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The results from this exercise, presented in table 6, support our identifying assumption, showing small and not statistically significant point estimates for each characteristic. A joint test of significance for the covariates in table 6 further supports the identifying assumption, failing to reject the null hypothesis that the covariates are jointly unable to predict the gender of the exogenously assigned GP (⁠

p

-value of 0.557).^²⁶

Table 6.

Balance Test

	Birth order	Siblings	Born in Norway	Mother years of education	Mother age	Mother married	Mother log income	Mother not in labor force
Same-gender GP	0.044	0.049	−0.025	0.004	0.086	0.009	−0.004	0.009
	(0.042)	(0.055)	(0.017)	(0.109)	(0.195)	(0.020)	(0.021)	(0.012)
Mean	1.865	1.698	0.861	14.146	28.974	0.567	12.740	0.066
Observations	8,424	8,424	8,424	8,034	8,423	8,034	8,357	8,424

	Birth order	Siblings	Born in Norway	Mother years of education	Mother age	Mother married	Mother log income	Mother not in labor force
Same-gender GP	0.044	0.049	−0.025	0.004	0.086	0.009	−0.004	0.009
	(0.042)	(0.055)	(0.017)	(0.109)	(0.195)	(0.020)	(0.021)	(0.012)
Mean	1.865	1.698	0.861	14.146	28.974	0.567	12.740	0.066
Observations	8,424	8,424	8,424	8,034	8,423	8,034	8,357	8,424

The table shows the $β_{1}$ coefficients obtained through estimation of equation (1) as described in the text and reproduced here for clarity: $y_{i} = α + β_{1} G P_M a t c h_{i} + τ_{t} + π_{m} + θ_{c} + ρ_{d} + ε_{i}$ ⁠. $y_{i}$ is a general term denoting the outcome listed at the top of each column, and each estimation includes municipality (⁠ $π_{m}$ ⁠), year of swap (⁠ $τ_{t}$ ⁠), birth year (⁠ $θ_{c}$ ⁠), and previous GP (⁠ $ρ_{d}$ ⁠) fixed effects. The point estimates depicted in the table should be interpreted as the effect of random assignment to same-gender GP in childhood on the outcome listed at the top of the column. Standard errors are clustered at the level of the exogenously assigned GP. Sample includes all girls born between 1988 and 1996 who were subject to at least one exogenous GP swap prior to age 15. Mother's age and marital status are calculated at the year of birth. Mother's earnings, education, and employment are measured when the child is 15 years old (when the children in our sample make their high school choices; our data do not extend far back enough for us to get this information at the year of birth). Significant at $^{*}$ 10%, $^{* *}$ 5%, $^{* * *}$ 1%.

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