Parenting with Patience: Del Boca, Flinn, Verriest & Wiswall (2026)

What this is. The paper’s core results, the dynamic model of parent-child interaction (utility functions, cognitive skill production, CCT design, discount factor dynamics), and the Method of Simulated Moments estimation: enough to understand what the paper found and how, without reading all 76 pages. To replicate or extend the model, read the full source at 10.1086/738481 and use the replication package at Harvard Dataverse.

TL;DR

The paper builds a Markov Perfect Equilibrium model in which parents and children jointly determine cognitive skill formation over childhood (ages 3-17). Parents choose how to allocate their own time, expenditure, and whether to use a Conditional Cash Transfer (CCT) that links child consumption to study time; the child simultaneously chooses self-investment time given parental decisions. The novel feature is that the child’s discount factor (patience) is endogenous: it evolves stochastically with age but is stochastically reduced by CCT use, capturing the intrinsic-motivation crowding-out effect documented by Deci, Koestner, and Ryan (1999). Estimated by the Method of Simulated Moments on PSID-CDS household data, cross-national discount factor data from Steinberg et al. (2009), and adult patience data from the Osaka Preference Parameter Survey, the model finds: CCTs reduce child patience by 13-17%; the primary deterrent to CCT use is this crowding-out cost rather than the direct disutility; maternal time inputs are most productive in early childhood while child self-investment time dominates by adolescence; and SES gaps in child outcomes are primarily explained by differences in parental time productivity and initial discount factor distributions, not by income or wage differences.

Core results

Magnitudes are as reported in the paper. Locators point into the source PDF.

#	Result	Locator	Magnitude
R1	CCT use stochastically reduces child patience: expected discount factor falls 13% at age 11	Sect. 5.3, p. 60	From 0.493 (no CCT) to 0.427 (CCT use)
R2	CCT use reduces child patience by 17% at age 17	Sect. 5.3, p. 60	From 0.503 (no CCT) to 0.418 (CCT use)
R3	Removing CCT access raises final patience to 0.88 but reduces final cognitive skills by 37% of a SD	Table 13, col. 1, p. 69	Cognitive skills fall 0.17 log-units (37% of SD); patience rises from 0.81 to 0.88 at age 17
R4	Removing the patience crowding-out channel causes CCT use to jump to 90% and cognitive skills to rise 85% of a SD	Table 13, col. 3, p. 70	Cognitive skills rise 0.38 log-units (85% of SD); patience rises to 0.88
R5	Maternal time is most productive in early childhood	Sect. 5.2, p. 58	1 SD more maternal time at age 6 raises Letter Word score 9-11% of a SD
R6	Child self-investment time surpasses parental time in productivity by adolescence	Sect. 5.2, p. 58	1 SD more study time at age 15 raises Letter Word score more than 5% of a SD
R7	SES gaps in cognitive skills are driven mainly by parental time productivity and discount factor heterogeneity, not wages or income	Table 14, col. 4, p. 73	Homogenizing productivity and discount factors closes 84% of simulated high/low-SES cognitive-skills gap and 79% of patience gap

Overall (paper’s conclusion). Parents rationally limit CCT use because CCTs stochastically reduce child patience, not primarily because of the direct utility cost. The model unifies cognitive and non-cognitive skill formation: study incentives boost cognitive outcomes but erode patience, creating a tradeoff that explains the declining use of CCTs with child age and the lower CCT use among college-educated parents whose children are already more patient. SES gaps in child outcomes are primarily rooted in heterogeneous parental time productivity and patience distributions, suggesting that income or wage redistribution alone would close little of the gap.

Theory / model

The model covers ages $t = t_0, t_0+1, \ldots, 17$ with the terminal period at $M+1$. State variables at each age are the current cognitive skill stock $k_t$, the child’s current discount factor $\beta_{c,t}$, and a set of parental characteristics (wages, education, non-labor income) collected in $\Gamma_t$.

Preferences. The child’s instantaneous utility over leisure $l_{c,t}$, private consumption $x_t$, and cognitive skill $k_t$ is (p. 11):

$$u_{c,t} = \lambda_1 \ln l_{c,t} + \lambda_2 \ln x_t + \lambda_3 \ln k_t$$

Parents are altruistic toward the child. Their composite utility (Eq. 1, p. 12), combining own consumption and altruistic terms over child leisure, child consumption, and skill, is:

$$\tilde{u}_{p,t} = \tilde{\alpha}_1 \ln l_{1,t} + \tilde{\alpha}_2 \ln l_{2,t} + \tilde{\alpha}_3 \ln c_t + \tilde{\alpha}_4 \ln k_t + \tilde{\alpha}_5 \ln l_{c,t} + \tilde{\alpha}_6 \ln x_t \tag{1}$$

where $l_{1,t}, l_{2,t}$ are mother’s and father’s leisure, $c_t$ is parental consumption, and the $\tilde{\alpha}$ parameters embed a convex combination of parental own preferences and child preferences weighted by the altruism parameter $\varphi$. When the parent uses a CCT, a random fixed utility cost $\zeta$ drawn from an exponential distribution is deducted (Eq. 6, p. 19):

$$\tilde{u}_{p,t}(\mathbf{a}_{p,t}) = \tilde{\alpha}_1 \ln l_{1,t} + \tilde{\alpha}_2 \ln l_{2,t} + \tilde{\alpha}_3 \ln c_t + \tilde{\alpha}_4 \ln k_t + \tilde{\alpha}_5 \ln l_{c,t} + \tilde{\alpha}_6 \ln x_t - \zeta \cdot \mathbf{1}[CCT_t = 1] \tag{6}$$

Terminal values. At period $M+1$ the model closes with an infinite-horizon continuation. The child’s terminal value (Eq. 2, p. 13) is:

$$V_{c,M+1}(k_{M+1}, \beta_{c,M+1}) = \frac{\lambda_3 \ln k_{M+1}}{1 - \beta_{c,M+1}} \tag{2}$$

reflecting that with patience $\beta_{c,M+1}$ the child will continue to value the skill stock at rate $\lambda_3 / (1 - \beta_{c,M+1})$ into the adult perpetuity. The parent’s terminal value (Eq. 3, p. 14) combines the parent’s own long-run discount factor with the imputed value of the child’s terminal stock, weighting both $(1-\varphi)\alpha_4 / (1 - \beta_p)$ (parent’s own valuation of $k_{M+1}$) and the altruistic share $\varphi \lambda_3 / (1 - \beta_{c,M+1})$.

Cognitive skill production. Skill evolves via a Cobb-Douglas log-linear production function following Cunha, Heckman, and Schennach (2010) (Eq. 4, p. 14):

$$\ln k_{t+1} = \ln R_t + \delta_{1,t} \ln \tau_{1,t} + \delta_{2,t} \ln \tau_{2,t} + \delta_{3,t} \ln \tau_{c,t} + \delta_{4,t} \ln e_t + \delta_{5,t} \ln k_t \tag{4}$$

where $\tau_{1,t}, \tau_{2,t}$ are mother’s and father’s time with the child, $\tau_{c,t}$ is child self-investment time, $e_t$ is monetary expenditure on the child, $k_t$ is the lagged skill stock, $R_t$ is age-specific total factor productivity, and the $\delta$ parameters are age-varying input elasticities. The persistence parameter $\delta_{5,t}$ (“skills beget skills”) is estimated at 0.79 in early childhood and rises to 0.84 by age 16.

CCT incentive contract. When a parent uses a CCT, child consumption is linked to study time (Eq. 5, p. 17):

$$\ln x_t(\tau_{c,t};\, r_t, b_t) = b_t + r_t \ln \tau_{c,t} \tag{5}$$

with floor parameter $b_t$ (base consumption) and slope $r_t > 0$ (study-time elasticity of consumption). A higher $r_t$ provides stronger incentives to study. The parent jointly chooses $CCT_t \in \{0,1\}$ and, when $CCT_t = 1$, the contract parameters $(r_t, b_t)$.

Endogenous discount factor. The child’s discount factor evolves via a Markov chain (Eq. 7, p. 22) with $Z$ discrete support points:

$$\Pr(\beta_{c,t+1,h} = \beta_c^{j'} \mid \beta_{c,t,h} = \beta_c^j,\, t,\, CCT_{t,h}) \quad \forall\, (j,j') = 1,\ldots,Z \tag{7}$$

The transition probabilities depend on current patience, age, and whether a CCT was used. The key restriction, identified from the Steinberg et al. and Osaka PPS data, is that CCT use stochastically shifts probability mass toward lower patience states: the estimated CCT-on transition matrix puts more weight on low-$\beta_c$ values than the CCT-off matrix.

Equilibrium. The game is a Markov Perfect Equilibrium in the tradition of Del Boca, Flinn, and Wiswall (2014) and Doepke and Zilibotti (2017). Each period the parent announces actions $\mathbf{a}_{p,t} = (\tau_{1,t}, \tau_{2,t}, e_t, CCT_t, r_t, b_t)$ before the child chooses $\tau_{c,t}$. The child’s Bellman equation is (p. 24):

$$V_{c,t}(\Gamma_t \mid \mathbf{a}_{p,t}) = \max_{\tau_{c,t}} \Bigl[ u_c(l_{c,t}, x_t, k_t) + \beta_{c,t}\, \mathbb{E}_t V_{c,t+1}(\Gamma_{t+1} \mid \tau_{c,t}, \mathbf{a}_{p,t}, \Gamma_t) \Bigr]$$

The parent’s Bellman equation is (p. 25):

$$V_{p,t}(\Gamma_t) = \max_{\mathbf{a}_{p,t}} \Bigl[ \tilde{u}_p(\mathbf{a}_{p,t}) + \beta_p\, \mathbb{E}_t V_{p,t+1}(\Gamma_{t+1} \mid \mathbf{a}_{p,t}, \Gamma_t) \Bigr]$$

Under the Cobb-Douglas structure the child’s optimal study time has a closed-form linear reaction function: without a CCT it is proportional to available non-parental time $(\tilde{T}_t - \tau_{p,t}^0)$ at a state-dependent rate $\gamma_t^0(\Gamma_t)$; with a CCT the proportionality constant $\gamma_t^1(r_t, \Gamma_t)$ also depends on the CCT elasticity $r_t$ (Eqs. 8 and 10, pp. 26-27). Parental CCT choice then follows from comparing $V_{p,t}(\Gamma_t \mid \mathbf{a}_{p,t}^0)$ and $V_{p,t}(\Gamma_t \mid \mathbf{a}_{p,t}^1)$ at each state.

Method

Solution. The model is solved by backward induction (value function iteration starting at $t = M+1$ and rolling back to $t = t_0$). At each age-state grid node, the child’s reaction function and the parent’s optimality conditions are solved in closed form given the known next-period value function, then rolled back. The key analytic result (Proposition in Section 2.4, pp. 28-29) is that in equilibrium, child study time is a fixed fraction of remaining non-parental time, which makes the parent’s optimization tractable. The value-function-iteration approach uses a discretized state space for $k_t$ and $\beta_{c,t}$ (integrating out the Markov transition at each step).

Estimation. Parameters are estimated by the Method of Simulated Moments. Let $\boldsymbol{\theta}$ be the vector of structural parameters. Given a draw of household heterogeneity, the model simulates histories of all endogenous variables; simulated moments $\hat{m}(\boldsymbol{\theta})$ are matched to empirical counterparts $m_{\text{data}}$ by minimizing:

$$\hat{\boldsymbol{\theta}} = \arg\min_{\boldsymbol{\theta}} \bigl(\hat{m}(\boldsymbol{\theta}) - m_{\text{data}}\bigr)' \hat{W} \bigl(\hat{m}(\boldsymbol{\theta}) - m_{\text{data}}\bigr)$$

where $\hat{W}$ is a diagonal weighting matrix. Standard errors are computed from the Jacobian of simulated moments; 1,000 simulated households are used per parameter evaluation. The method-of-simulated-moments estimator builds on the principal-agent parent-child game framework and the life-cycle-model specification of parental wages and non-labor income.

Empirical specifications

Cognitive skill production function. The age-specific input elasticities $\boldsymbol{\delta}_t$ and persistence $\phi_t$ are first estimated from a reduced-form log-linear specification (Eq. 12, p. 49):

$$\ln k_{h,t+1} = \ln R_t + \mathbf{Z}_{h,t} \boldsymbol{\delta}_t + \phi_t \ln k_{h,t} + \varepsilon_{h,t} \tag{12}$$

where $\mathbf{Z}_{h,t}$ is the vector of log time and expenditure inputs for household $h$ at age $t$. These first-stage estimates are used as calibrated starting values and production-function moments in the structural estimation.

Structural moment conditions. The MSM matches 211 moments from three datasets:

• PSID-CDS moments: age-conditional means and correlations of parental time inputs, child study time, CCT use (conditional-allowance indicator), test scores (Woodcock-Johnson Letter Word and Applied Problems), wages, household income, and CCT use by parental education group.
• Steinberg et al. (2009) moments: age-conditional means and variances of elicited child discount factors (ages 10-30), and correlation of discount factors with IQ scores across sites.
• Osaka PPS moments: mean and variance of adult discount factors by age group (ages 25-65), and education-conditional means.

The CCT-patience crowding-out parameters (the off-diagonal elements of the CCT-on relative to the CCT-off discount factor transition matrix) are identified from the conditional covariance between CCT use and changes in the simulated patience distribution, cross-validated against the Steinberg et al. and Osaka PPS moments.

Datasets used

Dataset	Role in paper	Wiki page
PSID-CDS (Panel Study of Income Dynamics, Child Development Supplement)	Primary structural estimation: parental time inputs (Childhood Activity Study modules), child study time, CCT use (conditional-allowance questions), Woodcock-Johnson Letter Word and Applied Problems test scores, household income, wages, demographics	No page yet
Steinberg et al. (2009) experimental data	Discount factor moments: age profile of patience from 935 individuals ages 10-30 across 11 study sites; pins down $\beta_{c,t}$ age dynamics and CCT crowding-out parameters	No page yet
Osaka Preference Parameter Survey (Osaka PPS)	Adult discount factor moments: mean and variance for 4,625 adults ages 25-65; anchors the terminal patience distribution used in the structural model	No page yet

Sample: 247 PSID-CDS households, three waves (1997, 2002, 2007), children ages 3-16. Replication code and processed data: Del Boca, Flinn, Verriest, and Wiswall (2025), Harvard Dataverse (10.7910/DVN/F7QVQ5).

When to read the full paper

Read the source at doi.org/10.1086/738481 if you are:

• Building or extending structural models of child development that treat children as active players with endogenous time preferences; Section 2.4 derives the closed-form equilibrium reaction functions.
• Studying parenting-style economics (CCT vs. unconditional transfers) and need the MPE solution method and identification argument.
• Calibrating age-varying skill production elasticities from PSID-CDS; Table 12 (p. 57) lists all input-elasticity estimates by age group.
• Running SES-heterogeneity counterfactuals: Table 14 (pp. 72-73) decomposes the simulated high/low-SES gap into wage, productivity, time-preference, and initial-condition channels.
• Extending the Doepke and Zilibotti (2017) or Cunha, Heckman, and Schennach (2010) frameworks to a game-theoretic setting with endogenous patience.

The comparative statics of CCT cost and crowding-out parameters (Table 13, pp. 69-70) and the SES decomposition (Table 14) are the headline policy-relevant outputs; the formal game solution and MSM algorithm are in Appendices A-C.

Attribution and rights

Source: peer-reviewed, Journal of Political Economy 134(1), January 2026. This distillation was extracted by an LLM on 2026-06-26 and is not human-verified or independently reproduced. The VoR is paywalled (University of Chicago Press); this page is extract-only.

Del Boca, Daniela, Christopher Flinn, Ewout Verriest, and Matthew Wiswall. “Parenting with Patience: Parental Incentives and Child Development.” Journal of Political Economy 134, no. 1 (January 2026): 210-284. DOI: 10.1086/738481. Replication data: Del Boca, Flinn, Verriest and Wiswall (2025), Harvard Dataverse, https://doi.org/10.7910/DVN/F7QVQ5.