Commuting, Migration and Local Joblessness

Michael Amior, CEP and Hebrew University, JerusalemAlan Manning, CEP and LSE

PRELIMINARY – COMMENTS WELCOME

The Question

• How do local demand shocks affect local joblessness?• Would expect a number of mechanisms to insure against local demand shocks:

• Commuting• Migration

• (Subtext): These mechanisms don’t seem to be working very well• Most compelling evidence that they don’t ‐ exhibit A

Exhibit A

The persistence in local joblessness in the UK

Often thought to be little/no migration response ‐but population trends do not support this

But is increased commuting also a viable alternative?

• UK is a relatively small country in which areas of high and low joblessness are often not far apart

• Projects like HS3 are partly designed to make commuting more possible

• Little academic literature on how commuting responds to economic shocks and the role that plays in insuring against local shocks

• Monte, Redding, Rossi‐Hansberg

UK Travel to Work Areas, 2011

London 8,369,000Manchester 2,664,000Birmingham 1,741,000Slough and Heathrow 1,662,000Glasgow 1,256,000Newcastle 1,057,000Liverpool 990,000Leicester 952,000

Sheffield 851,000Bristol 835,000

Commuting rates across TTWA boundaries

year UK1981 .1421991 .1822001 .1952011 .201

Road Map of the Paper

• Integrated model of commuting/migration that can be estimated on small‐area data

• Commuting (distribution of workers across areas given distribution of population across areas):

• Simple theoretical model• Estimation of model – does commuting respond to local demand shocks?• Determination of the employment rate• The value of commuting as insurance against local shocks• The response to local demand shocks

• Migration (distribution of population across areas, much taken from Amior‐Manning, 2015) :

• ‘Sufficient statistic’ argument – can use employment rate as summary measure of well‐being• Simple model of migration in response to economic shocks:

Data

• 5 censuses 1971‐2011 inclusive

• Use 9975 wards or 270 TTWAs (2001 definition)

• All population/employment counts based on age 16‐64

• Commuting flows between every pair of wards for 1981‐2011

• Ward‐level employment data by industry from various sources

• Amenity controls: climate, migrant enclaves, log population density in 1921, area

Commuting Model: Have separability between non‐employment and employment: value of non‐employment does not affect probability of working in area A relative to area B

Model of decision to work in different areas a simple multinomial logit• Utility from living in a and working in b at time t

• Utility from working in b

• Usual distribution of error leads to MNL specification for commuting rates (will treat wage variable as destination‐time fixed effect)

0abt abt a at abtU V lnQ ò

abt ab btV d lnW

ab bt

ai it

d lnW

abt d lnW

i

ece

Estimating the Commuting Model

• Cannot identify so define:

• These are the most that can be defined from commuting data (though other normalizations possible)

• Commuting probabilities are then

, logab btd W

11

11,

bt bab b

it iai i

lnW lnWd lnW

ab bt lnW lnWd lnW

i i

e eD Ze e

ab btabt

ai iti

D ZcD Z

Estimating the Commuting Model

• Use ML estimation• 99.5m parameters so use following procedure:

• Fix , then simple formula for MLE of

• Use estimate of , then simple formula for MLE of

• Iterate until convergence

• This gives estimates of ,ab btD Z

abD btZ

btZ abD

Modelling Dab

• 10k x 10k Markov matrix• Individual elements have a MNL form• Model this using equivalence between Poisson and MNL with:

• Origin fixed effects (for Poisson equivalence)• Destination fixed effects (for Wb1)• A function of distance between a and b

• Use iterative procedure (Aitkin‐Francis) to estimate this • Main result is that the cost of distance is very large:

• A job 5km away has, ceteris paribus, a commuting rate 8% of the rate of a job 1km away

Modeling Zbt• In the theory this is a function of the change in wages• Do not have direct data on wages so construct a simple model for local wage determination

• Construct simple model of this:• Commuting decisions give labour supply to firms in an area given offered wages• Output produced facing downward‐sloping demand curve with demand shocks

• Leads to prediction that:• Wages depend positively on local demand shocks and those in surrounding areas• Wages depend negatively on weighted average of local population• The weights are functions of commuting patterns/distribution of population ‐ Ωmatrices

• Measure:• Local demand shocks by Bartik shocks• Instrument local population using Altonji‐Card migrant instrument

Results

The determination of the local employment rate• The IIA assumption tells us that the probability of working will be a function of the difference between the inclusive value from working and the expected utility from being non‐employed.

• Model the utility from not working as (assuming benefits partially indexed to local housing costs):

• The commuting rate model gives us an estimate of the inclusive value from working up to a residence fixed effect, a time fixed effect and local amenities and housing costs.

• This is a model we can estimate – (population possible other regressorbecause of possible house price effects)

0 0 1 ha t a t atV lnB lnQ

Estimate of Employment Rate

Application 1: Value of Commuting

• How much does the ability to change commuting patterns affect the inclusive value and hence the employment rate

• Define EU(Vab ,pab) to be the maximized expected utility of workers living in a if the systematic pay‐offs from working in different areas are V ab but pab is the fraction of individuals living in a who are forced to work in b.

• MNL implies this has the form:

• Compute change in EU for one year’s set of returns with another year’s commuting patterns

,ab ab ab ab ab abb b

EU V p p V p lnp

These are the results

• When converted to predicted impact on employment rates these are small relative to cross‐ward differences in employment rates

• But value of ability to change commuting patterns also depends on size of changes in returns

The Migration Decision

• Largely taken from Amior and Manning (2015)• Simple model of migration in which people move from areas with low expected utility to areas with higher utility

• But how can we measure expected utility in a simple way?• Use a ‘sufficient statistic’ result• Extension of Amior‐Manning (2015) that assumed people live and work in same area (applied to US CZs)

The ‘sufficient statistic’ argument – Amior‐Manning, 2015Real wage

employment rate

Higher worker utility

A generalized version:

• Utility from living in a and working in j is given by:

• Where εab is idiosyncratic shock• Utility from not working is:• Assume distribution of errors is generalized McFadden (1978) form:

• Where G is monotonic, Hod1

ab ab abU V

0 0 0j j jU V

0 1, ,..., AG e e eF e

Results

• From McFadden (1978), probability of choosing option j is

• Expected level of maximized utility

• In general, this is very complicated, but make the following assumption:

• Assumption: The probability of being employed in area i relative to the probability of being employed in area j does not depend on the utility of being unemployed V0 (the IIA assumption)

0 1 0 0

1 0 0

1, ,.....,

1, ,.....,

j A

A

V V V V V Vj

j V V V V

e G e ep

G e e

1 0 00 ln 1, ,..... 0, .5772156649AV V V VEU V G e e

The Sufficient Statistic Result

• If assumption is satisfied expected utility can be written as:

• Where (n‐l) is log employment rate• Expected utility of living in an area a function of:

• utility when unemployed• employment rate

• Even if can work in many areas, can reduce expected utility to two dimensions

• This can be thought of as a CCP Hotz‐Miller type result

0EU V n l

Intuition for Sufficient Statistic Result

• Expected utility conditional on being in employment independent of V0 – call this IV

• Overall expected utility is some function of V0 and IV‐ V0

• Employment rate is a function of IV‐ V0

0 0 0Pr ,EU V employed V IV IV V

0 0Pr ,employed V IV IV V

Migration Model (from Amior‐Manning, 2015)

• Assume that population increase related to utility offered in an area• Simple model of migration:

• Population rises if utility higher

• Leads to the following ECM specification for population change:

• Estimate this on decadal data 1971‐2011

0 1 2 1 1 3 4 1rt rt rt rt rt rt t rtl n n l a a d

1rt

rt rt at rt rt rt rtl u a n l at

Empirical Issues

• Δnrt and (nrt‐1‐lrt‐1) are endogenous• If include area fixed effects then ‘Nickell’ bias – short panels with something like a lagged dependent variable

• Solve both issues by instrumenting Δnrt and (nrt‐1‐lrt‐1) using Bartikshock and lagged Bartik shock – first stages are strong

• Estimate model at TTWA and Ward level• Estimate 3 models:

• Without area FE but with area controls• With area FE• In first‐difference i.e. dependent variable is Δ2lrt

Model works well at ward level

But it also works well at TTWA level (theory says it should)

What does this mean..

• Estimated population response to shocks in UK is similar to US• One‐off shock to labour demand causes: employment rate to fall but population then falls and employment rate eventually goes back to initial level

• But permanent shocks to labour demand cause deviations in steady‐state employment rate – suppose

• From ‘stripped‐down’ ECM• Which implies a steady‐state of:

rt rn b

1 2 1 1rt rt rt rtl n n l

1

2

1rt rt r rn l b b

Conclusion

• Local demand shocks do affect commuting patterns• The extent to which this provides insurance against shocks depends on:

• How responsive commuting is• The spatial autocorrelation of shocks• Benefits for local residents partly at expense of more distant residents

• These shocks do affect the local employment rate• The local employment rate affects the migration rate• If shocks have a high degree of autcorrelation in time and space then the adjustment mechanisms will be weak