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Applying spatial techniques: What can we learn about theory?PowerPoint Presentation

Applying spatial techniques: What can we learn about theory?

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### 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:
- Methodological
- Applied

- For applied papers the key question is do we learn anything new about:
- 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

- 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?

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
- 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

First generation – location measures (2005)

- 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 (2005)

- 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: (2005)5 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)

Measuring localisation (2005)

- 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

Spatial point pattern techniques solve these problems … (2005)

- 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)

… and we learn something (2005)

- 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

1 (2005)st 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 (2005)

- 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 (2005)

Harrigan (1997) classical trade theory + simple translog revenue function + hicks neutral technology

- a and r vary across industries, technologies and factors

Location theory (2005)

- 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

Industry intensities (2005)

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

Another interaction model (2005)

Some comments (2005)

- 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 (2005)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? (2005)

- 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 (2005)

- 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 (2005)

- 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 (2005)

- NEG (here) = theories that follow the approach put forward by Krugman’s 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

Antecedents & Novelties (2005)

- 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 (2005)

- 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 (2005)

- Access advantages raise factor prices
- Access advantages induce factor inflows
- Home market / magnification effects
- Lower t.c. increase HME
- More product differentiation (IRS? – same parameter) increases HME

- Trade induces agglomeration
- Increases for high IRS, high diff
- t.c. inverted u?

- Catastrophe
- Small change t.c. large change location
- Temporary shocks can have permanent effects

Strategy (2005)

- 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 (2005)

- 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 (2005)

- 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?

- 1st order issue

Structural estimation (2005)

- 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? (2005)

- 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 (2005)

- 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 (2005)

- 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 (2005)

- 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 (2005)

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

Lessons (cont) (2005)

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

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