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Table 2

OLS and IV regressions of log labor force participation rate on log cohort share, 1984–2016

Ages 16–24Ages 25–49Ages 50–59Ages 60–69
OLSIVOLSIVOLSIVOLSIV
Both Sexes 
 ln(cohort size / population aged 16–69) 0.081* –0.222 –0.036 –0.257* 0.032 0.295* –0.074 0.385 
[0.037] [0.178] [0.039] [0.111] [0.024] [0.122] [0.052] [0.231] 
 IV: ln(cohort births / births aged 16–69) 
   Reduced-form coefficient (dependent variable = ln(LFPR))  –0.061  –0.086*  0.055*  0.103 
 [0.048]  [0.034]  [0.021]  [0.054] 
   First-stage coefficient (dependent variable = ln(cohort size / population aged 16–69))  0.276**  0.336**  0.188**  0.267** 
 [0.048]  [0.063]  [0.041]  [0.064] 
 Incremental R2 (first stage)  .046  .015  .005  .011 
 First-stage F statistic  33.00  28.10  21.05  17.48 
 Durbin-Wu-Hausman test for endogeneity (p value)  .068  .006  .017  .014 
Men 
 ln(cohort size/population aged 16–69) 0.014 –0.200 –0.031* –0.114 0.012 0.241 –0.046 0.255 
[0.036] [0.193] [0.014] [0.077] [0.020] [0.224] [0.053] [0.223] 
 IV: ln(cohort births/births 16–69)         
   Reduced-form coefficient (dependent variable = ln(LFPR))  –0.054  –0.041  0.031  0.071 
 [0.052]  [0.027]  [0.026]  [0.064] 
   First-stage coefficient (dependent variable = ln(cohort size/population aged 16–69))  0.272**  0.364**  0.130**  0.279** 
 [0.051]  [0.064]  [0.047]  [0.058] 
 Incremental R2 (first-stage)  .042  .016  .003  .010 
 First-stage F statistic  28.51  32.59  7.75  23.57 
 Durbin-Wu-Hausman test for endogeneity (p value)  .242  .238  .241  .152 
Women 
 ln(cohort size/population aged 16–69) 0.085 –0.277 –0.059 –0.411* 0.071 0.477** –0.013 0.627 
[0.043] [0.200] [0.067] [0.187] [0.042] [0.183] [0.044] [0.338] 
 IV: ln(cohort births/births 16–69)         
   Reduced-form coefficient (dependent variable = ln(LFPR))  –0.079  –0.132*  0.099*  0.138** 
 [0.054]  [0.057]  [0.039]  [0.050] 
   First-stage coefficient (dependent variable = ln(cohort size/population 16–69))  0.284**  0.321**  0.207**  0.221** 
 [0.054]  [0.068]  [0.041]  [0.075] 
 Incremental R2 (first-stage)  .040  .010  .005  .007 
 First-stage F statistic  27.63  22.31  25.97  8.66 
 Durbin-Wu-Hausman test for endogeneity (p value)  .047  .011  .019  .005 
Ages 16–24Ages 25–49Ages 50–59Ages 60–69
OLSIVOLSIVOLSIVOLSIV
Both Sexes 
 ln(cohort size / population aged 16–69) 0.081* –0.222 –0.036 –0.257* 0.032 0.295* –0.074 0.385 
[0.037] [0.178] [0.039] [0.111] [0.024] [0.122] [0.052] [0.231] 
 IV: ln(cohort births / births aged 16–69) 
   Reduced-form coefficient (dependent variable = ln(LFPR))  –0.061  –0.086*  0.055*  0.103 
 [0.048]  [0.034]  [0.021]  [0.054] 
   First-stage coefficient (dependent variable = ln(cohort size / population aged 16–69))  0.276**  0.336**  0.188**  0.267** 
 [0.048]  [0.063]  [0.041]  [0.064] 
 Incremental R2 (first stage)  .046  .015  .005  .011 
 First-stage F statistic  33.00  28.10  21.05  17.48 
 Durbin-Wu-Hausman test for endogeneity (p value)  .068  .006  .017  .014 
Men 
 ln(cohort size/population aged 16–69) 0.014 –0.200 –0.031* –0.114 0.012 0.241 –0.046 0.255 
[0.036] [0.193] [0.014] [0.077] [0.020] [0.224] [0.053] [0.223] 
 IV: ln(cohort births/births 16–69)         
   Reduced-form coefficient (dependent variable = ln(LFPR))  –0.054  –0.041  0.031  0.071 
 [0.052]  [0.027]  [0.026]  [0.064] 
   First-stage coefficient (dependent variable = ln(cohort size/population aged 16–69))  0.272**  0.364**  0.130**  0.279** 
 [0.051]  [0.064]  [0.047]  [0.058] 
 Incremental R2 (first-stage)  .042  .016  .003  .010 
 First-stage F statistic  28.51  32.59  7.75  23.57 
 Durbin-Wu-Hausman test for endogeneity (p value)  .242  .238  .241  .152 
Women 
 ln(cohort size/population aged 16–69) 0.085 –0.277 –0.059 –0.411* 0.071 0.477** –0.013 0.627 
[0.043] [0.200] [0.067] [0.187] [0.042] [0.183] [0.044] [0.338] 
 IV: ln(cohort births/births 16–69)         
   Reduced-form coefficient (dependent variable = ln(LFPR))  –0.079  –0.132*  0.099*  0.138** 
 [0.054]  [0.057]  [0.039]  [0.050] 
   First-stage coefficient (dependent variable = ln(cohort size/population 16–69))  0.284**  0.321**  0.207**  0.221** 
 [0.054]  [0.068]  [0.041]  [0.075] 
 Incremental R2 (first-stage)  .040  .010  .005  .007 
 First-stage F statistic  27.63  22.31  25.97  8.66 
 Durbin-Wu-Hausman test for endogeneity (p value)  .047  .011  .019  .005 

Notes: Data source is described in notes to Fig. 1, and specification details are described in notes to Table 1. The table reports estimates of Eq. (1). Regression is weighted by average state population through the sample period. Standard errors are clustered by state. The IV used for the cohort share is the total number of births within an age cohort by state and year divided by the total number of births for 16- to 69-year-olds by state and year. We exclude certain years and states with missing birth data for the cohorts because only a handful of states started reporting births in 1915. N = 1,326.

p < .10; *p < .05; **p < .01

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