Irreversible investment and R&D spillovers in a dynamic duopoly

Investments in new production processes usually involve a significant amount of R&D, generating spillovers that lowers the second comer's investment cost. We show that these spillovers substantially affect the equilibrium of the dynamic game. Even for low spillover values, the leader delays her investment until the stochastic fundamental has gone past the level such that the follower's optimal strategy is to invest as soon as he attains the spillover. This bears several interesting implications. First, because the follower invests as he benefits from the spillover, in equilibrium the average time delay between the two investments is short, as it should be expected. Second, in case of a major innovation, an optimal public policy requires an intervention in favor of the investment activity; an increase in uncertainty - delaying the equilibrium - calls for higher subsidization rates. Third, numerical simulations show that the spillover reduces the difference between the leader's and the follower's maximum value functions. Accordingly, our model can help generate realistic market betas.     

Incomplete markets, ambiguity, and irreversible investment

The problem of irreversible investment with idiosyncratic risk is studied by interpreting market incompleteness as a source of ambiguity over the appropriate no-arbitrage discount factor. The maxmin utility over multiple priors framework is used to model and solve the irreversible investment problem. Multiple priors are modeled using the notion of κ‐ignorance. This set-up is used to analyze finitely lived options. For infinitely lived options the notion of constant κ‐ignorance is introduced. For these sets of density generators the corresponding optimal stopping problem is solved for general (in-)finite horizon optimal stopping problems driven by geometric Brownian motion. It is argued that an increase in the set of priors delays investment, whereas an increase in the degree of market completeness can have a non-monotonic effect on investment.     

Heuristics,learning and the business angel investment decision-making process

ABSTRACT

This paper extends the literature on the investment decision-making of business angels.

Using insights from the emerging body of research on entrepreneurial learning processes, particularly the use of heuristics and the nature of learning from meagre experience, we explore whether angels learn from experience, how they learn and what they learn. These issues are addressed using verbal protocol analysis, a methodology for examining decision-making in real time, with three groups of business angels with differing levels of investment experience, and with follow-up debriefing interviews with these angels. This reveals some differences in the speed of decision making and the emphasis given to various investment criteria. There is some evidence for the use of heuristics in the decision making process, and for the critical role played by vicarious learning from the experience of others. Learning in the individual angel decision making process is a social as well as an individual phenomenon.     

Bayesian learning with variable prior

How much can be learned from a noisy signal about the state of the world not only depends on the accuracy of the signal, but also on the distribution of the prior. Therefore, we define a general information system as a tuple consisting of both a signal technology and a prior. In this paper we develop a learning order for general information systems and characterize the order in two different ways: first, in terms of the dispersion of posterior beliefs about state quantiles and, second, in terms of the value of learning for two different classes of decision makers. The first class includes all agents with quasi-linear quantile preferences, and the second class contains all agents with supermodular quantile preferences.     

Good signals gone bad: Dynamic signalling with switched effort levels

This paper examines signalling when the sender exerts effort and receives benefits over time. Receivers only observe a noisy public signal about the effort, which has no intrinsic value.The modelling of signalling in a dynamic context gives rise to novel equilibrium outcomes. In some equilibria, a sender with a higher cost of effort exerts strictly more effort than his low-cost counterpart. The low-cost type can compensate later for initial low effort, but this is not worthwhile for a high-cost type. The interpretation of a given signal switches endogenously over time, depending on which type the receivers expect to send it.     

Bayesian persuasion with optimal learning

We study a model of Bayesian persuasion between a designer and a receiver with one substantial deviation from the standard setup—the designer offers once and for all a single statistical experiment from which the receiver can acquire costly i.i.d. signals over time. Taking a 2-state-2-action environment and employing a tractable continuous-time framework, we fully characterize the optimal persuasion policy. When the receiver features high skepticism, the optimal policy is to immediately reveal the truth, which is true for a large set of primitives. We construct the designer’s maximum payoff and find a discontinuous drop in it as compared with the standard model. Unlike in many standard persuasion models, the designer is not able to appropriate all the rents of information disclosure while the receiver often achieves the highest possible benefit from being able to repeatedly sample from the strategically offered information structure.     

Real options and human capital investment

This paper extends the standard human capital model with real options. Real options influence investment behavior when risky investments in human capital are irreversible and individuals can affect the timing of the investment. Option values make individuals more reluctant to invest in human capital and, as a result, required returns on the investment increase. Real options may help to explain a larger human capital premium for higher education, smaller responsiveness of higher educational investments to financial incentives, and larger sensitivity of higher educational investments to low-return outcomes and human capital risks. Higher tax rates (or lower subsidies) depress human capital investments, but to a lesser extent than in the standard human capital model if not all direct costs are tax-deductible. A flat income tax remains neutral if education expenditures are fully deductible.     

Estimating dynamic panel data discrete choice models with fixed effects

This paper considers the estimation of dynamic binary choice panel data models with fixed effects. It is shown that the modified maximum likelihood estimator (MMLE) used in this paper reduces the order of the bias in the maximum likelihood estimator from O(T^-1) to O(T^-2), without increasing the asymptotic variance. No orthogonal reparametrization is needed. Monte Carlo simulations are used to evaluate its performance in finite samples where T is not large. In probit and logit models containing lags of the endogenous variable and exogenous variables, the estimator is found to have a small bias in a panel with eight periods. A distinctive advantage of the MMLE is its general applicability. Estimation and relevance of different policy parameters of interest in this kind of models are also addressed.     

Explicit investment rules with time-to-build and uncertainty

We establish explicit socially optimal rules for an irreversible investment decision with time-to-build and uncertainty. Assuming a price sensitive demand function with a random intercept, we provide comparative statics and economic interpretations for three models of demand (arithmetic Brownian, geometric Brownian, and the Cox–Ingersoll–Ross). Committed capacity, that is, the installed capacity plus the investment in the pipeline, must never drop below the best predictor of future demand, minus two biases. The discounting bias takes into account the fact that investment is paid upfront for future use; the precautionary bias multiplies a type of risk aversion index by the local volatility. Relying on the analytical forms, we discuss in detail the economic effects. For example, the impact of volatility on the optimal investment is negligible in some cases. It vanishes in the CIR model for long delays, and in the GBM model for high discount rates.     

Adaptive learning and distributional dynamics in an incomplete markets model

Recent research shows that several DSGE models provide a closer fit to the data under adaptive learning. This paper extends this research by introducing adaptive learning in the model of Krusell and Smith (1998) with uninsurable idiosyncratic risks and aggregate uncertainty. A first contribution of this paper establishes that the equilibrium of this framework is stable under least-squares learning. The second contribution consists of showing that bounded rationality enhances the ability of this model to match the distribution of income in the US. Learning increases significantly the Gini coefficients because of the opposite effects on consumption of the capital-rich and of the capital-poor agent. The third contribution is an empirical exercise that shows that learning can account for increases in the income Gini coefficient of up to 25% in a period of 28 years. Overall, these findings suggest that adaptive learning has important distributional repercussions in this class of models.     

Solving DSGE portfolio choice models with dispersed private information

Noisy rational expectations models, in which agents have dispersed private information and extract information from an endogenous asset price, are widely used in finance. However, these linear partial equilibrium models do not fit well in modern macroeconomics that is based on non-linear dynamic general equilibrium models. We develop a method for solving a DSGE model with portfolio choice and dispersed private information. We combine and extend existing local approximation methods applied to public information DSGE settings with methods for solving noisy rational expectations models in finance with dispersed private information.     

Biased Bayesian learning with an application to the risk-free rate puzzle

Based on the axiomatic framework of Choquet decision theory, we develop a closed-form model of Bayesian learning with ambiguous beliefs about the mean of a normal distribution. In contrast to rational models of Bayesian learning the resulting Choquet Bayesian estimator results in a long-run bias that reflects the agent's ambiguity attitudes. By calibrating the standard equilibrium conditions of the consumption based asset pricing model we illustrate that our approach contributes towards a resolution of the risk-free rate puzzle. For a plausible parameterization we obtain a risk-free rate in the range of 3.5–5%. This is 1–2.5% closer to the empirical risk-free rate than according calibrations of the rational expectations model.     

Growth, public investment and corruption with failing institutions

Corruption is thought to prevent poor countries from catching up with richer ones. We analyze one channel through which corruption hampers growth: public investment can be distorted in favor of specific types of spending for which rent-seeking is easier and better concealed. To study this distortion, we propose a dynamic model where households vote for the composition of public spending, subject to an incentive constraint reflecting individuals’ choice between productive activity and rent-seeking. In equilibrium, the structure of public investment is determined by the predatory technology and the distribution of political power. Among different regimes, the model shows a possible scenario of distortion without corruption in which there is no effective corruption but the possibility of corruption still distorts the allocation of public investment. We test the implications of the model on a set of countries using a two-stage least squares estimation. We find that developing countries with high predatory technology invest more in housing and physical capital in comparison with health and education. The reverse is true for developed countries.      

E-stability and stability of adaptive learning in models with private information

The paper demonstrates how the E-stability principle introduced by Evans and Honkapohja [2001. Learning and Expectations in Macroeconomics. Princeton University Press, Princeton, NJ] can be applied to models with heterogeneous and private information in order to assess the stability of rational expectations equilibria under learning. The paper extends already known stability results for the Grossman and Stiglitz [1980. On the impossibility of informationally efficient markets. American Economic Review 70, 393–408] model to a more general case with many differentially informed agents and to the case where information is endogenously acquired by optimizing agents. In both cases it turns out that the rational expectations equilibrium of the model is inherently E-stable and thus locally stable under recursive least squares learning.     

Equilibria under monetary and fiscal policy interactions in a portfolio choice model

This paper studies how the presence of income-taxes changes the properties of general equilibrium models with monetary and fiscal policy interactions. It is found that from a global perspective, the only policy regime that leads to a unique equilibrium is one where fiscal policy is active, i.e. the fiscal theory of the price level regime in Sims (1994). From a local perspective, there are three regimes. In particular, and relative to the previous literature following Leeper (1991), a new third regime exists where a passive fiscal rule combined with a passive monetary rule can still deliver determinacy where the same area of the parameter space would lead to multiple solutions if taxes were lump sum. To obtain the size of the new regime, the paper characterizes analytically the extent to which tax cuts are self-financing and how the distortionary tax Laffer curve looks near the steady state. In the new regime, monetary and fiscal backstops are brought into play so as to rule out off equilibrium dynamics, and inflation can temporarily increase in order to increase seigniorage revenues. With this flexibility, the monetary policy is consistent with the real debt remaining bounded, and the arithmetic that follows is monetarist and unpleasant in the sense of Sargent and Wallace (1981).     

A model for irreversible investment with construction and revenue uncertainty

This paper presents a model of investment in projects that are characterized by uncertainty over both the construction costs and revenues. Both processes are modeled as spectrally negative Lévy jump-diffusions. The optimal stopping problem that determines the value of the project is solved under fairly general assumptions. It is found that the current value of the benefit-to-cost ratio (BCR) decreases in the frequency of negative shocks to the construction process. This implies that the cost overruns that can be expected if one ignores such shocks are increasing in their frequency. Based on calibrated data, the model is applied to the proposed construction of high-speed rail in the UK and it is found that its economic case cannot currently be made and is unlikely to be met at any time in the next decade. In addition it is found that ignoring construction uncertainty leads to a substantial probability of an erroneous decision being taken.     

Understanding how heterogeneous agents affect Principal's returns: Perspectives from short-termism and Bayesian learning

We consider a general framework of optimal contract design under the heterogeneity and short-termism of agents. Our research shows that the optimal contract must weigh the agent's information rent, incentive cost, and benefit to overcome the contract's adverse selection and moral hazards. Agents with higher moral levels were more likely to choose higher effort and lower manipulation. Simultaneously, the principal offers lower incentives and receives more significant payoff. We also extend our model to investigate the benefits of Bayesian learning. Furthermore, we compare the principal's returns in general and learning models and find that the learning contract can bring more profit to the principal.     

A remark on rational expectation equilibria with incomplete markets and real assets

In this note, I established the existence, for a generic set of endowments, of a fully revealing rational expectation equilibrium (REE) in an economy characterized by incomplete markets and real assets.     

Arbitrage and price revelation with asymmetric information and incomplete markets

This paper deals with the issue of arbitrage with differential information and incomplete financial markets, with a focus on information that no-arbitrage asset prices can reveal. Time and uncertainty are represented by two periods and a finite set S of states of nature, one of which will prevail at the second period. Agents may operate limited financial transfers across periods and states via finitely many nominal assets. Each agent i has a private information about which state will prevail at the second period; this information is represented by a subset S_i of S. Agents receive no wrong information in the sense that the “true state” belongs to the “pooled information” set ∩_iS_i, hence assumed to be non-empty.Our analysis is two-fold. We first extend the classical symmetric information analysis to the asymmetric setting, via a concept of no-arbitrage price. Second, we study how such no-arbitrage prices convey information to agents in a decentralized way. The main difference between the symmetric and the asymmetric settings stems from the fact that a classical no-arbitrage asset price (common to every agent) always exists in the first case, but no longer in the asymmetric one, thus allowing arbitrage opportunities. This is the main reason why agents may need to refine their information up to an information structure which precludes arbitrage.     

Intertemporal choice with different short-term and long-term discount factors

This paper proposes a new axiomatic model of intertemporal choice that allows for dynamic inconsistency. We weaken the classical assumption of stationarity into two related axioms: stationarity in the short-term and stationarity in the long-term. We obtain a model with two independent discount factors, which is flexible enough to capture different time preferences, including a greater impatience for more immediate outcomes (when a long-term discount factor exceeds a compounded short-term discount factor). Our proposed model can accommodate some experimental results that cannot be rationalized by other existing models of dynamic inconsistency (such as quasi-hyperbolic discounting and generalized hyperbolic discounting).