Business Cycles
New Approaches

A CEPR conference on 'New Approaches to the Study of Business Cycles' was held in Madrid on 30/31 January 1998. The conference, which was organised by Lucrezia Reichlin (ECARE, Université Libre de Bruxelles and CEPR), assembled recent contributions on the measurement and theory of the business cycle from different methodological perspectives. One theme of the conference was the relationship between micro- and macroeconomic dynamics; another was trend-cycle decompositions for macroeconomic indicators. There were also papers on equilibrium business-cycle theory and simulation results. In all, 12 papers were presented.

'Capital accumulation with incomplete markets' was presented by Francesc Obiols-Homs (ULB and ECARE) and written jointly with Albert Marcet (Universitat Pompeu Fabra, London Business School and CEPR) and Philippe Weil (ULB, ECARE, CEPR and NBER). The authors asked whether the lack of perfect insurability implies that there will always be precautionary savings in the steady state. When markets are complete, economic agents can get perfect insurance against major fluctuations in their wealth and do not therefore need to save for precautionary motives. When markets are incomplete, however, precautionary savings are likely to ensue, thus allowing both a higher rate of capital accumulation and faster growth. Previous research has suggested that, in an economy with a fixed labour supply, the availability of precautionary savings implies an aggregate stock of capital around 2-3% larger than under complete markets. Consequently, if incomplete markets were always characterized by positive aggregate precautionary savings, a better allocation of risk would lead to an increase in welfare, but would cause output to fall.

The authors argued that the answer to their question must rely heavily on the elasticity of, and the wealth effects on, labour supply. When labour supply is endogenous, wealth effects will shrink the size of incomplete, relative to complete, market economies. In

these circumstances, the existence of precautionary savings will depend on aggregate ex-post wealth, and on the complementarity between the input creating the wealth effect and other productive inputs. For a sufficiently high employment rate, the wealth level of employed agents will be such that the aggregate labour supply under incomplete markets will be smaller than under complete markets. Hence incomplete markets per se do not necessarily imply either the existence of precautionary savings or an increase in the size of the economy relative to complete markets. Instead, if there were complementarities in production, and some of the inputs were able to create wealth effects, then completing the markets would increase not only welfare, but also output. This result called for a cautionary approach to the design of an optimal taxation scheme. A positive tax on capital income would be likely to move the economy even further from the optimal state. The authors' own simulations indicated that their results were robust with respect to the introduction of substitution effects implied by a particular form of aggregate uncertainty.

Empirical studies of the financial decisions of firms have revealed important differences in the behaviour of large and small firms. In 'Monetary policy and the financial decisions of firms', Thomas F Cooley (University of Rochester) and Vincenzo Quadrini (Universitat Pompeu Fabra) developed a general equilibrium model to help to explain this feature, among others. In the model, the capital structure of firms changes endogenously over time and over the business cycle as a result of the firms' financial decisions, and in response to idiosyncratic technology shocks, as well as to aggregate real and monetary shocks. One of the objectives of the paper, which was presented by Quadrini, was to provide a general equilibrium framework for describing the transmission of monetary shocks to the economy, where the effect of the shocks was to change liquidity levels in the economy.

Four interdependent sectors of the economy are considered: households, firms, financial intermediaries and mutual funds. There is a continuum of firms which, in each period, are heterogeneous in their initial equity capital. The firms' equity is endogenous and changes over time as profits are reinvested, this being the only source of increased equity. Firms finance their working capital by borrowing (up to a maximum defined by the firm's liquidation value) from financial intermediaries through a standard debt contract based on a non-contingent interest rate.

The authors derived several results. First, they determined the industry-wide dynamics and the equilibrium distribution of firms. Second, their model predicted that small and large firms would respond differently to aggregate real and monetary shocks. Small firms were found to be more sensitive to monetary shocks, whereas the response to real shocks was slightly greater for big firms. Third, the behaviour of households and firms had business-cycle implications. Firm heterogeneity was found to generate more persistence in the economy's response to monetary and real shocks, although the real effects of monetary policy were found to be very small. Fourth, monetary shocks led to considerable volatility in financial markets, particularly in stock-market returns. Monetary policy shocks and their effects on stock-market fluctuations could thus serve as an explanation for the puzzle of excess volatility of stock returns for representative-agent economies.

The model was calibrated to generate quantitative implications broadly consistent with aggregate data. Sumru Altug (Koç University and CEPR) noted, however, that it did not test whether this was true also of firms at the individual level. Since firms' decision rules depended on a specific set of observable state variables, a simple test could determine their significance for the firms' behaviour.

International agreements – such as the Maastricht and Amsterdam Treaties – to formalize stabilization pacts for debt and public deficits arise from the perception that national deficit spending imposes negative externalities on foreign countries. The possibility of such externalities is not new – interest-rate transmission channels, for instance, have long posed such a threat. In EMU, however, their potential will be accentuated by the creation of the European Central Bank, which may be called upon to bail out a heavily indebted member country, thereby ultimately threatening union-wide price stability. In a paper written with Soren Bo Nielsen (Copenhagen Business School) and entitled 'Is coordination of fiscal deficits necessary?', Harry Huizinga (CenTER, Tilburg University, and CEPR) examined the scope for fiscal rules to restrict government borrowing in the case where government financing stems from capital income taxation. The paper stressed interest-rate and tax externalities as a rationale for international restrictions on national budget deficits. In a two-period model, the authors generalized the existing literature by allowing for public expenditures in each period to be financed by distortionary taxes on investment and saving, with the possibility of first-period public deficits.

Where governments had access to both source- and residence-based capital income taxes, the predictions of the model were familiar: there was no need to coordinate national borrowing. The assumption that both investment and saving taxes were available, however, was crucial for the result. In practice, the residence-based tax on the return to savings is increasingly eroded by tax avoidance and evasion. If a savings tax was not available, there was still scope for fiscal-policy coordination. Allowing for government borrowing in the first period, however, introduced an additional international interest-rate externality: borrowing by one government pushed up international interest rates, thereby increasing borrowing costs for all governments. The tax-competition and interest-rate externalities worked in opposite directions, with the result that in the absence of fiscal-policy coordination net public borrowing could be either too high or too low. The paper showed that there will be excessive borrowing without coordination if 

'Spanish unemployment and inflation persistence: Are there Phillips trade-offs?' was written by Juan J Dolado (Universidad Carlos III, Madrid, and CEPR), J David Lopez-Salido (Banco de España) and Juan Luis Vega (European Monetary Institute), and presented by Juan Dolado. The paper considered the evolution of inflation and unemployment in Spain during the period 1964–95, including what appears, at first sight, to be an unemployment-inflation trade-off close to 1:1 since the mid-1970s. The authors analysed the implications of hysteresis effects – related in Spain to high firing costs and long unemployment-benefit duration – and of high-inflation persistence for both the Phillips trade-off and the sacrifice ratio. They employed a bivariate VAR model, with both the inflation and unemployment rates in first differences. The structural innovations associated with the latter two variables were defined to be the demand and supply shocks, which were recovered from the estimated VAR residuals.

This methodology allowed the authors to address a number of relevant issues: (1) estimation of the short- and long-run effects of both demand and supply shocks on unemployment and inflation; (2) estimation of the Phillips curve trade-off; and (3) testing for both the long- and short-run neutrality of the Phillips curve. They considered three identification schemes: a real business-cycle model; a neoclassical-monetarist-rational expectations model; and a Keynesian model. The monetarist identification scheme was found to be best-suited for the unemployment-inflation joint dynamics. The authors were unable to reject the existence of a permanent output loss of half a percentage point for each percentage point of permanent disinflation. When the VAR was augmented by a fiscal-policy variable, however, namely logged government current expenditures (in second differences), in an attempt to disentangle monetary from non-monetary demand shocks, the data favoured a transitory trade-off with a cumulative output loss of about six percentage points of GDP (notwithstanding the high degree of hysteresis in the Spanish labour market). None-the-less, the authors argued that the benefits from lower inflation were positive and similar in both cases.

A claim that the traditional VAR approaches to identification of the impact of a monetary-policy shock on output mean that the conclusions are not drawn directly from the data, but rather result from the imposition of either a causal ordering of the variables, or contemporaneous or long-run restrictions, formed the starting-point for the paper by Harald Uhlig (CenTER, Tilburg University, and CEPR). Entitled 'What are the effects of monetary policy? Results from an agnostic identification procedure', the paper proposed an alternative method of directly imposing sign restrictions on the responses of prices, non-borrowed reserves and the US federal funds rate (FFR) to a monetary shock. More specifically, Uhlig assumed that a contractionary shock leads to no increase in prices, no increase in non-borrowed reserves and no decrease in the FFR for a certain period (the 'response horizon') following the shock. Unlike the previous VAR literature, moreover, this approach sought the identification of a single (monetary) shock alone, with no restrictions imposed on the response of output, thus leaving the data to 'speak for themselves'.

The monetary shock was identified from an impulse vector, which minimized a criterion dependent upon the response horizon, and a function for 'penalizing' responses of price, non-borrowed reserves and FFR with signs different from those desired. The results, which broadly confirmed those of previous studies, constituted what Uhlig termed a 'new Keynesian-new classical synthesis': even though the general price level reacts sluggishly, money has no real effects. More specifically, he found that: (1) contractionary monetary policy shocks had an ambiguous effect on real GDP; (2) the GDP price deflator fell only slowly following a contractionary shock, possibly indicating price stickiness, while the commodity price index fell more quickly; and (3) monetary policy shocks accounted for only a small fraction of the forecast-error variance in prices and, except at horizons shorter than half a year, in the FFR as well.

The fact that monetary shocks appeared to capture so little variation in future inflation could be interpreted to mean that US monetary policy had been largely successful, in that it was predictable. As Uhlig acknowledged, however, this result could also imply faulty identifying assumptions – a point taken up in the ensuing discussion. Fabio Canova (Universitat Pompeu Fabra and CEPR) argued that even where the identification was concerned only with a single shock and no restrictions were imposed on the response of real GDP, this did not get rid of the indeterminacy problem. Some response variables therefore do need to be restrained; and, if some of the restrictions turn out to be incompatible with economic reality, the identified shock becomes meaningless. Canova also pointed to the sensitivity of Uhlig's method with respect to the specification of both the impulse-response horizon and the penalty function. None-the-less, Uhlig had refined the method for identifying a monetary shock and his results did seem strongly consistent with prior expectations.

Vanghelis Vassilatos (IMOP and IOBE) introduced his paper, 'A small open economy with transaction costs in foreign capital', which was written with Tryphon Kollintzas (Athens University, CEPR, IMOP and IOBE). Vassilatos noted that, with a few notable exceptions (Canada, France, Portugal, Sweden and the United Kingdom), the successful application of real business cycle (RBC) models to the US economy had not been accomplished for other countries. He and Kollintzas were attempting to remedy this by extending the standard RBC model to incorporate the behaviour of a small open economy in which access to foreign capital markets was impeded by transaction costs and in which the public sector was large and distorting. They calibrated their model on data for the Greek economy from 1960 to 1992. A second objective was to analyse the response of the major Greek macroeconomic variables to various temporary and permanent policy changes, most notably the effects of foreign transfers and the so-called 'Delors I and II' packages.

The model successfully reproduced several stylized facts of the Greek business cycle, and the impulse-response analysis predicted that increases in the GDP share of government consumption would adversely affect output and factor productivity, and would increase net foreign asset holdings. A higher GDP share of domestic transfers would have qualitatively similar, but quantitatively smaller, effects. Increases in the GDP share of government investment, however, would raise output and all kinds of capital but decrease labour. These results suggested that the relative increases in government consumption and in foreign and domestic transfers over the last 20 years had worked to the detriment of the Greek economy, owing to distortions to the incentives to save and work.

The model proved weak, however, in reproducing labour-market behaviour. In the authors' view, this was because of the high degree of centralization of the Greek labour market. Graziella Bertocchi (Università di Modena and CEPR) concurred and suggested an alternative modelling strategy, based on the fact that capital controls can be introduced as protection for the bargaining power of labour. Oved Yosha (Tel-Aviv University) explored the possibility of incorporating an 'optimally behaving' public sector, but the authors argued that the model's results were qualitatively insensitive to the role of government consumption in preferences. Fabio Canova commented that the growth-oriented nature of the 'Delors packages' was not fully captured by a model focusing primarily on short- and medium-term fluctuations.

'New approaches for modelling dynamics of large cross-sections' was written by Christophe Croux (ECARE), Mario Forni (Università di Modena), Marc Hallin (ECARE and ISRO), Marco Lippi (Università di Roma and ECARE) and Lucrezia Reichlin (ECARE and CEPR), and was presented by Lucrezia Reichlin. Although the empirical co-movement of macroeconomic aggregates is one of the few stylized facts of economics, it is – paradoxically – also one of the least well-documented and understood facts. 'Co-movement' is a loosely used term with many different interpretations. Moreover, persistent aggregate fluctuations often can be explained by micro shocks, propagated locally by co-movements of microeconomic units through input-output relations, spillovers and other interactions. Observed aggregate fluctuations caused by such local, rather than aggregate, shocks thus require explanantion through a different class of macroeconomic models.

Accordingly, the authors offered two lines of analysis. The first developed a measure of co-movement, which was close to the notion of dynamic correlation, but which also took into account differences in drifts and variances. Being defined in the frequency domain, the measure could be used to study business-cycle as well as short- or long-run questions. It could also be generalized to provide a summary index of 'cohesion', i.e. the degree of co-movement either within or between groups of variables (or individuals). The authors provided two illustrations. First, by analysing the 'local interaction hypothesis' in a panel of sectoral output data for 450 US manufacturing sectors since 1958, they demonstrated that both the extent and shape of cohesion between different sectoral groups conveyed information about the nature of the shocks and the propagation mechanisms. Second, they used per capita output data for US states and European countries to evaluate differences in overall intra-group cohesion. In both illustrations, bootstrap confidence intervals for the co-movement measure were computed.

In the second line of analysis, the paper proposed an econometric framework for studying the propagation of micro shocks (with possibly local effects) and of aggregate shocks. The model – a dynamic approximate factor model – generalized the usual (static) principal-components analysis to a dynamic framework and, more specifically, to the frequency domain. The authors obtained a consistent result for their estimator, as well as encouraging preliminary simulation results.

Margherita Borella (University College London) presented 'Stochastic components of individual consumption: a time series analysis of grouped data', written with Orazio Attanasio (University College London and CEPR). The authors noted that although the well-known dynamic properties of aggregate consumption had stimulated development of different theoretical models of consumption behaviour, most empirical studies had focused on some version of an Euler equation, estimating and testing the structural model by exploiting the over-identified restrictions implied by such an equation. Little was known, however, about the stochastic properties of consumption at the individual level. Previous studies had either modelled only the labour-market variables or focused solely on the dynamics of purely idiosyncratic components, treating aggregate shocks and business-cycle patterns as nuisance parameters to be eliminated in preliminary regressions. 

The authors therefore proposed a new methodology for analysing the time-series properties of individual consumption expenditure. Their aim was to characterize, at the individual level, the variance-covariance matrix of innovations to consumption, its components and other variables. They considered joint modelling of several components of consumption important, since the presence and nature of common factors could provide information about the empirical relevance of consumption-behaviour models. In particular, it allowed different models of individual behaviour and of market interactions, such as the existence of complete contingent markets, to be tested. Given the lack of panel data, a distinguishing feature of the proposed approach was the focus on big T-asymptotics, which were required for a proper inference of the dynamic properties, rather than N-asymptotics.

With the life-cycle model in mind, the authors examined consumption in relation to age, dividing the sample into cohorts of individuals that were followed over time. They also considered educational and occupational characteristics, and modelled the cross-sectional heterogeneity among groups. The empirical results suggested that consumption was highly sensitive to output, and that durable consumption was much the most volatile component. Harald Uhlig commented that this result was to be expected, given the behavioural similarities between durable consumption and investment. It was also unsurprising that the volatility of non-durable consumption was almost invariant with respect to cyclical frequency, whereas durable consumption fluctuated more at business-cycle frequencies than in the short or long run.

Fabio Canova (Universitat Pompeu Fabra and CEPR) presented his paper, 'Testing for heterogeneities in the cross-sectional dimension of a panel: a predictive density approach'. Recent theoretical research on growth and development suggests the possibility of 'convergence clubs' emerging within groups of countries or regions. This clustering may be induced by intra-group similarities in preferences and technologies or in government policies. Hitherto, however, there has been little formal empirical examination of the existence of such a tendency. Canova thus proposed a general technique for determining the number of such 'clubs' and the location of break points in cross-sectional data. The test – within the Bayesian tradition – allowed for heterogeneity within groups, and used predicitive densities to estimate the hyperparameters of each club, and posterior analysis to draw inferential conclusions about functions of the model coefficients. No distributional assumptions were required about the errors in the model, as long as the quasi-likelihood of the data, conditional on the hyperparameters, could be computed.

The author applied the technique to both a simulated and an observed data set, the former to establish the power and size properties of the tests and the features of the estimated parameter distributions, and the latter to test empirically the existence of convergence clubs among European regions. The observed data comprised per capita incomes for 144 European regions, measured relatively to the European average, for the period 1980-92. Four clusters were identified, each characterized by parameters controlling their speed of adjustment to the steady state and the (relative) mean level of per capita steady-state income. A high dispersion of steady states across each group was found, and inter-cluster heterogeneity was confirmed by differences in the long-run mobility indices across groups.

Christophe Croux commented on the limitations both of using a Bayesian-based predictive density, and of seeking an optimal solution to the clustering problem via a technique in which it is computationally impossible to consider all possible partitions of n individuals into a given number of groups. He wondered whether similar results could not be obtained using more traditional ad hoc clustering techniques, which are model-free and independent of prior beliefs about the clustering structure.

Daniel Peña (Universidad Carlos III de Madrid) presented 'Forecasting with leading indicators by partial least squares', written with Juan Antonio Gil (Universidad Carlos III de Madrid). The use of a limited number of indicators to summarize the responses of a large number of highly correlated variables with respect to changes in a variable (or variables) whose behaviour is to be predicted is well-established. Examples include the business cycle 'diffusion indices' constructed by Quah and Sargent, and, in Spain, the use of a synthetic leading index to predict the inflation rate. Although principal components analysis (PCA) and factor analysis (FA) are the most commonly used procedures for such exercises, they do not exploit the relationship between the explanatory variables and the variables to be predicted. Partial least squares (PLS) estimation methods, by contrast, do exploit these relationships and have been used extensively in Chemometrics. Calling for greater use of PLS in econometrics, Gil and Peña argued that it had major advantages over traditional regression methods. For example, PLS allowed for the number of explanatory variables to be larger than the number of observations, and offered a means for correcting for possible strong multicollinearity between the regressands. Moreover, the PLS estimate could be interpreted as a 'shrinkage' of the usual least squares estimate.

The authors applied the algorithm to simulated dynamic data, and to the forecasting of the Spanish inflation rate for the period February 1977 to August 1997. For the latter application, the method provided better estimation and forecasting results than traditional time-series analyses. Given its characteristics, however, Marc Hallin found it puzzling that PLS could lead to any satisfactory results in the presence of highly-correlated or collinear regressors. Its best selling-point might be the shrinkage argument, although even then there were important qualifications. Enrique Sentana (CEMFI and CEPR) noted that if the specification criteria for the number of PLS factors did not converge, more factors would have to be added to the model to capture the dynamics of the regressor.

'A review of systems cointegration tests' was written by Kirstin Hubrich (Humboldt-Universität zu Berlin), Helmut Lütkepohl (Humboldt-Universität zu Berlin) and Pentti Saikkonen (University of Helsinki), and was presented by Kirstin Hubrich. Determination of the number of long-run equilibrium paths linking the variables in a system is one of the primary motivations for cointegration testing. Although a wide range of procedures is now available, there is no consensus that any single method outperforms all the others. The authors reviewed the systems cointegration literature, and compared the various assumptions for the asymptotic validity of the different tests within a general unifying framework, presenting local power analyses, where available. A major contribution of the paper, in their view, was that it placed simulations-based comparisons of the size and power properties of the full range of tests on a common footing, using a bivariate vector process. The paper also reviewed systematically the differing assumptions regarding the deterministic terms, and it considered the performance of tests that do not depend on the values of the mean and the trend parameter in the Data Generating Process (DGP). In the latter case, it was noted that some newly suggested Lagrange multiplier-type tests performed similarly to standard likelihood ratio tests in small samples, whereas other tests were outperformed. Discussion focused on issues for further research, including the set-up of simulations in tests for a larger set of variables, and the robustness of results with respect to the possibility of some cointegrated variables exhibiting structural breaks.

Shifts in relations among economic variables over time – such as those induced by regime changes – may introduce deterministic breaks in data series which may be difficult to detect both by visual inspection and by available statistical methods. Current practice with unit root univariate processes, or with cointegrated error correction systems, is to circumvent this problem by preliminarily fitting the data with dummy variables. Studies of the effects of such procedures have concluded that the inclusion of dummy variables, as well as the size or the timing of the breaks, affects the critical values of the unit root or cointegration tests. In 'Detrending procedures and cointegration testing: ECM tests under structural breaks', Alvaro Escribano (Universidad Carlos III de Madrid) and Miguel Arranz (Universidad de Alicante) followed a different direction by examining robust procedures to test for unit roots in the presence of structural breaks in an error correction mechanism (ECM) context.

Instead of including dummy variables in ECM models, the authors set out to approximate these breaks by extending the number of lags in the models, as determined by the Schwartz-Bayesian information criterion (SBIC). In doing so, they looked at the critical values, studied the size of the ECM test under different MA(1) errors and analysed the power of the test with Monte Carlo simulations. The robustness properties of the test were examined by applying the same procedure not to the observable variables but to their (unobserved) trend and cyclical components, obtained from appropriate filters. Three types of structural breaks were considered: full cobreaking, cobreaking in levels, and cobreaking in differences. In all cases, bootstrap methods were used to compute the tests' critical values. The simulation results showed that in ECM tests the critical values depend upon the type of break and other nuisance parameters, and that, in some special cases, the test with structural breaks may have large size distortions. The use of trend and cycle decomposition procedures improved robustness in terms of size and with respect to MA error processes. The authors also argued that test performance can be improved by augmenting the number of lags – a conclusion that was considered surprising by Massimiliano Marcellino (European University Institute), who thought this would lead to potential overspecification of the model and, consequently, more inefficiency.