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Dots to boxes: Do the size and shape of spatial units jeopardize economic geography estimations?

Dots to boxes: Do the size and shape of spatial units jeopardize economic geography estimations?. Briant, P.-P. Combes, M. Lafourcade Journal of Urban Economics 67 (2010). Research questions. Does size and shape could affect the geographic estimations

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Dots to boxes: Do the size and shape of spatial units jeopardize economic geography estimations?

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  1. Dots to boxes: Do the size and shape of spatial units jeopardize economicgeography estimations? Briant, P.-P. Combes, M. Lafourcade Journal of Urban Economics 67 (2010) CMSSE Summer School

  2. Research questions • Does size and shape could affect the geographic estimations • Size (equivalently the number of spatial units) • Shape (equivalently the drawing of boundaries) • Does the way of data aggregating matter? • Averaging vs summing CMSSE Summer School

  3. Empirical questions to be addressed: • Spatial concentration • Evaluating the degree of SC/types of zoning systems • Comparing the difference between the results (Gini vs. Ellison and Glaeser) • Agglomeration effects • Estimation of employment density on labor productivity • Comparing the magnitude of agglomeration economies across zoning systems and econometric specification • Elasticity of trade flows • Estimation - how changes in size and shape of spatial units affect the trade flow elasticities CMSSE Summer School

  4. Motivation • The Modifiable Areal Unit Problem/the MAUP: sensitivity of statistical results to the choice of zoning system • Policy: agglomeration effects, cluster-formation strategies, concentration measures. CMSSE Summer School

  5. Modifiable Areal Unit Problem Correlation coefficients could vary across zoning systems: • correlation between male juvenile delinquency and median equivalent monthly housing rent increases monotonically with the size of spatial units (1934, Gehlke, Beihl) • correlation between the percentage of Republican voters and the percentage of the population over 60 (1979, Openshaw and Taylor) • Economists paid little attention to this problem up until last decade CMSSE Summer School

  6. Modifiable Areal Unit Problem CMSSE Summer School

  7. Zoning systems and data • Administrative zoning system: • 21 administrative “Regions” (LZS) • 94 “Departements” (MZS) • 341 unit (employment areas) Weaknesses: • Do not capture the “true” boundaries of economic phenomena • Could be changed by political reasons • Grid zoning system: • 22 Large squares • 91 medium squares • 341 small squares • Partly random zoning systems: • 4662 French “Cantons” • Equivalent to administrative ones CMSSE Summer School

  8. Zoning systems and dataSmall zoning system: CMSSE Summer School

  9. Zoning systems and dataLarge zoning system: CMSSE Summer School

  10. Zoning systems and dataMedium zoning system: CMSSE Summer School

  11. Zoning systems and data • Sectoral time-series data at the municipal level: • Three dimension panel of employment • Number of plants • Wages for 18 years (1976-1996) • 98 industries (manufacturing + services) • Averaging or summing • Summed: employment and trade flows • Averaged: others as job density and wages • Straightforward: size of the units • Not summed nor averaged variables: • Distance • Market potential CMSSE Summer School

  12. Zoning systems and data CMSSE Summer School

  13. Estimation strategy • Simulation • Correlation - Spatial concentration • Gini • Ellison-Glaeser • Agglomeration economies • baseline: gross wages • net wages • gross wages+ market potential as a control variable • net wages + market potential as a control variable • Gravity equation • Baseline • Augmented gravity (migration+networks) CMSSE Summer School

  14. (1) Simulation CMSSE Summer School

  15. (1) Simulation CMSSE Summer School

  16. (1) Simulation: conclusions • with low within-unit heterogeneity (e.g. spatialsorting) and low between-unit heterogeneity (e.g. identicallyshapedunits), the first moments of the distribution are not toomuch distorted by aggregation and changes in the size of units. • with strong within-unit heterogeneity (e.g. unsorteddata), aggregation yields a loss of information, even if unitsare shaped homogeneously • when spatial units do not have the sameshape, averaging is less sensitive to changes in size than summation,though part of the information is lost when data are not spatiallysorted. CMSSE Summer School

  17. (2 .a.) Spatial concentration: Gini CMSSE Summer School

  18. (2 .b.) Spatial concentration: Ellison-Glaeser CMSSE Summer School

  19. (2) Spatial concentration: Gini vs Ellison-Glaeser CMSSE Summer School

  20. (2) Spatial concentration: conclusions • Gini • the ranking of industries is virtually unaffected by changes in the shape of units • size has a slightly greater effect on concentration. • EG • the rank correlations for EG are generally lower than those for the Gini • size distortions are slightly aggravated in case of EG than Gini • Gini vs EG • index choice produces greater distortions than the choice of zoning system, in terms of both size or shape CMSSE Summer School

  21. (3.a) Agglomeration economies: gross wages CMSSE Summer School

  22. (3.b.) Agglomeration economies: net wages 1. 2. Net wage for an individual: 3. Avg net wages for an area 4. Agglomeration economy: CMSSE Summer School

  23. (3.c.) Agglomeration economies: gross wages+market potential CMSSE Summer School

  24. (3.d.) Agglomeration economies: net wages+market potential CMSSE Summer School

  25. (3.d.) Agglomeration economies: net wages+market potential CMSSE Summer School

  26. (3) Agglomeration economies: conclusions • differences due to sizeand shape are much less pronounced than those resulting from achange in specification • a good specificationis an efficient way to circumvent the MAUP • the loss ofinformation (as the cause of MAUP) can be mitigated when the process of aggregation is of the average-typeand when the raw information is not too much heterogeneouswithin-unit. CMSSE Summer School

  27. (4.a.) Gravity equation: baseline CMSSE Summer School

  28. (4.b.) Gravity equation: migration +networks CMSSE Summer School

  29. (4) Gravity equations : conclusions • size matters more than shape • size distortions are definitely largerthan in our previous exercises because gravity regressions involve variables aggregated under different processes • MAUP distortions remain of smaller magnitude than mis-specification biases. CMSSE Summer School

  30. Conslusions • although the size effect of the MAUP is of second-ordercompared to mis-specification • shape distortions remainof only third-order concern • the MAUP distortionsare negligible when both the dependent and explanatoryvariables are averaged • the MAUP distortions are more jeopardizingwhen the aggregation processes are not consistent on both sidesof the regression CMSSE Summer School

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