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12/05/2005
Five Variations on the Economics of Location

  1. Pioneers of location theory: The study of where and why trees, firms, illnesses, crimes, cities, satellites, and prices locate opens up lines of inquiry useful for gaining insights into markets and other phenomena. Such studies start with Johan Von Thunen's description of  the types of economic activity in rural Germany as forming concentric circles based on the cost of transporting various kinds of goods into the city. In such a model, the most productive uses of land with the highest yield relative to cost, or the highest transportation cost, would tend to cluster around the center. In an agricultural economy, vegetables would be closer to the central city than wheat, which would be closer than cattle. In a more modern economy, the central city would have department stores and financial centers, and concentric circles of intensive farming, forests, and ranching would branch outward. Amazingly, this model applies to modern cities of today, and gives insights into many location decisions of firms. A variant developed by Ernest Burgess describes cities like Chicago as having a central business district where transportation is most propitious, surrounded by concentric circles of factories, workers' residences, residential zones, and commerce zones. The key variables in the Burgess model are the commuting time to work, which is lowest in the central district, and the quality of housing which is greatest the further you are from the factories and noise of the central business districts. A discussion of site selection as it relates to the stock market is contained in the work of the Spec Duo and David Hillman, and the extensions of the central business model to the decision where to locate commerce and residences may be found in a summary on the Economic and Business Geography site The Four Classical Traditions of Location Theory.
  2. Regularities and clusters: Central to any studies in this area is a proper method for classifying locations. Such descriptions attempt to classify clusters of similar entities, as well as regularities in the characteristics of the entities such as their averages and variabilities. An excellent area here with well developed applications and methods appropriate to all fields is forestry. The paper Point Process Methods in Forestry Statistics provides methods of analysis based on spatial patterns, descriptions of variability, correlation methods, nearest neighbors, growth models, point process models with complete randomness relative to the density of points, and linked processes that treat the bivariate distribution of points classified by two main characteristics. One of the characteristics of trees is that they show clustering at the beginning of their life cycle and regularities at the end. At the beginning stages trees "show clumping caused by environmental heterogeneity, seed dispersion and competitions with other species, that are sometimes called environmental, morphological, and sociological causes." But as evolution proceeds, the regularities dominate. "This can be mainly explained by competition among neighboring trees and by dependence of mortality on local population density. Also, environmental variables such as ground cover vegetations, light conditions, microclimate, soil characteristics, profile and ecological history of the forest area play an important part." The application of these concepts and conclusions to markets is quite direct and useful.
  3. Methods of study. The main way of studying location data is to compare the characteristics of the distances between points to random distributions. Most studies start out with the density of the trees or stocks in a unit area. One variant is to look at the distance of each point in a area to its nearest neighbor, and then calculate the variance of these numbers. One approach is Bitterlich sampling, which is based on the mean of the sum of all cross-sectional areas at breast height divided by the area of the stand. A variant is to count the number of trees that can be seen in an angle larger than some small number like pi/36. The standard for measuring concentration is Ripley's K function. It's calculated in many statistical packages that contain spatial relations modules, but is difficult to tally by hand even for simple diagrams. It's defined as "the mean number of points in a disc of radius r centered at a typical point in the sampled area centered at a typical point which is not counted." If you draw a circle around each point in the area samples and calculate how many points there are at various small distances from it, and compare this to an identical calculation for points randomly placed in the area by simulation, you come up with a good practical estimate of K. Another statistical technique that is useful for extensions to markets is the coefficient of segregation. What's counted here is the number of times that each of two stocks (or trees) A and B have a return or price that is closest to itself, or to the other one, relative to the total number of times that it's nearest to any of the other stocks in the sample space. All these fancy statistics merely serve to refine the analysis. The basics of any study of location data are the mean distances from the points in one area to another, and their variabilities.
  4. Applications to markets. The cities for markets tend to be places where they cluster or reach milestones. One milestone for stocks are the round numbers of $100 or $50 or the price of $5 where stocks become marginable. Stocks may be envisioned as traveling to the cities of $100. How far away are they now? Are the coming or going? Do they tend to show an affinity for the cities based on their nearness? Another approach was suggested by Brian Haag: are stocks affected by the central business district of the market factor itself? Concentric rings from the market might be formed by low idiosyncratic volatility companies such as GE and KO, while the farthest rings would be highly idiosyncratic stocks. Burgess hypothesized that there is a tendency to move from an inner circle to an outer circle. Is the same true for stocks? Academic papers have applied Haag's ideas to the study of the degree of idiosyncratic volatility in DJIA stocks during periods of important news announcements.
  5. Location of companies. Companies in the old days chose their location based on where their raw materials were, where their customers were, and where the costs of transportation and communication were least. Modern companies choose their locations based on the ease of entering into transactions, or their ability to find superior ideas, educated employees or cutting-edge innovations. I remember when one-quarter of the companies in the Fortune 500 had their primary location in New York. Changes in the degree of envy, and the belief that companies  were static entities with resources that could be exploited at will, like oil reserves, led the authorities to tax them into areas where they could keep more of their output for their stockholders' and employees' wealth, future growth, and current stability. A line of studies that relates company performance to geographic location vis-a-vis the tax rate has been inspired by Arthur Laffer, who applied his theory that the lower the tax rate, the higher the revenues that government will receive relative to the performance of individual companies. Ten years ago, I saw data that showed superior returns to companies headquartered in low-tax states such as Arizona, Nevada, North and South Carolina, Florida, and Texas. Numerous studies show these states are growing much faster than the high-tax states, but no one has updated the Laffer results to modern times. Ironically, since it's against its leitmotif, Bloomberg provides ready data on this by calculating the daily performance of companies classified by city and reporting them each day.

Dr. Alex Castaldo adds:

Performance of stock indexes for 6 low-tax states:

                                                             SPX
                Start   StartDate     Cur   CurDate  PrcChg  PrcChg
Arizona           100  12/31/1994  514.94 12/5/2005 414.94% 175.55%
Nevada            Not available
North Carolina    100    1/2/2002  125.70 12/5/2005  25.70%   9.56%
South Carolina    100  12/31/2001  148.33 12/5/2005  48.33%  10.19%
Florida           100  12/31/1994  131.82 12/5/2005  31.82% 175.55%
Texas             100  12/31/1994  347.52 12/5/2005 247.52% 175.55%

Four out of the five available indexes outperformed the S&P over the same time period.

Data from Bloomberg LP.

Kim Zussman speculates:

  1. Better, more adaptable companies move to low tax jurisdictions.
  2. Low-tax states provide advantageous low overhead and higher profit margin, goosing the stock.
  3. The number of in-state companies is far less than SP500, and the higher return is due to greater risk.
  4. All of the above.
  5. Sacajawea.

Andrew Moe notes:

One problem is that the K function is based on circular measures. The benchmark is K(t) = pi * (distance)^2. We deal in "flatland" by comparison, as our ranges only go up and down.

But an adaptation may be to count how many points (say closes) occur within n points of a given trigger day. For example, how many closes occur within 10 points of a new 20 day low? Or how many within 10 of a round number. Then compare that to random. Lots of variations here.

Another adaptation would be to take expiration into account. Instead of saying how many cases within n days, you keep on counting instances until x number of days have passed since price has been in the study range. I have this nagging feeling that somehow this count should supplant pi in the K function, but no real clarity on the matter yet.

Jim Sogi comments:

"Universal Geometry of Circles", Chapter 11, gives the formula to compute the diameter and chords of circles in quadrance (distance squared) thus avoiding use of pi. as well as the spreads. The use of the xy coordinate would be apt for charts of prices and time in respect to the circles and clusters of spatial geometry. The quandrances can be analyzed statistically for significance of clustering as in Ripley's K, but with simplified computations. Not sure if this refers to chart formations or actual geography, but would work on lat=long as Cartesian.

Kim Zussman comments:

The cost of transport would seem to relate to historical location of centers of commerce adjacent to shipping: ocean ports, lake ports, and rivers. Later, this was supplanted somewhat by railroads, and eventually highway and airport hubs. Locations of transport for industrial goods attracted manufacturing and trading enterprises, which brought opportunities and jobs so populations swelled.

Most of the great cities are on advantageous harbors, but this is based on heavy industry. The recent trend is on informational commerce, which does not dictate particular geography and can be accomplished, with the aid of low cost mail and shipping, more remotely than in the past. Thus a trend toward many industries locating away from port cities, to areas attractive for employee family life (examples include Google, Microsoft, and Amgen).

One investment thesis is that the gradient between coastal port city real estate prices and that in suburbs/rural areas should decline over long periods. Of course cities serve numerous other social purposes, including facilitation of s#xual commerce, which will likely preserve much of the premium.

What about prior inverse-radial advantages of the denizens of Wall Street? Whereas in prior eras there were great informational advantages to physical association with the machine, now stat-arbs everywhere have easy access to market data. The only barriers now are delocalized desire, the ability to find discrepancies, and willingness to take your chances and test your strength against all the other maniacs. Nature abhors a gradient.

Dr. Alex Castaldo adds:

Additional details are found in:

Economic clustering and urban form: The case of Hamilton, Ontario

{We want] to consider the firm population of a [geographic] sector and to test for firm clustering, considering complete spatial randomness (CSR) as the alternative hypothesis. Using as input the location coordinates of the firms, the method commonly used for such analysis is to estimate an empirical univariate K-function. Intuitively this function provides the number of firms within a given distance of a randomly selected firm. The estimated K function is then compared to a set of simulated K functions for the same number of firms that are constructed under the CSR assumption. The test is simple in its conception but computationally intensive. Details for the estimation of the K function are provided in Bailey and Gatrell (1995) and Cuthbert and Anderson (2002).
While the univariate K function provides an explicit test for the spatial dependence among firms of the same type, it is not useful in studying the co-location of firms that belong to different sectors. An extension of the univariate K function is the bi-variate function, which tests for interdependence in clustering between two patterns in space. The function provides the expected number of points of one type from a randomly selected point of the other type within a specified distance. For a more detailed description see Bailey and Gatrell (1995)

Sushil Kedia adds:

Investing involves transporting expectations and risks of the future to the present moment.

The rent is the cost of investing. Cost of invested capital, or the opportunity cost of the invested capital, is the rent. In any economic enterprise, so long as the cost of the enterprise is less than the incentives of the enterprise it remains viable. Opportunity cost of investing is the amount of risk one undertakes in the venture of a particular investment.

Thus the analogous economics such as Von Thunen's Economic Location Theory brings about layers/concentric circles of risk (volatility) organized farther and farther consistent with an optimality with the cost of investing, which could be a function of the cost of transacting (commissions, slippage, impact cost, average contango etc. etc.) the investment.

High transportation cost /quickly perishable trade-generating high-frequency trading programs, or the day traders, are closest to the city centre.

The view-based counting-oriented speculators' bets of a small time frame -- a few days -- are next in the circle.

Medium-term 'trend-seeking' specinvestors' bets form the next circle.

The lowest cost, lowest volume-producing investors' bets are farthest in the circle.

The optimal rent of a particular layer would be deciphered from time to time by a function of the amount of risk perceived and the amount of drift/move in prices that one expects to capture from a particular pool/shoal of stocks. Say for example, if the optimal rent estimates were highest for the coal producing companies during the FWW or if it was the steel companies near the SWW or if it was the Software/Tech producing firms towards 1999-Y2K and the Oil companies in 2002-2005 it is essentially a similar reflection as the Economic Theory of Location of Von Thunen. Sectors getting the highest rent (allocations/attention), not necessarily highest rewards is but a function of the perceived maximum optimal point of cost of investing and expected returns. By a similar set of tautomerisation it is possible to see that sector rotations over shorter time frames are also running on the theory of Economic Location.

Dave Whitesel comments:

Two interesting modern-day examples where this theory is applied is Blockbuster and Starbucks. Blockbuster seems to be a magnet for Starbucks; where you see one you will often find the other within line of sight. Recently "The Undercover Economist" did a study on Starbucks with respect to rents. Interesting study though not very complete. The primary goal of these placements is surrounding ingress and egress points to specific populations. Therefore you might find two Blockbusters or Starbucks very close together. These placements are not random; they are targeting known paths of trafffic, with a goal of surrounding destinations.

Rob Fotheringham remembers:

About ten years ago I was working for a retail auto parts chain (about 650 retail stores in the Western U.S.), that had a real estate department dedicated to finding and securing optimal store sites. They studied demographics and traffic patterns and other indicators but could not predict successful locations better than their competitors could (i.e. AutoZone). So they did the logical thing and opened up a store right across the street from a newly opened, very large AutoZone, and it quickly became their highest volume store. Imitative behavior in this regard seems common. For example, a couple of years ago, while trying to attract a grocery store chain to our small city, we were told that by several major chains that we did not have sufficient population density to justify even a small store (35-40k square feet). Soon thereafter Wal-Mart declared their intent to build a superstore on the same site, whereupon Home Depot inquired about the land across the street, and the major grocery chains developed interest.

 

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