Dots to boxes Do the size and shape

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

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

Empirical questions to be addressed: 1. Spatial concentration a. Evaluating the degree of SC/types of zoning systems b. Comparing the difference between the results (Gini vs. Ellison and Glaeser) 2. Agglomeration effects a. Estimation of employment density on labor productivity b. Comparing the magnitude of agglomeration economies across zoning systems and econometric specification 3. Elasticity of trade flows a. Estimation - how changes in size and shape of spatial units affect the trade flow elasticities CMSSE Summer School

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

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

Modifiable Areal Unit Problem CMSSE Summer School

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

Zoning systems and data Small zoning system: CMSSE Summer School

Zoning systems and data Large zoning system: CMSSE Summer School

Zoning systems and data Medium zoning system: CMSSE Summer School

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

Zoning systems and data CMSSE Summer School

Estimation strategy 1. 2. Simulation Correlation - Spatial concentration a. Gini b. Ellison-Glaeser 3. Agglomeration economies a. baseline: gross wages b. net wages c. gross wages+ market potential as a control variable d. net wages + market potential as a control variable 4. Gravity equation a. Baseline b. Augmented gravity (migration+networks) CMSSE Summer School

(1) Simulation CMSSE Summer School

(1) Simulation CMSSE Summer School

(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. CMSSE Summer School

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

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

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

(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

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

(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

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

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

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

(3) Agglomeration economies: 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. CMSSE Summer School

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

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

(4) Gravity equations : 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 misspecification biases. CMSSE Summer School

Conslusions • 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 CMSSE Summer School