. | Ages 16–24 . | Ages 25–49 . | Ages 50–59 . | Ages 60–69 . | ||||
---|---|---|---|---|---|---|---|---|

OLS . | IV . | OLS . | IV . | OLS . | IV . | OLS . | IV . | |

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 R^{2} (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 R^{2} (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 R^{2} (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 16–24 . | Ages 25–49 . | Ages 50–59 . | Ages 60–69 . | ||||
---|---|---|---|---|---|---|---|---|

OLS . | IV . | OLS . | IV . | OLS . | IV . | OLS . | IV . | |

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 R^{2} (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 R^{2} (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 R^{2} (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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