Internal Migration

A.4.1 American-borns

If the passage of compulsory schooling was an instrument used by states to attract American migrants (or Americans took ideas over compulsory schooling with them as they migrated across states), and that the location of the foreign-born groups we focus on in Table 2 is interlinked with the internal migration of white American-borns, this would generate a spurious correlation between the presence of these foreign-born groups and the cross-state passage of compulsory schooling. To check for this, we use data on the internal migration of Americans from the 1880 census to plot the cross-state variation in Americans born out-of-state (but in the US) and the foreign-born

population group shares core to our analysis (

1880). Figure A3 shows the result (and line of best …t): we …nd no signi…cant relationship between the population share of out-of-state American- borns, with the population shares of Europeans with and without long exposure to compulsory schooling at home, or non-Europeans. This suggests our …ndings are not merely picking up the internal migration of white American-borns.51

A.4.2 Foreign-borns

We can further check whether the passage of compulsory schooling in state  by census year , is associated with subsequent changes in the composition of the migrant population within the state. This sheds light on the narrower issue of whether any process by which natives and migrants sort into states is signi…cantly altered by the introduction of compulsory schooling law. We use two speci…cations to check for whether population trends shift in response to compulsory schooling:

 = 1(= 1) + + + X (  1850) +  (18) _ =  +  [(_{¡ })1(= 1)] + +  (19) where 

 corresponds to measures of the state-year population, and 1( = 1) is a dummy for whether compulsory schooling law has been adopted in state  by census year . Speci…cation (18) allows for a complete set of state and year …xed e¤ects ( ), and also allows for there to be long run reversion to the mean in populations across states, as captured in the 

1850 term. Speci…cation (19) is a standard trend break model, that allows for state …xed e¤ects, but assumes population follows a linear time trend () and then tests for a break in this linear trend in the years after compulsory schooling law has been adopted in state .

Table A8 presents the results: Panel A shows estimates of  from (18), and Panel B shows estimates of  and  from (19). In Columns 1 to 3 we focus on the partial correlation between the passage of compulsory schooling in a state on the subsequent total state population ( =P_). Examining Panel A, we see that unconditionally, states with compulsory schooling subsequently have signi…cantly larger populations, but this result is not robust: including state …xed e¤ects reduces the magnitude of the partial correlation by 90%, and allowing for reversion to the mean eliminates any signi…cant correlation between the total population and the earlier passage of compulsory schooling. Columns 4 to 7 focus on the composition of the foreign-born population in the state. We …nd no evidence that after compulsory schooling laws are passed, the foreign 51_{Rocha et al. [2015] provide long run evidence on the economic/industrial development of Brazilian municipal-} ities that explicitly used settlement policies to attract high skilled migrants into them in the late 19th and early 20th century.

born population, European migrants from countries with a long history of compulsory schooling, European migrants from countries without a long history of compulsory schooling, or the ratio of the two groups of European migrant, are signi…cantly di¤erent. These results go …rmly against the idea that native or migrant population movements are endogenously driven by the earlier passage of compulsory schooling in a state. Equally, the results suggests migrant groups were not resisting the civic values being imparted onto them via compulsory schooling by moving to other states. These conclusions are reinforced if we move to Panel B where (19) is estimated: we again …nd little evidence of native or migrant populations being responsive to the earlier passage of compulsory schooling (b = 0 in …ve out of six speci…cations).

A.5 IV Method

We use a control function (CF) approach to implement an instrumental variables strategy based on a Bartik-Card style instrument for migrant shares. The non-linear hazard model in (4) is a special case of a generalized regression model:  =  ( ) for  : R ! R a known non- degenerate and monotonic function and  :_R2 _{! R monotonic in each variable [Han 1987].}52 _To overcome potential endogeneity of one of the regressors in such generalized regression models, the CF approach can be adopted where the unobservable covariate is directly controlled for (rather than instrumenting the endogenous variable as for 2SLS linear models). Terza et al. [2008a, 2008b] and Wooldridge [2010] show the consistency of such a two-stage residual inclusion (2SRI) methods for non-linear models.

To make explicit the nature of the endogeneity problem, we …rst let 

 denote the exogenous variables (

, ) and add a state-migrant-speci…c unobservable to the empirical speci…cation in (4), denoted 

, with  an  £  matrix of state-migrant unobservables. These unobservables enter additively in the proportional hazard model, that can be written in the regression form,

() = exp(_¡¡ ¡ ) +  (20)

where () = R

0() is the integrated hazard function,  » (1), with  ? (  ),  ?  but  6? . Hence the migrant shares are endogenous in that they correlate with unobservable determinants of compulsory schooling law. The endogenous migration shares 

 are assumed to relate to some instrument 

 according to the following parametric model, _ =  +  + 



 (21)

52_{For the Cox proportional hazard model, }

= ¡1( + ) with  () = logR₀( ) , and  being the hazard function,   0, ()  0, and »  (1) [Han 1987].

where 

is an error term. We assume the rank condition holds, that the instruments are exogenous (

 ?    



) and that E[  j     ] = 0. The unobserved  

 component can be decomposed into a term that is potentially correlated with 

 and a residual,  = 0 + 



 (22)

where 

? , and wlog,E[exp()] = 1. The key to the CF approach is to obtain the population expectation conditional on 

, which under the above assumptions is,

E[()j  ] = exp(¡¡ ¡ ) (23) where  is a  £  matrix of residuals from (21). In the …rst stage, consistent estimates of ( ^,

^

) are obtained by OLS, and predicted values of the residuals are obtained as ^=  ¡^. In the second stage, ^ = (^1  ^) is then included in (23),

E[()j  ^] = exp(¡¡ ¡ ^) (24) If the …rst stage is correctly speci…ed, estimating this exponential regression model conditioning on ^ gives consistent estimates of ( ) [Wooldridge 2010]. The need to include additional covariates when estimating the second stage equation is demanding given our data dimensions: hence we …rst present result from the most parsimonious model that excludes the exogenous covariates  = (, ) from both stages.