## Abstract

Since 1963, changes in the family composition of the US labor force explain more than half of the variability in US total factor productivity growth. Using the Current Population Survey Annual Social and Economic Supplement, we document the rise of two (and single) working-parent families in the USA. We augment a standard growth-accounting equation to differentiate between parental and nonparental labor inputs and find that accounting for the parental composition of the labor force explains roughly 50 % of total factor productivity growth, the productivity slowdown of the 1970s, and the productivity rise of the 1990s. The parental composition of the workforce also helps to explain labor productivity differences across US states while controlling for differences in the age and gender profile of workers across states does not.

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## Notes

These time demands are nontrivial and to the extent that they are mismeasured may also imply that the labor input to production is misreported. Bureau of Labor Statistics (BLS) attempts to control for actual labor effort by constructing data from the Hours at Work Survey (HWS) rather than from payroll data. However, there are at least two reasons to be suspicious of the HWS data. First, the response rate for the survey appears to be in continual decline, from 75 % in 1994 to 50 % in 2000. Second, the survey sample is small, encompassing only 5,500 establishments.

We are not seeking to explain fertility decisions but are instead using fertility and the family structure to explain total factor productivity growth. Since fertility operates with a lag of typically three quarters (not accounting for delays between the decision and the initiation), we do not believe that realized total factor productivity growth is endogenously linked to live births. Moreover, there seems little reason to suspect that labor force shares, the explanatory variables that we use, are endogenously related to TFP growth. Nevertheless, we test for, and reject, the endogeneity of labor force shares. We acknowledge that parents may have different and changing incentives to engage in full-time work that are unrelated to TFP.

We pool monthly data from the CPS over the period from January 2000 until April 2007. While this time period does not cover the entire period of the sample discussed in Section 3, we believe it is sufficient to support the argument that parents and nonparents may be different labor inputs. Moreover, not all data we report are collected over our entire sample. While we acknowledge that CPS data have some drawbacks, time-use diary data of which we are aware are not appropriate for our study because spousal labor market data are not collected.

These results may be somewhat suspected as they are based on a sample of roughly 50,000 observations out of a possible sample of 1.5 million individuals. The overwhelming majority of respondents are coded as Not-in-Universe. We also acknowledge that 3.9 % of female nonparents took maternity leave. We argue that this may reflect the timing of the question—are women who are pregnant not counted as parents?

Clearly, \(\lambda^\textrm{n} = 1 -\lambda^\textrm{p}\) and we could rewrite our growth equation accordingly. We choose not to do so because at this point, we are simply motivating a decomposition and not an estimation strategy.

The dataset is available at www.bls.gov/mfp/ under the title Historical multifactor productivity measures.

The BLS methodology is described in www.bls.gov/mfp/mprtech.pdf, see in particular page 3.

As a preliminary step, we confirm that female labor force shares are not statistically significant explanatory factors by regressing female labor force participation against TFP growth and find that the increase in female labor force participation does not explain TFP growth. We obtain a coefficient estimate that is not significantly different from zero at a 10 % level of significance and an

*R*^{2}of 0.04 (results available from the authors upon request). We also estimate the female share of the workforce against TFP growth and find the same conclusion.Subfamilies account for roughly 2 % of our sample.

We conduct a robustness check in which we set \(\bar{l} =25\) and find almost no difference in our results.

See, for instance, chapter 10 of the

*BLS Handbook of Methods, Bulletin 2490*. Admittedly, the terminology used in chapter 10 is a little vague, so we contacted the BLS and received assurances that our interpretation is correct.Our method of interpolation does not appear to affect our results. Using equal weights gives almost identical results. Birth data are reported in

*Vital Statistics of the United States, Volume I, Natality, 1994–2002*. We are unable to find quarterly birth records prior to 1994 though we are not too concerned as there is relatively little variation in quarter weights across available years.We note that there is no scope for parental productivity to be included indirectly in the error term of Eq. 14 and thus no obvious correlation between the regressors and the errors. Although the argument is mathematical in nature, it suffices to note that parental productivity is explicitly linked to the shares of parents and thus including these shares as

*data*precludes such a correlation. We note that there would, however, be correlation present in any regression based on demographic regressors that did not include the shares of parents since the shares of parents are correlated with age and gender cohort shares if parents have different productivity profiles.Here and throughout the paper, we define the age of child as the age of the youngest child in the family.

We are also concerned by the discontinuous jump in labor force shares in 1968 and 1994/95, and we also estimate our models without these observations. We find that the results of these regressions tend to increase both the level and significance of our estimated coefficients. The results of these regressions are available from the authors upon request.

We note that one could argue that the estimating equation should include a constant intercept in addition to the time-varying intercept measured by the labor share. Including a constant improves the significance of our parental share estimates but does not change our qualitative results. It does, however, lower our estimated true TFP growth to 1.3 %.

One advantage of their test is that it tests against a large class of breaking processes. A second advantage is that it appears to have reasonable size and power properties in small samples. We thank Baum (2007) for code to implement the qll test.

We note that this approach also captures demographic changes in the labor force since the shares of individuals in cohorts are highly correlated with total cohort shares.

These results are available upon request to the authors. We do not report them here as they do not change our conclusions and also because the small number of annual observations likely render these results probative. We address the distinction between family shares and female shares in Section 6.

Tests for autocorrelation and ARCH effects in our residuals suggest that neither is present.

We also conduct IV regressions using lagged values of the labor force shares as instruments and find no evidence that labor force shares are endogenous. However, our coefficient estimates in the second stage regression are less precise and this is one area, in particular, where more observations would help refine the results.

We choose a smoothing parameter of 6.25, as suggested by Ravn and Uhlig (2002), because we have annual data.

We thank C. Baum, M. Schaffer, and S. Stillman for making publicly available the Stata code, ivendog, to calculate the test statistic and Stata code, ivhettest, and to calculate the Pagan–Hall test statistic.

These results in detail are available upon request from the authors.

The labor supplied by various groups is highly autocorrelated—a simple one-period autoregressive model returns a autocorrelation coefficient of 0.98 for the labor supply of both parents of young children and parents of older children.

Over the sample period examined here, the CPS changed the state identification such that smaller states in similar geographic regions are aggregated and thus we have only 21 separate observations by year 1970–2006 (the construction of the regions and a summary of the state-level data are in the Appendix in Tables 6 and 7, respectively).

BEA data obtained from www.bea.gov/regional/gsp/doi.02/2009. Real data at the state level were not available for a sufficient sample period.

Theoretically, we should choose to include lags,

*m*> 0, of our dependent variable if the residuals in our regression model exhibit autocorrelation. Simple diagnostic tests on the residuals from a regression without lagged terms suggest that the residuals are autocorrelated. See Drukker (2003) and Wooldridge (2002).We used the data presented in Han et al. (2007) to construct this dummy variable.

Nickell (1981) shows that the asymptotic bias of these estimators is

*O*(1/*T*) in standard dynamic panel data. Alvarez and Arellano (2003) suggest limited information maximum likelihood (LIML) estimators perform best in finite samples if N and T both tend to infinity. However, McKenzie (2004) shows that fixed-effect estimators are consistent in dynamic pseudopanel data and arguably the state labor productivity data is a pseudopanel. Nevertheless, for completeness, we present both OLS and LIML estimation results. We thank Schaffer (2007) for code to implement the panel estimators.We do not report the estimates for the lagged average labor productivity, year dummies, nor the included dummy variables above to conserve on space. The full results are available upon request to the authors.

The unweighted single-state results are skewed a little due to differences between the working parent effects for California, New York, and Texas. Using either transfer-to-income ratios or workforce weights (or both) yields significant results for the effect of working parents on labor productivity.

The birth data were retrieved from the Birth Data Files accessed doi. 21/07/10 at http://www.cdc.gov/nchs/data_access/vitalstats/VitalStats_Births.

## References

Alvarez J, Arellano M (2003) The time-series and cross-section asymptotics of dynamic panel data estimators. Econometrica 71:1121–1159

Angrist J, Evans W (1998) Children and their parents’ labor supply: evidence from exogenous variation in family size. Am Econ Rev 88(3):450–477

Arellano M, Bond S (1991) Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Rev Econ Stud 58: 277–297

Barro R (1991) Economic growth in a cross-section of countries. Q J Econ 106(2):407–443

Barro R (1996) Democracy and growth. J Econ Growth 1(1):1–27

Barro R, Lee JW (1994) Sources of economic growth. Carn-Roch Conf Ser Pub Pol 40:1–46

Baum CF (2007) qll: Stata module to perform Elliott-Müller efficient test for general persistent time variation in regression coefficients. http://ideas.repec.org/c/boc/bocode/s456862.html

Becker GS (1988) Family economics and macro behavior. Am Econ Rev 78(1):1–13

Bianchi S, Robinson J, Milkie M (2006) Changing rhythms of American family life. Am Soc Assoc Rose Series in Soc, Russell Sage Foundation Publications

Bruno M (1984) Raw materials, profits, and the productivity slowdown. Q J Econ 99(1):1–30

Davidson R, MacKinnon JG (2004) Econometric Theory and Methods, Oxford University Press, New York

Drukker DM (2003) Testing for serial correlation in linear panel-data models. Stata J (3)2:1–10

Durlauf SN, Quah D (1999) The new empirics of economic growth. In: Taylor JB, Woodford M (eds) Handbook of macroeconomics vol 1A. Elsevier, Amsterdam, pp 231–304

Elliot G, Müller U (2006) Efficient tests for general persistent time variation in regression coefficients. Rev Econ Stud 73:907–940

Feyrer J (2007) Demographics and productivity. Rev Econ Stat 89:100–109

Feyrer J (2011) The US productivity slowdown, the baby boom, and management quality. J Popul Econ 24:267–284

Griliches Z, Jorgenson DW (1966) Capital theory, technical progress and capital structure. Am Econ Rev 56(2):50–61

Han WJ, Ruhm C, Waldfogel J (2007) Parental leave policies and parents employment and leave-taking. IZA D Paper 3244

Kleibergen F, Paap R (2006) Generalized reduced rank tests using the singular value decomposition. J Econometrics 133:97–126

Kogel T (2001) Youth dependency and total factor productivity. MPIDR WP 2001–030

McKenzie DJ (2004) Asymptotic theory for heterogeneous dynamic pseudo-panels. J Econom 120:235–262

Nickell S (1981) Biases in dynamic models with fixed effects. Econometrica 49:1417–1426

Nordhaus WD (2002) Productivity growth and the new economy. Brookings Pap Econ Act 2002(2):211–244

Papp KK, Stoller EP, Sage P, Aikens J E, Owens J, Avidan A, Phillips B, Rosen R, Strohl KP (2004) The effects of sleep loss and fatigue on resident-physicians: a Multi-institutional, mixed-method study. Acad Med 79(5):394–406

Ravn M, Uhlig H (2002) On adjusting the Hodrick-Prescott filter for the frequency of observations. Rev Econ Stat 84(2):371–375

Schaffer ME (2007) xtivreg2: Stata module to perform extended IV/2SLS, GMM and AC/HAC, LIML and k-class regression for panel data models. http://ideas.repec.org/c/boc/bocode/s456501.html

Schone P (2009) New technologies, new work practices and the age structure of the workers. J Popul Econ 22:803–826

Simonsen M, Skipper L (2006) The costs of motherhood: an analysis using matching estimators. J Appl Econ 21(7):919–934

Stock JH, Yogo M (2005) Testing for weak instruments in linear IV regression. In: Andrews DWK, Stock JH (eds) Identification and inference for econometric models: essays in honor of Thomas Rothenberg. Cambridge University Press, Cambridge, pp 80–108

Waldfogel J (1998) Understanding the family gap in pay for women with children. J Econ Perspect 12:137–156

Wolff EN (1996) The productivity slowdown: the culprit at last? Follow-up on Hulten and Wolff. Am Econ Rev 86(5):1239–1252

Wooldridge JM (2002) Econometric analysis of cross section and panel data. MIT Press, Cambridge

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## Additional information

*Responsible editor:* Alessandro Cigno

We gratefully thank, without implicating, Kim Huynh, Gregor Smith, Krishna Pendakur, Brian Krauth, David Andolfatto and two anonymous referees for insightful comments on earlier drafts. Any errors or omissions are our own.

## Appendices

### Appendix

### Aggregation of states

Our state-level results are based on an aggregation by the CPS of small states (at least in 1967) in geographically similar regions. As noted in the text, the CPS does not collect data over the sample period for each state individually. The exact groupings are reproduced in Table 6 (we do not calculate labor productivity for the reference State, Washington, DC). Table 7 presents some summary statistics for working parent shares across states.

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Dunbar, G.R., Easton, S.T. Working parents and total factor productivity growth.
*J Popul Econ* **26**, 1431–1456 (2013). https://doi.org/10.1007/s00148-012-0426-8

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DOI: https://doi.org/10.1007/s00148-012-0426-8

### Keywords

- Total factor productivity
- Growth accounting
- Working parents
- Productivity slowdown

### JEL Classification

- E23
- E32
- O47