D4_1_Manual_for_tests_of_spatial_econometric_models_final

Work Package No. 4 August 2011 D4.1 Manual for the tests of spatial econometric model Authors: Vincent Linderhof, Peter Nowicki, Eveline van Leeuwen, Stijn Reinhard and Martijn Smit Document status Internal use Confidential use Draft No. 2 Final Submitted for internal review x x 31-7-2011 29-3-2013 22-3-2013 1 Table of contents Figures ___________________________________________________________________ ii Abbreviations _____________________________________________________________ iii Summary ________________________________________________________________ iv 1 Introduction ____________________________________________________________ 5 1.1 1.2 1.3 1.4 1.5 1.6 2.1 2.2 2.3 3.1 3.1 3.2 Objective of WP4.1 _______________________________________________________ 5 Objective of this document _________________________________________________ 6 General methodology of spatial econometric analysis_____________________________ 7 Logical Diagrams of Impact (LDI) and measures ________________________________ 8 Selection of variables, functional form and tests ________________________________ 10 Outline of the report ______________________________________________________ 10 Selection of variables based on the economic theory ____________________________ 11 Check for correlation with dependent variable _________________________________ 12 Tests for correlations between independent and dependent variables. _______________ 12 Choice of weight matrix___________________________________________________ 14 ESDA analysis: Life-long learning example ___________________________________ 15 Spatial autocorrelation and Moran’s I: Average farm size example _________________ 18 21 22 23 24 25 26 27 28 28 29 29 31 33 33 34 34 35 2 Selection procedure of variables __________________________________________ 11 3 Spatial analyses of the data _______________________________________________ 14 4 Testing the econometric specification ______________________________________ 21 4.1 Test for spatial model_____________________________________________________ 4.1.1 Spatial lag model ______________________________________________________ 4.1.2 Spatial error model ____________________________________________________ 4.1.3 Testing for spatial lag or spatial error model _________________________________ 4.1.4 Creating spatially lagged variables ________________________________________ 4.2 Model specification test (diagnostics) ________________________________________ 4.2.1 Test on independence of observations ______________________________________ 4.2.2 Test on endogeneity of regressors _________________________________________ 4.2.3 Test on omitted variables: Ramsey test _______________________ ______________ 4.2.4 Test on multicollinearity of explanatory variables ____________________________ 4.2.5 Test on homogeneity ___________________________________________________ 4.2.6 Test on distribution of the residuals________________________________________ 4.3 Tests on coefficients ___

1

Table of contents

Figures ___________________________________________________________________ ii Abbreviations _____________________________________________________________ iii Summary ________________________________________________________________ iv 1 Introduction ____________________________________________________________ 5

1.1

1.2

1.3

1.4

1.5

1.6

2.1

2.2

2.3

3.1

3.1

3.2 Objective of WP4.1 _______________________________________________________ 5 Objective of this document _________________________________________________ 6 General methodology of spatial econometric analysis _____________________________ 7 Logical Diagrams of Impact (LDI) and measures ________________________________ 8 Selection of variables, functional form and tests ________________________________ 10 Outline of the report ______________________________________________________ 10 Selection of variables based on the economic theory ____________________________ 11 Check for correlation with dependent variable _________________________________ 12 Tests for correlations between independent and dependent variables. _______________ 12 Choice of weight matrix ___________________________________________________ 14 ESDA analysis: Life-long learning example ___________________________________ 15 Spatial autocorrelation and Moran’s I: Average farm size example _________________ 18 2 Selection procedure of variables __________________________________________ 11 3 Spatial analyses of the data _______________________________________________ 14 4 Testing the econometric specification ______________________________________ 21

4.1 Test for spatial model _____________________________________________________ 21

4.1.1 Spatial lag model ______________________________________________________ 22

4.1.2 Spatial error model ____________________________________________________ 23

4.1.3 Testing for spatial lag or spatial error model _________________________________ 24

4.1.4 Creating spatially lagged variables ________________________________________ 25

4.2 Model specification test (diagnostics) ________________________________________ 26

4.2.1 Test on independence of observations ______________________________________ 27

4.2.2 Test on endogeneity of regressors _________________________________________ 28

4.2.3 Test on omitted variables: Ramsey test _____________________________________ 28

4.2.4 Test on multicollinearity of explanatory variables ____________________________ 29

4.2.5 Test on homogeneity ___________________________________________________ 29

4.2.6 Test on distribution of the residuals ________________________________________ 31

4.3 Tests on coefficients _____________________________________________________ 33

4.3.1 Test on linear restrictions of coefficients ____________________________________ 33

4.3.2 Test on structural change ________________________________________________ 34

4.3.3 Tests on linearity in variables ____________________________________________ 34

4.4 Goodness of fit tests of the model ___________________________________________ 35 5 Concluding remarks ____________________________________________________ 35 Acknowledgement _________________________________________________________ 36 References _______________________________________________________________ 37 i

Figures

Figure 1 Logical Diagramme of Impact for measure 121 modernisation .................................. 8

Figure 2 Logical Diagramme of Impact for measure 214 .......................................................... 9

Figure 3 Logical Diagramme of Impact for measure 311 .......................................................... 9

Figure 4 Life-long learning in Europe, by NUTS2 region, for 2009. ...................................... 17

Figure 5 LISA map for life-long learning in Europe, by NUTS2 region, for 2009. ................ 18

Figure 6 Average area farm size in Europe, in ha, by NUTS2 region, for 2007. ..................... 19 Figure 7 Scatterplot of average area farm size in Europe in a region (x-axis) and its

neighbouring regions (y-axes) for 2007. .................................................................................. 20

Figure 8 LISA map for average area farm size in Europe, by NUTS2 region, for 2007. ........ 21

Figure 9 Decision model, from Anselin (2005). ...................................................................... 25

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Abbreviations CMEF EAFRD EU

LDI

NUTS RD

RDP

Common Monitoring and Evaluation Framework European Agricultural Fund for Rural Development European Union Logical Diagram of Impact French abbreviation for nomenclature des unités territoriales statistiques, a geocode standard for referencing the subdivisions of EU countries for statistical purposes Rural Development Rural Development Plan iii