Search

The papers in this special issue cover a wide range of areas in the methodology and application of spatial econometrics. The first develops a generalized method of moments (GMM) estimator for the spatial regression model from a second-order approximation to the maximum likelihood (ML). The second develops Bayesian estimation in a stochastic frontier model with network dependence in efficiencies, with application to industry dynamics. The third studies cross-country convergence under the Lotka–Volterra model and obtains new insights into spatial spillovers. The penultimate paper develops robust specification tests for the social interactions model under both ML and GMM frameworks. The final paper proposes identification and GMM estimation in a high-order spatial autoregressive model with heterogeneity, common factors and spatial error dependence.

Summary An understanding of the spatial dimension of economic and social activity requires methods that can separate out the relationship between spatial units that is due to the effect of common factors from that which is purely spatial even in an abstract sense. The same applies to the empirical analysis of networks in general. We use cross-unit averages to extract common factors (viewed as a source of strong cross-sectional dependence) and compare the results with the principal components approach widely used in the literature. We then apply multiple testing procedures to the de-factored observations in order to determine significant bilateral correlations (signifying connections) between spatial units and compare this to an approach that just uses distance to determine units that are neighbours. We apply these methods to real house price changes at the level of Metropolitan Statistical Areas in the USA, and estimate a heterogeneous spatio-temporal model for the de-factored real house price changes and obtain significant evidence of spatial connections, both positive and negative. Copyright © 2015 John Wiley & Sons, Ltd.

It is widely believed that setting monetary policy through a majority voting committee has major benefits. A monetary policy committee can take personalities out of monetary policy decisions. Critical to understanding these claims is an assessment of how such a committee functions. In this paper we examine interactions and influences between committee members when there is heterogeneity among members. We are able to identify significant interactions and directions of influence among Monetary Policy Committee members at the Bank of England.

Both casual observation and empirical research suggest that developed equity markets around the world, including the major European markets, are now highly integrated. Financial integration is a key goal of the European Union (EU) and was one motive for the adoption of the euro. In this article, we examine how far the process of financial integration has gone in the equity markets of the EU. We use an econometric methodology that permits us to measure the equity market convergence while allowing for a range of possible time paths, and for heterogeneity across countries. Our tests reject the hypothesis of overall convergence in the European equity markets. We do, however, find evidence of convergence within three distinct and economically meaningful subgroups of European markets. We find no evidence that the Euro has hastened equity market convergence amongst its members, above and beyond the broader global trends of lowered institutional and legal barriers and market liberalization.

Summary The paper explores time variation in the distribution of firm level growth of total sales. Three novel results are reported. First, firms on the left-hand side of the distribution, i.e. firms that are growing more slowly or declining, are typically more responsive to aggregate shocks than those on the right-hand side of the distribution. Second, trending behaviour in the volatility of firm growth is predominantly driven by increasing dispersion in the growth of highly performing firms. Third, shifts in the probability mass on either side of the mode may act as important propagators of business fluctuations. Financial frictions emerge as a mechanism that is capable of accounting for these facts.

A multiplicative form of the habit term in the utility function has some undesirable properties if the habit function is itself still additive (Wendner, 2003). A geometric form for the way the stock of habit accumulates can resolve these shortcomings.

This paper provides a method for the analysis of the spatial and temporal diffusion of shocks in a dynamic system. We use changes in real house prices within the UK economy at the level of regions to illustrate its use. Adjustment to shocks involves both a region specific and a spatial effect. Shocks to a dominant region – London – are propagated contemporaneously and spatially to other regions. They in turn impact on other regions with a delay. We allow for lagged effects to echo back to the dominant region. London in turn is influenced by international developments through its link to New York and other financial centers. It is shown that New York house prices have a direct effect on London house prices. We analyse the effect of shocks using generalised spatio-temporal impulse responses. These highlight the diffusion of shocks both over time (as with the conventional impulse responses) and over space.

Until recently, considerable effort has been devoted to the estimation of panel data regression models without adequate attention being paid to the drivers of interaction amongst cross-section and spatial units. We discuss some new methodologies in this emerging area and demonstrate their use in measurement and inferences on cross-section and spatial interactions. Specifically, we highlight the important distinction between spatial dependence driven by unobserved common factors and those based on a spatial weights matrix. We argue that purely factor-driven models of spatial dependence may be inadequate because of their connection with the exchangeability assumption. The three methods considered are appropriate for different asymptotic settings; estimation under structural constraints when N is fixed and T → ∞, whilst the methods based on GMM and common correlated effects are appropriate when T ≫ N → ∞. Limitations and potential enhancements of the existing methods are discussed, and several directions for new research are highlighted.

This paper provides an empirical analysis of changes in real house prices in the USA using State level data. It examines the extent to which real house prices at the State level are driven by fundamentals such as real per capita disposable income, as well as by common shocks, and determines the speed of adjustment of real house prices to macroeconomic and local disturbances. We take explicit account of both cross-sectional dependence and heterogeneity. This allows us to find a cointegrating relationship between real house prices and real per capita incomes with coefficients ( 1 , − 1 ) , as predicted by the theory. We are also able to identify a significant negative effect for a net borrowing cost variable, and a significant positive effect for the State level population growth on changes in real house prices. Using this model we then examine the role of spatial factors, in particular, the effect of contiguous states by use of a weighting matrix. We are able to identify a significant spatial effect, even after controlling for State specific real incomes, and allowing for a number of unobserved common factors. We do, however, find evidence of departures from long run equilibrium in the housing markets in a number of States notably California, New York, Massachusetts, and to a lesser extent Connecticut, Rhode Island, Oregon and Washington State.

Many have questioned the empirical relevance of the Calvo–Yun model. This paper adds a term structure to three widely studied macroeconomic models (Calvo–Yun, hybrid and Svensson). We back out from observations on the yield curve the underlying macroeconomic model that most closely matches the level, slope and curvature of the yield curve. With each model we trace the response of the yield curve to macroeconomic shocks. We assess the fit of each model against the observed behaviour of interest rates and find limited support for the Calvo–Yun model in terms of fit with the observed yield curve, we find some support for the hybrid model but the Svensson model performs best.

This paper investigates why the U.K. has experienced steadily higher unemployment at cyclical peaks since 1965 using a structural model of the U.K. labor market. The mo del emphasizes the differences in experience and structure of the man ufacturing and nonmanufacturing private sectors using a bargaining ap proach to wage determination. Empirical results for the post-1965 per iod suggest that adverse supply shocks, such as tax increases, as wel l as demand deficiencies have played an important role in determinin g the increase in the level of unemployment and the degree of real wa ge stickiness, which is the corollary of this rise. Copyright 1987 by Blackwell Publishing Ltd

We study the impact of the macroeconomic environment on business exit in a world where acquisition and bankruptcy are co-determined. We estimate competing risk hazard regression models using data on UK quoted firms spanning a 38-year period that witnessed several business cycles. We find that the processes determining bankruptcies and acquisitions depend on the macroeconomic environment. In particular, macroeconomic instability has opposing effects on bankruptcy hazard and acquisition hazard, raising the former and lowering the latter. While bankruptcy hazard is counter-cyclical and acquisition hazard pro-cyclical, the US business cycle is a better predictor than the UK cycle itself.

We examine how macroeconomic instability affects risk of bankruptcy and liquidation. In periods of macroeconomic instability more firms become financially distressed, while the number of potential acquirers falls. Reorganization systems such as Chapter 11 can decouple liquidation from macroeconomic conditions. We develop a model in which a firm's bankruptcy and acquisition hazards are co-determined by firm-level and sector-level factors, and by macroeconomic conditions. As a control, we also estimate the model for the UK, which is an economy without an equivalent system to Chapter 11. Differences in the responsiveness of bankruptcy to instability are largely attributable to reorganization under Chapter 11.

We bring to light a significant aspect of firm level heterogeneity over the business cycle. Analysing the responsiveness of firm growth (quoted UK companies) to aggregate shocks, we find that the effects of aggregate shocks are more pronounced for firms in the middle range of growth. Rapidly growing and rapidly declining firms are less sensitive to aggregate shocks than firms in the interior of the growth range. This is consistent with the fact that the higher moments of the distribution of firm growth rates have significant cyclical patterns. These findings throw new light on growth of firms as well as on business cycle dynamics.

This paper uses Monte Carlo methods to investigate the effects of asymmetric adjustment on estimates of the parameters of the equilibrium relationship between a set of variables. We demonstrate that simple least squares estimates and the implicit estimates from a symmetric error correction model both lead to biases in the constant term. This bias increases with the size of the asymmetry and shows no tendency to decline with the sample size. We also show that if the biased estimates of the equilibrium relationship are then used to devide the sample into different regimes to test for assymmetric adjustment, then the resulting test has low power. The power of tests for asymmetry can be increased significantly by using simultaneous estimation of the parameters of the equilibrium relationship and the asymmetric adjustment process.

Modern interest in business cycles has focussed on the co-movements and correlations in the major macroeconomic aggregates. In this paper we offer another dimension to business cycle analysis which looks at the time series of cross-sectional distributions of the growth rates of sales by US quoted companies from 1950 to 1999. We detect correlations between aggregate business cycle fluctuations and the higher moments of the cross-sectional distribution. We find a significant negative correlation between the rate of growth of gdp and the cross-sectional variance and skewness of growth rates of sales. On the other hand there is positive correlation, at business cycle frequencies with kurtosis. In order to explore this further we turn to the dynamic evolution of firms and analyse the sensitivity of growth rates to aggregate shocks conditioning on firm size. The results suggest that despite considerable heterogeneity macroeconomic shocks have pervasive effects that are, however, more pronounced for firms in the middle range of growth. This has implications for both macro and industrial economics.

A novel approach is presented for the analysis of regime switching behaviour based upon the use of Geary's runs test. The proposed method is used to examine recent evidence presented concerning the application of alternative models of asymmetric error correction. The results derived show the runs test to detect a significant difference in regime switching behaviour under the rival models.

The theoretical analysis of investment under uncertainty has been revolutionized over the last decade by the importation of ideas from finance. If investment is irreversible, there is a return to waiting. So although circumstances may suggest that it is profitable to invest, there may also be an incentive to postpone the decision until better opportunities arise. Identifying and valuing the option to invest has become the standard way to solve the firm's irreversible-investment problem. Empirical studies of investment that incorporate the insights of the real-options approach are now beginning to appear. These show that investment can have a nonlinear relationship to q and may show insensitivity for some threshold level to the shadow value of investment (Barnett and Sakellaris 1998). Abel and Eberly (1997) and Bohm and Funke (1999) have also shown how the real-options approach to investment can be combined with the traditional q approach. In this case the relationship between q and the rate of investment is discontinuous. Over a range of inaction there will be no investment, although q is in excess of one. This paper builds a theoretical model that explains the determinants of this investment discontinuity. In contrast to much of the literature, we use a mean-reverting stochastic process, of which the geometric Brownian motion process is a special case. Under the assumption of a production function with constant returns to scale and a specific functional form for the investment adjustment function, it is possible to derive a tractable analytical form for the shadow value of the investment project. We then analyze the comparative properties of the value of q under different assumptions about the stochastic process governing output. The advantage of using a mean-reverting process is that it better captures the undoubted persistence in the shocks that face firms, especially at the macroeconomic level. We then consider what the implications would be for the aggregate relationship between investment, q, and the business cycle. We first carry out Monte Carlo simulations of a discrete version of the theoretical model. We find that for many parameter values, aggregating suppresses any nonlinearities in the micro adjustment processes. Moreover, where we do detect nonlinearity at the aggregate level, it varies with the type of stochastic process. It is greatest when this is a random walk—corresponding to the Brownian motion in continuous time—and least when the stochastic process follows an i.i.d. process. Mean reversion lies in between. We turn finally to an empirical examination using aggregate data and explore how sensitive investment is to q in different regimes. To do this, we apply a generalization of the Granger-Lee method (Arden et al. 2000) that uses a linear spline function to approximate different regions for investment.

There is now a plethora of non-linear time-series models of output over the business cycle, and considerable empirical evidence that there are key non-linear, poorly understood mechanisms at work. Though they account for a small part of the total flow of national income, inventories play a disproportionately large role in fluctuations in output. It would seem natural to try to determine what role inventories play in the non-linear behaviour of the business cycle. The first question is, are there economic models of firm behaviour suggesting that the movement of inventories over the business cycle is non-linear? The second issue is whether we can detect such non-linearity in the data. In this paper we use data on the aggregate behaviour of UK manufacturing, but disaggregated according to the stage of fabrication. We find that the asymmetric adjustment of inventories varies with the stage of fabrication.

This paper uses an asymmetric multivariate model to investigate asymmetries in employment and pricing behaviour by firms. This generalises the approach of Granger and Lee (1989) and also exploits the cross equation restrictions on the equations for prices and employment implied by a restricted cost function—the dual to a Cobb-Douglas production function. Our results suggest that both prices and employment respond asymmetrically to shocks to costs and demand.

The statistical properties of UK house prices are considered at a disaggregated level, where disaggregation occurs according to the age, or 'vintage', of the housing. Given the frequency of transactions in the housing market and the sophistication of the estate agent system, it might be expected that the series would share long-run relationships and be subject to common short-run shocks. It is found via conventional techniques that both the long-run and short-run relationships are less pronounced than might be expected. However, by extending recent research concerning the testing of common features, commonality in the (short-run) cycles of the house price series is uncovered, albeit with a partial lag. Despite this, the cycles are shown to differ in terms of their asymmetric behaviour.

Davidson et al.'s data set is used to demonstrate the existence of a significant asymmetry in the adjustment of consumption towards equilibrium. The Granger-Lee and Escribano-Pfann methods of partitioning the error correction term are compared and it is shown that the latter produces better results in this case. It is concluded that adjustment is faster under conditions of recession than it is during boom periods.

We examine the power of the Granger-Lee [Granger, C.W.J., Lee, T.H., 1989. Investigation of production, sales and inventory relationships using multicointegration and non-symmetric error correction models. Journal of Applied Econometrics 4, S145–S159.] test for asymmetric adjustment in an error correction model. Monte Carlo simulations indicate that such tests typically have low power in rejecting the null of symmetric adjustment. The power of the test increases with the sample size and with the ratio of the variance of the independent variable to the dependent variable.

The possible presence of non-linear dynamics in macro-systems has become a preoccupation of much recent research in macroeconomics. In this paper we explore some of the empirical issues in the context of a New-Keynesian model with rational expectations in asset markets and nominal inertia in pricing and Wdges. We inject non-linearities into the pricing and investment decisions of firms and explore how this affects the way in which the economy responds to supply and demand shocks of varying magnitude. We find that when the shocks are mild the response to negative and positive shocks is more or less linear. However, when the shocks are large, major asymmetries are triggered. There are significant differences in the response of the economy to shocks of different signs and different sizes. Since the non-linearities we identify in pricing and investment are empirically founded, our results have a number of implications for the conduct of economic policy.

An understanding of the spatial dimension of economic and social activity requires methods that can separate out the relationship between spatial units that is due to the effect of common factors from that which is purely spatial even in an abstract sense. The same applies to the empirical analysis of networks in general. We are able to distinguish between cross-sectional strong dependence and weak dependence. Strong dependence in turn suggests that there are common factors. We use cross unit averages to extract common factors and contrast this to a principal components approach widely used in the literature. We then use a multiple testing procedure to determine significant bilateral correlations (signifying connections) between spatial units and compare this to an approach that just uses distance to determine units that are neighbours. We apply these methods to real house price changes at the level of Metropolitan Statistical Areas in the USA, and estimate a heterogeneous spatiotemporal model for the de-factored real house price changes and obtain significant evidence of spatial connections, both positive and negative.

Prior to the fi nancial crisis mainstream monetary policy practice had become disconnected from money. We outline the basic rationale for this development using a simple model of money and credit in which we explore the conditions under which money matters directly for the conduct of policy. Then, drawing on Goodfriend and McCallum’s (2007) DSGE model, we examine the circumstances under which money becomes more closely linked to infl‡ation. We fi nd that money matters when the variance of the supply of lending dominates productivity and the velocity of money demand. This is because amplifying the role of loans supply leads to an expansion in aggregate demand, via a ompression of the external finance premium, which is infl‡ationary. We consider a number of alternative monetary policy rules, and find that a rule which exploits the joint information from money and the external fi nance premium performs best.

‘Operating leverage’describes the extent to which a …Firm’s operating costs are fi…xed in the short term. Operating leverage ampli…es the earnings impact of a change in revenues; an effect which is further amplified by fi…nancial leverage and by non-proportionality in the tax system. Since the costs of adjusting capacity are likely to vary depending on the nature of the inputs, we expect to see sectoral differences in operating leverage around the business cycle and, indeed, differential adjustment costs underlie the distinction between cyclical and non-cyclical fi…rms that is popular with fi…nancial market practitioners. We fi…nd using a large data set on quoted UK companies between 1966 and 2010 that there are significant differences among sectors in the way it which operating leverage adjusts.

Using a data set from 1939 to 1994, we are able to provide a much longer perspective on the behaviour of house prices in the UK than is common in the literature. This allows us to look at the effects of a number of factors such as real income, demography, interest rates and the housing stock over a number of business cycles and periods of low and high inflation. We find that the single most important determinant of real house prices is real income. Over the last 60 years real house prices have risen broadly in line with income. Nevertheless, there have also been protracted periods of disequilibrium associated with demographic shifts and building society lending. We also find that the adjustment of house prices to innovations in income depends upon whether real house prices are above or below the trend implied by the long run determinants of house prices. Real house prices come back towards equilibrium much more quickly when they are above the cointegrating relationship than when they are below.

The relationship between inflation and price variability has been of interest to economists for many years. Recently, Ball and Mankiw [1995] have proposed a menu-cost model of price stickiness in which the skewness of relative price infla tion matters as well as the standard deviation. In this paper their model is test ed on Japanese wholesale price data. The results are mixed. When we use the single equation approach of Ball and Mankiw the results appear to favour their model. However, once we condition inflation on the growth in the money stock and allow for the simultaneity of inflation and relative price variability pre d i c t ed by a Lucas type misperceptions model, then the effects postulated by Ball and Mankiw largely disappear, while inflation seems to drive both the standard devi

Unpredictable fluctuations in the exchange rate can increase the uncertainty that suppliers face in overseas markets if contracts are written in foreign currency. There is an extensive literature on how the volatility of exchange rates can affect trade patterns. In this paper, the author does two things. First he examines how exchange rate uncertainty can affect both the supply of and demand for exports. He then uses a generalized ARCH process to represent the volatility of the exchange rate. Our results suggest that exchange rate volatility does have a role to play in explaining the supply of exports but does not have a significant effect on the demand for exports. However, the effect, though significant statistically, is small. Copyright 1995 by Scottish Economic Society.

This paper argues that factor demand linkages can be important for the transmission of both sectoral and aggregate shocks. We show this using a panel of highly disaggregated manufacturing sectors together with sectoral structural VARs. When sectoral interactions are explicitly accounted for, a contemporaneous technology shock to all manufacturing sectors implies a positive response in both output and hours at the aggregate level. Otherwise there is a negative correlation, as in much of the existing literature. Furthermore, we find that technology shocks are important drivers of the business cycle. © 2012 The President and Fellows of Harvard College and the Massachusetts Institute of Technology.

The consistent threshold estimation method is used to improve the threshold specification of the Granger-Lee asymmetric error correction model. Although only previously considered in the context of univariate analysis, the approach is found to uncover asymmetry undetected under the typical mean-based partitioning scheme of the Granger-Lee method.

1. New instruments of monetary policy Jagjit S. Chadha and Sean Holly 2. Liquidity and monetary policy Douglas Gale 3. Interest rate policies and the stability of banking systems Hans Gersbach and Jan Wenzelberger 4. Handling liquidity shocks: QE and Tobin's q Marcus Miller and John Driffill 5. Asset purchase policies and portfolio effects: a DSGE analysis Richard Harrison 6. Financial intermediaries in an estimated DSGE model for the UK Stefania Villa and Jing Yang 7. Unconventional monetary policy, central bank balance sheets and long term forward rates Sharon Kozicki, Eric Santor and Lena Suchanek 8. Non-standard monetary policy measures and monetary developments Domenico Giannone, Michele Lenza, Huw Pill and Lucrezia Reichlin 9. Quantitative easing: one year on Spencer Dale 10. What saved the banks: unconventional monetary or fiscal policy? Mike Wickens 11. Non-conventional monetary policies: three views from the DSGE literature Evren Caglar, Jack Meaning, Alex Waters, James Warren and Jagjit Chadha.

We assess recent developments in monetary policy practice following the financial crisis drawing on papers from a specially convened conference in March 2010. In particular, we consider why central banks throughout the world have injected substantial quantities of liquidity into the financial system and seen their balance sheets expand to multiples of GDP. We outline the rationale for balance sheet operations: (i) portfolio balance of the non-bank financial sector; (ii) an offset for the zero bound; (iii) signalling mechanism about medium term inflation expectations and (iv) the alleviation of the government's budget constraint. We briefly outline the recent experience with QE and draw a distinction between liquidity and macroeconomic stabilisation operations.

This paper argues that important insights into the business cycle can be obtained by exploring the micro-structure of macroeconomic fluctuations. We fit firm-level growth data with the Asymmetric Exponential Power density, which accounts for asymmetric dispersion and kurtosis on either side of the modal rate. Three novel results are reported. First, firms in the left side of the distribution, that is firms that are growing more slowly or declining, are typically more responsive to aggregate shocks than those in the right side of the distribution. Second, trending behavior in the volatility of firm growth is predominantly driven by increasing dispersion in the growth of highly performing firms. Last, we deliver evidence in support of the view that shifts in the probability mass on either side of the mode may act as important propagators of business fluctuations. The analysis points to financial frictions as one of the mechanisms capable of inducing non-linear micro adjustment consistent with both aggregate and cross-sectional dynamics.

In this paper, using composite predictors we examine whether the use of survey information on consumer confidence would have helped to predict fluctuations in economic activity. We also consider the implications of the new literature on time-series modelling when the underlying processes are not stationary. We then examine what implications this has for the construction of composite predictors. We find that it is essential that any forecast—used as part of a composite predictor—is co-integrated with the outcome. It is likely that this will hold in practice, but if it does not then the forecast errors will be non-stationary and the interpretation of the composite predictor hazardous.

While much of the literature on cross-section dependence has focused on estimation of the regression coefficients in the underlying model, estimation and inferences on the magnitude and strength of spillovers and interactions has been largely ignored. At the same time, such inferences are important in many applications, not least because they have structural interpretations and provide useful inferences and structural explanation for the strength of any interactions. In this paper we propose GMM methods designed to uncover underlying (hidden) interactions in social networks and committees. Special attention is paid to the interval censored regression model. Small sample performance is examined through a Monte Carlo study. Our methods are applied to a study of committee decision making within the Bank of England's Monetary Policy Committee. RESUME Bien qu'une grande partie de la litterature sur la dependance transversale se soit concentree sur l'estimation des coefficients de regression dans le mo...

This paper provides a method for the analysis of the spatial and temporal diffusion of shocks in a dynamic system. We use changes in real house prices within the UK economy at the level of regions to illustrate its use. Adjustment to shocks involves both a region specific and a spatial effect. Shocks to a dominant region - London - are propagated contemporaneously and spatially to other regions. They in turn impact on other regions with a delay. We allow for lagged effects to echo back to the dominant region. London in turn is influenced by international developments through its link to New York and other financial centers. It is shown that New York house prices have a direct effect on London house prices. We analyse the effect of shocks using generalised spatio-temporal impulse responses. These highlight the diffusion of shocks both over time (as with the conventional impulse responses) and over space.

This paper argues that factor demand linkages can be important for the transmission of both sectoral and aggregate shocks. We show this using a panel of highly disaggregated manufacturing sectors together with sectoral structural VARs. When sectoral interactions are explicitly accounted for, a contemporaneous technology shock to all manufacturing sectors implies a positive response in both output and hours at the aggregate level. Otherwise there is a negative correlation, as in much of the existing literature. Furthermore, we find that technology shocks are important drivers of the business cycle.

We expect a firm's competitive advantage to manifest itself in a return on invested capital that is higher than the opportunity cost of capital. Deviations of returns from the cost of capital are a signal for competitive entry or for exit, while the speed of convergence indicates the strength of competitive forces. It is widely believed that, in some sense, the world is becoming more competitive, and that this is may be the effect of globalisation, facilitated by innovations in information technology. It also be the effect of determined actions by governments over two or three decades, to deregulate and open up markets to competition. So for example, in Europe one purpose of both the common currency and the Single Market project was to accelerate the process of economic convergence and, presumably, of competitive convergence. This paper examines the process of competitive convergence in profitability of listed companies in 7 countries of the European Union. We cast our examination of the convergence process in terms of three questions. The first is whether, and to what extent, we observe convergence in profitability through time. The second question is whether there are national differences in the extent of convergence or the speed at which it takes place. Thirdly, we look at the dynamics of convergence through time to see whether there is evidence that convergence in profitability has become more rapid, by which we mean above average or below average profitability persists for a shorter space of time because of increases in competition. The extent to which this can be related to economic and monetary convergence in the European Union remains an open question.