We introduce an original method of measuring the extent of the overall balance of migration among countries within a region which allows comparisons of the balance over time as well as between regions and various possible sub-regions

Biswas, T.

McHardy, J.

English

White Rose Research Online

This is a repository copy of Measuring the Balance of Intra-Regional Trade.White Rose Research Online URL for this paper:http://eprints.whiterose.ac.uk/9891/Monograph:Biswas, T. and McHardy, J. (2004) Measuring the Balance of Intra-Regional Trade. Working Paper. Department of Economics, University of Sheffield ISSN 1749-8368 Sheffield Economic Research Paper Series 2004005eprints@whiterose.ac.ukhttps://eprints.whiterose.ac.uk/Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version - refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher’s website. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request.   Sheffield Economic Research Paper Series  SERP Number: 2004005     Tapan Biswas*  and Jolian P. McHardy  MEASURING THE BALANCE OF INTRA-REGIONAL MIGRATION  June 2004   * Corresponding author1 Department of Economics University of Sheffield 9 Mappin Street Sheffield S1 4DT  United Kingdom www.shef.ac.uk/economics                                                             1 Corresponding author: Dr TK Biswas, Cottingham Road, Hull, HU6 7RX. Email: t.k.biswas@hull.ac.uk, Tel.: + 44 (0) 1482 465879, Fax.: +44 (0) 1482 466216. Abstract  We introduce an original method of measuring the extent of the overall balance of migration among countries within a region which allows comparisons of the balance over time as well as between regions and various possible sub-regions.    JEL Numbers:  F22, J61, O52 Keywords:  Migration Balance, Perron-Frobenius Root  1 1. Introduction   In recent years, activities for regional integration have gained pace alongside the push for globalisation.  In Europe in particular, the progressive liberalisation of internal labor markets (e.g. the Schengen agreement, 1995) and the recent xpansion of the EU have fuelled fears in some countries of large influxes of migrants, e pecially from poorer countries, pressurising job markets and social services.  Whilst Krugman (1987) argues that such regional integration should, in the long-run, result in more balanced migration through technology transfers and an improved distribution of labor skills, Zimmerman (1995) notes the importance of monitoring regional migration and intervening to redress balances if necessary.  This paper proposes a new measure which may be used to monitor the balance of migration within a region.  Section 2 introduces a measure of overall (strong) balance in migration.  Section 3 uses this measure to examine and compare the balance of migration within two regions of the EU.  Section 4 is a conclusion.    2. A Measure of Overall (Strong) Balance in Intra-Regional Migration    Let  be the number of migrants from country i to country j.  We define  as the index of bilateral balance in migration, ijm ijI1 /( )ij ij ji ij jiI m m m m⎡ ⎤= − − +⎣ ⎦ ijI.   varies from 0 (perfect imbalance) to 1 (perfect balance).2  Defining r as the group of countries in the region excluding country i,  may be used as a partial (weak) index of balance for each i.irI3  However, a perfect weak balance ( 1irI = , i∀ ) in a region is not inconsistent with perfectly                                                            2 This measure is analogous to the Grubel-Lloyd index (1975), widely used in the intra-industry trade literature.   3 Biswas and McHardy (forthcoming), use this partial measure of balance in the context of European migration.  2imbalanced country-wise bilateral migration ( 0ijI =  , ;i j i j∀ ≠ ) e.g., countries A, B and C with equal migrant flows from A to B, B to C and C to A.  In this section, we develop an alternative (strong) index for intra-regional migration balance.  Suppose, there are n countries in a region and the n x n matrix  is the matrix of bilateral migration.  [ ]ijA I=  Proposition 1: The matrix A has the following properties: (i) A is a symmetric, non-negative matrix (1≥ Iij ≥ 0) with diagonal elements Iii = 1; (ii) If bilateral migration is perfectly imbalanced, A is an identity matrix.  (iii) If bilateral migration is perfectly balanced, all the elements of A are 1 (unity).            ฀   The properties of A follow from the definition of ijI .  Let ρ  be the Perron-Frobenius root (henceforth, PFR) of the non-negative matrix A.   Proposition 2: The PFR, ρ, has the following properties: (i)  implies *A A≥ *ρ ρ≥ , i.e., ρ is non-decreasing for increases in any element of A.  (ii) 1n ρ≥ ≥ .                   ฀   Proof:  Part (i) is a general property of the PFR for any non-negative matrix A. If A is indecomposable, ρ is strictly increasing in Iij. The proof of part (ii) is as follows.  Since,  for i  and , the elements of A attain their minimum when A is an identity matrix (bilateral migration is perfectly imbalanced) and 1 0ijI≥ ≥ j≠ 1iiI =1ρ = .  The elements of A attain their maximum (each equals 1) when bilateral migration is perfectly balanced and nρ = .  To see this, note Ax xρ=  and normalise the characteristic vector x to 1ix =∑ .  Denoting the ith row of A as Ai we get i in A x xρ ρ= = =∑ ∑ .  By part (i), ρ must lie between 1 and n.                 ฀   3 The root ρ is the basis of our proposed index.  The corresponding characteristic vector x may be regarded as the vector of weights given to the countries in the region.    Proposition 3: Elements of the characteristic vector x  corresponding to ρ  generate a scheme of weighted bilateral indices of balance for each country which sum to ρ .                 ฀   Proof: Using ix  as the weight given to country i, iA x  is the weighted bilateral index of migration.  Since i iA x xρ=  and ixρ ρ=∑ , the weighted bilateral index equals the contribution of the ith country to the value of ρ .  If all countries have an identical balance,  ( ), and ijI k= , ;i j i j∀ ≠ iC A x xiρ= = , hence, /ix C ρ= : all countries have equal weights.  In the special case of an identity matrix (perfect imbalance), iC x=  and 1ρ = , therefore satisfying the above equality.  In the case of a perfect balance 1C = , nρ =  and 1/ix n= , which also satisfies the above equality.             ฀   Whilst any scheme of weights can be subject to criticism, the ix  weights have the desirable property that when countries should be treated equally, the weights given to the countries are the same. Moreover, since /i j iA x A x x x/ j= , the country with the higher weighted bilateral index for balanced migration contributes more to the overall balance than the other country.     Proposition 4: In view of propositions 1 and 2 we propose to use the index, ( 1) /( 1n )β ρ= − − , as the measure of strong balance for intra-regional migration.     ฀   The value of β is non-decreasing with increases in any  and lies between 0 (perfect imbalance) and 1 (perfect balance).  One benefit of the normalised index β, is that it allows ijI 4the comparison of balance betwen two or more regions (or sub-regions) with varying numbers of member countries.    3. An Application   In this section we construct the indices and associated strong indices of regional balance ijIβ  using Eurostat (2003) data for four southern EU countries, henceforth SE4: Greece, Italy, Spain and Portugal, and five northern EU countries, henceforth NE5: Denmark, Germany, Netherlands, Sweden and the UK.4  For the period 1992-98 (the limit of available SE4 data), the average values of β  for these regions are  and .  A two-sided t-test rejects the null hypothesis of equal means at the 0.5% level: bilateral migration is significantly more balanced within the NE5 than the SE4.  As for changes in balance over time, Table 1 reports the time-series of 92 985 0.845NEβ− = 92 984 0.614SEβ− =5NEβ  for the period 1989-2000.  The slope of the OLS regression for this time-series is positive and significant at the 0.5% level: the migration balance within the NE5 has improved significantly over time. 5 Table 1 – Time-series of 5NEβ  for the period 1989-2000 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 0.822 0.838 0.828 0.806 0.842 0.847 0.869 0.849 0.844 0.861 0.859 0.890   Finally, from Proposition 3, the elements of the normalised characteristic vector associated with the PFR can be interpreted as weights of the contribution of each country to the overall balance ρ .  The relevant figures for the nine countries in our study over the period 1992-98 are reported in Table 2.  It appears the weights attached to the NE5 countries are almost equal.  Regarding the SE4 countries, the weights are almost equal except for Portugal which seems to                                                            4 The configuration of these sub-groupings is determined by data availability. 5 For the SE4, whose time-series is much shorter, the slope of the regression line is positive but insignificant.  5be an outlier.  The reason for this lies in the facttha  migration for Portugal with respect to the other SE4 countries is relatively unbalanced (the s are closer to zero). ijI Table 2 – Average weights in the overall balance for the period 1992-98 by country   NE5    SE4 Denmark GermanyNetherlands Sweden UK  Greece Italy Portugal Spain 0.20 0.20 0.20 0.19 0.21  0.26 0.26 0.21 0.27   4. Conclusions   This paper uses the properties of the PFR to construct a new index β  of the balance of bilateral intra-regional migration, which allows comparisons of migratory balance between regions and over time.  Increases in β  over time indicate improvements in the overall balance of bilateral migration within a region, and a region with a high β has a greater bilateral migration balance than a region or sub-region with a low β .  Furthermore, normalisation of the characteristic vector for the PFR allows the interpretation of its elements as a measure of each country’s contribution to the overall migration balance.  Finally, it is important to note that the methods introduced here are directly applicable to examinations of the overall (strong) balance of intra-industry trade within a region.   6References   Biswas, T. and J.P. McHardy, forthcoming, ‘On the intensity and balance of Intra-European migration’, International Economic Journal.  Eurostat, (2003), Population and Social Conditions: International Migration Flows, Eurostat: Luxembourg.  Grubel, H. and P.J. Lloyd, (1975), Intra-Industry Trade: The Theory and Measurement of International Trade in Differentiated Products (New York, Wiley).  Krugman, P.R., (1987), ‘Economic Integration in Europe: Some Conceptual Issues’, in: T. Padro-Schioppa, ed., Efficiency, Stability and Equity (London, Oxford University Press).  Zimmermann, K.F, (1995), ‘Tackling the European Migration Problem’, Journal of Economic Perspectives, 9, 45-62.  7

Measuring the Balance of Intra-Regional Trade

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Measuring the Balance of Intra-Regional Trade

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