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How the Allocation of Children s Time Affects Cognitive and Non-Cognitive Development Mario Fiorini, University of Technology Sydney Michael P. Keane, University of Oxford October 16, 2012 Abstract The

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How the Allocation of Children s Time Affects Cognitive and Non-Cognitive Development Mario Fiorini, University of Technology Sydney Michael P. Keane, University of Oxford October 16, 2012 Abstract The allocation of children s time among different activities may be important for their cognitive and non-cognitive development. In our work we exploit time use diaries from the Longitudinal Study of Australian Children to study the effect of time allocation across a wide range of alternative activities. By doing so we characterize the trade-off between the activities to which a child is exposed. On the one hand, our results suggest that time spent in educational activities, particularly with parents, is the most productive input for cognitive skill development. On the other hand, non-cognitive skills appear insensitive to alternative time allocations. Instead, these skills are greatly affected by the mother s parenting style. We wish to thank Frank Wolak, Katrien Stevens, Jennifer Bowes and seminar participants at the NBER summer institute 2010, the University of New South Wales, the University of Sydney, Queensland University of Technology and the University of Wollongong for helpful comments. 1 Introduction In the last decade a number of research studies have found that skills measured at early ages (e.g., age 3 to 6) are strong predictors of later life outcomes such as educational attainment, wages, employment, and choice of occupation; as well as adolescent risky behaviors such as teenage pregnancy, criminal activity, smoking and alcohol use. The factors found to predict later outcomes include both cognitive and non-cognitive skills (e.g., perseverance, motivation, risk aversion, self-esteem). Examples of these findings can be found in the work by Cameron and Heckman (1998, 2001), Keane and Wolpin (1997), Bernal and Keane (2011, 2010), Heckman, Stixrud, and Urzua (2006a),Cunha, Heckman, and Lochner (2006). Given the growing evidence of the importance of early childhood skills for later life outcomes - particularly economic outcomes - there has been a growing interest in investigating the determinants of these skills. Many studies have focused on how early childhood activities, as well as other influences like household income, school quality, child care, etc., affect the development of skills or abilities. However the current literature is confronted with two main problems. First is the difficulty of measuring all of of a child s activities, not to mention the many other inputs to child development. Second is the empirical problem of distinguishing a mere correlation between activities and skills from a true causal effect. To illustrate this, let us define the production function for skill Y of individual i observed at age a as: Y ia = X i{k a}θ {K a} +γ a µ i +ǫ ia (1) where X is the matrix of K inputs from ageabackwards (the complete history of inputs), µ i is the innate ability/personality of the child (at age 0) and ǫ is a transitory error term that captures shocks to the child development path. The inputs in X can be time inputs, such as time in school or with parents; goods inputs, such as number of books, intake of calories; and measures of the quality of these inputs, such as, e.g., parental education or teacher-student ratios. The first problem, measurement of a child s activities, originates from the fact that most surveys include only a limited amount of information about what a child does, where and with whom. As a result, researchers have tended to focus on the effect of just a few of the many inputs into child development, and to group child time into very broad categories, such as time spent with the mother vs. time spent in child care. This is problematic however, because the estimated effect of any input depends on what other inputs are omitted in the equation. To clarify this point, consider a simple world where a child s time T can only be 1 allocated between child care T C, time with parents T P and time watching television alone T V, so that T C +T P +T V = T. For simplicity, consider the special case where time not in child care is equally shared between time with parents and time watching television, so thatt P = T V = T T C 2. Finally, let these three time inputs, and a latent ability endowment µ (likely correlated with thetime inputs), beall that matter in thedevelopment ofskill Y, so that the production function is simply Y i = β 0 +β C T ic +β P T ip +β V T iv +γµ i +ǫ i where ǫ i is orthogonal to all other variables. A researcher, who has imperfect knowledge of this simple world, but who is interested in the effect of child care on skill Y, might estimate Y i = γ 0 + γ C T ic + u i. Suppose the researcher is lucky enough to have a consistent estimator for γ C such that p N γ lim C = γ C, and finds that γ C 0. It is tempting to conclude that child care is good for the child. Yet, it is easy to show that in our simple ). Thus γc is a relative effect. Whether or not child care is world γ C = β C ( β P +β V 2 beneficial to the child depends on what substitutes for child care. 1 For instance, let β C = 2, β P = 3 and β V = 0. As a result γ C = 0.5 0. But spending time in child care increases Y only if child care substitutes for time watching television (since β C β V ). In contrast, child care lowers Y if it substitutes for time with parents (since β C β P ). This simple world could be generalized to several activities and to goods inputs, where, given a financial constraint, parents substitute one good for another. In any case, the estimated coefficient of the observed input captures an effect relative to that of the unobserved/omitted inputs that act as substitutes. Thus, when a researcher studies the effect of a few inputs in isolation what we learn might be quite limited or misleading, even if the estimator is consistent. Our aim is to extend earlier work by estimating child (cognitive + non-cognitive) skill production functions with a much richer set of time and other inputs than in previous work. To do so we exploit diary data contained in the Longitudinal Study of Australian Children (LSAC), a survey following a cohort of children born in 1999 and surveyed biannually since The LSAC includes 24-hour diaries where parents provide information about what the child is doing, where and with whom. It also contains exceptionally rich data on other inputs to child development. In the first component of this paper we analyze the diary data to get a better view of how Australian s children spend their time during a typical week. This has a value in itself because there are not many studies documenting children s time use. In the second and main component of our research we link the diary data to cognitive and non-cognitive measures of ability, demographics, and parental background information. This additional data is provided in the LSAC main survey. We then investigate whether alternative time 1 More generally, let α be the share of time not in child care that is spent with the parents. Then T P = α(t T C ) and T V = (1 α)(t T C ). It follows that γ C = β C αβ P (1 α)β V. 2 allocations lead to different levels of cognitive and non-cognitive development: e.g. time with parents vs other adult relatives, time in educational vs. other activities, time with other children vs time using media, etc. Thus, our production function can be expressed as follows: Y ia = TI i{k a}β {K a} +PB i{g a}δ {G a} +e ia (2) where TI is a matrix of K time inputs measured from age a backwards while PB is a matrix of G parental background characteristics (that proxy for both goods inputs and innate ability µ i ) and parenting style measures. The error term e, includes omitted variables, measurement error and shocks to the child development path. We construct the K time inputs such that K k=1 TI ia{k} = 168, the number of hours in a full week. By explicitly modeling the complete weekly time allocation we are able to rank time inputs according to their productivity: a ranking of the β {a} vector is informative about how a reallocation of a child s time from unproductive (bottom ranked) to productive (top ranked) time inputs at age a can enhance skill development. In other words, we characterize the trade-off between all alternative activities, home and school, to which a child is exposed. To our knowledge, this research is the first to estimate the effect of alternative overall time allocations on children s development - as opposed to examining effects of only one or two time inputs in isolation. As we will see, from an econometric point of view the paper which is closest to ours is Todd and Wolpin (2007). However, their work differs from ours in that they do not attempt to estimate the effects of a range of alternative time allocations and other inputs. Instead, they proxy for a wide range of inputs into child development using the home environment index (HOME) in the US National Longitudinal Survey of Youth. All home inputs are proxied by this scalar index, obtained by adding up responses to a battery of questions about the home environment. In addition, school inputs are proxied by state and county level information on pupil-teacher ratios. We believe there are three important ways in which our work goes beyond Todd and Wolpin (2007). First, our measures of child inputs are more extensive. Note that the HOME index still fails to measure many important home inputs, such as the amount of time the child spends in activities with mothers and other care givers, the amount of time spent watching TV or playing video games, etc.. Second, our input measures are more concrete. For instance, it is not at all clear what levers a parent or a policy maker would have to pull to move the HOME index. But time in child care, length of the school day, etc. can be altered in obvious ways. Third, we are able to characterize the trade-off between alternative home inputs (e.g. TV time versus parents time), which one cannot 3 do using one scalar HOME input. The second problem faced by the literature, distinguishing a mere correlation between activities and skills from a true causal effect, is also very severe. In equation (1) endogeneity can come in three forms: (1) omitted variables, since we do not observe µ or some of the other inputs in X; (2) simultaneity, if Y causes X and not vice versa (e.g. does reading books make children smarter or, do smart children read more books?); (3) measurement error in X, e.g. it is legitimate to ask whether the parent knows exactly (or truthfully reports) how many hours the child spent reading. The literature has proposed different estimation strategies to deal with these problems. The papers by Todd and Wolpin (2003, 2007) specify a production function where a test score is a function of home and school inputs together with unobserved initial ability. They then discuss a set of non-nested estimators and the assumptions under which each of these estimators identifies the production function. The set of estimators include OLS, Fixed Effects (within family and within child) and Value Added, among others. They attempt to address the identification problem by comparing results from these different statistical models. Since they have no strong prior on what model best deals with endogeneity, Todd and Wolpin (2007) pick the model that minimizes the out-of-sample root mean-squared error(rmse). They then focus on inferences from the preferred model. Our objective is rather different. That is, we will eschew any attempt to choose a best model, as any criterion we could use would necessarily be controversial. 2 Rather, our goal is to determine whether there exists a ranking of inputs that is robust across the whole range of the most popular models used in the literature (e.g., value added, fixed effects, etc.). As each estimation method attempts to handle endogeneity in a different way, relying on different maintained assumptions, we would have more confidence in a ranking of inputs that is robust across methods. A robust ranking of the time inputs, if it exists, implies that a reallocation of time use can enhance child development. 3 The simple example we presented earlier shows that analyzing one input in isolation conveys only partial and potentially misleading information because we cannot characterize the trade-off between inputs. We have argued that this makes it important to try to measure all of a child s activities. Clearly, having multiple endogeneous inputs makes the 2 For instance, the RMSE criterion used by Todd and Wolpin (2007) chooses the best model based on fit, but the best fitting model does not necessarily deal with the endogeneity issues. 3 The papers by Cunha and Heckman (2007, 2008) propose a different approach in order to investigate the self-productivity and dynamic complementarities between cognitive and non-cognitive skills. They use a system of equations where future cognitive and non-cognitive skills are simultaneously determined by their current level (self and cross), a measure of the current parental investment and unobserved inputs. Identification in their system relies on cross-equation covariance restrictions. We do not replicate Cunha and Heckman (2007, 2008) strategy inasmuch as it is not our aim to uncover self-productivity and dynamic complementarities between cognitive and non-cognitive skills. Moreover we are interested in the effect of several (K) alternative time inputs rather than a one dimensional investment factor. 4 estimation problem much more difficult. If our model contained just one endogenous input, then an instrumental variable or equally suitable quasi-natural experiment approach might be possible. But estimating the entire β vector in equation (2) by IV requires K 1 exclusion restrictions. 4 Finding such a large set of valid instruments is not feasible in our application. Even if we could overcome the highly difficult task of finding such a set of instruments, the interpretation of the Local Average Treatment Effects would be very problematic. Therefore, we feel that in rich models like ours it is more practical to deal with endogeneity using other approaches (e.g. fixed effects, value added models) combined with sensitivity analysis. 5 Our results suggest that time spent in educational activities, particularly with parents, is the most productive input for cognitive skills. A reallocation of children s time which favors these kinds of activities by substituting away from less productive ones would have a positive effect on cognitive skill. This result is robust to different identification assumptions. Perhaps surprisingly, we also find that, for reading skills, media time does not appear to be any worse that other non-educational time uses, like time in before/after school care. However, non-cognitive skills like behavioral problems, social skills and emotional problems appear insensitive to alternative time allocations. Instead, these skills greatly depend on some aspects of parenting style. A style that combines effective (but not harsh) discipline with parental warmth leads to the best non-cognitive outcomes. This finding on parenting style is new in the economics literature. 2 Data The Longitudinal Study of Australian Children (LSAC) is a biannual survey which began in The LSAC follows two cohorts of children: one born March 1999-February 2000 (4983 children) and one born March 2003-February 2004 (5107 children). These are known as the K cohort and the B cohort. Both cohorts have been surveyed three times, in2004, 2006and2008(a fourthsurvey iscurrently inthefield). Table 1illustrates the average age at interview for each Cohort/Wave pair. For both cohorts the survey collected a rich set of information about the children s 4 Instruments also have to satisfy the monotonicity assumption (i.e. following a change in the value of the instrument all parents have to re-allocate their children s time in the same way). For further discussion, see Heckman, Urzua, and Vytlacil (2006b) and Imbens and Angrist (1994). 5 We do not mean to say that IV would necessarily be the preferred approach if it were feasible. On the contrary, even if IV were feasible, it would merely provide another alternative method of dealing with endogeneity whose advantages/disadvantages would have to be compared to the other approaches we employ. Like them, IV is not assumption free. The Journal of Economic Perspectives, 2010, 24(2), has an excellent discussion on this topic. The point we are trying to make is that an IV approach is hardly an option in our context. 5 Table 1: Average Age at Interview Wave 1 Wave 2 Wave 3 K Cohort 4 years and 9 months 6 years and 10 months 8 years and 10 months B Cohort 9 months 2 years and 10 months 4 years and 10 months skills, demographics and parental background. In addition, the LSAC collected time use diaries, where parents recorded their children s activities over 24 hours. As far as we are aware, the only other data set combining information on children s skills/background with time use diaries is the US Child Development Supplement (CDS), a sample of children from households in the PSID. The CDS included time use diaries in 1997 (0-12 yearold children), in 2002 (5-18 year-olds) and in 2007 (10-19 year-olds). Compared to the CDS, LSAC has the advantage of focussing on only two cohorts with a larger sample size. LSAC children are generally much younger than those in the CDS, who were born between LSAC children are also surveyed biannually in contrast to the five year gap between the two waves of the CDS. This makes the LSAC an excellent data set to analyze early childhood development. In the rest of the paper we limit our attention to the K Cohort. The data for the younger B Cohort lack consistent measures of skill because the type of test changes across waves. This prevents us from using some estimators like Value Added and Fixed Effects. 2.1 Time Use Diaries The Time Use Diary(TUD) collects details ofthe activities of thestudy children inlsac over two 24-hour periods: one a specified weekday and one a specified weekend day. After the LSAC personal interview, the respondents were left with some self-complete forms, including the Time Use Diaries. The interviewer worked through an example of how to complete the diary with the respondent, and the respondent was advised of the dates for which they should complete the diary. These dates were selected by the interviewer to ensure a random allocation of weekdays and a random allocation of weekend days. The diaries divided the 24-hour day into minute intervals. 6 For each child the diaries classified separately the activity (26 alternatives), where the activity took place (5) and who with (7). Most diaries were completed by the child s 6 Parents were given specific dates to fill the diary, like Tuesday-July 26 for the weekday diary and Saturday-July 30 for the weekend diary. They were also asked if they could not complete the diary on their allocated date to wait another week before completing it, such that the completion day was on the same day of the week as was the date selected for them. The objective was to have an even distribution along the 5 weekday days and along the 2 weekend days. We assume the activity recorded in each time period lasted for the full 15 minutes. This may result in an overestimation of time spent in specific activities, when those activities take less than 15 minutes. 6 mother (approx 91%), with 7% completed by the child s father. The remaining 2% were completed by other family or carers. This is stable across waves Original and Re-coded Time Use Figure A-1 in the Appendix gives an example of the diary and its coding. This is the examplethatparentswereshown. Thediariesdidnotchangebetween waves 2and3. The diary at wave 1 (see figure A-2) is slightly different to account for age specific activities. If we divide the day into activities, where they took place and who they were w

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