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Education, Intelligence, and Well-Being: Evidence from a Semiparametric Latent Variable Transformation Model for Multiple Outcomes of Mixed Types

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Abstract

This paper uses a semiparametric latent variable transformation model for multiple outcomes to examine the effect of education and maternal education on female multidimensional well-being and proposes a procedure to build a well-being index that is less susceptible to functional form misspecification. We model multidimensional well-being as an unobserved common factor underlying the observed well-being outcomes. The semiparametric methodology allows us to alleviate misspecification bias by combining multiple indicators into a latent construct in an unspecified, data-driven way. Using data from female participants of the 1974–2010 waves of the US General Social Survey, we find that education, intelligence, and maternal education contribute positively to multidimensional well-being. However, the effects of education and maternal education on female multidimensional well-being declined steadily between the mid-1970s and the 1990s, and have not rebounded since.

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Notes

  1. The joint normal framework usually links the measureable outcomes to the latent variable using a probit function, whereas GLLAMM typically employs a log or logit link.

  2. Better-educated mothers have higher ability, which could be transmitted to their children. Therefore, children’s schooling attainment is likely to be the outcome of this ability transmission.

  3. Di Tommaso (2007) considers only weight, height, and work status, and Krishinamukar and Balon (2008) consider literacy, level of schooling, the quality of basic services in the house, and the quality and habitability conditions of the house.

  4. See, for example, Di Tommaso (2007) and Krishinamukar and Balon (2008).

  5. These estimating equations are based on the marginal probability of \(Y_{ij} \le y_{j}\). Please see Lin et al. (2013) for details.

  6. See Stiglitz et al. (2009), p. 14. Apart from the dimensions considered here, Stiglitz et al. (2009) suggest that well-being also depends on natural environment, security, and political voice. We ignore these macro aspects of well-being since they are largely determined by country- and regional-level factors and are less likely to be affected by individual-level characteristics such as education and maternal education.

  7. We choose not to control for paternal education primarily to alleviate the selection problem. Another reason is that dropping observations with missing values for paternal education reduces the sample size by 20 %.

  8. Our analyses were based on women, because we fail to achieve convergence for the male sample. It is a limitation of this study that the effects of education on male well-being cannot be analyzed, but it is a direction for future research using different data sets.

  9. Wolfle (1980) finds that the correlation between Army General Classification Test (AGCT)—a measure of general intelligence—and WORDSUM is 0.71, confirming that verbal skills are a good measure of general intelligence.

  10. Cor et al. (2012) document that between 1975 and 2011, WORDSUM is used in more than 100 social science studies.

  11. The WORDSUM test—the test that provides us with a measure of general intelligence—was administered to 14,552 women in the GSS sample. After dropping cases with missing values for the other variables used, we are left with 4,634 observations.

  12. As our model considers both discrete and continuous outcome measures, conventional goodness-of-fit measures such as \(\chi^{2}\) statistic, root mean squared error of approximation (RMSEA), and comparative fit index (CFI), which are based on the discrepancy between the sample variance–covariance matrix and the variance–covariance matrix implied by the model with the coefficient estimates, are not applicable. As such, we assess the model fit graphically.

  13. Blanchflower and Oswald (1999) show that approximately 51 % of the respondents answered ‘very satisfied’ to the job satisfaction question in the 1970s. By the 1990 s, that percentage fell to 46. Using the GSS data, Blanchflower and Oswald (2004) establish that from the period from 1972 to 1976 to the period from 1994 to 1998, the percentage of females reporting being very happy with their life fell from 36 to 29.

  14. Zack et al. (2004) note that self-rated health worsened from 1993 to 2001. Using data from the Behavioral Risk Factor Surveillance System (BRFSS), Salomon et al. (2009) show that Americans were increasingly likely to report ‘‘fair’’ or ‘‘poor’’ health over the period from 1993 to 2007. Zheng et al. (2011) establish that mean self-rated health in the National Health Interview Survey (NHIS) increased from 1984 to 1990, declined through the mid-1990 s, improved afterward, and worsened again from the late 1990 s through 2007.

  15. The standardized factor loading is calculated by multiplying the unstandardized factor loading by the ratio of the standard deviation of the fitted value of well-being to the standard deviation of the fitted value of the transformed observed outcome.

  16. The standardized coefficient is calculated by multiplying the estimated coefficient by the ratio of the standard deviation of the covariate to the standard deviation of the dependent variable.

  17. According to the coefficient estimates in Table 4, the response of well-being in units of standard deviation for a one standard deviation change in education for a person with 12 years of education in the 2000s is calculated as \({{\left[ {1.1868 + 2 \times ( - 0.0207) \times 12 - 0.2688} \right] \times 2.587} \mathord{\left/ {\vphantom {{\left[ {1.1868 + 2 \times ( - 0.0207) \times 12 - 0.2688} \right] \times 2.587} {1.7797}}} \right. \kern-0pt} {1.7797}} = 0.6122,\) where 1.7797 is the standard deviation of the fitted value of well-being. The well-being change for a person with 16 years of education is calculated analogously.

  18. Given that the standard deviation for the fitted value of well-being is 1.7797, based on the coefficient estimates in Table 4, the response of well-being in units of standard deviation for a unit change in the dummy variable indicating whether the respondent was not living with both parents at age 16 is calculated as \({{0.5437 \times 0.434} \mathord{\left/ {\vphantom {{0.5437 \times 0.434} {1.7797}}} \right. \kern-0pt} {1.7797}} = 0.1326.\)

  19. See Buehn and Farzanegan (2012, 2013), Navarro and Ayala (2008), and Navarro et al. (2010) for similarly constructed indices of smuggling, air pollution, and housing deprivation based on MIMIC models.

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Authors and Affiliations

  1. School of Statistics, Southwestern University of Finance and Economics, Chengdu, 611130, Sichuan, China

    Ling Zhou & Huazhen Lin

  2. Department of Economics, Tamkang University, 151 Yingzhuan Rd., Tamsui District, New Taipei City, 25137, Taiwan

    Yi-Chen Lin

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Zhou, L., Lin, H. & Lin, YC. Education, Intelligence, and Well-Being: Evidence from a Semiparametric Latent Variable Transformation Model for Multiple Outcomes of Mixed Types. Soc Indic Res 125, 1011–1033 (2016). https://doi.org/10.1007/s11205-015-0865-1

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