Market Potential, MAUP, NUTS and other spatial mysteries

Fernando BrunaJesus Lopez-Rodriguez

Andres Faina

11th International Workshop Spatial Econometrics and Statistics15-16 November 2012Avignon – France

SPATIAL INTERACTIONS WITH MARKET POTENTIAL

• Physics Magnetic or electric fields "Population potential" (Stewart, 1947) Market Potential function (Harris, 1954) Widely used in Regional Economics.

• Krugman (1991), Fujita et al. (1999)… New Economic Geography (NEG): Micro-foundations of “market potential” Many tests of the wage equation.

SPATIAL INTERACTION DEPENDS ON “SPACE”!

• Modifiable Areal Unit Problem (MAUP): The results of the analysis depends on the modifiability of the spatial partitions (areal units) => We study it estimating an equation with a variable of Market Potential.

Motivation

ECONOMIC REASONS

• The relative power of the various economic agglomerating and spreading forces are not scale-neutral but heterogeneous.

• Different economic forces (theories) are active at different spatial scales => Analyses at different scales provide different insights: the MAUP is only a “problem” when it is not recognized (ESPON, 2006).

STATISTICAL REASONS – The two sides of MAUP:

• Scale effect (ecological fallacy): for a given space, results can depend on the number of units representing it.

• Zoning (or “aggregation” ) effect: for a given scale, results can depend on how the study area is divided up.

Motivation: reasons for the MAUP

• Is a general form of the wage equation robust to different aggregation levels of European data and different non spatial econometric specifications?:

– Long-term relationships: cross-section (variables in levels)

– Short-term relationships: Panel data with fixed effects (growth rates)

• Is the MAUP affecting the estimation of these relationships with spatial econometric models?

– SEM and SAR

• How does the sample selection affect the results?

– Broad sample: 25 countries (260 NUTS 2 regions)

– Restricted sample: 15 countries (206 NUTS 2 regions)

Software – R packages: "spdep" (Bivand 2012); "plm" (Croissant and Millo, 2008) and "splm" (Millo and Piras, 2012). “Amelia II” (Honaker et al., 2011).

Motivation: empirical questions

• The NEG's wage equation explains the equilibrium industrial nominal wages as a function of the sum of demands from other regions, weighted by prices and transport costs: NEG’s Market Potential ().

• To go from the NEG’s Market Potential to the Harris’s (1954) initial formulation (), some simplifications are needed.

• But two works using European data find similar results with than with a more complex measure derived from gravity equations: Breinlich (2006) and Head and Mayer (2006).

• Both Breinlich (2006) and Ahlfeldt and Feddersen (2008) find similar results proxying trade costs with travel times or with geographical distances.

• Many empirical applications use real per capita income instead of nominal wages.

• We insert a NEG-type of equation with in a Makiw-Romer-Weil extension of Solow’s model (Mankiw et al., 1992).

New Economic Geography: The wage equation

• Long-run (cross-section): pooling with time-varying intercept:

• Short-run (growth): Panel with fixed individual and time effects:

Time-demeaning estimation of fixed effects:

• Spatial Error Model (SEM: ; • Spatial Autoregressive (Lag) Model (SAR):

• Nomenclature of territorial units for statistics (NUTS): 0, 1, 2• – Baseline weight matrix for each NUTS level and sample:

symmetrized row-standardized binary matrix of the 5 nearest neighbors, pooled for 14 years when necessary.

Specifications: variables and notation

• lGVAp – log of per capita Gross Value Added (GVA). Units: 2000 euro / inhabitant. Source: Cambridge Econometrics. Dependent variable.

• lKSp – log of per capita Capital Stock. Units: 2000 euro / inhabitant. Source: Cambridge Econometrics. Explanatory variable.

• lhrstc_pop – log of the share of population with third level studies in Science and Technology (S&T) and working in a S&T occupation: core human resources in S&T. Source: Eurostat. Explanatory variable. Imputed missing data with hrstc_popit = ß0 + ß1t + ß2t2

• lMP2GVA – log of GVA Market Potential () defined as Harris (1954). Units: Units: millions of 2000 euro. Source: Own elaboration with GVA Cambridge Econometrics data. Explanatory variable. It is a measure of the region accessibility to both internal () and external () markets (), depending on distances () as a proxy of trade costs:

• Here, the market size is measured as GVA (in real terms) and internal

distances are based on the radius () of a circular region, corrected as in

Keeble et al. (1982): 0.188

Specifications: variables and notation

Spatial distribution of the variables

Spatial distribution of the variables

Spatial distribution of the variables

• Market Potential (lagged one year) is meaningful but its presence does not alter dramatically the results.

• Residuals are spatially autocorrelated for NUTS 1 and 2: a positive spatial autocorrelation tends to increase with the disaggregation level

Pooled estimations 1996-2008 with time dummies: broad sampleOLS

(1) N0 (1) N1 (1) N2 (2) N0 (2) N1 (2) N2 (Intercept) 1.171** 0.771*** 0.662*** -0.408 -0.266 -0.279** (0.374) (0.161) (0.086) (0.425) (0.186) (0.104) lKSp 0.859*** 0.878*** 0.884*** 0.745*** 0.815*** 0.834*** (0.024) (0.011) (0.006) (0.029) (0.012) (0.007) lhrstc_pop 0.394*** 0.273*** 0.245*** 0.459*** 0.236*** 0.214*** (0.067) (0.025) (0.012) (0.064) (0.025) (0.012) lMP2GVA 0.320*** 0.172*** 0.147*** (0.049) (0.017) (0.010) R-squared 0.861 0.903 0.904 0.878 0.910 0.910 Adj. R-squared 0.855 0.902 0.904 0.872 0.909 0.910 F 137.13 775.18 2272.60 148.24 791.34 2277.48 Log likelihood -115.67 -75.77 -8.93 -94.46 -27.25 100.61 AIC 263.33 183.54 49.86 222.92 88.50 -167.23 p-value Moran's I 0.357 0.000 0.000 0.559 0.000 0.000 Moran's I residuals -0.004 0.375 0.563 -0.058 0.366 0.574 Sum squared errors 38.77 78.73 198.95 34.03 72.53 186.46 N 325 1183 3380 325 1183 3380

• And the winner is… the SEM model! => OLS estimates are not efficient

Particular cases:

• Contradiction Moran’s I-LM tests for NUTS 0 in the restricted sample

• Both robuts tests are highly significant in some cases: thought the decision rule choses the SEM, caution with misspecification.

Lagrange Multiplier tests for spatial dependence In the pooled OLS estimations with time dummies and lagged Market Potential

Statistic p-value

Spatial significance

NUTS 0: LMerr 1.484 0.223 NUTS 0: LMlag 0.025 0.875 NUTS 0: RLMerr 1.880 0.170 NUTS 0: RLMlag 0.421 0.516 NUTS 1: LMerr 36.184 0.000 *** NUTS 1: LMlag 8.598 0.003 ** NUTS 1: RLMerr 28.200 0.000 *** NUTS 1: RLMlag 0.614 0.433 NUTS 2: LMerr 214.689 0.000 *** NUTS 2: LMlag 82.663 0.000 *** NUTS 2: RLMerr 145.735 0.000 *** NUTS 2: RLMlag 13.709 0.000 ***

Statistic p-value

Spatial significance

NUTS 0: LMerr 316.622 0.00 *** NUTS 0: LMlag 29.589 0.00 *** NUTS 0: RLMerr 291.241 0.00 *** NUTS 0: RLMlag 4.209 0.04 * NUTS 1: LMerr 1526.87 0.00 *** NUTS 1: LMlag 255.878 0.00 *** NUTS 1: RLMerr 1289.921 0.00 *** NUTS 1: RLMlag 18.928 0.00 *** NUTS 2: LMerr 4676.884 0.00 *** NUTS 2: LMlag 1191.116 0.00 *** NUTS 2: RLMerr 3500.427 0.00 *** NUTS 2: RLMlag 14.659 0.00 ***

Broad sample Restricted sample

SEM: one year cross-section (1) and pooling with time effects (2) (1) N0 (1) N1 (1) N2 (2) N0 (2) N1 (2) N2 lambda -0.737 0.651*** 0.806*** 0.565*** 0.757*** 0.827*** (0.425) (0.094) (0.039) (0.058) (0.020) (0.010) (Intercept) -0.630 0.370 0.312 -1.204** -0.177 -1.325*** (0.800) (0.766) (0.481) (0.403) (0.194) (0.135) lKSp 0.813*** 0.784*** 0.698*** 0.769*** 0.844*** 0.870*** (0.081) (0.044) (0.026) (0.028) (0.013) (0.008) lhrstc_pop 0.356* 0.276*** 0.229*** 0.498*** 0.271*** 0.124*** (0.164) (0.083) (0.035) (0.056) (0.025) (0.011) lMP2GVA 0.224* 0.136* 0.230*** 0.389*** 0.139*** 0.194*** (0.101) (0.064) (0.043) (0.046) (0.020) (0.013) Log likelihood 2.72 32.11 144.74 -59.53 341.97 1451.22 AIC 6.57 -52.22 -277.49 155.07 -647.94 -2866.45 p-value LR test 0.114 0.000 0.000 0.000 0.000 0.000 p-value Moran's I 0.326 0.305 0.764 0.808 0.603 0.537 Moran's I of residuals -0.000 0.018 -0.029 -0.029 -0.005 -0.001 Sum squared errors 1.10 2.39 4.21 25.75 33.53 69.64 N 25 91 260 325 1183 3380

Broad sample

Broad sample Restricted sample

ML estimation

SAR: one year cross-section (1) and pooling with time effects (2)

Broad sample Restricted sample

(1) N0 (1) N1 (1) N2 (2) N0 (2) N1 (2) N2 rho 0.021 0.178** 0.309*** -0.016 0.153*** 0.271*** (0.132) (0.062) (0.034) (0.035) (0.016) (0.011) (Intercept) -0.175 -0.317 -0.207 -0.310 -0.738*** -0.574*** (1.286) (0.539) (0.269) (0.457) (0.183) (0.095) lKSp 0.785*** 0.718*** 0.601*** 0.751*** 0.737*** 0.655*** (0.090) (0.050) (0.030) (0.031) (0.015) (0.010) lhrstc_pop 0.403 0.246** 0.247*** 0.460*** 0.220*** 0.185*** (0.212) (0.080) (0.034) (0.062) (0.024) (0.011) lMP2GVA 0.199 0.098* 0.088*** 0.319*** 0.150*** 0.098*** (0.143) (0.050) (0.025) (0.048) (0.017) (0.009) Log likelihood 1.48 22.95 103.93 -94.36 17.80 387.79 AIC 9.04 -33.90 -195.86 224.71 0.40 -739.58 p-value LR test 0.876 0.004 0.000 0.654 0.000 0.000 p-value Moran's I 0.860 0.000 0.000 0.000 0.000 0.000 Moran's I of residuals -0.139 0.256 0.304 0.322 0.466 0.415 Sum squared errors 1.30 3.20 6.72 34.01 66.94 155.25 N 25 91 260 325 1183 3380

Broad sample

ML estimation

Pooled (1) and fixed effects (2) estimations with time effects

Broad sample Restricted sample

Broad sample

(1) N0 (1) N1 (1) N2 (2) N0 (2) N1 (2) N2 lKSp 0.739*** 0.812*** 0.833*** 0.177*** 0.332*** 0.274*** (0.028) (0.012) (0.007) (0.047) (0.025) (0.014) lhrstc_pop 0.431*** 0.223*** 0.206*** -0.094* -0.017 -0.005 (0.062) (0.024) (0.011) (0.037) (0.015) (0.007) lMP2GVA 0.342*** 0.183*** 0.151*** 3.570*** 2.056*** 2.396*** (0.049) (0.017) (0.010) (0.341) (0.091) (0.068) R-squared 0.867 0.905 0.905 0.326 0.382 0.361 Adj. R-squared 0.825 0.893 0.901 0.288 0.350 0.333 F 723.03 3985.19 11534.84 49.92 240.91 632.37 p-value Moran's I 0.539 0.000 0.000 0.021 0.000 0.000 Moran's I residuals -0.052 0.370 0.579 0.273 0.411 0.404 Sum squared errors 39.49 82.36 210.60 1.59 3.73 9.62 N 350 1274 3640 350 1274 3640

OLS

SEM: Pooled (1) and fixed effects (2) estimations with time effect

Broad sample Restricted sample

Broad sample

(1) N0 (1) N1 (1) N2 (2) N0 (2) N1 (2) N2 lambda -0.156 0.677*** 0.840*** 0.596*** 0.673*** 0.665*** (0.104) (0.024) (0.009) (0.053) (0.024) (0.015) lKSp 0.751*** 0.752*** 0.693*** 0.135*** 0.333*** 0.386*** (0.027) (0.013) (0.007) (0.037) (0.021) (0.012) lhrstc_pop 0.416*** 0.234*** 0.177*** -0.057 0.032* 0.013* (0.058) (0.024) (0.010) (0.030) (0.013) (0.006) lMP2GVA 0.347*** 0.191*** 0.259*** 3.239*** 2.078*** 2.607*** (0.045) (0.022) (0.014) (0.277) (0.080) (0.072) p-value Moran's I 0.458 0.754 0.407 0.499 0.492 0.583 Moran's I residuals -0.025 -0.061 0.007 -0.031 -0.008 -0.010 Sum squared errors 39.53 84.98 242.82 1.60 3.77 9.87 N 350 1274 3640 350 1274 3640

ML

Broad sample Restricted sample

Broad sample

(1) N0 (1) N1 (1) N2 (2) N0 (2) N1 (2) N2 rho 0.142*** 0.258*** 0.386*** 0.589*** 0.523*** 0.468*** (0.043) (0.018) (0.010) (0.050) (0.025) (0.016) lKSp 0.714*** 0.679*** 0.574*** 0.128*** 0.271*** 0.276*** (0.028) (0.014) (0.009) (0.038) (0.021) (0.013) lhrstc_pop 0.372*** 0.190*** 0.174*** -0.062* -0.011 -0.001 (0.063) (0.022) (0.009) (0.030) (0.012) (0.006) lMP2GVA 0.258*** 0.101*** 0.065*** 3.267*** 1.677*** 1.739*** (0.053) (0.017) (0.008) (0.273) (0.080) (0.067) p-value Moran's I 0.455 0.806 0.634 0.362 0.478 0.625 Moran's I residuals -0.027 -0.068 -0.019 0.024 -0.011 -0.017 Sum squared errors 38.20 69.65 137.02 1.13 2.69 7.55 N 350 1274 3640 350 1274 3640

SAR: Pooled (1) and fixed effects (2) estimations with time effectML

• With the exception of the fixed effects estimation in the restricted sample, , residuals are autocorrelated and their autocorrelation and estimated spatial parameters increase with disaggregation.

• The general wage equation is very robust to the short-and-long-run specifications, to this three NUTS levels and to the broad and the restricted sample.

• Many test of the wage equation in the literature do not distinguish the short-and-long-run specifications. But the estimation with individual effects give a whole different view (Acemoglu et al., 2008).

Preliminary conclusions

• Results from NUTS 1 and 2: the estimated elasticities are very robust for the non spatial and the SEM and SAR models (FE non checked) => No problem with MAUP (but we have not studied NUTS 3!).

• Results from NUTS 0 are more sensitive to sample selection. Maybe higher heterogeneity than when pooling regions from different countries at NUTS 1-3.

• Some of the detected patterns in the change of estimates by NUT level are economically meaningful: at least from NUTS 1 to NUTS 2 the elasticity to Market Potential always increases => More severe problems if this variable is omitted at higher levels of disaggregation.

Preliminary conclusions

• Sensitivity analysis (at least in the pooled model):– Kelejian and Prucha’s (1998) instrumentation of the spatially

lagged dependent variable in the SAR model

– spatial heteroskedasticity and autocorrelation consistent (HAC) estimators

– A graphical W instead of a matrix of the 5 nearest neighbours - but LeSage and Pace (2012)!-

– Now annual data: Short-run models for several years panels

• GWR ( “conditional parametric approach”) – local variation of estimates: At each NUTS level, what countries are de drivers of the fixed estimates?

• The zoning effect internal to each MAUP – The areas by country at each NUTS level: Does size matters? – Weighted regression

– Recalculate Market Potential: with distances among centroids, bigger regions are further apart from their markets

Current research and possible extensions

• Results change more using NUTS 0: thoughts welcomed.

• Similar elasticities in the not spatial and in the SEM and SAR models in spite of being a simple equation. Thoughts: Is this because the SAR was not recommended by the LM tests?. So much effort with spatial models for this?....

• Endogeneity – Proper instruments for Market Potential.

• Endogeneity – In the SAR model both market potential and the endogenous spatial lag of the dependent variable are endogenous: How to deal with this?

• Which would be the best W matrix to compare models using data with different aggregation?

• Results of the pooled estimation different when using “spdep” or “splm” R packages: why?

Questions

COMMENTS WELCOMEDTHANK YOU

Fernando Bruna f.bruna@udc.es)

University of A Coruña, Spain