How Family Size Affects Parents’ Labour Market Outcomes: A Meta-Analysis

• Název práce v češtině: Jak velikost rodiny ovlivňuje pracovní výsledky rodičů: Meta-analýza
• Název v anglickém jazyce: How Family Size Affects Parents’ Labour Market Outcomes: A Meta-Analysis
• Akademický rok vypsání: 2019/2020
• Typ práce: diplomová práce
• Jazyk práce: angličtina
• Ústav: Institut ekonomických studií (23-IES)
• Vedoucí / školitel: doc. PhDr. Zuzana Havránková, Ph.D.
• Řešitel: skrytý - zadáno vedoucím/školitelem
• Datum přihlášení: 17.02.2022
• Datum zadání: 29.06.2022
• Datum a čas obhajoby: 18.09.2024 09:00
• Místo konání obhajoby: Opletalova, O109, AULA Michala Mejstříka č. 109
• Datum odevzdání elektronické podoby: 31.07.2024
• Datum proběhlé obhajoby: 18.09.2024
• Oponenti: Mgr. Barbara Pertold-Gebicka, M.A., Ph.D.

Seznam odborné literatury

Agüero, J. M., & Marks, M. S. (2011). Motherhood and female labor supply in the developing world evidence from infertility shocks. Journal of Human Resources, 46(4), 800-826.
Angrist, J. D., & Evans, W. N. (1998). Children and Their Parents’ Labor Supply: Evidence from Exogenous Variation in Family Size. American Economic Review, 88(3), 450–477.
Amini, S. M., & Parmeter, C. F. (2012). Comparison of model averaging techniques: Assessing growth determinants. Journal of Applied Econometrics, 27(5), 870-876.
Andrews, I., & Kasy, M. (2019). Identification of and correction for publication bias. American Economic Review, 109(8), 2766-94.
Chevalier, A. and Viitanen, T.K. (2003) The long-run labour market consequences of teenage motherhood in Britain. Journal of Population Economics, 16(2), 323-343.
Cukrowska-Torzewska, E., & A. Matysiak (2020). The Motherhood Wage Penalty: A Meta-Analysis. Social Science Research, 88-89, art. 102416.
Bom, P. R., & Rachinger, H. (2019). A kinked meta‐regression model for publication bias correction. Research synthesis methods, 10(4), 497-514.
Bronars, S. G., & Grogger, J. (1994). The Economic Consequences of Unwed Motherhood: Using Twin Births as a Natural Experiment. American Economic Review, 84(5), 1141-1156.
Browning, M. (1992). Children and household economic behavior. Journal of Economic Literature, 30(3), 1434-1475.
Cáceres-Delpiano, J. (2006). The impacts of family size on investment in child quality. Journal of Human Resources, 41(4), 738-754.
Cáceres-Delpiano, J. (2008). Keeping the best for last. Impact of fertility on mother's employment. Evidence from developing countries. Working paper 08-68 Economic Series (32).
Cáceres-Delpiano, J. (2012). Can we still learn something from the relationship between fertility and mother’s employment? Evidence from developing countries. Demography, 49(1), 151-174.
Chun, H., & Oh, J. (2002). An instrumental variable estimate of the effect of fertility on the labour force participation of married women. Applied Economics Letters, 9(10), 631-634.
Cools, S., Markussen, S., & Strøm, M. (2017). Children and careers: How family size affects parents’ labor market outcomes in the long run. Demography, 54(5), 1773-1793.
Egger, M., Smith, G. D., Schneider, M., & Minder, C. (1997). Bias in meta-analysis detected by a simple, graphical test. Bmj, 315(7109), 629-634.
Elliott, G., Kudrin, N., & Wüthrich, K. (2022). Detecting p‐Hacking. Econometrica, 90(2), 887-906.
Fletcher, J. M. (2012). The effects of teenage childbearing on the short-and long-term health behaviors of mothers. Journal of Population Economics, 25(1), 201-218.
Furukawa, C. (2019). Publication bias under aggregation frictions: Theory, evidence, and a new correction method. Unpublished paper, MIT.
Guo, R., Li, H., Yi, J., & J. Zhang (2018). Fertility, household structure, and parental labor supply: Evidence from China. Journal of Comparative Economics 46(1), 145-156.
Havranek, T., Irsova, Z., Laslopova, L., & Zeynalova, O. (2022). Publication and attenuation biases in measuring skill substitution. The Review of Economics and Statistics, 1-37.
Holmlund, H. (2005). Estimating long-term consequences of teenage childbearing: An examination of the siblings approach. The Journal of Human Resources, 40(3), 716-743.
Ioannidis, J. P., Stanley, T. D., & Doucouliagos, H. (2017). The power of bias in economics research. Economic Journal, 127(605), 236-265.
Krueger A.B. (2017). Where Have All the Workers Gone? An Inquiry into the Decline of the U.S. Labor Force Participation Rate. Brookings Papers on Economic Activity, 2, 1-87.
Miller, A. R. (2011). The effects of motherhood timing on career path. Journal of Population Economics, 24(3), 1071-1100.
de Linde Leonard, M., & T. D. Stanley (2020). The Wages of Mothers' Labor: A Meta‐Regression Analysis. Journal of Marriage and Family, 82(1), art. 2693.
Lundborg, P., Plug, E., & Rasmussen, A. W. (2014). Fertility effects on female labor supply: IV evidence from IVF treatments. IZA Discussion Papers, No. 8609.
Matysiak, A. & D. Vignoli (2008). Fertility and Women’s Employment: A Meta-analysis. European Journal of Population, 24, 363-384.
Stanley, T. D. (2005). Beyond publication bias. Journal of economic surveys, 19(3), 309-345.
Zhang, J. (2017). The Evolution of China's One-Child Policy and Its Effects on Family Outcomes. Journal of Economic Perspectives, 31(1), 141-60.

Předběžná náplň práce v anglickém jazyce

Motivation

Female labor force participation has significantly increased in recent years (Aguero & Marks, 2011; Lundborg et al., 2014), a phenomena often attributed to decreasing childbirth rates (Browning, 1992). Women are more likely than men to adjust their labor supply in response to changes in family size (Cools et al., 2017). One of the intuitive reasons happens to be the disproportional distribution of parental responsibilities (Aguero & Marks, 2008). Although the negative correlation between fertility and labor market participation seems to be well established, the interpretation of the relationship gets complicated due to endogenous nature of fertility choices.

The spuriousness of the relationship between family size and labor market outcomes happens for two reasons: the first one is reverse causality (when labor market outcomes drive the decision of parents to have an additional child), the second one is omitted variable bias (when unobservables such as parental ability or career ambition drives their decision to have an additional child). Some studies treat the endogeneity of the relationship using a natural experiment (Bronars & Grogger, 1994, and Guo et al., 2018, who use twin births as an unplanned exogenous event), some apply quasi-experimental methods (for example by instrumenting fertility by instrumental variables such as twins, parental preferences for a mixed sibling-sex composition, fertility shocks and miscarriage as in Angrist & Evans, 1998; Cáceres-Delpiano, 2012; Chun & Oh, 2002; Fletcher, 2012; Miller, 2011), others use between-effects with data of siblings (Holmlund, 2005) or matching methods (Chevalier and Viitanen, 2003). Some studies suggest the relationship is substantial (Chun & Oh, 2002), while others find it negligible (Zhang, 2017).

To my knowledge, there are three meta-analyses by Matysiak & Vignoli (2008), Cukrowska-Torzewska & Matysiak (2020), and de Linde Leonard & Stanley (2020) that have specifically focused on a motherhood wage penalty (the output of a Mincer equation where wages are regressed on an indicator of parenthood). I should stress that the examined literature deals with partial effects and is mostly not causal, nor do the previous meta-studies examine the causal relationship in detail. My meta-analysis would be inspired by Clarke (2018) who dives into the details of causality in the literature. My ambition is to take both correlational and causal estimates and use the novel meta-analysis methods to evaluate the true effect beyond biases, including the effects relevant to fathers which are rather scarce in the literature. As Krueger (2017) points out, the prime-age male participation in labor markets has been steadily declining over last decades without a convincing explanation.


Hypotheses

1. Publication bias exaggerates the true causal effect.
2. Publication bias is mitigated by attenuation bias in the opposite direction.
3. The estimated effect decreases with the mother's age at birth.


Methodology

First, I will identify the most relevant studies of the literature (using Clarke 2018) and based on those studies I will construct a search query for Google Scholar search engine. The previous meta-analyses show that this literature is quite heterogeneous. Most importantly, the studies use different definitions of the effect as well as identification strategies used for the estimation of the effect. For example, a simple regression analysis (such as the one of Mincer-type equation) uses labor market outcome defined as a decision whether to work at all (dummy variable), how many hours to work given one is already employed (continuous variable), or most typically, how much does one earn (continuous variable such as wage or income). On the other hand, the family size can be defined as the number of children (categorical variable) or the logarithm of it, or as an indicator variable for parenthood status such as whether the individual has one or more children (dummy variable), or the effect of an additional child that could be identified from an unanticipated childbirth (such as twins). Indeed, in all cases, the interpretation of the estimated coefficient is different and one has to find some common grounds to make the collected metrics comparable. I plan to split my analysis to two samples: those for mothers and those for fathers.

To test for the publication bias in the literature I will collect all the measures of precision available in the literature (standard errors, confidence intervals, p-values, or standard deviations with the number of observations). Publication bias appears when some estimates have a higher probability of being reported. Ioannidis et al. (2017) concluded that in economics literature, the true effect is often exaggerated twofold by the presence of publication bias. To test for the presence of publication bias in this literature, I will first use the visual test called the funnel plot (Egger et al., 1997) and its rigorous version, the funnel asymmetry test by Stanley (2005). I will also apply different weighting schemes to this linear test. Withal, since there is no strong reason to claim that the relationship between the effect and its standard error is linear, I will also perform some recently published methods of a non-linear nature (Andrews & Kasy, 2019; Bom & Rachinger, 2019; Furukawa, 2019; Ioannidis et al., 2017) and apply other methods relaxing the exogeneity assumption (Elliott et al., 2022). If I have enough data, I will test for the present of the attenuation bias: I will divide the studies into three groups based on the used methodology: Ordinary Least Squares (OLS), Instrumental Variables (IV) and natural experiments, as suggested by Havranek et al. (2022). The possible differences in reported results among the groups will reveal the extent of attenuation bias.

The second part of my thesis will be dedicated to the analysis of the heterogeneity in the literature. For example, mother’s age at birth appears to influence the individual-level outcomes and the corresponding hypothesis will be tested in my analysis. Effect for fathers could be larger (more negative) for recent data samples, and country-specific samples may play a role. Since my regression will contain a large number of independent variables, many of them will possibly be redundant which would amplify the variance of the estimated coefficients in the frequentist settings. But there is no intuitive way to forecast which variables are be important. The removal of variables based on the sequential t-tests (stepwise regression) is deemed statistically invalid by many. Instead, I will apply the model averaging approach (the Bayesian model averaging approach) to address the model uncertainty, which is intrinsically present in any meta-analysis. On top of that, as a robustness check, I will use the Frequentist model averaging method (Amini & Parmeter, 2012).


Expected Contribution

My contribution is expected to be two-fold: first, I will collect an original dataset since none of the previous studies published their own for replication. I will analyse the recent relevant literature in more detial and argue for reasons for potential publication selectivity. I plan to include wider range of heterogeneity variables than the previous studies, more importantly, those that describe personal attributes of the authors of the primary studies (such as gender). I will attempt to analyse the extent of attenuation bias as well and keep my focus on experimental and quasi-experimental estimates. I will also design the best practice and comment on the true value of the effect based on the mentioned estimate. At each step of my study, I will apply modern methods of meta-analysis.


Outline

• Introduction
• Introducing the topic and describing the effect in previous studies:
I will summarise the most prominent studies and underline the significance of the chosen topic, highlighting the contribution of my analysis and its relevance to the recent labour market trends.
• Data collection and summary statistics:
I will briefly comment on how the data was collected (including search query and inclusion criteria) and provide a description of the most eye-catching patterns.
• Publication and attenuation bias:
After a short introduction to the said biases, I will apply linear and non-linear tests to identify and address the issues (if any will be found).
• What else drives the results?
I will discover the main sources of heterogeneity and derive the best-practice estimate based on the Bayesian model averaging analysis.
• Conclusion