96-41
UNIVERSITY OF CALIFORNIA, SAN DIEGO
DEPARTMENT OF ECONOMICS
INTERVENING OPPORTUNITIES, COMPETING SEARCHERS, AND THE
INTRA-METROPOLITAN FLOW OF MALE YOUTH LABOR
BY
STEVEN RAPHAEL
DISCUSSION PAPER 96-41
DECEMBER 1996
Intervening Opportunities, Competing Searchers, and the Intra-Metropolitan
Flow of Male Youth Labor
Steven Raphael
University of California, San Diego
Department of Economics, 0508
9500 Gilman Drive
La Jolla, CA 92093-0508
email: [email protected]
This paper is forthcoming in the Journal of Regional Science
I would like to thank John Quigley for many helpful comments and suggestions on earlier drafts
of this paper.
Abstract
This paper analyzes the determinants of the journey-to-work commute patterns for male teenage
workers within a single local labor market: the Oakland Primary Metropolitan Statistical Area.
Controlling for the intervening opportunities and the intervening labor supply between a given
origin and destination reduces the estimated negative effect of distance on the inter-zonal flow of
labor by nearly ninety percent.
Nonetheless,
physical distance has a significant and substantial
negative effect on intra-metropolitan youth labor flows.
Despite the high correlation between
intervening opportunities and intervening competing workers, both spatial variables have sizable,
and independent, effects on labor flows.
JEL Codes: R100, R230
1. INTRODUCTION
The
geographic mobility of labor is a vital adjustment mechanism in all modern
industrialized economies. As the spatial configuration of employment changes with technological
innovation and population shifts, residential mobility permits individual workers to adapt to the
evolving economic landscape and supports the equalization of wages and unemployment rates over
space.
For many segments of the population, however, the residential location decision is
severely constrained.
For example, African Americans suffering from housing discrimination,
low-income workers, teenagers living at home, and dual-earner families face various limitations
to residential mobility. For these workers, geographically accessible opportunities are limited to
the set of jobs within a reasonable distance of their residential locations.
Overall accessibility to
employment opportunities will be sensitive to the particular spatial distribution of employment and
the distribution of the competing labor supply within the local labor market.
Furthermore, one's
access to employment opportunities may strongly affect one's wages and the relative ease of
locating acceptable employment.
Given the fact that the workers with the most constrained residential choices are also
among the most vulnerable in the labor market, a sound understanding of the spatial aspects of
job search may provide important clues to understanding the relatively poor labor market
performance of geographically constrained groups.
For workers that search from a fixed
residential location, job search is a form of spatial interaction that determines a worker-employer
match and a concurrent journey-to-work path.
The probability of a given residence-work place
interaction will depend on a host of variables that describe the relative proximity of the work place
location to the residential location.
Conventional spatial models of the labor market emphasize
2
the importance of commute costs that increase with distance (Strazheim, 1980) or employment
information flows that erode with distance (Ihlanfeldt, 1992).
Recent theoretical advances in the
modelling of spatial search processes (Jayet, 1990a; 1990b) stress the importance of the
geographic distribution and density of competing job searchers and intervening opportunities in
affecting the spatial partitioning of existing residence-work place matches.
Few papers attempt
to empirically disentangle the relative importance of various aspects of accessibility in explaining
the fluidity of labor within a given local labor market.
This paper analyzes the determinants of the journey-to-work commute patterns for male
teenage workers within a single local labor market: the Oakland Primary Metropolitan Statistical
Area.
Aggregate commute flows between origin and destination traffic analysis zones are
analyzed. I find that controlling for the intervening opportunities and the intervening labor supply
between a given origin and destination reduces the estimated negative effect of distance on the
inter-zonal flow of labor by nearly ninety percent. Nonetheless, physical distance has a significant
and substantial negative effect on intra-metropolitan youth labor flows, even after controlling for
the other spatial variables.
Despite the high correlation between intervening opportunities and
intervening competing workers, both spatial variables have sizable, and independent, effects on
labor flows. I interpret these findings as evidence of the importance of spatial search models that
emphasize the correlates of distance -- i.e., the cumulative intervening opportunities and the
increasing stock of competing workers -- as well as distance itself in impeding intra-metropolitan
labor mobility.
These findings are important in that they highlight the need for geographic
accessibility measures that, in addition to physical distance, incorporate the spatial distributions
of labor supply and labor demand.
3
The remainder of this paper is organized as follows. First, I provide a theoretical
discussion of distance related frictions to labor mobility, their implications for theoretical models
of spatial job search, and the implications for the specification of empirical models of aggregate
spatial interaction. Various specification of the gravity model are offered as tests for competing
theories of spatial search and interaction. Next, the negative binomial regression used to estimate
the gravity models is presented. A description of the data and the presentation of the main results
follows. Finally, I offer conclusions.
Throughout the paper I assume that workers obtain employment through job search from
a fixed residential location -- i.e., residential locations are exogenously given.
The focus on male
youth labor flows justifies this assumption, since the overwhelming majority of male teenagers
are either living with their parents or another relative.
In the absence of exogenously given
residences, it is difficult to empirically interpret the distribution of work trips as journey-to-work
flows are determined by two search processes: job search and the search for housing.
2. DISTANCE, COMPETITION, AND LABOR MOBILITY
Alternative Models of Aggregate Spatial Interaction
The inter-zonal commuting of labor is one form of spatial interaction between individual
neighborhoods or zones within a local economy. Economic geographers and sociologists who
study aggregate spatial interaction, such as migration or the distribution of shopping trips, liken
such interactions to the gravitational attractions between two physical masses.
Analogous to
gravitational force, the population or characteristics of a given destination zone exert an attractive
pull on the population of a given origin.
Also akin to gravitational force, "demographic force"
exerted by one region on another erodes with the friction injected by the intervening distance.
4
Extending the gravity analogy to intra-metropolitan labor mobility, the factors that
determine aggregate commute flows between neighborhoods fall into three categories: (1) the
supply of labor in the given origin, (2) the demand for labor at a given destination, and (3) the
distance between the origin and destination.
This provides the specification of the unconstrained
gravity model,
T
(1)
ij
'
$
"
kL i E j
(
,
d ij
where
i=(1,...,I)
indexes
the
origin
neighborhoods,
j=(1,...,J)
indexes
destination
neighborhoods, Tij is the aggregate flow of labor between zones i and j, Li is the supply of labor
in the origin zone i, Ej is the demand for labor in the destination zone j, dij is the distance between
neighborhoods i and j, k is a constant, and
", $, and ( are positive parameters.
The scale of the
possible labor flow between zones is captured by the origin labor supply and destination labor
demand. By entering labor supply and demand multiplicatively, the potential scale of interaction
is increasing in the total possible combinations of workers and jobs.
The inverse relationship between distance and the total flow of workers in Equation (1)
represents the spatial content of the model.
Here, distance is measured by commute time so as
to neutralize any geographic structure that creates a divergence between physical distance and the
facility of a particular commute.
Several factors motivate the inverse relationship between
distance and labor flows. First, commuting is costly both in terms of direct cash outlays and time.
All else held equal, workers prefer jobs closer rather than farther from home.
impedes the flow of information travelling through informal channels.
Second, distance
In a search theoretical
5
framework, the rate at which job offers from a given work place location are received decreases
with distance from the location.
Hence, both workers' preferences and the geography of
information flows yield an inverse relationship between the aggregate commute flow between a
pair of zones and the intervening distance.
Several researchers have criticized the basic gravity model of Equation (1) as being unable
to distinguish between a pure decay effect of distance on social interaction and the effects of
spatial structure -- i.e., the spatial configuration of origins and destinations (Johnston, 1975;
Fotheringham, 1981; 1983; Sheppard, 1984).
Johnston (1973) demonstrates that the gravity
equation in (1) misleadingly provides a good fit to a trip distribution generated by an intervening
opportunities process. Since intervening opportunities increases with distance, the aggregate flow
between a given origin-destination pair declines with distance.
However, distance itself has no
meaningful effect on spatial interaction and the mis-application of a distance-decay model to data
generated by an intervening-opportunities process leads to faulty conclusions.
The empirical
findings that distance-decay parameter estimates vary widely across study areas (Sheppard, 1984)
and, when estimated separately by origin, within study areas (Fotheringham, 1981) provide
additional evidence of the importance of spatial structure and the potential peril of interpreting
basic gravity model parameter estimates as "pure" distance effects.
Fotheringham (1983, 1985) offers an alternative model of aggregate spatial interaction that
incorporates the interdependence among destinations.
Specifically, in the log-linear gravity
model, adding a variable to the right hand side measuring the accessibility of a given destination
to all other destinations incorporates the competitive effects of the destination's proximity to
alternative interaction opportunities.
A positive parameter estimate on the accessibility variable
6
provides evidence of an agglomeration effect while a negative parameter estimate is evidence of
competition effects. Lo (1991) further refines this "competing-destination" model by defining the
economic and locational sources of destination interdependence.
A model better suited than the competing-destinations model for analyzing the importance
of spatial structure in determining aggregate journey-to-work flows is offered by Jayet (1990a,
1990b). The author provides a rigorous connection between spatial search theory and aggregate
spatial interaction models and demonstrate the theoretical importance of variables that are highly
correlated with distance. Jayet (1990a) defines three sets of factors that determine the probability
that a worker searching from a fixed location obtains employment at a given point in space.
First
are those factors under the worker's control, such as search intensity and the sequence of areas
visited. Next, are the spatial and temporal aspects of the process that generates new opportunities.
Finally, are the interactions of the search process and residential locations of other competing
searchers.
These factors together determine the shape of the spatial search hazard function,
defined as the probability that a worker with a fixed residential location searching for a time t will
locate employment in the time interval t+dt within a given location.
The spatial element of this model and the implication for aggregate labor flows comes from
assumptions concerning the spatial trajectory of the search process.
Jayet defines a sequential
search process where space is partitioned into three area, a starting point (or area), a core, and
an ending point.
neighborhood.
The starting point is the area in the immediate vicinity of a worker's
The search process is defined as sequential if the probability of locating an
acceptable opportunity in the starting area decreases with the length of the search spell and the
probability
of locating an opportunity in the final area increases with the time spent searching.
7
In equilibrium, the probability that a particular residence-work place match occurs, or
alternatively stated, that a given journey-to-work path is realized, depends on the volume of
intervening opportunities between the residence and potential work place and a law of vacancy
duration for the given employment opportunity.
While the spatial distribution of employment
determines the intervening opportunities between a pair of origin and work place zones, the
sequential search processes of competing searchers determine the durations of particular job
vacancies.
In the specification of the aggregate spatial interaction equation, this leads to the
inclusion of a variable measuring the average number of searchers arriving at a given destination
from all origins per unit of time.
Hence, the duration of a given vacancy depends on the vacancy's spatial proximity, or
accessibility, to all competing searchers.
This aspect of the model resembles the competing-
destinations effect of Fotheringham (1983, 1985) where the flow between a given origin and
destination is a function of the destination's spatial accessibility to all other destinations.
However, as noted by Jayet (1990b), the competing-searchers and competing-destinations effects
are
quite
distinct.
While the competing destinations-effect results from competition (or
complementarities in the case of agglomeration) among destinations, the competing-searchers
effect results from competition between searching workers.
The attractive feature of this model is that it provides a direct link between spatial search
and aggregate spatial interaction. The aggregation of the set of individual intervening opportunity
models for the residents of each origin zone determines the aggregate commute patterns between
neighborhoods. The resulting aggregate interaction (or flow) function is strikingly similar to the
basic gravity equation. Labor flows between areas are proportional to the count of workers in the
8
origin and the count of jobs in the destination. However, the arrival rate of competing searchers
per unit of time qualifies the attracting force of jobs in the destination zone.
Furthermore, the
total flow declines with increasing intervening opportunities rather than with increasing distance.
In fact, distance does not enter the aggregate interaction function (Jayet, 1990b).
Empirical Specification of
the Jayet Model
While it is difficult to empirically implement an aggregate labor flow function which
depends on the destination-specific arrival rates of competing searchers, it is possible to re-specify
Equation (1) in a manner implied by Jayet's theoretical argument.
Specifically, defining the
quantity of intervening opportunities by the variable
IO
(2)
ij
'
j
E
k
œ(k*d ik<dij)
k
and symmetrically defining the quantity of competing labor by
IC
(3)
ij
'
j
L
k
œ(k*d kj<dij),
k
the aggregate flow function suggested by Jayet's spatial search model is
T
(4)
ij
'
"
$
*
0
kL i E j IC ij IO ij .
The theory suggests positive values for the parameters,
parameters,
* and 0.
"
and
$,
and negative values for the
Figure 1 graphically depicts the intervening opportunities and intervening
competition variables of Equations (2) and (3) for a typical origin-destination observation.
Labor
flows from the origin neighborhood, A, to the destination neighborhood, B, travelling the
distance, dAB.
Drawing a circle of radius, dAB, around the point of origin, A, and summing all
9
employment opportunities within the area of the circle provides the intervening opportunities
between A and B.
Similarly, sweeping a ray of length dAB around the destination point, B, and
summing the labor supply within the area of this circle gives the number of workers who are in
direct competition with the workers in A for job opportunities in B.
Showing the spurious negative correlation in the model of Equation (4) between the total
flow of labor and physical distance is simple when employment and labor supply are uniformly
distributed over space.
Let De be the density per square unit of distance for employment and Dl
be the densities per square unit of distance for labor supply.
Given the uniformity assumptions
and employing the formula for the area of a circle, intervening opportunities and intervening
Bdij2, and ICij=DlBdij2.
competition can be rewritten as IOij = De
Substituting into Equation (4)
gives
T ' CL "E $d
(5)
i
ij
B)*(DeB)0.
where C=k(Dl
j
*%0)
2(
ij
,
Given that the theory predicts
0, * < 0, Equation (5) illustrates the
negative empirical relationship between distance and the total labor flow.
Nonetheless, this
negative relationship is driven by the accumulation of intervening opportunities and intervening
competition with increasing distance rather than by distance-related commute costs.
One
problem
with
defining
intervening
competition
symmetrically
to
intervening
opportunities concerns the implication that searching workers residing close to the opportunities
in a given destination have a competitive advantage over workers residing in distant origins.
In
Jayet's model, the competing searchers effect qualifies the accessibility of a given vacancy to all
1
searchers regardless of search origin.
An alternative competing searchers variable that better
10
conforms to Jayet's definition is
CS '
(6)
j
j L(
i
(1
& IO /TOTAL), œi,
ij
i
where Li is origin labor , IOij is the intervening opportunities variable defined in Equation (2), and
TOTAL is the sum of employment opportunities in all destinations.
The competing-searchers
variable in (6) provides a weighted sum of all workers where the weight given to a specific
origin's labor supply declines in the intervening opportunities between the origin and the
destination being characterized.
Hence, this variable provides a rough approximation of the
number of competing searchers arriving in a given destination per unit of time.
Substituting the
variable, CSj, for the variable, ICij, in Equation (4) yields an alternative specification of the
aggregate flow function.
While
the
competing
searchers variable defined
in
Equation (6)
is closer
to the
specification suggested by Jayet's model, the alternative specification of competing labor given
in Equation (3) also deserves attention.
If the filling of vacancies is affected by the flow of
information and if information flows erode with distance, workers residing relatively close to an
opportunity will have better information and be more likely to fill the vacancy.
Conversely, as
the set of intervening workers increases between an origin and destination, the size of the flow
between the origin and destination will decrease.
Hence, in the empirical work below, I estimate
separate models using both labor supply variables: the intervening competition variable in
Equation (3) and the competing searchers variable in Equation (5).
The basic gravity model of Equation (1) and the intervening opportunities and competing
searchers model of Equation (4) represent extreme versions of the competing hypotheses
11
concerning the relationship between distance and spatial interaction.
The relative importance of
each hypothesis in explaining the intra-metropolitan flow of youth labor is an empirical question
that is the main purpose of this paper.
The empirical strategy is to fit Equation (1) to commute
flow data for Oakland and generate an initial estimate of the effect of distance between zones
(measured in travel time) on the aggregate flow of teenage labor.
Next, I add intervening
opportunities, intervening competition, and competing searchers to the equation individually, and
simultaneously, and analyze the changes in the estimated effect of distance.
If the relationship
between distance and aggregate flows is simply a function of spatial structure, adding these
variables to the simple gravity model specification should diminish the coefficient estimate on
distance. Before proceeding to the results, the next sections describes the statistical model used.
3. ESTIMATION METHODOLOGY
In the past, researchers estimating the unconstrained gravity equation often assumed a log-
normally distributed dependent variable which allows one to simply take the log of Equation (1)
and apply ordinary least squares.
This approach is inappropriate when there are many small or
zero flows as is often the case with journey-to-work data (Flowerdew and Aitken, 1982).
Furthermore, the simple log-normal model tends to underpredict large flows and underpredict the
total of all flows (Senior, 1979).
In realization of these short comings, recent research has
modelled the dependent variable as a discrete probability process, an approach more appropriate
in the analysis of count data (Flowerdew and Aitkin, 1982; Guy, 1987; Yun and Sen, 1994).
In
the estimation procedure used here, I follow this latter line of research.
The simplest statistical model of count data is the Poisson regression.
Let Xij be the
observed commute flow of male teenage workers between neighborhoods i and j.
Assuming that
12
the movement of individuals are independent and that the flow of workers from i to j has a
Poisson distribution, then for the basic model of Equation (1),
&8 )8
x!
x
Prob(X 'x *8 ) '
(7)
ij
exp(
ij
ij
ij
ij
ij
,
ij
where
E(X ) ' V(X ) ' 8 '
(8)
ij
ij
ij
kL "E $
j
i
d(
.
ij
Equation (7) is the Poisson distribution with parameter
the parameratization of
8
ij
8.
ij
The model is estimated by substituting
given by (8) into Equation (7), constructing the maximum likelihood
function, and employing an iterative optimization procedure.
The main drawback of the Poisson model is that the variance of the dependent variable is
constrained to being equal to the mean.
While this does not affect the consistency of the
estimates, the presence of overdispersion in the data -- i.e., the variance being greater than the
mean -- causes a downward bias in the standard errors of the parameter estimates.
Applying a
test for overdispersion derived by Cameron and Trivedi (1990) to initial Poisson regression
estimates
of Equations (1) and (4) with the data used here revealed strong evidence of
overdispersion.
(9)
Hence, a distribution that relaxes the variance constraint is necessary.
2 '
ij
kL "E $
j
i
d(
ij
13
One solution is to suppose that the Poisson parameter itself has a random distribution
(Hausman, Hall, and Griliches, 1984). Assume that
8
has a gamma distribution with parameters
ij
2 ,*), where and * is constant across all origin-destination pairs.
(
Using the gamma distribution
ij
to take expectations of equation (7) yields the negative binomial distribution
Prob(X 'x *2 ,*) '
(10)
ij
ij
ij
'(2 %x )
*2
'(2 )'(x %1) (1%*)2 %
ij
ij
ij
ij
ij
ij
,
x
ij
with the conditional mean and variance
E(X ) '
(11)
ij
2
, V(X ) ' 2
*
ij
%*) .
*2
(1
ij
ij
Similar to the Poisson regression, the ratio of the variance to the mean is constant.
Unlike the
Poisson model, however, the variance-mean ratio is greater than one -- i.e., V(Xij)/E(Xij) =
* * > 1.
(1+ )/
In the estimations below, estimates of the parameter
implying a variance to mean ratio of approximately 34.
* are on the order of .03,
This clearly illustrates the restrictiveness
of the variance assumptions in the Poisson regression model.
I estimate the negative binomial model in Equations (9), (10) and (11) using maximum
likelihood techniques.
Multiplying the conditional probabilities of Equation (10) for all i and j
and taking logs gives the log-likelihood function
ln(‹)
(12)
'
jj
i
2
j
[ln
'(2 %x )&ln'(2 )&ln'(x %1)%
* &(2 %x
ln( )
ij
ij
ij
ij
After substituting the parameratization of
2
ij
ij
ij
%*)].
)ln(1
ij
in Equation (9) into Equation (12), the likelihood
14
function is maximized with respect to the parameters of the model using iterative numerical
optimization techniques.
4. DESCRIPTION OF THE DATA AND EMPIRICAL RESULTS
Description of the Data and Construction of the Variables
The data used here are for 1990 and are drawn from several sources.
By special request,
the U.S. Census Bureau calculated an inter-zonal labor flow matrix for male teenager workers in
the San Francisco-Oakland-San Jose Consolidated Metropolitan Statistical Area.
The matrix gives
the aggregate, inter-zonal journey-to-work flows for male teenagers between all possible origin-
destination combinations of 1990 census tracts in the Bay Area CMSA. The flows were computed
from the Census Bureau's confidential microdata files.
The tabulations were calculated in the
exact same manner as the journey-to-work flows for all workers in the Urban Element of the 1990
Census Transportation and Planning Package, with the sole difference being the restriction of the
sample to male workers between the ages of 16 and 19 years of age.
In addition, tract-level
population counts of male teenage workers by employment status were obtained in the special
tabulations request.
The Bay Area Metropolitan Transportation Commission (MTC) provided a
complete zone-to-zone matrix of AM peak period travel times by private vehicle.
Association of Bay Area Governments provided tract-level employment totals.
Finally, the
These data are
2
calculated from state ES-202 files.
While the journey-to-work flow calculations received from the Census Bureau are
calculated at the tract level, the MTC travel time matrix is computed for their own regional travel
analysis zone (RTAZ) system. For the most part, the 1,382 census tract system of the Bay Area
CMSA is nested within the 700 RTAZ system of the MTC and matching the journey-to-work and
15
employment data simply requires the appropriate aggregation of the Census Bureau data.
In a
hand full of cases, however, the MTC system split census tracts into two or more RTAZs.
these cases, inter-zonal travel times are aggregated to the tract level by averaging.
In
After all the
necessary adjustments, the matched data set encompasses a 660 zone system with 435,600 origin-
destination observations.
The origin supply of male teenage labor is defined as all male teenagers in the origin zone.
Destination employment opportunities is measured by the count of jobs located in the destination
zone.
Distance between zones is measured by the private vehicle, AM peak period travel time
and is measured in minutes.
Intervening opportunities and intervening competing labor are
calculated as follows. For the intervening opportunities variable, the data are sorted in ascending
order by the origin zone codes and by inter-zonal travel times.
A variable is then created by
cumulating destination employment counts, with a new running total starting for each new origin.
I then subtract destination employment from the cumulative variable for each observation to obtain
the number of jobs between a given origin and destination that are closer to the origin than the
employment located in the particular destination.
For intra-zonal observations -- i.e., Tij, where
3
i=j -- the intervening opportunities variable is set equal to zone employment.
Similarly, intervening competing labor is calculated by sorting the observations in
ascending order by destination zone codes and travel time, and by then creating running totals of
origin labor within destinations.
Origin labor for each observation is then subtracted from the
running total yielding the count of workers for a given origin-destination pairing who are
physically closer to the employment in the destination zone than workers in the origin zone.
Similar to intervening opportunities, intervening competing labor is set to zone labor supply for
16
intra-zonal observations.
After computing intervening opportunities, the competing searchers variable in Equation
(6) is calculated as follows.
After sorting the data by destination zone codes, I create a variable
for each destination-origin pair equal to the product of the count of origin teenagers and the
weight specified in Equation (6), (1-IOij/Total Employment).
I then sum the variable within each
destination, yielding 660 destination-specific values for competing searchers.
This series is then
merged by destination to the 435,600 origin-destination observations.
In the estimations below, I restrict the sample to all observations with origins in the
Oakland PMSA. Given that the Oakland PMSA is the most centrally located of the five PMSAs
in the region and the fact that the only constraint placed on destinations is that they lie within the
much larger CMSA, the set of possible destinations most likely encompasses the complete set of
employment opportunities available to male teenage workers living in Oakland.
I further restrict
the sample to observation where origin labor supply and destination labor demand are positive.
Note, when either variable is equal to zero, the predicted flows of Equations (1) and (4) above
are zero. After the various restrictions, there are 158,078 origin-destination observations.
Empirical Results
Table 1 presents basic descriptive statistics for the sample.
standard deviation for each variable.
Panel A gives the means and
The average zone has approximately 116 potential teenage
workers and the average destination has approximately 4,700 jobs.
The average totals of
intervening opportunities and intervening competition between zones are large.
This is as
expected given that both counts are increasing in the square of the distance between zones.
average time between zones is a little over a half of an hour.
The
The minimum travel time recorded
17
is slightly over a minute for one intra-zonal observation while the maximum travel time is slightly
over two hours. As can be seen, the average flow between zones is quite small (.14).
This is due
to the fact that the overwhelming majority of observation are zero flows (approximately 95
percent). This is a common characteristic in intra-metropolitan journey-to-work data.
Panel B of Table 1 provides the correlation matrix for the total flow variable and the four
spatial determinants: distance, intervening opportunities, intervening labor competition, and
competing searchers.
All four spatial variables are highly correlated.
As argued by proponents
of intervening opportunity models, distance is strongly correlated with both the intervening
opportunities variable (.90) and the intervening competition variable (.80).
Moreover, the
positive correlations between distance and intervening opportunities and distance and intervening
competition, coupled with the negative correlations between these spatial structure variables and
aggregate flows indicate the potential for an omitted variable bias that overstates the decay effect
of distance.
The competing searchers variable has an unexpected positive correlation with
aggregate flows.
Moreover, the competing searchers variable is negatively correlated with
distance, intervening opportunities, and intervening competition.
Table 2 presents the estimation results for six specifications of the negative binomial
gravity model: the basic model of Equation (1), Equation (1) controlling for intervening
opportunities, Equation (1) controlling for intervening labor competition, Equation (1) with both
intervening opportunities and intervening competition, Equation (1) controlling for competing
searchers, and Equation (1) controlling for both intervening opportunities and competing
searchers.
With the exception of the competing searchers variable, all of the spatial variables
have the expected signs and are highly significant.
Likelihood ratios tests of regressions (2), (3),
18
(4), and (6) against the basic gravity model estimated in regression (1) strongly fail to accept the
hypotheses that the spatial structure variables -- i.e., intervening opportunities and intervening
competition -- have no effect on intra-metropolitan labor mobility patterns.
The most striking
pattern is the decline in the distance parameter as the spatial variables are sequentially added to
the basic specification of the first regression.
A simple test of the intervening opportunities
hypothesis against the hypothesis of a pure distance-decay effect is to add the intervening
opportunity variable to the basic gravity specification in regression (1) and analyze the change in
the estimated distance-decay parameters.
If the decay parameter estimate declines, then the
negative relationship between aggregate commute flows and distance is in part driven by
intervening opportunities and the basic gravity model is mis-specified.
originating in the Oakland PMSA, this in fact is the case.
For youth commute flows
Adding intervening opportunities in
regression (2) nearly halves the distance-decay parameter estimate (from 1.426 to .7484).
This
confirms the results from past research that find intervening opportunities to be an important
4
determinant of spatial interaction.
Similarly, when entered individually in regression (3) the intervening competition variable
has a strong negative effect on aggregate commute flows and causes an even larger decline in the
distance decay parameter estimate (from 1.426 to .5470).
This lends support to the hypothesis
that workers closer to a given destination enjoy a competitive advantage in filling the opportunities
within the destination over workers that reside further away. Despite the high correlation between
intervening opportunities and intervening competition (.7304), when entered simultaneously in
regression (4) both variables have substantial and statistically significant effects on aggregate labor
flows. The independently significant effects can be seen in both the high absolute values of the
19
t-statistics for the parameter estimates in regression (4) and in likelihood ratio tests of regression
(4) against both regressions (3) and (2).
5
Furthermore, the distance-decay parameter estimate
declines by nearly ninety percent between regressions (1) and regression (4) (from 1.426 to
.1821).
Hence, the results from regressions (1) through (4) provide strong evidence of the
importance of spatial structure in determining aggregate spatial interaction.
Nonetheless, a
statistically significant and non-negligible distance-decay effect remains.
The competing searchers variable entered in regressions (5) and (6) perform poorly.
While the parameter estimates on competing searchers in regression (5) and (6) are negative (as
predicted by theory), neither estimate is statistically significant.
Likelihood ratio tests for
regression (5) against regression (1) and for regression (6) against regression (2) fail to reject the
hypothesis that the constructed competing searchers variable has no effect on intra-metropolitan
youth labor flows.
This result, however, is most likely due to the variable’s lack of variance.
Comparing the standard deviation of the competing searchers variable given in Table 1 to the
standard deviations of the other spatial structural variables illustrates the relative constancy of the
competing searchers variable.
Hence, the constructed competing searchers variable provides a
poor empirical experiment for testing Jayet’s model.
To demonstrate the severity of the omitted variables bias when a simple gravity model is
fitted to a trip distribution partially determined by spatial structure, Figure 2 plots the effects of
distance on aggregate commute flows implied by the parameter estimates in the first and fourth
regressions of Table 2. This provides a depiction of the inferred distance-decay effect when (1)
the basic gravity model is estimated ignoring spatial structure, and (2) the spatial configuration
of origins and destinations is taken into account.
The difference between the two distance-decay
20
profiles indicates the severity of the omitted variables bias.
and 1/d
.1821
1.426
The figure plots the functions, 1/d
, effectively normalizing the impact of all other variables.
Hence, one minus the
vertical coordinate is interpreted as the percentage reduction in the total flow of labor below the
hypothetical flow that would occur in the absence of distance-injected frictions.
The predicted
flow drops off quickly with distance using the parameter estimate from regression (1).
Within
three minutes, the estimated labor flow is eighty percent less than that which would exist in the
absence of a distance effect.
Controlling
for
At twenty minutes, there is a 99 percent reduction.
intervening
opportunities
significantly flattens the distance-decay profile.
and
intervening
competition,
however,
At five minutes, the estimated flow is 74 percent
of the hypothetical frictionless flow, at ten minutes 65 percent, at twenty minutes 57 percent, and
at thirty minutes 53 percent.
Hence, while the
independent decaying effect is still substantial
after controlling for the other spatial variables, the distance-decay effect is considerably smaller
than that implied by the parameters of regression (1).
5. CONCLUSION
The results of this paper demonstrate the importance of spatial structure in determining
aggregate spatial interaction.
In addition to providing evidence for the intervening opportunities
hypothesis thus confirming the notion that the spatial distribution of destinations matters, the
empirical results confirm the importance of intervening competing labor and the distribution of
origins. The model of spatial interaction motivated by Jayet's theoretical work and implemented
here differs fundamentally from past models of aggregate interaction.
destinations
models
of
Fotheringham
(1983,
1985)
and
the
In the competing-
discussion
of
locational
interdependence by Lo (1991), competition or complementarities between destinations leads to a
21
competing-destinations effect. In the model estimated here, competition between origin labor for
destination opportunities suggests the modifications of the basic gravity model.
In choosing
between alternative specifications, the nature of the interaction and underlying microeconomic
incentives and constraints must be considered.
The strong performance of the intervening competing labor variable carries implications
for measuring and reconceptualizing access to employment opportunities.
While the spatial
mismatch literature emphasizes commute costs associated with physical distance, little attention
is paid to the spatial dimension
of competition among workers.
The empirical work presented
here does find a statistically significant and non-negligible distance-decay effect even after
controlling for spatial structure.
workers
is
mechanisms.
especially
Nonetheless, the deterrent effect of intervening competing
pronounced.
This
empirical
finding
suggests
several
determining
If employers prefer workers that live relatively close to the establishment, spatial
proximity will impart a competitive advantage.
Alternatively,
declines with distance, proximity again translates into advantage.
if the quality of information
Future theoretical research on
the microeconomic foundations of aggregate spatial labor market interaction should incorporate
such aspects of spatial competitive advantage.
22
References
Cameron, Colin and Pravin Trivedi. 1990. "Regression Based Estimates for Overdispersion in
the Poisson Model," Journal of Econometrics, 46, 347-364.
Flowerdew, Robin and Murray Aitkin. 1982. "A Method of Fitting the Gravity Model Based on
the Poisson Distribution," Journal of Regional Sciences, 22(2), 191-202.
Fotheringham, A. Stewart. 1981. "Spatial Structure and Distance-Decay Parameters," Annals of
the Association of American Geographers, 71(3), 424-436.
Fotheringham, A. Stewart. 1983. "A New Set of Spatial Interaction Models: The Theory of
Competing Destinations," Environment and Planning A, 15, 15-36.
Fotheringham, F. Stewart. 1985. "Spatial Competition and Agglomeration in Urban Modelling,"
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Guy, C.M. 1987. "Recent Advances in Spatial Interaction Modelling: An Application to the
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Hausman, Jerry, Brownwyn Hall and Zvi Griliches. 1984. "Econometric Models for Count Data
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Haynes, Kingsley, Dudley Poston and Paul Schnirring. 1973. "Intermetropolitan Migration in
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Ihlanfeldt, Keith R. 1992. Job Accessibility and the Employment and School Enrollment of
Teenagers, Kalamazoo: W.E. Upjohn Institute for Employment Research.
Jayet, H. 1990a. "Spatial Search Processes and Spatial Interaction: 1. Sequential Search,
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Jayet, H. 1990b. "Spatial Search Processes and Spatial interaction: 2. Polarization, Concentration,
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Johnston, R. L. 1973. "On Frictions of Distance and Regression Coefficients," Area, 5: 187-191.
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Johnston, R. L. 1975. "Map Patterns and Friction of Distance Parameters: A Comment,"
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Lo, Lucia. 1991. "Substitutability, Spatial Structure, and Spatial Interaction," Geographical
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Senior, Martyn L. 1979. "From Gravity Modelling to Entropy Maximizing: A Pedagogic Guide,"
Progress in Human Geography, 3, 175-210.
Sheppard, Eric S. 1979. "Gravity Parameter Estimation," Geographical Analysis, 11, 121-132.
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J.
Willmott (eds.) Spatial Statistics and Models, D Reidel Publishing Company: 367-388.
Straszheim, Mahlon R. 1980. "Discrimination and the Spatial Characteristics of the Urban Labor
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Gravity Model Parameters," Journal of Regional Sciences, 34(2), 199-216.
24
TABLE 1: Descriptive Statistics
Panel A
Variables
Mean
Standard Deviation
.14
2.53
115.59
77.56
4,686.01
7208.73
Intervening Opportunities
30,471.38
17,618.49
Intervening Competition
31,991.03
18,539.87
Competing Searchers
81,529.54
201.66
34.59
17.85
Flowij
Origin Labor
Destination Employment
Drive Alone Travel Time
Panel B
Variables
Intervening
Intervening
Competing
Travel
Opportunities
Competition
Searchers
Time
1
-
-
-
-
Intervening Opportunities
-.0823
1
-
-
-
Intervening Competition
-.0792
.7304
1
-
-
.0370
-.6343
-.1355
1
-.0854
.9032
.8039
.-.6359
Flowsij
Competing Searchers
Travel Time
There are 158,078 observation.
Flowij
1
25
TABLE 2: Estimation Results from Various Specifications of the Negative Binomial
Gravity Model, Dependent Variable=Inter-Zonal Flow of Male Teenage Labor in the
Oakland PMSA
Variables
(1)
(2)
(3)
(4)
(5)
(6)
ln(Constant)
-9.8576
-8.5899
-7.4614
-6.6350
11.3759
99.3429
(-56.79)
(-37.91)
(-29.50)
(-26.19)
(.07)
(.6733)
.6487
.7412
.9253
.8893
.6487
.7427
(23.54)
(23.86)
(27.16)
(25.83)
(23.53)
(23.58)
Destination
.6266
.8033
.7228
.8186
.6269
.8059
Employment
(35.49)
(38.50)
(38.72)
(39.46)
(34.95)
(38.06)
1/Drive Alone
1.4260
.7484
.5470
.1821
1.4267
.7541
Travel Time
(141.85)
(21.84)
(11.72)
(3.65)
(139.37)
(21.82)
Intervening
-
-.5611
-
-.4316
-
-.5602
Origin Labor
Opportunities
Intervening
(-23.99)
-
-
Competition
Competing
-
-
(-15.84)
-.7507
-.5941
(-21.19)
(-15.73)
-
-
Searchers
*
(-23.99)
-
-
-1.8775
-9.5452
(-.1338)
(-.7314)
.0332
.0333
.0345
.0342
.0332
.0333
(25.98)
(26.35)
(27.25)
(27.10)
(25.96)
(26.37)
Log of Likelihood
-13,969
-13,780
-13,770
-13,687
-13,969
-13,780
N
158,078
158,078
158,078
158,078
158,078
158,078
T-statistics are in parentheses. The inter-zonal flows include all labor flows originating
in the Oakland PMSA with destinations anywhere in the 9-county Bay Area CMSA.
The
intervening opportunities and intervening competition variables include job opportunities
and competing labor outside of the Oakland PMSA.
The competing searchers variable
accounts for competing searchers residing outside of the Oakland PMSA.
26
1.I wish to thank an anonymous referee for making this point and for suggesting the following
specification of the competing-searchers variable.
2.The ES-202 files are the state Unemployment Insurance (UI) records that all employers are
required to file.
The Association of Bay Area Governments bases their tract level employment
counts on geocoded data from these state UI records.
3.Since intervening opportunities and intervening competition enters the aggregate interaction
function in Equation (4) multiplicatively, intra-zonal observations must have
for both variables.
non-zero values
I experimented with setting intervening opportunities and intervening
competing labor to one for intra-zonal observation rather than zone employment and labor
supply. This had no effect on the results.
4.Several researchers offer alternative tests of the intervening opportunities hypothesis that
also yield affirmative results.
Sheppard (1979) shows that when a basic gravity model is fitted
to trip distributions generated by an intervening opportunities process and when separate decay
parameters are estimated for each origin, an inverse relationship exists between the absolute
value of the distance-decay parameter estimates and the log of the distance around the origin.
Fotheringham (1981) finds such a pattern in airline passenger interaction data.
In an
alternative test, Haynes, Poston and Schnirring (1973) find that the distance-decay parameter
estimate for inter-metropolitan migration is more negative in regions with relatively dense
populations -- i.e., high opportunity regions.
5.Both likelihood ratio test strongly fail to accept the parameter restrictions implied by
regressions (2) and (3) relative to the specification in regression (4).