Market Potential, panel data, and aggregate fluctuations: All that glitters is not gold

Market Potential, panel data, and aggregate fluctuations: All that glitters is not gold | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Market Potential, panel data, and aggregate fluctuations: All that glitters is not gold Fernando Bruna This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4979299/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The New Economic Geography (NEG) provides a historical explanation for the spatial agglomeration of economic activity. One of its predictions, the ‘wage equation’, relates regional income to market accessibility. Although the NEG is a long-term theory, empirical literature has tested it using panel data methods, which capture short-term relationships between temporal changes in variables. For a sample of European regions, I show that panel data estimations of the wage equation identify only potential spillover effects of the European business cycle on the synchronic evolution of regional per capita income. That is, the panel data results are not due to the mechanisms proposed by the NEG. The paper concludes with a cautionary note about misinterpretation of panel data estimations. JEL Classification : C18, C23, F12, R12, E32 NEG agglomeration wage equation fixed effects first differences European cycle Figures Figure 1 Figure 2 1 Introduction Krugman’s ( 1991 , 1993 ) development of the New Economic Geography (NEG) provided an explanation of economic agglomeration—that is, of the formation of clusters in the spatial distribution of economic activity. The so-called ‘wage equation’ of the NEG is a long-run prediction relating higher income to locations with higher Market Potential, an indicator of the accessibility and market size of the other regions. The cross-sectional form of the equation has been widely studied in the empirical literature (Redding 2011 ). More generally, location theory establishes “fundamental determinants” of economic activity (Redding and Venables 2004 ) based on long-term consequences of centrifugal and centripetal agglomeration forces. These historical explanations should thus be tested using cross-sectional data (Baltagi and Griffin 1984 ), not panels of data at intervals of one or a few years. Starting with Hanson ( 2005 ) and Mion ( 2004 ), however, this equation has been estimated using panel data. The author who has studied the NEG wage-type equation most using panel data techniques is Bernard Fingleton (e.g., Fingleton ( 2008 ), Baltagi et al. ( 2014 )). Other important articles on the empirics of the NEG have used panel data: Breinlich ( 2006 ), Boulhol and de Serres ( 2010 ), de Sousa and Poncet ( 2011 ), Head and Mayer ( 2011 ). Their results are not satisfactory. Panel data models are designed to capture short-term relationships. Why is an indicator of Market Potential statistically significant in panel data models if that indicator is designed to synthesize forces underlying location decisions over centuries? The goal of this paper is to provide an explanation for this anomaly. It employs European regional data to study the properties of the time series of the time-demeaned data used to derive fixed effects panel data estimates. I illustrate the intuitions behind the black box estimations through a graphical and correlation analysis for a few regions with very different access to European markets. Finally, I compare estimation results obtained using the indicator of Market Potential and an artificial indicator calculated for the whole European sample, the evolution of which summarizes the European business cycle. The conclusions are as follows. The evolution of income per capita in European regions displays high synchronicity (Giannone and Reichlin 2006 ; Kunroo 2023 ). The average changes of regional income per capita may be captured by either the average variations of regional Market Potential or the variations of an aggregated indicator with identical European data for all the regional observations of the same year. Average temporal changes in regional Market Potential thus capture only the common economic cycle, reflecting synchronicity, or global spillovers. For the case of Europe at least, the panel data results of a NEG equation should not be interpreted in terms of the NEG hypotheses. This result is another example of the ‘Marshallian’ (Duranton and Puga 2004 ) or ‘observational’ equivalence of the NEG (Head and Mayer 2004 , p. 2,663; Bruna 2024a ). Some of these conclusions may be generalized to many studies in different fields, that ignore the statistical properties of the transformed data when interpreting results from panel data models. Fixed effects estimations are usually justified by the need to control for time-invariant regional factors. Researchers who attend only to this argument may forget that results from cross-sectional and panel models have different interpretation. Estimating an equation with data on first differences or time-demeaned data means studying the effects of temporal changes in the explanatory variable on temporal changes in the dependent variable. Although this is well known, it is not discussed in many papers comparing cross-sectional and panel data estimates. The remainder of the paper is structured as follows. The second section introduces the wage equation and the literature estimating it with panel data. Section 3 reviews the interpretation of estimation results when using cross-sectional and panel data models. Section 4 presents the data and methodology, and Section 5 the results. The final section draws conclusions. 2 The empirical wage-type equation and panel data A variety of NEG models focus on different mechanisms to explain agglomeration (Baldwin et al. 2003 ), even in the absence of any pure external economies. Using Krugman’s ( 1993 ) model of metropolitan areas as a benchmark and assuming all other conditions equal, firms that have an incentive to concentrate production at a limited number of locations prefer locations with good access to markets. Yet access to markets will be good precisely where a large number of firms choose to locate. This positive feedback loop drives the formation of urban centers. It also implies that the location of such centers is not wholly determined by the underlying natural geography, that there are typically multiple locational equilibria. To capture this intuition, the formal model has three features. First, location matters because of transportation costs. Second, some immobile production factors provide a form of ‘first nature’ that constrains the possible spatial structure of the economy. Finally, economies of scale in the production of at least some goods provide an incentive for concentration. The existence of the metropolis thus creates a ‘second nature’ that drags the optimal location of firms with it. Krugman’s initial models “suggest an explanation for the nineteenth-century formation of real-world core-periphery patterns, notably the emergence of the United States’ manufacturing belt and Europe’s ‘hot banana’” (Krugman 2011 ). Krugman recognizes, however, the increasing importance of technology and information spillovers: “Ever since the beginnings of New Economic Geography, and up until very recently, I and others have had a slightly guilty sense that we were talking about was the past, not the present, and much less the future (Krugman 2011 ). In sum, the NEG establishes “fundamental determinants” of economic activity (Redding and Venables 2004 ) based on long-term consequences of agglomeration forces. The so-called ‘wage equation’ is a market-clearing condition of the basic NEG model in which labor is a unique production factor. I will now present a one-sector generalized form of this equation in which the dependent variable is not wages but marginal costs and thus encompasses many of the ‘wage equations’ previously derived in the literature (Combes et al. 2008 , Chap. 12; Bruna 2015 ). For a firm in region \(\:i\) ( \(\:i=1,\dots\:,\:\:R\) ) with zero profit, the maximum value of marginal cost ( \(\:{m}_{i}\) ) the firm can afford to pay depends on its access to markets. Marginal cost is thus proportional to firm’s (region’s) Real Market Potential ( \(\:{RMP}_{i}\) ) (to use Head and Mayer’s ( 2006 ) term) or Market Access (to use Redding and Venables’ ( 2004 ) term), as follows: $$\:{m}_{i}=Constant·{\left({RMP}_{i}\right)}^{\frac{1}{\sigma\:}}=Constant·{\left(\sum\:_{j}^{R}{{T}_{ij}}^{1-\sigma\:}\frac{{E}_{j}}{{S}_{j}}\right)}^{\frac{1}{\sigma\:}}$$ (1) where, \(\:\sigma\:>1\) is the elasticity of substitution between any pair of varieties of goods in a love-of-variety utility function. \(\:{RMP}_{i}\) is a weighted sum of the market conditions in the other \(\:j\) regions, where \(\:{T}_{ij}\) is the trade cost from firm-or-region \(\:i\) to region \(\:\:j\) , and \(\:{E}_{j}\) is total expenditure in \(\:j\) . \(\:{S}_{j}\) is called the ‘competition index’ to stress that it measures the level of competition among varieties in \(\:j\) market, given consumers’ characteristic tastes. The NEG’s long-term prediction is that firms and regions with higher Market Potential tend to earn more profit and pay higher remuneration to production factors, resulting in higher regional income per capita. If trade costs are proxied by physical distances ( \(\:{d}_{ij}\) ), the explanatory variable of Eq. (1) becomes \(\:{RMP}_{i}=\sum\:_{j}^{R}{{d}_{ij}}^{1-\sigma\:}\frac{{E}_{j}}{{S}_{j}}\) . As in some previous literature, marginal cost ( \(\:{m}_{i}\) ) can be proxied by data on gross value added per capita ( \(\:GVApc\) ) and total expenditure ( \(\:{E}_{j}\) ) by data on \(\:GVA\) . Harris’ ( 1954 ) index of accessibility to markets, in contrast, can be defined as \(\:{HMP}_{i}=\sum\:_{j}^{R}{{d}_{ij}}^{-1}{GVA}_{j}\) . Since a \(\:-1\) trade elasticity to distance is an extremely robust empirical finding in the literature on gravity equations (Head and Mayer 2014 ), the major difference between \(\:{RMP}_{i}\) and \(\:{HMP}_{i}\) lies in \(\:{S}_{j}\) , which is not directly measurable in NEG theory. For samples of European regions, Breinlich ( 2006 ) and Head and Mayer ( 2006 ) obtained similar empirical results using both Harris’ indicator and the more sophisticated procedure of Redding and Venables ( 2004 ) to proxy \(\:{S}_{j}\) . Bruna ( 2024a ) shows that both approaches capture the core-periphery spatial patterns in the data in a similar way. Moreover, when calculating Market Potential with areal data, the access of firms to markets also depends on the market size of their own region—that is, on so-called self-potential or Internal Market Potential. Not only does considering this potential in applied work add endogenous information, but the measurement of internal distances ( \(\:{d}_{ii}\) ) is controversial (Bruna 2024b ). This study therefore avoids self-potential and uses External Market Potential, defined as \(\:{EMP}_{i}=\sum\:_{j\ne\:i}^{R-1}{{d}_{ij}}^{-1}{GVA}_{j}\) . Taking natural logarithms to Eq. (1) and replacing variables with my proxies, I thus obtain the following estimable cross-sectional equation: $$\:\text{log}{GVApc}_{i}=C+{\beta\:\text{log}{EMP}_{i}+u}_{i}$$ (2) Hanson ( 2005 ) and Mion ( 2004 ) estimated the first panel data model of the wage equation and discussed the advisability of using the generalized method of moments (GMM) or nonlinear least squares. They also carefully discussed justification of a panel data version of Eq. (2), including time-invariant individual effects, as in Eq. (5) below. Breinlich ( 2006 ) justified these fixed effects to capture persistent factors such as institutional quality or climatic or other amenities of a region. Fingleton ( 2008 ) assumed that the dependent variable in a time-varying version of Eq. (1) also depends on level of efficiency ( \(\:{A}_{it}\) )—a useful trick to model complexity by making \(\:{A}_{it}\) depend on past efficiency, the efficiency of neighboring regions (spillovers), and time-invariant regional characteristics. For the NEG equation and areal data, Fingleton applied the fixed effects estimator and the Kapoor-Kelejian-Prucha (KKP) GMM estimator of random effects models, including serially and spatially autocorrelated disturbances (Fingleton 2008 , 2009 ; Fingleton and Fischer 2010 ; Gómez-Antonio and Fingleton 2012 ; Fingleton and Palombi 2013 ). Amaral et al. ( 2010 ) and Wang and Haining ( 2017 ) have also used this methodology. Further, Fingleton was a coauthor in Baltagi et al.’s ( 2014 ) proposal of a KKP method to estimate a complex spatial econometric dynamic panel data model, proposal that is illustrated with a NEG wage-type equation. Using microdata, Fingleton and Palombi ( 2013 ) and Fingleton and Longhi ( 2013 ) estimated a fixed effects panel data model for individuals’ wages. Some panel data literature has used the NEG framework to study other topics (e.g., Gómez-Antonio and Fingleton 2012 , for public capital; de Sousa and Poncet 2011 , for migration). For instrumental variables estimation, Boulhol and de Serres ( 2010 ) and Head and Mayer ( 2011 ) included time-invariant instruments and time dummies in the first stage regression. Some of these studies have used samples of European regions (Breinlich 2006 ; Fingleton and Fischer 2010 ; Baltagi et al. 2014 ). Others used data for one European country—Mion ( 2004 ) for Italy, Gómez-Antonio and Fingleton ( 2012 ) for Spain, three of Fingleton’s studies for the United Kingdom, and Rokicki and Cieślik ( 2023 ) for Poland. Although many of these panel data studies find significant effects of Market Potential on income per capita, their results may be described as an anomaly. As the next section shows, panel data estimates capture short-term effects, so those significant effects are an unexpected result from a theory explaining the historical causes of agglomeration. 3 Interpreting panel data estimations of the NEG equation To establish key ideas, it is useful to review interpretation of the coefficients in several econometric models. Readers who feel comfortable with these basics may skip to the end of the section. The cross-sectional wage-type equation derived from the NEG produces an estimable equation for region \(\:i\) ( \(\:i=1\dots\:R\) ) in a given period \(\:t\) , such as the following: $$\:{y}_{i}=C+\beta\:{x}_{i}+{u}_{i}$$ (3) Pooling data for T periods ( \(\:t=1\dots\:T\) ) in each region \(\:i\) (group), we get the following model: $$\:{y}_{it}=C+\beta\:{x}_{it}+{u}_{it}$$ (4) The fixed effects extension of Eq. (4) includes unobserved time-invariant individual effects, \(\:{u}_{i}\) , as follows: $$\:{y}_{it}=C+\beta\:{x}_{it}+{u}_{i}+{u}_{it}$$ (5) where \(\:{u}_{i}\) collects omitted regional variables assumed to have a roughly constant role in explaining regional differences of \(\:{y}_{it}\) . Averaging Eq. (5) over the \(\:T\) periods produces the following between-group model, capturing cross-sectional average relationships: $$\:{\stackrel{-}{y}}_{i}=C+\beta\:{\stackrel{-}{x}}_{i}+{u}_{i}+{\stackrel{-}{u}}_{i}$$ (6) Subtracting Eq. (6) from (5) produces the estimable fixed effects panel model, with the variables as deviations to the regional means: $$\:{y}_{it}-{\stackrel{-}{y}}_{i}=\beta\:\left({x}_{it}-{\stackrel{-}{x}}_{i}\right)+\left({u}_{it}-{\stackrel{-}{u}}_{i}\right)$$ (7) This is the within-group model, and the transformed variables are temporal variations within each region. We can estimate the model using standard ordinary least squares (OLS) by pooling the demeaned data. The \(\:\widehat{\beta\:}\) estimate will be identical to that of Eq. (4) after including (controlling out) \(\:R-1\) regional dummy variables. Boulhol and de Serres ( 2010 )—and Acemoglu et al. ( 2008 ) in another field—summarize the standard argument in favor of defining the model as in Eq. (7). The major source of potential bias in a regression of Market Potential on income per capita is region-specific, historical factors that influence both Market Potential and economic development. If these omitted characteristics are, on first approximation, time-invariant ( \(\:{u}_{i}\) ), inclusion of fixed effects will remove them and this source of bias. Paying attention only to that possible unobserved individual heterogeneity has, however, led some researchers to mistaken conclusions when interpreting results, as described below. The cross-sectional, pooled, and between models of Equations (3), (4), and (6), respectively, are about relative levels of regional variables. The estimate of these models, which I term \(\:{\widehat{\beta\:}}_{c}\) , captures the effect of cross-sectional variations of \(\:{x}_{i}\) on cross-sectional variations of \(\:{y}_{it}\) . A cross-sectional wage equation thus implies that regions with higher Market Potential will be richer. Conversely, the estimate from the fixed effects Eq. (7), which I term \(\:{\widehat{\beta\:}}_{f}\) , captures the effect of time variations of \(\:{x}_{it}\) on time variations of \(\:{y}_{it}\) . In Acemoglu et al.’s ( 2008 ) terminology, a fixed effects panel model of the wage equation implies that regions with increasing Market Potential will become richer. This is not what the NEG predicts for a time span of either one or a few years. The NEG’s historical explanation should thus be studied using cross-sectional/pooled estimations ( \(\:{\widehat{\beta\:}}_{c}\) ), while fixed effects estimations ( \(\:{\widehat{\beta\:}}_{f}\) ) are more suitable for studying short-run relationships (Baltagi and Griffin 1984 ). To better interpret the fixed effects estimator, it is useful to compare it to a model in first differences. The time lag of Eq. (5) is the following: $$\:{y}_{it-1}=C+\beta\:{x}_{it-1}+{u}_{i}+{u}_{it-1}$$ (8) Subtracting Eq. (8) from (5) produces the following first difference estimator: $$\:{y}_{it}-{y}_{it-1}=\beta\:\left({x}_{it}-{x}_{it-1}\right)+\left({u}_{it}-{u}_{it-1}\right)$$ (9) where the first differences for period \(\:t=1\) are lost. If we use the notation \(\:{\widehat{\beta\:}}_{d}\) for the first difference estimate, its magnitude will be similar to \(\:{\widehat{\beta\:}}_{f}\) . \(\:{\widehat{\beta\:}}_{d}\) in Eq. (9) makes clearer, however, that we are estimating the short-run effects of changes in \(\:{x}_{it}\) on changes in \(\:{y}_{it}\) . Moreover, since \(\:{y}_{it}\) is the log of income per capita and \(\:{x}_{it}\) is the log of Market Potential, the first difference of the logarithm of a variable is the instantaneous growth rate of that variable, which is very similar to the discrete growth rate ( \(\:g\) ) of the variable. In sum, in a wage equation, \(\:{\widehat{\beta\:}}_{f}\) will be very similar to the estimate of a model for the growth rates of the levels of Market Potential and income per capita. Calling \(\:{X}_{it}={e}^{{x}_{it}}\) and \(\:{Y}_{it}={e}^{{y}_{it}}\) , the fixed effects estimate will be similar to that obtained with the following pooled model of the variables in levels, for \(\:t=2\dots\:T\) : $$\:{g}_{Yit}=C+\beta\:{g}_{Xit}+{u}_{it}$$ (10) As mentioned in Section 2, nothing in (long-term) location theory predicts that yearly growth rates of an indicator of regional Market Potential should have a significant impact on regional growth rates of income per capita. I, however, obtain positive significant \(\:{\widehat{\beta\:}}_{f}\) estimates below. Why? 4 Data and methodology The sample includes Eurostat regional data for 233 regions from 25 countries (but not Switzerland), for the years 1995–2022. The explanatory variable is Harris’ indicator of External Market Potential. As mentioned above, my estimation of a wage-type equation uses real \(\:GVApc\) to proxy regional marginal costs and real \(\:GVA\) to proxy regional market size. The data come from the ARDECO database (see online Supplementary Appendix for further details). Inter-regional distances ( \(\:{d}_{ij}\) ) are measured as great-circle distances between regional centroids. I now begin to disentangle the reasons we obtain a significant fixed effects estimate of Market Potential in my European wage-type equation. I start by estimating the following cross-sectional and pooled panel models, expecting to find similar values for \(\:\widehat{\beta\:}\) : \(\:\text{log}{GVApc}_{i}=C+\beta\:\text{log}{EMP}_{i}+\:{u}_{i}\) Model 1 \(\:\text{log}{GVApc}_{it}=C+\beta\:\text{log}{EMP}_{it}+\:{u}_{it}\) Model 2 I then estimate the model in first differences, as in Eq. (9), and the within-region model, as in Eq. (7), expecting to find similar values for \(\:\widehat{\beta\:}\) , as follows: \(\:\text{log}{GVApc}_{it}-\text{log}{GVApc}_{it-1}=C+\beta\:(\text{log}{EMP}_{it}-{log}{EMP}_{it-1})+({u}_{it}-{u}_{it-1})\) Model 3 \(\:\text{log}{GVApc}_{it}-\stackrel{-}{{log}{GVApc}_{i}}=C+\beta\:(\text{log}{EMP}_{it}-\stackrel{-}{{log}{EMP}_{i}})+({u}_{it}-\stackrel{-}{{u}_{i}})\) Model 4 For a cross-sectional European sample, Bruna ( 2024a ) shows that the estimation results of a wage-type equation are spurious because the data are spatially nonstationary. The spatial distribution of Market Potential and many other variables roughly matches the core-periphery spatial patten of European regional income, which cannot be used to confirm the NEG explanation. Inspired by this finding, I conjecture that the significant effect of Market Potential in the fixed effects estimation of Model 4 might be due to a common time pattern in the series of GVA per capita and EMP. To test this hypothesis, I calculate an artificial indicator of European Market Potential ( \(\:EuMP\) ). As with the definition of \(\:{EMP}_{it}=\sum\:_{j\ne\:i}^{R-1}{{d}_{ij}}^{-1}{GVA}_{jt}\) , I build the following indicator \(\:{EuMP}_{t}={{d}_{m}}^{-1}\sum\:_{j=1}^{R}{GVA}_{jt}\) , where \(\:{d}_{m}\) is the median of the average distances from each region to each of the others. Note that \(\:{EMP}_{it}\) changes by region and period, whereas \(\:{EuMP}_{t}\) is the same for any region in the same period and captures the aggregate business cycle. Model 5 repeats the fixed effects equation of Model 4 but replaces \(\:{EMP}_{it}\) with \(\:{EuMP}_{t}\) . Since \(\:{EuMP}_{t}\) only varies by year, the estimation of Model 5 cannot include time effects. For reasons of comparability, I estimate all models without time effects. Model 6 includes both \(\:{EMP}_{it}\) and \(\:{EuMP}_{t}\) . I use R’s ‘plm’ package (Croissant and Millo 2008 ) to estimate all these panel data models. Moreover, \(\:{EMP}_{it}\) can be seen as a spatially lagged endogenous variable of the wage equation and thus also captures global spillovers (Mion 2004 ; Bruna et al. 2016 ). This interpretation is useful to test the robustness of results to the estimation of spatial econometrics panel data models, using R’s ‘splm’ package (Millo and Piras 2012 ). I define a spatial weights matrix ( \(\:W\) ) as a row-standardized binary matrix that includes the four nearest neighbors (see online Appendix for additional details). With this \(\:W\) , the spatial lag of a variable \(\:{y}_{i}\) for region \(\:i\) is the mean of \(\:{y}_{j}\) for its four nearest \(\:j\) regions. Starting from a generic representation of the fixed effects models, \(\:{y}_{t}=\beta\:{x}_{t}+u+\:{u}_{t}\) , the Spatial Error Model (SEM) assumes that possible ignored explanatory factors can correlate spatially, as captured by the following spatial model of the unexplained cross-sectional variation of the dependent variable: \(\:{u}_{t}=\lambda\:\text{W}{u}_{t}+{ϵ}_{t}\) . The Spatial Autoregressive Model (SAR), however, assumes spillovers from income per capita of neighboring regions, adding the spatial lag of the dependent variable ( \(\:W{y}_{t}\) ) as an explanatory variable: \(\:{y}_{t}=\beta\:{x}_{t}+\rho\:\text{W}{y}_{t}+u+{u}_{t}\) . Since \(\:{y}_{t}\) and \(\:{x}_{t}\) are the logs of GVApc and External Market Potential, respectively, the SAR model introduces some duplicate information about external markets: \(\:W{y}_{t}=\sum\:_{j\ne\:i}^{4}{{w}_{ij}}^{-1}\text{log}{GVApc}_{jt}\) partially overlaps with \(\:{x}_{t}=\text{log}{EMP}_{it}=\text{log}\sum\:_{j\ne\:i}^{R-1}{{d}_{ij}}^{-1}{GVA}_{jt}\) , where \(\:{{w}_{ij}}^{-1}\) is the corresponding non-diagonal element of my \(\:W\) matrix (displayed here in a format comparable to the weighting scheme in EMP). Additionally, estimation residuals of my fixed effects estimations tend to display not only spatial autocorrelation but also serial dependence. Further, I analyze the robustness of the panel results to the inclusion of the time lag of the dependent variable, \(\:{y}_{t-1}\) . The SEM and SAR models to be estimated are thus as follows: \(\:{y}_{t}=\beta\:{x}_{t}+{\gamma\:}{y}_{t-1}+\lambda\:\text{W}{u}_{t}+u+\:{ϵ}_{t}\) Model 7 \(\:{y}_{t}=\beta\:{x}_{t}+{\gamma\:}{y}_{t-1}+\rho\:\text{W}{y}_{t}+u+{u}_{t}\) Model 8 The calculation of time lags for Models 3, 7, and 8 use data for 1995. To facilitate comparability, however, I estimate all panel data models with the same number of observations for 27 years (1996–2022). I do not estimate Models 1–8 with methods that correct for biases due to potential endogeneity of the explanatory variables, as is common in causal analysis in the NEG empirical literature. My story is not about causality but about the statistical properties of the variables transformed to short-term variations. I argue that these properties do not capture what they are supposed to within NEG framework. To illustrate the intuitions about the statistical features behind the black box estimations, I compare data aggregated for the entire European sample with data of four regions, selected based on their different access to the main European markets (see online Appendix for details): Mittelfranken, Algarve, Kriti, and Nord-Norge. Figure 1 shows their location and the time series of their log GVApc, as well as the latter variable for the whole sample (solid line). For the period 1996–2022, the Pearson correlations of the times series of Algarve and Kriti with the European time series are 0.24 and − 0.08, respectively. This correlation is lower than 0.4 for 15% of the regions but higher than 0.8 for 77% of the regions, indicating that regional European income per capita evolves quite synchronically (Giannone and Reichlin 2006 ; Kunroo 2023 ). 5 Results Figure 2 represents the time series of lEMP and its time-demeaned version for the four regions selected and the European sample. The latter is measured by the artificial indicator \(\:{EuMP}_{t}\) . The plot on the left shows that the region of Norway has low Market Potential due to both its peripherality and its larger size (Bruna 2024a ). Geographical centrality and small rich neighborhoods give the German region high Market Potential. For two reasons, all these series evolve similarly, following the evolution of the sum of GVA for the whole sample (solid line). Firstly, the general synchronicity of the time series of regional GVA (see Fig. 1 for GVApc) tends to produce similar movements in data aggregated for several regions. Secondly, the smoothing effects of the sum for \(\:R-1\) regions in Harris’s accessibility index tend to dissipate local differences of the temporal changes in GVA. Given that the regional indicators of Market Potential tend to move together, the time-demeaned series in the right-hand plot are very similar. In other words, in a fixed effects estimation, Market Potential does not really capture relevant changes in the accessible market size for firms in each region. Rather, it captures the European business cycle. To test this explanation, Table 1 compares estimation of the eight models described in Section 4. As expected, \(\:{\widehat{\beta\:}}_{c}\) estimates of log External Market Potential are similar in Columns (1) and (2). They are also similar in Columns (3) and (4), which refer to \(\:{\widehat{\beta\:}}_{d}\) and \(\:{\widehat{\beta\:}}_{f}\) , respectively, and take values of around 1. This means that a 1% increase in the growth rate of \(\:{EMP}_{it}\) generates a 1% increase in the growth rate of \(\:{GVApc}_{it}\) . Under a NEG interpretation of the results, these estimates could be considered biased due to the endogeneity of Market Potential. I argue, however, that this high estimate reflects only the translation of the European economic cycle in GVA to the common movements in the regional times series of GVA per capita. As I discuss below, this high unitary elasticity collapses to 0.06 if the lagged dependent variable is added to the equation in Column (4) (see online Appendix), suggesting that the results of Market Potential are driven by the business cycle. Column (5) of Table 1 shows the paper’s main contribution. When the regional values of External MP ( \(\:{EMP}_{it}\) ) are replaced by the artificial variable of European MP ( \(\:{EuMP}_{t}\) ), adjusted R 2 and the estimate are very similar to those in Column (4). The regional differences of time-demeaned External MP thus make little difference compared to the aggregate evolution of European GVA, as shown in Fig. 2 . This result has nothing to do with NEG theory, as the explanation of the fixed effects results must be confined to the purely statistical domain. The key issue explaining the synchronic evolution of regional GVApc is the aggregate evolution of European GVA. Table 1 Cross-sectional and panel data models of the effects of two variables of Market Potential (MP) on gross value added per capita ( \(\:lGVApc\) ) Cross-section Pooled panel First differences Within group panel (regional fixed effects) Nonspatial Spatial (1) (2) (3) (4) (5) (6) (7) (8) \(\:log\:External\:MP\) 0.608 *** 0.671 *** 1.034 *** 1.014 *** 3.858 *** (0.174) (0.083) (0.030) (0.048) (0.479) \(\:log\:European\:MP\) 0.964 *** -2.893 *** 0.051 *** -0.023 *** (0.051) (0.467) (0.010) (0.007) \(\:log\:GVApc\:(t-1)\) 0.926 *** 1.003 *** (0.005) (0.012) \(\:Wu\) [ \(\:\lambda\:\) parameter] 0.670 *** (0.010) \(\:Wlog\:GVAp\) [ \(\:\rho\:\) ] 0.189 *** (0.007) Adjusted R 2 0.209 0. 217 0.345 0.567 0.499 0.650 Log likelihood -5,236 12,236 Note: Cross-sectional data (233 observations) refer to 2019 and panel data (6,291 obs.) to 1996–2022. The intercept in Columns (1) and (2) is not reported. Standard errors (in brackets) are clustered by country in Column (1) and by region and year, and robust to persistent common shocks, in Columns (2) to (6). Coefficients of variables in Column (8) are total impact estimates after 300 simulations to compute the impact distribution. * p < 0.1; ** p < 0.05; *** p < 0.01. Column (6) presents the results when both variables of Market Potential are included in the fixed effects estimation. Their estimates are statistically significant but with opposing signs, due to multicollinearity: The average correlation of all regional series of \(\:{EMP}_{it}\) with the artificial variable \(\:{EuMP}_{t}\) is 0.997. Tests reveal the presence of temporal and spatial dependence in the residuals of the previous models. Columns (7) and (8) shows estimations of the model in Column (5) after considering temporal and spatial dependence. The inclusion of the time lag of the dependent variable captures inertia in the regional business cycle. To correct for spatial autocorrelation, Columns (7) and (8) show result of a SEM and SAR models, respectively. Both spatial parameters are statistically significant. SEM estimation shows a way of capturing departures from the European cycle due to spatially autocorrelated omitted variables. Controlling for that, Column (7) shows that the regional effects of the contemporary European cycle, as captured by European Market Potential, are still significant, with a parameter of 0.05. The SAR model in Column (8) includes the spatial lag of the dependent variable, thus capturing spillovers from the evolution of the dependent variable of nearest neighbors. Once the local business cycle in each area of the map is incorporated, the effects of the aggregate cycle captured by European MP become negative. The reason, again, is multicollinearity. The correlation between the times series of the spatial lag of the dependent variable and the log of European MP is lower than 0.4 for 12% of the regions but higher than 0.8 for 85% of the regions. This result means that the spatial lag of the dependent variable also follows the European cycle but is more precise in capturing local departures from it to explain the evolution of regional income per capita. 6 Conclusions Panel data literature emphasizes the need to control for individual heterogeneity to avoid biases caused by time-invariant regional factors. It should not be forgotten, however, that controlling for unobserved regional fixed effects forces use of transformed data on temporal changes. The resulting within-region estimates are not comparable to the between-region estimates obtained using cross-sectional data. For data in log form defined at intervals of one or a few years, panel data estimates approximate the effects of the short-term growth rates of variables and are thus not a good way of testing long-term theoretical predictions. This study shows that the evolution of regional income per capita is highly synchronic in Europe, following the European cycle. The smoothing effects of summation when constructing the variable Market Potential intensify this variable’s synchronicity: the temporal changes in Market Potential are very similar for all regions. Changes in Market Potential thus capture changes in the European business cycle, which explain the average changes in regional income per capita well. Short-term growth rates in Market Potential capture short-term growth rates of aggregate European economic activity, which are also similar to the average short-term growth rates of income in neighboring regions. The panel data estimates capture correlations or spillovers from the aggregate cycle but not the mechanisms studied by the NEG. When using these data, therefore, a variable of Market Potential that is statistically significant in a fixed effects estimation does not confirm the NEG. This research should be extended to study other geographical samples. For long-run theories, panel data methods are more appropriate when using long historical data sets for time intervals of decades. The ‘pooled mean group estimator’ (Pesaran et al. 1999 ) of dynamic panels with a large number of time and spatial units takes into account possible common long-run relationships across spatial units. An alternative approach comes from the literature on spatial and temporal unit roots and cointegration in panel data (Banerjee 1999 ; Baltagi and Shu 2024 ). Ultimately, researchers should choose statistical methods based on the time frame of the underlying theory. They also should be careful with the temporal and spatial properties of the (transformed) data and use graphical and statistical tools before black box estimations. Declarations Author Contribution All authors whose names appear on the submission1) made substantial contributions to the conception or design of the work; or the acquisition, analysis, or interpretation of data; or the creation of new software used in the work;2) drafted the work or revised it critically for important intellectual content;3) approved the version to be published; and4) agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. Acknowledgement I thank Javier Barbero and Mariano Matilla-García for very useful suggestions. The usual disclaimers apply. References Acemoglu D, Johnson S, Robinson JA, Yared P (2008) Income and Democracy. Am Econ Rev 98:808–842 Amaral PV, Lemos M, Simões R, Chein F (2010) Regional Imbalances and Market Potential in Brazil. Spat Economic Anal 5:463–482. https://doi.org/10.1080/17421772.2010.516441 Baldwin RE, Forslid R, Martin P et al (2003) Economic Geography and Public Policy. Princeton University Press, Princeton, N.J Baltagi BH, Fingleton B, Pirotte A (2014) Estimating and Forecasting with a Dynamic Spatial Panel Data Model. Oxf Bull Econ Stat 76:112–138. https://doi.org/10.1111/obes.12011 Baltagi BH, Griffin JM (1984) Short and Long Run Effects in Pooled Models. Int Econ Rev 25:631–645. https://doi.org/10.2307/2526223 Baltagi BH, Shu J (2024) A Survey of Spatial Unit Roots. Mathematics 12:1052. https://doi.org/10.3390/math12071052 Banerjee A (1999) Panel Data Unit Roots and Cointegration: An Overview. Oxf Bull Econ Stat 61:607–629. https://doi.org/10.1111/1468-0084.0610s1607 Boulhol H, de Serres A (2010) Have developed countries escaped the curse of distance? J Econ Geogr 10:113–139. https://doi.org/10.1093/jeg/lbp015 Breinlich H (2006) The spatial income structure in the European Union—what role for Economic Geography? J Econ Geogr 6:593–617. https://doi.org/10.1093/jeg/lbl018 Bruna F (2024a) Market Potential, spatial theories, and spatial trends. Spat Econ Anal. https://doi.org/10.1080/17421772.2024.2325517 Bruna F (2015) A generalized NEG wage-type equation. In: Díaz-Roldán C, Perote J (eds) Advances on International Economics. Cambridge Scholars Publishing, Newcastle, pp 63–82 Bruna F (2024b) Market potential: the measurement of domestic market size. Lett Spat Resour Sci 17:1–13. https://doi.org/10.1007/s12076-024-00378-8 Bruna F, Lopez-Rodriguez J, Faíña A (2016) Market Potential, Spatial Dependences and Spillovers in European Regions. Reg Stud 50:1551–1563. https://doi.org/10.1080/00343404.2015.1048796 Combes P-P, Mayer T, Thisse J-F (2008) Economic geography: the integration of regions and nations. Princeton University Press, Princeton, N.J Croissant Y, Millo G (2008) Panel Data Econometrics in R: The plm Package. J Stat Softw 27:1–43 de Sousa J, Poncet S (2011) How are wages set in Beijing? Reg Sci Urban Econ 41:9–19. https://doi.org/10.1016/j.regsciurbeco.2010.07.004 Duranton G, Puga D (2004) Micro-foundations of urban agglomeration economies. In: Henderson JV, Thisse J-F (eds) Handbook of Regional and Urban Economics 4. North Holland, Amsterdam, pp 2063–2117 Elhorst JP (2024) Raising the bar in spatial economic analysis: two laws of spatial economic modelling. Spat Economic Anal 19:115–132. https://doi.org/10.1080/17421772.2024.2334845 Fingleton B (2008) Competing models of global dynamics: evidence from panel models with spatially correlated error components. Econ Model 25:542–558 Fingleton B (2009) Testing the NEG model: Further evidence from panel data. Région Dév 30:141–158 Fingleton B, Fischer MM (2010) Neoclassical theory versus new economic geography: competing explanations of cross-regional variation in economic development. Ann Reg Sci 44:467–491. https://doi.org/10.1007/s00168-008-0278-z Fingleton B, Longhi S (2013) The Effects of Agglomeration on Wages: Evidence from the Micro-Level. J Reg Sci 53:443–463. https://doi.org/10.1111/jors.12020 Fingleton B, Palombi S (2013) The wage curve reconsidered: is it truly an empirical law of economics? Région Dév 38:49–92 Giannone D, Reichlin L (2006) Trends and cycles in the euro area: how much heterogeneity and should we worry about it? ECB Working Paper Gómez-Antonio M, Fingleton B (2012) Analyzing the Impact of Public Capital Stock Using the Neg Wage Equation: A Spatial Panel Data Approach. J Reg Sci 52:486–502. https://doi.org/10.1111/j.1467-9787.2011.00725.x Hanson GH (2005) Market potential, increasing returns and geographic concentration. J Int Econ 67:1–24. https://doi.org/10.1016/j.jinteco.2004.09.008 Harris CD (1954) The Market as a Factor in the Localization of Industry in the United States. Ann Assoc Am Geogr 44:315–348. https://doi.org/10.1080/00045605409352140 Head K, Mayer T (2011) Gravity, market potential and economic development. J Econ Geogr 11:281–294 Head K, Mayer T (2004) The empirics of agglomeration and trade. In: Henderson JV, Thisse J-F (eds) Handbook of Regional and Urban Economics 4. North Holland, Amsterdam, pp 2609–2669 Head K, Mayer T (2006) Regional wage and employment responses to market potential in the EU. Reg Sci Urban Econ 36:573–594. https://doi.org/10.1016/j.regsciurbeco.2006.06.002 Head K, Mayer T (2014) Gravity equations: workhorse, toolkit, and cookbook. In: Gopinath G, Helpman E, Rogoff K (eds) Handbook of International Economics 4. Elsevier, Amsterdam, pp 131–195 Krugman P (1991) Increasing returns and economic geography. J Polit Econ 99:483–499. https://doi.org/10.1086/261763 Krugman P (1993) First Nature, Second Nature, and Metropolitan Location. J Reg Sci 33:129–144. https://doi.org/10.1111/j.1467-9787.1993.tb00217.x Krugman P (2011) The New Economic Geography, Now Middle-aged. Reg Stud 45:1–7. https://doi.org/10.1080/00343404.2011.537127 Kunroo MH (2023) Business cycle synchronization and its determinants in the OECD countries: panel data evidence. Appl Econ 0:1–16. https://doi.org/10.1080/00036846.2023.2288049 Millo G, Piras G (2012) splm: Spatial Panel Data Models in R. J Stat Softw 47:1–38 Mion G (2004) Spatial externalities and empirical analysis: the case of Italy. J Urban Econ 56:97–118. https://doi.org/10.1016/j.jue.2004.03.004 Ottaviano GIP, Pinelli D (2006) Market potential and productivity: Evidence from Finnish regions. Reg Sci Urban Econ 36:636–657. https://doi.org/10.1016/j.regsciurbeco.2006.06.005 Pesaran MH, Shin Y, Smith RP (1999) Pooled Mean Group Estimation of Dynamic Heterogeneous Panels. J Am Stat Assoc 94:621–634. https://doi.org/10.1080/01621459.1999.10474156 Redding SJ (2011) Economic Geography: a Review of the Theoretical and Empirical Literature. In: Bernhofen D, Falvey R, Greenaway D, Kreickemeier U (eds) Palgrave Handbook of International Trade. Palgrave Macmillan, London, pp 497–531 Redding SJ, Venables AJ (2004) Economic geography and international inequality. J Int Econ 62:53–82. https://doi.org/10.1016/j.jinteco.2003.07.001 Rokicki B, Cieślik A (2023) Rethinking regional wage determinants: regional market potential versus trade partners’ potential. Spat Econ Anal 18:126–142. https://doi.org/10.1080/17421772.2022.2070657 Wang C-Y, Haining R (2017) Testing the new economic geography’s wage equation: a case study of Japan using a spatial panel model. Ann Reg Sci 58:417–440. https://doi.org/10.1007/s00168-016-0804-3 Footnotes Empirical NEG literature does not clearly distinguish pecuniary external economies due to market size from other possible spillovers due to knowledge or expectations. In Eq. (2), regional gross value added (GVA) per capita is affected by the GVA of other regions, a condition compatible with a variety of explanations. See Duranton and Puga ( 2004 ), Bruna et al. ( 2016 ), Elhorst ( 2024 ), Bruna ( 2024a ), and discussion below. The following papers use Harris’ indicator of Market Potential: Breinlich ( 2006 ), Fingleton ( 2008 ), Amaral et al. ( 2010 ), Baltagi et al. ( 2014 ), Wang and Haining ( 2017 ), and Rokicki and Cieślik ( 2023 ). For reasons explained in the following section, I do not include time effects in any of these models. Considering time effects does not change the results obtained in the paper (see online Supplementary Appendix). I have repeated the calculations in this paper for a panel of seven time-observations defined for four-year data averages. The online Supplementary Appendix shows that the empirical results are very similar. When there is high serial correlation in the idiosyncratic random term, \:{\widehat{\beta\:}}_{d} is more efficient than \:{\widehat{\beta\:}}_{f} (Boulhol and de Serres 2010 ). Ottaviano and Pinelli ( 2006 ) propose another model derived from an interpretation of the wage equation assuming that regions fluctuate around a balanced growth path. These authors define the growth rate \:{g}_{Yit} within a time span of ten years and regress it on the logs of Market Potential and per capita income for the initial year. I do not study their model here. Bruna ( 2024a ) shows that the spatial patterns of European EMP and a pure indicator of geographical centrality are almost identical. For 2019, the correlations of the log of EMP with the logs of GVApc and inverse mean distance to all the other regions are 0.46 and 0.88, respectively. With this definition, the GVA of each region is used to build the European MP, which is later used to explain each region’s GVApc. The resulting endogeneity of the European variable is similar to the results obtained using regional income to measure Internal Market Potential in the NEG literature (Bruna 2024b ). The consequences are minor, however. The median weight of \:{GVA}_{jt} in \:\sum\:_{j=1}^{R}{GVA}_{jt} is 0.26%. Unlike the notation in the ‘splm’ package, I use \:\lambda\: for the spatial parameter of the SEM model. A key difference is that \:{{d}_{ij}}^{-1} is measured as inverse absolute distances, while standardized \:W matrices ignore sample geography to focus on local issues. See Bruna et al. ( 2016 ). Panel unit root tests reveal that the time series of lGVApc are generally stationary (see online Supplementary Appendix). In any case, my argument involves not potential spurious results due to nonstationarity but the misinterpretation of the empirical results of the fixed effects wage equation. To detect covariation, or synchronicity, Pearson’s (linear) correlation is more stringent than Kendall or Spearman correlations, which are rank-based coefficients. Norwegian regions are an exception to the rough core-periphery pattern of GVApc around the so-called European ‘blue (or hot) banana’. They are relatively rich (Fig. 1 ) but peripheral and so have low EMP (Fig. 2 ). See: https://en.wikipedia.org/wiki/Blue_Banana . For the four regions chosen, the mean correlation between the time series of EMP in first difference and in discrete growth rates is 0.988. I conducted Breusch-Godfrey tests for serial dependence and Pesaran’s tests for cross-sectional dependence in the residuals of the models in Columns (4) and (5). See online Supplementary Appendix. Conclusions derived from Columns (7) and (8) are very similar if these models are based on the equation for External Market Potential in Column (4). See Appendix. Panel Lagrange Multiplier tests for spatial dependence in the equation in column (5) reveal a weak preference for the SAR over the SEM correction for spatial autocorrelation. See Appendix. The estimate of European MP in Column (5) becomes 0.050 when the time lag of the dependent variable is added to the equation (see Appendix). The similarity of this number to the SEM 0.051 estimate in Column (7) indicates correct specification of the model including \:{EuMP}_{t} and \:{log}{GVApc}_{it-1} . Additional Declarations No competing interests reported. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4979299","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":350300908,"identity":"793660ec-fe64-42bf-9754-4c2f353348b2","order_by":0,"name":"Fernando Bruna","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAApklEQVRIiWNgGAWjYBAC9gYeMC3HwJBApBaeAxAtxqRrSWwgXgsD77HPvDvs0jccT37A8OEPUVr4kmfznknO3XDmmQHjzDYitNgz8Bgz87Yx5264kcPAzNtAlC1gLfXpBiAtf4hzGFjL4QSwFgY2YrQw8yUzzm07bjgT6JeDvcT4hYe99zDD27Zqeb7jyQ8f/CDGYUDHIMABYjSMglEwCkbBKCACAAAPey+1oIG/3gAAAABJRU5ErkJggg==","orcid":"","institution":"Universidade da Coruña","correspondingAuthor":true,"prefix":"","firstName":"Fernando","middleName":"","lastName":"Bruna","suffix":""}],"badges":[],"createdAt":"2024-08-26 16:21:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4979299/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4979299/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":65597319,"identity":"f04ad486-d030-49c0-afb1-b03e4ea8a292","added_by":"auto","created_at":"2024-09-30 11:19:31","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":82114,"visible":true,"origin":"","legend":"\u003cp\u003eLocation of selected regions and evolution of their income per capita.\u003c/p\u003e","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-4979299/v1/b6de05622d9f0301e13c105a.png"},{"id":65597320,"identity":"6a285c84-d27a-4736-b427-bc6d80861616","added_by":"auto","created_at":"2024-09-30 11:19:31","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":55301,"visible":true,"origin":"","legend":"\u003cp\u003eMarket Potential for selected regions and its time-demeaned version.\u003c/p\u003e","description":"","filename":"Onlinefloatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-4979299/v1/59aeac61cd46884462d7f80b.png"},{"id":70710528,"identity":"90cfe1d7-c0a0-418d-adfe-7d68f9a2d52c","added_by":"auto","created_at":"2024-12-05 23:46:35","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":690815,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4979299/v1/95f945a1-f8c4-4adb-b035-68b70a464867.pdf"},{"id":65597321,"identity":"9c267db8-1e7b-4e48-abb8-aae781a8a4de","added_by":"auto","created_at":"2024-09-30 11:19:31","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":252438,"visible":true,"origin":"","legend":"","description":"","filename":"zNEGpanelSupplementaryAppendixV03.docx","url":"https://assets-eu.researchsquare.com/files/rs-4979299/v1/2d10ee34e2311f3a2331b716.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Market Potential, panel data, and aggregate fluctuations: All that glitters is not gold","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eKrugman\u0026rsquo;s (\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e1991\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e1993\u003c/span\u003e) development of the New Economic Geography (NEG) provided an explanation of economic agglomeration\u0026mdash;that is, of the formation of clusters in the spatial distribution of economic activity. The so-called \u0026lsquo;wage equation\u0026rsquo; of the NEG is a long-run prediction relating higher income to locations with higher Market Potential, an indicator of the accessibility and market size of the other regions. The cross-sectional form of the equation has been widely studied in the empirical literature (Redding \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). More generally, location theory establishes \u0026ldquo;fundamental determinants\u0026rdquo; of economic activity (Redding and Venables \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2004\u003c/span\u003e) based on long-term consequences of centrifugal and centripetal agglomeration forces. These historical explanations should thus be tested using cross-sectional data (Baltagi and Griffin \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e1984\u003c/span\u003e), not panels of data at intervals of one or a few years.\u003c/p\u003e \u003cp\u003eStarting with Hanson (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2005\u003c/span\u003e) and Mion (\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2004\u003c/span\u003e), however, this equation has been estimated using panel data. The author who has studied the NEG wage-type equation most using panel data techniques is Bernard Fingleton (e.g., Fingleton (\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2008\u003c/span\u003e), Baltagi et al. (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2014\u003c/span\u003e)). Other important articles on the empirics of the NEG have used panel data: Breinlich (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2006\u003c/span\u003e), Boulhol and de Serres (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2010\u003c/span\u003e), de Sousa and Poncet (\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2011\u003c/span\u003e), Head and Mayer (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). Their results are not satisfactory. Panel data models are designed to capture short-term relationships. Why is an indicator of Market Potential statistically significant in panel data models if that indicator is designed to synthesize forces underlying location decisions over centuries?\u003c/p\u003e \u003cp\u003eThe goal of this paper is to provide an explanation for this anomaly. It employs European regional data to study the properties of the time series of the time-demeaned data used to derive fixed effects panel data estimates. I illustrate the intuitions behind the black box estimations through a graphical and correlation analysis for a few regions with very different access to European markets. Finally, I compare estimation results obtained using the indicator of Market Potential and an artificial indicator calculated for the whole European sample, the evolution of which summarizes the European business cycle.\u003c/p\u003e \u003cp\u003eThe conclusions are as follows. The evolution of income per capita in European regions displays high synchronicity (Giannone and Reichlin \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Kunroo \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). The average changes of regional income per capita may be captured by either the average variations of regional Market Potential or the variations of an aggregated indicator with identical European data for all the regional observations of the same year. Average temporal changes in regional Market Potential thus capture only the common economic cycle, reflecting synchronicity, or global spillovers. For the case of Europe at least, the panel data results of a NEG equation should not be interpreted in terms of the NEG hypotheses. This result is another example of the \u0026lsquo;Marshallian\u0026rsquo; (Duranton and Puga \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2004\u003c/span\u003e) or \u0026lsquo;observational\u0026rsquo; equivalence of the NEG (Head and Mayer \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2004\u003c/span\u003e, p. 2,663; Bruna \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2024a\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eSome of these conclusions may be generalized to many studies in different fields, that ignore the statistical properties of the transformed data when interpreting results from panel data models. Fixed effects estimations are usually justified by the need to control for time-invariant regional factors. Researchers who attend only to this argument may forget that results from cross-sectional and panel models have different interpretation. Estimating an equation with data on first differences or time-demeaned data means studying the effects of temporal changes in the explanatory variable on temporal changes in the dependent variable. Although this is well known, it is not discussed in many papers comparing cross-sectional and panel data estimates.\u003c/p\u003e \u003cp\u003eThe remainder of the paper is structured as follows. The second section introduces the wage equation and the literature estimating it with panel data. Section 3 reviews the interpretation of estimation results when using cross-sectional and panel data models. Section 4 presents the data and methodology, and Section 5 the results. The final section draws conclusions.\u003c/p\u003e"},{"header":"2 The empirical wage-type equation and panel data","content":"\u003cp\u003eA variety of NEG models focus on different mechanisms to explain agglomeration (Baldwin et al. \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2003\u003c/span\u003e), even in the absence of any pure external economies. Using Krugman\u0026rsquo;s (\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e1993\u003c/span\u003e) model of metropolitan areas as a benchmark and assuming all other conditions equal, firms that have an incentive to concentrate production at a limited number of locations prefer locations with good access to markets. Yet access to markets will be good precisely where a large number of firms choose to locate. This positive feedback loop drives the formation of urban centers. It also implies that the location of such centers is not wholly determined by the underlying natural geography, that there are typically multiple locational equilibria. To capture this intuition, the formal model has three features. First, location matters because of transportation costs. Second, some immobile production factors provide a form of \u0026lsquo;first nature\u0026rsquo; that constrains the possible spatial structure of the economy. Finally, economies of scale in the production of at least some goods provide an incentive for concentration. The existence of the metropolis thus creates a \u0026lsquo;second nature\u0026rsquo; that drags the optimal location of firms with it.\u003c/p\u003e \u003cp\u003eKrugman\u0026rsquo;s initial models \u0026ldquo;suggest an explanation for the nineteenth-century formation of real-world core-periphery patterns, notably the emergence of the United States\u0026rsquo; manufacturing belt and Europe\u0026rsquo;s \u0026lsquo;hot banana\u0026rsquo;\u0026rdquo; (Krugman \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). Krugman recognizes, however, the increasing importance of technology and information spillovers: \u0026ldquo;Ever since the beginnings of New Economic Geography, and up until very recently, I and others have had a slightly guilty sense that we were talking about was the past, not the present, and much less the future (Krugman \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). In sum, the NEG establishes \u0026ldquo;fundamental determinants\u0026rdquo; of economic activity (Redding and Venables \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2004\u003c/span\u003e) based on long-term consequences of agglomeration forces.\u003c/p\u003e \u003cp\u003eThe so-called \u0026lsquo;wage equation\u0026rsquo; is a market-clearing condition of the basic NEG model in which labor is a unique production factor. I will now present a one-sector generalized form of this equation in which the dependent variable is not wages but marginal costs and thus encompasses many of the \u0026lsquo;wage equations\u0026rsquo; previously derived in the literature (Combes et al. \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2008\u003c/span\u003e, Chap.\u0026nbsp;12; Bruna \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). For a firm in region \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003e (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i=1,\\dots\\:,\\:\\:R\\)\u003c/span\u003e\u003c/span\u003e) with zero profit, the maximum value of marginal cost (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{m}_{i}\\)\u003c/span\u003e\u003c/span\u003e) the firm can afford to pay depends on its access to markets. Marginal cost is thus proportional to firm\u0026rsquo;s (region\u0026rsquo;s) Real Market Potential (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{RMP}_{i}\\)\u003c/span\u003e\u003c/span\u003e) (to use Head and Mayer\u0026rsquo;s (\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) term) or Market Access (to use Redding and Venables\u0026rsquo; (\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2004\u003c/span\u003e) term), as follows:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:{m}_{i}=Constant\u0026middot;{\\left({RMP}_{i}\\right)}^{\\frac{1}{\\sigma\\:}}=Constant\u0026middot;{\\left(\\sum\\:_{j}^{R}{{T}_{ij}}^{1-\\sigma\\:}\\frac{{E}_{j}}{{S}_{j}}\\right)}^{\\frac{1}{\\sigma\\:}}$$\u003c/div\u003e\u003c/div\u003e(1) \u003c/p\u003e \u003cp\u003ewhere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sigma\\:\u0026gt;1\\)\u003c/span\u003e\u003c/span\u003e is the elasticity of substitution between any pair of varieties of goods in a love-of-variety utility function. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{RMP}_{i}\\)\u003c/span\u003e\u003c/span\u003e is a weighted sum of the market conditions in the other \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:j\\)\u003c/span\u003e\u003c/span\u003e regions, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{T}_{ij}\\)\u003c/span\u003e\u003c/span\u003e is the trade cost from firm-or-region \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003e to region\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:j\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{E}_{j}\\)\u003c/span\u003e\u003c/span\u003e is total expenditure in \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:j\\)\u003c/span\u003e\u003c/span\u003e. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{S}_{j}\\)\u003c/span\u003e\u003c/span\u003e is called the \u0026lsquo;competition index\u0026rsquo; to stress that it measures the level of competition among varieties in \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:j\\)\u003c/span\u003e\u003c/span\u003e market, given consumers\u0026rsquo; characteristic tastes. The NEG\u0026rsquo;s long-term prediction is that firms and regions with higher Market Potential tend to earn more profit and pay higher remuneration to production factors, resulting in higher regional income per capita.\u003c/p\u003e \u003cp\u003eIf trade costs are proxied by physical distances (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{d}_{ij}\\)\u003c/span\u003e\u003c/span\u003e), the explanatory variable of Eq.\u0026nbsp;(1) becomes \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{RMP}_{i}=\\sum\\:_{j}^{R}{{d}_{ij}}^{1-\\sigma\\:}\\frac{{E}_{j}}{{S}_{j}}\\)\u003c/span\u003e\u003c/span\u003e. As in some previous literature, marginal cost (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{m}_{i}\\)\u003c/span\u003e\u003c/span\u003e) can be proxied by data on gross value added per capita (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:GVApc\\)\u003c/span\u003e\u003c/span\u003e) and total expenditure (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{E}_{j}\\)\u003c/span\u003e\u003c/span\u003e) by data on \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:GVA\\)\u003c/span\u003e\u003c/span\u003e. Harris\u0026rsquo; (\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e1954\u003c/span\u003e) index of accessibility to markets, in contrast, can be defined as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{HMP}_{i}=\\sum\\:_{j}^{R}{{d}_{ij}}^{-1}{GVA}_{j}\\)\u003c/span\u003e\u003c/span\u003e. Since a \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:-1\\)\u003c/span\u003e\u003c/span\u003e trade elasticity to distance is an extremely robust empirical finding in the literature on gravity equations (Head and Mayer \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2014\u003c/span\u003e), the major difference between \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{RMP}_{i}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{HMP}_{i}\\)\u003c/span\u003e\u003c/span\u003e lies in \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{S}_{j}\\)\u003c/span\u003e\u003c/span\u003e, which is not directly measurable in NEG theory. For samples of European regions, Breinlich (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) and Head and Mayer (\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) obtained similar empirical results using both Harris\u0026rsquo; indicator and the more sophisticated procedure of Redding and Venables (\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2004\u003c/span\u003e) to proxy \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{S}_{j}\\)\u003c/span\u003e\u003c/span\u003e. Bruna (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2024a\u003c/span\u003e) shows that both approaches capture the core-periphery spatial patterns in the data in a similar way.\u003c/p\u003e \u003cp\u003eMoreover, when calculating Market Potential with areal data, the access of firms to markets also depends on the market size of their own region\u0026mdash;that is, on so-called self-potential or Internal Market Potential. Not only does considering this potential in applied work add endogenous information, but the measurement of internal distances (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{d}_{ii}\\)\u003c/span\u003e\u003c/span\u003e) is controversial (Bruna \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2024b\u003c/span\u003e). This study therefore avoids self-potential and uses External Market Potential, defined as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{EMP}_{i}=\\sum\\:_{j\\ne\\:i}^{R-1}{{d}_{ij}}^{-1}{GVA}_{j}\\)\u003c/span\u003e\u003c/span\u003e. Taking natural logarithms to Eq.\u0026nbsp;(1) and replacing variables with my proxies, I thus obtain the following estimable cross-sectional equation:\u003ca class=\"FNLink\" href=\"#Fn1\" id=\"#FNLinkFn1\"\u003e\u003c/a\u003e\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:\\text{log}{GVApc}_{i}=C+{\\beta\\:\\text{log}{EMP}_{i}+u}_{i}$$\u003c/div\u003e\u003c/div\u003e(2) \u003c/p\u003e \u003cp\u003eHanson (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2005\u003c/span\u003e) and Mion (\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2004\u003c/span\u003e) estimated the first panel data model of the wage equation and discussed the advisability of using the generalized method of moments (GMM) or nonlinear least squares. They also carefully discussed justification of a panel data version of Eq.\u0026nbsp;(2), including time-invariant individual effects, as in Eq.\u0026nbsp;(5) below. Breinlich (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) justified these fixed effects to capture persistent factors such as institutional quality or climatic or other amenities of a region. Fingleton (\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) assumed that the dependent variable in a time-varying version of Eq.\u0026nbsp;(1) also depends on level of efficiency (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{A}_{it}\\)\u003c/span\u003e\u003c/span\u003e)\u0026mdash;a useful trick to model complexity by making \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{A}_{it}\\)\u003c/span\u003e\u003c/span\u003e depend on past efficiency, the efficiency of neighboring regions (spillovers), and time-invariant regional characteristics.\u003c/p\u003e \u003cp\u003eFor the NEG equation and areal data, Fingleton applied the fixed effects estimator and the Kapoor-Kelejian-Prucha (KKP) GMM estimator of random effects models, including serially and spatially autocorrelated disturbances (Fingleton \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2008\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Fingleton and Fischer \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; G\u0026oacute;mez-Antonio and Fingleton \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Fingleton and Palombi \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). Amaral et al. (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2010\u003c/span\u003e) and Wang and Haining (\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) have also used this methodology. Further, Fingleton was a coauthor in Baltagi et al.\u0026rsquo;s (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) proposal of a KKP method to estimate a complex spatial econometric dynamic panel data model, proposal that is illustrated with a NEG wage-type equation. Using microdata, Fingleton and Palombi (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) and Fingleton and Longhi (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) estimated a fixed effects panel data model for individuals\u0026rsquo; wages. Some panel data literature has used the NEG framework to study other topics (e.g., G\u0026oacute;mez-Antonio and Fingleton \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2012\u003c/span\u003e, for public capital; de Sousa and Poncet \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2011\u003c/span\u003e, for migration). For instrumental variables estimation, Boulhol and de Serres (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2010\u003c/span\u003e) and Head and Mayer (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2011\u003c/span\u003e) included time-invariant instruments and time dummies in the first stage regression.\u003c/p\u003e \u003cp\u003eSome of these studies have used samples of European regions (Breinlich \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Fingleton and Fischer \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Baltagi et al. \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). Others used data for one European country\u0026mdash;Mion (\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2004\u003c/span\u003e) for Italy, G\u0026oacute;mez-Antonio and Fingleton (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2012\u003c/span\u003e) for Spain, three of Fingleton\u0026rsquo;s studies for the United Kingdom, and Rokicki and Cieślik (\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) for Poland.\u003ca class=\"FNLink\" href=\"#Fn2\" id=\"#FNLinkFn2\"\u003e\u003c/a\u003e\u003c/p\u003e \u003cp\u003eAlthough many of these panel data studies find significant effects of Market Potential on income per capita, their results may be described as an anomaly. As the next section shows, panel data estimates capture short-term effects, so those significant effects are an unexpected result from a theory explaining the historical causes of agglomeration.\u003c/p\u003e"},{"header":"3 Interpreting panel data estimations of the NEG equation","content":"\u003cp\u003eTo establish key ideas, it is useful to review interpretation of the coefficients in several econometric models. Readers who feel comfortable with these basics may skip to the end of the section.\u003c/p\u003e \u003cp\u003eThe cross-sectional wage-type equation derived from the NEG produces an estimable equation for region \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003e (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i=1\\dots\\:R\\)\u003c/span\u003e\u003c/span\u003e) in a given period \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:t\\)\u003c/span\u003e\u003c/span\u003e, such as the following:\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\:{y}_{i}=C+\\beta\\:{x}_{i}+{u}_{i}$$\u003c/div\u003e\u003c/div\u003e(3) \u003c/p\u003e \u003cp\u003ePooling data for T periods (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:t=1\\dots\\:T\\)\u003c/span\u003e\u003c/span\u003e)\u003ca class=\"FNLink\" href=\"#Fn3\" id=\"#FNLinkFn3\"\u003e\u003c/a\u003e in each region \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003e (group), we get the following model:\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e\n$$\\:{y}_{it}=C+\\beta\\:{x}_{it}+{u}_{it}$$\u003c/div\u003e\u003c/div\u003e(4) \u003c/p\u003e \u003cp\u003eThe fixed effects extension of Eq.\u0026nbsp;(4) includes unobserved time-invariant individual effects, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{u}_{i}\\)\u003c/span\u003e\u003c/span\u003e, as follows:\u003cdiv id=\"Eque\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Eque\" name=\"EquationSource\"\u003e\n$$\\:{y}_{it}=C+\\beta\\:{x}_{it}+{u}_{i}+{u}_{it}$$\u003c/div\u003e\u003c/div\u003e(5) \u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{u}_{i}\\)\u003c/span\u003e\u003c/span\u003e collects omitted regional variables assumed to have a roughly constant role in explaining regional differences of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{it}\\)\u003c/span\u003e\u003c/span\u003e. Averaging Eq.\u0026nbsp;(5) over the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:T\\)\u003c/span\u003e\u003c/span\u003e periods produces the following between-group model, capturing cross-sectional average relationships:\u003cdiv id=\"Equf\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equf\" name=\"EquationSource\"\u003e\n$$\\:{\\stackrel{-}{y}}_{i}=C+\\beta\\:{\\stackrel{-}{x}}_{i}+{u}_{i}+{\\stackrel{-}{u}}_{i}$$\u003c/div\u003e\u003c/div\u003e(6) \u003c/p\u003e \u003cp\u003eSubtracting Eq.\u0026nbsp;(6) from (5) produces the estimable fixed effects panel model, with the variables as deviations to the regional means:\u003cdiv id=\"Equg\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equg\" name=\"EquationSource\"\u003e\n$$\\:{y}_{it}-{\\stackrel{-}{y}}_{i}=\\beta\\:\\left({x}_{it}-{\\stackrel{-}{x}}_{i}\\right)+\\left({u}_{it}-{\\stackrel{-}{u}}_{i}\\right)$$\u003c/div\u003e\u003c/div\u003e(7) \u003c/p\u003e \u003cp\u003eThis is the within-group model, and the transformed variables are temporal variations within each region. We can estimate the model using standard ordinary least squares (OLS) by pooling the demeaned data. The \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\widehat{\\beta\\:}\\)\u003c/span\u003e\u003c/span\u003e estimate will be identical to that of Eq.\u0026nbsp;(4) after including (controlling out) \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:R-1\\)\u003c/span\u003e\u003c/span\u003e regional dummy variables.\u003c/p\u003e \u003cp\u003eBoulhol and de Serres (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2010\u003c/span\u003e)\u0026mdash;and Acemoglu et al. (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) in another field\u0026mdash;summarize the standard argument in favor of defining the model as in Eq.\u0026nbsp;(7). The major source of potential bias in a regression of Market Potential on income per capita is region-specific, historical factors that influence both Market Potential and economic development. If these omitted characteristics are, on first approximation, time-invariant (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{u}_{i}\\)\u003c/span\u003e\u003c/span\u003e), inclusion of fixed effects will remove them and this source of bias. Paying attention only to that possible unobserved individual heterogeneity has, however, led some researchers to mistaken conclusions when interpreting results, as described below.\u003c/p\u003e \u003cp\u003eThe cross-sectional, pooled, and between models of Equations (3), (4), and (6), respectively, are about relative levels of regional variables. The estimate of these models, which I term \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\beta\\:}}_{c}\\)\u003c/span\u003e\u003c/span\u003e, captures the effect of cross-sectional variations of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{i}\\)\u003c/span\u003e\u003c/span\u003e on cross-sectional variations of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{it}\\)\u003c/span\u003e\u003c/span\u003e. A cross-sectional wage equation thus implies that regions with higher Market Potential will be richer. Conversely, the estimate from the fixed effects Eq.\u0026nbsp;(7), which I term \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\beta\\:}}_{f}\\)\u003c/span\u003e\u003c/span\u003e, captures the effect of time variations of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{it}\\)\u003c/span\u003e\u003c/span\u003e on time variations of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{it}\\)\u003c/span\u003e\u003c/span\u003e. In Acemoglu et al.\u0026rsquo;s (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) terminology, a fixed effects panel model of the wage equation implies that regions with increasing Market Potential will become richer. This is not what the NEG predicts for a time span of either one or a few years.\u003ca class=\"FNLink\" href=\"#Fn4\" id=\"#FNLinkFn4\"\u003e\u003c/a\u003e The NEG\u0026rsquo;s historical explanation should thus be studied using cross-sectional/pooled estimations (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\beta\\:}}_{c}\\)\u003c/span\u003e\u003c/span\u003e), while fixed effects estimations (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\beta\\:}}_{f}\\)\u003c/span\u003e\u003c/span\u003e) are more suitable for studying short-run relationships (Baltagi and Griffin \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e1984\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eTo better interpret the fixed effects estimator, it is useful to compare it to a model in first differences. The time lag of Eq.\u0026nbsp;(5) is the following:\u003cdiv id=\"Equh\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equh\" name=\"EquationSource\"\u003e\n$$\\:{y}_{it-1}=C+\\beta\\:{x}_{it-1}+{u}_{i}+{u}_{it-1}$$\u003c/div\u003e\u003c/div\u003e(8) \u003c/p\u003e \u003cp\u003eSubtracting Eq.\u0026nbsp;(8) from (5) produces the following first difference estimator:\u003cdiv id=\"Equi\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equi\" name=\"EquationSource\"\u003e\n$$\\:{y}_{it}-{y}_{it-1}=\\beta\\:\\left({x}_{it}-{x}_{it-1}\\right)+\\left({u}_{it}-{u}_{it-1}\\right)$$\u003c/div\u003e\u003c/div\u003e(9) \u003c/p\u003e \u003cp\u003ewhere the first differences for period \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:t=1\\)\u003c/span\u003e\u003c/span\u003e are lost. If we use the notation \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\beta\\:}}_{d}\\)\u003c/span\u003e\u003c/span\u003e for the first difference estimate, its magnitude will be similar to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\beta\\:}}_{f}\\)\u003c/span\u003e\u003c/span\u003e. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\beta\\:}}_{d}\\)\u003c/span\u003e\u003c/span\u003e in Eq.\u0026nbsp;(9) makes clearer, however, that we are estimating the short-run effects of changes in \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{it}\\)\u003c/span\u003e\u003c/span\u003e on changes in \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{it}\\)\u003c/span\u003e\u003c/span\u003e.\u003ca class=\"FNLink\" href=\"#Fn5\" id=\"#FNLinkFn5\"\u003e\u003c/a\u003e Moreover, since \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{it}\\)\u003c/span\u003e\u003c/span\u003e is the log of income per capita and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{it}\\)\u003c/span\u003e\u003c/span\u003e is the log of Market Potential, the first difference of the logarithm of a variable is the instantaneous growth rate of that variable, which is very similar to the discrete growth rate (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:g\\)\u003c/span\u003e\u003c/span\u003e) of the variable. In sum, in a wage equation, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\beta\\:}}_{f}\\)\u003c/span\u003e\u003c/span\u003e will be very similar to the estimate of a model for the growth rates of the levels of Market Potential and income per capita. Calling \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{X}_{it}={e}^{{x}_{it}}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Y}_{it}={e}^{{y}_{it}}\\)\u003c/span\u003e\u003c/span\u003e, the fixed effects estimate will be similar to that obtained with the following pooled model of the variables in levels, for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:t=2\\dots\\:T\\)\u003c/span\u003e\u003c/span\u003e:\u003ca class=\"FNLink\" href=\"#Fn6\" id=\"#FNLinkFn6\"\u003e\u003c/a\u003e\u003cdiv id=\"Equj\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equj\" name=\"EquationSource\"\u003e\n$$\\:{g}_{Yit}=C+\\beta\\:{g}_{Xit}+{u}_{it}$$\u003c/div\u003e\u003c/div\u003e(10) \u003c/p\u003e \u003cp\u003eAs mentioned in Section 2, nothing in (long-term) location theory predicts that yearly growth rates of an indicator of regional Market Potential should have a significant impact on regional growth rates of income per capita. I, however, obtain positive significant \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\beta\\:}}_{f}\\)\u003c/span\u003e\u003c/span\u003e estimates below. Why?\u003c/p\u003e"},{"header":"4 Data and methodology","content":"\u003cp\u003eThe sample includes Eurostat regional data for 233 regions from 25 countries (but not Switzerland), for the years 1995\u0026ndash;2022. The explanatory variable is Harris\u0026rsquo; indicator of External Market Potential. As mentioned above, my estimation of a wage-type equation uses real \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:GVApc\\)\u003c/span\u003e\u003c/span\u003e to proxy regional marginal costs and real \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:GVA\\)\u003c/span\u003e\u003c/span\u003e to proxy regional market size. The data come from the ARDECO database (see online Supplementary Appendix for further details). Inter-regional distances (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{d}_{ij}\\)\u003c/span\u003e\u003c/span\u003e) are measured as great-circle distances between regional centroids.\u003c/p\u003e \u003cp\u003eI now begin to disentangle the reasons we obtain a significant fixed effects estimate of Market Potential in my European wage-type equation. I start by estimating the following cross-sectional and pooled panel models, expecting to find similar values for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\widehat{\\beta\\:}\\)\u003c/span\u003e\u003c/span\u003e:\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{log}{GVApc}_{i}=C+\\beta\\:\\text{log}{EMP}_{i}+\\:{u}_{i}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eModel 1\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{log}{GVApc}_{it}=C+\\beta\\:\\text{log}{EMP}_{it}+\\:{u}_{it}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eModel 2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"2\"\u003eI then estimate the model in first differences, as in Eq.\u0026nbsp;(9), and the within-region model, as in Eq.\u0026nbsp;(7), expecting to find similar values for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\widehat{\\beta\\:}\\)\u003c/span\u003e\u003c/span\u003e, as follows:\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabb\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{log}{GVApc}_{it}-\\text{log}{GVApc}_{it-1}=C+\\beta\\:(\\text{log}{EMP}_{it}-{log}{EMP}_{it-1})+({u}_{it}-{u}_{it-1})\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eModel 3\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{log}{GVApc}_{it}-\\stackrel{-}{{log}{GVApc}_{i}}=C+\\beta\\:(\\text{log}{EMP}_{it}-\\stackrel{-}{{log}{EMP}_{i}})+({u}_{it}-\\stackrel{-}{{u}_{i}})\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eModel 4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFor a cross-sectional European sample, Bruna (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2024a\u003c/span\u003e) shows that the estimation results of a wage-type equation are spurious because the data are spatially nonstationary. The spatial distribution of Market Potential and many other variables roughly matches the core-periphery spatial patten of European regional income, which cannot be used to confirm the NEG explanation. Inspired by this finding, I conjecture that the significant effect of Market Potential in the fixed effects estimation of Model 4 might be due to a common time pattern in the series of GVA per capita and EMP. To test this hypothesis, I calculate an artificial indicator of European Market Potential (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:EuMP\\)\u003c/span\u003e\u003c/span\u003e). As with the definition of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{EMP}_{it}=\\sum\\:_{j\\ne\\:i}^{R-1}{{d}_{ij}}^{-1}{GVA}_{jt}\\)\u003c/span\u003e\u003c/span\u003e, I build the following indicator \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{EuMP}_{t}={{d}_{m}}^{-1}\\sum\\:_{j=1}^{R}{GVA}_{jt}\\)\u003c/span\u003e\u003c/span\u003e, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{d}_{m}\\)\u003c/span\u003e\u003c/span\u003e is the median of the average distances from each region to each of the others.\u003ca class=\"FNLink\" href=\"#Fn7\" id=\"#FNLinkFn7\"\u003e\u003c/a\u003e Note that \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{EMP}_{it}\\)\u003c/span\u003e\u003c/span\u003e changes by region and period, whereas \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{EuMP}_{t}\\)\u003c/span\u003e\u003c/span\u003e is the same for any region in the same period and captures the aggregate business cycle. Model 5 repeats the fixed effects equation of Model 4 but replaces \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{EMP}_{it}\\)\u003c/span\u003e\u003c/span\u003e with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{EuMP}_{t}\\)\u003c/span\u003e\u003c/span\u003e. Since \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{EuMP}_{t}\\)\u003c/span\u003e\u003c/span\u003e only varies by year, the estimation of Model 5 cannot include time effects. For reasons of comparability, I estimate all models without time effects. Model 6 includes both \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{EMP}_{it}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{EuMP}_{t}\\)\u003c/span\u003e\u003c/span\u003e. I use R\u0026rsquo;s \u0026lsquo;plm\u0026rsquo; package (Croissant and Millo \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) to estimate all these panel data models.\u003c/p\u003e \u003cp\u003eMoreover, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{EMP}_{it}\\)\u003c/span\u003e\u003c/span\u003e can be seen as a spatially lagged endogenous variable of the wage equation and thus also captures global spillovers (Mion \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Bruna et al. \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). This interpretation is useful to test the robustness of results to the estimation of spatial econometrics panel data models, using R\u0026rsquo;s \u0026lsquo;splm\u0026rsquo; package (Millo and Piras \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). I define a spatial weights matrix (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:W\\)\u003c/span\u003e\u003c/span\u003e) as a row-standardized binary matrix that includes the four nearest neighbors (see online Appendix for additional details). With this \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:W\\)\u003c/span\u003e\u003c/span\u003e, the spatial lag of a variable \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{i}\\)\u003c/span\u003e\u003c/span\u003e for region \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003e is the mean of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{j}\\)\u003c/span\u003e\u003c/span\u003e for its four nearest \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:j\\)\u003c/span\u003e\u003c/span\u003e regions.\u003c/p\u003e \u003cp\u003eStarting from a generic representation of the fixed effects models, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{t}=\\beta\\:{x}_{t}+u+\\:{u}_{t}\\)\u003c/span\u003e\u003c/span\u003e, the Spatial Error Model (SEM) assumes that possible ignored explanatory factors can correlate spatially, as captured by the following spatial model of the unexplained cross-sectional variation of the dependent variable: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{u}_{t}=\\lambda\\:\\text{W}{u}_{t}+{ϵ}_{t}\\)\u003c/span\u003e\u003c/span\u003e.\u003ca class=\"FNLink\" href=\"#Fn8\" id=\"#FNLinkFn8\"\u003e\u003c/a\u003e The Spatial Autoregressive Model (SAR), however, assumes spillovers from income per capita of neighboring regions, adding the spatial lag of the dependent variable (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:W{y}_{t}\\)\u003c/span\u003e\u003c/span\u003e) as an explanatory variable:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{t}=\\beta\\:{x}_{t}+\\rho\\:\\text{W}{y}_{t}+u+{u}_{t}\\)\u003c/span\u003e \u003c/span\u003e. Since \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{t}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{t}\\)\u003c/span\u003e\u003c/span\u003e are the logs of GVApc and External Market Potential, respectively, the SAR model introduces some duplicate information about external markets: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:W{y}_{t}=\\sum\\:_{j\\ne\\:i}^{4}{{w}_{ij}}^{-1}\\text{log}{GVApc}_{jt}\\)\u003c/span\u003e\u003c/span\u003e partially overlaps with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{t}=\\text{log}{EMP}_{it}=\\text{log}\\sum\\:_{j\\ne\\:i}^{R-1}{{d}_{ij}}^{-1}{GVA}_{jt}\\)\u003c/span\u003e\u003c/span\u003e, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{w}_{ij}}^{-1}\\)\u003c/span\u003e\u003c/span\u003e is the corresponding non-diagonal element of my \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:W\\)\u003c/span\u003e\u003c/span\u003e matrix (displayed here in a format comparable to the weighting scheme in EMP).\u003ca class=\"FNLink\" href=\"#Fn9\" id=\"#FNLinkFn9\"\u003e\u003c/a\u003e\u003c/p\u003e \u003cp\u003eAdditionally, estimation residuals of my fixed effects estimations tend to display not only spatial autocorrelation but also serial dependence. Further, I analyze the robustness of the panel results to the inclusion of the time lag of the dependent variable, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{t-1}\\)\u003c/span\u003e\u003c/span\u003e. The SEM and SAR models to be estimated are thus as follows:\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabc\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{t}=\\beta\\:{x}_{t}+{\\gamma\\:}{y}_{t-1}+\\lambda\\:\\text{W}{u}_{t}+u+\\:{ϵ}_{t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eModel 7\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{t}=\\beta\\:{x}_{t}+{\\gamma\\:}{y}_{t-1}+\\rho\\:\\text{W}{y}_{t}+u+{u}_{t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eModel 8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe calculation of time lags for Models 3, 7, and 8 use data for 1995. To facilitate comparability, however, I estimate all panel data models with the same number of observations for 27 years (1996\u0026ndash;2022).\u003c/p\u003e \u003cp\u003eI do not estimate Models 1\u0026ndash;8 with methods that correct for biases due to potential endogeneity of the explanatory variables, as is common in causal analysis in the NEG empirical literature. My story is not about causality but about the statistical properties of the variables transformed to short-term variations. I argue that these properties do not capture what they are supposed to within NEG framework.\u003c/p\u003e \u003cp\u003eTo illustrate the intuitions about the statistical features behind the black box estimations, I compare data aggregated for the entire European sample with data of four regions, selected based on their different access to the main European markets (see online Appendix for details): Mittelfranken, Algarve, Kriti, and Nord-Norge. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows their location and the time series of their log GVApc, as well as the latter variable for the whole sample (solid line).\u003ca class=\"FNLink\" href=\"#Fn10\" id=\"#FNLinkFn10\"\u003e\u003c/a\u003e For the period 1996\u0026ndash;2022, the Pearson correlations\u003ca class=\"FNLink\" href=\"#Fn11\" id=\"#FNLinkFn11\"\u003e\u003c/a\u003e of the times series of Algarve and Kriti with the European time series are 0.24 and \u0026minus;\u0026thinsp;0.08, respectively. This correlation is lower than 0.4 for 15% of the regions but higher than 0.8 for 77% of the regions, indicating that regional European income per capita evolves quite synchronically (Giannone and Reichlin \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Kunroo \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"5 Results","content":"\u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e represents the time series of lEMP and its time-demeaned version for the four regions selected and the European sample. The latter is measured by the artificial indicator \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{EuMP}_{t}\\)\u003c/span\u003e\u003c/span\u003e. The plot on the left shows that the region of Norway has low Market Potential due to both its peripherality and its larger size (Bruna \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2024a\u003c/span\u003e).\u003ca class=\"FNLink\" href=\"#Fn12\" id=\"#FNLinkFn12\"\u003e\u003c/a\u003e Geographical centrality and small rich neighborhoods give the German region high Market Potential. For two reasons, all these series evolve similarly, following the evolution of the sum of GVA for the whole sample (solid line). Firstly, the general synchronicity of the time series of regional GVA (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e for GVApc) tends to produce similar movements in data aggregated for several regions. Secondly, the smoothing effects of the sum for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:R-1\\)\u003c/span\u003e\u003c/span\u003e regions in Harris\u0026rsquo;s accessibility index tend to dissipate local differences of the temporal changes in GVA. Given that the regional indicators of Market Potential tend to move together, the time-demeaned series in the right-hand plot are very similar. In other words, in a fixed effects estimation, Market Potential does not really capture relevant changes in the accessible market size for firms in each region. Rather, it captures the European business cycle.\u003c/p\u003e \u003cp\u003eTo test this explanation, Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e compares estimation of the eight models described in Section 4. As expected, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\beta\\:}}_{c}\\)\u003c/span\u003e\u003c/span\u003e estimates of log External Market Potential are similar in Columns (1) and (2). They are also similar in Columns (3) and (4), which refer to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\beta\\:}}_{d}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\widehat{\\beta\\:}}_{f}\\)\u003c/span\u003e\u003c/span\u003e, respectively, and take values of around 1. This means that a 1% increase in the growth rate of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{EMP}_{it}\\)\u003c/span\u003e\u003c/span\u003e generates a 1% increase in the growth rate of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{GVApc}_{it}\\)\u003c/span\u003e\u003c/span\u003e.\u003ca class=\"FNLink\" href=\"#Fn13\" id=\"#FNLinkFn13\"\u003e\u003c/a\u003e Under a NEG interpretation of the results, these estimates could be considered biased due to the endogeneity of Market Potential. I argue, however, that this high estimate reflects only the translation of the European economic cycle in GVA to the common movements in the regional times series of GVA per capita. As I discuss below, this high unitary elasticity collapses to 0.06 if the lagged dependent variable is added to the equation in Column (4) (see online Appendix), suggesting that the results of Market Potential are driven by the business cycle.\u003c/p\u003e \u003cp\u003eColumn (5) of Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the paper\u0026rsquo;s main contribution. When the regional values of External MP (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{EMP}_{it}\\)\u003c/span\u003e\u003c/span\u003e) are replaced by the artificial variable of European MP (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{EuMP}_{t}\\)\u003c/span\u003e\u003c/span\u003e), adjusted R\u003csup\u003e2\u003c/sup\u003e and the estimate are very similar to those in Column (4). The regional differences of time-demeaned External MP thus make little difference compared to the aggregate evolution of European GVA, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. This result has nothing to do with NEG theory, as the explanation of the fixed effects results must be confined to the purely statistical domain. The key issue explaining the synchronic evolution of regional GVApc is the aggregate evolution of European GVA.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eCross-sectional and panel data models of the effects of two variables of Market Potential (MP) on gross value added per capita (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:lGVApc\\)\u003c/span\u003e\u003c/span\u003e)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eCross-section\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003ePooled panel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eFirst differences\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"5\" nameend=\"c9\" namest=\"c5\"\u003e \u003cp\u003eWithin group panel (regional fixed effects)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e \u003cp\u003eNonspatial\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003eSpatial\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(1)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(4)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(6)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e(7)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e(8)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:log\\:External\\:MP\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.608\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.671\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.034\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.014\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e3.858\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(0.174)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(0.083)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(0.030)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(0.048)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(0.479)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:log\\:European\\:MP\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.964\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-2.893\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.051\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.023\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(0.051)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(0.467)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e(0.010)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e(0.007)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:log\\:GVApc\\:(t-1)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.926\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.003\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e(0.005)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e(0.012)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Wu\\)\u003c/span\u003e\u003c/span\u003e [\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\lambda\\:\\)\u003c/span\u003e\u003c/span\u003e parameter]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.670\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e(0.010)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Wlog\\:GVAp\\)\u003c/span\u003e\u003c/span\u003e [\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\rho\\:\\)\u003c/span\u003e\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.189\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e(0.007)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAdjusted R\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.209\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0. 217\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.345\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.567\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.499\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.650\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLog likelihood\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-5,236\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e12,236\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"9\"\u003eNote: Cross-sectional data (233 observations) refer to 2019 and panel data (6,291 obs.) to 1996\u0026ndash;2022. The intercept in Columns (1) and (2) is not reported. Standard errors (in brackets) are clustered by country in Column (1) and by region and year, and robust to persistent common shocks, in Columns (2) to (6). Coefficients of variables in Column (8) are total impact estimates after 300 simulations to compute the impact distribution. \u003csup\u003e*\u003c/sup\u003ep\u0026thinsp;\u0026lt;\u0026thinsp;0.1; \u003csup\u003e**\u003c/sup\u003ep\u0026thinsp;\u0026lt;\u0026thinsp;0.05; \u003csup\u003e***\u003c/sup\u003ep\u0026thinsp;\u0026lt;\u0026thinsp;0.01.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eColumn (6) presents the results when both variables of Market Potential are included in the fixed effects estimation. Their estimates are statistically significant but with opposing signs, due to multicollinearity: The average correlation of all regional series of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{EMP}_{it}\\)\u003c/span\u003e\u003c/span\u003e with the artificial variable \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{EuMP}_{t}\\)\u003c/span\u003e\u003c/span\u003e is 0.997.\u003c/p\u003e \u003cp\u003eTests reveal the presence of temporal and spatial dependence in the residuals of the previous models.\u003ca class=\"FNLink\" href=\"#Fn14\" id=\"#FNLinkFn14\"\u003e\u003c/a\u003e Columns (7) and (8) shows estimations of the model in Column (5)\u003ca class=\"FNLink\" href=\"#Fn15\" id=\"#FNLinkFn15\"\u003e\u003c/a\u003e after considering temporal and spatial dependence. The inclusion of the time lag of the dependent variable captures inertia in the regional business cycle. To correct for spatial autocorrelation, Columns (7) and (8) show result of a SEM and SAR models, respectively.\u003ca class=\"FNLink\" href=\"#Fn16\" id=\"#FNLinkFn16\"\u003e\u003c/a\u003e Both spatial parameters are statistically significant.\u003c/p\u003e \u003cp\u003eSEM estimation shows a way of capturing departures from the European cycle due to spatially autocorrelated omitted variables. Controlling for that, Column (7) shows that the regional effects of the contemporary European cycle, as captured by European Market Potential, are still significant, with a parameter of 0.05.\u003ca class=\"FNLink\" href=\"#Fn17\" id=\"#FNLinkFn17\"\u003e\u003c/a\u003e\u003c/p\u003e \u003cp\u003eThe SAR model in Column (8) includes the spatial lag of the dependent variable, thus capturing spillovers from the evolution of the dependent variable of nearest neighbors. Once the local business cycle in each area of the map is incorporated, the effects of the aggregate cycle captured by European MP become negative. The reason, again, is multicollinearity. The correlation between the times series of the spatial lag of the dependent variable and the log of European MP is lower than 0.4 for 12% of the regions but higher than 0.8 for 85% of the regions. This result means that the spatial lag of the dependent variable also follows the European cycle but is more precise in capturing local departures from it to explain the evolution of regional income per capita.\u003c/p\u003e"},{"header":"6 Conclusions","content":"\u003cp\u003ePanel data literature emphasizes the need to control for individual heterogeneity to avoid biases caused by time-invariant regional factors. It should not be forgotten, however, that controlling for unobserved regional fixed effects forces use of transformed data on temporal changes. The resulting within-region estimates are not comparable to the between-region estimates obtained using cross-sectional data. For data in log form defined at intervals of one or a few years, panel data estimates approximate the effects of the short-term growth rates of variables and are thus not a good way of testing long-term theoretical predictions.\u003c/p\u003e \u003cp\u003eThis study shows that the evolution of regional income per capita is highly synchronic in Europe, following the European cycle. The smoothing effects of summation when constructing the variable Market Potential intensify this variable\u0026rsquo;s synchronicity: the temporal changes in Market Potential are very similar for all regions. Changes in Market Potential thus capture changes in the European business cycle, which explain the average changes in regional income per capita well. Short-term growth rates in Market Potential capture short-term growth rates of aggregate European economic activity, which are also similar to the average short-term growth rates of income in neighboring regions. The panel data estimates capture correlations or spillovers from the aggregate cycle but not the mechanisms studied by the NEG. When using these data, therefore, a variable of Market Potential that is statistically significant in a fixed effects estimation does not confirm the NEG.\u003c/p\u003e \u003cp\u003eThis research should be extended to study other geographical samples. For long-run theories, panel data methods are more appropriate when using long historical data sets for time intervals of decades. The \u0026lsquo;pooled mean group estimator\u0026rsquo; (Pesaran et al. \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e1999\u003c/span\u003e) of dynamic panels with a large number of time and spatial units takes into account possible common long-run relationships across spatial units. An alternative approach comes from the literature on spatial and temporal unit roots and cointegration in panel data (Banerjee \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e1999\u003c/span\u003e; Baltagi and Shu \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eUltimately, researchers should choose statistical methods based on the time frame of the underlying theory. They also should be careful with the temporal and spatial properties of the (transformed) data and use graphical and statistical tools before black box estimations.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eAll authors whose names appear on the submission1) made substantial contributions to the conception or design of the work; or the acquisition, analysis, or interpretation of data; or the creation of new software used in the work;2) drafted the work or revised it critically for important intellectual content;3) approved the version to be published; and4) agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eI thank Javier Barbero and Mariano Matilla-Garc\u0026iacute;a for very useful suggestions. 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Elsevier, Amsterdam, pp 131\u0026ndash;195\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKrugman P (1991) Increasing returns and economic geography. J Polit Econ 99:483\u0026ndash;499. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1086/261763\u003c/span\u003e\u003cspan address=\"10.1086/261763\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKrugman P (1993) First Nature, Second Nature, and Metropolitan Location. 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J Urban Econ 56:97\u0026ndash;118. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.jue.2004.03.004\u003c/span\u003e\u003cspan address=\"10.1016/j.jue.2004.03.004\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eOttaviano GIP, Pinelli D (2006) Market potential and productivity: Evidence from Finnish regions. Reg Sci Urban Econ 36:636\u0026ndash;657. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.regsciurbeco.2006.06.005\u003c/span\u003e\u003cspan address=\"10.1016/j.regsciurbeco.2006.06.005\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePesaran MH, Shin Y, Smith RP (1999) Pooled Mean Group Estimation of Dynamic Heterogeneous Panels. J Am Stat Assoc 94:621\u0026ndash;634. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1080/01621459.1999.10474156\u003c/span\u003e\u003cspan address=\"10.1080/01621459.1999.10474156\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRedding SJ (2011) Economic Geography: a Review of the Theoretical and Empirical Literature. In: Bernhofen D, Falvey R, Greenaway D, Kreickemeier U (eds) Palgrave Handbook of International Trade. Palgrave Macmillan, London, pp 497\u0026ndash;531\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRedding SJ, Venables AJ (2004) Economic geography and international inequality. J Int Econ 62:53\u0026ndash;82. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.jinteco.2003.07.001\u003c/span\u003e\u003cspan address=\"10.1016/j.jinteco.2003.07.001\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRokicki B, Cieślik A (2023) Rethinking regional wage determinants: regional market potential versus trade partners\u0026rsquo; potential. Spat Econ Anal 18:126\u0026ndash;142. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1080/17421772.2022.2070657\u003c/span\u003e\u003cspan address=\"10.1080/17421772.2022.2070657\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang C-Y, Haining R (2017) Testing the new economic geography\u0026rsquo;s wage equation: a case study of Japan using a spatial panel model. Ann Reg Sci 58:417\u0026ndash;440. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s00168-016-0804-3\u003c/span\u003e\u003cspan address=\"10.1007/s00168-016-0804-3\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"},{"header":"Footnotes","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003e Empirical NEG literature does not clearly distinguish pecuniary external economies due to market size from other possible spillovers due to knowledge or expectations. In Eq.\u0026nbsp;(2), regional gross value added (GVA) per capita is affected by the GVA of other regions, a condition compatible with a variety of explanations. See Duranton and Puga (\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2004\u003c/span\u003e), Bruna et al. (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), Elhorst (\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), Bruna (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2024a\u003c/span\u003e), and discussion below.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e The following papers use Harris\u0026rsquo; indicator of Market Potential: Breinlich (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2006\u003c/span\u003e), Fingleton (\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2008\u003c/span\u003e), Amaral et al. (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2010\u003c/span\u003e), Baltagi et al. (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2014\u003c/span\u003e), Wang and Haining (\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2017\u003c/span\u003e), and Rokicki and Cieślik (\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e For reasons explained in the following section, I do not include time effects in any of these models. Considering time effects does not change the results obtained in the paper (see online Supplementary Appendix).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e I have repeated the calculations in this paper for a panel of seven time-observations defined for four-year data averages. The online Supplementary Appendix shows that the empirical results are very similar.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e When there is high serial correlation in the idiosyncratic random term, \u003cdiv id=\"IEq57\" class=\"InlineEquation\"\u003e\u003cdiv format=\"TEX\" class=\"mathinline\" id=\"FileID_IEq57\" name=\"EquationSource\"\u003e\u003cscript type=\"math/tex; mode=inline\"\u003e\\:{\\widehat{\\beta\\:}}_{d}\u003c/script\u003e\u003c/div\u003e\u003c/div\u003e is more efficient than \u003cdiv id=\"IEq58\" class=\"InlineEquation\"\u003e\u003cdiv format=\"TEX\" class=\"mathinline\" id=\"FileID_IEq58\" name=\"EquationSource\"\u003e\u003cscript type=\"math/tex; mode=inline\"\u003e\\:{\\widehat{\\beta\\:}}_{f}\u003c/script\u003e\u003c/div\u003e\u003c/div\u003e (Boulhol and de Serres \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2010\u003c/span\u003e).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e Ottaviano and Pinelli (\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) propose another model derived from an interpretation of the wage equation assuming that regions fluctuate around a balanced growth path. These authors define the growth rate \u003cdiv id=\"IEq66\" class=\"InlineEquation\"\u003e\u003cdiv format=\"TEX\" class=\"mathinline\" id=\"FileID_IEq66\" name=\"EquationSource\"\u003e\u003cscript type=\"math/tex; mode=inline\"\u003e\\:{g}_{Yit}\u003c/script\u003e\u003c/div\u003e\u003c/div\u003e within a time span of ten years and regress it on the logs of Market Potential and per capita income for the initial year. I do not study their model here. Bruna (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2024a\u003c/span\u003e) shows that the spatial patterns of European EMP and a pure indicator of geographical centrality are almost identical. For 2019, the correlations of the log of EMP with the logs of GVApc and inverse mean distance to all the other regions are 0.46 and 0.88, respectively.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e With this definition, the GVA of each region is used to build the European MP, which is later used to explain each region\u0026rsquo;s GVApc. The resulting endogeneity of the European variable is similar to the results obtained using regional income to measure Internal Market Potential in the NEG literature (Bruna \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2024b\u003c/span\u003e). The consequences are minor, however. The median weight of \u003cdiv id=\"IEq81\" class=\"InlineEquation\"\u003e\u003cdiv format=\"TEX\" class=\"mathinline\" id=\"FileID_IEq81\" name=\"EquationSource\"\u003e\u003cscript type=\"math/tex; mode=inline\"\u003e\\:{GVA}_{jt}\u003c/script\u003e\u003c/div\u003e\u003c/div\u003e in \u003cdiv id=\"IEq82\" class=\"InlineEquation\"\u003e\u003cdiv format=\"TEX\" class=\"mathinline\" id=\"FileID_IEq82\" name=\"EquationSource\"\u003e\u003cscript type=\"math/tex; mode=inline\"\u003e\\:\\sum\\:_{j=1}^{R}{GVA}_{jt}\u003c/script\u003e\u003c/div\u003e\u003c/div\u003e is 0.26%.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e Unlike the notation in the \u0026lsquo;splm\u0026rsquo; package, I use \u003cdiv id=\"IEq99\" class=\"InlineEquation\"\u003e\u003cdiv format=\"TEX\" class=\"mathinline\" id=\"FileID_IEq99\" name=\"EquationSource\"\u003e\u003cscript type=\"math/tex; mode=inline\"\u003e\\:\\lambda\\:\u003c/script\u003e\u003c/div\u003e\u003c/div\u003e for the spatial parameter of the SEM model.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e A key difference is that \u003cdiv id=\"IEq108\" class=\"InlineEquation\"\u003e\u003cdiv format=\"TEX\" class=\"mathinline\" id=\"FileID_IEq108\" name=\"EquationSource\"\u003e\u003cscript type=\"math/tex; mode=inline\"\u003e\\:{{d}_{ij}}^{-1}\u003c/script\u003e\u003c/div\u003e\u003c/div\u003e is measured as inverse absolute distances, while standardized \u003cdiv id=\"IEq109\" class=\"InlineEquation\"\u003e\u003cdiv format=\"TEX\" class=\"mathinline\" id=\"FileID_IEq109\" name=\"EquationSource\"\u003e\u003cscript type=\"math/tex; mode=inline\"\u003e\\:W\u003c/script\u003e\u003c/div\u003e\u003c/div\u003e matrices ignore sample geography to focus on local issues. See Bruna et al. (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2016\u003c/span\u003e).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e Panel unit root tests reveal that the time series of lGVApc are generally stationary (see online Supplementary Appendix). In any case, my argument involves not potential spurious results due to nonstationarity but the misinterpretation of the empirical results of the fixed effects wage equation.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e To detect covariation, or synchronicity, Pearson\u0026rsquo;s (linear) correlation is more stringent than Kendall or Spearman correlations, which are rank-based coefficients.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e Norwegian regions are an exception to the rough core-periphery pattern of GVApc around the so-called European \u0026lsquo;blue (or hot) banana\u0026rsquo;. They are relatively rich (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) but peripheral and so have low EMP (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). See: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://en.wikipedia.org/wiki/Blue_Banana\u003c/span\u003e\u003cspan address=\"https://en.wikipedia.org/wiki/Blue_Banana\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e For the four regions chosen, the mean correlation between the time series of EMP in first difference and in discrete growth rates is 0.988.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e I conducted Breusch-Godfrey tests for serial dependence and Pesaran\u0026rsquo;s tests for cross-sectional dependence in the residuals of the models in Columns (4) and (5). See online Supplementary Appendix.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e Conclusions derived from Columns (7) and (8) are very similar if these models are based on the equation for External Market Potential in Column (4). See Appendix.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e Panel Lagrange Multiplier tests for spatial dependence in the equation in column (5) reveal a weak preference for the SAR over the SEM correction for spatial autocorrelation. See Appendix.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e The estimate of European MP in Column (5) becomes 0.050 when the time lag of the dependent variable is added to the equation (see Appendix). The similarity of this number to the SEM 0.051 estimate in Column (7) indicates correct specification of the model including \u003cdiv id=\"IEq132\" class=\"InlineEquation\"\u003e\u003cdiv format=\"TEX\" class=\"mathinline\" id=\"FileID_IEq132\" name=\"EquationSource\"\u003e\u003cscript type=\"math/tex; mode=inline\"\u003e\\:{EuMP}_{t}\u003c/script\u003e\u003c/div\u003e\u003c/div\u003e and \u003cdiv id=\"IEq133\" class=\"InlineEquation\"\u003e\u003cdiv format=\"TEX\" class=\"mathinline\" id=\"FileID_IEq133\" name=\"EquationSource\"\u003e\u003cscript type=\"math/tex; mode=inline\"\u003e\\:{log}{GVApc}_{it-1}\u003c/script\u003e\u003c/div\u003e\u003c/div\u003e.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"NEG, agglomeration, wage equation, fixed effects, first differences, European cycle","lastPublishedDoi":"10.21203/rs.3.rs-4979299/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4979299/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe New Economic Geography (NEG) provides a historical explanation for the spatial agglomeration of economic activity. One of its predictions, the ‘wage equation’, relates regional income to market accessibility. Although the NEG is a long-term theory, empirical literature has tested it using panel data methods, which capture short-term relationships between temporal changes in variables. For a sample of European regions, I show that panel data estimations of the wage equation identify only potential spillover effects of the European business cycle on the synchronic evolution of regional per capita income. That is, the panel data results are not due to the mechanisms proposed by the NEG. The paper concludes with a cautionary note about misinterpretation of panel data estimations.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eJEL Classification\u003c/strong\u003e: C18, C23, F12, R12, E32\u003c/p\u003e","manuscriptTitle":"Market Potential, panel data, and aggregate fluctuations: All that glitters is not gold","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-09-30 11:19:27","doi":"10.21203/rs.3.rs-4979299/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"ab26e547-4ee9-4d2a-8fd3-13869ca7fc5f","owner":[],"postedDate":"September 30th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-12-05T23:38:25+00:00","versionOfRecord":[],"versionCreatedAt":"2024-09-30 11:19:27","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4979299","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4979299","identity":"rs-4979299","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}