spatial econometrics (presentation in the university of madrid (14-07-2010))

Vítor Domingues Martinho - Adjunct Vítor Domingues Martinho - Adjunct Professor of the Polytechnic Institute of Professor of the Polytechnic Institute of

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Analysis of Spatial Effects in Analysis of Spatial Effects in Vine and Olive Crops across Vine and Olive Crops across

Portuguese RegionsPortuguese Regions


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Objectives

The study analyses, through cross-The study analyses, through cross-section estimation methods:section estimation methods: the influence of spatial effects in the the influence of spatial effects in the

NUTs III vine and olive crops of mainland NUTs III vine and olive crops of mainland Portugal, in 1999 (the last data Portugal, in 1999 (the last data available), considering the Verdoorn available), considering the Verdoorn relationship as a base of study.relationship as a base of study.


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StructureStructure The presentation is structured in seven The presentation is structured in seven

parts: parts: in the first part some theoretical considerations about in the first part some theoretical considerations about

Verdoorn´law are presented; Verdoorn´law are presented; in the second part some studies which have already been in the second part some studies which have already been

developed in the area of spatial econometrics, specifically developed in the area of spatial econometrics, specifically concerning Verdoorn’s Law, are presented; concerning Verdoorn’s Law, are presented;

in the third, some theoretical considerations about spatial in the third, some theoretical considerations about spatial econometric are explained;econometric are explained;

in the fourth, the models considered are explained;in the fourth, the models considered are explained; in the fifth the data is analysed based on techniques of in the fifth the data is analysed based on techniques of

spatial econometrics developed to explore spatial data; spatial econometrics developed to explore spatial data; the sixth presents estimations, taking into account spatial the sixth presents estimations, taking into account spatial

effects; effects; and in the seventh part the main conclusions obtained and in the seventh part the main conclusions obtained

through this study are presented. through this study are presented.

Theoretical considerations Theoretical considerations about the Verdoorn about the Verdoorn

relationship relationship In 1949 Verdoorn detected that there In 1949 Verdoorn detected that there

was an important positive relationship was an important positive relationship between the growth of productivity of between the growth of productivity of work and the growth of output. He work and the growth of output. He defended that causality goes from defended that causality goes from output to productivity, with an elasticity output to productivity, with an elasticity of approximately 0.45 on average (in of approximately 0.45 on average (in cross-section analyses), thus assuming cross-section analyses), thus assuming that the productivity of work is that the productivity of work is endogenous. endogenous.


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Kaldor’s laws refer to the following: Kaldor’s laws refer to the following: i) there is a strong link between the rate of i) there is a strong link between the rate of

growth of national product and the rate of growth of national product and the rate of growth of industrial product, in such a way that growth of industrial product, in such a way that industry is the motor of economic growth; industry is the motor of economic growth;

ii) The growth of productivity in industry and ii) The growth of productivity in industry and endogeny is dependent on the growth of endogeny is dependent on the growth of output (Verdoorn’s law); output (Verdoorn’s law);

iii) There is a strong link between the growth of iii) There is a strong link between the growth of non-industrial product and the growth of non-industrial product and the growth of industrial product, so that the growth of output industrial product, so that the growth of output produces externalities and induces the growth produces externalities and induces the growth of productivity in other economic of productivity in other economic sectors.sectors.


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Empirical contributions Empirical contributions based on spatial effectsbased on spatial effects

There have been various studies carried out There have been various studies carried out concerning Verdoorn’s Law considering the concerning Verdoorn’s Law considering the possibility of there being spatial spillover effects:possibility of there being spatial spillover effects: Bernat (1996), for example, tested Kaldor’s three laws Bernat (1996), for example, tested Kaldor’s three laws

of growth in North American regions from 1977-1990. of growth in North American regions from 1977-1990. The results obtained by Bernat clearly supported the The results obtained by Bernat clearly supported the first two of Kaldor’s laws and only marginally the third;first two of Kaldor’s laws and only marginally the third;

Fingleton and McCombie (1998) analysed the Fingleton and McCombie (1998) analysed the importance of scaled growth income, through Verdoorn’s importance of scaled growth income, through Verdoorn’s Law, with spatial lag effects in 178 regions of the Law, with spatial lag effects in 178 regions of the European Union in the period of 1979 to 1989 and European Union in the period of 1979 to 1989 and concluded that there was a strong scaled growth concluded that there was a strong scaled growth income;income;


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Fingleton (1999), with the purpose of Fingleton (1999), with the purpose of presenting an alternative model between presenting an alternative model between Traditional and New Geographical Traditional and New Geographical Economics, also constructed a model with Economics, also constructed a model with the equation associated to Verdoorn’s Law, the equation associated to Verdoorn’s Law, augmented by endogenous technological augmented by endogenous technological progress involving diffusion by spillover progress involving diffusion by spillover effects and the effects of human capital. effects and the effects of human capital. Fingleton applied this model (Verdoorn) to Fingleton applied this model (Verdoorn) to 178 regions of the European Union and 178 regions of the European Union and concluded there was significant scaled concluded there was significant scaled growth income with interesting results for growth income with interesting results for the coefficients of independent variables the coefficients of independent variables (variable dependent lagged, rurality, (variable dependent lagged, rurality, urbanisation and diffusion of technological urbanisation and diffusion of technological innovations) in Verdoorn’s equation. innovations) in Verdoorn’s equation.


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Theoretical considerations Theoretical considerations about spatial effectsabout spatial effects

Tests:Tests: Moran´I tests the global and local spatial Moran´I tests the global and local spatial

autocorrelation;autocorrelation; Jarque-Bera tests the stability of parameters;Jarque-Bera tests the stability of parameters; Breuch-Pagan and Koenker-Bassett, in turn, tests for Breuch-Pagan and Koenker-Bassett, in turn, tests for

heteroskedasticityheteroskedasticity;; To find out if there are spatial lag and spatial error To find out if there are spatial lag and spatial error

components in the models, two robust Lagrange components in the models, two robust Lagrange Multiplier tests are used (LME for “spatial error” and LML Multiplier tests are used (LME for “spatial error” and LML for “spatial lag”)for “spatial lag”)::

In brief, the LME tests the null hypothesis of spatial non-In brief, the LME tests the null hypothesis of spatial non-correlation against the alternative of the spatial error correlation against the alternative of the spatial error model (“lag”) and LML tests the null hypothesis of spatial model (“lag”) and LML tests the null hypothesis of spatial non-correlation against the alternative of the spatial lag non-correlation against the alternative of the spatial lag model to be the correct specification.model to be the correct specification.


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Recommendations of Florax et al. (2003):Recommendations of Florax et al. (2003): 1) Estimate the initial model using the 1) Estimate the initial model using the

procedures using OLS; procedures using OLS; 2) Test the hypothesis of spatial non-2) Test the hypothesis of spatial non-

dependency due to the omission spatially dependency due to the omission spatially redundant variables or spatially autoregressive redundant variables or spatially autoregressive errors, using the robust tests LME and LML; errors, using the robust tests LME and LML;

3) If none of these tests has statistical 3) If none of these tests has statistical significance, opt for the estimated OLS model, significance, opt for the estimated OLS model, otherwise proceed to the next step, otherwise proceed to the next step,

4) If both tests are significant, opt for spatial 4) If both tests are significant, opt for spatial lag or spatial error specifications, whose test lag or spatial error specifications, whose test has greater significance, otherwise go to step 5;has greater significance, otherwise go to step 5;

5) If LML is significant while LME is not, use the 5) If LML is significant while LME is not, use the spatial lag specification; spatial lag specification;

6) If LME is significant while LML is not, use the 6) If LME is significant while LML is not, use the spatial error specification.spatial error specification.


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Verdoorn’s model with Verdoorn’s model with spatial effectsspatial effects

ln(Pit/Pit-1)=alpha+rho.Wij.pit+gama.ln(Qit/Qit-ln(Pit/Pit-1)=alpha+rho.Wij.pit+gama.ln(Qit/Qit-1)+epsilonit1)+epsilonit

In this equation:In this equation: P is sector productivity (used the area in level as a proxy);P is sector productivity (used the area in level as a proxy); p is the rate of growth of sector productivity in various p is the rate of growth of sector productivity in various

regions;regions; Q is sector product (used the number of farms in level as a Q is sector product (used the number of farms in level as a

proxy);proxy); W is the matrix of distances;W is the matrix of distances; gama is the Verdoorn coefficient;gama is the Verdoorn coefficient; rho is the autoregressive spatial coefficient (of the spatial rho is the autoregressive spatial coefficient (of the spatial

lag component);lag component); and epsilon is the error term (of the spatial error and epsilon is the error term (of the spatial error

component); component); the indices i, j and t, represent the regions under study, the the indices i, j and t, represent the regions under study, the

neighbouring regions and the period of time respectively.neighbouring regions and the period of time respectively.


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Data analysisData analysis ANNEX I

Figure 1: “Scatterplots” the relationship between area and number of farms for vine and olive

a ) Olive

b) Vine

Note: DIM = Area;

NE = Number of farms.


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ANNEX II Figure 2: Distribution of the vine and olive crops between the different NUTS III of

Portugal Continental

a) Olive

010.000

20.000

30.000

40.000

50.000

60.000

Min

ho

-Lim

a

Av

e

Ta

me

ga

Do

uro

Ba

ixo

Vo

ug

a

Pin

ha

l L

ito

ral

Pin

ha

l In

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or

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Se

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da

Es

tre

la

Be

ira

In

teri

or

Su

l

Oe

ste

Pe

nin

su

la d

e S

etu

ba

l

Le

zir

ia d

o T

ejo

Alt

o A

len

tejo

Ba

ixo

Ale

nte

jo

Á rea (ha)

Nº de explorações

b) Vine

05.000

10.00015.00020.00025.00030.00035.00040.00045.00050.000

Min

ho

-Lim

a

Av

e

Ta

me

ga

Do

uro

Ba

ixo

Vo

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a

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Pin

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da

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nin

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la d

e S

etu

ba

l

Le

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ejo

Alt

o A

len

tejo

Ba

ixo

Ale

nte

jo

Á rea (ha)

Nº de explorações


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ANNEX III

Figure 3: “Moran Scatterplots” the relationship between area and number of farms for vine and olive crops

a) Olive

b) Vine

Note: DIM = Area;

NE = Number of farms.


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ANNEX IV

Figura 4: “LISA Cluster Map” the relationship between area and number of farms for vine and olive crops

a) Olive

f) Vine

Note: Strong red – values “high-high”;

Strong blue – values “low-low”;

Weak red - values “high-low”;

Weak blue – values “low-high”.


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Empirical evidence with Empirical evidence with spatial effects as spatial effects as

conditioning variablesconditioning variables Table 1: OLS cross-section estimates with spatial specification tests

Equation: iii NEDIM

Con. Coef. M’I LMl LMRl LMe LMRe R2 N.O.

Olive 160.29 (0.05)

2.08* (4.64)

2.12* 3.57* 2.03 2.01 0.48 0.45 28

Vine -663.88 (-0.34)

0.99* (5.52)

2.42* 0.00 3.37** 2.35 5.72* 0.52 28

Note: M’I, Moran’s I statistics for spatial autocorrelation; LM l, LM test for spatial lag component; LMR l, robust LM test for spatial lag component; LMe, LM test for spatial error component; LMRe, robust LM test for spatial error component;R2, coefficient of adjusted determination; N.O., number of observations; *, statistically significant for 5%


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Table 2: Results for ML estimates with spatial effects

Equation: iiiiji NEDIMWDIM , com W

Constant Coefficient Coefficient(S) R2 N.Observations

Vine -1761.73 (-0.72)

1.11* (5.75)

0.38* (1.54)

0.58 28

Note: Coefficient(S), spatial coefficient for the spatial error model; *, statistically significant to 5%; **, statistically significant to 10%.


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Empirical evidence with Empirical evidence with human capital as a structural human capital as a structural

variablevariable


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Table 3: Empirical evidence of the importance of the level of schooling in the convergence of

productivity in the various economic sectors

itiiit XPbPPT 00 log)/log()/1( Con. Coef.1 Coef.2 JB BP KB M’I LMl LMRl LMe LMRe R2 N.O.

Agriculture

Prim. -0.200 (-1.552)

0.037* (3.302)

-0.220* (-2.249)

8.486* 5.007** 2.054 -0.089 0.243 3.284** 0.632 3.672** 0.453 28

Sec. -0.440* (-4.401)

0.040* (3.508)

0.253 (1.684)

8.890* 7.908* 3.232 -0.112 0.129 3.723** 0.996 4.591* 0.409 28

High.. -0.370* (-3.882)

0.039* (3.477)

0.414* (2.098)

1.085 2.466 1.526 -0.053 0.672 3.914* 0.223 3.466** 0.440 28

Industry

Prim. 0.578* (6.197)

-0.050* (-5.700)

-0.116* (-2.198)

0.565 18.144* 12.359* 0.076 0.010 0.180 0.461 0.630 0.547 28

Sec. 0.448* (4.809)

-0.048* (-5.212)

0.118 (1.426)

0.746 13.761* 10.875* 0.109** 0.049 0.339 0.943 1.234 0.500 28

High.. 0.521* (6.285)

-0.053* (-6.062)

0.271* (2.544)

3.450 33.593* 16.957* 0.016 0.054 0.161 0.021 0.128 0.570 28

Services

Prim. 0.371* (2.059)

-0.032** (-1.853)

-0.034 (-1.231)

0.323 6.990* 5.055** 0.101 1.890 6.694* 0.819 5.623* 0.061 28

Sec. 0.234** (1.801)

-0.021 (-1.435)

0.021 (0.596)

0.033 5.873** 5.031** 0.093 1.607 7.047* 0.685 6.125* 0.018 28

High. 0.284* (2.203)

-0.025** (-1.872)

0.051 (1.157)

0.553 10.749* 7.736* 0.105 1.791 3.734** 0.875 2.818** 0.054 28

Total of sectors

Prim. 0.307* (3.405)

-0.024* (-2.900)

-0.070* (-2.427)

0.662 0.302 0.402 -0.078 2.239 2.672 0.482 0.914 0.201 28

Sec. 0.188* (2.816)

-0.018* (-2.326)

0.072** (1.727)

0.775 0.223 0.290 -0.075 1.572 1.952 0.448 0.828 0.118 28

High.. 0.213* (3.001)

-0.019* (-2.461)

0.106** (1.929)

0.130 1.134 1.072 -0.165 3.354** 1.331 2.178 0.156 0.140 28

Note: Prim., estimate with primary education; Sec., estimate with secondary education; High., estimate with higher education; Con., constant; Coef.1, coefficient of convergence; Coef. 2 coefficient of level of schooling; JB, Jarque-Bera test; BP, Breusch-Pagan test; KB, Koenker-Bassett test: M’I, Moran’s I; LMl, LM test for spatial lag component”; LMRl, robust LM test for spatial lag component; LMe, LM test for spatial error component; LMRe, robust LM test for spatial error component; R2, r squared adjusted; N.O., number of observations *, statistically significant to 5%; **, statistically significant to 10%.


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ConclusionsConclusions

Considering the analysis of the cross-Considering the analysis of the cross-section data previously carried out section data previously carried out and of the estimate results, it can be and of the estimate results, it can be seen that:seen that:it appears that the olive is the it appears that the olive is the

permanent agricultural crop with larger permanent agricultural crop with larger areas, reflecting its geographical areas, reflecting its geographical location. Olives and vines are crops with location. Olives and vines are crops with greater signs of spatial autocorrelation.greater signs of spatial autocorrelation.


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As a final conclusion, considering As a final conclusion, considering that this two crops are showing that this two crops are showing strong evidence of positive spatial strong evidence of positive spatial autocorrelation, that must be taken autocorrelation, that must be taken in count to make interventions in the in count to make interventions in the background (political, technological, background (political, technological, etc.) in the sectors of activity etc.) in the sectors of activity associated with them (both upstream associated with them (both upstream and downstream). and downstream).

Especially in olive, since the vine, Especially in olive, since the vine, because of the economic dynamics because of the economic dynamics associated with it, does not need associated with it, does not need government assistance as directed. government assistance as directed. The positive spatial autocorrelation The positive spatial autocorrelation clearly indicates that any clearly indicates that any intervention in a region is necessarily intervention in a region is necessarily reflected in neighbouring regions. So, reflected in neighbouring regions. So, this brings unique opportunities to this brings unique opportunities to implement technical assistance, as implement technical assistance, as well-based theory of the "oil stain".well-based theory of the "oil stain".


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spatial econometrics (presentation in the university of madrid (14-07-2010))

Education