Optimal investment models with vintage capital: Dynamic programming approach

The dynamic programming approach for a family of optimal investment models with vintage capital is here developed. The problem falls into the class of infinite horizon optimal control problems of PDE’s with age structure that have been studied in various papers (12, 11, 33 and 35) either in cases when explicit solutions can be found or using Maximum Principle techniques.     

Modeling data revisions: Measurement error and dynamics of “true” values

Policy makers must base their decisions on preliminary and partially revised data of varying reliability. Realistic modeling of data revisions is required to guide decision makers in their assessment of current and future conditions. This paper provides a new framework with which to model data revisions.Recent empirical work suggests that measurement errors typically have much more complex dynamics than existing models of data revisions allow. This paper describes a state-space model that allows for richer dynamics in these measurement errors, including the noise, news and spillover effects documented in this literature. We also show how to relax the common assumption that “true” values are observed after a few revisions.The result is a unified and flexible framework that allows for more realistic data revision properties, and allows the use of standard methods for optimal real-time estimation of trends and cycles. We illustrate the application of this framework with real-time data on US real output growth.     

Dynamics of fiscal financing in the United States

General equilibrium models that include policy rules for government spending, lump-sum transfers, and distortionary taxation on labor and capital income and on consumption expenditures are fit to US data under rich specifications of fiscal policy rules to obtain several results. First, the best-fitting model allows many fiscal instruments to respond to debt. Second, responses of aggregates to fiscal policy shocks under rich rules vary considerably from responses where only non-distortionary fiscal instruments finance debt. Third, in the short run, all fiscal instruments except labor taxes react strongly to debt, but long-run intertemporal financing comes from all components of the government’s budget constraint. Fourth, debt-financed fiscal shocks trigger long-lasting dynamics; short-run and long-run multipliers can differ markedly.     

Modelling and Forecasting Fiscal Variables for the Euro Area*

In this paper, we assess the possibility of producing unbiased forecasts for fiscal variables in the Euro area by comparing a set of procedures that rely on different information sets and econometric techniques. In particular, we consider autoregressive moving average models, Vector autoregressions, small‐scale semistructural models at the national and Euro area level, institutional forecasts (Organization for Economic Co‐operation and Development), and pooling. Our small‐scale models are characterized by the joint modelling of fiscal and monetary policy using simple rules, combined with equations for the evolution of all the relevant fundamentals for the Maastricht Treaty and the Stability and Growth Pact. We rank models on the basis of their forecasting performance using the mean square and mean absolute error criteria at different horizons. Overall, simple time‐series methods and pooling work well and are able to deliver unbiased forecasts, or slightly upward‐biased forecast for the debt–GDP dynamics. This result is mostly due to the short sample available, the robustness of simple methods to structural breaks, and to the difficulty of modelling the joint behaviour of several variables in a period of substantial institutional and economic changes. A bootstrap experiment highlights that, even when the data are generated using the estimated small‐scale multi‐country model, simple time‐series models can produce more accurate forecasts, because of their parsimonious specification.     

Ratio-based estimators for a change point in persistence

We study estimation of the date of change in persistence, from I(0)$I\left(0\right)$ to I(1)$I\left(1\right)$ or vice versa. Contrary to statements in the original papers, our analytical results establish that the ratio-based break point estimators of Kim [Kim, J.Y., 2000. Detection of change in persistence of a linear time series. Journal of Econometrics 95, 97–116], Kim et al. [Kim, J.Y., Belaire-Franch, J., Badillo Amador, R., 2002. Corringendum to “Detection of change in persistence of a linear time series”. Journal of Econometrics 109, 389–392] and Busetti and Taylor [Busetti, F., Taylor, A.M.R., 2004. Tests of stationarity against a change in persistence. Journal of Econometrics 123, 33–66] are inconsistent when a mean (or other deterministic component) is estimated for the process. In such cases, the estimators converge to random variables with upper bound given by the true break date when persistence changes from I(0)$I\left(0\right)$ to I(1)$I\left(1\right)$. A Monte Carlo study confirms the large sample downward bias and also finds substantial biases in moderate sized samples, partly due to properties at the end points of the search interval.     

The relationship between the Beveridge–Nelson decomposition and other permanent–transitory decompositions that are popular in economics

The Beveridge–Nelson (BN) decomposition is a model-based method for decomposing time series into permanent and transitory components. When constructed from an ARIMA model, it is closely related to decompositions based on unobserved components (UC) models with random walk trends and covariance stationary cycles. The decomposition when extended to I(2)$I\left(2\right)$ models can also be related to non-model-based signal extraction filters such as the HP filter. We show that the BN decomposition provides information on the correlation between the permanent and transitory shocks in a certain class of UC models. The correlation between components is known to determine the smoothed estimates of components from UC models. The BN decomposition can also be used to evaluate the efficacy of alternative methods. We also demonstrate, contrary to popular belief, that the BN decomposition can produce smooth cycles if the reduced form forecasting model is appropriately specified.     

Theorems on the core of an economy with infinitely many commodities and consumers

It is known that the classical theorems of Grodal [Grodal, B., 1972. A second remark on the core of an atomless economy. Econometrica 40, 581–583] and Schmeidler [Schmeidler, D., 1972. A remark on the core of an atomless economy. Econometrica 40, 579–580] on the veto power of small coalitions in finite dimensional, atomless economies can be extended (with some minor modifications) to include the case of countably many commodities. This paper presents a further extension of these results to include the case of uncountably many commodities. We also extend Vind’s [Vind, K., 1972. A third remark on the core of an atomless economy. Econometrica 40, 585–586] classical theorem on the veto power of big coalitions in finite dimensional, atomless economies to include the case of an arbitrary number of commodities. In another result, we show that in the coalitional economy defined by an atomless individualistic model, core–Walras equivalence holds even if the commodity space is non-separable. The above-mentioned results are also valid for a differential information economy with a finite state space. We also extend Kannai’s [Kannai, Y., 1970. Continuity properties of the core of a market. Econometrica 38, 791–815] theorem on the continuity of the core of a finite dimensional, large economy to include the case of an arbitrary number of commodities. All of our results are applications of a lemma, that we prove here, about the set of aggregate alternatives available to a coalition. Throughout the paper, the commodity space is assumed to be an ordered Banach space which has an interior point in its positive cone.     

Markov-switching and the Beveridge–Nelson decomposition: Has US output persistence changed since 1984?

We show that, for a class of univariate and multivariate Markov-switching models, exact calculation of the Beveridge–Nelson (BN) trend/cycle components is possible. The key to exact BN trend/cycle decomposition is to recognize that the latent first-order Markov-switching process in the model has an AR(1) representation, and that the model can be cast into a state-space form. Given the state-space representation, we show that impulse-response function analysis can be processed with respect to either an asymmetric discrete shock or to a symmetric continuous shock. The method presented is applied to Kim, Morley, Piger’s [Kim, C.-J., Morley, J., Piger, J., 2005. Nonlinearity and the permanent effects of recessions. Journal of Applied Econometrics 20, 291–309] univariate Markov-switching model of real GDP with a post-recession ‘bounce-back’ effect and Cochrane’s [Cochrane, J.H., 1994. Permanent and transitory components of GNP and stock prices. Quarterly Journal of Economics 109, 241–263] vector error correction model of real GDP and real consumption extended to incorporate Markov-switching. The parameter estimates, the BN trend/cycle components, and the impulse-response function analysis for each of these empirical models suggest that the persistence of US real GDP has increased since the mid-1980’s.     

A flexible approach to parametric inference in nonlinear and time varying time series models

Many structural break and regime-switching models have been used with macroeconomic and financial data. In this paper, we develop an extremely flexible modeling approach which can accommodate virtually any of these specifications. We build on earlier work showing the relationship between flexible functional forms and random variation in parameters. Our contribution is based around the use of priors on the time variation that is developed from considering a hypothetical reordering of the data and distance between neighboring (reordered) observations. The range of priors produced in this way can accommodate a wide variety of nonlinear time series models, including those with regime-switching and structural breaks. By allowing the amount of random variation in parameters to depend on the distance between (reordered) observations, the parameters can evolve in a wide variety of ways, allowing for everything from models exhibiting abrupt change (e.g. threshold autoregressive models or standard structural break models) to those which allow for a gradual evolution of parameters (e.g. smooth transition autoregressive models or time varying parameter models). Bayesian econometric methods for inference are developed for estimating the distance function and types of hypothetical reordering. Conditional on a hypothetical reordering and distance function, a simple reordering of the actual data allows us to estimate our models with standard state space methods by a simple adjustment to the measurement equation. We use artificial data to show the advantages of our approach, before providing two empirical illustrations involving the modeling of real GDP growth.