A meta-analysis of the investment-uncertainty relationship.

• Author: Koetse, Mark J.

1. Introduction

   The relationship between investment and uncertainty has been extensively analyzed in both the theoretical and the empirical literature since the 1970s. One of the most salient features of the theoretical literature is the inconclusiveness about the direction of the relationship. Early models can be found in Hartman (1972), Pindyck (1982), and Abel (1983), among others. Hartman (1972) uses a neoclassical model without capital stock adjustment costs and analyzes the relationship between capital productivity and uncertainty. Under the convexity of this relationship, and by Jensen's inequality, the incentive to produce and invest increases when uncertainty increases, implying a positive relationship. Hartman's model is, however, restricted to markets with perfect competition and relies on assumptions of constant returns to scale and substitutability of capital for other input factors. Also, adjustment costs are assumed to be symmetric. In real-world situations, however, this assumption is likely violated for most capital investments. Pindyck (1982) allows for asymmetric adjustment costs and argues that the effects of uncertainty on investment spending are in fact dependent on the characteristics of the adjustment cost function. Abel (1983) argues that increased uncertainty leads to increased investment spending, regardless of the characteristics of the adjustment cost function, effectively confirming the results of Hartman (1972). However, he also shows that adjustment costs matter for the relationship between investment and Tobin's Q. As a result, uncertainty has a direct effect on investment but also an indirect effect through Q in the Abel (1983) model. The overall effect is positive when adjustment costs are convex but is ambiguous when adjustment costs are concave.

   More recent thinking about uncertainty is dominated by the concept of capital investment irreversibility (see Pindyck 1991; Dixit and Pindyck 1994). For a neoclassical model with asymmetric capital adjustment costs, that is, a certain degree of irreversibility of capital investment, Dixit and Pindyck show that an increase in uncertainty creates an option value of waiting for new information to arrive in the future. The central point of the irreversibility or real options literature is that an increase in uncertainty will ceteris paribus result in more investment projects being delayed. This argument has major implications for the timing of investment, implying that short-run investment levels may be affected but long-run investment levels will not. We can therefore distinguish between two general branches of research regarding the investment-uncertainty relationship: a first branch in which uncertainty is related to the timing of investment, and a second branch that analyzes the impact of uncertainty on the investment level. (1) This article focuses primarily on the second branch.

   Given the ambiguity of the theoretical literature, there is no way to determine the direction of the relationship between investment and uncertainty a priori, let alone to draw inferences on the magnitude of the effect and its economic relevance. Various explanations for this ambiguity have been brought forward. One of the most obvious sources of heterogeneity is the degree of irreversibility of investment itself; that is, the smaller the possibilities to disinvest, the larger the negative impact of uncertainty on investment spending. A similar argument holds for risk aversion. (2) Numerous attempts have been made to resolve this issue empirically, but these attempts seem to have added to, rather than resolved, the existing ambiguity. In Carruth, Dickerson, and Henley (2000) an excellent overview is provided of the most relevant topics in the theoretical debate on the investment-uncertainty relationship. Major issues in the empirical literature are also discussed, such as the possible consequences of data aggregation and the differences between operational measures of uncertainty. However, although the Carruth, Dickerson, and Henley (2000) study is obviously useful and important in its own right, it is qualitative in nature and does not attempt to quantify the importance of differences in study characteristics for the variation in study outcomes.

   In this article we therefore perform a meta-analysis on the relationship between uncertainty and investment spending. Meta-analysis is a form of quantitative research synthesis originally developed in experimental medicine and later extended to fields such as biomedicine and experimental behavioral sciences, specifically education and psychology. During the last two decades it has also been widely applied in economics.3 The intuitive appeal of meta-analysis rests on its ability to combine sometimes widely scattered empirical evidence on a certain topic and the associated increase in statistical power of hypothesis testing when combining independent research results. Moreover, by controlling for variations in characteristics across studies, meta-analysis provides quantitative insight into which factors are relevant in explaining the variation in study outcomes. As such, meta-analysis provides a quantitative analytic assessment in addition to the more qualitative judgment provided by a narrative literature review (Stanley 2001).

   The remainder of this article is organized as follows: Section 2 discusses the type of estimates used in this study, as well as the way in which they have been sampled from the literature. We also provide descriptive statistics for the resulting meta-sample. Section 3 discusses the operationalization of moderator variables, which represent differences in study characteristics that may systematically affect a study's outcome. The model and estimation procedure are presented in section 4, while section 5 discusses the estimation results. Section 6 concludes.

2. Effect Size, Sampling Procedure, and Sample Characteristics

   Empirical studies on investment behavior are heterogeneous in many respects. Studies generally include a wide variety of explanatory variables; they operationalize investment and uncertainty in different ways; and they are performed on samples that vary over time and space. The impact of these sources of heterogeneity will be assessed in the meta-regression analysis. An important observation is that the investment-uncertainty literature is focused on the sign of the relationship and not on its magnitude. In order to focus on the main issue in the literature we define an effect size that does not include the magnitude of the relationship. In our attempt to create a sample of effect sizes that included the magnitude of the relationship we faced several restrictions, the most important being that most of the study results are not defined in a common, scale-free metric. In the empirical literature, three different functional forms are used in primary studies: linear, semilogarithmic, and double-log specifications. Coefficients from double-log models can be interpreted as elasticities, which is generally a good measure for an effect size. Coefficients from linear and semilogarithmic models, however, are not scale-free, implying that results from these studies are incomparable and that a transformation into elasticities is necessary. This was only feasible for a limited subset of linear and semilog coefficients, implying that the resulting sample of elasticities would be substantially smaller than the original sample of study results. In order to use the full sample of study results, while still focusing on the main issue in the literature, we focus on the direction and statistical significance of the estimates rather than on the magnitude of the elasticities. In our empirical analysis we ultimately distinguish between significantly negative, insignificant, and significantly positive study results.

   In creating our sample of studies we first searched through titles and abstracts of studies using keywords in standard online search engines such as Econlit, Picarta, and RePEc. Keywords used were "investment," "uncertainty," and "volatility." We subsequently looked for papers and articles in the reference lists of studies that were collected. Ultimately, we collected 48 studies that empirically analyze the relationship between uncertainty and investment. These studies provided a total of 957 estimates, but some studies and estimates had to be excluded from the database for one of the following reasons. First, as suggested by Abel and Eberly (1999), among others, one of the potential reasons for the theoretical ambiguity on the direction of the relationship is that the relationship is potentially hump shaped. (4) Two studies in our sample use a model specification in which uncertainty is included in a linear and a quadratic fashion to test this hypothesis (Lensink 2002; Bo and Lensink 2005). (5) In these studies, the effect of uncertainty on investment is conditional on the degree of uncertainty. We therefore excluded these observations from the analysis (32 estimates). Second, some studies use a logit or probit model to estimate the relationship. In these models the dependent variable is either binary or ordered; that is, the analysis is concerned with estimating the impact of factors determining the probability that investment actually takes place. As such, the results from these models do not provide information on the change in the level of investment and are therefore excluded from the analysis (59 estimates). Third, standard errors or /-statistics are essential for constructing our dependent variable, since they are used to calculate the/)-values (statistical significance) of study estimates. We exclude the estimates for which no standard errors or t statistics were provided in the study (24 estimates). Fourth, some models provide information on the relationship between investment and an uncertainty measure that was interacted with another variable. For these models...