Bayesian model averaging and identification of structural breaks in time series

Bayesian Model Averaging (BMA) is used for testing for multiple break points in univariate series using conjugate normal-gamma priors. This approach can test for the number of structural breaks and produce posterior probabilities for a break at each point in time. Results are averaged over specifications including: stationary; stationary around trend and unit root models, each containing different types and number of breaks and different lag lengths. The procedures are used to test for structural breaks on 14 annual macroeconomic series and 11 natural resource price series. The results indicate that there are structural breaks in all of the natural resource series and most of the macroeconomic series. Many of the series had multiple breaks. Our findings regarding the existence of unit roots, having allowed for structural breaks in the data, are largely consistent with previous work.     

Testing For and Dating Common Breaks in Multivariate Time Series

This paper develops methods for constructing asymptotically valid confidence intervals for the date of a single break in multivariate time series, including I(0) , I(1) , and deterministically trending regressors. Although the width of the asymptotic confidence interval does not decrease as the sample size increases, it is inversely related to the number of series which have a common break date, so there are substantial gains to multivariate inference about break dates. These methods are applied to two empirical examples: the mean growth rate of output in three European countries, and the mean growth rate of U.S. consumption, investment, and output.     

Detecting break in oil price series using the Box-Tiao method

This paper presents an Autoregressive Integrated Moving Average procedure which allows one to test a time series for a structural break at an unknown point in time. It is a variation of the Box-Tiao method designed to test for a structural break due to an intervention at a known time. Applying the procedure to the crude oil market, we were able to statistically show the existence of a structural break in the oil price series and to pinpoint the month during which it took place, January 1986. The results also underscore the need for testing the stability of models estimated using oil price data covering both sides of the structural break and may assist those who study the political events of the period.     

Testing fiscal sustainability in Poland: a Bayesian analysis of cointegration

Fiscal sustainability is a central topic for most of the transition economies of Eastern Europe. This paper focuses on a particular country: Poland. The main purpose is to investigate, empirically, whether the post-transition fiscal policy is consistent with the intertemporal budget constraint, used as a formal theoretical framework. To test debt stabilization, the empirical analysis is made in two steps: first, we use a Bayesian methodology to conduct inference about the cointegrating relationship between budget revenues and (inclusive of interest) expenditures and to select the cointegrating rank. Second, we apply Bayesian inference to the estimation of the cointegrating vector and of the adjustment parameters. With a single cointegrating relation, we make use of some known results concerning the posterior density of the cointegrating vector, which belongs to the poly-t densities class. In this way, we experiment the usefulness of Bayesian inference in precisely assessing the magnitude of the cointegrating vector. Moreover, we show to what extent the likelihood of the data is important in revising the available prior information, relying on numerical integration techniques.     

Mechanisms,Bayesianism, and process tracing

ABSTRACT

This essay examines the role of mechanisms and Bayesian inference in process tracing. With respect to mechanisms, I argue that the core of process tracing with causal inference is the identification of mechanisms understood as intervening events. Events are different from standard intervening variables when used with process tracing, because events are treated as sets in which cases can have membership. With respect to Bayesian analysis, I concur with recent writings that suggest Bayesian inference is at the heart of process tracing. The Bayesian nature of process tracing explains why it is inappropriate to view qualitative research as suffering from a small-N problem and certain standard causal identification problems. More generally, the paper shows how the power of process tracing as a qualitative methodology depends on and grows from its set-theoretic underpinnings.     

Innis Lecture: Inference on income distributions

Abstract This paper attempts to provide a synthetic view of varied techniques available for performing inference on income distributions. Two main approaches can be distinguished: one in which the object of interest is some index of income inequality or poverty, the other based on notions of stochastic dominance. From the statistical point of view, many techniques are common to both approaches, although of course some are specific to one of them. I assume throughout that inference about population quantities is to be based on a sample or samples, and, formally, all randomness is due to that of the sampling process. Inference can be either asymptotic or bootstrap based. In principle, the bootstrap is an ideal tool, since in this paper I ignore issues of complex sampling schemes and suppose that observations are IID. However, both bootstrap inference and, to a considerably greater extent, asymptotic inference can fall foul of difficulties associated with the heavy right‐hand tails observed with many income distributions. I mention some recent attempts to circumvent these difficulties.     

Time series approaches to Italian regional convergence

This article investigates the evolution of the gap between Italian regions and Italy as a whole during the period of 1980 to 2007. We tested for the presence of the stochastic and β-convergence hypotheses using different time series approaches. The former was studied, first, for the entire sample period and then, with an exogenous instantaneous break in the series. The presence of β-convergence, instead, was estimated considering a known and an unknown trend break date model. Our results show that most of the regions do not converge in an ‘actual’ way, since they do not present a stochastic and β-convergence simultaneously.     

Expectation formation and regime switches

Economic agents often have to make decisions in environments affected by regime switches but expectation formation has hardly been explored in this context. We report about a laboratory experiment whose participants judgmentally forecast three time series subject to regime switches. The participants make forecasts without context knowledge and without support from statistical software. Their forecasts are only based on the previous realizations of the time series. Our interest is the explanation of the average forecasts with a simple model, the bounds & likelihood heuristic. In previous studies it was shown that this model can explain average forecasting behavior very well given stable and stationary time series. We find that the forecasts after a structural break are characterized by a higher variance and less accuracy over several periods. Considering this transition phase in the model, the heuristic performs even slightly better than the Rational Expectations Hypothesis.     

Reallocation and learning over the business cycle

This paper shows how cyclical aggregate shocks can stimulate structural reallocation activities, which in turn amplify the effect of the shock. It analyses the informational aspects of restructuring activities and their interplay with aggregate shocks. A model is developed in which production units are uncertain about the value of staying in the market and learn about it over time in a Bayesian fashion. In addition to their own private assessment, they can also learn from observing other units’ decisions. Given that adjusting is costly, each unit has an incentive to delay action and wait for other players to act in order to make a better informed decision. If delay is more costly in a downturn, a negative aggregate shock can break the inertia and induce the most pessimistic agents to exit. The information released by such actions will induce more action, thus generating a burst in restructuring activities that reinforces the initial effect of the aggregate shock. This process of information accumulation and revelation offers both a powerful amplification mechanism of relatively modest aggregate shocks and a potential explanation of why restructuring tends to be concentrated in recessions.     

Postwar slowdowns and long-run growth: a Bayesian analysis of structural break models

Using Bayesian methods, we re-examine the empirical evidence from Ben-David, Lumsdaine, and Papell (Empir Econ 28:303–319, 2003) regarding structural breaks in the long-run growth path of real output series for a number of OECD countries. Our Bayesian framework allows the number and pattern of structural changes in trend and variance to be endogenously determined. We find little evidence of postwar growth slowdowns across countries, and smaller output volatility for most of the developed countries after the end of World War II. Our empirical findings are consistent with neoclassical growth models, which predict increasing growth over the long run. The majority of the countries we analyze have grown faster in the postwar era as opposed to the period before the first break.     

Bayesian analysis of periodic unit roots in the presence of a break

A Bayesian testing approach for a periodic unit root in quarterly and monthly data is presented. Further a Bayesian test is introduced to test for unit roots at (non)seasonal spectral frequencies. All procedures admit one structural break in the periodic trend function, where the occurrence of a break and the associated timing are treated as additional model parameters. A Bayesian model averaging (BMA) approach is proposed and power functions of the tests are computed. Overall the results indicate that the BMA periodic unit root test exhibits favourable test properties even in small samples. In an empirical application the presented testing procedures are used to test for (non)seasonal forms of unemployment persistence among OECD countries.     

Public support for reducing US reliance on fossil fuels: Investigating household willingness-to-pay for energy research and development

In order to reduce future dependence on foreign oil and emissions of CO₂, how much would US households be willing to pay annually to support increased energy research and development (R&D) activities designed to replace fossil fuels? Does it matter whether the R&D includes nuclear energy options? We explore these questions using data from a unique set of national telephone and Internet surveys. Using a national advisory referendum format, the contingent valuation method is applied to estimate annual household willingness-to-pay (WTP) for US household support of a national Energy Research and Development Fund (ERDF) for investments in energy sources not reliant on fossil fuels. While accounting for the level of (un)certainty in voting responses, the WTP modeling includes a comparison of both classic maximum likelihood estimation (MLE) and Bayesian analysis. Evidence indicates that MLE and Bayesian analysis achieve similar statistical inference, while the Bayesian analysis provides a narrower confidence interval around estimated WTP.     

PRIOR ELICITATION IN MULTIPLE CHANGE‐POINT MODELS*

This article discusses Bayesian inference in change‐point models. The main existing approaches treat all change‐points equally, a priori, using either a Uniform prior or an informative hierarchical prior. Both approaches assume a known number of change‐points. Some undesirable properties of these approaches are discussed. We develop a new Uniform prior that allows some of the change‐points to occur out of sample. This prior has desirable properties, can be interpreted as “noninformative,” and treats the number of change‐points as unknown. Artificial and real data exercises show how these different priors can have a substantial impact on estimation and prediction.     

Does corruption impede economic growth in Pakistan?

The present study reinvestigates the impact of corruption on economic growth by incorporating financial development and trade openness in growth model in case of Pakistan. We have used time series data over the period of 1987–2009. We have applied structural break unit root test to test the integrating order of the variables. The structural break cointegration has also been applied to examine the long run relationship between the variables.The long run relationship between the variables is validated in case of Pakistan. We find that corruption impedes economic growth. Financial development adds in economic growth. Trade openness stimulates economic growth. The causality analysis has exposed the feedback effect between corruption and economic growth and same inference is drawn for trade openness and corruption. Trade openness and economic growth are interdependent. Financial development Granger causes economic growth implying supply-side hypothesis in case of Pakistan.     

Analysing shock transmission in a data-rich environment: a large BVAR for New Zealand

We analyse a large Bayesian Vector Autoregression (BVAR) containing almost 100 New Zealand macroeconomic time series. Methods for allowing multiple blocks of equations with block-specific Bayesian priors are described, and forecasting results show that our model compares favourably to a range of other time series models. Examining the impulse responses to a monetary policy shock and to two less conventional shocks—net migration and the climate—we highlight the usefulness of the large BVAR in analysing shock transmission.     

Valid Inference in Partially Unstable Generalized Method of Moments Models

This paper considers time series Generalized Method of Moments (GMM) models where a subset of the parameters are time varying. We focus on an empirically relevant case with moderately large instabilities, which are well approximated by a local asymptotic embedding that does not allow the instability to be detected with certainty, even in the limit. We show that for many forms of the instability and a large class of GMM models, usual GMM inference on the subset of stable parameters is asymptotically unaffected by the partial instability. In the empirical analysis of presumably stable parameters—such as structural parameters in Euler conditions—one can thus ignore moderate instabilities in other parts of the model and still obtain approximately correct inference.     

Testing for negativity in a demand system: A Bayesian approach

The paper introduces Bayesian inference into a demand model. This allows us to test for the negativity condition of the substitution matrix which is difficult to handle directly in the traditional approach. To illustrate the Bayesian inference procedures, we estimate the Rotterdam model and test the demand properties using Japanese data. The empirical results show the importance of specifically considering negativity in demand analysis. First version received: September 1997/final version received: February 1998     

Robust Bayesian analysis of a parameter change in linear regression

Robust Bayesian analyses in a conjugate normal framework have been developed by Learner (1978) and Polasek and Pötzelberger (1987). Fixing the prior mean and varying the prior covariance Matrix yields a so-called feasible ellipsoid for the posterior mean and robust HPD regions, also called HiFi-regions. This paper considers the application of this approach to gain robust Bayesian inference in case of a parameter change in regression models.     

Forecasting the US real house price index: Structural and non-structural models with and without fundamentals

We employ a 10-variable dynamic structural general equilibrium model to forecast the US real house price index as well as its downturn in 2006:Q2. We also examine various Bayesian and classical time-series models in our forecasting exercise to compare to the dynamic stochastic general equilibrium model, estimated using Bayesian methods. In addition to standard vector-autoregressive and Bayesian vector autoregressive models, we also include the information content of either 10 or 120 quarterly series in some models to capture the influence of fundamentals. We consider two approaches for including information from large data sets — extracting common factors (principle components) in factor-augmented vector autoregressive or Bayesian factor-augmented vector autoregressive models as well as Bayesian shrinkage in a large-scale Bayesian vector autoregressive model. We compare the out-of-sample forecast performance of the alternative models, using the average root mean squared error for the forecasts. We find that the small-scale Bayesian-shrinkage model (10 variables) outperforms the other models, including the large-scale Bayesian-shrinkage model (120 variables). In addition, when we use simple average forecast combinations, the combination forecast using the 10 best atheoretical models produces the minimum RMSEs compared to each of the individual models, followed closely by the combination forecast using the 10 atheoretical models and the DSGE model. Finally, we use each model to forecast the downturn point in 2006:Q2, using the estimated model through 2005:Q2. Only the dynamic stochastic general equilibrium model actually forecasts a downturn with any accuracy, suggesting that forward-looking microfounded dynamic stochastic general equilibrium models of the housing market may prove crucial in forecasting turning points.     

Has the Feldstein-Horioka puzzle waned? Evidence from time series and dynamic panel data analysis

This objective of this paper is to examine the Feldstein-Harioka puzzle by using both time series analysis that accommodates structural breaks, and dynamic panel error-correction method. Our sample consists of 118 countries over the period 1981–2013. Results from ARDL model suggest that long-run capital is highly mobile in high-income countries (HIC), moderately mobile for both middle- and low-income countries. Our finding of the low long-run saving coefficient for HICs shows that failure to account for a structural break may overstate the long-run saving coefficient. Findings from the pooled mean group estimators suggest that capital is moderately mobile in the middle-income countries, and highly immobile in the high- and low-income countries in the long run. Our findings highlight that ignoring structural break, the type of data (time series/panel), and econometric method used can affect the conclusion about capital mobility. The adjustment coefficient in the time series analysis is comparatively higher than the panel data analysis. We also test whether country size and openness affect the saving–investment correlation. While the effect of country size on the saving coefficient is mixed, the saving estimate is found to be a function of the degree of openness. We also discuss policy implications of our findings on the current account sustainability.