Child Skill Production: Accounting for Parental and Market-Based Time and Goods Investments
Bibliographic record
Abstract
This paper studies the multidimensional nature of investments in children within a dynamic framework. In particular, we examine the roles of parental time investments, purchased home goods/services inputs, and market-based child care services. We first document strong increases in total investment expenditures by maternal education; yet expenditure shares, which skew heavily towards parental time, vary little with parental schooling. Second, we develop an intergenerational lifecycle model with multiple child investment inputs to study these patterns and the impacts of policies that alter the prices of different inputs. We analytically characterize investment behavior, focusing on the substitutability of different investment inputs and the way parental skills affect the productivity of family-based inputs. Third, we develop an estimation strategy that exploits intratemporal optimality conditions based on relative demand to estimate substitutability between inputs, the relative productivity of different inputs, and the role played by parental education. This approach requires no assumptions about the dynamics of skill investment, preferences, or credit markets. We also account for mismeasured inputs and wages, as well as unobserved heterogeneity in parenting skills. We further show how noisy measures of child achievement (measured several years apart) can also be incorporated in a generalized method of moments approach to additionally identify the dynamics of skill accumulation. Fourth, we use data from the Child Development Supplement of the Panel Study of Income Dynamics to estimate the skill production technology for children ages 12 and younger. Our estimates suggest complementarity between parental time and home goods/services inputs as well as between these family-based inputs and market-based child care, with elasticities of substitution ranging from 0.2 to 0.5. We find no systematic effects of parental education on the relative productivity of parental time and other home inputs. Finally, we use counterfactual simulations to explore the extent and sources of variation in investments across families, as well as investment responses to changes in input prices. We find that variation in prices explains 48% of the overall variance in investment expenditures, and differences in wages explain more than half of the investment expenditure gap between college-educated and non-college-educated parents. We further show that accounting for the degree of input complementarity implied by our estimates has important implications for the responses of individual inputs to any price change and for the responses in total investments and skill accumulation to large (but not small) price changes.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".