IDENTIFICATION METHODS IN VECTOR‐ERROR CORRECTION MODELS: EQUIVALENCE RESULTS

In a structural vector‐error correction (VEC) model, it is possible to decompose the shocks into those with permanent and transitory effects on the levels of the variables. Pagan and Pesaran derive the restrictions which the permanent–transitory decomposition of the shocks imposes on the structural VEC model. This paper shows that these restrictions are equivalent to a set of restrictions that are applied in the methods of Gonzalo and Ng and King et al. (KPSW). Using this result, it is shown that the Pagan and Pesaran method can be used to recover the structural shocks with permanent effects identically to those from the Gonzalo and Ng and KPSW methods. In the former case, this is illustrated in the context of Lettau and Ludvigson's consumption model and in the latter case in KPSW's six variable model. There are also two other methods for which the Pagan and Pesaran approach can deliver identical permanent shocks which are also discussed.     

Regression‐based Tests for a Change in Persistence*

We show that the minimal forward (reverse) recursive unit tests of Banerjee, Lumsdaine and Stock [Journal of Business and Economics Statistics (1992) Vol. 10, pp. 271–288] are consistent against the alternative of a change in persistence from I(0) to I(1) [I(1) to I(0)]. However, these statistics are also shown to diverge for series which are I(0) throughout. Consequently, a rejection by these tests does not necessarily imply a change in persistence. We propose a further test, based on the ratio of these statistics, which is consistent against changes either from I(0) to I(1), or vice versa, yet does not over‐reject against constant I(0) series. Consistent breakpoint estimators are proposed.     

Further Evidence on the Statistical Properties of Real GNP*

The well‐known lack of power of unit‐root tests has often been attributed to the short length of macroeconomic variables and also to data‐generating processes (DGPs) departing from the I(1)–I(0) models. This paper shows that by using long spans of annual real gross national product (GNP) and GNP per capita (133 years), high power can be achieved, leading to the rejection of both the unit‐root and the trend‐stationary hypothesis. More flexible representations are then considered, namely, processes containing structural breaks (SB) and fractional orders of integration (FI). Economic justification for the presence of these features in GNP is provided. It is shown that both FI and SB formulations are in general preferred to the autoregressive integrated moving average (ARIMA) [I(1) or I(0)] formulations. As a novelty in this literature, new techniques are applied to discriminate between FI and SB. It turns out that the FI specification is preferred, implying that GNP and GNP per capita are non‐stationary, highly persistent but mean‐reverting series. Finally, it is shown that the results are robust when breaks in the deterministic component are allowed for in the FI model. Some macroeconomic implications of these findings are also discussed.     

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.     

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.     

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.     

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.     

The permanent income hypothesis in five major industrial countries: a multivariate trend-cycle decomposition test

This paper presents a new test of the permanent income hypothesis in five major industrial countries. The test first decomposes consumption and income into their long run trend (permanent) and short run cyclical (transitory) components, using the recently developed multivariate stochastic detrending approach developed by Vahid and Engle (1997), among others. This approach exploits the presence of possible common stochastic trends and cycles among the variables in the system to arrive at a more efficient decomposition of these variables. Using the decomposition results, and in contrast to many articles in the literature, the paper finds support for the permanent income hypothesis. Specifically, the paper finds that, while permanent consumption is related to permanent income, transitory consumption is related to neither permanent nor transitory income.

Long‐run neutrality of demand shocks: Revisiting Blanchard and Quah (1989) with independent structural shocks

With reference to a stylized theoretical macromodel, Blanchard and Quah (American Economic Review, 1989, 79, 655–673) identify empirical aggregate supply (e.g., productivity) and demand shocks by assuming that the latter are neutral for economic activity in the long run. Taking advantage of recent contributions to the structural VAR literature and data‐based identification, we find that effects of unique independent non‐Gaussian structural shocks support this assumption. Moreover, unlike the results in Blanchard and Quah, statistically identified supply shocks exhibit (insignificantly) opposite impacts on gross domestic product and unemployment in the short run. In comparison with benchmark results obtained under assumed long‐run neutrality, statistical identification points to a stronger role of aggregate supply shocks for shaping temporary profiles of US unemployment during the recessionary period 1973:Q3–1975:Q1.     

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.     

A simple,robust and powerful test of the trend hypothesis

In this paper we develop a simple test procedure for a linear trend which does not require knowledge of the form of serial correlation in the data, is robust to strong serial correlation, and has a standard normal limiting null distribution under either I(0)$I(0)$ or I(1)$I(1)$ shocks. In contrast to other available robust linear trend tests, our proposed test achieves the Gaussian asymptotic local power envelope in both the I(0)$I(0)$ and I(1)$I(1)$ cases. For near-I(1)$I(1)$ errors our proposed procedure is conservative and a modification for this situation is suggested. An estimator of the trend parameter, together with an associated confidence interval, which is asymptotically efficient, again regardless of whether the shocks are I(0)$I(0)$ or I(1)$I(1)$, is also provided.     

Do TFP and the relative price of investment share a common I(1) component?

Results from cointegration tests clearly suggest that TFP and the relative price of investment (RPI) are not cointegrated. Evidence on the alternative possibility that they may nonetheless contain a common I(1) component generating long-horizon co-variation between them crucially depends on the fact that (i) structural breaks are, or are not allowed for, and (ii) the precise nature and timing of such breaks. Not allowing for breaks, evidence points towards the presence of a common component inducing positive long-horizon covariation, which is compatible with the notion that the technology transforming consumption goods into investment goods is non-linear, and the RPI is also impacted upon by neutral shocks. Allowing for breaks, evidence suggests that long-horizon covariation is either nil or negative.Assuming, for illustrative purposes, that the two series contain a common component inducing negative long-horizon covariation, evidence based on structural VARs shows that this common shock (i) plays an important role in macroeconomic fluctuations, explaining sizeable fractions of the forecast error variance of main macro series, and (ii) generates ‘disinflationary booms’, characterized by transitory increases in hours, and decreases in inflation.     

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.     

Testing for Flexible Nonlinear Trends with an Integrated or Stationary Noise Component

This paper proposes a new test for the presence of a nonlinear deterministic trend approximated by a Fourier expansion in a univariate time series for which there is no prior knowledge as to whether the noise component is stationary or contains an autoregressive unit root. Our approach builds on the work of Perron and Yabu ( 2009a ) and is based on a Feasible Generalized Least Squares procedure that uses a super‐efficient estimator of the sum of the autoregressive coefficients α when α = 1. The resulting Wald test statistic asymptotically follows a chi‐square distribution in both the I(0) and I(1) cases. To improve the finite sample properties of the test, we use a bias‐corrected version of the OLS estimator of α proposed by Roy and Fuller ( 2001 ). We show that our procedure is substantially more powerful than currently available alternatives. We illustrate the usefulness of our method via an application to modelling the trend of global and hemispheric temperatures.     

Testing for Multicointegration in Panel Data with Common Factors*

This paper addresses the concept of multicointegration in a panel data framework and builds upon the panel data cointegration procedures developed in Pedroni [Econometric Theory (2004), Vol. 20, pp. 597–625]. When individuals are either cross‐section independent, or cross‐section dependence can be removed by cross‐section demeaning, our approach can be applied to the wider framework of mixed I(2) and I(1) stochastic processes. The paper also deals with the issue of cross‐section dependence using approximate common‐factor models. Finite sample performance is investigated through Monte Carlo simulations. Finally, we illustrate the use of the procedure investigating an inventories, sales and production relationship for a panel of US industries.     

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.     

PITFALLS IN CROSS‐SECTION STUDIES WITH INTEGRATED REGRESSORS: A SURVEY AND NEW DEVELOPMENTS

In cross‐section studies, if the dependent variable is I(0) but the regressor is I(1), the true slope must be zero in the resulting “unbalanced regression.” A spuriously significant relationship may be found in large cross‐sections, however, if the integrated regressor is related to a stationary variable that enters the DGP but is omitted from the regression. The solution is to search for the related stationary variable, in some cases the first difference of the integrated regressor, in other cases, a categorical variable that can take on limited number of values which depend on the integrated variable. We present an extensive survey, new developments, and applications particularly in finance.     

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.     

Properties of nonlinear transformations of fractionally integrated processes

This paper shows that the properties of nonlinear transformations of a fractionally integrated process strongly depend on whether the initial series is stationary or not. Transforming a stationary Gaussian I(d) process with d>0 leads to a long-memory process with the same or a smaller long-memory parameter depending on the Hermite rank of the transformation. Any nonlinear transformation of an antipersistent Gaussian I(d) process is I(0)). For non-stationary I(d) processes, every polynomial transformation is non-stationary and exhibits a stochastic trend in mean and in variance. In particular, the square of a non-stationary Gaussian I(d) process still has long memory with parameter d, whereas the square of a stationary Gaussian I(d) process shows less dependence than the initial process. Simulation results for other transformations are also discussed.