced by the technology specifications (of. (16) and (17) in the text). The variation introduced by these approximation errors raises V [u v'] relative to V [uQ], making it more likely that the inequality (B.6) valid under the null hypothesis will hold. The approximation errors are not introduced explicitly for notational simplicity and because of a lack of information about their relative variances.

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can derive the following expressions for the variances of the Q and Euler errors: V [u Q] = V[a],

(B.4)

V[u e] = Via] + V[~] + V[R*a,+I] - 2 E { R * a , + l a , } , = Via] + V I i i + V [ a ] ( M [ R * ] 2 + V [ R * ] ) - 2 p M [ R * ] Via],

= V[a]{~c + 1.78 - 1.77p}.

(B.5)

The derivations of (B.4) and (B.5) are based on the independence of R* from a, and the orthogonality of st+ 1 and a,. The numerical values are determined by replacing population moments of observable variables with their sample moments. Under the null hypothesis, the variance ratio statistic (VR) obeys the following relation: V R - - V[uQ]/V[u E ] < 1 iff { t c + 1 . 7 8 - 1 . 7 7 p } > l .

(B.6)

Sufficient conditions for the inequality in (B.6) to hold are either 1) the adjustment cost shock is not excessively serially correlated (p < 0.45) or 2) the variance of the adjustment cost shock is less than the variance of expectation errors (x _> 1). (The formula is quite similar if the adjustment cost shock follows an MA(1) process, a, = m t + Omt_ 1; in this case, p is replaced by 0/(1 + 0) in (B.6).) Under the alternative hypothesis of bubbles (B,) and an inactive financing mechanism (suggested by the specification tests), u,° = - at + Bt,

(B.7)

u~ = et+ l + R* at+ l -- at.

(B.8)

It is important to note that V[u E] is independent of the bubble but V[u Q] is affected by Bt. A sufficiently large bubble, coupled with the plausible assumption that the bubble and the adjustment cost shock are uncorrelated, implies that the inequality in (B.6) is reversed, VR - V [ u ° ] / V [ u E] > 1.

(B.9)

A rejection of(B.6) can be interpreted in terms of a bubble in the Q equation that raises V[u°]. The VR's are robust to either AR(1) or MA(1) processes for at, and are reported in the Tables 3-5. Autocorrelation test

The above variance ratio test exploits the structure of the error terms implied by the formal model to extract testable implications concerning variances.

R.S. Chirinko, H. Schaller / Journal of Moneta~ Economics 38 (1996) 4 7 - 7 6

73

Additionally, this structure has testable implications for the presence of AR(1) or MA(1) adjustment cost shocks evaluated in terms of the sign and magnitude of autocorrelation coefficients. Given that our specification tests indicate that the Euler equation is unaffected by bubbles, we focus on the Euler equation error term, u~ = e,,+l + R ' a , + 1 - a,,

(B.10)

where we assume that the discount factor is constant at its mean value of R* = 0.884. Consider the following autoregression for the Euler residuals:

(B.11)

u ~, -- [1~uLj + ,7,,

where th is an innovation. If the adjustment cost shock is AR(I), at = p a t - 1 + st,

p >_ 0,

(B. 12)

then the [1's in (B.11) should obey the following monotonically declining relations: [11 = p X ,

(B.13a)

[12 = P2 X ,

(B.13b)

[13 = p3 X ,

(B.13c)

where X is a function of variances, R*, and p, and is always nonnegative (X = ~2 V[a] { 1 + V [w]/~ 2V [a]) - l, where ~ = (R* p - 1) and wt = e, + 1 + R* st + 1)Hence, the [1's are always nonnegative. Alternatively, if the adjustment cost shock is MA(1), at = m t + Ornt_ ~,

0 >_ O,

(B.14)

then the//'s should obey the following relations: [11 = (R* - O)(R*O - 1) V*,

(B.15a)

[12 = -- R * O V * ,

(B.15b)

/33 = 0,

(B.15c)

where V* = V [ m ] / V [ u ~ ] . Note that [1~ is positive (negative) if 0 is greater than (less than) R* and that [12 is always nonpositive. An important distinction between the AR(1) and MA(1) models is that [1z is always nonnegative under the AR(1) process and always nonpositive under MA(1) process. The estimated autocorrelations are presented in Table 6.

R.S. Chirinko, H. Schaller / Journal of Monetary Economics 38 (1996) 47-76

74

Appendix C The measure of the bubble

In the Lucas asset pricing model, the equilibrium condition is P t U ' (D,) = flE,{U' (Ot+ ,)EPt+ a + Dr+l]},

where P is the asset price, U' (D,) is the marginal utility of consumption, D is the dividend, and/3 is the subjective discount factor. Assuming a Constant Relative Risk Aversion (CRRA) utility function,

u(c,) =- (1 + ~)-' c~, +,, where 7 is the coefficient of relative risk aversion, gives the following stochastic difference equation for equilibrium prices: Pt'P• = f l ' E t { D • + ,

"(Pt+ 1 + O,+1)}.

This yields the following equation for fundamental price: P* = O f - " ~ flk. E,{O,*+~}. k=l

Assuming that log dividends is a random walk with drift, dt = ~o + d~+l + et, where d, is the logarithm of dividends, eo is the drift parameter, and e, is a sequence of independent, identically distributed normal random variables with mean zero and variance a:, then P* = mDt,

where m =/~"

e ~°(1 + 7 ) + (1 + 7)~ a2/2/(

1 _ ~. e~o(1+ ~.)+(1

+ 1')2 o'2/2) ,

Under the null hypothesis of no bubbles, Pt = P*, so m = E [P/D]. The measure of the bubble (normalized by the current stock price) is (Pt -- P*)/P, = 1 -- m (Dt/Pt).

References Blanchard, J. Olivier, Changyong Rhee, and Lawrence H. Summers, 1993, The stock market, profit and investment, Quarterly Journal of Economics CVIII, 115-134.

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75

Blanchard, J. Olivier and Mark Watson, 1982, Bubbles, rational expectations and financial markets, in: P. Wachtel, ed., Crises in the economic and financial structure (Lexington, Lexington, MA). Blundell, Richard, Stephen Bond, Michael Devereux, and Fabio Schiantarelli, 1992, Investment and Tobin's Q, Journal of Econometrics 51,233 257. Bosworth, Barry P., 1975, The stock market and the economy, Brookings Papers on Economic Activity 2, 257-290. Chirinko, Robert S., 1993, Business fixed investment spending: Modeling strategies, empirical results, and policy implications, Journal of Economic Literature 31, 1875 1911. Chirinko, Robert S. and Steven M. FazzarL 1988, Tobin's Q, non-constant returns to scale, and imperfectly competitive product markets, Recherches Economiques de kouvain 54, 259 275. Chirinko, Robert S. and Huntley Schaller, 1995, Why does liquidity matter in investment equations?, Journal of Money, Credit, and Banking 27, 527 548. Cutler, David M., James M. Poterba, and Lawrence H, Summers, 1989, What moves stock prices'?, Journal of Portfolio Management 15, 4-12. De Long, J. Bradford, Andrei Shleifer, Lawrence H. Summers, and Robert J. Waldmann, 1990, Noise trader risk in financial markets, Journal of Political Economy 98, 703 738. Durlauf, Steven N. and Robert E. Hall, 1990, Bounds on the variances of specification errors in models with expectations (University of Wisconsin, Madison, WI). Eichenbaum, Martin S., Lars Peter Hansen, and Kenneth J. Singleton. 1988, A time series analysis of representative agent models of consumption and leisure choice under uncertainty, Quarterly Journal of Economics 103, 5l 78. Fischer, Stanley and Robert C. Merton, 1984, Macroeconomics and finance: The role of the stock market, in: Karl Brunner and Allan H. Meltzer, eds., Essays on macroeconomic implications of financial and labor markets and political processes. Carnegie Rochester Conference Series on Public Policy 21, 57 q08. Galeotti, Marzio and Fabio Schiantarelli, 1994, Stock market volatility and investment: Do only fundamentals matter?, Economica 61, 147 165. Gallant, Ronald A. and Dale W. Jorgenson, 1979, Statistical inference for a system of simultaneous nonlinear, implicit equations in the context of instrumental variables estimation, Journal of Econometrics 11,275-302. Gordon, Robert J., 1969, $45 billion of U.S. private investment has been mislaid. American Economic Review 60, 221-238. Hansen, Lars Peter, 1982, Large sample properties of generalized method of moments estimators, Econometrica 50, 1029-1054. Hayashi, Fumio, 1982, Tobin's marginal q and average q: A neoclassical interpretation, Econometrica 50, 213 224. Loughran, Tim and Jay R. Ritter, 1995, The new issues puzzle, Journal of Finance 50, 23 51. Morck, Randall, Andrei Shleifer, and Robert W. Vishny, 1990, The stock market and investment: Is the market a sideshow?, Brookings Papers on Economic Activity 2, 157 202. Newey, Whitney K. and Kenneth D. West, 1987, Hypothesis testing with efficient method of moments estimation, International Economic Review 28, 777 787. Poterba, James M. and Lawrence H. Summers, 1988, Mean reversion in stock prices: Evidence and implications, Journal of Financial Economics 22, 27 59. Rhee, Changyong and Wooheon Rhee, 1991, Fundamental value and investment: Micro data evidence, Center Economic Research working paper no. 282 (University of Rochester, Rochester,

NY). Shiller, Robert, 1984, Stock prices and social dynamics, Brookings Papers on Economic Activity 2, 457~498. Summers, L.H., 1986, Does the stock market rationally reflect fundamental values?, Journal of Finance XLI, 591 603.

76

R.S. Chirinko, H. Schaller / Journal of Monetary Economics 38 (1996) 47-76

Tauchen, George, 1986, Statistical properties of generalized method-of-moments estimators of structural parameters obtained from financial market data, Journal of Business and Economic Statistics 4, 397416. Tirole, J., 1982, On the possibility of speculation under rational expectations, Econometrica 50, 1163-1181. Tirole, J., 1985, Asset bubbles and overlapping generations, Econometrica 53, 1071 1100. West, Kenneth D., 1987, A specification test for speculative bubbles, Quarterly Journal of Economics 102, 553-580.