Applying spatial techniques:
What can we learn about theory?
Henry G. Overman
LSE, CEP & CEPR
Lecture for the 19th Advance Summer School in Regional Science
Publishing papers in spatial economics
•
Types of paper:
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–
•
Methodological
Applied
For applied papers the key question is do
we learn anything new about:
–
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Theory
Policy
Some casual empiricism
• Based on a spatial econ workshop (Kiel ’05)
• 60 papers at the conference
– 12 methodological
– 48 empirical
• 10 growth in EU regions
• Theoretical and empirical issues
– Econometric theory and empirical work
– Economic theory and empirical work
• What do we learn from spatial econometric papers
about theories of economic growth and location?
Some less casual empiricism
• Abreu, Groot and Florex ‘space and growth’
– 63 papers between 1995 and 2004
– Data
• 68% EU
• 11% country
• 8% US/Canada
– Relationship to theory
• 63% standard spatial
• 11% derive explicit models from theory
Lessons from less casual empiricism
1. Spatial econometrics literature should think
about underlying reasons for spatial dependence
2. Non-spatial literature should worry about spatial
dependence of residuals
3. Spatial economics literature unduly concentrated
on methodological issues
HGO: What new things do we learn about growth?
Space as nuisance
• “For better or worse, spatial correlation is
often ignored in applied work because
correcting the problem can be difficult”
Wooldridge, p. 7
• Key assumption
– We know the relationship we want to estimate
• Conclusion
– We should use spatial econometric toolbox to
correct residuals where appropriate
An analogy
• The returns to education
– Wage = f (ability, education)
– Ability unobserved but correlated with
education
 Fixed/Random effects estimation to get
coefficient on education
• Slightly unfair comparison because dealing
with spatial correlation harder
– FE/RE maintains i.i.d. assumption
– Need different asymptotic theory etc
The challenge
• The problem
– Way too many papers focus on space as nuisance
– Standard spatial techniques to correct the
coefficient estimates (63%)
– Important to understand these techniques but …
– … revised coefficient estimates often do not tell us
anything new!
• How can we use spatial data or spatial
techniques to learn something new?
The empirics of location
• Four types of papers on the location of
economic activity (or people):
–
–
–
–
Descriptive papers
Empirical models
Class of model approaches
Structural approaches
Descriptive work
• Good descriptive work should
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–
–
–
–
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Give us a feel for the data
Give us a feel for patterns in the data …
.. Without getting too hung up on the details
Hopefully tell us something about theory …
… Without claiming to tell us lots about theory
Give us a feel for how we might best analyse
the data
Location patterns
• For concreteness consider something specific – the
spatial location of economic activity.
• First important point – define your terms:
– Are places specialised in particular activities?
– Are activities localised in particular places?
• Second important point – plot the data (GIS)
– Cross check from statistical results to data plot
Source: Duranton and Overman, Review of Economic Studies (2005)
Source: Duranton and Overman, Review of Economic Studies (2005)
First generation – location measures
• Typical way to proceed is to calculate some
summary statistic for each industry/location
– Specialisation: Is the production structure of a
particular region similar or different from other
regions?; how different is the production structure?
– Localisation: Is economic activity in a particular
activity broadly in line with overall economic activity
or is the activity concentrated in a few regions?; how
concentrated is the economic activity?
A typical paper
• Variety of measures to capture spatial
location patterns
• Discussion of why some measures better
than others
• But, no systematic attempt to outline criteria
by which to assess these methods
• Arguments usually statistical and one
dimensional
Measuring localisation:
5 key properties
1. Comparable across industries
•
(e.g. can Lorenz curves be compared)
2. Conditioning on overall agglomeration
3. Spatial vs. Industrial concentration
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•
(The lumpiness problem)
Ellison and Glaeser (JPE, 1997) dartboard
approach; Maurel and Sedillot (RSUE, 1999);
Devereux et al (RSUE, 2005)
Measuring localisation
4. Scale and aggregation
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Dots on a map to units in a box
Problem I – scale of localisation
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Problem II – size of units
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California 150 x Rhode Island
Problem III – MAUP
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Cutlery in Sheffield versus Motor cars in Thames valley
Spurious correlations across aggregated variables
Problem IV – Downward bias
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Treat boxes separately
Border problems
5. Significance
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Null hypothesis of randomness
Spatial point pattern techniques
solve these problems …
1. Select relevant establishments
2. Density of bilateral distances between all
pairs of establishments (4)
3. Construct counterfactuals
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•
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Same number of establishments (3)
Randomly allocate across existing sites (2)
Local and global confidence intervals (5)
… and we learn something
• Excess localisation not as frequent as previous studies
– Significance versus border bias
• Highly skewed
– Some sectors very localised;
– Others weakly
– Many not significantly
• Scale of localisation
– Urban/metropolitan
– Regional for 3d
• Broad sector effects
– 4d behave similarly within 3d
• Size of localised establishments
– Big or small depending on industry
1st generation: Concentration regressions
• Get measures of industry characteristics and
run a “concentration regression”
• CONC(s) = a + bTRCOSTS(s) +
cIRS(s) + dLINKAGES(s) +
eRESOURCE(s) +
fHIGH_TECH(s)
Conceptual limitations
• Theory tells us nothing about the
relationship between indices and industry
characteristics when more than two regions
• Given availability of shares, why throw
away lots of information by calculating only
one summary statistic?
Using industry shares
Harrigan (1997) classical trade theory +
simple translog revenue function + hicks
neutral technology
G
F
s   agk ln    rgf ln v cf   gc
c
g
k 1
c
k
f 1
– a and r vary across industries, technologies and
factors
Location theory
• Ellison and Glaeser (1999) – sequential
plant choice + expected profits depend on
location specific and spillovers
• Expected shares a non-linear function of:
F
F
f 1
f 1
c
c
r
p


y
p
 gf f  f g f
– Interaction of industry/country characteristics
– No theoretical justification for using intensities
Industry intensities
• Midelfart et al (2002) CRS + CES
preferences + differentiate goods +
Armington + transport costs + # of
industries proportional to country size
F
F
f 1
f 1
c
c
r
p


y
p
 gf f  f g f
Another interaction model
Some comments
• Number of firms in industry s, region r as a
function of interaction between industry and
regional characteristics
• E.g. first expression interacts vertical
linkages intensity (mu), sectoral labour
intensity (phi) with regional wages
• Problems
– Hardly any data available
– No firm movement (short run)
– End up estimating sectoral transport variable
An improvement over
first generation?
• A much clearer link from theory to the
empirical specification that is estimated
• Spatial interactions modelled explicitly
• But could still be spatial correlation in the
residuals
Get out the spatial econometrics toolbox?
2nd order issue relative to first order issue of
identification
What do we learn about theory?
• Harrigan is a straightforward neo-classical
trade model
• E&G is a very stylised geography model
with black box assumptions to get to
functional form
• Midelfart et. al. has some geography effects
but no IRS
• Gaigne et. al. have a functional form that is
very far from what they estimate
An alternative strategy
• Take one particular class of models and test
whether the data are consistent with the
model
• Even better – nest one class of models
within another class of models and test
whether the data allow us to reject the
implied restrictions
Testing agglomeration
• Agglomeration has two senses:
– A process by which things come together
– A pattern in which economic activity is
spatially concentrated
• Two paths approach
– Test mechanisms
– Test predictions
• We will consider NEG models
Defining and delimiting NEG
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NEG (here) = theories that follow the
approach put forward by Krugman’s 1991
JPE article
Five key ingredients
1.
2.
3.
4.
5.
IRS internal to the firm; no tech externalities
Imperfect competition (Dixit-Stiglitz)
Trade costs (iceburg)
Endogenous firm locations
Endogenous location of demand
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Mobile workers
I/O linkages
Antecedents & Novelties
• Ingredients 1-4 all appeared in New Trade
Theory literature  home market effects in
Krugman 1980
• Key innovation of NEG relative to NTT is
assumption 5
• With all 5 assumptions, initial symmetry
can be broken and agglomeration form
through circular causation
Testing NEG predictions
• Leamer and Levinsohn (1995)
“Estimate don’t test”
• Empiricists need to take theory seriously, but not
too seriously
• False confirmation – housing prices very
expensive in areas with concentrated activity
• False rejection – Kruman’s prediction of complete
concentration
NEG predictions
1. Access advantages raise factor prices
2. Access advantages induce factor inflows
3. Home market / magnification effects
1. Lower t.c. increase HME
2. More product differentiation (IRS? – same
parameter) increases HME
4. Trade induces agglomeration
1. Increases for high IRS, high diff
2. t.c. inverted u?
5. Catastrophe
1. Small change t.c. large change location
2. Temporary shocks can have permanent effects
Strategy
• Take these predictions to the data
• Empirical specifications that are “close” to
the underlying theory
• Allows us to assess whether these
mechanisms and predictions are consistent
with data (not prove that these are the
mechanisms)
Empirical NEG
• Papers that model spatial linkages explicitly
consistent with “class of models” approach
– Redding and Venables (2004): income across
countries
– Davis and Weinstein (2004): testing for home
market effect
– Davis and Weinstein (2005): Catastrophe for
location of Japanese industry
Lessons from NEG work
• Methods should connect closely to theory but not
be reliant upon features introduced for tractability
or clarity rather than realism
• Better to have a limited number of parameters to
distinguish models?
– e.g. beta/sigma convergence
• Much more work needed on observational
equivalence
– 1st order issue
• A more accurate estimate of (say) a beta coefficient?
• Discriminating between alternative models of differences
across space?
Structural estimation
• Estimation of specification directly derived from
the theoretical model without any further
simplifying/function form assumptions
• Clear identification of which variables are
endogenous
• Interpretations easier?
• Computation of the model parameters: possible
simulation of the model on real data
Lessons from structural models?
• Endogeneity
– Structural econometric specification identifies
precisely which variables are endogenous
– In simpler situations (eg neighbourhood effects)
may get through intuition
• Which variables should be on RHS/LHS
– Working with structural theory suggests these
are more complicated than expected
• Structural identification of parameters
The downside
• Do we really believe that the world looks
like a NEG model plus some random
shocks?
• Two issues here
– Is the world NEG?
– What are the shocks?
Estimation versus testing
• Estimation – assume NEG model is valid and
estimate its parameters under this assumption
• Need to be confident that the model is true before
estimating it
– A crazy model (D-S) might not be so bad an
approximation
– Models place restrictions on parameters
– Reality checks with parameter values
• Testing requires nested structural models
An alternative approach
• Structural estimation works well in simple
situations where we can observe agents actions
and where the real world is close to the model
(e.g. some IO situations)
• A bounds approach can work well in situations
which are very complicated, but where different
classes of models consistently place restrictions on
the relationships between variables (Sutton)
Lessons
1. Mainstream economics increasingly
recognising importance of space
2. Huge scope for geo-referenced data to
increase our understanding of socioeconomic processes
3. Spatial econometrics providing a rapidly
expanding toolbox for dealing with some
problems encountered with spatial data
Lessons (cont)
3. Too much emphasis on application of methods
[c.f. heteroscedastic robust errors]
4. Too little attention on issues of role of theory
and importance of identification
a. Why include a spatial lag?
b. If answer to (a) is
•
•
“robustness for particular parameter estimate” see (3)
“spatial interactions” then identification is everything
5. Class of models approaches to identification
may be better than structural