Editorial

A visit to the optician and acquiring a new pair of spectacles puts a new perspective on the world. What was not in focus comes into focus, and small invisible print suddenly becomes readable. This experience led to thoughts about why we are interested in spatial economics. Why is a spatial perspective valuable? The answer, we would argue, is that it allows us to put on a particular pair of spectacles, so that we see what was perhaps unclear and gives a vision that is informative. Considering economic distributions from the spatial angle, in other words doing economic geography, gives a special perspective. We instantly become aware of inequalities that are with us now, between rich and poor, developed and undeveloped. Economic time series are, of course, the meat and drink of the economist's trade, giving insight into the way economies evolve. But they can be misleading. Taking a whole economy and examining its progress in terms of the level of GDP per capita or price levels conceals the diversity in levels and growth rates lying behind the aggregate data. Reality is much more complex than a line on a graph. Rather than one time series, let us have a multiplicity of interrelated time series; we are now developing the theoretical and quantitative tools to be able to make sense of such information. Time series per se can also be misleading because they often embody changes in definition of key variables over time, so that we are not comparing like with like when we evaluate two points on the graph. For example there have been numerous changes to the UK's definition of unemployment, so whilst we can all agree that the recession is increasing the level of unemployment, we cannot be as precise as we might like to be about the numbers. Similarly, boundary definitions over time complicate matters. Anyone working with employment data taken from Nomis, a service provided by the UK's Office for National Statistics to give free access to labour market statistics from official sources, will be aware of the many geographies that exist, some of which are now redundant, so that care has to be taken when measuring changing employment levels across local areas through time. What a spatial economic perspective does is make prominent the advantages of cross-sectional data analysis, which avoids some of these issues. Many developing countries do not have long series of data to allow in-depth time series econometrics, but there are often sufficient cross-sectional data for regions within countries to permit insightful analysis. Similarly, cross-country analysis has long been a valuable tool allowing analysts of international economic growth variations to evaluate competing theoretical models.

When we put on our spatial economics spectacles, what do we see about the ongoing global recession in the wake of the sub-prime mortgage crisis? Diversity of impact is the answer; some areas have been relatively immune, thus far, while others have been hit very hard indeed. With regard to property prices, we can do no better than quote Behrens & Robert-Nicoud (2009, p. 468), who argue that ‘though the crisis is global, it does not affect all countries or regions equally deeply’. The Economist's house price indicator showed US house prices falling dramatically, while at the same time they continued to rise, albeit at a slower pace than previously, in Hong Kong and Singapore. At the regional level we observe similar variation; for example, within the USA there have been significant local contrasts. As Behrens & Robert-Nicoud (2009, p. 468) note, ‘all of this reminds us that location does matter’. But spatial economics is not just about eyeballing data on maps, it is also about providing explanations for the patterns we see. Why do some locations suffer more than others from the impact of recession? What does theory tell us about the likely path of development in the future? Prominent among our theories is new economic geography (NEG). This has been much heralded in this journal (Brakman & Garretsen, 2009) and elsewhere—perhaps it can come to the rescue and provide some insights?

When we look at the basic and pure form of NEG one thing is obvious—it is self-contained. The distribution of economic activity is determined endogenously. In some versions, real wage differences drive migration and in this way economic activity relocates, until we reach one of the several long-run equilibria that are possible. Can this theory predict anything about a global system suffering from severe shock? It says nothing about sub-prime mortgages, the credit crunch and a banking system that has had to be rescued by taxpayers’ money. Can we tweak the model, so that it is helpful in predicting the long-run outcome of the recession? Clearly we need a different model if that is what we are interested in. But there is one prediction from the model at least that does provide valuable insights—it is what Behrens & Robert-Nicoud refer to as the most fundamental result in Krugman's 1980 paper, namely the home market effect. Big economies provide advantages to firms because they have larger markets, lower trade costs and greater increasing returns. Recession can mean loss of markets, in which case protectionism rears its head. Adding tariffs to restrict imports and protect home industry is tantamount to raising trade costs. Also, there is an increase in cross-border transaction costs because of the collapse of international banking. Increasing trade costs (broadly defined) are particularly bad news for all those regions or locations that are ‘remote’ and/or not part of a large market. This is very much the take on NEG that comes out of the recent World Development Report by the World Bank (2009), which argues that long-term growth and development will be promoted most effectively by policies that encourages economic integration.

There has been some exploration of shock effects within the NEG context. These are temporary shocks, which hopefully the global recession is also. Some ‘natural’ experiments suggest that the processes described by the NEG model are so profound that the economic system reverts to its initial path (leading to one of several equilibrium states) once the impact of the shock has dissipated. The paper by Davis & Weinstein (2002), for example, looks at the outcome of the rebuilding of Japanese cities in the post-war era. Did they emerge as before, as though nothing had happened when in fact they were razed to the ground by Allied bombing? The answer is broadly yes; the economic forces were strong and overcame the temporary disruption of warfare. However, other work has shown that reversion to what was is not an inevitable outcome. Bosker et al. (2008) show that the post-war urban system of Germany is very unlike the pre-war one. The devastation in Germany was so profound, and the economic, political and institutional re-alignment that ensued so different from what existed before, that the urban system took on a very different shape. The division of Germany and the emergence of strong federal states were all-important. What this tells us is that there are fundamental forces at work creating an economic geography that will withstand temporary economic shocks, but hysteresis is also a possibility, with permanent effects, in terms of geography, from a temporary impact. Certainly, in our analysis of the current shock to the world economy, it appears that if radically different institutions emerge, what we will see in the future will not be simply a rerun of what we have seen in the past. However, predicting the precise nature of any NEG is a very difficult task, which can only be described as work in progress for the spatial economics community.

In the first paper of this issue, Peter Nijkamp & Soushi Suzuki (2009) apply an innovative development of data envelopment analysis (DEA) to analyse efficiency improvement in local government finance in Japan. DEA, which is also known as frontier analysis, has become ‘an established benchmark tool’ in efficiency strategies, and has been used extensively in microeconomics. However, applications to analyse interregional productivity differences are almost unknown, exceptions being Angeriz et al. (2006) and Roberts et al. (2007). Nijkamp & Suzuki's application, based on Japanese cities, adds to the small number of regional DEA analyses. At its simplest, we can conceive of DEA as a graph with two axes measuring, say, productivity in two sectors. The productivity of each region (or country or city or firm or other unit of analysis) in terms of output per unit of input in each of the two sectors defines each region's position on the graph. As spatial economists, we might be interested in plotting the regions in terms of industrial and agricultural productivity. Some regions will clearly perform better than others, and the graph allows us to draw an efficiency frontier (or convex hull) which envelopes the data (hence the name DEA). The efficiency frontier connects the best-performing regions and is where other regions, striving to reach the highest standard of productivity performance, should be. The actual positions of regions with respect to the efficiency frontier allow analysis of what needs to change in each region to achieve what is commonly referred to as ‘best practice’. For instance, a region may reduce its inputs while keeping output the same, or increase its production while keeping inputs constant, or perhaps some combinations of both. DEA can also be used to monitor the shifting positions of regions with respect to the efficiency frontier over time. In practice, of course, there can be numerous sectors and DEA then becomes an application of a nonlinear optimization programme which can be solved using linear programming methods. As academics we often strive to develop new tools, as in Nijkamp & Suzuki (2009), but the standard tools are readily available as a point of entry into the subject matter, and these have powerful capabilities which can be applied to problems of academic interest. Software that can be used for DEA includes Solver (Microsoft Excel), Frontier Analyst by Banxia Software, and Performance Improvement Management Software by DEASoftware.

Charles Okeahalam (2009) studies bank branch location in South Africa. Each branch is treated as a point in space, and, given this, Okeahalam uses techniques familiar to ecologists in their studies of the spatial distribution of trees and plants. Likewise, geographers have long been aware of the usefulness of point pattern analysis (as described, for example, by Boots & Getis, 1988) and there are countless applications in disciplines as diverse as archaeology, biology and astronomy. In economics, the recent spatial perspective has also seen application of point-pattern methods. For example, Duranton & Overman (2008) use a point-pattern methodology to explore the detailed location patterns of UK manufacturing industries. There are reasons why banks may not be distributed at random across space. Trees need water and fertile soil; likewise, banks also need inputs, in the form of customers with enough money to be able to open an account. However, as with trees, banks cannot be too close to each other, it seems. If they are, they may suffer from competition effects and not prosper as they might otherwise do. So a degree of spatial monopoly is also advisable. What this indicates is that a random (Poisson) process is not a good model for the distribution of either trees or bank branches, since random allocation will produce clustering by chance. There are many alternative models to choose from, and Okeahalam (2009) considers a range of options. Intriguingly, he finds evidence that bank branches are clustering together, which seems irrational in a competitive world. The spatial behaviour of banks suggests that they do not live in a competitive world, but may be involved in some form of oligopolistic collusion. Of course, we shall never know, because bank branch location decisions are taken behind closed doors, but their behaviour is suggestive of something less than true competition.

The paper by Jihai Yu & Lung-fei Lee (2009), entitled ‘Spatial Nonstationarity and Spurious Regression: The Case with a Row-normalized Spatial Weights Matrix’, takes a look at some work initiated a decade ago by our managing editor (Fingleton, 1999) who explored the question of spurious spatial regression and related issues. Consider, for example, the data-generating process y ₁=ρ ₁ W ₁ y ₁+ε ₁ in which the dependent variable y ₁ is an n×1 vector and n is the number of locations, the endogenous spatial lag W ₁ y ₁ is an n×1 vector, ρ ₁ is the spatial lag coefficient, and ε₁ is an n×1 vector of errors. In this, W ₁ is a non-stochastic n×n weights matrix, intended to capture the strength of connectivity between pairs of locations, typically standardized so that rows sum to equal 1. Assume that there is also a parallel process y ₂=ρ ₂ W ₂ y ₂+ε ₂ with similar definitions. The essential problem is that as the ρ s approach 1, we encounter problems similar to those encountered in time series analysis, where completely independent series such as y ₁ and y ₂ appear to be related, producing so-called spurious spatial regression. Spurious regression led to a revolution in time series methodology (cointegration and error correction modelling) to handle the consequences of non-stationary resulting from the presence of unit roots. Such a revolution has not occurred in the analysis of spatial series for various reasons, for example with multilateral dependence rather than unidirectional time series dependence the problem of spurious spatial regression, and its resolution, becomes somewhat different. There are only a handful of papers on this topic, of which that by Jihai Yu & Lung-fei Lee (2009) is the latest. The Monte Carlo results of Yu & Lee (2009) essentially parallel the results given in Fingleton (1999), although, interestingly, they find that spurious regression is stronger in time series than in spatial series with near unit root processes.

The paper by Bob Rowthorn (2009), entitled ‘Returns to Scale and the Economic Impact of Migration: Some New Considerations’, reminds us that there is new theory being created that is not simply an offshoot of NEG but is an example of geographical economics, and, unsurprisingly, it too makes assumptions about returns to scale. Increasing returns is a problem that Rowthorn has had in mind for a very long time, way before the current wave of theory brought increasing returns within the comfort zone of neoclassically oriented economists. Rowthorn was indeed critical of the way in which economists typically handled increasing returns in the pre-Krugman era, namely in the form of Verdoorn's law,1 which at its simplest is a linear relationship between the exponential rate of growth of manufacturing employment (the dependent variable) and manufacturing output growth, which is treated as exogenous. The coefficient on output growth usually indicates that increasing returns to scale exist in the manufacturing sector. However, in what has been referred to as ‘Rowthorn's critique’, Bob Rowthorn turned this equation around, making output growth depend on employment growth, and this led to a serious debate about whether there was real evidence for increasing returns. The best place to read about all this is in the book that co-editor John McCombie co-edited (McCombie et al., 2003). In any case, subsequent work on Verdoorn's law and the weight of other evidence has led us to the position that probably a majority of spatially aware economists adhere to in the present era, that is that increasing returns to scale are a real phenomenon, and we cannot properly understand disparities in economic development without them. Nonetheless, in the paper in the current issue Rowthorn does hedge his bets by embodying alternative assumptions about returns to scale, in order to assess the economic impact of migration, developing further the thesis set out in his earlier paper published in this journal (Rowthorn, 2008).

As evidence that we are not restricted to publishing papers by distinguished economists with significant reputations in our field, but are open to any contribution of high quality, our final paper is by a young up-and-coming researcher Vassilis Tselios (2009), whose paper is entitled ‘Growth and Convergence in Income Per Capita and Income Inequality in the Regions of the EU’. While above we have emphasized the role of increasing returns to scale, that assumption remains an assumption rather than an established fact. In the case of Tselios, the model underpinning his econometrics is the neoclassical growth model, which, of course, embodies diminishing returns to inputs and usually2 a constant returns to scale assumption, so that doubling inputs only doubles outputs. Conditional on this, the model makes some predictions about the reduction of income per capita disparities over time. One might argue that, certainly at the global scale, this flies in the face of reality, because what we see is a definite lack of convergence. Likewise, at the level of EU regions, it is evident that while national economies have tended to converge, regions within countries have tended to become more dissimilar. However, a saving grace of the neoclassical growth model is the phenomenon of conditional convergence, so that each economy converges to its own steady state, not a global one. So, we can have constant returns to scale, with diminishing returns to inputs, and yet permanent disparities in GDP per capita levels. This is what Tselios assumes in his analysis. Although this is not particularly novel, what is novel is the application of state-of-the-art panel regression models with spatial interaction effects, and, interestingly, he finds that ‘the process of regional convergence in income inequality takes place even without conditioning variables’.

Notes

1. Nowadays, Verdoorn's law is only one of several ways to accommodate increasing returns.

2. While constant returns to scale is a standard assumption, it is not essential to the theory. Solow (1994) points out that ‘the model can perfectly well get along without constant returns to scale’, although its presence facilitates simplification.