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 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.

Minu, Startu and all that:- Pitfalls in estimating the sensitivity of a worker’s wage to aggregate unemployment

In this paper we show that the inclusion of unemployment-tenure interaction variates in Mincer wage equations is subject to serious pitfalls. These variates were designed to test whether or not the sensitivity to the business cycle of a worker’s wage varies according to her tenure. We show that three canonical variates used in the literature - the minimum unemployment rate during a worker’s time at the firm(min u), the unemployment rate at the start of her tenure(Su) and the current unemployment rate interacted with a new hire dummy(δu) - can all be significant and "correctly" signed even when each worker in the firm receives the same wage, regardless of tenure (equal treatment). In matched data the problem can be resolved by the inclusion in the panel of firm-year interaction dummies. In unmatched data where this is not possible, we propose a solution for min u and Su based on Solon, Barsky and Parker’s(1994) two step method. This method is sub-optimal because it ignores a large amount of cross tenure variation in average wages and is only valid when the scaled covariances of firm wages and firm employment are acyclical. Unfortunately δu cannot be identified in unmatched data because a differential wage response to unemployment of new hires and incumbents will appear under both equal treatment and unequal treatment.

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.

Optimal taxation and the skill premium

The stylized facts suggest a negative relationship between tax progressivity and the skill premium from the early 1960s until the early 1990s, and a positive one thereafter. They also generally imply rising tax progressivity, except for the 1980s. In this paper, we ask whether optimal tax policy is consistent with these observations, taking into account the demographic and technological factors that have also affected the skill premium. To this end, we construct a dynamic general equilibrium model in which the skill premium and the progressivity of the tax system are endogenously determined, with the latter being optimally chosen by a benevolent government. We find that optimal policy delivers both a progressive tax system and model predictions which are generally consistent, except for the 1980s, with the stylized facts relating to the skill premium and progressivity. To capture the patterns in the data over the 1980s requires that we adopt a government policy which is biased towards the interests of skilled agents. Thus, in addition to demographic and technological factors, changes in the preferences of policy-makers appear to be a potentially important factor in determining the evolution of the observed skill premium.

Time is Running Out: The 2°C Target and Optimal Climate Policies

The quintessence of recent natural science studies is that the 2 degrees C target can only be achieved with massive emission reductions in the next few years. The central twist of this paper is the addition of this limited time to act into a non-perpetual real options framework analysing optimal climate policy under uncertainty. The window-of-opportunity modelling setup shows that the limited time to act may spark a trend reversal in the direction of low-carbon alternatives. However, the implementation of a climate policy is evaded by high uncertainty about possible climate pathways.

A balance of questions: what can we ask of climate change economics?

The standard approach to the economics of climate change, which has its best known implementation in Nordhaus's DICE and RICE models (well described in Nordhaus's 2008 book, A Question of Balance) is not well equipped to deal with the possibility of catastrophe, since we are unable to evaluate a risk averse representative agent's expected utility when there is any signi cant probability of zero consumption. Whilst other authors attempt to develop new tools with which to address these problems, the simple solution proposed in this paper is to ask a question that the currently available tools of climate change economics are capable of answering. Rather than having agents optimally choosing a path (that differs from the recommendations of climate scientists) within models which cannot capture the essential features of the problem, I argue that economic models should be used to determine the savings and investment paths which implement climate targets that have been suggested in the physical science literature.

How Optimal is US Monetary Policy?

Most of the literature estimating DSGE models for monetary policy analysis assume that policy follows a simple rule. In this paper we allow policy to be described by various forms of optimal policy - commitment, discretion and quasi-commitment. We find that, even after allowing for Markov switching in shock variances, the inflation target and/or rule parameters, the data preferred description of policy is that the US Fed operates under discretion with a marked increase in conservatism after the 1970s. Parameter estimates are similar to those obtained under simple rules, except that the degree of habits is significantly lower and the prevalence of cost-push shocks greater. Moreover, we find that the greatest welfare gains from the ‘Great Moderation’ arose from the reduction in the variances in shocks hitting the economy, rather than increased inflation aversion. However, much of the high inflation of the 1970s could have been avoided had policy makers been able to commit, even without adopting stronger anti-inflation objectives. More recently the Fed appears to have temporarily relaxed policy following the 1987 stock market crash, and has lost, without regaining, its post-Volcker conservatism following the bursting of the dot-com bubble in 2000.