College Education Matters for Happier Marriages and Higher Salaries ----Evidence from State Level Data in the US

College Education Matters for Happier Marriages and Higher Salaries ----Evidence from State Level Data in the US Anonymous Authors: SH, AL, YM Contact TF: Kevin Rader Abstract It is a general consensus in society that education provides individuals with the necessary opportunities to rise through society. Using simple and multiple linear regressions, this paper shows that there is a significant negative correlation between the divorce rate and percentage of population with bachelors degree in state within the United States (P<0.001), but no significant correlation between the divorce rate and the percentage of population with high school education (P>0.05). Meanwhile, there is a significant positive correlation between the proportion of population with bachelor s degree in a state and the state s average salary (P<0.001); however, the correlation between the average salary and the proportion of population with a high school diploma is almost insignificant (P 0.05). Comparing results based on statistics from 2006, 2000, and 1990, the paper also finds that the relationship between college education and average salary has strengthened over time. The paper therefore concludes that college education has important implications for a society s overall level of family happiness and fiscal well-being. I. Introduction The impact of college education, because of its relevance to everyone s personal development, has long been a discussion drawing the attention of all members of society. Scholars started studying college education from a very early time. C. Robert Pace (1941, 1979), James Trent and Leland Medsker (1968), and Kenneth Feldman and Theodore Newcomb (1969) are among the earliest scholars to systematically analyze college outcomes. Through interviews and subject tracking, their studies used individual level data to explore basic distinctions between those who attended college and those who did not. In the end, they all found that college did make a difference. This paper recognizes that the impact of college education may well be multi-dimensional. Consequently, this paper chooses to look into the aggregate-level effects of college education on two particular social characteristics: divorce rate and average salary. It tries to determine whether one s college experience would improve the quality and long-term sustainability of people s marriage prospects, for marriage has a significant influence on people s daily lives and social well-being. It also tries to determine whether going to college will help people fiscally in the long run, since income is the foundation of everyone s quality of life. Using state level data, this paper investigates how the proportion of population with college education in a state is associated with its divorce rate and average salary. The paper compares the effect of college education with that of high school education. It also uses data from three 1

different years (2006, 2000 and 1990) to see if the impact of college education has changed over time. II. Methods The data used in the analysis are retrieved from two sources, the U.S. Census website and Gallup.com, a website that offers research in economics, sociology and psychology. The U.S. Census website provides data on salaries, divorce rates, unemployment rate, poverty rate, and educational attainment in 1990, 2000, and 2006. Gallup.com provides data on the church attendance rate in 2006. Table 1: Description of Data Variable Name Description Mean (Standard deviation) Source Divorcerate06 Rate of divorce per 1,000 population in 2006 (by state) 3.89 (0.99) US Census Salary06 Annual personal income per capita in constant dollars in 2006 (by state) 31380 (5417) US Census Salary00 Annual personal income per capita in constant dollars in 2000 (by state) 28690 (4662) US Census Salary90 Annual personal income per capita in constant dollars in 1990 (by state) 23240 (3833) US Census Bachelor06 % of people with bachelor s degree or above in 2006 (by state) 26.7 (5.41) US Census Bachelor00 % of people with bachelor s degree or above in 2000 (by state) 24.1 (4.80) US Census Bachelor90 % of people with bachelor s degree or above in 1990 (by state) 20.0 (4.20) US Census HighSchool06 % of people with high school diploma or above in 2006 (by state) 85.38 (3.60) US Census HighSchool00 % of people with high school diploma or above in 2000 (by state) 81.8 (4.35) US Census HighSchool90 % of people with high school diploma or above in 1990 (by state) 76.1 (5.61) US Census Church06 % of people who attend church a week or almost every week (by state) 42.1 (9.25) Gallup.com Unem05 Unemployment rate in 2005 (by state) 4.93 (1.07) US Census Poverty06 Poverty rate in 2006 13 (3.19) US Census The first set of models tests the relationship between divorce rate and education level. Model 1.1.1 is a simple linear regression of divorce rate with percentage of population with college education as the explanatory variable, while Model 1.1.2 is a step-wise regression of divorce rate with the addition of several controlling variables. Models 1.2.1 and 1.2.2 perform the same regressions, only with percentage of population with high school diploma replacing percentage of population with bachelor s degree. Since data for divorce rate in California, Georgia, Idaho, Iowa, Maine and Mississippi are not available, these states are not included 2

2 3 4 5 6 7 in the regression. The church attendance rate for Alaska is not available, so in the regression controlling for church attendance, Alaska is also excluded. In this case, it is difficult to compare how the correlation between divorce rate and education attainment has evolved over time because the divorce rate data are only available for years after 2000. The second set of models investigates the relationship between average salary in a state and the state s percentage of population with college and high school education. Models 2.1.1, 2.1.2 and 2.1.3 are simple linear regression models that test the correlation between percentage of college graduates and average salary, and Models 2.2.1, 2.2.2 and 2.2.3 test the correlation between the percentage of high school graduates and average salary, based on data in 2006, 2000 and 1990 respectively. All 50 states are included. In all regressions, a variable is considered statistically significant if P < 0.05. 1. Education Attainment and Divorce Rate III. Results Table 2: Divorce Rate and Education Attainment Model 1.1.1 Model 1.1.2 Model 1.2.1 Model 1.2.2 Percentage of Population with College Education -0.110*** (0.022) -0.138*** (0.024) Percentage of Population with High School Education -0.084* (0.042) -0.095* (0.048) Percentage of Frequent Church-goers -0.034** (0.015) -0.004 (0.018) Constant 6.824*** (0.591) 8.984*** (1.117) 11.14** (3.614) 12.19** (4.426) Observations 44 43 44 43 R-squared 0.38 0.45 0.09 0.10 Adjusted R-squared 0.36 0.42 0.07 0.05 ***p<0.001, **p<0.05, *P<0.1 1) College Education and Divorce Rate Based on data from 2006, a scatter plot with divorce rate on the y-axis and percentage of population with college education on the x-axis demonstrates that a linear relationship exist between the two variables. 10 20 30 40 50 Bachelor DivorceRate 3

2 3 4 5 6 7 Model 1.1.1 is a simple linear regression to test the correlation between the two variables, assuming education attainment as the only factor that influences divorce rate. Model 1.1.1 shows: E(DivorceRate06)= 6.824-0.110 Bachelor06 The linear regression shows, without controlling for other variables, a 1% increase in the proportion of population with college degree lowers the divorce rate by 0.11% on average. The model is statistically significant (P<0.001); it explains around 36.5% variation of divorce rates (adjusted R-squared=0.3647) and it fairly precisely predicts divorce rate (Root MSE=0.792). Model 1.1.2 tries to control for several other variables. It uses a backward stepwise regression with divorce rate as the dependent variable and percentage of population with college education, percentage of population with regular church attendance, poverty rate and unemployment rate in the previous year. Poverty rate and unemployment rate are dropped at the 5% significance level, and the regression result is: E(DivorceRate06)= 8.982-0.137Bachelor06 0.034Church06 Controlling for church attendance rates, a 1% increase in the proportion of population with college degree lowers divorce rate by 0.14% on average. The influence of percentage of college graduates in the population is highly statistically significant (P<0.001). The model can explain around 41.8% of the variation of divorce rates across states, and the model fairly precisely predicts the divorce rate (Root MSE =0.760). 2) High School Education and Divorce Rate Based on data from 2006, a scatter plot with divorce rate on the y-axis and percentage of population with high school education on the x-axis doesn t seem to show a strong linear relationship between the two variables. 75 80 85 90 HighSchool DivorceRate Model 1.2.1 is a simple linear regression similar to Model 1.1.1 to test the correlation between the two variables: E(DivorceRate06)= 11.14-0.084HighSchool06 4

In this case, the model is almost insignificant (P=0.051) and this model explains only 6.6% of the variation in divorce rate. Since Model 1.1.2 shows that church attendance is negatively correlated with divorce rate, therefore, Model 1.2.2 also controls for frequent church attendance rate. E(DivorceRate06)= 12.19-0.095HighSchool06-0.004Church06 However, in this case, neither explanatory variable is significant at the 5% level, though no problem of multicollinearity is detected (correlation of HighShcool06 and Church 06 is -0.2). This set of models suggests that college education may have important influence on the happiness of marriage. States with higher percentage of college graduates have lower divorce rates, but states with higher percentage of high school graduates don t necessarily have lower divorce rates. 2. Education Attainment and Average Salary Percentage of Population with College education Percentage of Population with High School education Table 3. Average Salary and Education Attainment Model 2.1.1 Model 2.1.2 Model 2.1.3 Model 2.2.1 Model 2.2.2 Model 2.2.3 821.8*** (82.35) 805.4*** (78.51) 5 720.0*** (80.67) 458.1** (207.1) 346.8** (146.5) 9426*** 9301*** 8825*** -7730 322.6 Constant (2244) (1926) (1650) (17700) (12000) Observations 50 50 50 50 50 50 R-squared 0.67 0.69 0.62 0.09 0.10 0.17 278.0** (90.10) 2074 (6877) Adjusted R-squared 0.67 0.68 0.61 0.07 0.09 0.15 ***p<0.001, **p<0.05, *P<0.1 1) College Education and Average Salary Model 2.1.1 uses a simple linear regression to test the relationship between percentage of college graduates and average salary based on data from 50 US states in 2006. Models 2.1.2 and 2.1.3 test the same relationship in 2000 and 1990 respectively. The regression results of the three models are: E(Salary06)= 9391+819.6 Bachelor06 [P<0.001, R-squared: 0.663, Root MSE:3190] E (Salary00)=9221+803.9 Bachelor00 [P<0.001, R-squared: 0.664, Root MSE: 2740] E(Salary90)= 8729+721.0 Bachelor90 [P<0.001, R-squared: 0.612, Root MSE :2410] An interesting result is that not only is percentage of college graduates in the population significantly positively correlated with average salary in the state (P<0.001), but the correlation has become stronger in the past two decades. This is indicated by increases in the

values of the coefficient and slight increases in the R-squared values. This finding confirms with the general perception that as technology advances increase the demand for high-skilled workers, higher education becomes more and more important to securing high-paying jobs. 2) High School Education and Average Salary Similar to the models in the previous subsection, Models 2.2.1, 2.2.2 and 2.2.3 are simple linear regression models that test the relationship between percentage of high school graduates and average salary based on data from all 50 states in 2006, 2000 and 1990 respectively. The regression results are: E(Salary06)= -3955+412.5 HighSchool06 [P=0.049, R-squared:0.077, Root MSE:5240] E (Salary00)= 3628+304.7 HighSchool00 [P=0.043, R-squared:0.081, Root MSE: 4540] E(Salary90)= 3228+261.5 HighSchool90 [P=0.006, R-squared:0.145, Root MSE:3590] Compared with regression results in the last subsection, it s clear from the R-squared values that the percentage of population with a high school education explains a much smaller portion of variation in average salary. Also, the Root MSE values indicate that models in this subsection are consistently less precise in predicting a state s average salary than their counterparts in the last subsection. An interesting result to note is that, whereas the explanatory power of the percentage of college graduates on average salary has become stronger and stronger, the explanatory power of the percentage of high school graduates has significantly decreased since 1990 (as demonstrated by the R-squared value). The results suggest that college education, compared to high school education, has become more important over time. IV. Conclusion and Discussion As this paper demonstrated, the percentage of population with college education is significantly negatively correlated with the divorce rate in a state (P<0.001), whereas the percentage of population with high school education is not (P>0.05). Controlling for church attendance rates, a 1% increase in the proportion of population with college degree lowers divorce rate by 0.14%, on average. College education is also significantly positively correlated with average salary (P<0.001). The linear regression shows that, without controlling for other variables, a 1% increase in the proportion of population with college degree increases average salary by around $800 on average, and that the correlation has strengthened from 1990 to 2006. High school graduation was correlated with average salary in 1990 (P=0.006), but the correlation became barely significant after 2000 (P=0.043). Therefore, this paper concludes that college education matters for happier families and higher salaries at the state level. One weakness of this study is that not enough control variables are included in the models. For example, for the second model regressing the state-level average salaries, only educational attainment is used as an explanatory variable, which may not be sufficient. In addition, the result that states with more college graduates have higher average salaries may be attributable to industrial differences. For instance, states where the major industry is financial services may attract more people with higher education and at the same time pay higher salaries than agricultural states. It may also be true that states with higher average 6

salary attract more college graduates than states with lower income. However, this reasoning cannot very well explain the increasing strength of correlation between percentage of population with college education and average salary. Another potential weakness may come from the nature of the data. People who are currently enrolled in college are not counted as people with a college education, but rather simply with a high school education. However, the proportion of people currently enrolled in college may not be big enough to have a major impact on the regression results. The obvious broader implication of this study is that institutions and governmental organizations should recognize the critical importance of college education on the general well-being of the society and try to promote college education for more American. It may also imply that students and parents should be aware of the increasing importance of college education and seriously consider college decisions. Possible future studies may probe the influence of college on other social characteristics and other types of social capital, for example, levels of discrimination, trust, innovation and etc. It may also be worthwhile to investigate what factors influence the percentage of population with college education and get a better understanding of how to effectively promote college education. V. References: "College and Its Effect on Students - Early Work on the Impact of College, Nine Generalizations, Later Studies, Pascarella and Terenzini." StateUniversity.com. Web. 2 Dec. 2010. <http://education.stateuniversity.com/pages/1844/college-its-effect-on- Students.html>. Newport, Frank. "Church Attendance Lowest in New England, Highest in South." Gallup.Com. 27 Apr. 2006. Web. 26 Nov. 2010. http://www.gallup.com/poll/22579/church-attendance-lowest-new-england-highestsouth.aspx StataCorp. Stata. 11.0 ed. College Station, 2009 United States. U.S. Census Bureau. Educational Attainment by State: 1990 to 2007. U.S. Census Bureau. Web. 2010. <http://www.census.gov/>.3 United States. U.S. Census Bureau. Marriages and Divorces Number and Rate by State: 1990 to 2007. U.S. Census Bureau. Web. 26 Nov. 2010. <http://www.census.gov/>. United States. U.S. Census Bureau. Personal Income Per Capita in Current and Constant (2000) Dollars by State: 2000 to 2008. 2010. Web. 26 Nov. 2010. <http://www.census.gov/compendia/statab/2010/tables/10s0665.pdf>. 7

-2-1 0 1 2 2 3 4 5 6 7 VII. Appendix Model 1.1.1 Using percentage of population with bachelor s degree to explain divorce rate. 10 20 30 40 50 Bachelor DivorceRate regress divorcerate06 bachelor06 Source SS df MS Number of obs = 44 F( 1, 42) = 25.69 Model 16.1298965 1 16.1298965 Prob > F = 0.0000 Residual 26.3744244 42.627962487 R-squared = 0.3795 Adj R-squared = 0.3647 Total 42.504321 43.988472581 Root MSE =.79244 divorcera~06 Coef. Std. Err. t P> t [95% Conf. Interval] bachelor06 -.1096284.0216309-5.07 0.000 -.1532812 -.0659755 _cons 6.823936.5913593 11.54 0.000 5.630525 8.017347 2 3 4 5 Note: Even though D.C. (at the far left) and Nevada (at the top) appear to be an outlier in the residual plot, they are not excluded because they do not significantly change the shape of the fitted line as shown in the scatter plot. Model 1.1.2 Using percentage of population with bachelor s degree to explain divorce rate (controlling for other variables). 8

2 3 4 5 6 7-2 -1 0 1 2. sw regress divorcerate06 bachelor06 church poverty06 unem05, pr(0.05) begin with full model p = 0.0657 >= 0.0500 removing poverty06 p = 0.2366 >= 0.0500 removing unem05 Source SS df MS Number of obs = 43 F( 2, 40) = 16.39 Model 19.1019696 2 9.55098482 Prob > F = 0.0000 Residual 23.3031496 40.582578739 R-squared = 0.4505 Adj R-squared = 0.4230 Total 42.4051192 42 1.0096457 Root MSE =.76327 divorcera~06 Coef. Std. Err. t P> t [95% Conf. Interval] bachelor06 -.1378186.0242896-5.67 0.000 -.1869097 -.0887275 church06 -.0337216.0149523-2.26 0.030 -.0639414 -.0035018 _cons 8.984258 1.117126 8.04 0.000 6.726462 11.24205 1 2 3 4 5 Model 1.2.1 Using percentage of population with high school degree to explain divorce rate. 75 80 85 90 HighSchool DivorceRate 9

-2-1 0 1 2 3 regress divorcerate06 highschool06 Source SS df MS Number of obs = 44 F( 1, 42) = 4.04 Model 3.72720671 1 3.72720671 Prob > F = 0.0510 Residual 38.7771143 42.923264625 R-squared = 0.0877 Adj R-squared = 0.0660 Total 42.504321 43.988472581 Root MSE =.96087 divorcera~06 Coef. Std. Err. t P> t [95% Conf. Interval] highschool06 -.0848486.0422295-2.01 0.051 -.1700712.000374 _cons 11.14358 3.61372 3.08 0.004 3.850796 18.43636 3.5 4 4.5 Model 1.2.2 Using percentage of population with high school degree to explain divorce rate (controlling for other variables).. regress divorcerate06 highschool06 church06 Source SS df MS Number of obs = 43 F( 2, 40) = 2.17 Model 4.15560657 2 2.07780329 Prob > F = 0.1271 Residual 38.2495126 40.956237816 R-squared = 0.0980 Adj R-squared = 0.0529 Total 42.4051192 42 1.0096457 Root MSE =.97787 divorcera~06 Coef. Std. Err. t P> t [95% Conf. Interval] highschool06 -.0951447.0476705-2.00 0.053 -.1914904.001201 church06 -.0043129.0179063-0.24 0.811 -.0405029.0318771 _cons 12.18816 4.42604 2.75 0.009 3.242796 21.13352 10

20000 30000 40000 50000-2 -1 0 1 2 3 3 3.5 4 4.5 Model 2.1.1 Using percentage of population with bachelor s degree to explain average salary in 2006. 10 20 30 40 50 Bachelor Salary06. regress salary06 bachelor06 Source SS df MS Number of obs = 50 F( 1, 48) = 99.58 Model 970055078 1 970055078 Prob > F = 0.0000 Residual 467585686 48 9741368.45 R-squared = 0.6748 Adj R-squared = 0.6680 Total 1.4376e+09 49 29339607.4 Root MSE = 3121.1 salary06 Coef. Std. Err. t P> t [95% Conf. Interval] bachelor06 821.8216 82.35488 9.98 0.000 656.236 987.4072 _cons 9426.051 2244.031 4.20 0.000 4914.123 13937.98 11

20000 25000 30000 35000 40000-10000 -5000 0 5000 10000 20000 30000 40000 50000 Note: The point on the far right (D.C.) seems to be an outlier in the residual plot, however, the scatter plot shows that it fits in the fitted line very well. Therefore, it is still included in the model. Model 2.1.2 Using percentage of population with bachelor s degree to explain average salary in 2000. 15 20 25 30 35 40 Bachelor00 Salary00. regress salary00 bachelor00 Source SS df MS Number of obs = 50 F( 1, 48) = 105.26 Model 731319602 1 731319602 Prob > F = 0.0000 Residual 333507219 48 6948067.06 R-squared = 0.6868 Adj R-squared = 0.6803 Total 1.0648e+09 49 21731159.6 Root MSE = 2635.9 salary00 Coef. Std. Err. t P> t [95% Conf. Interval] bachelor00 805.4191 78.50554 10.26 0.000 647.5731 963.2651 _cons 9300.843 1925.991 4.83 0.000 5428.378 13173.31 12

-5000 0 5000 15000 20000 25000 30000 35000-10000 -5000 0 5000 10000 20000 25000 30000 35000 40000 Model 2.1.3 Using percentage of population with bachelor s degree to explain average salary in 1990. 10 15 20 25 30 35 Bachelor90 Salary90. regress salary90 bachelor90 Source SS df MS Number of obs = 50 F( 1, 48) = 79.65 Model 449114439 1 449114439 Prob > F = 0.0000 Residual 270642180 48 5638378.75 R-squared = 0.6240 Adj R-squared = 0.6161 Total 719756619 49 14688910.6 Root MSE = 2374.5 salary90 Coef. Std. Err. t P> t [95% Conf. Interval] bachelor90 719.9763 80.67089 8.92 0.000 557.7766 882.176 _cons 8825.232 1649.732 5.35 0.000 5508.224 12142.24 15000 20000 25000 30000 35000 13

-10000 0 10000 20000 25000 30000 35000 40000 45000 50000 Model 2.2.1 Using percentage of population with high school degree to explain average salary in 2006. 75 80 85 90 HighSchool Salary06. regress salary06 highschool06 Source SS df MS Number of obs = 50 F( 1, 48) = 4.89 Model 132968960 1 132968960 Prob > F = 0.0318 Residual 1.3047e+09 48 27180662.6 R-squared = 0.0925 Adj R-squared = 0.0736 Total 1.4376e+09 49 29339607.4 Root MSE = 5213.5 salary06 Coef. Std. Err. t P> t [95% Conf. Interval] highschool06 458.1109 207.1216 2.21 0.032 41.6649 874.5569 _cons -7729.839 17698.58-0.44 0.664-43315.22 27855.55 28000 30000 32000 34000 Model 2.2.2 Using percentage of population with high school degree to explain average salary in 2000. 14

-5000 0 5000 10000 15000 20000 25000 30000 35000 40000 70 75 80 85 90 HS00 Salary00. regress salary00 highschool00 Source SS df MS Number of obs = 50 F( 1, 48) = 5.60 Model 111326700 1 111326700 Prob > F = 0.0220 Residual 953500120 48 19864585.8 R-squared = 0.1045 Adj R-squared = 0.0859 Total 1.0648e+09 49 21731159.6 Root MSE = 4457 salary00 Coef. Std. Err. t P> t [95% Conf. Interval] highschool00 346.8833 146.529 2.37 0.022 52.26707 641.4995 _cons 322.6364 11997.99 0.03 0.979-23800.95 24446.22 26000 27000 28000 29000 30000 31000 Model 2.2.3 Using percentage of population with high school degree to explain average salary in 1990. 15

-10000-5000 0 5000 10000 15000 20000 25000 30000 35000 65 70 75 80 85 HS90 Salary90. regress salary90 highschool90 Source SS df MS Number of obs = 50 F( 1, 48) = 9.52 Model 119144791 1 119144791 Prob > F = 0.0034 Residual 600611828 48 12512746.4 R-squared = 0.1655 Adj R-squared = 0.1482 Total 719756619 49 14688910.6 Root MSE = 3537.3 salary90 Coef. Std. Err. t P> t [95% Conf. Interval] highschool90 278.0391 90.10413 3.09 0.003 96.87263 459.2056 _cons 2074.297 6877.582 0.30 0.764-11754.01 15902.6 20000 22000 24000 26000 16