In this section, we extend the dynamic location choice model to incorporate knowledge spillovers theory and transaction cost economics perspectives. The model takes account of three agglomerative factors – natural advantages, knowledge spillovers, and transaction costs – that the geographic concentration of an industry is driven by these factors considered by each profit maximizing location decisions of individual plants. Natural advantages of some locations and inter-industry knowledge spillovers lead plants to cluster together, and transaction costs and idiosyncratic plant-specific considerations that provide the counterbalance to keep the entire industry from concentrating at a single point.
The Dynamic Location Choice Mode
The location choice model, developed by Ellison and Glaeser (1997), takes account of two agglomerative factors – natural advantages and industry-specific spillover – to interpret industry clustering. We base on the dynamic location choice model to generate the indicator of geographic
based firms.
concentration. Suppose the geographic region is divided into M subunits, and x1,x2,...,xM is defined as labor shares of total employment, s1,s2,...,sM as labor shares of a given industry’s employment, and z1,z2,...,zN as labor shares of plant j in the industry. The probabilities of the plants choosing to locate in area 1, 2…, M arep1,p2,...,pM, and p is higher when the area is i larger, that is, pi = . The fraction of the industry’s employment located in geographic unit i is xi shown as
Due to the fact that employees are major components in a plant, most of the clustering indicators in the literatures applied employment data to measure the geographic concentration level.5 An area with more plants clustered implies that there are comparatively more labors in the area. In considering the size distribution of the plants, a natural measure of the concentration degree is reflected by employment in the industry departs from the overall pattern of employment.
The difference between the labor share of an industry locating at area i and the labor share of all the industry locating at area i measures the competitive geographic concentration of an industry.
Given G and H above, the expected value of G, E(G), is derived in the form of (3) E(G)=H
(
1−∑ipi2)
+∑i(
pi −xi)
2 ,2 is the Herfindahl index of the industry’s plant size distribution.
Furthermore, under the condition of (p1,p2,...,pM)= (x1,x2,...,xM), the model is then reduced to the form that the expected value of the geographic concentration indicator G equal to the Herfindahl index. The profit πki of the kth firm locating in area i (make its location choicev =i) is as follow k
(4) logπki =logπi +gi(v1,...,vk−1)+εki
where πi reflects the profitability of the plant locating in area i in the industry, while the profitability is concerned with the fitness of natural advantages of the area to the characteristics of the industry. Here gi(v1,...vk−1) is the spillover effects created by firms locating in area i, and εki is a random component containing the characteristics of plant k and follows Weibull
5 See Henderson (2003).
distribution.
{ }
π i is measure of average profitability of area i and reflects the effect of natural advantages to locate in area i. It allows for the industry’s characteristics or preferences captivated by the distinguished features of locations. Two parameters γna∈[0,1] and γs∈[0,1] are assumed to symbolize the importance of natural advantages and spillovers respectively. The location choice model is then derived as(5) H
The DLC Model with KST and TCE Perspectives
In this paper, transaction costs are considered important dimension which should be incorporated in the location choice model. The DLC model is extended to incorporate agglomerative force and transaction costs. Different from natural advantages which emphasize the importance of localized feature of an industry, spillovers and transaction costs focus on the relationship and interdependence of plant-to-plant in the industry. Formally, we denote the influence of transaction costs to the location choice to beγtc∈
[ ]
0,1 , and the profits received by the kth business unit locating in area i in the form of Bernoulli random variables equal to one with probability γtc, u is an indicator for whether lii
vl = , and
{ }
εki are independent Weibull random variables independent of{ }
ekl and{ }
fkl . The first term log(xi) is profits dependence on aggregate employment necessary to reproduce (on average) overall pattern of employment. And the total effect of spillovers and transaction costs is signified with ∑ − −≠k
l ekluli fkl(1 uli), both related to u . To simplify the model, we li assume that the effect of plant l’s location on plant k’s profit depends only on whether they are in the same area without considering the distance between them. Besides, spillovers and transaction costs could be estimated as a changeable value or a function of other factors. That is, ekl =elk =1 if mutual spillover effects strongly affect plant k’s and plant l’s profits, and so as fkl = flk =1. In other words, when the transaction costs between two plants account for a great part of their profits, they would tend to locate together. The higher the index γs and γtc are, the higher probability ekl and fkl equal to one. Otherwise, the spillover effects and the transaction effects would be presented zero reflecting that plant k’s profits are independent of plant l’s location.
If two firms locate in the same area (uli =1), then transaction costs reduce to zero disregard
the fact whether the two firms are correlated with transaction costs. In this case, what deserves to be noted is whether there exists spillover effects (ekl =1 or else). However, if two firms didn’t locate together (uli =0), the spillover effects won’t exist and what matters is transaction costs. So we derive the total effect of spillovers and transaction costs to be ∑ − −
≠k
l ekluli fkl(1 uli). In this model, the business units’ location choices v1,v2,...,vN are identically distributed random variables, each taking on the value i∈
{
1,2,...,M}
with probability x (without the effects of i natural advantages). Nevertheless,{ }
vj are not independent since each plant’s location choice would take others’ choices into consideration. The correlation relationship is assumed to betc distribution of the plant size through H.
Combining the model of spillovers and transaction costs into DLC model, the aggregate factors can be put together to form a more general model,
(8) ki
where log(πi) stands for the natural advantages effect to profitability of the plant to locate in area i. It reflects the fitness of natural advantages. And ∑ − −
≠k
l ekluli fkl(1 uli) represents the aggregate externality effects of spillovers and transaction costs resulted from location choices of related plants. εki is a random component containing the characteristics of plant k and follows Weibull distribution. In that, we can derive the expected value of G6,
(9) E G x
[
H]
aggregate employment in an industry group is characterized by the tendency of plants in each individual industry to agglomerate as captured by the single parameter, γ0, which reflects the influence of natural advantage, spillovers, and transaction costs on geographic concentration. It also reflects the fact that average profit levels are perfectly correlated across industries and intra- and inter-industry spillovers exist in all industries. In that, the index of geographic concentration can be derived
6 See Ellison and Glaeser (1997, p. 898) proposition 1 for more detailed derivation.
(10) take additional consideration of the agglomerative forces and transaction costs, and we derive a more general form of the location choice model.