An Empirical Investigation of the Quantity-Quality Model in Mexico Emla Fitzsimons Bansi Malde Institute for Fiscal Studies, London 30th August 2008

Introduction Objective: to estimate the causal effect of family size on children’s education Quantity-quality model (Becker,1960; Becker and Lewis,1973; Becker and Tomes,1976): As quantity (number of children) rises, total cost of quality (investment into children) also rises, thus decreasing the demand for quality  So frequently observed negative correlation b/w family size and child quality consistent with theory 1st instrument is based on parental preferences for having at least one boy. Mention that we experimented with bb but not powerful in first stage

Introduction But fertility is endogenous to empirically test whether family size has a causal effect on quality requires exogenous changes in fertility that are uncorrelated with preferences/budget constraints We use two natural experiments as instrumental variables for family size (1) having successive births of females (2) birth of twins 1st instrument is based on parental preferences for having at least one boy. Mention that we experimented with bb but not powerful in first stage

Related Literature Similar instruments have been used in previous Twins - Rosenzweig and Wolpin,1980 (-); Rosenzweig and Zhang,2006 (-); Li, Zhang and Zu, 2007 (-); Ponczek and Souza,2007 (-); Qian, 2006 (-,+); Cáceres,2006 (-) Sex composition - Angrist, Lavy and Schlosser,2006 (0); Lee, 2004 (-); Baez,2007 (-) Note here I have omitted refs that do not look at children’s educ as outcome

Methodology Estimate the model Y=b0+b1X+b2F+u OLS  b2 biased if omitted variables affect both Y and F So estimate using IV methodology Mention: where Y: 0-1 indicator of child participation in school; years of schooling X: child characteristics such as age, sex, birth order; parental characteristics such as age, education F: family size u: unobserved factors that affect Y and that may be correlated with F Mention: Coefficient of interest is b2 Parent’s preferences an e.g. of omitted vbles

F = a0 + a1g2 + a2g3 + a3g1g2g3 +a5t3 + a6X + u Methodology We consider first- and second-born children separately; also separately by sex Instruments for family size: First-born girls Exogenous increase in family size from 2 to 3: - 1st 2 births are females; twins at 2nd birth F = a0 + a1g1g2 + a2t2 + a3X + x First- and second-born girls Exogenous increase in family size from 3 to 4: - 1st 3 births are females; twins at 3rd birth F = a0 + a1g2 + a2g3 + a3g1g2g3 +a5t3 + a6X + u Parent’s preferences an e.g. of omitted vbles The 2nd 1st stage eqn is for first-borns: for second-borns, practically the same but control for g1 instead of g3. I wouldn’t even go into this unless someone is confused and asks! F = a0 + a1g1 + a2g3 + a3g1g2g3 +a5t3 + a6X + u Mention: the gg instrument assumes parents want to have at least one boy, which is valid in our context Mention that in this way we can test sensitivity of 1st born girl results to different instruments F = a0 + a1g1g2 + a2t2 + a3X + x F = a0 + a1g2 + a2g3 + a3g1g2g3 + a5t3 + a6X + u

Methodology First-born boys Exogenous increase in family size from 2 to 3: - twins at 2nd birth First- and second-born boys Exogenous increase in family size from 3 to 4: - twins at 3rd birth Parent’s preferences an e.g. of omitted vbles Mention: the gg instrument assumes parents want to have at least one boy, which is valid in our context F = a0 + a1g1g2 + a2t2 + a3X + x F = a0 + a1g2 + a2g3 + a3g1g2g3 + a5t3 + a6X + u

Data Cross-sectional socio-economic Census data collected across households in marginalised rural areas throughout 31 states in Mexico b/w 1996 and 1999 (ENCASEH) School participation and years of schooling of 12-17 year olds Sample of 617,807 households across 42,186 villages Large samples contained in these data are extremely advantageous and provide us with sufficient variation in these 2 random events Note sample selection: drop households in which both parents are not married, households in which the eldest child is 18 or above, households that reported more than one household head and some suspect observations.

Is sex composition random? Comparison of mean characteristics by sex composition of 2 first-borns, for hhs with female first-borns Female, male=1 female=1 Difference Father’s age 40.979 40.976 -0.002 Mother’s age 36.878 36.86 -0.018 Mother’s age at first birth 21.805 21.777 -0.028 Father’s years of education 3.691 3.687 -0.003 Mother’s years of education 3.326 3.32 -0.006 Birth spacing b/w 1st and 2nd children 2.831 2.833 0.002 Family size 4.186 4.249 0.063* Explain what family size is; here we do really well despite v large sample sizes Put * when diffs signif

Difference after matching Are twin births random? Comparison of mean characteristics by twins at 2nd birth Twins at second birth=0 birth=1 Difference Difference after matching Father’s age 41.036 42.215 1.179* 0.106 Mother’s age 36.926 37.939 1.013* 0.880* Mother’s age at first birth 22.272 23.236 0.963* 0.015 Father’s years of education 3.68 3.736 0.056 0.032 Mother’s years of education 3.315 3.488 0.174* 0.079 Birth spacing b/w 1st and 2nd children 2.825 3.346 0.521* 0.492* Family size 4.242 4.583 0.341* 0.367* Explain how we do the matching Mention that we get a similar picture when we look at ggg, twins at 3rd birth etc For father’s age and mother’s age in final column, we control for mother’s age at first birth

Results - School participation FEMALE FIRST-BORNS 12-14 15-17 LPM IV1 IV2 Family size -0.025** (0.001) -0.001 (0.016) -0.031 (0.030) -0.023** (0.025) -0.059+ (0.033) N 88,649 78,701 95,850 87,273 Over-identification test - 0.588 1.223 0.043 0.810 First stage 2nd birth girl 0.149** (0.009) 0.107** (0.012) 2nd birth twins 0.694** (0.061) 0.459** (0.066) 2nd and 3rd births girls 0.083** (0.017) 0.087** (0.020) 3rd birth twins 0.646** (0.057) 0.603** (0.069) F test 192.09 69.58 61.92 48.65 - We are showing trimmed results throughout Estimate using linear IV - results robust to non-linear IV Std errors clustered at village level Stress that we have v strong 1st stages throughout; also we can do overid tests for females

Results - School participation MALE FIRST-BORNS 12-14 15-17 LPM IV1 IV2 Family size -0.021** (0.001) -0.025 (0.043) 0.021 (0.027) -0.015 (0.041) 0.048 (0.040) N 93,593 82,119 112,929 102,254 First stage 2nd birth twins - 0.450** (0.065) 0.440** (0.057) 3rd birth twins 0.581** (0.061) 0.496** (0.054) F test 47.51 91.34 58.72 83.31

Results - School participation SECOND-BORNS FEMALES 12-14 MALES 12-14 LPM IV Family size -0.027** (0.001) -0.039 (0.027) -0.021** -0.038 (0.039) N 83,151 86,039 Over-identification test - 0.217 First stage 3rd birth girl 0.105** (0.019) 3rd birth twins 0.640** (0.069) 0.467** (0.061) F test 52.89 59.62 Mention that 15-17 not robust - weak 1st stage - so we don’t consider them

Results - Years of schooling FEMALE FIRST-BORNS 12-14 15-17 OLS IV1 IV2 Family size -0.104** (0.004) 0.081 (0.084) 0.081 (0.110) -0.166** (0.006) 0.059 (0.128) -0.067 (0.152) N 91,429 91,888 99,885 99,993 Over-identification test - 0.955 0.917 0.077 0.196 First stage 2nd birth girl 0.143** (0.009) 0.105** (0.011) 2nd birth twins 0.675** (0.060) 0.450** (0.065) 2nd and 3rd births girls 0.072** (0.016) 0.075** (0.018) 3rd birth twins 0.623** (0.050) 0.581** (0.063) F test 191.02 82.80 61.54 48.59 I would go v quickly through these results

Results - Years of schooling MALE FIRST-BORNS 12-14 15-17 OLS IV1 IV2 Family size -0.106** (0.004) 0.347* (0.159) -0.104 (0.104) -0.159** (0.005) 0.061 (0.187) 0.162 (0.199) N 95,961 95,269 117,506 117,118 First stage 2nd birth twins - 0.443 (0.068)** 0.441**(0.056) 3rd birth twins 0.597** (0.054) 0.499** (0.048) F test 42.42 122.47 62.01 110.21

Results - Years of schooling SECOND-BORNS FEMALES 12-14 MALES 12-14 OLS IV Family size -0.114** (0.004) 0.154 (0.099) -0.112** (0.005) -0.107 (0.143) N 85,803 88,272 Over-identification test - 0.552 First stage 3rd birth girl 0.112** (0.019) 3rd birth twins 0.626** (0.067) 0.473 (0.061)** F test 55.46 59.98

Identification assumption Sex composition of first n births / twin births have no direct effect on children’s education. Only affect it through effect on family size Concern – economies of scale from same-sex children? If so, this may affect household resources and thereby education (Rosenzweig and Wolpin, 2000) May bias upwards the effects of family size on education Mention Rosenzweig and Zhang,2006 if someone mentions lower birthweight

Validity of Instruments Any evidence of economies of scale, for example via sharing of clothing? Can look at this using Mexican data set PROGRESA, where we observe expenditures on children’s clothing and shoes, separately by sex 2 (reassuring) things to note:  only 2.2% (2.1%) of total household expenditure is on children’s clothing (shoes)  in our sample, amongst gg=1 households: ave # girls=3.1, ave # boys=1.2 gb=1 households: ave # girls=2.1, ave # boys=2.1 - large family sizes in both - so similar opportunities for economies of scale in both? Progresa much smaller sample but can think of it as representative of ours Mention we’re considering v poor rural hhs, so this argument less valid Stress that hhs are really spending v little on these goods to begin with so alleviates concerns about extent of importance of ec of scale

Validity of Instruments Compare monthly expenditures across households with gg=1 and gb=1 Notes: tobit estimation; control for total household expenditure, family size Expenditure on Food Non food Children’s clothing shoes gg -9.197 (9.122) 7.573 (8.660) 0.844 (1.997) -0.563 (1.30) N 1,977 1,970 1,966 Detail: gg=1: ave # girls=3.3, ave # boys=1.3 gb=1: ave # girls=2.2, ave # boys=2.2 Mention: observe no statistical differences in children’s clothing or shoes (or in food, which we wouldn’t expect to have observed – though maybe boys consume more calories etc so not so clear to me)

Ongoing Work 1. Obtain bounds on the IV parameter estimates, for different correlations b/w the instruments and model errors - do this using method of Ashley (2007): provide ‘guess’ as to sign and size of correlation b/w endog vble and error term 2. Additional instruments (1st 4 births female; twins at 4th birth) 3. Child labour as an outcome (Deb and Rosati, 2004; Ponzcek and Souza, 2007) Apart from deeper investigation of economies of scale work, here is what we’re planning to do Note as far as I can see Ashley is unpublished – I saw ages ago that it’s forthcoming in J of Applied Econometrics, but I can’t find that anymore! If someone asks, it’s definitely an 07 working paper Child labour: mention that only these 2 papers take into a/c endogeneity of family size and consider effects on child labour