EMPLOYMENT ACCESSIBILITY POTENTIAL APPROACH TO RELATIVE LAND VALUES

The Potential at a equals the Jobs at a,
divided by the Distance between a and b (its nearest neighbor),
plus the sum for all tracts (x) from b through i
of the Jobs at each tract (x)
divided by the Distance from that tract (x) to tract a.

Did you get all that?

In other words, Brigham's Employment Accessibility Potential creates an index, which can then be multiplied or divided by an appropriate factor to generate realistic estimates of property values or rents for residential property of a given type all over a given city. Brigham argues that residential value reflects the way most of us pay for our housing, i.e., through jobs. He reasons that access to jobs is a major determinant of residential property value or rent. The effect of jobs reflects the number of jobs in the immediate area and the jobs throughout the city to which one can commute, taking into account the distance of the commute.

Brigham, then, approaches the question of accessibility and location rent from an entirely different angle than did von Thünen and all his intellectual descendents. Brigham's approach could not even be attempted until the arrival of computer technology. It does provide a rigorous analysis of location rent even in the multi-nucleated and sprawling contemporary urban area, where the von Thünen-derived approaches break down. Brigham successfully performed this analysis on Los Angeles, which has been most intractable to conventional analyses of location rent.

This exercise involves an imaginary town, conveniently square in shape, containing nine Census tracts, each also conveniently square in shape. Each tract is precisely 1 km on a side. Let us give each tract a letter, from a through i. Below is a map of the town, showing the actual number of jobs in that tract. Also shown is a place to enter the employment accessibility potential, which you'll be calculating in this exercise.

                                    _________ _________ _________
                                   |a        |b        |c        |
                                   | J=10000 | J= 8000 | J= 1000 |
                                   | P=      | P=      | P=      |
                                   |_________|_________|_________|
                                   |d        |e        |f        |
                                   | J= 6000 | J=   50 | J= 6000 |
                                   | P=      | P=      | P=      |
                                   |_________|_________|_________|
                                   |g        |h        |i        |
                                   | J= 1000 | J= 3000 | J=12000 |
                                   | P=      | P=      | P=      |
                                   |_________|_________|_________|
          
               

Note that the center of each tract is one kilometer from neighbors sharing a common border with it; about 1.4 km from neighbors sharing one corner from it; and 2 km from the second tract to the north, south, east, or west. For the four corner tracts, there is 2.9 km separating their centers from those of the tracts at the very opposite corners from them. For all other tracts (i.e., those one tract off in one direction and two tracts off in the other), there are 2.3 km between their centers.

To do this exercise, it is best to use a spreadsheet (e.g., Excel or Lotus 1-2-3). Create a spreadsheet, which will have two rows and nine columns. The first row will represent the actual jobs as shown on the map above, while the columns stand for the names of the tracts above. Go on ahead and enter these numbers in the appropriate cells of Row 1.

1. On the basis of just these numbers, which tract would you expect to be the lowest rent district?

   
                  Tract letter: __________
   
   

   In the second row, you'll be factoring in, not just the jobs at each tract, but the jobs in all other tracts in the town and the distance from each of those tracts. This will entail the application of the formula above, Brigham's Employment Accessibility Potential.

   To calculate P, enter the following formulae into the appropriate cells of Row 2. They represent Brigham's accessibility potential for each tract. First, the hard way: You move the spreadsheet cursor to each cell and then manually type each formula into the entry box. You need to be VERY careful about typos and punctuation! Alternatively, a much easier way: You open your browser in one window and your spreadsheet in another. You can highlight each formula and then click on the "copy" function in the browser's edit menu (or just hit CNTL-C). Then, going to the right cell in your spreadsheet, you can activate the spreadsheet's edit menu and select "paste" (or, in Excel, CNTL-V).

   Note that the formulae I'm giving below assume you're in the Excel spreadsheet, which is widely available on campus: You have to include an "=" at the beginning of any formula. If you're using Works, you'd use a "+" instead. Some other spreadsheets don't require this first character at all, as formulae are their default.

   

   Cell   Formula
   
   A2     =(A1/.5)+B1+D1+(E1/1.4)+(C1/2)+(G1/2)+(F1/2.3)+(H1/2.3)+(I1/2.9)
   
   B2     =(B1/.5)+A1+C1+E1+(D1/1.4)+(F1/1.4)+(G1/2.3)+(I1/2.3)+(H1/2)
   
   C2     =(C1/.5)+B1+F1+(A1/2)+(I1/2)+(E1/1.4)+(D1/2.3)+(H1/2.3)+(G1/2.9)
   
   D2     =(D1/.5)+A1+E1+G1+(B1/1.4)+(H1/1.4)+(C1/2.3)+(I1/2.3)+(F1/2)
    
   E2     =(E1/.5)+B1+F1+H1+D1+(A1/1.4)+(C1/1.4)+(G1/1.4)+(I1/1.4)
   
   F2     =(F1/.5)+C1+E1+I1+(B1/1.4)+(H1/1.4)+(A1/2.3)+(G1/2.3)+(D1/2)
   
   G2     =(G1/.5)+D1+H1+(A1/2)+(I1/2)+(E1/1.4)+(B1/2.3)+(F1/2.3)+(C1/2.9)
   
   H2     =(H1/.5)+G1+I1+I1+(D1/1.4)+(F1/1.4)+(A1/2.3)+(C1/2.3)+(B1/2)
   
   I2     =(I1/.5)+H1+F1+(G1/2)+(C1/2)+(E1/1.4)+(D1/2.3)+(B1/2.3)+(A1/2.9)
   
   

   

2. On the basis of employment accessibility potential, which of the tracts turned out to be the lowest rent district?

   
                  Tract letter: __________
   
   

   

3. Is this the same tract you identified in the first question?

      
                   __________ yes      ________ no
   
   

   

4. Explain in your own words the results of Question 3:

   
        ______________________________________________________________________
   
        ______________________________________________________________________
   
        ______________________________________________________________________
   
        ______________________________________________________________________
   
        ______________________________________________________________________
   
        ______________________________________________________________________
   
   
   

   

   For the totally bored or totally "techie": You could try to make this model somewhat more realistic by adding more cells to the imaginary town (say, a 5 x 5 grid?), modifying the equations in row 2 of your spreadsheet and adding formulae. The more tracts in the city, the less overwhelming will the edge effects be (the corner tracts, with their paucity of neighbors, are fully 44 percent of the available tracts).

   Alternatively, you could experiment with different values in Row 1 of your spreadsheet (whether the original 3 x 3 or a 5 x 5 grid).

   If you're really ambitious, you could try to figure out multipliers for the index, which would bring the numbers in line with rents or home values in another small city (e.g., Chico, with its eight core tracts).

   Now, imagine doing this for a city as large as Los Angeles, with thousands of tracts, and all of odd shapes. Trying to figure out the centroids for each of these and measuring the distances from each centroid to ALL of the others and then contemplating the math is enough to make you ... nervous. This was done in the 1960s with the mainframe computers of the day. It could be done more easily today with GIS technology, given GIS capacities to compute centroids and determine distances. Even so, it turned out that P correlated closely with actual real estate "comps" and rents.

   

   © Dr. Christine M. Rodrigue
   Last revised: 02/12/99