Applying spatial techniques: What can we learn about theory?

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Applying spatial techniquesWhat can we learn
about theory?

• Henry G. Overman
• LSE, CEP CEPR

Lecture for the 19th Advance Summer School in
Regional Science
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Publishing papers in spatial economics

• Types of paper
• Methodological
• Applied
• For applied papers the key question is do we
  learn anything new about
• Theory
• Policy

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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?

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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

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Lessons from less casual empiricism

• Spatial econometrics literature should think
  about underlying reasons for spatial dependence
• Non-spatial literature should worry about spatial
  dependence of residuals
• Spatial economics literature unduly concentrated
  on methodological issues
• HGO What new things do we learn about growth?

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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

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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

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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?

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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

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Descriptive work

• Good descriptive work should
• 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

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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

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Source Duranton and Overman, Review of Economic
Studies (2005)
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Source Duranton and Overman, Review of Economic
Studies (2005)
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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?

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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

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Measuring localisation5 key properties

• Comparable across industries
• (e.g. can Lorenz curves be compared)
• Conditioning on overall agglomeration
• Spatial vs. Industrial concentration
• (The lumpiness problem)
• Ellison and Glaeser (JPE, 1997) dartboard
  approach Maurel and Sedillot (RSUE, 1999)
  Devereux et al (RSUE, 2005)

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Measuring localisation

• Scale and aggregation
• Dots on a map to units in a box
• Problem I scale of localisation
• Cutlery in Sheffield versus Motor cars in Thames
  valley
• Problem II size of units
• California 150 x Rhode Island
• Problem III MAUP
• Spurious correlations across aggregated variables
• Problem IV Downward bias
• Treat boxes separately
• Border problems
• Significance
• Null hypothesis of randomness

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Spatial point pattern techniques solve these
problems

• Select relevant establishments
• Density of bilateral distances between all pairs
  of establishments (4)
• Construct counterfactuals
• Same number of establishments (3)
• Randomly allocate across existing sites (2)
• Local and global confidence intervals (5)

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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

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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)

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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?

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Using industry shares

• Harrigan (1997) classical trade theory simple
  translog revenue function hicks neutral
  technology
• a and r vary across industries, technologies and
  factors

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Location theory

• Ellison and Glaeser (1999) sequential plant
  choice expected profits depend on location
  specific and spillovers
• Expected shares a non-linear function of
• Interaction of industry/country characteristics
• No theoretical justification for using
  intensities

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Industry intensities

• Midelfart et al (2002) CRS CES preferences
  differentiate goods Armington transport costs
  of industries proportional to country size

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Another interaction model
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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

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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

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What do we learn about theory?

• Harrigan is a straightforward neo-classical trade
  model
• EG 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

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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

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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

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Defining and delimiting NEG

• NEG (here) theories that follow the approach
  put forward by Krugmans 1991 JPE article
• Five key ingredients
• IRS internal to the firm no tech externalities
• Imperfect competition (Dixit-Stiglitz)
• Trade costs (iceburg)
• Endogenous firm locations
• Endogenous location of demand
• Mobile workers
• I/O linkages

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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

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Testing NEG predictions

• Leamer and Levinsohn (1995)
• Estimate dont test
• Empiricists need to take theory seriously, but
  not too seriously
• False confirmation housing prices very
  expensive in areas with concentrated activity
• False rejection Krumans prediction of complete
  concentration

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NEG predictions

1. Access advantages raise factor prices
2. Access advantages induce factor inflows
3. Home market / magnification effects
4. Lower t.c. increase HME
5. More product differentiation (IRS? same
   parameter) increases HME
6. Trade induces agglomeration
7. Increases for high IRS, high diff
8. t.c. inverted u?
9. Catastrophe
10. Small change t.c. large change location
11. Temporary shocks can have permanent effects

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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)

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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

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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?

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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

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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

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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?

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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

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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)

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Lessons

1. Mainstream economics increasingly recognising
   importance of space
2. Huge scope for geo-referenced data to increase
   our understanding of socio-economic processes
3. Spatial econometrics providing a rapidly
   expanding toolbox for dealing with some problems
   encountered with spatial data

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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
• Why include a spatial lag?
• 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