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We report evidence that the relation between the financial-sector share, private saving, and growth in the United States in 1948-96 is characterized by several regime shifts. The finding is based on vector autoregressions on quarterly data that allow for Markov switching regimes. The evidence may be interpreted as support for a hypothesis that the relation between financial development and growth evolves in a stepwise fashion. Theoretical models in which structural financial developments entail fixed costs imply such stepwise patterns. The estimated variable relations are roughly consistent with the patterns to be expected from such models, although our data do not admit definite conclusions. The timing of the shifts coincides with changes in regulation and in the financial-market structure.

The theoretical analysis of investment under uncertainty has been revolutionized over the last decade by the importation of ideas from finance. If investment is irreversible, there is a return to waiting. So although circumstances may suggest that it is profitable to invest, there may also be an incentive to postpone the decision until better opportunities arise. Identifying and valuing the option to invest has become the standard way to solve the firm's irreversible-investment problem. Empirical studies of investment that incorporate the insights of the real-options approach are now beginning to appear. These show that investment can have a nonlinear relationship to q and may show insensitivity for some threshold level to the shadow value of investment (Barnett and Sakellaris 1998). Abel and Eberly (1997) and Böhm and Funke (1999) have also shown how the real-options approach to investment can be combined with the traditional q approach. In this case the relationship between q and the rate of investment is discontinuous. Over a range of inaction there will be no investment, although q is in excess of one.This paper builds a theoretical model that explains the determinants of this investment discontinuity. In contrast to much of the literature, we use a mean-reverting stochastic process, of which the geometric Brownian motion process is a special case. Under the assumption of a production function with constant returns to scale and a specific functional form for the investment adjustment function, it is possible to derive a tractable analytical form for the shadow value of the investment project. We then analyze the comparative properties of the value of q under different assumptions about the stochastic process governing output. The advantage of using a mean-reverting process is that it better captures the undoubted persistence in the shocks that face firms, especially at the macroeconomic level.We then consider what the implications would be for the aggregate relationship between investment, q, and the business cycle. We first carry out Monte Carlo simulations of a discrete version of the theoretical model. We find that for many parameter values, aggregating suppresses any nonlinearities in the micro adjustment processes. Moreover, where we do detect nonlinearity at the aggregate level, it varies with the type of stochastic process. It is greatest when this is a random walk—corresponding to the Brownian motion in continuous time—and least when the stochastic process follows an i.i.d. process. Mean reversion lies in between. We turn finally to an empirical examination using aggregate data and explore how sensitive investment is to q in different regimes. To do this, we apply a generalization of the Granger-Lee method (Arden et al. 2000) that uses a linear spline function to approximate different regions for investment.

We show that a class of microeconomic behavioral models with interacting agents, derived from Kirman (1991) and Kirman (1993), can replicate the empirical long-memory properties of the two first-conditional moments of financial time series. The essence of these models is that the forecasts and thus the desired trades of the individuals in the markets are influenced, directly or indirectly, by those of the other participants. These "field effects" generate "herding" behavior that affects the structure of the asset price dynamics. The series of returns generated by these models display the same empirical properties as financial returns: returns are I (0), the series of absolute and squared returns display strong dependence, and the series of absolute returns do not display a trend. Furthermore, this class of models is able to replicate the common long-memory properties in the volatility and covolatility of financial time series revealed by Teyssière (1997, 1998a). These properties are investigated by using various model-independent tests and estimators, that is, semiparametric and nonparametric, introduced by Lo (1991), Kwiatkowski et al. (1992), Robinson (1995), Lobato and Robinson (1998), and Giraitis et al. (2000, forthcoming). The relative performance of these tests and estimators for long memory in a nonstandard data-generating process is then assessed.

This paper investigates topologically semiconjugate dynamics as a macrorepresentation of microeconomic dynamics. The condition for its existence, its summarizing property, and its inferability property are discussed. As an example, we present a model of a temporary equilibrium price dynamic that has a topologically semiconjugate one-dimensional income dynamic, from which the nature of the original price dynamic will be inferred.