Housing costs and fertility

The problem discussed is the existence of low and falling birthrates in many developed countries, which carries adverse economic consequences such as slower growth, reduced innovation, and higher pension and healthcare costs. Achieving long-run demographic sustainability requires policymakers to consider how birth rates might be raised, with housing identified as a promising lever.

The motivation for this research stems from the rising costs of housing, which is hypothesized to deter additional births because larger families demand more housing, increasing the marginal cost, consistent with a standard child quantity-quality model. Critically, existing empirical evidence linking housing costs and fertility is limited because it is often affected by geographic selection bias (where high-fertility households sort into lower-cost locations), neglects the nonlinear cost of housing over unit size, and does not incorporate the impact of housing supply policies. Couillard addresses these shortcomings by specifying a dynamic model of joint housing-fertility choice to provide causal estimates of the impact of housing costs on fertility net of sorting bias.

 

The structural model framework developed by Couillard is a dynamic model of joint housing-fertility choice that captures the interconnected decisions regarding housing location, unit size, fertility, and household formation.

This framework nests a static residential choice model within a broader dynamic ‘living arrangement’ model, which includes the fertility decision. The model allows agents to choose combinations of neighborhood and house size (number of bedrooms), and it is designed to explicitly account for geographic sorting bias.

Key features of the structural framework include:

1. Economic Foundation: The model is motivated by and extends the Beckerian quantity-quality model (Becker, 1960) to incorporate housing costs.
2. Heterogeneity and Preferences: Housing preferences are modeled as heterogeneous across dimensions like age, tenure, family/roommate households, and household size. This structure ensures that changes in housing characteristics, such as costs, have heterogeneous impacts on the values of living arrangement choices. The underlying estimates confirm that larger families are more sensitive to housing costs and have stronger tastes for larger units.
3. Dynamic Living Arrangements: The "living arrangement" choice set encompasses fertility (having children) and household formation decisions, including options like living with parents or other family members. This accounts for the mechanism where high housing costs can disincentivize fertility by increasing the long-run cost associated with the endogenous probability that adult children or other family members will choose to live in the household.
4. Estimation Method: To address data constraints (unobserved joint distributions) and incorporate rich heterogeneity, the model employs and extends IO "micro-moment" techniques. This extension allows for demographic-varying utility residuals to prevent potential model misspecification. A crucial assumption for tractability is that housing and fertility preferences are additively separable, and housing choice does not affect state transition probabilities.

The methodology employed involves specifying a dynamic model of joint housing-fertility choice, which allows for choices over location and house size. This framework aims to provide causal estimates of the impact of housing costs on fertility, explicitly accounting for geographic selection bias.

Estimation Techniques and Data

The estimation relies on applying and extending IO "micro-moment" techniques (Petrin, 2002; Berry et al., 2004a) using US Census Bureau data.

1. Addressing Data Constraints: The primary challenge addressed by the methodology is the constraint of not observing the joint distribution of household counts over census tracts and various demographic characteristics. The approach uses a set of publicly available marginal distributions (e.g., tract by age, tract by sex, age by sex by city) and demonstrates that these are sufficient statistics for the parameters of the model.
2. Iterative Proportional Fitting (IPF): These marginal distributions are first combined using the Iterative Proportional Fitting (IPF) algorithm to create a rectangular estimate of the unobserved joint distribution, which can then be used in standard computational routines.
3. Heterogeneous Residuals: The methodology extends standard techniques to incorporate heterogeneous utility residuals ($\xi$). This is a crucial step, as restricting the residual to be homogeneous over demographics, as done in standard IO tools, can lead to model misspecification when the number of micro-moments is large.
4. Multi-Step Estimation: Housing demand parameters are estimated in two steps:
   • Step 1 (Maximum Likelihood): Heterogeneity parameters (which determine how different demographic groups value housing characteristics) are estimated using maximum-likelihood, exploiting the logit-Poisson equivalence.
   • Step 2 (2SLS/Identification): Baseline preferences (the overall sensitivity to costs) are estimated using Two-Stage Least Squares (2SLS). The necessary identifying variation for rents is generated using the "donut instrument". This instrument averages amenities—such as railway noise pollution or share of single-family detached homes—in a surrounding ring to shift the quality of substitutable locations and thus rents in the focal tract.

Dynamic Model Estimation

After estimating housing demand utility components, the dynamic ‘living arrangement’ model (which includes the fertility decision) is estimated to isolate the effects of the housing market by holding constant all non-housing determinants of fertility. This involves:

• Hotz-Miller Inversion: This technique is used to solve for the flow utility of living arrangements ($\alpha^x_g$) from choice probabilities, given the housing utility components, by factoring the fertility utility out of the choice probability.
• Continuation Value Simulation: The continuation value ($c^x_g$) is calculated using simulation, incorporating expectations of future states, partnership dissolution rates, and the endogenous probability that adult children or other family members will choose to live in the household.

The structural model provides causal estimates, corrected for sorting bias, confirming that rising housing costs are a major cause of declining fertility in the US.

The key causal findings derived from varying rents directly in a partial-equilibrium decomposition include:

1. Aggregate Fertility Decline: Rising housing costs since 1990 are responsible for 13 million (11%) more children not being born between 1990 and 2020.
2. Recent Fertility Rate Impact: Housing costs are accountable for 51% of the total fertility rate (TFR) decrease observed between the 2000s and the 2010s. They also contributed 42% to the decline in the General Fertility Rate (GFR) over the same period.
3. Household Formation: Rising housing costs caused a 7 percentage point (7pp) decrease in the share of 20-29 year olds who have started families.
4. Primary Mechanism: The decrease in fertility is primarily driven by the general rise in housing costs (average rents), which are responsible for roughly 67-75% of the effect, rather than the rising relative rents of large units (the steepening size-cost gradient).

In policy counterfactuals comparing housing supply shifts based on equal subsidy expenditures:

• A supply shift targeting large units (3+ bedrooms) is significantly more effective, generating 2.3 times more births than an equal-cost shift for small units (1 bedroom).
• The large unit policy causes 4.7 million (4%) more children to be born over three decades, while the small unit policy achieves only 43% of this number of births.

The general equilibrium (GE) policy counterfactuals are designed to study the effects of forward-looking housing policy, acknowledging that housing costs are endogenous and cannot be directly controlled by policy. The analysis compares two distinct housing supply strategies that target unit size:

1. Small Unit Policy (YIMBY): This policy targets the supply shift of 1 bedroom units. This is considered the de facto YIMBY (Yes In My Backyard) policy, focusing on small and low-cost units.
2. Large Unit Policy: This policy targets the supply shift of 3+ bedroom units and is a direct attempt at family-friendly housing policy.

General Equilibrium Framework and Policy Design

The cost reductions in these counterfactuals are conceptually treated as reductions in distortionary local regulatory taxes on development. However, to place the two policies on equal footing for comparison, the magnitude of the supply shifts is defined as if they resulted from subsidies generating equal aggregate funding (equivalent to 5% of annual aggregate rental expenditures based on initial rents and quantities).

Because small units have lower construction costs, the equal-expenditure constraint allows the small unit policy to generate a larger total number of units.

Policy Mechanisms and Findings

The structural model assessed how these policies impact fertility based on contrasting mechanisms:

• Small Unit Policy Mechanism: This policy generates a larger decrease in average rents and potentially reduces the long-run housing cost of fertility by prompting young adults to move out of their parents’ homes. However, this policy also steepens the size-cost gradient (making large units relatively more expensive).
• Large Unit Policy Mechanism: This policy generates a smaller effect on average rents but achieves a crucial objective: it flattens the size-cost gradient.

Key Findings:

The analysis found that the Large Unit Policy significantly outperforms the small unit policy in generating births:

• The supply shift targeting large units generates 2.3 times more births than the equal-cost shift for small units.
• The large unit policy causes 4.7 million (4%) more children to be born over three decades.
• The small unit policy achieves only 43% of the number of births generated by the large unit policy, primarily because its strongest effect is making living alone more attractive for young adults.

The conclusion drawn is that if housing is to be a successful lever for family policy and demographic sustainability, the focus must be on producing the housing that families actually want.