Uncorrelated Shocks Research Articles

Too Many Shocks Spoil the Interpretation

We show that when a model has more shocks than observed variables the estimated filtered and smoothed shocks will be correlated. This is despite no correlation being present in the data generating process. Additionally the estimated shock innovations may be autocorrelated. These correlations limit the relevance of impulse responses, which assume uncorrelated shocks, for interpreting the data. Excess shocks occur frequently, e.g. in Unobserved-Component (UC) models, filters, including Hodrick- Prescott (1997), and some Dynamic Stochastic General Equilibrium (DSGE) models. Using several UC models and an estimated DSGE model, Ireland (2011), we demonstrate that sizable correlations among the estimated shocks can result.

Too Many Shocks Spoil the Interpretation

We show that when a model has more shocks than observed variables the estimated filtered and smoothed shocks will be correlated. This is despite no correlation being present in the data generating process. Additionally the estimated shock innovations may be autocorrelated. These correlations limit the relevance of impulse responses, which assume uncorrelated shocks, for interpreting the data. Excess shocks occur frequently, e.g. in Unobserved-Component (UC) models, filters, including Hodrick-Prescott (1997), and some Dynamic Stochastic General Equilibrium (DSGE) models. Using several UC models and an estimated DSGE model, Ireland (2011), we demonstrate that sizable correlations among the estimated shocks can result.

Exchange Rates Co-Movement and International Trade

Nominal exchange rates strongly co-move. However, little is known about the economic source of common variation. This paper examines how international trade links nominal exchange rates. First, I document that two countries that trade more intensively with each other have more correlated exchange rates against the U.S dollar. Second, I develop a general equilibrium multi-country model, where a shock to a single country propagates to the exchange rates of its trading partners and serves as a source of common variation. In the baseline three-country model, I show that the sign and the strength of correlation between exchange rates depend on the elasticities of trade balances of countries with respect to both exchange rates. As a result, the model’s prediction about the relationship between bilateral trade intensity and exchange rates correlation depends on the currency in which international prices are set. Lastly, an augmented model is calibrated to twelve countries to quantitatively assess the importance of trade linkages. I find that trade linkages alone, with uncorrelated shocks across countries, account for 50% of the empirical trade-exchange-rates-correlation slope coefficient.

Financial Integration and Liquidity Crises

This paper analyzes the effects of financial integration on the stability of the banking system. Financial integration allows banks in different regions to smooth local liquidity shocks by borrowing and lending on a world interbank market. We show under which conditions financial integration induces banks to reduce their liquidity holdings and to shift their portfolios toward more profitable but less liquid investments. Integration helps reallocate liquidity when different banks are hit by uncorrelated shocks. However, when a correlated (systemic) shock hits, the total liquid resources in the banking system are lower than in autarky. Therefore, financial integration leads to more stable interbank interest rates in normal times but to larger interest rate spikes in crises. These results hold in a setup in which financial integration is welfare improving from an ex ante point of view. We also look at the model’s implications for financial regulation and show that, in a second-best world, financial integration can increase the welfare benefits of liquidity requirements. The online appendix is available at https://doi.org/10.1287/mnsc.2017.2841 . This paper was accepted by Neng Wang, finance.

The Reaction of Oil Producers to the Uncorrelated Oil Market Shocks

This study investigates the relationship between oil production and oil market shocks taking into account endogeneity of the oil market factors, during 1986 to 2016. Using the structural VAR framework, we compute the main oil market structural shocks, namely flow supply shocks, global demand shocks that are uncorrelated to supply shocks, and the real crude oil price shocks that are uncorrelated to supply and demand shocks. Next, we apply a PMG method to regress OPEC and non-OPEC oil productions against the three uncorrelated shocks. We find that when the global oil supply and demand increase, producers increase their production, however an increase in the real crude oil prices only weekly trigger OPEC production. Finally, the asymmetric responses are found, as OPEC and non-OPEC producers asymmetrically respond to demand and supply shocks, respectively.

Isometric Operators on Hilbert Spaces and the Classical Wold Decomposition for Stationary Time Series

The Wold Theorem plays a fundamental role in the decomposition of weakly stationary time series. From an empirical point of view, it enables to identify uncorrelated shocks, for instance in macroeconomic and financial time series. More theoretically, the decomposition of weakly stationary stochastic processes can be seen as a special case of the Abstract Wold Theorem that allows to decompose Hilbert spaces by using isometric operators. In this work we explain this link in detail by using the Hilbert space spanned by a weakly stationary time series and the lag operator as isometry. Our methodology, fully based on operator theory, provides some tools that are useful for discovering new Wold-type decompositions of stochastic processes, in which the involved isometry is no more the lag operator. Examples may be given by rescaling operators inherited from multiresolution analyses of time series, which may deliver a persistence-based decomposition.

Trade in Intermediate Inputs and Business Cycle Comovement

Does input trade synchronize business cycles across countries? I incorporate input trade into a dynamic multisector model with many countries, calibrate the model to match bilateral input-output data, and estimate trade-comovement regressions in simulated data. With correlated productivity shocks, the model yields high trade-comovement correlations for goods, but near-zero correlations for services and thus low aggregate correlations. With uncorrelated shocks, input trade generates more comovement in gross output than real value added. Goods comovement is higher when (i) the aggregate trade elasticity is low, (ii) inputs are more substitutable than final goods, and (iii) inputs are substitutable for primary factors. (JEL E23, E32, F11, F14, F43, F44)

Can structural small open-economy models account for the influence of foreign disturbances?

This paper demonstrates that an estimated, structural, small open-economy model of the Canadian economy cannot account for the substantial influence of foreign-sourced disturbances identified in numerous reduced-form studies. The benchmark model assumes uncorrelated shocks across countries and implies that U.S. shocks account for less than 3% of the variability observed in several Canadian series, at all forecast horizons. Accordingly, model-implied cross-correlation functions between Canada and U.S. are essentially zero. Both findings are at odds with the data. A specification that assumes correlated cross-country shocks partially resolves this discrepancy, but still falls well short of matching reduced-form evidence. One central difficulty resides in the model's inability to account for comovement without generating counter factual implications for the real exchange rate, the terms of trade and Canadian inflation.

Equivalence of a one-dimensional driven-diffusive system and an equilibrium two-dimensional walk model

It is known that a single product shock measure in some of the one-dimensional driven-diffusive systems with nearest-neighbor interactions might evolve in time quite similarly to a random walker moving on a one-dimensional lattice with reflecting boundaries. The nonequilibrium steady state of the system in this case can be written in terms of a linear superposition of such uncorrelated shocks. Equivalently, one can write the steady state of this system using a matrix-product approach with two-dimensional matrices. In this paper, we present an equilibrium two-dimensional one-transit walk model and find its partition function using a transfer matrix method. We will show that there is a direct connection between the partition functions of these two systems. We will explicitly show that in the steady state, the transfer matrix of the one-transit walk model is related to the matrix representation of the algebra of the driven-diffusive model through a similarity transformation. The physical quantities are also related through the same transformation.

Can Structural Small Open Economy Models Account for the Influence of Foreign Disturbances?

This paper demonstrates that an estimated, structural, small open-economy model of the Canadian economy cannot account for the substantial influence of foreign-sourced disturbances identified in numerous reduced-form studies. The benchmark model assumes uncorrelated shocks across countries and implies that U.S. shocks account for less than 3 percent of the variability observed in several Canadian series, at all forecast horizons. Accordingly, model-implied cross-correlation functions between Canada and U.S. are essentially zero. Both findings are at odds with the data. A specification that assumes correlated cross-country shocks partially resolves this discrepancy, but still falls well short of matching reduced-form evidence.

An Optimal Orthogonal Variance Decomposition

Let e and Sigma be respectively the vector of shocks and its variance covariance matrix in a linear system of equations in reduced form. This article shows that a unique orthogonal variance decomposition can be obtained if we impose a restriction that maximizes the trace of A, a positive definite matrix such that Az=e where z is vector of uncorrelated shocks with unit variance. Such a restriction is meaningful in that it associates the largest possible weight for each element in e with its corresponding element in z. It turns out that A=Sigma^1/2, the square root of Sigma.

A note on the two assumptions of standard unobserved components models

In this note, I consider a general class of unobserved components (UC) models and derive a relevant inequality. This inequality implies that either of the two assumptions of standard UC models, namely, a random walk trend and uncorrelated shocks, is not satisfied if the impulse response measure introduced by [Campbell, J.Y. and N.G. Mankiw, 1987a. Are output fluctuations transitory? Quarterly Journal of Economics 102, 857–880, Campbell, J.Y. and N.G. Mankiw, 1987b. Permanent and transitory components in macroeconomic fluctuations, American Economic Review (Papers and Proceedings) 77, 111–117] is greater than 1.

THE SOLOW RESIDUAL FOR AUSTRALIA: TECHNOLOGY SHOCKS OR FACTOR UTILIZATION?

I. INTRODUCTION In macroeconomics a standard way of measuring technology shocks is to use the Solow residual, Solow [1957]. However a growing body of evidence suggests the Solow residual is at best a noisy measure of technology shocks. A number of hypotheses have been advanced as to why this might be the case. These include: the existence of imperfect competition and increasing returns to scale (Hall [1988; 1990]), spillover externalities (Caballero and Lyons [1992]) and variations in factor utilization rates (Basu [1995], Burnside [1996], Burnside et at. [1993; 1995a,b], Burnside and Eichenbaum [1994] and Finn [1995]). Recent work by Basu [1995] and Burnside et al. [1995a], using data for United States (U.S.) manufacturing industries, suggests that changes in capital utilization are the most likely cause of the mis-measurement of technology by the Solow residual. This paper presents an econometric analysis of the behavior of the Solow residual for the Australian economy.(1) The preliminary analysis examines whether the Solow residual for Australia can be characterized as a strictly exogenous variable. Following Evans [1992], I test whether the Solow residual is Grangercaused by a number of other macroeconomic variables including: foreign prices and production, government spending, interest rates and a monetary aggregate. Fluctuations in such variables are frequently proposed as sources of business cycles in small open economies. Consistent with results obtained for the U.S. by Evans, I find that the Solow residual for Australia is not a strictly exogenous variable. However while Evans finds money supply growth and government spending Granger-cause the U.S. Solow residual, neither of these variables is a significant predictor in the Australian case. For Australia, the terms of trade and a measure of the term spread have the strongest predictive content for the Solow residual. What these results indicate is that the standard measure of the Solow residual for Australia is affected by shocks other than pure technological innovations. In an attempt to quantify the contribution of other (non-technology) shocks to fluctuations in the Solow residual for Australia, I employ the Structural Vector Autoregression (SVAR) methodology developed by Shapiro and Watson [1988], Blanchard and Quah [1989] and Cochrane [1994]. It is assumed that the measured Solow residual is affected by two types of mutually uncorrelated shocks. One of these has a permanent effect on the level of the Solow residual and the other has only a temporary effect. To identify these two disturbances I use information from a second variable, capacity utilization, where this choice is influenced by the recent work of Burnside and Eichenbaum [1994] and Burnside et al. [1995b]. Neither of the two shocks affecting the Solow residual has a permanent effect on the level of capacity utilization. The shock which has a permanent effect on the Solow residual is identified with a true technology disturbance, while the other shock is assumed to reflect aggregate demand disturbances. The remainder of this paper is organized as follows. In section II a measure of the Solow residual for Australia is constructed and its predictability examined. Section III contains a discussion of the SVAR model used to analyze the Solow residual and capacity utilization. The empirical results from this model are presented in section IV. Section V considers the robustness of the results and section VI concludes. II. PROPERTIES OF THE SOLOW RESIDUAL In macroeconomics a standard means of computing the (logarithm of the) Solow residual [a.sub.1] is to use the following equation, (1) [a.sub.t] = [y.sub.t] - [S.sub.N] [n.sub.t] - (1 - [S.sub.N])[k.sub.t] where y is the log of aggregate output, n is the log of total hours worked, k is the log of the aggregate capital stock and [S.sub.N] is labour's share of national income (assumed to be constant). …

On the adjustment matrix in error correction models

This paper explores the determinants of the adjustment matrix in error correction models within two intertemporal models of the firm. In a production smoothing model of inventories, it is shown that the adjustment matrix contains the speed of adjustment of inventories as conjectured in previous work but this parameter matrix also contains the parameters from the autoregressive polynomials associated with the stochastic, unobservable shocks in the model. Two empirical examples are provided suggesting that these unobservable shocks cannot be assumed to be serially uncorrelated. In a flexible wage model of a labor market, the impact upon the adjustment matrix of normalizing the cointegrating matrix is studied. In contrast to one-state variable problems, normalization of the cointegrating matrix is arbitrary on economic and statistical grounds in this model and it is shown that, even with serially uncorrelated shocks, estimating the elements of the adjustment matrix may not provide an estimate of the speed of adjustment under some normalizations of the cointegrating matrix. The implication of the analysis is that without guidance from an economic model about the interpretation of elements of the adjustment matrix under alternative normalizations of the cointegrating matrix, or when unobservable shocks are serially correlated, economic interpretation of estimates of the adjustment matrix will be hazardous.

Spatial chaos in weakly dispersive and viscous media: A nonperturbative theory of the driven KdV-Burgers equation

The asymptotic travelling wave solution of the KdV-Burgers equation driven by the long scale periodic driver is constructed. The solution represents a shock-train in which the quasi-periodic sequence of dispersive shocks or soliton chains is interspersed by smoothly varying regions. It is shown that the periodic solution which has the spatial driver period undergoes period doublings as the governing parameter changes. Two types of chaotic behavior are considered. The first type is a weak chaos, where only a small chaotic deviation from the periodic solution occurs. The second type corresponds to the developed chaos where the solution “ignores” the driver period and represents a random sequence of uncorrelated shocks. In the case of weak chaos the shock coordinate being repeatedly mapped over the driver period moves on a chaotic attractor, while in the case of developed chaos it moves on a repeller. Both solutions depend on a parameter indicating the reference shock position in the shock-train. The structure of a one dimensional set to which this parameter belongs is investigated. This set contains measure one intervals around the fixed points in the case of periodic or weakly chaotic solutions and it becomes a fractal in the case of strong chaos. The capacity dimension of this set is calculated.

COINTEGRATION AND COMMON FACTORS

Abstract. Alternative common factor representations for cointegrated vectors are studied. This is done by embedding them into the dynamic factor model proposed by Peña and Box (Identifying a simplifying structure in time series. J. Am. Statist. Assoc. 82 (1987), 836–43). It is shown that dynamic factor models produce as a particular case the alternative common trend representations for cointegrated variables available in the literature. Furthermore a new normalization is proposed which has the advantage of producing common trend representations with moving‐average polynomials and under certain circumstances with uncorrelated shocks.