Do Divariate SVAR Models with Long-Run Identifying

Do Divariate SVAR Models with Long-Run Identifying Restrictions Yield Reliable Results? An Investigation into the Case of Germany JAN G O T T S C H A L K and W I L L E M V A N Z A N D W E G H E *

JEL classification: E32, C32 Keywords: Business Cycle Fluctuations, Structural Vector Autoregression Models, Long-run Restrictions

1. INTRODUCTION In 1989, BLANCHARD and QUAH introduced in their seminal article "The Dynamic Effects of Aggregate Demand and Supply Disturbances" an econometric procedure based on the Structural Vector Autoregression (SVAR) methodology to identify aggregate demand and supply disturbances in a bivariate framework. A key contribution of this article was the introduction of an identification strategy which employed long-run identifying restrictions. Variations of the bivariate BLANCHARD/QUAH procedure proved popular in the literature thereafter. Applications include BAYOUMI and EICHENGREEN (1993) and WHITT (1995), who use this methodology to identify aggregate demand and supply shocks for a sample of countries belonging to the European Union. They proceed to investigate whether there are substantial positive correlations of demand and supply shocks, since such findings would suggest that these countries are good candidates for monetary union. Another application is found in the work by STERNE and BAYOUMI (1995) and BERGMAN (1996). These authors focus on the dynamic responses of the economy to aggregate demand and supply disturbances in order to measure the relative importance of these two types of disturbances for output fluctuations. This line of research is related to earlier work by authors like NELSON and PLOSSER (1982) and CAMPBELL

and MANKIW (1987), who attempt to determine in an univariate framework whether output fluctuations are dominated by permanent innovations or by temporary deviations from a deterministic time trend, which proxies a fairly constant underlying growth rate of output. The latter hypothesis corresponds to the "Keynesian synthesis" view of output fluctuations being the result of the interaction of transitory shocks with a sticky aggregate price level, while the former hypothesis reflects the view of Real Business Jan Gottschalk was with the Kiel Institute for World Economics when writing this article and Willem Van Zandweghe participated in the Advanced Study Program. We are grateful to Kai Carstensen, Jörg Döpke and Robert Kokta for helpful comments. All remaining errors are ours alone.

Schweiz. Zeitschrift für Volkswirtschaft und Statistik

2003, Vol. 139(1)55-81

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GOTTSCHALK/VAN ZANDWEGHE

Cycle (RBC) models 1 , which emphasise the role of supply shocks for output fluctuations at business cycle horizons. Since QUAH (1992) has shown that this issue cannot be settled within a univariate framework, it was a logical next step to turn to bivariate models. This line of inquiry was also part of the motivation of the BLANCHARD and QUAH (1989) paper. 2 In recent years the use of long-run identifying restrictions has also become popular in larger models. A non-exhaustive list of examples include GALI (1992), CLARIDA and G A L I (1994), FACKLER and M A C M I L L I N (1998) and ASTLEY and YATES (1999). Still, the

availability of more elaborate models is no reason to abandon the bivariate framework. After all, the low dimension of bivariate models is sufficient for many purposes and has some advantages of its own, since bivariate models do not require much data input, are simple to implement and produce intuitive results in the sense that these models impose the structure of simple textbook models on the data. However, if the low dimension is liable to lead to misleading inferences, this would be a strong argument to turn to larger models instead. The problem with the low dimension of bivariate models is that even if the assumption is maintained that all shocks buffeting the economy can be classified as belonging either to the class of supply shocks or to demand shocks, which is central to the BLANCHARD/QUAH methodology, there are still many different types of those shocks. For example, the class of supply shocks is likely to comprise productivity and labour supply shocks, while the class of demand shocks comprises foreign and domestic demand shocks. This implies that the identified shocks derived from a bivariate SVAR model have to be viewed as aggregates of a larger number of underlying shocks. This raises the possibility that the identification scheme may fail to preserve the shock categories, so that the identified shocks commingle the underlying demand and supply disturbances, thereby invalidating their economic interpretation. It is the objective of this paper to investigate the reliability of results from bivariate SVAR models employing long-run identifying restrictions by checking the consistency of results across different models. To this end, different types of bivariate BLANCHARD/QUAH models, which have been employed in the literature, are re-estimated for German data and their consistency is evaluated using the test procedure proposed for this purpose by FAUST and LEEPER (1997). Moreover, the robustness of the results is investigated with respect to the estimated impulse response functions, variance decompositions and historical decompositions. The paper is organised as follows. In section 2 the BLANCHARD/QUAH methodology is introduced and its possible limitations are discussed. In section 3 the empirical results for a number of bivariate models are presented and their consistency is evaluated. Section 4 contains the conclusion.

1. 2.

See for instance LONG and PLOSSER (1983). Another application of the BLANCHARD/QUAH methodology is given by FUNKE (1997), who employs it to estimate supply potential and output gaps in West German manufacturing.

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2. IDENTIFICATION OF DEMAND AND SUPPLY SHOCKS USING BIVARIATE SVAR MODELS 2.1. The Blanchard/Quah

Methodology

Theoretically, the BLANCHARD/QUAH methodology is motivated by a traditional Keynesian view of fluctuations.3 It is assumed that business cycle fluctuations can be attributed to aggregate supply and demand disturbances buffeting the economy. These disturbances are assumed to be orthogonal to each other. The economy is characterised by nominal rigidities, which ensure that demand disturbances have real effects in the shortrun, and by a vertical supply curve, which implies that in the long-run demand disturbances have no effect on the level of output. This neutrality assumption is central for the BLANCH ARD/QUAH methodology. They show how the corresponding long-run restriction can be imposed on a bivariate model consisting of output growth and a second variable, which represents in this paper either the unemployment rate controlled for the underlying trend or a differenced price series. The model comprised of output growth and the unemployment rate has been employed by BLANCHARD and QUAH in their seminal contribution. Using a Keynesian model, the two authors show that shocks to the unemployment rate can be interpreted as aggregate demand shocks and shocks to the growth rate of output as aggregate supply shocks. The model comprised of output growth and a differenced price series has been popularised by BAYOUMI and EICHENGREEN (1993). Here, shocks to the price variable correspond to aggregate demand shocks. The intuition behind this model can be illustrated with the familiar aggregate demand and aggregate supply (AD-AS) diagram. The AD-AS diagram is typically depicted in the price output plane and contains a vertical long-run aggregate supply curve, an upward sloping short-run aggregate supply curve and a downward sloping aggregate demand curve. An important result of this model is that demand and supply shocks have different effects on prices. In particular, positive demand shocks increase output and prices while positive supply shocks increase output but reduce prices. This yields an overidentifying restriction, which will turn out useful in the empirical section to verify whether the supply and demand shocks have been correctly identified. From a statistical point of view, an important requirement for the second variable is that it be stationary. In the following, output growth is denoted as Ayt, while the second variable is denoted as wt. For a more compact notation the vector Xt is introduced, defined as Xt = (

). The vector et = (

s,/

) contains the two structural shocks,

where sS:t and e(u denote the aggregate supply and aggregate demand shock respectively. A convenient starting point to illustrate the BLANCH ARD/QUAH methodology is 3.

An extensive discussion of the theoretical basis of the BLANCH ARD/QUAH methodology can be found in the Kiel Working Paper version (no. 1068) of this paper.

GOTTSCHALK/VAN ZANDWEGHE

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the vector moving average representation of the theoretical model. Using the lag operator L, this model can be written as "Ay,

= 5> 021,/

£*4

(1)

or in a more compact form Xt = 60£t + Oiet-x + 92et-2 + 0 3 e,- 3 • • • = J2

U6 £

*^

W

where 6 contains the four elements of the second matrix in (1) and 9(L) = 9Q + 9\L + Oo L2 + . . . denotes a matrix polynomial in the lag operator. The matrices 0/ represent the impulse response functions of the shocks to the elements of Xt. Since output enters this model in differenced form, the identifying restriction that the demand shock has no long-run effect on the level of output is equivalent to the restriction that the cumulative effect of this disturbance on the change of output (At/,) is zero. Formally this restriction can be imposed on the model by requiring that

X>2./ = 0

(3)

To estimate the structural model defined by equation (2) together with the restriction given by (3), as a first step a reduced form vector autoregression (VAR) system is estimated, where each element of Xt is regressed on n lagged values of the elements of X. Using A to denote the estimated coefficients, this yields: Xt = AxXt-X + AoXt-2 + . • • + AnXt-n

+ e,,

(4)

or Xt = A(L)X,-l+eti

(5)

where e represents the residuals from the reduced form equations estimated here. In order to make equation (4) comparable with (2), it is useful to write down its moving average form: Xt=et

+ $ie,_i + $ 2 e,- 2 + $3^-3 + . . . .

(6)

Comparison of equation (6) with (2) shows that the reduced form disturbances and the structural shocks are related by 0Qet=eti

(7)

and Oi = $Ì6Q holds for all i = 1,2,... Once one has determined with the help of identifying restrictions the matrix 0Q, the structural shocks et can be recovered from the esti-

BIVARIATE SVAR MODELS

59

mated reduced form disturbances et and the structural impulse responses 0, from the estimated reduced form VMA coefficients $,. Since the matrix 0O has four elements, four identifying restrictions are needed to construct an empirical estimate of this matrix. Two of those are simple normalisations, which define the variance of the structural shocks es