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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
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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
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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
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• 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
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• 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
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• 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
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• 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
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Spatial distribution of the variables
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Spatial distribution of the variables
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Spatial distribution of the variables
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• 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
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• 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
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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
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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
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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
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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
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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
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• 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
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• 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
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• 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
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• 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