I would like to study what factors make people interested in economics and business. Specifically, I would like to know if education level and income level make a difference in one’s interest in economics and business. People with higher education may be more interested in economic and business because they understand economics and business better than those who are less educated. For example, principle economics are required courses in most universities. These courses can inspire people’s interests in economics and business. Additionally, people who earn more money may be more interested in economics and business because they may have extra money to make investment, or they more care about economics and business because their income may be correlated to current economic and business conditions.
I used three variables from General Social Survey (GSS) to build my model.
My dependent variable is how interested the respondent finds economic and business conditions to be. Answers include options “very interested”, “moderately interested”, and “not at all interested”. I reverse-coded this variable to make 3 represents very interested, and 1 represents not at all interested.
I have two independent variables. The first one is the highest grade you finished, ranging from no formal school (0) to 20, which means graduate degree.
My second independent variable is one’s income before taxes last year, ranging from “under $1,000” to “$150,000 or over”.
with(ds, do.call(rbind, tapply(educ, rintecon, function(x) c(M = mean(x,na.rm=T), SD = sd(x,na.rm=T)))))
## M SD
## 1 11.40525 3.385845
## 2 13.24409 3.047087
## 3 14.05467 2.821593
with(ds, do.call(rbind, tapply(rincom06, rintecon, function(x) c(M = mean(x,na.rm=T), SD = sd(x,na.rm=T)))))
## M SD
## 1 11.94118 6.284102
## 2 13.89021 5.742128
## 3 15.51925 5.880042
As we can see from the table above, the average school grade of choosing “very interested” is obviously higher than those choosing “moderately interested” and “not at all interested”. Also, if we look at the average income level of each answer, we can conclude that income and interest in economics and business are positively related. Therefore, we can tell that income and education can be good predictors to one’s interest in economics and business.
I select multinomial logistic regression to analyze our question because multinomial logistic regression can be used to estimate nominal outcome variables.
mult = multinom(rncoe ~ rincom06 + educ, data=ds)
## # weights: 12 (6 variable)
## initial value 2054.404980
## iter 10 value 1652.157162
## final value 1651.919786
## converged
summary(mult)
## Call:
## multinom(formula = rncoe ~ rincom06 + educ, data = ds)
##
## Coefficients:
## (Intercept) rincom06 educ
## 1 0.8539507 -0.03042548 -0.15976318
## 3 -1.0157764 0.03896451 0.04874032
##
## Std. Errors:
## (Intercept) rincom06 educ
## 1 0.3861335 0.015316329 0.03006256
## 3 0.2480782 0.008922461 0.01821465
##
## Residual Deviance: 3303.84
## AIC: 3315.84
z <- summary(mult)$coefficients/summary(mult)$standard.errors
z
## (Intercept) rincom06 educ
## 1 2.211542 -1.986473 -5.314357
## 3 -4.094581 4.367014 2.675886
options(scipen=999)
p <- (1 - pnorm(abs(z), 0, 1))*2
p
## (Intercept) rincom06 educ
## 1 0.0269983036 0.04698078279 0.0000001070346
## 3 0.0000422932 0.00001259568 0.0074532089458
From the P values we can tell that all variables are significant at 5% level.
Z test for income:
ztestincome = ((0.03042548-0.03896451)^2)/( 0.015316329^2 + 0.008922461^2)
ztestincome
## [1] 0.2320655
pchisq(0.2320655, df = 1, lower.tail = F)
## [1] 0.6299965
Based on the Chi-sq test, the slope of income for going from “not at all interested” to “moderately interested” equals to the slope of income for going from “moderately interested” to “very interested”. Alternatively speaking, income has same impact on making people interested in economics and business between from “not at all interested” to “moderately interested” and from “moderately interested” to “very interested”.
Z test for education:
ztesteduc = ((0.15976318-0.04874032)^2)/( 0.03006256^2 + 0.01821465^2)
ztesteduc
## [1] 9.976339
pchisq(9.976339, df = 1, lower.tail = F)
## [1] 0.001585646
Based on the Chi-sq test, the slope of education for going from “not at all interested” to “moderately interested” does not equal to the slope of education for going from “moderately interested” to “very interested”. Alternatively speaking, education has greater impact on making people interested in economics and business from “not at all interested” to “moderately interested”, but education has less impact of moving from “moderately interested” to “very interested”.
exp(coef(mult))
## (Intercept) rincom06 educ
## 1 2.3489083 0.9700327 0.8523456
## 3 0.3621212 1.0397336 1.0499477
d10 <- expand.grid(educ = c(0:20), rincom06 = mean(ds$rincom06, na.rm=T))
pp10.educ <- data.frame(educ=d10$educ, predict(mult, newdata = d10, type = "probs", se = TRUE))
pp10.educ
## educ X2 X1 X3
## 1 0 0.3174938 0.48079019 0.2017160
## 2 1 0.3380887 0.43638184 0.2255295
## 3 2 0.3570739 0.39283479 0.2500913
## 4 3 0.3741001 0.35079657 0.2751034
## 5 4 0.3889000 0.31082878 0.3002712
## 6 5 0.4012991 0.27338029 0.3253206
## 7 6 0.4112163 0.23877293 0.3500108
## 8 7 0.4186574 0.20719975 0.3741429
## 9 8 0.4237022 0.17873388 0.3975640
## 10 9 0.4264886 0.15334491 0.4201665
## 11 10 0.4271959 0.13091962 0.4418845
## 12 11 0.4260285 0.11128382 0.4626877
## 13 12 0.4232021 0.09422300 0.4825749
## 14 13 0.4189327 0.07950037 0.5015669
## 15 14 0.4134285 0.06687150 0.5197000
## 16 15 0.4068842 0.05609539 0.5370204
## 17 16 0.3994778 0.04694234 0.5535798
## 18 17 0.3913692 0.03919894 0.5694319
## 19 18 0.3826995 0.03267092 0.5846296
## 20 19 0.3735925 0.02718425 0.5992232
## 21 20 0.3641551 0.02258507 0.6132599
pp10.educ <-pp10.educ %>% gather(Interest, Probability, X2:X3)
pp10.educ$Interest[pp10.educ$Interest == 'X1'] <- 'not at all interested'
pp10.educ$Interest[pp10.educ$Interest == 'X2'] <- 'moderately interested'
pp10.educ$Interest[pp10.educ$Interest == 'X3'] <- 'very interested'
ggplot(pp10.educ, aes(x = educ, y = Probability, colour = Interest)) +
geom_line() + xlab('Education Level')
I set the income at its mean value and estimate the averaged predicted probabilities for each level of grade. The prediction shows that the probabilities of being very interested in economics and business increase when the grade increases. Another obvious finding is the predicted probabilities of being “not at all interested” in economics and business decrease when the grade increases.
d11 <- expand.grid(educ = mean(ds$educ, na.rm=T), rincom06 = c(1:25))
pp11.rincome <- data.frame(rincom06=d11$rincom06, predict(mult, newdata = d11, type = "probs", se = TRUE))
pp11.rincome
## rincom06 X2 X1 X3
## 1 1 0.5004922 0.14864534 0.3508624
## 2 2 0.4957889 0.14283582 0.3613753
## 3 3 0.4908420 0.13717295 0.3719850
## 4 4 0.4856602 0.13165751 0.3826822
## 5 5 0.4802526 0.12629008 0.3934573
## 6 6 0.4746288 0.12107095 0.4043002
## 7 7 0.4687988 0.11600019 0.4152010
## 8 8 0.4627729 0.11107761 0.4261495
## 9 9 0.4565619 0.10630280 0.4371353
## 10 10 0.4501769 0.10167510 0.4481480
## 11 11 0.4436291 0.09719364 0.4591772
## 12 12 0.4369301 0.09285731 0.4702126
## 13 13 0.4300914 0.08866481 0.4812438
## 14 14 0.4231248 0.08461463 0.4922605
## 15 15 0.4160423 0.08070507 0.5032526
## 16 16 0.4088556 0.07693424 0.5142101
## 17 17 0.4015767 0.07330010 0.5251232
## 18 18 0.3942173 0.06980043 0.5359823
## 19 19 0.3867891 0.06643287 0.5467780
## 20 20 0.3793037 0.06319493 0.5575014
## 21 21 0.3717724 0.06008399 0.5681436
## 22 22 0.3642064 0.05709730 0.5786963
## 23 23 0.3566167 0.05423205 0.5891513
## 24 24 0.3490138 0.05148531 0.5995009
## 25 25 0.3414081 0.04885409 0.6097378
pp11.rincome <-pp11.rincome %>% gather(Interest, Probability, X2:X3)
pp11.rincome$Interest[pp11.rincome$Interest == 'X1'] <- 'not at all interested'
pp11.rincome$Interest[pp11.rincome$Interest == 'X2'] <- 'moderately interested'
pp11.rincome$Interest[pp11.rincome$Interest == 'X3'] <- 'very interested'
ggplot(pp11.rincome, aes(x = rincom06, y = Probability, colour = Interest)) +
geom_line() + xlab('Income Level')
I set the grade at its mean value and estimate the averaged predicted probabilities for each level of income. The prediction shows that the probabilities of being very interested in economics and business increase when the income increases, while the predicted probabilities of being “moderately interested” and “not at all interested” decrease as income increases in general.
By the analysis I have done above, we are able to conclude that both income level and education level influence one’s interest in economic issues and business conditions. Further research can study the exact reasons why more education and earnings lead higher interest in economics and business.