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.

Using Effluent Charges in Promoting Investment in Water Pollution Control Technology: A Model of Coordination Failure among Firms

Untreated wastewater being directly discharged into rivers is a very harmful environmental hazard that needs to be tackled urgently in many countries. In order to safeguard the river ecosystem and reduce water pollution, it is important to have an effluent charge policy that promotes the investment of wastewater treatment technology by domestic firms. This paper considers the strategic interaction between the government and the domestic firms regarding the investment in the wastewater treatment technology and the design of optimal e­ffluent charge policy that should be implemented. In this model, the higher is the proportion of non-investing firms, the higher would be the probability of having to incur an e­ffluent charge and the higher would be that charge. On one hand the government needs to impose a sufficiently strict policy to ensure that firms have strong incentive to invest. On the other hand, it cannot be too strict that it drives out firms which cannot afford to invest in such expensive technology. The paper analyses the factors that affect the probability of investment in this technology. It also explains the difficulty of imposing a strict environment policy in countries that have too many small firms which cannot afford to invest unless subsidised.

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).

Model Switching and Model Averaging in Time- Varying Parameter Regression Models

This paper investigates the usefulness of switching Gaussian state space models as a tool for implementing dynamic model selecting (DMS) or averaging (DMA) in time-varying parameter regression models. DMS methods allow for model switching, where a different model can be chosen at each point in time. Thus, they allow for the explanatory variables in the time-varying parameter regression model to change over time. DMA will carry out model averaging in a time-varying manner. We compare our exact approach to DMA/DMS to a popular existing procedure which relies on the use of forgetting factor approximations. In an application, we use DMS to select different predictors in an in ation forecasting application. We also compare different ways of implementing DMA/DMS and investigate whether they lead to similar results.

Contagious Illiquidity I: Contagion through Time

This paper is an investigation into the dynamics of asset markets with adverse selection a la Akerlof (1970). The particular question asked is: can market failure at some later date precipitate market failure at an earlier date? The answer is yes: there can be "contagious illiquidity" from the future back to the present. The mechanism works as follows. If the market is expected to break down in the future, then agents holding assets they know to be lemons (assets with low returns) will be forced to hold them for longer - they cannot quickly resell them. As a result, the effective difference in payoff between a lemon and a good asset is greater. But it is known from the static Akerlof model that the greater the payoff differential between lemons and non-lemons, the more likely is the market to break down. Hence market failure in the future is more likely to lead to market failure today. Conversely, if the market is not anticipated to break down in the future, assets can be readily sold and hence an agent discovering that his or her asset is a lemon can quickly jettison it. In effect, there is little difference in payoff between a lemon and a good asset. The logic of the static Akerlof model then runs the other way: the small payoff differential is unlikely to lead to market breakdown today. The conclusion of the paper is that the nature of today's market - liquid or illiquid - hinges critically on the nature of tomorrow's market, which in turn depends on the next day's, and so on. The tail wags the dog.

IInflation and Globalisation: A Dynamic Factor Model with Stochastic Volatility

National inflation rates reflect domestic and international (regional and global) influences. The relative importance of these components remains a controversial empirical issue. We extend the literature on inflation co-movement by utilising a dynamic factor model with stochastic volatility to account for shifts in the variance of inflation and endogenously determined regional groupings. We find that most of inflation variability is explained by the country specific disturbance term. Nevertheless, the contribution of the global component in explaining industrialised countries’ inflation rates has increased over time.

Learning about Risk and Return: A Simple Model of Bubbles and Crashes

This paper demonstrates that an asset pricing model with least-squares learning can lead to bubbles and crashes as endogenous responses to the fundamentals driving asset prices. When agents are risk-averse they need to make forecasts of the conditional variance of a stock’s return. Recursive updating of both the conditional variance and the expected return implies several mechanisms through which learning impacts stock prices. Extended periods of excess volatility, bubbles and crashes arise with a frequency that depends on the extent to which past data is discounted. A central role is played by changes over time in agents’ estimates of risk.

Fear of model misspecifcation and the robustness premium

Robust decision making implies welfare costs or robustness premia when the approximating model is the true data generating process. To examine the importance of these premia at the aggregate level we employ a simple two-sector dynamic general equilibrium model with human capital and introduce an additional form of precautionary behavior. The latter arises from the robust decision maker s ability to reduce the effects of model misspecification through allocating time and existing human capital to this end. We find that the extent of the robustness premia critically depends on the productivity of time relative to that of human capital. When the relative efficiency of time is low, despite transitory welfare costs, there are gains from following robust policies in the long-run. In contrast, high relative productivity of time implies misallocation costs that remain even in the long-run. Finally, depending on the technology used to reduce model uncertainty, we fi nd that while increasing the fear of model misspecfi cation leads to a net increase in precautionary behavior, investment and output can fall.

Forecasting Inflation Using Dynamic Model Averaging

We forecast quarterly US inflation based on the generalized Phillips curve using econometric methods which incorporate dynamic model averaging. These methods not only allow for coe¢ cients to change over time, but also allow for the entire forecasting model to change over time. We nd that dynamic model averaging leads to substantial forecasting improvements over simple benchmark regressions and more sophisticated approaches such as those using time varying coe¢ cient models. We also provide evidence on which sets of predictors are relevant for forecasting in each period.

Forecasting Inflation Using Dynamic Model Averaging

We forecast quarterly US inflation based on the generalized Phillips curve using econometric methods which incorporate dynamic model averaging. These methods not only allow for coe¢ cients to change over time, but also allow for the entire forecasting model to change over time. We nd that dynamic model averaging leads to substantial forecasting improvements over simple benchmark regressions and more sophisticated approaches such as those using time varying coe¢ cient models. We also provide evidence on which sets of predictors are relevant for forecasting in each period.

Time-consistent fiscal policy under heterogeneity: Conflicting or common interests?

This paper studies the aggregate and distributional implications of Markov-perfect tax-spending policy in a neoclassical growth model with capitalists and workers. Focusing on the long run, our main fi ndings are: (i) it is optimal for a benevolent government, which cares equally about its citizens, to tax capital heavily and to subsidise labour; (ii) a Pareto improving means to reduce ine¢ ciently high capital taxation under discretion is for the government to place greater weight on the welfare of capitalists; (iii) capitalists and workers preferences, regarding the optimal amount of "capitalist bias", are not aligned implying a conflict of interests.

Baysian Model Averaging, Learning and Model Selection

Agents have two forecasting models, one consistent with the unique rational expectations equilibrium, another that assumes a time-varying parameter structure. When agents use Bayesian updating to choose between models in a self-referential system, we find that learning dynamics lead to selection of one of the two models. However, there are parameter regions for which the non-rational forecasting model is selected in the long-run. A key structural parameter governing outcomes measures the degree of expectations feedback in Muth's model of price determination.

A New Model Of Trend Inflation

This paper introduces a new model of trend (or underlying) inflation. In contrast to many earlier approaches, which allow for trend inflation to evolve according to a random walk, ours is a bounded model which ensures that trend inflation is constrained to lie in an interval. The bounds of this interval can either be fixed or estimated from the data. Our model also allows for a time-varying degree of persistence in the transitory component of inflation. The bounds placed on trend inflation mean that standard econometric methods for estimating linear Gaussian state space models cannot be used and we develop a posterior simulation algorithm for estimating the bounded trend inflation model. In an empirical exercise with CPI inflation we find the model to work well, yielding more sensible measures of trend inflation and forecasting better than popular alternatives such as the unobserved components stochastic volatility model.

Large Time-Varying Parameter VARs

In this paper we develop methods for estimation and forecasting in large timevarying parameter vector autoregressive models (TVP-VARs). To overcome computational constraints with likelihood-based estimation of large systems, we rely on Kalman filter estimation with forgetting factors. We also draw on ideas from the dynamic model averaging literature and extend the TVP-VAR so that its dimension can change over time. A final extension lies in the development of a new method for estimating, in a time-varying manner, the parameter(s) of the shrinkage priors commonly-used with large VARs. These extensions are operationalized through the use of forgetting factor methods and are, thus, computationally simple. An empirical application involving forecasting inflation, real output, and interest rates demonstrates the feasibility and usefulness of our approach.

Time Variation in the Dynamics of Worker Flows: Evidence from the US and Canada

VAR methods have been used to model the inter-relationships between inflows and outfl ows into unemployment and vacancies using tools such as impulse response analysis. In order to investigate whether such impulse responses change over the course of the business cycle or or over time, this paper uses TVP-VARs for US and Canadian data. For the US, we find interesting differences between the most recent recession and earlier recessions and expansions. In particular, we find the immediate effect of a negative shock on both in ow and out flow hazards to be larger in 2008 than in earlier times. Furthermore, the effect of this shock takes longer to decay. For Canada, we fi nd less evidence of time-variation in impulse responses.