Duke University Press

Table 2

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

	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^†
ln(cohort size / population aged 16–69)	[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^†
Reduced-form coefficient (dependent variable = ln(LFPR))		[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
ln(cohort size/population aged 16–69)	[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
Reduced-form coefficient (dependent variable = ln(LFPR))		[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^†
ln(cohort size/population aged 16–69)	[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**
Reduced-form coefficient (dependent variable = ln(LFPR))		[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 16–24		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^†
ln(cohort size / population aged 16–69)	[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^†
Reduced-form coefficient (dependent variable = ln(LFPR))		[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
ln(cohort size/population aged 16–69)	[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
Reduced-form coefficient (dependent variable = ln(LFPR))		[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^†
ln(cohort size/population aged 16–69)	[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**
Reduced-form coefficient (dependent variable = ln(LFPR))		[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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