Adaptive Continuous time Markov Chain Approximation Model to General Jump-Diusions

We propose a non-equidistant Q rate matrix formula and an adaptive numerical algorithm for a continuous time Markov chain to approximate jump-diffusions with affine or non-affine functional specifications. Our approach also accommodates state-dependent jump intensity and jump distribution, a flexibility that is very hard to achieve with other numerical methods. The Kolmogorov-Smirnov test shows that the proposed Markov chain transition density converges to the one given by the likelihood expansion formula as in Ait-Sahalia (2008). We provide numerical examples for European stock option pricing in Black and Scholes (1973), Merton (1976) and Kou (2002).

A Simple Characterization of Dynamic Completeness in Continuous Time

This paper investigates dynamic completeness of financial markets in which the underlying risk process is a multi-dimensional Brownian motion and the risky securities dividends geometric Brownian motions. A sufficient condition, that the instantaneous dispersion matrix of the relative dividends is non-degenerate, was established recently in the literature for single-commodity, pure-exchange economies with many heterogenous agents, under the assumption that the intermediate flows of all dividends, utilities, and endowments are analytic functions. For the current setting, a different mathematical argument in which analyticity is not needed shows that a slightly weaker condition suffices for general pricing kernels. That is, dynamic completeness obtains irrespectively of preferences, endowments, and other structural elements (such as whether or not the budget constraints include only pure exchange, whether or not the time horizon is finite with lump-sum dividends available on the terminal date, etc.)

Bayesian Inference in the Time Varying Cointegration Model

There are both theoretical and empirical reasons for believing that the parameters of macroeconomic models may vary over time. However, work with time-varying parameter models has largely involved Vector autoregressions (VARs), ignoring cointegration. This is despite the fact that cointegration plays an important role in informing macroeconomists on a range of issues. In this paper we develop time varying parameter models which permit cointegration. Time-varying parameter VARs (TVP-VARs) typically use state space representations to model the evolution of parameters. In this paper, we show that it is not sensible to use straightforward extensions of TVP-VARs when allowing for cointegration. Instead we develop a specification which allows for the cointegrating space to evolve over time in a manner comparable to the random walk variation used with TVP-VARs. The properties of our approach are investigated before developing a method of posterior simulation. We use our methods in an empirical investigation involving a permanent/transitory variance decomposition for inflation.

The Distribution Dynamics of Output Multipliers in Scotland 1998–2007

In an input-output context the impact of any particular industrial sector is commonly measured in terms of the output multiplier for that industry. Although such measures are routinely calculated and often used to guide regional industrial policy the behaviour of such measures over time is an area that has attracted little academic study. The output multipliers derived from any one table will have a distribution; for some industries the multiplier will be relatively high, for some it will be relatively low. The recentpublication of consistent input-output tables for the Scottish economy makes it possible to examine trends in this mdistribution over the ten year period 1998-2007. This is done by comparing the means and other summary measures of the distributions, the histograms and the cumulative densities. The results indicate a tendency for the multipliers to increase over the period. A Markov chain modelling approach suggests that this drift is a slow but long term phenomenon which appears not to tend to an equilibrium state. The prime reason for the increase in the output multipliers is traced to a decline in the relative importance of imported (both from the rest of the UK and the rest of the world) intermediate inputs used by Scottish industries. This suggests that models calibrated on the set of tables might have to be interpreted with caution.

Large Bayesian VARMAs

Vector Autoregressive Moving Average (VARMA) models have many theoretical properties which should make them popular among empirical macroeconomists. However, they are rarely used in practice due to over-parameterization concerns, difficulties in ensuring identification and computational challenges. With the growing interest in multivariate time series models of high dimension, these problems with VARMAs become even more acute, accounting for the dominance of VARs in this field. In this paper, we develop a Bayesian approach for inference in VARMAs which surmounts these problems. It jointly ensures identification and parsimony in the context of an efficient Markov chain Monte Carlo (MCMC) algorithm. We use this approach in a macroeconomic application involving up to twelve dependent variables. We find our algorithm to work successfully and provide insights beyond those provided by VARs.

Technology shocks and aggregate fluctuations in an estimated hybrid RBC model

This paper contributes to the on-going empirical debate regarding the role of the RBC model and in particular of technology shocks in explaining aggregate fluctuations. To this end we estimate the model’s posterior density using Markov-Chain Monte-Carlo (MCMC) methods. Within this framework we extend Ireland’s (2001, 2004) hybrid estimation approach to allow for a vector autoregressive moving average (VARMA) process to describe the movements and co-movements of the model’s errors not explained by the basic RBC model. The results of marginal likelihood ratio tests reveal that the more general model of the errors significantly improves the model’s fit relative to the VAR and AR alternatives. Moreover, despite setting the RBC model a more difficult task under the VARMA specification, our analysis, based on forecast error and spectral decompositions, suggests that the RBC model is still capable of explaining a significant fraction of the observed variation in macroeconomic aggregates in the post-war U.S. economy.

Stochastic Search Variable Selection in Vector Error Correction Models with an Application to a Model of the UK Macroeconomy

This paper develops methods for Stochastic Search Variable Selection (currently popular with regression and Vector Autoregressive models) for Vector Error Correction models where there are many possible restrictions on the cointegration space. We show how this allows the researcher to begin with a single unrestricted model and either do model selection or model averaging in an automatic and computationally efficient manner. We apply our methods to a large UK macroeconomic model.

Global Warming And Extreme Events: Rethinking The Timing And Intensity Of Environmental Policy

The possibility of low-probability extreme events has reignited the debate over the optimal intensity and timing of climate policy. In this paper we therefore contribute to the literature by assessing the implications of low-probability extreme events on environmental policy in a continuous-time real options model with “tail risk”. In a nutshell, our results indicate the importance of tail risk and call for foresighted pre-emptive climate policies.

Bayesian Model Averaging in the Instrumental Variable Regression Model

This paper considers the instrumental variable regression model when there is uncertainty about the set of instruments, exogeneity restrictions, the validity of identifying restrictions and the set of exogenous regressors. This uncertainty can result in a huge number of models. To avoid statistical problems associated with standard model selection procedures, we develop a reversible jump Markov chain Monte Carlo algorithm that allows us to do Bayesian model averaging. The algorithm is very exible and can be easily adapted to analyze any of the di¤erent priors that have been proposed in the Bayesian instrumental variables literature. We show how to calculate the probability of any relevant restriction (e.g. the posterior probability that over-identifying restrictions hold) and discuss diagnostic checking using the posterior distribution of discrepancy vectors. We illustrate our methods in a returns-to-schooling application.

Dark Clouds or Silver Linings? Knightian Uncertainty and Climate Change

This paper examines the impact of Knightian uncertainty upon optimal climate policy through the prism of a continuous-time real option modelling framework. We analytically determine optimal intertemporal climate policies under ambiguous assessments of climate damages. Additionally, numerical simulations are provided to illustrate the properties of the model. The results indicate that increasing Knightian uncertainty accelerates climate policy, i.e. policy makers become more reluctant to postpone the timing of climate policies into the future.

Global Warming and Fat Tailed-uncertainty: Rethinking the Timing and Intensity of Climate Policy

The possibility of low-probability extreme natural events has reignited the debate over the optimal intensity and timing of climate policy. In this paper, we contribute to the literature by assessing the implications of low-probability extreme events on environmental policy in a continuous-time real options model with “tail risk”. In a nutshell, our results indicate the importance of tail risk and call for foresighted pre-emptive climate policies.