Model Comparison

Table 4.3 presents the results from estimating various specifications of binary mobility decisions consistent with the assumptions made about 𝑐𝑐𝐼𝐼𝑣𝑣[𝐹𝐹_{𝑖𝑖𝑡𝑡}𝑎𝑎_𝑖𝑖] and𝑐𝑐𝐼𝐼𝑣𝑣[𝐹𝐹_{𝑖𝑖𝑡𝑡}𝐼𝐼_{𝑖𝑖𝑡𝑡}] described in section five. The most restrictive model that assumes no correlation between time-invariant and time-varying components across equations is the random effects probit model, presented in Model 1. Model 2 is a correlated random effects probit model that allows for the correlation between time-invariant components across equations by including the individual means of the time-varying explanatory variables. Model 3 and Model 4 consider simultaneous-equations models in which the equations for mobility and fertility are estimated jointly in the form of

36 _{The left censoring creates bias on the total number of moves that have ever occurred since the housing periods} can start before the survey date. The model does include the duration of stay to capture the mobility history of households.

37 _{Staying for at least six years is grouped into one category. The specification of one dummy variable for each} residence duration leads to highly singular variance matrix of the coefficients.

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correlated random effects models. Model 3 maintains the same assumption as Model 2. Model 4 allows for the unobserved time-invariant and time-varying components associated with relocation and fertility to be correlated.

Table 4. 3. Model Comparison

Model 1 2 3 4 5

Probit RE Probit CRE Joint CRE Joint CRE IV(IV1,2)

Assumptions cov[Fit ai]=0 cov[Fit ai]≠0 cov[Fit ai]≠0 cov[Fit ai]≠0 cov[Fit ai]≠0

cov[Fit eit ]=0 cov[Fit eit]=0 cov[Fit eit]=0 cov[Fit eit]≠0 cov[Fit eit]≠0

Fertility Intention γ 0.0019** 0.0030*** 0.0030*** 0.0043* 0.0018 (se) (0.0009) (0.0012) (0.0011) (0.0012) (0.0141) Log-likelihood -8826.66 -7696.16 -32320.73 -32297.77 -60984.78 Chi-sq Model 1 vs 2 2261.36 (df; p-value) (17; 0.00) Chi-sq Model 3 vs 4 24.23 (df; p-value) (1; 0.00) cov(eit ɛit) -0.0228 (se) (0.0149)

Notes: Notes: Model 1 is a standard random effects model of mobility. Model 2 is a correlated random effects model of mobility that includes additionally the individual means of time-varying variables in the mobility equation. Model 3 is a simultaneous-equations model of mobility and fertility in the form of correlated random effects model that restricts the cross-equation correction of time varying errors to be zero. Compared to Model 3, Model 4 allows the unobserved time-varying components in mobility and fertility processes to be correlated. A likelihood ratio test comparing Model 1 and 2 rejects Model 1, and a likelihood ratio test comparing Model 3 and 4 rejects Model 3. Model 5 is IV estimation with Baby Bonus scheme and women’s education as instruments. * p<0.1, ** p<0.05, *** p<0.01.

Comparing Model 2 with Model 1, the likelihood ratio test rejects Model 1 at the one percent significance level, suggesting that the inclusion of individual means of the time-varying mobility covariates significantly improves the model fit. The model comparison test also indicates the presence of correlation between unobserved time-invariant influences and observed predictors in Model 1. Note that the magnitude of the fertility intention estimates increases from Model 1 to Model 2, suggesting that women who have a higher preference for fertility on average display a lower propensity to move.38 This implies that omission of the individual heterogeneity would lead to a downward bias in the estimated impact on fertility intention.

38 _{Ermisch and Steele (2016) found a negative correlation between unmeasured woman-level influences on}

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Model 3 presents a simultaneous-equations extension of the correlated random effects probit model (Model 2). As expected, the estimates on the fertility intention 𝛾𝛾 in Model 2 and 3 are of the similar magnitude. Relative to Model 3, Model 4 allows for the correlation of time- varying error terms across fertility and mobility equations. A likelihood ratio test that compares Model 3 with Model 4 rejects the former, which suggests that the least restricted simultaneous- equations model has better model fit. The estimate of 𝑐𝑐𝐼𝐼𝑣𝑣 [𝐼𝐼_{𝑖𝑖𝑡𝑡}𝜀𝜀_{𝑖𝑖𝑡𝑡}] is negative but insignificant.39 The negative albeit insignificant correlation of the residuals in fertility and mobility equations indicates that the shocks that increase the childbearing intentions of a woman decrease her residential mobility. The negative estimate of 𝑐𝑐𝐼𝐼𝑣𝑣 [𝐼𝐼_{𝑖𝑖𝑡𝑡} 𝜀𝜀_{𝑖𝑖𝑡𝑡}] leads to a larger estimate of 𝛾𝛾 in Model 4. Allowing for the negative correlation between the disturbances of two equationsleads to an increase in the estimated effect of fertility intention on mobility.

Model 5 presents the instrumental variable model that takes an alternative approach to addressing the endogeneity issue. The two-stage least squares procedure is performed by replacing the endogenous variable fertility intention in the structural equation by the fitted values obtained from the first-stage regression. The consistency of the estimates in the instrumental variable model depends on theoretically sound and statistically reliable instrumental variables. As discussed, given the test results in the relevance and validity checks in Table 4.2, women’s education and the Baby Bonus scheme are selected as instruments. The estimated coefficient of main interest is not statistically significant in the IV estimation.

All the models consistently report a positive relationship between fertility intention and residential move. The results on the estimated average marginal effect of fertility intention indicate that an intention to have additional children in the future is associated with an increase in the moving probability of 0.0019 percentage points in Model 1, 0.0030 in Model 2 and 3, 0.0043 in Model 4, and 0.0018 in Model 5. Since there is evidence of correlation between unobserved influences in mobility and fertility decisions, Model 2 and 4 are selected for further interpretation.

39 _{Ermisch and Steele (2016) estimated the relationship between fertility expectation and residential mobility in} Britain using yes/no fertility expectation questions and found a negative but insignificant correlation of cross- equation residuals.

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