Econ 4621: Urban Economics (Holmes)

Minneapolis/St. Paul Density Gradient Problem for Homework 1

The two excel worksheets, Hennepin_city.xls and Hennepin_tract.xls contain data for Hennepin county at the city and Census tract level. The data is from the 2000 Census. Included in each file is geographic information and population information. I excluded geographic units with less than 1,000 in total population.

The geographic information is the same as discussed in class. There is information about land area (AREA_LAND), as well as a variable DISTANCE which is the distance from a point in the geographic unit (usually the center) to the Central Business District (here taken to be lat=44.975653, long=-93.272287, the coordinates of the IDS building).

The population data includes pop2000, which is total population in the geographic unit in 2000. It also includes data by race. Census 2000 reports information about the number of people who report one race, as well as the number of people who report two races, or three races, etc. There are numerous possible combinations. To keep things manageable, I restrict attention only to only the individuals who report a single race.

Your task is to calculate for each geographic unit (cities and tracts) three different density gradients. The first is total poulation. Here you use the pop2000 variable like in class. For the second and third gradients, you are to calculate the densities for whites and blacks. For example, to calculate the white density gradient, first calculate the density of whites per square mile, then take logs, then regress this on distance.

With three regressions for each geographic type, and with two geographic types, you will run a total of 6 regressions. Make a 3x2 table of the slope coefficients. Make a second table 3x2 of the R² of the regressions.

In what way is the white density gradient different from the black density gradient and how to they differ from the total population gradient. Why do you think the R² are higher for the track-level regressions as compared to the city-level regressions?

Excel Tips. To calculate the natural log with Excel, use the ln(x) function. To run a regression in Excel, use the Data Analysis option of the Tools menu. If the option is missing from your copy of Excel, you can add it by selecting the Add-Ins option from the Tools menu. For tips on using Excel to run a regression, click here for a helpful web site.