Very Preliminary: Comments welcome
Explaining the Diversity of Industry Investment Responses to Uncertainty Using Long Run Panel Survey Data
Ciaran Driver ¶, Katsushi Imai †, Paul Temple‡1 and Giovanni Urga † ¶ Imperial College Management School, London (U.K.) † City University Business School, London (U.K.) ‡ Department of Economics, University of Surrey (U.K.)
This version: April 3, 2001 Abstract Real options theory is frequently cited as the most likely explanation for the negative relationship between uncertainty and investment reported in the literature. However, there are various other alternatives and being able to distinguish between them is important for policy purposes. This paper presents an empirical study of the various channels of influence using long run survey data from the Confederation of British Industry’s Industrial Trends Survey. Based on data from 48 UK manufacturing sectors and different measures of uncertainty, the paper estimates the negative impact of uncertainty on investment using panel data methods and individual industry regressions. Considerable industrial heterogeneity is uncovered and a major focus of the paper is to explain this variation. The cross-industry pattern of results is checked for consistency with the pattern that would be expected based on the various channels of influence from uncertainty to investment. A specially constructed data set of industrial characteristics is used in a logit analysis to effect a discrimination between the competing hypotheses. Only qualified support can be found for real option theory.
J.E.L. classifications: E22, C23 Key-words: Investment, Real Options, Uncertainty
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Corresponding author: Paul Temple, Department of Economics, University of Surrey, Guildford, Surrey GU2 5XH (U.K.). Tel. +/44/1483/300800 (ext.6949); Fax. +/44/1483/259548; e-mail:
[email protected]. ESRC funding under grant N. R.022250159 is gratefully acknowledged.
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1. Introduction The literature now contains a large set of studies that report a (generally) negative influence of uncertainty on fixed investment spending (for a recent survey, see Carruth et al 2000). To date however, there has been little applied research on the mechanism by which that influence is exerted. Much of the literature assumes without question that the real option framework is the main channel of influence. Within that rubric, attention has focussed on a single dichotomy – perfect versus imperfect competition – in explaining cross-section variation in the effect of uncertainty on investment. This paper takes a broader perspective. In Section 1 we explain that there are a variety of mechanisms by which uncertainty can affect investment. Section 2 introduces the basic investment model used in the paper. Section 3 describes data and modelling issues. Section 4 reports the results of estimating the model with indicators of uncertainty. Section 5 assesses whether the cross-section pattern of uncertainty effects can be reconciled with any of the theories discussed in Section 1. Section 6 concludes.
2. The theoretical effect of uncertainty on investment demand The modern theory of investment under uncertainty has been greatly influenced by real options theory of irreversible investment with an option to delay. In their seminal contribution Dixit and Pindyck (1994) argued that this theory could explain why hurdle rates of return are about twice the rate than would be expected under neo-classical theory. Further research however has resulted in a more subtly nuanced approach. While it is possible for the theory to explain a delay in investment, there are at least two important considerations that complicate the picture. First, the theory predicts the behaviour of the threshold rule for investment rather than investment itself. Put differently, uncertainty should raise the hurdle rate but as it also makes the hurdle rate more variable it will result in a greater probability of an investment burst so that the effect on investment itself can generally only be obtained by simulation results. In most cases, however, simulations do seem to confirm that when the hurdle rate is lowered, investment also drops (Hassett and Metcalf 1999). A more serious concern with the theory is that – even when control over timing of the investment is possible - there are a number of circumstances when the effect of delay is reversed and where uncertainty causes projects to be brought forward. One example is where the information set depends on investment, as with R&D expenditures or pilot projects (Dixit and Pindyck 1994). Other possible cases arise where there are delays due to construction (Bar-Ilan and Strange, 1996); where tax incentives alternate between “on” and “off” modes and where there is an option to abandon (Darby et al 1999); or where the investment creates an option to expand (Abel et al 1996). In the last case, investment may be encouraged if the option confers the right to expand output in the event of high demand. The effect of uncertainty also depends on the nature of the underlying
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stochastic process since this in part determines the value of waiting. Most research has assumed a random walk. However, where the uncertain variable is mean-reverting or trend stationary, the bias predicted by real options theory is blunted.(Bloom et al 1999). 2 The predicted sign of the uncertainty-investment relationship is thus highly modelspecific. Even where the option to delay is a dominant factor, the existence and strength of the effect of uncertainty on investment is controversial. Different assumptions with regard to price competition can affect the sign of the relationship at firm level.(Pindyck1991; Caballero 1991).3 Whatever its merits however, real option theory is only one of a set of ways in which uncertainty enters the decision framework of most firms. At least three other channels of influence are worthy of consideration (see for example, Aiginger 1987). Convexity First, the traditional view of price uncertainty has been that it creates an incentive to build excess capacity because of the bias arising due to the convexity of marginal profit in the uncertain variable. Although the direction and magnitude of the bias will depend on technology, demand and the form of the stochastic error, the most quoted effect is the result that uncertainty raises investment. For example, with price p and where capacity q which for simplicity is fixed-coefficient and fully utilised we have: q =upε , with E[u] =1: E[P]= [q(q/u)1/ε+1 - c(q)]f(u)du The derivative of this with respect to q will contain a term in u, not present in the certainty case, and where u=1 this will lead to higher investment under uncertainty.
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Indeed some authors argue that in the latter case, with uncertain stochastic parameters, the traditional NPV approach is superior (Slade1998). The estimation of real options models also raises methodological concern . It would be inconsistent to argue that because economic theory investigated and adopted real option theory in the 1990s that firms themselves have been consistently using such techniques . Indeed some early advocates of real options theory regarded it as a critique of firm practice (Hayes and Garvin 1982). NPV theory was discovered by Fisher in 1917 but not consistently used until the 1960s. We can probably safely conclude that real option theory is only one of a set of ways in which uncertainty enters the decision framework of most firms and other channels of influence will be important. Among these may be mentioned convexity effects which are generally held to increase investment under risk but more accurately give rise to ambiguous results depending on assumptions with regard to capacity utilisation (Hartman 1972, 1976;Kon 1983). Other channels of influence include the marginal cost of uncertainty - which relates, like inventory models, to a balancing of the cost of excess capacity and non-supply – and the effects of risk aversion (Aiginger 1987;Driver and Moreton 1992; Driver and Temple 1999) 3
However, if the time horizon of firms stretches to a consideration of new entry uncertainty under an option to delay tends to constrain investment irrespective of the market structure (Leahy and Whited 1995).
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For these kinds of models, standard results with q the decision variable and p the stochastic variable may be derived (Rothschild and Stiglitz 1971; Aiginger 1987): q(opt) < q(cert) if Π q is concave in p i.e. Π q pp q(cert) if Π q is convex in p i.e. Π q pp>0 q(opt) = q(cert) if Π q is linear in p i.e. Π q pp=0 The intuition behind this can be seen by assuming that he marginal impact on profit of an extra unit of q is convex in the price. This means that the expected value of the marginal profit with respect to q is greater than the marginal profit under certainty. Under certainty the point of zero marginal profit will be met sooner i.e. with lower q and so, q(opt)>q(cert) . For example, consider a constant elasticity demand curve shifted by a random term u. The marginal revenue function is: M(q,u) =(1+1/ε)q1/ε u-1/ε. This is concave in u for elastic demand and so the optimal q is smaller than under certainty. Extension to a two-factor setting with perfect competition and price uncertainty is sometimes known as the Hartman-Abel model (Hartman 1972; Abel 1983). Then optimal level of K will be determined by: E[pFK{K,L(K,w/p}-c]=0 where K is capital fixed in advance of the price but where L/K could be varied ex-post. The function in the square brackets is linear in p if L does not vary with p e.g. as in a fixed coefficients model. If L rises in response to higher P - as would be indicated by the usual marginal productivity conditions if there is flexibility - FK will rise as well. The function in square brackets will then be convex in p, imparting an upward bias to capital input.4 The intuitive reason for the result is that as the price rises and labour input has to be increased to sub-optimal levels, the value of a unit of capital is increasing non-linearly in p. Disequilibrium or Fix-Price Models The second and perhaps more interesting case is the Newsboy inventory model applied to capital input. The previous models have assumed that there is no rationing. Firms can always meet demand and price adjusts upward so that demand is met. This would not appear to be always sensible at least at the level of the individual firm, where a forecasting error could cause a firm to run out of capacity. Because of this we must 4
Where there are sharp diseconomies of scale it is possible that the rise in FK could be reversed: the exact condition is that σ>1/(1-η) where σ is the elasticity of substitution and η is the economies of scale parameter. However this case may be considered as unlikely. With constant returns, and σ < 1 we get the standard result.
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consider a new set of models where sales are distinct from production. This turns out to have the radical implication that we cannot use the usual convexity/concavity formulation of the Rothschild-Stiglitz condition because we now have three distinct variables: the decision variable e.g. output; the stochastic variable e.g. price; and a new variable distinct from output - demand. This context is sometimes known as “stochastic rationing” and the usual condition imposed is that Sales =min[Production, Demand]. With fixed price margins, the effect of uncertainty is to encourage investment only if the unit profit at full capacity is above a threshold; otherwise the bias is negative. For the arguably more realistic case where price is not exogenous but is set ex-ante along with irreversible capacity, the Newsboy model yields the result that price is always higher under uncertainty (Karlin and Carr 1962)..This result has been extended to show that under mild restrictions investment too is biased downwards (Driver et al 1993).Finally, even where price is market-clearing the same result is obtained under realistic restrictions (Driver et al 1996). Risk Attitude Finally, the role of risk aversion should not be underestimated. In most models demand uncertainty results in a lower optimal capital stock. Survey-based evidence also suggests that this may be the primary method by which uncertainty has an effect on investment, at any rate for large projects (Aiginger 1987; Nakomura 1999). Hypothesised effects of uncertainty on investment Of the four models above (real options, convexity, disequilibrium and risk aversion) only the convexity model predicts an unambiguous sign for the investment-uncertainty relationship and that sign is positive. Each of the other models is, however likely to yield a negative sign, at least under the specific circumstances as set out in Table 1 below. The final column notes discrimination between the models may be possible in the context of an examination of industrial heterogeneity. However, it can be seen that this may be difficult in practice, since proxies for different channels of influence may be similar. For example, in contrasting the real option and the risk-aversion effect it is difficult to disentangle the effects of irreversibility and risk since both depend on the capital intensity of production. If we assume identical risk attitudes across our industry sample then a high share of capital could impact negatively on investment either through risk aversion (due to low elasticity of output to labour), or through irreversibility.
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TABLE 1 Summary of Hypotheses Concerning the Impact of Uncertainty Model
Likely sign
Condition for the sign
circumstances affecting the strength of the relationship
Proxy variable to use in discriminating
REAL OPTION
