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We consider a variety of vintage-capital models of a firm's choice of technology under uncertainty in the presence of adjustment costs and technology-specific learning. Similar models have been studied in a deterministic setting. Part of our objective is to examine the robustness of the implications of the certainty models to uncertainty. Our analysis highlights the role of the specification of costs of adjustment: if an adjustment cost comes only in terms of accumulated technology-specific expertise (cf. Parente (1994)), we prove that the implications are robust for a variety of specifications of the firm's production function, however, once a cost paid in units of the produced good is introduced, predictions of an uncertainty model become increasingly different as uncertainty increases. Tractability of our models allows us to disentangle the effects of the models' assumptions, provide characterization of optimal policies, demonstrate the impact of uncertainty on the frequency of technology adoptions and growth in the economy, and present comparative statics. Download Paper
In this paper we critically examine the main workhorse model in asset pricing theory, the Lucas (1978) tree model (LT-Model), extended to include heterogeneous agents and multiple goods, and contrast it to the benchmark model in financial equilibrium theory, the real assets model (RA-Model). Households in the LT-Model trade goods together with claims to Lucas trees (exogenous stochastic dividend streams specified in terms of a particular good) and zero- net-supply real bonds, and are endowed with share portfolios. The RA-Model is quite similar to the LT-Model except that the only claims traded there are zero-net-supply assets paying out in terms of commodity bundles (real assets) and households’ endowments are in terms of commodity bundles as well. At the outset, one would expect the two models to deliver similar implications since the LT-Model can be transformed into a special case of the RA- Model. We demonstrate that this is simply not correct: results obtained in the context of the LT-Model can be strikingly different from those in the RA-Model. Indeed, specializing households’ preferences to be additively separable (over time) as well as log-linear, we show that for a large set of initial portfolios the LT-Model – even with potentially complete financial markets – admits a peculiar financial equilibrium (PFE) in which there is no trade on the bond market after the initial period, while the stock market is completely degenerate, in the sense that all stocks offer exactly the same investment opportunity – and yet, allocation is Pareto optimal. We then thoroughly investigate why the LT-Model is so much at variance with the RA-Model, and also completely characterize the properties of the set of PFE, which turn out to be the only kind of equilibria occurring in this model. We also find that when a PFE exists, either (i) it is unique, or (ii) there is a continuum of equilibria: in fact, every Pareto optimal allocation is supported as a PFE. Finally, we show that our results continue to hold true in the presence of various types of restrictions on transactions in financial markets. While our analysis is carried out in the framework of the traditional two-period Arrow-Debreu-McKenzie pure exchange model with uncertainty (encompassing, in particular, many types of contingent commodities), we show that similar results hold for the analogous continuous-time martingale model of asset pricing. Download Paper