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03.20.2013 - Flavio Cunha

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Eliciting Maternal Beliefs about the Technology of Skill Formation

Eliciting Maternal Beliefs about the Technology of Skill Formation


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  • 1. Eliciting Maternal Beliefs about the Technology of Skill Formation Jennifer Culhane, Flávio Cunha, and Irma Elo CHOP and University of Pennsylvania March 2013
  • 2. Inequality in Skills Arise Early in Life of Individuals Figure   Dynamics of Cognitive Skills For Different Groups of Permanent Income 0.8 0.6 0.4 0.2 0.0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ‐0.2 ‐0.4 ‐0.6 ‐0.8 Bottom Quartile Second Quartile Third Quartile Top Quartile
  • 3. Inequality in Skills and Inequality in Investments Investments in Human Capital of Children by Quartiles of Permanent Income .8 .6 .4 .2 0 0 1 2 3 4 5 Investments (hours per day) kdensity Bottom kdensity Second kdensity Third kdensity Top
  • 4. Figure Choice Set and Preferences 120 100 Preferences 80Other Expenditures 60 40 Choice Set 20 0 0 5 10 15 20 25 30 35 40 Child Development
  • 5. Parental Information about the Technology of SkillFormation 1. Iodine De¢ ciency:Field, Robles, and Torero (2009); Roy (2009). 2. The 1964 Surgeon General Report on Smoking: Aizer and Stroud (2010). 3. Time spent and appropriateness of activities: Kalil, Ryan, and Corey (2012).
  • 6. Figure Choice Set and Preferences 120 Red: Mother underestimates returns 100 Blue: Mother has unbiased returns 80Other Expenditures 60 40 20 0 0 5 10 15 20 25 30 35 40 Child Development
  • 7. The Technology of Skill Formation I Let xi denote investment. I Let qi ,0 denote the human capital of the child at birth. I Let qi ,1 denote the human capital of the child at age 24 months. I Let θ i and νi denote unobservable components. ln qi ,1 = ln A + ρ ln qi ,0 + γ ln xi + θ i + νi
  • 8. Maternal Beliefs about the Technology Parameters I Mother has beliefs about γ.
  • 9. Maternal Beliefs about the Technology Parameters I Mother has beliefs about γ. I For mother i, γ is a random variable: γ N µγ,i , σ2 γ,i and µγ,i , σ2 are heterogeneous across mothers. γ,i
  • 10. Maternal Beliefs about the Technology Parameters I Mother has beliefs about γ. I For mother i, γ is a random variable: γ N µγ,i , σ2 γ,i and µγ,i , σ2 are heterogeneous across mothers. γ,i I Is this empirically important?
  • 11. Maternal Beliefs about the Technology Parameters I Mother has beliefs about γ. I For mother i, γ is a random variable: γ N µγ,i , σ2 γ,i and µγ,i , σ2 are heterogeneous across mothers. γ,i I Is this empirically important? I Unfortunately, it is not possible to answer this question with data on xi , qi ,0 , and qi ,1 unless one is willing to make strong assumptions.
  • 12. Today I Objective estimation of the technology of skill formation (based on the CNLSY/79 data). I Elicit subjective beliefs about the technology of skill formation (based on the MKIDS data). I Compare objective estimates with subjective beliefs.
  • 13. Objective Estimation of the Technology of Skill Formation: I Consider a Cobb-Douglas speci…cation (CHS, 2010). I Our goal is to estimate the parameters (especially γ) of the following equation: ln qi ,1 = ln A + ρ ln qi ,0 + γ ln xi + θ i + νi 1. Need to …nd a metric for q and x (time) 2. Account for measurement error in q and x (IRT analysis of MSD, factor analysis of HOME-SF). 3. Address endogeneity of x (FE, IVFE).
  • 14. Table 4 Objective Estimation of the Technology of Skill Formation Dependent variable: Natural log of skills around age 24 months1 FE Procedure 16 to 32  19 to 29  13 to 35 Months Months Months (1) (2) (5) (8) Overall Overall Overall Overall 2Natural Logarithm of health conditions at birth 0.588*** 0.597*** 0.517** 0.608* (0.17) (0.17) (0.21) (0.34) 3Natural logarithm of investments 0.206*** 0.204*** 0.235*** 0.363*** (0.03) (0.03) (0.04) (0.06)Constant 2.222*** ‐1.516*** ‐1.624*** ‐1.943** (0.38) (0.39) (0.50) (0.91)Dummy for the childs age at the time of the  Yes No No NointerviewNatural logarithm of childs age at the time of the  No Yes Yes YesinterviewObservations 2,984 2,984 2,218 1,400R‐squared 0.775 0.769 0.676 0.502Number of Mothers 2,168 2,168 1,757 1,202Robust standard errors in parentheses. All regressions have dummy variables for the childs gender, birthorder, and year of birth to capture cohort effects. All the regressions also have dummy variables for maternal age at the time of the childs birth. In column (1), we add dummy variables for the age of the child at the time of the interview. In columns (2)‐(12), we replace the dummies with one continuous variable (the natural log of the childs age at the time of the interview). *** p<0.01, ** p<0.05, * p<0.1
  • 15. Table 4 Objective Estimation of the Technology of Skill Formation Dependent variable: Natural log of skills around age 24 months1 FE Procedure 13 to 35 Months 16 to 32 Months 19 to 29 Months (3) (4) (6) (7) (9) (10) Black White Black White Black White 2Natural Logarithm of health conditions at birth 0.550** 0.621*** 0.782** 0.377 ‐0.405 0.533 (0.24) (0.22) (0.35) (0.28) (0.53) (0.55) 3Natural logarithm of investments 0.202*** 0.198*** 0.216*** 0.230*** 0.459*** 0.436*** (0.04) (0.04) (0.06) (0.06) (0.11) (0.10)Dummy for the childs age at the time of the  No No No No No NointerviewNatural logarithm of childs age at the time of the  Yes Yes Yes Yes Yes YesinterviewObservations 867 2,117 658 1,560 403 997R‐squared 0.827 0.771 0.812 0.681 0.900 0.504Number of Mothers 641 1,527 519 1,238 350 852Robust standard errors in parentheses. All regressions have dummy variables for the childs gender, birthorder, and year of birth to capture cohort effects. All the regressions also have dummy variables for maternal age at the time of the childs birth. In column (1), we add dummy variables for the age of the child at the time of the interview. In columns (2)‐(12), we replace the dummies with one continuous variable (the natural log of the childs age at the time of the interview). *** p<0.01, ** p<0.05, * p<0.1
  • 16. Objective Estimation of the Technology of Skill Formation: I The …xed-e¤ect procedure requires strict exogeneity of parental investments. I This rules out any form of feedback from ν to x. I Consider two di¤erent instruments: permanent income between ages 0-36 months of the child. I Advantage: allows for some form of feedback from ν to x. I However, imposes no feedback from ν to permanent income.
  • 17. Table 4 Objective Estimation of the Technology of Skill Formation Dependent variable: Natural log of skills around age 24 months1 FE Procedure 13 to 35 Months 16 to 32 Months 19 to 29 Months (3) (4) (6) (7) (9) (10) Black White Black White Black White 2Natural Logarithm of health conditions at birth 0.550** 0.621*** 0.782** 0.377 ‐0.405 0.533 (0.24) (0.22) (0.35) (0.28) (0.53) (0.55) 3Natural logarithm of investments 0.202*** 0.198*** 0.216*** 0.230*** 0.459*** 0.436*** (0.04) (0.04) (0.06) (0.06) (0.11) (0.10)Dummy for the childs age at the time of the  No No No No No NointerviewNatural logarithm of childs age at the time of the  Yes Yes Yes Yes Yes YesinterviewObservations 867 2,117 658 1,560 403 997R‐squared 0.827 0.771 0.812 0.681 0.900 0.504Number of Mothers 641 1,527 519 1,238 350 852Robust standard errors in parentheses. All regressions have dummy variables for the childs gender, birthorder, and year of birth to capture cohort effects. All the regressions also have dummy variables for maternal age at the time of the childs birth. In column (1), we add dummy variables for the age of the child at the time of the interview. In columns (2)‐(12), we replace the dummies with one continuous variable (the natural log of the childs age at the time of the interview). *** p<0.01, ** p<0.05, * p<0.1
  • 18. Objective Estimation of the Technology of Skill Formation: I We consider a second instrument. To see motivation, consider the di¤erence between the third and second child in the household: ln q3,1 ln q2,1 = ρ (ln q3,0 ln q2,0 ) + γ (ln x3,1 ln x2,1 ) + (ν3,1 ν I Now, suppose that 1. ν3,1 ν2,1 = η 3,1 . 2. η 3 is not revealed to the parent until the third child is born. I Then, if we look at families in which ln x2,1 and ln x1,1 were chosen before the birth of the third child, the di¤erence ln x2,1 ln x1,1 is not correlated with η 3,1 if (1) and (2) are true. I Allows feedback from η 3,1 to ln x3,1 , but imposes assumption on the serial correlation of ν.
  • 19. Table 4 Objective Estimation of the Technology of Skill Formation Dependent variable: Natural log of skills around age 24 months1 IV 13 to 35 Months (11) (12) Overall Overall 2Natural Logarithm of health conditions at birth 0.602*** 0.56 (0.21) (0.45)Natural logarithm of investments3 0.428* 0.417** (0.25) (0.21)Constant ‐1.635*** ‐2.648*** (0.50) (0.98)Dummy for the childs age at the time of the  No NointerviewNatural logarithm of childs age at the time of the  Yes YesinterviewObservations 2,798 1,254R‐squaredNumber of Mothers 2,134 1,048 3 First Stage ‐ Dependent variable: Natural logarithm of investmentsNatural logarithm of family income (average between  0.142***ages 0 and 36 months) (0.044) 3Lagged Natural logarithm of investments ‐0.298*** (0.077)
  • 20. Eliciting Beliefs about the Technology of Skill Formation I Let E [ ln q1 j q0 , x, θ ] denote the maternal expectation of child development at age 24 months when the unobserved component is θ, investment is x, and the child’ health s condition at birth is q0 . I To estimate µγ,i , we need to measure E [ ln q1 j q0 , x, θ ] for two di¤erent levels of x. To see why: E [ ln q1 j q0 , x, θ ] = ln A + ρ ln q0 + µγ,i ln x + θ i ¯ ¯ E [ ln q1 j q0 , x, θ ] = ln A + ρ ln q0 + µγ,i ln x + θ i ¯ ¯ I Subtracting and reorganizing terms: E [ ln q1 j q0 , x, θ ] ¯ E [ ln q1 j q0 , x, θ ] µγ,i = ¯ ln x ¯ ln x ¯
  • 21. Eliciting Beliefs about the Technology of Skill Formation I In order to measure returns to investments, we need to come up with a way to measure maternal expectation of child development, E [ ln q1 j q0 , x, θ ] . I Take the Motor-Social Development Instrument, but instead of asking: “Has your child ever spoken a partial sentence with three words or more?” I Suppose we ask: “What do you think is the youngest age and the oldest age a baby learns to speak a partial sentence with three words or more?” I We need to do it for two di¤erent levels of x.
  • 22. Eliciting Beliefs about the Technology of Skill Formation I Transform the information of age range into probability. I Assumption: The mother believes that development is logistically distributed within the age range she supplies.
  • 23. Figure 3 Transforming age range into probability 1 .75Probability .5 .25 0 0 4 8 12 16 20 24 28 32 36 40 44 48 Age (in months)
  • 24. Figure 3 Transforming age range into probability 1 .75Probability .5 .25 0 0 4 8 12 16 20 24 28 32 36 40 44 48 Age (in months) Logistic prediction, high High investment
  • 25. Figure 3 Transforming age range into probability 1 .75Probability .5 .25 0 0 4 8 12 16 20 24 28 32 36 40 44 48 Age (in months) Logistic prediction, high High investment
  • 26. Figure 3 Transforming age range into probability 1 .75Probability .5 .25 0 0 4 8 12 16 20 24 28 32 36 40 44 48 Age (in months) Logistic prediction, high High investment Logistic prediction, low Low investment
  • 27. Figure 3 Transforming age range into probability 1 .75Probability .5 .25 0 0 4 8 12 16 20 24 28 32 36 40 44 48 Age (in months) Logistic prediction, high High investment Logistic prediction, low Low investment
  • 28. Transform the Probability into Expected Human Capital I Remember that the NHANES contains data on a representative set of children from ages 2 to 47 months. I The NHANES dataset allows us to estimate the probability that a child age A has already spoken a partial sentence with three words or more.
  • 29. Figure 4 1 .75Probability .5 .25 0 Probability as a Function of Childs Age 0 4 8 12 16 20 24 28 32 36 40 44 48 Child Age (Months) Speak partial sentence, data Speak partial sentence, predicted
  • 30. Ignoring Measurement Error I If we are willing to ignore measurement error (i.e., assume that the response to “speak partial sentence” exactly measures maternal expectation), we can obtain µγ,i by comparing the response for the two di¤erent levels of investments. I Suppose that x = 3 months per year (i.e., x = 6 hours per ¯ ¯ day) and x = 1 month per year (i.e., x = 2 hours per day). ¯ ¯ Then: ln(22) ln(16) µγ,i = 29%. ln(3) ln(1)
  • 31. Accounting for Measurement Error I One way to allow for measurement error is to include other (repeated) measurements. I Added bonus: Because MSD items vary in di¢ culty, they provide a way to check whether answers are consistent.
  • 32. Figure 5 Comparing answers across scenarios Age range into probability Probability into expected development1 1 Speaks partial sentence Speaks partial sentence.25 .5 .75 .25 .5 .75 Knows own age and sex Knows own age and sex0 0 0 4 8 12 16 20 24 28 32 36 40 44 48 0 4 8 12 16 20 24 28 32 36 40 44 48 Age (in months) Child Age (Months)1 1 Speaks partial sentence Speaks partial sentence Knows own age and sex.75 .75.5 .5.25 .25 Knows own age and sex0 0 0 4 8 12 16 20 24 28 32 36 40 44 48 0 4 8 12 16 20 24 28 32 36 40 44 48 Age (in months) Child Age (Months)
  • 33. Eliciting Beliefs about the Technology of Skill Formation I We create four hypothetical scenarios: 1. (qh , xh ) = child is healthy at birth and investment is high. 2. (qu , xh ) = child is not healthy at birth and investment is high. 3. (qh , xl ) = child is healthy at birth and investment is low. 4. (qu , xl ) = child is not healthy at birth and investment is low. I A video explains to participants what we mean by healthy, not healthy, high, low. I Why create more scenarios? We can test the Cobb-Douglas speci…cation.
  • 34. Eliciting Beliefs about the Technology of Skill Formation I Taking di¤erences between scenarios (qh , xh ) and (qh , xl ) yields: E [ ln q1 j qh , xh , θ i ] E [ ln q1 j qh , xl , θ i ] µh = γ,i . ln xh ln xl I Analogously, take di¤erences between scenarios (qu , xh ) and (qu , xl ): E [ ln q1 j qu , xh , θ i ] E [ ln q1 j qu , xl , θ i ] µu = γ,i . ln xh ln xl I If we …nd that µh 6= µu , then parents do not believe γ,i γ,i production function is Cobb-Douglas.
  • 35. Table 6 1 Average lowest and highest age by MSD item and scenario 2 2 Health condition at birth is "high" Health condition at birth is "low" Investment is "high"3 Investment in "low"3 Investment is "high"3 Investment in "low"3 Scenario 1 Scenario 3 Scenario 2 Scenario 4 Lowest age Highest age Lowest age Highest age Lowest age Highest age Lowest age Highest ageMSD 30: Let someone know, without crying, that wearing wet or soiled pants or diapers bothers him or  14.58 28.39 18.52 32.74 16.81 30.32 21.11 34.16her?MSD 35: Speak a partial sentence of 3 words or more? 22.26 35.69 26.63 39.02 24.66 37.88 29.09 40.53MSD 38: Count 3 objects correctly? 25.08 37.72 28.70 40.84 26.54 38.63 30.50 42.26MSD 40: Know his/her age and sex?  25.35 38.70 28.97 40.91 27.16 39.99 31.10 42.35MSD 41: Say the names of at least 4 colors? 26.06 38.85 30.23 41.84 28.24 39.86 32.08 43.30MSD 36: Say his/her first and last name together without  27.30 39.37 30.97 41.81 28.64 40.42 32.88 43.00someones help? MSD 47: Count out loud up to 10? 27.96 40.58 31.42 42.96 29.11 41.28 33.03 43.78MSD 48: Draw a picture of a man or woman with at least  33.42 43.35 35.85 44.59 34.16 43.78 37.13 45.342 parts of the body besides a head?
  • 36. Figure 7 Kernel density of expected human capital at age 24 months Health condition at birth is high Investment is high1 1.5 1 1.5.5 .50 0 2 2.5 3 3.5 4 2 2.5 3 3.5 4 x x High investment Low investment Health is high Health is low Health condition at birth is low Investment is low1 1.5 1 1.5.5 .50 0 2 2.5 3 3.5 4 2 2.5 3 3.5 4 x x High investment Low investment Health is high Health is low
  • 37. Figure 8 Importance of measurement error in responses0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Signal Item Noise Item‐Scenario Noise
  • 38. Table 9 Subjective expectations about the technology of skill formation Not accounting for measurement error 25th  75%  Std  Mean Median Percentile Percentile DeviationOverall items and Scenarios1 8.8% 4.5% ‐4.5% 23.0% 32.9%High versus low heath conditions at birthOverall items, only scenarios with high health conditions at birth 12.7% 7.2% 0.0% 29.1% 36.5%Overall items, only scenarios with low health conditions at birth 4.9% 2.9% ‐7.2% 21.1% 33.6%Primarily motor vs. primarily cognitive itemsCognitive items, all scenarios 7.6% 0.0% ‐0.9% 20.8% 33.4%Motor items, all scenarios 9.9% 4.6% ‐8.0% 23.7% 38.7%Primarily motor vs. primarily cognitive items by health condition at birthCognitive items, high health conditions at birth 10.3% 0.0% 0.0% 26.1% 35.6%Cognitive items, low health conditions at birth 4.9% 0.0% ‐1.8% 17.0% 34.5%Motor items, high health conditions at birth 14.8% 9.0% 0.0% 35.7% 43.8%Motor items, low health conditions at birth 4.9% 0.0% ‐6.1% 22.3% 41.2% Accounting for measurement error 25th  75%  Std  Mean Median Percentile Percentile DeviationOverall items and Scenarios1 7.4% 3.9% ‐3.4% 21.0% 32.9%High versus low heath conditions at birthOverall items, only scenarios with high health conditions at birth 11.8% 6.7% 1.3% 29.4% 36.1%Overall items, only scenarios with low health conditions at birth 3.0% 0.2% ‐8.2% 15.8% 32.8%Primarily motor vs. primarily cognitive itemsCognitive items, all scenarios 5.1% 2.1% ‐4.0% 16.3% 36.4%Motor items, all scenarios 6.9% 3.1% ‐5.0% 19.0% 35.4%Primarily motor vs. primarily cognitive items by health condition at birthCognitive items, high health conditions at birth 10.2% 4.2% ‐0.4% 24.7% 39.2%Cognitive items, low health conditions at birth 0.0% ‐4.4% ‐7.4% 13.3% 36.9%Motor items, high health conditions at birth 16.6% 10.4% 3.4% 36.1% 39.9%Motor items, low health conditions at birth ‐2.8% ‐4.1% ‐13.9% 7.3% 36.6%1 Health conditions at birth are "high" if (1) the babys weight at birth is 8 pounds, the babys length at birth is 20 inches, and the gestational age is 9 months. Health conditions at birth are low if the babys weight at birth is 5 pounds, the babys length at birth is 18 inches, and the gestational age is 7 months. When investments are "high", the mother spends 6 hours/day interacting with the baby. In contrast, when investment is "low", the mother spends only 2 hours/day interacting with the baby. 
  • 39. Table 11 Subjective beliefs about the technology of skill formation How do maternal mean beliefs change with definitions of health conditions at birth and investments? Gestation: 9 months Gestation: 9 months Gestation lasts 9 months Healthy Birth weight: 7 pounds Healthy Birth weight: 7 pounds Normal Birth weight: 8 pounds Birth length: 20 inches Hospital time: 3 days Birth length: 20 inchesHealth conditions at birth Gestation: 7 months Gestation: 7 months Gestation: 8.5 months Not Healthy Birth weight: 5 pounds Not Healthy Birth weight: 5 pounds Small Birth weight: 6 pounds Birth length: 19 inches Hospital time: 7 days Birth length: 19 inches High 6 hours/day High 4 hours/day High 4 hours/dayInvestments Low 2 hours/day Low 3 hours/day Low 3 hours/day Number of observations = 42 Number of observations = 71 Number of observations Mean Median Std Dev Mean Median Std Dev Mean Median Std DevOverall items and Scenarios 7.2% 6.9% 28.1% 18.7% 7.6% 48.4% 22.6% 1.8% 41.1%Overall items, only scenarios with high  8.3% 13.8% 37.9% 29.8% 11.9% 59.0% 28.9% 8.4% 49.5%health conditions at birthOverall items, only scenarios with low  6.1% 1.1% 29.2% 7.7% ‐3.2% 49.2% 16.3% 8.2% 42.4%health conditions at birthCognitive items, all scenarios 2.7% 1.0% 27.9% 9.7% ‐3.4% 65.1% 14.8% ‐3.7% 49.6%Motor items, all scenarios 9.3% 8.6% 32.5% 24.9% 16.9% 41.6% 24.2% 13.6% 52.1%
  • 40. Figure 9 Checking the robustness of logit assumption0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 12 16 20 24 28 32 36 Age Logit distribution Upper triangular distribution Lower triangular distribution
  • 41. Table 12 Subjective beliefs about the technology of skill formation Checking sensitivity of the logit assumption Not accounting for measurement error Logit Lower Triangular Upper Triangular Mean Median Std Dev Mean Median Std Dev Mean Median Std DevOverall items and Scenarios 8.8% 4.5% 32.9% 15.0% 6.7% 24.7% 16.7% 8.2% 27.5%Overall items, only scenarios with  12.7% 7.2% 36.5% 17.3% 8.0% 29.7% 18.6% 11.0% 32.4%high health conditions at birthOverall items, only scenarios with  4.9% 2.9% 33.6% 12.6% 4.7% 21.5% 14.8% 5.9% 24.9%low health conditions at birthCognitive items, all scenarios 7.6% 0.0% 33.4% 13.0% 0.7% 24.1% 15.2% 0.4% 28.1%Motor items, all scenarios 9.9% 4.6% 38.7% 16.7% 7.7% 29.6% 18.1% 9.6% 31.8%
  • 42. Parental preferences I Suppose that parental preferences are described by the following utility function: (c c )1 σ ¯ 1 1 q1 σ 1 u (c, q1 ) = +α 1 σ 1 σ I The parameters: 1. σ: How much parents are willing to substitute child development for other goods and services. 2. α: How much parents “value” child development relative to other goods and services. 3. c : Minimum expenditure on goods and services. ¯
  • 43. Parental preferences I The problem of the (representative) parent is: " # (c c )1 σ 1 ¯ 1 q1 σ 1 max E +α I c ,x 1 σ 1 σ I Parents face the constraints: Budget: c + πx = y Belief: ln q1 = ln A + ρ ln q0 + µγ ln x + θ + ν Information set: I = fπ, y , θ, µγ , σ2 g γ I And child development follows the “true” production function: ln q1 = ln A + ρ ln q0 + γ ln x + θ + ν
  • 44. Estimating parental preferences I In order to estimate the parameters σ, α, and c we collect ¯ data on hypothetical choices. I We tell the parent that q0 is high. I We present the parent with a scenario of y and π. I We ask them to choose how to allocate resources between c and x. I Then we vary y and π, one at a time. I We use the choices to estimate the parameters σ, α, and c . ¯
  • 45. Figure 10 Demand for investments2.121.91.81.71.6 25 30 35 40 45 50 Price low income medium income high income
  • 46. Model simulation I Suppose that γ = 0.2, µγ = 0.15, and σ2 = 0.05. γ I Question: How much higher would investments be if we were able to convince the parent that γ = 0.2? I Investments would increase by 6%. I Lower bound?
  • 47. Conclusion I In general, economic models of human development assume that mothers know the parameters of the technology of skill formation. I In this paper, we formulate a model of human development that allows for subjective beliefs about these parameters. I Policy relevance: Allows us to understand the channels through which information acquisition, di¤usion, and learning about parenting may a¤ect the developmental outcoumes of young children. I When such models are structurally estimated, the variation in observed investments across families is attributed to shocks, heterogeneity in the characteristics of the children or families, but not to the heterogeneity in the knowledge base of the mother. I Important for policy and methodological reasons.
  • 48. Conclusion I Methodological relevance: When models that don’ account t for beliefs are structurally estimated, the variation in observed investments across families is attributed to shocks, heterogeneity in the characteristics of the children or families, but not to the heterogeneity in the knowledge base of the mother. I Unfortunately, this arises because heterogeneity in information cannot be separately identi…ed from other unobserved heterogeneity. I To solve this problem, we develop and implement a survey methodology that elicits these subjective beliefs. I Future work: 1. Re…ne elicitation of beliefs; 2. Con…rm that elicited beliefs predict investment (if so, go to 3, if not back to 1) 3. Experimentally manipulate beliefs to estimate its causal e¤ect on investments.