Optimal monitoring to implement clean technologies when pollution is random

We analyze a model where firms chose a production technology which, together with some random event, determines the final emission level. We consider the coexistence of two alternative technologies: a "clean" technology, and a "dirty" technology. The environmental regulation is based on taxes over reported emissions, and on penalties over unreported emissions. We show that the optimal inspection policy is a cut-off strategy, for several scenarios concerning the observability of the adoption of the clean technology and the cost of adopting it. We also show that the optimal inspection policy induces the firm to adopt the clean technology if the adoption cost is not too high, but the cost levels for which the firm adopts it depend on the scenario.

Variational inequalities in Hilbert spaces with measures and optimal stopping problems

We study the existence theory for parabolic variational inequalities in weighted L2 spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for finite and infinite dimensional diffusions as a generalized solution of such a variational inequality. The weighted L2 setting allows us to cover some singular cases, such as optimal stopping for stochastic equations with degenerate diffusion coeficient. As an application of the theory, we consider the pricing of American-style contingent claims. Among others, we treat the cases of assets with stochastic volatility and with path-dependent payoffs.

Pareto-improving optimal capital and labor taxes

We show a standard model where the optimal tax reform is to cut labor taxes and leave capital taxes very high in the short and medium run. Only in the very long run would capital taxes be zero. Our model is a version of Chamley??s, with heterogeneous agents, without lump sum transfers, an upper bound on capital taxes, and a focus on Pareto improving plans. For our calibration labor taxes should be low for the first ten to twenty years, while capital taxes should be at their maximum. This policy ensures that all agents benefit from the tax reform and that capital grows quickly after when the reform begins. Therefore, the long run optimal tax mix is the opposite from the short and medium run tax mix. The initial labor tax cut is financed by deficits that lead to a positive long run level of government debt, reversing the standard prediction that government accumulates savings in models with optimal capital taxes. If labor supply is somewhat elastic benefits from tax reform are high and they can be shifted entirely to capitalists or workers by varying the length of the transition. With inelastic labor supply there is an increasing part of the equilibrium frontier, this means that the scope for benefitting the workers is limited and the total benefits from reforming taxes are much lower.

Three essays on the psychology of investment and financial markets

Préface My thesis consists of three essays where I consider equilibrium asset prices and investment strategies when the market is likely to experience crashes and possibly sharp windfalls. Although each part is written as an independent and self contained article, the papers share a common behavioral approach in representing investors preferences regarding to extremal returns. Investors utility is defined over their relative performance rather than over their final wealth position, a method first proposed by Markowitz (1952b) and by Kahneman and Tversky (1979), that I extend to incorporate preferences over extremal outcomes. With the failure of the traditional expected utility models in reproducing the observed stylized features of financial markets, the Prospect theory of Kahneman and Tversky (1979) offered the first significant alternative to the expected utility paradigm by considering that people focus on gains and losses rather than on final positions. Under this setting, Barberis, Huang, and Santos (2000) and McQueen and Vorkink (2004) were able to build a representative agent optimization model which solution reproduced some of the observed risk premium and excess volatility. The research in behavioral finance is relatively new and its potential still to explore. The three essays composing my thesis propose to use and extend this setting to study investors behavior and investment strategies in a market where crashes and sharp windfalls are likely to occur. In the first paper, the preferences of a representative agent, relative to time varying positive and negative extremal thresholds are modelled and estimated. A new utility function that conciliates between expected utility maximization and tail-related performance measures is proposed. The model estimation shows that the representative agent preferences reveals a significant level of crash aversion and lottery-pursuit. Assuming a single risky asset economy the proposed specification is able to reproduce some of the distributional features exhibited by financial return series. The second part proposes and illustrates a preference-based asset allocation model taking into account investors crash aversion. Using the skewed t distribution, optimal allocations are characterized as a resulting tradeoff between the distribution four moments. The specification highlights the preference for odd moments and the aversion for even moments. Qualitatively, optimal portfolios are analyzed in terms of firm characteristics and in a setting that reflects real-time asset allocation, a systematic over-performance is obtained compared to the aggregate stock market. Finally, in my third article, dynamic option-based investment strategies are derived and illustrated for investors presenting downside loss aversion. The problem is solved in closed form when the stock market exhibits stochastic volatility and jumps. The specification of downside loss averse utility functions allows corresponding terminal wealth profiles to be expressed as options on the stochastic discount factor contingent on the loss aversion level. Therefore dynamic strategies reduce to the replicating portfolio using exchange traded and well selected options, and the risky stock.

Optimal feedback control rules sensitive to controlled endogenous risk-aversion

The objective of this paper is to correct and improve the results obtained by Van der Ploeg (1984a, 1984b) and utilized in the theoretical literature related to feedback stochastic optimal control sensitive to constant exogenous risk-aversion (see, Jacobson, 1973, Karp, 1987 and Whittle, 1981, 1989, 1990, among others) or to the classic context of risk-neutral decision-makers (see, Chow, 1973, 1976a, 1976b, 1977, 1978, 1981, 1993). More realistic and attractive, this new approach is placed in the context of a time-varying endogenous risk-aversion which is under the control of the decision-maker. It has strong qualitative implications on the agent's optimal policy during the entire planning horizon.

Optimal Monetary Policy in a New Keynesian Model with Habits in Consumption

While consumption habits have been utilised as a means of generating a humpshaped output response to monetary policy shocks in sticky-price New Keynesian economies, there is relatively little analysis of the impact of habits (particularly,external habits) on optimal policy. In this paper we consider the implications of external habits for optimal monetary policy, when those habits either exist at the level of the aggregate basket of consumption goods (‘superficial’ habits) or at the level of individual goods (‘deep’ habits: see Ravn, Schmitt-Grohe, and Uribe (2006)). External habits generate an additional distortion in the economy, which implies that the flex-price equilibrium will no longer be efficient and that policy faces interesting new trade-offs and potential stabilisation biases. Furthermore, the endogenous mark-up behaviour, which emerges when habits are deep, can also significantly affect the optimal policy response to shocks, as well as dramatically affecting the stabilising properties of standard simple rules.

Optimal Martingales and American Option Pricing

Pricing American options is an interesting research topic since there is no analytical solution to value these derivatives. Different numerical methods have been proposed in the literature with some, if not all, either limited to a specific payoff or not applicable to multidimensional cases. Applications of Monte Carlo methods to price American options is a relatively new area that started with Longstaff and Schwartz (2001). Since then, few variations of that methodology have been proposed. The general conclusion is that Monte Carlo estimators tend to underestimate the true option price. The present paper follows Glasserman and Yu (2004b) and proposes a novel Monte Carlo approach, based on designing "optimal martingales" to determine stopping times. We show that our martingale approach can also be used to compute the dual as described in Rogers (2002).

Optimal Climate Change Policies When Governments Cannot Commit

This paper examines the optimal design of climate change policies in the context where governments want to encourage the private sector to undertake significant immediate investment in developing cleaner technologies, but the carbon taxes and other environmental policies that could in principle stimulate such investment will be imposed over a very long future. The conventional claim by environmental economists is that environmental policies alone are sufficient to induce firms to undertake optimal investment. However this argument requires governments to be able to commit to these future taxes, and it is far from clear that governments have this degree of commitment. We assume instead that governments cannot commit, and so both they and the private sector have to contemplate the possibility of there being governments in power in the future that give different (relative) weights to the environment. We show that this lack of commitment has a significant asymmetric effect. Compared to the situation where governments can commit it increases the incentive of the current government to have the investment undertaken, but reduces the incentive of the private sector to invest. Consequently governments may need to use additional policy instruments – such as R&D subsidies – to stimulate the required investment.

Endogenous Price Flexibility and Optimal Monetary Policy

Much of the literature on optimal monetary policy uses models in which the degree of nominal price flexibility is exogenous. There are, however, good reasons to suppose that the degree of price flexibility adjusts endogenously to changes in monetary conditions. This paper extends the standard New Keynesian model to incorporate an endogenous degree of price flexibility. The model shows that endogenising the degree of price flexibility tends to shift optimal monetary policy towards complete inflation stabilisation, even when shocks take the form of cost-push disturbances. This contrasts with the standard result obtained in models with exogenous price flexibility, which show that optimal monetary policy should allow some degree of inflation volatility in order to stabilise the welfarerelevant output gap.

Optimal contracting with private information on cost expectation and variability

We study the screening problem that arises in a framework where, initially, the agent is privately informed about both the expected production cost and the cost variability and, at a later stage, he learns privately the cost realization. The speci c set of relevant incentive constraints, and so the characteristics of the optimal mechanism, depend nely upon the curvature of the principal s marginal surplus function as well as the relative importance of the two initial information problems. Pooling of production levels is optimally induced with respect to the cost variability when the principal's knowledge imperfection about the latter is sufficiently less important than that about the expected cost.

The Timing of Asset Trade and Optimal Policy in Dynamic Open Economies

Using a standard open economy DSGE model, it is shown that the timing of asset trade relative to policy decisions has a potentially important impact on the welfare evaluation of monetary policy at the individual country level. If asset trade in the initial period takes place before the announcement of policy, a national policymaker can choose a policy rule which reduces the work effort of households in the policymaker’s country in the knowledge that consumption is fully insured by optimally chosen international portfolio positions. But if asset trade takes place after the policy announcement, this insurance is absent and households in the policymaker’s country bear the full consumption consequences of the chosen policy rule. The welfare incentives faced by national policymakers are very different between the two cases. Numerical examples confirm that asset market timing has a significant impact on the optimal policy rule.

Subsidies as Optimal Fiscal Stimuli

In the theoretical macroeconomics literature, fiscal policy is almost uniformly taken to mean taxing and spending by a ‘benevolent government’ that exploits the potential aggregate demand externalities inherent in the imperfectly competitive nature of goods markets. Whilst shown to raise aggregate output and employment, these policies crowd-out private consumption and hence typically reduce welfare. In this paper we consider the use of ‘tax-and-subsidise’ instead of ‘taxand- spend’ policies on account of their widespread use by governments, even in the recent recession, to stimulate economic activity. Within a static general equilibrium macro-model with imperfectly competitive good markets we examine the effect of wage and output subsidies and show that, for a small open economy, positive tax and subsidy rates exist which maximise welfare, rendering no intervention as a suboptimal state. We also show that, within a two-country setting, a Nash non-cooperative symmetric equilibrium with positive tax and subsidy rates exists, and that cooperation between trading partners in setting these rates is more expansionary and leads to an improvement upon the non-cooperative solution.

First-and second-best allocations under economic and environmental uncertainty

This paper uses a micro-founded DSGE model to compare second-best optimal environmental policy and the resulting allocation to first-best allocation. The focus is on the source and size of uncertainty, and how this affects optimal choices and the inferiority of second best vis-à-vis first best.

Realised and Optimal Monetary Policy Rules in an Estimated Markov-Switching DSGE Model of the United Kingdom

This paper investigates underlying changes in the UK economy over the past thirtyfive years using a small open economy DSGE model. Using Bayesian analysis, we find UK monetary policy, nominal price rigidity and exogenous shocks, are all subject to regime shifting. A model incorporating these changes is used to estimate the realised monetary policy and derive the optimal monetary policy for the UK. This allows us to assess the effectiveness of the realised policy in terms of stabilising economic fluctuations, and, in turn, provide an indication of whether there is room for monetary authorities to further improve their policies.