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3.2 Model <strong>of</strong> <strong>employment</strong> <strong>growth</strong><br />

We based our econometric model on a specification used by Blien et al. (2006), who<br />

considered a dynamic panel model for West Germany. We extend this specification <strong>in</strong> order<br />

to <strong>in</strong>tegrate <strong>the</strong> spatial dimension used by Elhorst (2005) specify<strong>in</strong>g a dynamic spatial panel<br />

data model. Our spatial panel data dynamic model will be:<br />

m<br />

m<br />

lemp s,<br />

d , t = α + ρWlemps,<br />

d , t + ∑ βllemps,<br />

d , t −l<br />

+ ∑δ<br />

l X s,<br />

d , t −l<br />

+ fs<br />

, d + ηt<br />

+ ε s,<br />

d , t<br />

l = 1<br />

l = 0<br />

lemp s,<br />

d , t is <strong>the</strong> log <strong>of</strong> <strong>employment</strong> rate <strong>of</strong> sector s , ( s = 1,...,<br />

S ), <strong>in</strong> <strong>area</strong> d ( d 1,...,<br />

n<br />

t ( t = 1,...,<br />

T ). Wlemp s,<br />

d , t is <strong>the</strong> spatially lagged dependant variable ( lemp s,<br />

d , t ) and lemps, d , t −l<br />

(6)<br />

= ) at time<br />

are <strong>the</strong> timely lagged dependent variables. X s,<br />

d , t −l<br />

are <strong>the</strong> current or lagged covariates<br />

(specialization, diversity, competition, agglomeration, size and wages). f s,<br />

d is a fixed time<br />

specific effect, ηt is a time effect and ε s , d , t is <strong>the</strong> standard error term.<br />

3.3 Tests and econometric estimation procedure<br />

3.3.1 Tests for spatial correlation<br />

To deal with dynamic spatial correlation, we use an Exploratory Spatial Data Analysis<br />

(ESDA), proposed by Ansel<strong>in</strong> (1996). The ESDA technique enables us to test and identify<br />

spatial configuration <strong>of</strong> <strong>in</strong>dustrial <strong>employment</strong> for each sector. The first step to deal with<br />

georeferenced data consists to check <strong>the</strong> presence <strong>of</strong> spatial dependence. Moran’s I <strong>in</strong>dex is<br />

<strong>the</strong> most commonly used <strong>in</strong>dex detect<strong>in</strong>g global autocorrelation <strong>of</strong> a variable <strong>of</strong> <strong>in</strong>terest, x i .<br />

Roughly speak<strong>in</strong>g <strong>the</strong> Moran <strong>in</strong>dex is a cross product correlation measure that <strong>in</strong>corporates<br />

“space” through a spatial weight matrix W .<br />

Formally, let n be <strong>the</strong> number <strong>of</strong> elementary spatial unit and x i <strong>the</strong> <strong>employment</strong> at <strong>the</strong> i<br />

spatial unit. The Moran’s <strong>in</strong>dex is def<strong>in</strong>ed as:<br />

I<br />

n<br />

n<br />

n<br />

∑∑<br />

=<br />

i=<br />

1 j=<br />

1<br />

ij<br />

n<br />

S<br />

w ( x − x)(<br />

x − x)<br />

∑<br />

0<br />

i=<br />

1<br />

i<br />

2<br />

( x − x)<br />

i<br />

j<br />

where x denote global mean, w ij is <strong>the</strong> ij th element <strong>of</strong> <strong>the</strong> spatial weight<strong>in</strong>g matrix W and<br />

S<br />

0<br />

=<br />

n<br />

n<br />

∑∑<br />

i=<br />

1 j=<br />

1<br />

w<br />

ij<br />

.<br />

Spatial filter<strong>in</strong>g<br />

After detect<strong>in</strong>g spatial autocorrelation us<strong>in</strong>g Moran’s <strong>in</strong>dex, <strong>the</strong> question is how to handle it.<br />

One approach deal<strong>in</strong>g with this problem is to spatially filter <strong>the</strong> data. This approach seeks to<br />

transform a spatially dependent variable <strong>in</strong>to two components: <strong>the</strong> filtered variable and <strong>the</strong><br />

purely spatial effect. In our analysis, we use <strong>the</strong> Getis’s G i specification to remove spatial<br />

effect. Getis’s <strong>in</strong>dex is presented as:<br />

n<br />

∑<br />

Gi ( d)<br />

=<br />

j = 1<br />

wij<br />

( d)<br />

x j<br />

n<br />

x<br />

, i ≠ j<br />

∑<br />

j = 1<br />

j<br />

(7)<br />

(8)<br />

8

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