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Dots to boxes: Do the size and shape Dots to boxes: Do the size and shape of spatial units jeopardize economicof spatial units jeopardize economic

geography estimations?geography estimations?

A. Briant, P.-P. Combes, M. Lafourcade

Journal of Urban Economics 67 (2010)

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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

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Empirical questions to be addressed:1. Spatial concentration

a. Evaluating the degree of SC/types of zoning systemsb. Comparing the difference between the results (Gini vs.

Ellison and Glaeser)

2. Agglomeration effectsa. Estimation of employment density on labor productivityb. Comparing the magnitude of agglomeration economies

across zoning systems and econometric specification

3. Elasticity of trade flowsa. Estimation - how changes in size and shape of spatial

units affect the trade flow elasticities

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MotivationMotivation

- The Modifiable Areal Unit Problem/the MAUPThe Modifiable Areal Unit Problem/the MAUP: sensitivity of statistical results to the choice of zoning system

- Policy: agglomeration effects, cluster-formation strategies, concentration measures.

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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

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Modifiable Areal Unit Problem

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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

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Zoning systems and data

Small zoning system:

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Zoning systems and data

Large zoning system:

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Zoning systems and data

Medium zoning system:

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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

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Zoning systems and data

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Estimation strategyEstimation strategy1. Simulation2. Correlation - Spatial concentration

a. Ginib. Ellison-Glaeser

3. Agglomeration economiesa. baseline: gross wagesb. net wagesc. gross wages+ market potential as a control variable d. net wages + market potential as a control variable

4. Gravity equationa. Baseline b. Augmented gravity (migration+networks)

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(1) Simulation(1) Simulation

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(1) Simulation(1) Simulation

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(1) Simulation: conclusions

• with low within-unit heterogeneity (e.g. spatial sorting) and low between-unit heterogeneity (e.g. identically shaped units), the first moments of the distribution are not too much distorted by aggregation and changes in the size of units.

• with strong within-unit heterogeneity (e.g. unsorted data), aggregation yields a loss of information, even if units are shaped homogeneously

• when spatial units do not have the same shape, averaging is less sensitive to changes in size than summation,though part of the information is lost when data are not spatially sorted.

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(2 .a.) Spatial concentration(2 .a.) Spatial concentration: : GiniGini

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(2 .b.) Spatial concentration(2 .b.) Spatial concentration: : Ellison-Ellison-GlaeserGlaeser

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(2) Spatial concentration(2) Spatial concentration: : Gini vs Gini vs Ellison-GlaeserEllison-Glaeser

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(2) Spatial concentration(2) Spatial concentration:: conclusions 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

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(3.a) Agglomeration economies: (3.a) Agglomeration economies: gross wagesgross wages

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(3.b.) Agglomeration economies: (3.b.) Agglomeration economies: net wagesnet wages

2. Net wage for an individual:

1.

3. Avg net wages for an area

4. Agglomeration economy:

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(3.c.) Agglomeration economies: (3.c.) Agglomeration economies: gross wages+market potentialgross wages+market potential

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(3.d.) Agglomeration economies: (3.d.) Agglomeration economies: net wages+market potentialnet wages+market potential

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(3.d.) Agglomeration economies: (3.d.) Agglomeration economies: net wages+market potentialnet wages+market potential

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(3) Agglomeration economies(3) Agglomeration economies:: conclusions conclusions

• differences due to size and shape are much less pronounced than those resulting from a change in specification

• a good specification is an efficient way to circumvent the MAUP

• the loss of information (as the cause of MAUP) can be mitigated when the process of aggregation is of the average-type and when the raw information is not too much heterogeneous within-unit.

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(4.a.) Gravity equation: baseline(4.a.) Gravity equation: baseline

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(4.b.) Gravity equation: migration +networks(4.b.) Gravity equation: migration +networks

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(4) Gravity equations (4) Gravity equations :: conclusions conclusions

• size matters more than shape• size distortions are definitely larger than in our previous

exercises because gravity regressions involve variables aggregated under different processes

• MAUP distortions remain of smaller magnitude than mis-specification biases.

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ConslusionsConslusions

• although the size effect of the MAUP is of second-order compared to mis-specification

• shape distortions remain of only third-order concern• the MAUP distortions are negligible when both the dependent

and explanatory variables are averaged• the MAUP distortions are more jeopardizing when the

aggregation processes are not consistent on both sides of the regression