Contributions
Determinants of education: Heckman, Stixrud, and Urzua (2006 ) , Almlund et al. (2011 ) , Björklund and Salvanes (2011 ) , Ichino, Rustichini, and Zanella (2022 )
Genes and environment in education : Rustichini et al. (2023 )
UK Household Longitudinal Study (2009-)
Working sample: 22 881 individuals
college: ever had HE degree as highest qualification
predicted discounted present value of earnings
cognitive test scores , Big 5 personality scores
parental background: education and employment status
College and individual characteristics
%>% as_survey_design (ids = c_psu, strata = c_strata, weights = c_indinub_xw) %>% group_by (gscorep_qnt, etap_fam_qnt, etap_big5_qnt) %>% summarise (cmean = survey_mean (college, vartype = 'ci' )) %>% ggplot (aes (x = gscorep_qnt, y = cmean, ymin = cmean_low, ymax = cmean_upp, colour = factor (etap_fam_qnt), group = factor (etap_fam_qnt))) + geom_pointrange () + geom_line () + facet_wrap (~ etap_big5_qnt, scales = 'fixed' , labeller = as_labeller (function (x) paste ('Big5 score quintile =' , x))) + labs (x = 'IQ score quintile' , y = 'Share with college degree' , colour = 'Fam score quintile' ) + scale_colour_viridis_d () + theme_minimal () + theme (legend.position = 'bottom' , axis.line = element_line ())
Probability of college
<- read_dta ('tab1.dta' )<- tab1 %>% rename (std.error = std_err)<- tab1 %>% mutate (p.value = pnorm (abs (estimate) / std.error, lower.tail = FALSE ))<- tab1 %>% nest (.by = c (cohort, spec)) %>% mutate (cohort = str_extract (cohort, '(?<=19)[:digit:]{2}' )) %>% unite ('id' , spec, cohort, sep = '' ) %>% deframe ()<- list (tidy = tab1_list$ ols50,glance = tab1_list$ ols50 %>% distinct (N))<- list (tidy = tab1_list$ logme50, glance = tab1_list$ logme50 %>% distinct (N))<- list (tidy = tab1_list$ ols65,glance = tab1_list$ ols65 %>% distinct (N))<- list (tidy = tab1_list$ ols65,glance = tab1_list$ ols65 %>% distinct (N))<- list (tidy = tab1_list$ ols80,glance = tab1_list$ ols80 %>% distinct (N))<- list (tidy = tab1_list$ ols80,glance = tab1_list$ ols80 %>% distinct (N))class (tab1_ols50) <- 'modelsummary_list' class (tab1_lme50) <- 'modelsummary_list' class (tab1_ols65) <- 'modelsummary_list' class (tab1_lme65) <- 'modelsummary_list' class (tab1_ols80) <- 'modelsummary_list' class (tab1_lme80) <- 'modelsummary_list' modelsummary (list (OLS = tab1_ols50, 'Logit ME' = tab1_lme50, OLS = tab1_ols65, 'Logit ME' = tab1_lme65, OLS = tab1_ols80, 'Logit ME' = tab1_lme80), coef_map = c (g_score_std = 'IQ score' , eta_fam_score_std = 'Fam score' , eta_big5_score_std = 'Big5 score' ), gof_map = list (list (raw = 'N' , clean = 'Obs.' , fmt = function (x) format (x, big.mark = ' ' ))), stars = c ('*' = .05 , '**' = .01 , '***' = 0.001 )) %>% group_tt (j = list ('Born in 1950-64' = 2 : 3 , 'Born in 1965-79' = 4 : 5 , 'Born in 1980-94' = 6 : 7 ))
tinytable_4swly9mdanz61a3nka3x
Born in 1950-64
Born in 1965-79
Born in 1980-94
OLS
Logit ME
OLS
Logit ME
OLS
Logit ME
* p < 0.05, ** p < 0.01, *** p < 0.001
IQ score
0.137***
0.152***
0.151***
0.151***
0.130***
0.130***
(0.005)
(0.007)
(0.005)
(0.005)
(0.006)
(0.006)
Fam score
0.050***
0.054***
0.077***
0.077***
0.074***
0.074***
(0.005)
(0.008)
(0.006)
(0.006)
(0.006)
(0.006)
Big5 score
0.006
0.015**
0.010*
0.010*
0.014*
0.014*
(0.006)
(0.006)
(0.006)
(0.006)
(0.006)
(0.006)
Obs.
9 539
9 539
10 586
10 586
8 409
8 409
SEM of college and wages
<- read_dta ('tab3.dta' )<- tab3 %>% rename (std.error = std_err)<- tab3 %>% mutate (p.value = pnorm (abs (estimate) / std.error, lower.tail = FALSE ))<- tab3 %>% nest (.by = c (cohort, depvar)) %>% mutate (cohort = str_extract (cohort, '(?<=19)[:digit:]{2}' )) %>% unite ('id' , depvar, cohort, sep = '' ) %>% deframe ()<- list (tidy = tab3_list$ wage4550,glance = tab3_list$ wage4550 %>% distinct (N))<- list (tidy = tab3_list$ college50, glance = tab3_list$ college50 %>% distinct (N))<- list (tidy = tab3_list$ wage4565,glance = tab3_list$ wage4565 %>% distinct (N))<- list (tidy = tab3_list$ college65,glance = tab3_list$ college65 %>% distinct (N))<- list (tidy = tab3_list$ wage4580,glance = tab3_list$ wage4580 %>% distinct (N))<- list (tidy = tab3_list$ college80,glance = tab3_list$ college80 %>% distinct (N))class (tab3_wage4550) <- 'modelsummary_list' class (tab3_college50) <- 'modelsummary_list' class (tab3_wage4565) <- 'modelsummary_list' class (tab3_college65) <- 'modelsummary_list' class (tab3_wage4580) <- 'modelsummary_list' class (tab3_college80) <- 'modelsummary_list' modelsummary (list ('Pred. wage' = tab3_wage4550, 'College' = tab3_college50, 'Pred. wage' = tab3_wage4565, 'College' = tab3_college65, 'Pred. wage' = tab3_wage4580, 'College' = tab3_college80), coef_map = c (college = 'College' , g_score_std = 'IQ score' , eta_fam_score_std = 'Fam score' , eta_big5_score_std = 'Big5 score' , indirect = 'Indirect effect' , total = 'Total effect' ), gof_map = list (list (raw = 'N' , clean = 'Obs.' , fmt = function (x) format (x, big.mark = ' ' ))), stars = c ('*' = .05 , '**' = .01 , '***' = 0.001 )) %>% group_tt (j = list ('Born in 1950-64' = 2 : 3 , 'Born in 1965-79' = 4 : 5 , 'Born in 1980-94' = 6 : 7 )) %>% style_tt (i = - 1 : 13 , fontsize = 0.75 , tabularray_inner = "rowsep = {-.22em}, colsep = {.4em}" ) %>% style_tt (i = 8 , line = 'b' , line_width = .001 )
tinytable_fr4x02d64q5bwcbxze3n
Born in 1950-64
Born in 1965-79
Born in 1980-94
Pred. wage
College
Pred. wage
College
Pred. wage
College
* p < 0.05, ** p < 0.01, *** p < 0.001
College
0.820***
0.804***
0.651***
(0.020)
(0.016)
(0.015)
IQ score
0.082***
1.018***
0.077***
0.917***
0.045***
0.788***
(0.009)
(0.046)
(0.007)
(0.039)
(0.007)
(0.044)
Fam score
0.382***
0.492***
0.453***
(0.051)
(0.040)
(0.041)
Big5 score
0.082*
0.081**
0.128***
(0.037)
(0.033)
(0.037)
Indirect effect
0.126***
0.136***
0.096***
(0.006)
(0.005)
(0.005)
Total effect
0.208***
0.213***
0.140***
(0.009)
(0.007)
(0.007)
Obs.
9 496
9 496
10 488
10 488
8 382
8 382
# kable_styling(font_size = 8) %>% # row_spec(8, hline_after = TRUE) %>% # add_header_above(c(' ' = 1, # 'Born in 1950-64' = 2, # 'Born in 1965-79' = 2, # 'Born in 1980-94' = 2))
Model
Individuals described by \(z \in Z = \Theta \times X \times Y\)
intelligence \(\theta \in \Theta\)
family advantage score \(x \in X\)
Big 5 personality score \(y \in Y\)
Human capital \(H \equiv \{nc, c\}\) (no college vs college)
DPV of earnings \(W(h, z, \delta) = \sum_{a = 18}^{65}\delta^{a - 18} W(h, z, a)\)
Choose effort \(e \in \mathbb{R}_{+}\) to acquire human capital \(h = c\) given cost \(\frac{c(e)}{\Gamma(z)}\)
\[
\max_e \pi(e) \left[W(c, z, \delta) - W(nc, z, \delta)\right] - \frac{c(e)}{\Gamma(z)}
\]
Solution
Denote \(A = \left(W(c, z, \delta) - W(nc, z, \delta)\right)\Gamma(z)\) . Then, optimal effort solution
\[
E^\star(A; \pi) \equiv \arg\max_e \pi(e)A - e
\]
\(\Pi\) is the set of functions \(\pi: \mathbb{R}_+ \rightarrow [0, 1]\) that are strictly increasing, concave, continuous at 0, \(\pi(0) = 0\) , \(\lim_{x \rightarrow \infty} \pi(x) = 1\) .
For \(P(A)\) increasing in \(A\) and upper semi-continuous in \(\Delta W\) , \(\exists \pi \in \Pi\) such that
\[P(A) = \pi\left(E^\star(A; \pi)\right)\]
Estimation
We consider four functional forms that can describe \(P(A)\) :
Linear probability model \(P(A) = A\)
Logit \(P(A) = (1 + e^{-A})^{-1}\)
Logit power \(P(A) = (1 + e^{-A})^{-\kappa}, ~\kappa \in \mathbb{R}_{+}\)
Cutoff power \(P(A) = \min\{\max\{A, 0\}^\kappa, 1\}, ~\kappa \in \mathbb{R}_{+}\)
Two-step estimation:
Given \(\delta\) and \(\kappa\) , fit \(P(A)\) to the observed college indicators.
Grid search \(\hat{\delta}\) and \(\hat{\kappa}\) that minimise sum of squared residuals.
Results
<- read_dta ('tab4.dta' )<- tab4 %>% rename (std.error = std_error)<- tab4 %>% mutate (print_error = if_else (is.na (boot_error), <- tab4 %>% mutate (p.value = pnorm (abs (estimate) / print_error, lower.tail = FALSE ))<- tab4 %>% nest (.by = c (spec)) %>% deframe ()<- list (tidy = tab4_list$ LPM,glance = tab4_list$ LPM %>% distinct (rmse, mean_cp, sd_cp, <- list (tidy = tab4_list$ Logit, glance = tab4_list$ Logit %>% distinct (rmse, mean_cp, sd_cp, <- list (tidy = tab4_list$ ` Logit power ` , glance = tab4_list$ ` Logit power ` %>% distinct (rmse, mean_cp, sd_cp, <- list (tidy = tab4_list$ ` Cutoff power ` , glance = tab4_list$ ` Cutoff power ` %>% distinct (rmse, mean_cp, sd_cp, class (tab4_lpm) <- 'modelsummary_list' class (tab4_log) <- 'modelsummary_list' class (tab4_logp) <- 'modelsummary_list' class (tab4_cutp) <- 'modelsummary_list' <- list (list (raw = 'N' , clean = 'Obs.' , fmt = function (x) format (x, big.mark = ' ' )), list (raw = 'delta' , clean = '$ \\ delta$' , fmt = 3 ), list (raw = 'power' , clean = '$ \\ kappa$' , fmt = 2 ), list (raw = 'mean_cp' , clean = 'College premium mean' , fmt = 2 ), list (raw = 'sd_cp' , clean = 'College premium sd' , fmt = 2 ))modelsummary (list ('LPM' = tab4_lpm, 'Logit' = tab4_log, 'Logit power \\ footnotemark[1]' = tab4_logp, 'Cutoff power \\ footnotemark[1]' = tab4_cutp), statistic = '({print_error})' , coef_map = c (g_score_std = 'IQ score' , eta_fam_score_std = 'Fam score' , eta_big5_score_std = 'Big5 score' , sdd_earn_2 = 'College premium, std' ), gof_map = gof_tab, stars = c ('*' = .05 , '**' = .01 , '***' = 0.001 ), width = c (0.27 , rep ((1 - 0.25 ) / 4 , 4 )), escape = FALSE , notes = list (` 1 ` = 'Bootstrapped standard errors' )) %>% style_tt (i = 0 : 15 , fontsize = 0.8 , tabularray_inner = "rowsep={-.22em}, colsep = {.4em}" )
tinytable_jqhm7yxnjayomelyg37b
LPM
Logit
Logit power\footnotemark[1]
Cutoff power\footnotemark[1]
1 Bootstrapped standard errors
IQ score
0.118***
0.089***
0.104***
0.108***
(0.005)
(0.007)
(0.006)
(0.006)
Fam score
0.061***
0.054***
0.058***
0.058***
(0.004)
(0.004)
(0.004)
(0.004)
Big5 score
0.025***
0.038***
0.032***
0.031***
(0.003)
(0.004)
(0.004)
(0.004)
College premium, std
0.026***
0.060***
0.042***
0.040***
(0.006)
(0.009)
(0.007)
(0.007)
Obs.
31 571
31 571
31 571
31 571
$\delta$
0.925
0.925
0.925
0.925
$\kappa$
2.90
1.20
College premium mean
36.95
36.95
36.95
36.95
College premium sd
9.77
9.77
9.77
9.77
Results with polygenic scores
Simple logit without college premium
<- read_dta ('tab6a.dta' )<- tab6a %>% rename (std.error = std_error)<- tab6a %>% mutate (p.value = pnorm (abs (estimate) / std.error, lower.tail = FALSE ))<- tab6a %>% nest (.by = c (spec)) %>% deframe ()<- list (tidy = tab6a_list$ LPM,glance = tab6a_list$ LPM %>% distinct (N))<- list (tidy = tab6a_list$ ` Logit ME ` , glance = tab6a_list$ ` Logit ME ` %>% distinct (N))class (tab6a_lpm) <- 'modelsummary_list' class (tab6a_log) <- 'modelsummary_list' <- list (list (raw = 'N' , clean = 'Obs.' , fmt = function (x) format (x, big.mark = ' ' )))modelsummary (list ('LPM' = tab6a_lpm, 'Logit ME' = tab6a_log), coef_map = c (pgs_std_cobs_hm3p = 'IQ PGS' , eta_fam_score_std = 'Fam score' , eta_big5_score_std = 'Big5 score' ), gof_map = gof_tab, stars = c ('*' = .05 , '**' = .01 , '***' = 0.001 ), width = 1 )
tinytable_xdsb534sqp4m03kc468h
LPM
Logit ME
* p < 0.05, ** p < 0.01, *** p < 0.001
IQ PGS
0.067***
0.066***
(0.007)
(0.007)
Fam score
0.094***
0.118***
(0.008)
(0.010)
Big5 score
0.019**
0.019**
(0.008)
(0.008)
Obs.
3 602
3 602
Results with polygenic scores
<- read_dta ('tab6.dta' )<- tab6 %>% rename (std.error = std_error)<- tab6 %>% mutate (p.value = pnorm (abs (estimate) / std.error, lower.tail = FALSE ))<- tab6 %>% nest (.by = c (spec)) %>% deframe ()<- list (tidy = tab6_list$ LPM,glance = tab6_list$ LPM %>% distinct (mean_cp, sd_cp, delta, power, N))<- list (tidy = tab6_list$ Logit, glance = tab6_list$ Logit %>% distinct (mean_cp, sd_cp, delta, power, N))<- list (tidy = tab6_list$ ` Logit power ` , glance = tab6_list$ ` Logit power ` %>% distinct (mean_cp, sd_cp, delta, power, N))<- list (tidy = tab6_list$ ` Cutoff power ` , glance = tab6_list$ ` Cutoff power ` %>% distinct (mean_cp, sd_cp, delta, power, N))class (tab6_lpm) <- 'modelsummary_list' class (tab6_log) <- 'modelsummary_list' class (tab6_logp) <- 'modelsummary_list' class (tab6_cutp) <- 'modelsummary_list' <- list (list (raw = 'N' , clean = 'Obs.' , fmt = function (x) format (x, big.mark = ' ' )), list (raw = 'delta' , clean = '$ \\ delta$' , fmt = 3 ), list (raw = 'power' , clean = '$ \\ kappa$' , fmt = 2 ), list (raw = 'mean_cp' , clean = 'College premium mean' , fmt = 2 ), list (raw = 'sd_cp' , clean = 'College premium sd' , fmt = 2 ))modelsummary (list ('LPM' = tab6_lpm, 'Logit' = tab6_log, 'Logit power' = tab6_logp, 'Cutoff power' = tab6_cutp), coef_map = c (pgsp_cobs_hm3p = 'IQ PGS' , etap_fam = 'Fam score' , etap_big5 = 'Big5 score' , diff4_earn = 'College premium, std' ), gof_map = gof_tab, stars = c ('*' = .05 , '**' = .01 , '***' = 0.001 ), escape = FALSE , width = c (0.27 , rep ((1 - 0.27 ) / 4 , 4 ))) %>% style_tt (i = 0 : 14 , fontsize = .9 , tabularray_inner = "rowsep={-.2em}, colsep = {.3em}" )
tinytable_1b5fg1b11wxtwynxlcvz
LPM
Logit
Logit power
Cutoff power
* p < 0.05, ** p < 0.01, *** p < 0.001
IQ PGS
0.038***
0.034**
0.036**
0.037***
(0.011)
(0.012)
(0.012)
(0.011)
Fam score
0.085***
0.154***
0.146***
0.134***
(0.008)
(0.011)
(0.011)
(0.010)
Big5 score
0.109***
0.102**
0.105**
0.115***
(0.031)
(0.034)
(0.034)
(0.034)
College premium, std
0.007**
0.006**
0.006**
0.007**
(0.002)
(0.002)
(0.002)
(0.002)
Obs.
3 602
3 602
3 602
3 602
$\delta$
0.925
0.925
0.925
0.925
$\kappa$
2.90
1.20
College premium mean
84.86
84.86
84.86
84.86
College premium sd
14.27
14.27
14.27
14.27
Summary
Revisit role of intelligence, personality and family characteristics in education choice
Conditions linking econometric specification to individual optimization
Further analysis with polygenic scores
Appendices
Intelligence score
Combine individual test scores using confirmatory factor analysis
Using "tree" as default layout
Big 5 personality score
Combine individual test scores using principal component analysis
Agreeableness
0.4408
Conscientiousness
0.4970
Extraversion
0.4628
Neuroticism
-0.3751
Openness
0.4514
PC1 explains 36% of variation in the data
Family advantage score
Combine education of parents and their employment status using principal component analysis
Years of education
0.4020
0.4286
Work
0.2243
0.5527
Dead
-0.0889
-0.2958
Absent
-0.2042
-0.4023
PC1 explains 23% of variation in the data
Polygenic score
%>% ggplot (aes (x = pgs_std_cobs_hm3p, y = g_score_std)) + geom_point () + geom_smooth () + labs (x = 'IQ PGS' , y = 'IQ score' ) + theme_minimal ()
`geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'
Warning: Removed 978 rows containing non-finite outside the scale range
(`stat_smooth()`).
Warning: Removed 978 rows containing missing values or values outside the scale range
(`geom_point()`).
Proposition (continuously differentiable)
Redefine the effort choice problem as \(e^\star(\alpha; \pi) \equiv \arg \max_e \pi(e) - \alpha e\) where \(\alpha = A^{-1}\) .
The set of endogenous probabilities is the set \(\mathcal{Q}\) of multivalued functions \(Q: \mathbb{R}_{+} \rightarrow [0,1]\) that are decreasing, closed valued, with \(\lim_{\alpha \rightarrow 0} Q(\alpha) = 1\) , \(Q(\overline{\alpha}) = 0\) for some \(\overline{\alpha} >0\) .
For any function \(Q \in \mathcal{Q}\) which is continuously differentiable strictly decreasing in the interval \([\underline{\alpha}, \overline{\alpha}]\) , with \(Q(\underline{\alpha}) =0\) , \(Q(\overline{\alpha}) =1\) , there exists a continuously differentiable function \(\pi \in \Pi\) such that for all \(\alpha \in \mathbb{R}_{+}\) , \(Q(\alpha) = \pi(h(\alpha; \pi))\) .
Proposition proof (continuously differentiable)
Note that \(Q(\alpha)=0\) for \(\alpha > \overline{\alpha}\) , so we may take the boundary condition
\[
h(\overline{\alpha}) = 0
\]
Consider the ordinary differential equation
\[
\frac{d h}{d \alpha} = \frac{Q^{\prime}}{\alpha}, \quad \alpha > 0
\]
We now define the function \(\pi\) as the solution of \(\pi(h(\alpha)) = Q(\alpha)\) . The function \(h\) satisfies the differential equation, which is the first order necessary and sufficient conditions for optimal effort choice problem, namely \(\pi^{\prime}(h(\alpha)) = \alpha\) . Thus, our claim follows.
Logit power
<- function (x, kappa) (1 + exp (- x))^ (- kappa)<- c (- 5 , 5 )ggplot () + geom_function (fun = function (x) logp_fun (x, 0.1 ), aes (colour = '0.1' ), xlim = logp_xlim) + geom_function (fun = function (x) logp_fun (x, 0.5 ), aes (colour = '0.5' ), xlim = logp_xlim) + geom_function (fun = function (x) logp_fun (x, 1 ), aes (colour = '1' ), xlim = logp_xlim) + geom_function (fun = function (x) logp_fun (x, 2 ), aes (colour = '2' ), xlim = logp_xlim) + geom_function (fun = function (x) logp_fun (x, 4 ), aes (colour = '4' ), xlim = logp_xlim) + labs (x = 'A' , y = 'P(A)' , colour = '' ) + scale_colour_brewer (palette = 'Set1' , labels = c (expression (kappa == 0.1 ), expression (kappa == 0.5 ), expression (kappa == 1 ), expression (kappa == 2 ), expression (kappa == 4 ))) + theme_minimal () + theme (legend.position = c (0.85 , 0.4 ))
Warning: A numeric `legend.position` argument in `theme()` was deprecated in ggplot2
3.5.0.
ℹ Please use the `legend.position.inside` argument of `theme()` instead.
Cutoff power
<- function (x, kappa) pmin (pmax (x, 0 )^ kappa, 1 )<- c (- 0.2 , 1.2 )ggplot () + geom_function (fun = function (x) cutp_fun (x, 0.1 ), aes (colour = '0.1' ), xlim = cutp_xlim) + geom_function (fun = function (x) cutp_fun (x, 0.5 ), aes (colour = '0.5' ), xlim = cutp_xlim) + geom_function (fun = function (x) cutp_fun (x, 1 ), aes (colour = '1' ), xlim = cutp_xlim) + geom_function (fun = function (x) cutp_fun (x, 2 ), aes (colour = '2' ), xlim = cutp_xlim) + geom_function (fun = function (x) cutp_fun (x, 4 ), aes (colour = '4' ), xlim = cutp_xlim) + labs (x = 'A' , y = 'P(A)' , colour = '' ) + scale_colour_brewer (palette = 'Set1' , labels = c (expression (kappa == 0.1 ), expression (kappa == 0.5 ), expression (kappa == 1 ), expression (kappa == 2 ), expression (kappa == 4 ))) + theme_minimal () + theme (legend.position = c (0.85 , 0.4 ))
Grid search
Figure 1: RMSE heatmap of grid search over \(\delta\) and \(\kappa\)
References
Almlund, Mathilde, Angela Lee Duckworth, James Heckman, and Tim Kautz. 2011.
“Personality Psychology and Economics.” In, 4:1–181. Elsevier.
https://doi.org/10.1016/B978-0-444-53444-6.00001-8 .
Björklund, Anders, and Kjell G. Salvanes. 2011.
“Education and Family Background.” In, 201–47. Elsevier.
https://doi.org/10.1016/b978-0-444-53429-3.00003-x .
Heckman, James, Jora Stixrud, and Sergio Urzua. 2006. “The Effects of Cognitive and Noncognitive Abilities on Labor Market Outcomes and Social Behavior.” Journal of Labor Economics 24 (3): 411–82.
Ichino, Andrea, Aldo Rustichini, and Giulio Zanella. 2022.
“College Education, Intelligence, and Disadvantage: Policy Lessons from the UK in 1960-2004.” http://www.andreaichino.it/wp-content/uploads/IRZ_Sorting.pdf .
Rustichini, Aldo, William G. Iacono, James J. Lee, and Matt McGue. 2023.
“Educational Attainment and Intergenerational Mobility: A Polygenic Score Analysis.” Journal of Political Economy 131 (10): 2724–79.
https://doi.org/10.1086/724860 .
Savage, Jeanne E., Philip R. Jansen, Sven Stringer, Kyoko Watanabe, Julien Bryois, Christiaan A. de Leeuw, Mats Nagel, et al. 2018.
“Genome-Wide Association Meta-Analysis in 269,867 Individuals Identifies New Genetic and Functional Links to Intelligence.” Nature Genetics 50 (7): 912–19.
https://doi.org/10.1038/s41588-018-0152-6 .
