Econometric Methods for Modelling Systems With a Mixture of i(1) and i(0) Variables

This paper considers structural models with both I(1) and I(0) variables. The structural shocks associated with either set of variables could be permanent or transitory. We classify the shocks as (P1,P0) and (T1,T0), where P/T distinguishes permanent/transitory, while 1/0 means they are attached to structural equations with either I(1) or I(0) variables as their ‘dependent’ variable. We show that P0 shocks can affect cointegration analysis and provide a formula to compute the permanent component if they are present. Finally, we reformulate a well‐known empirical structural vector autoregression showing the impact of P0 shocks when there are just long‐run parametric and sign restrictions. Copyright © 2015 John Wiley & Sons, Ltd.     

Stochastic trends and economic fluctuations in a small open economy

In this paper we describe how restricted vector autoregressions can be employed to examine the sources of macroeconomic fluctuations. We show how cointegration restrictions can be used to identify a VAR system with common stochastic trends subject to transitory and permanent changes in average growth, and how we may investigate the system's responses to permanent shocks, i.e. to innovations to the trends. Theoretical cointegration vectors are derived from a small open economy growth model for terms of trade, real GDP, real consumption, and real investments. Applying these methods to Swedish annual data (1875–1986) we find that permanent real (supply) shocks account for most of the fluctuations in GDP, even in the short run.     

Econometric analysis of structural systems with permanent and transitory shocks

This paper considers the implications of the permanent/transitory decomposition of shocks for identification of structural models in the general case where the model might contain more than one permanent structural shock. It provides a simple and intuitive generalization of the influential work of Blanchard and Quah [1989. The dynamic effects of aggregate demand and supply disturbances. The American Economic Review 79, 655–673], and shows that structural equations with known permanent shocks cannot contain error correction terms, thereby freeing up the latter to be used as instruments in estimating their parameters. The approach is illustrated by a re-examination of the identification schemes used by Wickens and Motto [2001. Estimating shocks and impulse response functions. Journal of Applied Econometrics 16, 371–387], Shapiro and Watson [1988. Sources of business cycle fluctuations. NBER Macroeconomics Annual 3, 111–148], King et al. [1991. Stochastic trends and economic fluctuations. American Economic Review 81, 819–840], Gali [1992. How well does the ISLM model fit postwar US data? Quarterly Journal of Economics 107, 709–735; 1999. Technology, employment, and the business cycle: Do technology shocks explain aggregate fluctuations? American Economic Review 89, 249–271] and Fisher [2006. The dynamic effects of neutral and investment-specific technology shocks. Journal of Political Economy 114, 413–451].     

Hours per capita and productivity: evidence from correlated unobserved components models

Recent studies debate the effect of a permanent productivity shock on hours per capita within a structural VAR context. This paper examines the issue using a correlated unobserved components (UC) framework. The estimates show that permanent shocks to productivity are negatively correlated with transitory shocks to hours. This result is robust for non‐stationary or levels stationary specifications of hours. Model comparisons indicate that the data do not favor imposing VAR‐type restrictions on the UC models. Copyright © 2008 John Wiley & Sons, Ltd.     

Leaning into the Wind: A Structural VAR Investigation of UK Monetary Policy*

This paper adapts Uhlig's [Journal of Monetary Economics (2005) forthcoming] sign restriction identification methodology to investigate the effects of UK monetary policy using a structural vector autoregression (VAR). It shows that shocks which can reasonably be described as monetary policy shocks have played only a small role in the total variation of UK monetary and macroeconomic variables. Most of the variation in UK monetary variables has been due to their systematic reaction to other macroeconomic shocks, namely non‐monetary aggregate demand, aggregate supply, and oil price shocks. We also find, without imposing any long run identifying restrictions, that aggregate supply shocks have permanent effects on output.     

Correlated income shocks and excess smoothness of consumption

In the literature, econometricians typically assume that household income is the sum of a random walk permanent component and a transitory component, with uncorrelated permanent and transitory shocks. Using data on realized individual incomes and individual expectations of future incomes from the Survey of Italian Households׳ Income and Wealth, I find that permanent and transitory shocks are negatively correlated. Relaxing the assumption of no correlation between the shocks, I explore the effects of correlated income shocks on the estimated consumption insurance against permanent and transitory shocks, and consumption smoothness using a life-cycle model with self-insurance calibrated to U.S. data. Negatively correlated income shocks result in smoother consumption, and upward-biased estimates of the insurance against transitory (and permanent when borrowing constraints are not tight) income shocks. While the life-cycle model with negatively correlated shocks fits well the sensitivity of consumption to current income shocks observed in U.S. data, it falls short of explaining the sensitivity of consumption to income shocks cumulated over a longer horizon.     

SALES,INVENTORIES AND REAL INTEREST RATES: A CENTURY OF STYLIZED FACTS

We use Bayesian time‐varying parameter structural vector autoregressions with stochastic volatility to investigate changes in reduced‐form and structural correlations between inventories and either sales growth or the real interest rate in the USA during both the inter‐war and post‐World War II periods. We identify four structural shocks by combining a single long‐run restriction to identify a permanent output shock with three sign restrictions to identify demand‐ and supply‐side transitory shocks. We show that during both the inter‐war and post‐war periods the structural correlation between inventories and real interest rate conditional on identified interest rate shocks is systematically positive; the reduced‐form correlation between the two series is positive during the post‐war period, but in line with the predictions of theory it is robustly negative during the inter‐war era; during that era the correlations between inventories and either of the two other series exhibit a remarkably strong co‐movement with output at business cycle frequencies. Copyright © 2014 John Wiley & Sons, Ltd.     

Shocking Stories

The paper provides a survey of methods that decompose multivariate series into permanent and transitory components by using ideas drawn from the co-integration literature. We adopt a two stage procedure to effect the decomposition. In the first stage a basic set of permanent and transitory components is formed by using standard definitions of the shocks which they are constituted from. The resulting measurements are not unique and further information needs to be employed to get uniqueness. Such information can come in many forms but a particularly important one involves the values of the long-run multipliers for permanent shocks that are available from many calibrated models. A comparison of the methods of effecting the decomposition is performed using a well known data set.     

Measuring the natural rate of interest: A note on transitory shocks

We present evidence that the natural rate of interest is buffeted by both permanent and transitory shocks. We establish this result by estimating a benchmark model with Bayesian methods and loose priors on the unobserved drivers of the natural rate. When subject to transitory shocks, the median estimate for the US economy is more procyclical, displays a less marked secular decline, and is therefore higher following the Great Recession than most estimates in the literature.     

Diagnostics for IV Regressions

The use of residuals from the structural equations in a simultaneous- equations model can lead to misleading measures of association and to invalid diagnostic statistics for heterosedasticity and functional form misspecifications. In an important paper, Pagan and Hall (1983) suggest a few principals upon which asymptotically valid tests can be constructed, while the issue of appropriate measures of goodness-of-fit for IV regressions is addressed in Pesaran and Smith (1994). This paper is concerned with the optimal construction of diagnostics for IV regression, and examines the finite-sample properties of several tests for functional form misspecifications and heteroscedasticity.     

Bancarization and violent attacks from guerrilla and other illegal groups in Colombia

Income shocks affect violence through the opportunity cost and rapacity effects. Existing studies focus on the impact of transitory shocks, especially commodity price innovations. This paper builds on this literature and studies the causal effect of permanent income shocks on armed conflict in Colombia. Using a rich dataset reporting all guerrilla and other armed groups' attacks by municipality between 2009 and 2014 and information on the provision of banking services, it shows that increasing bancarization leads to reductions in violence. These results have important implications for public policy in countries with a long history of violence. They suggest that promoting financial inclusion is useful for reducing conflict.     

Measuring the effects of fiscal policy

Measuring the effects of discretionary fiscal policy is both difficult and controversial, as some explicit or implicit identifying assumptions need to be made to isolate exogenous and unanticipated changes in taxes and government spending. Studies based on structural vector autoregressions typically achieve identification by restricting the contemporaneous interaction of fiscal and non-fiscal variables in a rather arbitrary way. In this paper, we relax those restrictions and identify fiscal policy shocks by exploiting the conditional heteroscedasticity of the structural disturbances. We use this methodology to evaluate the macroeconomic effects of fiscal policy shocks in the U.S. before and after 1979. Our results show substantive differences in the economy׳s response to government spending and tax shocks across the two periods. Importantly, we find that increases in public spending are, in general, more effective than tax cuts in stimulating economic activity. A key contribution of this study is to provide a formal test of the identifying restrictions commonly used in the literature.     

Bradford Smith: An Econometrician Decades Ahead of His Time*

This article attempts to rehabilitate Bradford Smith, who in 1926 published a short article in the Journal of the American Statistical Association in which he considered the implications of detrending time series by either deviations‐from‐trend or first‐differencing prior to regression. His discussion covers such topics as the permanent‐transitory innovation distinction inherent in difference and trend stationary processes, common factor restrictions and general‐to‐specific modelling. These have all become mainstays of modern time‐series econometrics, yet there does not appear to be even one reference to Smith's paper in all the years since its publication.     

DISENTANGLING DEMAND AND SUPPLY SHOCKS IN THE CRUDE OIL MARKET: HOW TO CHECK SIGN RESTRICTIONS IN STRUCTURAL VARS

Sign restrictions have become increasingly popular for identifying shocks in structural vector autoregressive (SVAR) models. So far there are no techniques for validating the shocks identified via such restrictions. Although in an ideal setting the sign restrictions specify shocks of interest, sign restrictions may be invalidated by measurement errors, data adjustments or omitted variables. We model changes in the volatility of the shocks via a Markov switching (MS) mechanism and use this device to give the data a chance to object to sign restrictions. The approach is illustrated by considering a small model for the market of crude oil. Earlier findings that oil supply shocks explain only a very small fraction of movements in the price of oil are confirmed and it is found that the importance of aggregate demand shocks for oil price movements has declined since the mid 1980s. Copyright © 2013 John Wiley & Sons, Ltd.     

The Effects of Household Income Volatility on Divorce

We extend the literature on the effects of earnings shocks on divorce by identifying separately the effects of transitory and permanent household income shocks and by allowing the shocks to have asymmetric effects across education and racial groups. The econometric evidence suggests negative (positive) transitory household income shocks increase (decrease) the probability of divorce, while there is only weak evidence that positive (negative) permanent household income shocks raise (lower) the probability of divorce. Some differences in the effects of household income shocks on divorce propensities arise for subsamples selected by education and race.     

Exogenous uncertainty and the identification of structural vector autoregressions with external instruments

We provide necessary and sufficient conditions for the identification (point‐identification) of structural vector autoregressions (SVARs) with external instruments considering the case in which r instruments are used to identify g structural shocks of interest, r ≥ g ≥ 1. Novel frequentist estimation methods are discussed by considering both a “partial shocks” identification strategy, where only g structural shocks are of interest and are instrumented, and a “full shocks” identification strategy, where despite g structural shocks being instrumented, all n=g+(n?g) structural shocks of the system can be identified under certain conditions. The suggested approach is applied to investigate empirically whether financial and macroeconomic uncertainty can be approximated as exogenous drivers of US real economic activity, or rather as endogenous responses to first moment shocks, or both. We analyze whether the dynamic causal effects of nonuncertainty shocks on macroeconomic and financial uncertainty are significant in the period after the global financial crisis.     

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.     

Simulation-based estimation of peer effects

The influence of peer behavior on an individual's choices has received renewed interest in recent years. However, accurate measures of this influence are difficult to obtain. Standard reduced-form methods lead to upwardly biased estimates due to simultaneity, common shocks, and nonrandom peer group selection. This paper describes a structural econometric model of peer effects in binary choice, as well as a simulated maximum likelihood estimator for its parameters. The model is nonparametrically identified under plausible restrictions, and can place informative bounds on parameter values under much weaker restrictions. Monte Carlo results indicate that this estimator performs better than a reduced form approach in a wide variety of settings. A brief application to youth smoking demonstrates the method and suggests that previous studies dramatically overstate peer influence.     

Identifying credit demand,financial intermediation,and supply of funds shocks: A structural VAR approach

In this paper, we identify three exogenous shocks to credit market: demand for credit, supply of funds into the financial system, and the willingness to lend of financial institutions (financial intermediation), and also, determine the contribution of these shocks to fluctuations in the credit market and overall economic activity. We estimate a structural vector autoregression model where the three credit shocks are identified with a set of sign restrictions motivated by a simple partial equilibrium model of financial intermediation. We find that the credit demand shock explains significantly the variations in the long-term loan rate proxied by the Moody’s Baa corporate bond yield, while the supply of funds shock contributes to most of the fluctuations in the short-term commercial paper rate. The financial intermediation shock drives most of the fluctuations in the quantity of loans as well as the spread between the Baa and commercial paper rates. Of the credit shocks, we find that the financial intermediation shock has the largest impact on real economic activity. In fact, our analysis implies that the sharp decline in output during the 2007–2009 financial crisis is largely attributable to the financial intermediation shock, along with shocks originating outside of the financial system.