How Education and Population Density Affect Average Wages at the State Level

An article in the February 1997 issue of Trends noted some variables that could not explain the differences in average wages across states (racial composition of the state and the overall size of the population). This article points out three variables that are statistically significant and can explain some of the differences in average wages. Just as in the previous article, the dependent variable is the 1995 Average Annual Wage for workers covered under unemployment insurance (see Footnote 1).

Table 1 is similar to the table published last month. However, instead of including the percent of white workers and the 1996 population estimate, three new variables are included, all of which were obtained from the Census Bureau. These new variables are: "1990 Percent Urban" (the percent of the state’s population that lives in urban areas--see Footnote 2--as of 1990), "1995 Percent College Graduates" (the percent of the population aged 25 and over with at least a 4-year college degree as of 1995) and "1992 Population per Square Mile" (the state's population as of 1992 divided by the area of the state in square miles).

A multiple regression analysis showed that all three of these variables are statistically significant (see Footnote 3) at the 5 percent level, and together they explain more than 50 percent of the variation in average wages (R2=0.589). The coefficients are shown in Table 2 and are interpreted as follows. First, the coefficient for college graduates is 218.723, meaning that if the percent of the population that has graduated from college were to increase by one percent from 21.2 to 22.2 percent, the model predicts the average annual wage to increase by $218.72. The coefficient for the second variable, 5.533, means that if the population per square mile were to increase from 4.8 to 5.8, we could predict the average annual wage to increase $5.53. Finally, if the percent of Wyoming’s population that lives in urban areas were to increase from 65.0 to 66.0 percent, we would expect an increase in average annual wages of $89.53. Polly Callaghan, an Economist with the Division of Economic Analysis, found similar results when she analyzed Wyoming’s 23 counties in Where are the Jobs? What do they Pay? (see Footnote 4).

It is interesting to note some variables that were not significant. Neither the percent of the population aged 25 and over with at least a high school diploma nor the overall size of the population is statistically significant.

An analysis like this has several weaknesses. First, the relationships expressed could be due to reverse causation. In other words, instead of wages increasing as a result of the percentage of the population with college degrees increasing, the college graduates could be moving to the places with high wage jobs. Or, in the case of the third variable, instead of urban areas creating high wage jobs, the high wage jobs could encourage people to settle in urban areas. In a cross sectional study like this, it is sometimes difficult to determine the direction of causality.

Another possible weakness of this analysis is that the variable could not really be the cause of the differences, but simply well correlated with an unobserved outside factor that is causing the differences. For example, the percent in urban areas could be correlated with an industry mix. Manufacturing industries tend to be concentrated in urban areas, while agricultural industries are most often found in rural areas. From the Wyoming 1995 Annual Covered Employment and Wages (see Footnote 4), we know that Agriculture is the second lowest paying industry in Wyoming ($15,400 per year compared to a state average of $22,054 per year) and Manufacturing has above average pay ($26,559 per year). Since different industries pay different wages, the percent in urban areas could really be signaling that a state with a better mix of industries will have a higher average wage.

In summary, in determining average wages, the population of the state doesn’t matter, but whether the population is urban or rural does. The population density does matter, as does the percent of the population with college degrees. Further research might suggest other variables more closely correlated with average wages across states.

David Bullard is a Statistician at Research & Planning, specializing in Standard Industrial Classification (SIC) coding and special projects. He is also the Associate Editor of Wyoming Labor Force Trends.

Footnote 1: Includes workers covered by Unemployment Insurance (UI). Source: U.S. Bureau of Labor Statistics.

Footnote 2: The Census Bureau defines an urban area as an incorporated city or town of at lease 2,500.

Footnote 3: For an explanation of statistical significance, please refer to the "Statistical Analysis" section in the article "Where Does the Wyoming Worker Come From?" (November 1996 issue of Trends).