Structural vector autoregressions with Markov switching: Combining conventional with statistical identification of shocks

In structural vector autoregressive (SVAR) analysis a Markov regime switching (MS) property can be exploited to identify shocks if the reduced form error covariance matrix varies across regimes. Unfortunately, these shocks may not have a meaningful structural economic interpretation. It is discussed how statistical and conventional identifying information can be combined. The discussion is based on a VAR model for the US containing oil prices, output, consumer prices and a short-term interest rate. The system has been used for studying the causes of the early millennium economic slowdown based on traditional identification with zero and long-run restrictions and using sign restrictions. We find that previously drawn conclusions are questionable in our framework.     

On the relationship between the current account and the fiscal balance: The case of Canada

This paper uses an Autoregressive Distributed Lag model to examine the long run and short run relationship between the current account and the fiscal balance, as well as other determinants, using Canadian quarterly data from 1981 to 2018. The results indicate that there is a long-run cointegrating relationship between the current account and the fiscal balance, investment, and private credit. Moreover, the relationship between the current account and the fiscal balance is positive in the long-run, thus providing support for the Keynesian Hypothesis of the fiscal balance driving the current account. Specifically, a one percentage point rise in the fiscal balance to GDP ratio yields a 0.43 percentage point rise in the current account as a percent of GDP. This positive relationship is present in the short-run as well. Finally, the findings from the error correction model yield a speed of adjustment of 0.225, hence 22.5% of the long-run adjustment in the current account occurs next period.     

Inference on impulse response functions in structural VAR models

Skepticism toward traditional identifying assumptions based on exclusion restrictions has led to a surge in the use of structural VAR models in which structural shocks are identified by restricting the sign of the responses of selected macroeconomic aggregates to these shocks. Researchers commonly report the vector of pointwise posterior medians of the impulse responses as a measure of central tendency of the estimated response functions, along with pointwise 68% posterior error bands. It can be shown that this approach cannot be used to characterize the central tendency of the structural impulse response functions. We propose an alternative method of summarizing the evidence from sign-identified VAR models designed to enhance their practical usefulness. Our objective is to characterize the most likely admissible model(s) within the set of structural VAR models that satisfy the sign restrictions. We show how the set of most likely structural response functions can be computed from the posterior mode of the joint distribution of admissible models both in the fully identified and in the partially identified case, and we propose a highest-posterior density credible set that characterizes the joint uncertainty about this set. Our approach can also be used to resolve the long-standing problem of how to conduct joint inference on sets of structural impulse response functions in exactly identified VAR models. We illustrate the differences between our approach and the traditional approach for the analysis of the effects of monetary policy shocks and of the effects of oil demand and oil supply shocks.     

Long-run Causality, with an Application to International Links Between Long-term Interest Rates

In this paper we give a precise definition of long-run causality in a multivariate non-stationary, possibly cointegrated, framework. A variable is said to be causal for another in the long-run if knowledge of the past of the former improves long-run predictions of the latter. In a VAR framework, we show that long-run non-causality can be easily tested with a Wald statistics, conditionally on the cointegration rank. The methodology is used to study long-run causal links between US, German, and French long-term interest rates from January 1990 to June 1997.     

The expectations hypothesis and decoupling of short- and long-term US interest rates: A pairwise approach

The link between short-term policy rates and long-term rates elucidate the potential effectiveness of monetary policy. We examine the US term structure of interest rates using a pairwise econometric approach advocated by Pesaran (2007). Our empirical modelling strategy employs a probabilistic test statistic for the expectations hypothesis of the term structure based on the percentage of unit root rejections among all interest rate differentials. We find support for the expectations hypothesis and provide new insights into the nature of interest rate decoupling which are of value to policymakers. The maturity gap associated with interest rate pairs negatively impacts on the probability of stationarity, and also on the speed of adjustment towards long-run equilibrium. We further show that the speed of adjustment has become more sensitive to the maturity gap over time.     

Bayesian stochastic search for VAR model restrictions

We propose a Bayesian stochastic search approach to selecting restrictions for vector autoregressive (VAR) models. For this purpose, we develop a Markov chain Monte Carlo (MCMC) algorithm that visits high posterior probability restrictions on the elements of both the VAR regression coefficients and the error variance matrix. Numerical simulations show that stochastic search based on this algorithm can be effective at both selecting a satisfactory model and improving forecasting performance. To illustrate the potential of our approach, we apply our stochastic search to VAR modeling of inflation transmission from producer price index (PPI) components to the consumer price index (CPI).     

Quantifying Structural Change in U.S. Agriculture: The Case of Research and Productivity

Previous work on structural change in agriculture has failed to distinguish long-run trends from structural breaks leading to new trends. We measure structural changes as statistically significant breaks in either stochastic or deterministic time trends, and apply these measures to agricultural productivity and research. Productivity has a break in 1925 accompanying agriculture's early experience with the Great Depression. Research trends shifted in 1930 as the Depression and new technology began to strongly influence efficient farm size and capitalization. After modeling lags between research and productivity impacts in a vector autoregression (VAR), we compare our results to earlier work by developing a procedure to estimate the rate of return to research from the impulse response function of the VAR.     

Common trends and cycles in I(2) VAR systems

This paper analyzes common cycles in I(2) vector autoregressive (VAR) systems. We consider different choices of stationary variables extracted from a VAR, including deviations from equilibria. This extension is based on the equilibrium dynamics representation of the system, introduced in this paper. Inference on the number of common features is addressed via reduced rank regression, as well as estimation of the cofeature relations and testing. An application to Australian prices is presented; it is found that the deviation from one equilibrium relation is an innovation process, whereas no common cycles can be obtained for the acceleration rates.     

Cointegration and joint efficiency of international commodity markets

This paper investigates the semi-strong efficiency hypothesis in the international commodity markets of four industrialized countries, using vector autoregression (VAR) and cointegration techniques. Efficiency in these markets requires the corresponding real exchange rates to be martingales with respect to any information set available in the public domain. In the context of a VAR consisting only of real exchange rates, we show that necessary and sufficient conditions for joint efficiency of all the markets under consideration amount to the VAR being of order one (Markovness) and non-cointegrated. On the contrary, in a VAR extended by other potentially “relevant” variables, such as the corresponding real interest rates, non-cointegration and Markovness are only sufficient conditions for the same commodity markets to be characterized as jointly efficient. We also suggest methods for efficiency testing in each individual market within a cointegrated VAR and, finally, we discuss possible long-run linkages among the real exchange rates and real interest rates in association with efficiency in the commodity markets. JEL Classification Number: F31     

Impact factors

In this paper we discuss sensitivity of forecasts with respect to the information set considered in prediction; a sensitivity measure called impact factor, IF, is defined. This notion is specialized to the case of VAR processes integrated of order 0, 1 and 2. For stationary VARs this measure corresponds to the sum of the impulse response coefficients. For integrated VAR systems, the IF has a direct interpretation in terms of long-run forecasts. Various applications of this concept are reviewed; they include questions of policy effectiveness and of forecast uncertainty due to data revisions. A unified approach to inference on the IF is given, showing under what circumstances standard asymptotic inference can be conducted also in systems integrated of order 1 and 2. It is shown how the results reported here can be used to calculate similar sensitivity measures for models with a simultaneity structure.     

A theory of robust long-run variance estimation

Long-run variance estimation can typically be viewed as the problem of estimating the scale of a limiting continuous time Gaussian process on the unit interval. A natural benchmark model is given by a sample that consists of equally spaced observations of this limiting process. The paper analyzes the asymptotic robustness of long-run variance estimators to contaminations of this benchmark model. It is shown that any equivariant long-run variance estimator that is consistent in the benchmark model is highly fragile: there always exists a sequence of contaminated models with the same limiting behavior as the benchmark model for which the estimator converges in probability to an arbitrary positive value. A class of robust inconsistent long-run variance estimators is derived that optimally trades off asymptotic variance in the benchmark model against the largest asymptotic bias in a specific set of contaminated models.     

Prioritization of government expenditure on health in India: A fiscal space perspective

Unequal distribution of fiscal resources and lower prioritization of budget towards healthcare are the most important challenges in achieving universal health coverage in India. This study has examined relationships between government health expenditure and fiscal space (i.e. tax revenue, non-tax revenue, fiscal transfer, and borrowings) in twenty-one states of India for the period of 1980–2014. Our panel regression results imply that mobilization of tax revenue has a positive impact, while borrowings have a negative impact on the allocation of government expenditure on healthcare in the long-run. The panel quantile regression results show that states associated with the low and middle level of revenue growth have been mobilizing finance through central government transfer and borrowings in short-run. Further, the panel vector error correction models show that sum of the lagged coefficients of borrowings have a greater impact on health financing process as compared to other sources of fiscal space at short-run, and the speed of adjustment towards long-run equilibrium is relatively slower. The overall analysis concludes that less domestic revenue mobilization and higher dependency of borrowings for healthcare financing may create fiscal stress on state finances in the long-run, and thereby it could possibly reduce the prioritization of spending. Therefore, improvement in revenue growth and proper utilization of fiscal transfer would be appropriate policy implications from this study.     

Short run and long run causality in time series: inference

We propose methods for testing hypothesis of non-causality at various horizons, as defined in Dufour and Renault (Econometrica 66, (1998) 1099–1125). We study in detail the case of VAR models and we propose linear methods based on running vector autoregressions at different horizons. While the hypotheses considered are nonlinear, the proposed methods only require linear regression techniques as well as standard Gaussian asymptotic distributional theory. Bootstrap procedures are also considered. For the case of integrated processes, we propose extended regression methods that avoid nonstandard asymptotics. The methods are applied to a VAR model of the US economy.     

The finite-sample effects of VAR dimensions on OLS bias,OLS variance,and minimum MSE estimators

Vector autoregressions (VARs) are important tools in time series analysis. However, relatively little is known about the finite-sample behaviour of parameter estimators. We address this issue, by investigating ordinary least squares (OLS) estimators given a data generating process that is a purely nonstationary first-order VAR. Specifically, we use Monte Carlo simulation and numerical optimisation to derive response surfaces for OLS bias and variance, in terms of VAR dimensions, given correct specification and several types of over-parameterisation of the model: we include a constant, and a constant and trend, and introduce excess lags. We then examine the correction factors that are required for the least squares estimator to attain the minimum mean squared error (MSE). Our results improve and extend one of the main finite-sample multivariate analytical bias results of Abadir, Hadri and Tzavalis [Abadir, K.M., Hadri, K., Tzavalis, E., 1999. The influence of VAR dimensions on estimator biases. Econometrica 67, 163–181], generalise the univariate variance and MSE findings of Abadir [Abadir, K.M., 1995. Unbiased estimation as a solution to testing for random walks. Economics Letters 47, 263–268] to the multivariate setting, and complement various asymptotic studies.     

Applied cointegration analysis in the mirror of macroeconomic theory

Cointegration analyses of macroeconomic time series are often not based on fully specified theoretical models. We use a theoretical model to scrutinize common procedures in applied cointegration analysis. Monte Carlo experiments show that (1) some tests of the cointegration vectors do not work well on series generated by an equilibrium business cycle model; (2) cointegration restrictions add little to forecasting; (3) structural VAR models based on weak long-run restrictions seem to work well. The main disadvantages of cointegration analysis without strong links to economic theory are that it makes it hard to estimate and interpret the cointegration vectors.     

Temperature shocks and welfare costs

This paper examines the welfare implications of rising temperatures. Using a standard VAR, we empirically show that a temperature shock has a sizable, negative and statistically significant impact on TFP, output, and labor productivity. We rationalize these findings within a production economy featuring long-run temperature risk. In the model, macro-aggregates drop in response to a temperature shock, consistent with the novel evidence in the data. Such adverse effects are long-lasting. Over a 50-year horizon, a one-standard deviation temperature shock lowers both cumulative output and labor productivity growth by 1.4 percentage points. Based on the model, we also show that temperature risk is associated with non-negligible welfare costs which amount to 18.4% of the agent’s lifetime utility and grow exponentially with the size of the impact of temperature on TFP. Finally, we show that faster adaptation to temperature shocks results in lower welfare costs. These welfare benefits become substantially higher in the presence of permanent improvements in the speed of adaptation.     

A component model for dynamic correlations

We propose a model of dynamic correlations with a short- and long-run component specification, by extending the idea of component models for volatility. We call this class of models DCC-MIDAS. The key ingredients are the Engle (2002) DCC model, the Engle and Lee (1999) component GARCH model replacing the original DCC dynamics with a component specification and the Engle et al. (2006) GARCH-MIDAS specification that allows us to extract a long-run correlation component via mixed data sampling. We provide a comprehensive econometric analysis of the new class of models, and provide extensive empirical evidence that supports the model’s specification.     

Methods for computing marginal data densities from the Gibbs output

We introduce two estimators for estimating the Marginal Data Density (MDD) from the Gibbs output. Our methods are based on exploiting the analytical tractability condition, which requires that some parameter blocks can be analytically integrated out from the conditional posterior densities. This condition is satisfied by several widely used time series models. An empirical application to six-variate VAR models shows that the bias of a fully computational estimator is sufficiently large to distort the implied model rankings. One of the estimators is fast enough to make multiple computations of MDDs in densely parameterized models feasible.     

Studying co-movements in large multivariate data prior to multivariate modelling

For non-stationary vector autoregressive models (VAR hereafter, or VAR with moving average, VARMA hereafter), we show that the presence of common cyclical features or cointegration leads to a reduction of the order of the implied univariate autoregressive-integrated-moving average (ARIMA hereafter) models. This finding can explain why we identify parsimonious univariate ARIMA models in applied research although VAR models of typical order and dimension used in macroeconometrics imply non-parsimonious univariate ARIMA representations.     

Spread determinants and the day-of-the-week effect

In this paper, we examine the determinants of the dollar bid–ask spread for each day of the week over the period 1998–2008. Using a panel cointegration approach, we estimate the determinants of the spread in both the short-run and long-run. Our main findings suggest that: (1) there are day-of-the-week effects for certain groups of firms; (2) the panel error correction model also reveals day-of-the-week effects, and the speed of adjustment to equilibrium following a shock is faster on Fridays; and (3) the effects of volume and volatility on the spread are mixed, with only some sectors experiencing the day-of-the-week effect.