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Regression-style models for parameter estimation in dynamic microsimulation: An empirical performance assessment

  1. Jessica M McLay  Is a corresponding author
  2. Roy Lay-Yee  Is a corresponding author
  3. Barry J Milne  Is a corresponding author
  4. Peter Davis  Is a corresponding author
  1. Centre of Methods and Policy Application in the Social Sciences, The University of Auckland, New Zealand
Research article
Volume 8(2) Autumn 2015
Cite this article as: J. M McLay, R. Lay-Yee, B. J Milne, P. Davis; 2015; Regression-style models for parameter estimation in dynamic microsimulation: An empirical performance assessment; International Journal of Microsimulation; 8(2); 83-127. doi: 10.34196/ijm.00117
4 figures and 26 tables

Figures

Figure 1
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Flowchart showing the cross validation method used to calculate the simulated means, observed means, and the mean absolute differences reported in the results.
Figure 2
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Comparison of the observed reading scores and the reading scores simulated under the six models.

(a) Cumulative distribution curves for the overall distributions.

(b) Means by age.

Figure 3
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Cumulative distribution curves of the observed reading scores and the reading scores simulated under the six models.

(a) Child-specific correlations of current and lagged score

(b) Child-specific standard deviations.

Figure 4
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Comparison of observed and simulated mean reading scores by predictors.

(a) By gender. (b) By father's education. (c) By socio-economic status. (d) By breast-feeding. (e) By mother's working hours. (f) By home-ownership. Lines joining points are added to make distinctions between models more clear.

Tables

Table 1
Statistical regression techniques used by other dynamic microsimulation models (Table legend).
OLS regression with an LVD Random effects Fixed effects
MINT3: Earnings of retirees who choose to work, earnings of social security beneficiaries (Toder et al., 2002) PenSim2: Earnings (Emmerson, Reed, & Shephard, 2004) MINT1: Earnings (Toder et al., 2002)
SVERIGE: Earnings (Rephann & Holm, 2004) MIDAS: Hours worked, wages (Dekkers et al., 2008) Income Distribution of the Dutch Elderly: Income (Knoef, Alessie, & Kalwij, 2013)
DYNAMOD-2: Earnings (Bækgaard, 2002) DYNASIM-3: Hours worked, earnings (Favreault & Smith, 2004) MINT3: Pre-retirement earnings after age 50 (Toder et al., 2002)
LifePaths: Hours worked (Wolfson, 1995) SAGE: Earnings (Zaidi et al., 2009)
MINT3: Non-pension wealth, home equity, non-pension assets (Toder et al., 2002)
SESIM: Earnings, interest paid, size of loan (Klevmarken & Lindgren, 2008)
Table 2
Predictors used in the regression models.
Variable Categories/description
Time-invariant Predictors Values available only at the child’s birth
Gender Male; Female
Mother’s education No formal qualifications; Secondary qualification; Tertiary qualification
Father’s education No formal qualifications, Secondary qualification; Tertiary qualification
Family’s socio-economic position Semi-skilled, Unskilled, unemployed; Clerical, technical, skilled; Professional, managerial
Based on the Elley-Irving scale (Elley & Irving, 1976)
Breast-feeding Duration in months
Time-variant Predictors Values available at each year
LDV The lagged dependent variable; The value of the reading score at the previous year
Child’s age 8 to 13 years
Mother’s hours worked The average number of hours of paid work performed per week by the mother/mother figure
Home ownership Owned or mortgaged; Rented
Father’s smoking The average number of cigarettes smoked per day by the father/father figure
Table 3
Assumptions made for each model. ✓A indicates that the assumption is made by the model. Following this may be either the result of testing for the assumption or a comment (A dash (-) indicates that the test is not relevant).
Assumption Test used OLS-LDV RE RE-AR(1) FE HYBRID GMM Dynamic Panel
1 No individual effects: μi = 0, εi,t = υi,t LR test for non-zero σb2, p-value based on a mixture of chi-squares (COVTEST in the GLIMMIX procedure, SAS 9.3). ✓ A, LDV in model: x2(1) = 0.00, p = .9999; LDV not in model: x2(1) = 7958, p < .0001 - - - - -
2 Individual effects independent of within-child errors: Cov(μi, υi,t = 0 Test for Pearson’s correlation between estimated individual effectsa and residuals - ✓A, Cor(μ^i,υ^i,t)=0.079, p < .0001 ✓A, Cor(μ^i,υ^i,t)=0.079, p < .0001
3 Individual effects independent of each other: μi~iid Assumed by virtue of the individuals being randomly selected and from different families - ✓A ✓A μis eliminated by transformation ✓A μis eliminated by transformation
4 μi~N(0.σb) Shapiro-Wilk test on the empirical BLUPsb of individual effects - ✓A, W = 0.99, p = .0001, but plotting shows distribution close to normal ✓A, W = 0.99, p < .0001, but plotting shows distribution close to normal ✓A, W = 0.99, p = .0001, but plotting shows distribution close to normal
5 Cross-sectional ‘between’ effects equal to within ‘fixed’ ,, . K = λ effects: k = λ Hausman test ✓A, x2(5) = 2.55, p = .7693 ✓A, x2(5) = 2.55, p = .7693 ✓A, x2(5) = 2.55, p = .7693 Only λ estimated λ and κ estimated separately Only λ estimated
6 Exogenous time-invariant predictors (TIPs): Cov(υi,t, xi,t) = 0, Cov(zi, υi,t) = 0, C statistic from endogtest in stata’s ivreg2c ✓A, null of exogeneity not rejected for any TIPsd. LDV endogenous by definition. ✓A, null of exogeneity rejected for most TIPse ✓A, no convenient test – refer to tests for RE model TIPs not used ✓A, null of exogeneity rejected for half of the TIPse Diff GMM: TIPs not used. System GMM: Assumption does not need to be made
7 Exogenous time-variant predictors (TVPs): Cov(εi,t, xi,t) = 0, Cov(μi, xi,t*) = 0 C statistic from endogtest in stata’s ivreg2 or xtivreg2c ✓A, null of exogeneity rejected for one TVPd ✓A, null of exogeneity rejected for two TVPse ✓A, no convenient test – refer to tests for RE model ✓A, null of exogeneity not rejected for any TVPsf ✓A, null of exogeneity rejected for one TVPe Assumption does not need to be madeg
8 υi,t~iid N(0, σ2): Within-child errors serially uncorrelated System GMM: Arellano-Bond test for AR in first differences Other models: xtserial in stata (Wooldridge 2002) ✓A, F(1, 1003) = 398.5, p < .0001 ✓A, F(1, 1043) = 115.5, p < .0001 Assumes an AR(1) structureh ✓A, F(1, 1043) = 115.5, p < .0001 ✓A, F(1, 1043) = 115.5, p < .0001 Assumption not made but choice of instruments depends on degree of serial correlation. instruments depends on degree of serial correlation. AR(2): z = 4.33, p < .0001. AR(3): z = -1.60, p = .109.
9 υi,t~iid N(0, σ2) Within-child errors independent across individuals (no cross-sectional dependence) Pesaran’s test (Pesaran 2004): xtcsd in stata - ✓A, statistic = 6.62, p < .0001 ✓A, no convenient test – refer to test for RE model ✓A, statistic = 6.45, p < .0001 ✓A, no convenient test – refer to tests for RE and FE models ✓A, no convenient test – refer to tests for RE and FE models
10 Validity of moment conditions (validity of instruments) for Difference GMM Hansen test - - - - - ✓A, x2(22) = 24.47, p = .323
11 Validity of additional moment conditions for System GMM Difference in Hansen test - - - - - ✓A, x2(4)=16.27, p=.003
12 Stationarity of within-child errors Hadri and Larsson (2005) Z = -2.80, p = .0051 Z = 19.31, p < .0001 Z = 19.46, p < .0001 Z = 19.34, p < .0001 Z = 19.32, p < .0001 System GMM: Z = -2.80, p = .0051
  1. a

    Estimated individual effects were the empirical BLUPs (best linear unbiased predictors) estimated by SAS

  2. b

    BLUP = best linear unbiased predictor. Empirical BLUPs estimated in SAS by requesting fitted values with and without BLUPS and taking the difference.

  3. c

    The tests utilised additional variables not included in any models as excluded instruments (each tested for exogeneity and relevance). Predictors were tested individually with all other variables in the model treated as exogenous. Each model was checked for identification and weak. Significance was set at the .05 level. Full results of the tests and stata code are available in the online Appendix.

  4. d

    LDV included in the model. cluster option not used (panel data structure ignored).

  5. e

    LDV not included in the model. cluster option used to indicate panel data structure.

  6. f

    LDV not included in the model. cluster option used to indicate panel data structure. fe option used.

  7. g

    Although the exogeneity if variables should be investigated so that the analyst has some indication of what variables need to be instrumented and which do not.

  8. h

    A test for whether the AR(1) structure was defensible compared to an unstructured structure was attempted in SAS but the model with the unstructured model would not converge

Table 4
Mean absolute differences (MAD) (smaller is better) and standardised mean absolute differences (SMAD) (more negative is better) between simulated and observed data.
Data characteristic OLS – LDV RE) RE-AR(1) FE HYBRID SYSTEM GMM
MAD SMAD MAD SMAD MAD SMAD MAD SMAD MAD SMAD MAD SMAD
PRESS statistica 0.53 −0.11 0.44 −0.66 0.81 1.59 0.39 −0.99 0.44 −0.64 0.68 0.80
Overall distributions 1.47 −0.97 2.66 0.07 4.70 1.86 2.08 −0.44 2.69 0.10 1.87 −0.62
Means across time 0.50 −1.42 0.69 −0.05 0.70 −0.01 0.73 0.23 0.93 1.66 0.64 −0.41
Child-specific correlations (dynamism) 0.09 −1.45 0.23 0.85 0.24 0.92 0.15 −0.46 0.23 0.82 0.14 −0.68
Child-specific standard deviations 0.76 −1.75 1.07 −0.27 1.38 1.19 1.16 0.14 1.13 0.02 1.27 0.66
Time invariant predictors:
Gender 0.72 −1.51 1.16 0.19 1.15 0.15 1.38 1.02 1.37 0.98 0.90 −0.82
Breast-feeding 1.69 −0.77 1.82 −0.42 2.74 1.97 1.77 −0.57 1.97 −0.04 1.92 −0.17
Father’s education 0.85 −1.64 1.19 −0.15 1.51 1.18 1.38 0.64 1.34 0.47 1.11 −0.51
Mother’s education 0.91 −1.46 1.29 −0.04 1.68 1.43 1.35 0.19 1.45 0.56 1.12 −0.67
Family’s socio-economic status 0.94 −1.49 1.06 −0.72 1.38 1.36 1.21 0.28 1.25 0.56 1.17 0.01
Time-variant predictors:
Home-ownership 1.07 −0.64 1.29 −0.45 1.60 −0.18 1.20 −0.53 1.57 −0.21 4.19 2.01
Mother’s hours worked 4.81 −0.61 4.95 −0.49 7.88 1.86 4.63 −0.75 5.01 −0.44 6.10 0.43
Father’s smoking 5.31 −0.80 5.73 −0.51 8.42 1.36 5.34 −0.78 5.80 −0.46 8.17 1.19
Weighted means
Scheme 1b −1.11 −0.11 1.11 −0.27 0.30 0.08
Scheme 2c −1.12 −0.07 1.11 −0.28 0.34 0.02
  1. a

    The PRESS statistic is not a mean absolute difference but a standardised measure of the distance between the observed and predicted values. Smaller values are better.

  2. b

    Time-invariant predictors given a weight of 1/5 each, time-variant predictors given a weight of 1/3 each. Other characteristics each given a weight of 1.

  3. c

    Means by predictor variables given a combined weight of 1 with the time-invariant predictors each given a weight of 0.1 and the time-variant predictors each given a weight of 1/6. Other characteristics each given a weight of 1.

Table 5
Overall weighted mean of the standardised mean absolute differences (using weighting scheme 1a) by age for each model.
AGE MEAN OVER AGEb
MODEL 9 10 11 12 13
OLS – LDV −1.11 −1.10 −1.10 −1.06 −1.04 −1.11
RE −0.08 −0.07 −0.06 −0.11 −0.11 −0.11
RE-AR (1) 1.22 1.18 1.09 0.94 0.74 1.11
FE −0.16 −0.24 −0.27 −0.30 −0.27 −0.27
Hybrid 0.42 0.34 0.28 0.28 0.24 0.30
System GMM −0.29 −0.09 0.05 0.25 0.44 0.08
  1. a

    Time-invariant predictors given a weight of 1/5 each, time-variant predictors given a weight of 1/3 each. Other characteristics each given a weight of 1.

  2. b

    The weighted mean of the SMADs that were averaged over age. This is the same value as shown in the second-to-last row of Table 4.

Table 6
Coefficients and standard errors estimated on the full dataset for each of the techniques.
Variable OLS – LDV RE RE-AR(1) FE Hybrid System GMM DPM 2 Step a System GMM DPM 1 Step a
Reading score previous centred (LDV) 0.90 0.83 0.82
(0.01) (0.04) (0.04)
Reading score previous centred squared (LDV squared) −0.00 −0.01 −0.01
(0.00) (0.00) (0.00)
Child’s age centred −0.33 8.02 7.98 8.01 8.02 0.23 0.27
(0.09) (0.05) (0.10) (0.05) (0.05) (0.41) (0.41)
Child’s age centred squared 0.13 −0.52 −0.06 −0.51 −0.52 −0.01 −0.02
(0.04) (0.03) (0.03) (0.03) (0.03) (0.10) (0.10)
Gender (reference: Female) 0.07 −3.78 −3.31 −3.79 0.51 0.49
(0.21) (0.98) (0.75) (0.98) (0.34) (0.35)
Father’s education (reference: No formal education) Tertiary 1.43 6.78 5.10 6.54 0.68 0.51
(0.39) (1.79) (1.37) (1.81) (0.58) (0.57)
Secondary 0.98 4.60 3.57 4.56 0.67 0.71
(0.25) (1.18) (0.90) (1.18) (0.36) (0.36)
Mother’s education (reference: No formal education) Tertiary 1.01 7.02 5.16 6.76 1.18 1.05
(0.32) (1.53) (1.17) (1.55) (0.55) (0.54)
Secondary 0.42 2.47 1.65 2.31 0.47 0.40
(0.26) (1.21) (0.92) (1.21) (0.37) (0.35)
Family’s socio-economic status (reference: Semi-skilled) Professional 0.22 4.28 3.37 3.76 0.71 0.22
(0.39) (1.79) (1.37) (1.82) (0.72) (0.77)
Clerical 0.03 2.43 1.97 2.02 0.18 −0.14
(0.27) (1.23) (0.93) (1.25) (0.54) (0.56)
Breast-feeding 0.07 0.26 0.20 0.25 0.05 0.06
(0.03) (0.13) (0.10) (0.13) (0.03) (0.03)
0.00 0.01 0.00 0.01 (D, M): 0.01, 0.01 −0.02 0.01
Mother’s hours worked (0.01) (0.01) (0.01) (0.01) (0.01), (0.04) (0.04) (0.04)
Father’s smoking 0.00 −0.03 −0.01 −0.03 (D, M): -0.02, -0.09 −0.16 −0.24
(0.01) (0.02) (0.02) (0.02) (0.02), (0.07) (0.12) (0.11)
Home-ownership (reference: owned/mortgaged) −0.72 −1.48 −1.15 −1.30 (D, M): -1.31, -3.75 3.66 2.29
(0.30) (0.43) (0.42) (0.44) (0.45), (1.62) (2.98) (3.18)

  1. D: For the hybrid technique, estimate of the within / fixed effect calculated from the deviation variable.

  2. M: For the hybrid technique, estimate of the between/cross-sectional effect calculated from the mean variable.

  3. a

    Windmeijer corrected standard errors are displayed

Table 1
Mean absolute differences (MAD) (smaller is better) and standardised mean absolute differences (SMAD) (more negative is better) between simulated and observed data for age 9.
OLS-LDV RE RE-AR (1) Hybrid FE System GMM DPM
Data Characteristic MAD SMAD MAD SMAD MAD SMAD MAD SMAD MAD SMAD MAD SMAD
PRESS statistica 0.26 −0.65 0.35 −0.21 0.79 2.01 0.35 −0.19 0.31 −0.43 0.28 −0.53
Overall distributions 1.50 −0.64 1.86 −0.43 5.96 2.01 2.10 −0.28 2.28 −0.18 1.78 −0.48
Means across time 0.50 −1.42 0.69 −0.05 0.70 −0.01 0.93 1.66 0.73 0.23 0.64 −0.41
Within-child correlations (dynamism) 0.09 −1.45 0.23 0.85 0.24 0.92 0.23 0.82 0.15 −0.46 0.14 −0.68
Within-child standard deviations 0.76 −1.75 1.07 −0.27 1.38 1.19 1.13 0.02 1.16 0.14 1.27 0.66
Time-invariant predictors:
Gender 0.82 −1.06 1.13 0.03 1.28 0.57 1.54 1.47 1.17 0.16 0.79 −1.17
Breast-feading 1.39 −0.71 1.57 −0.35 2.69 1.90 1.90 0.31 1.47 −0.55 1.45 −0.6
Father’s education 0.40 −1.24 1.23 −0.03 1.60 1.09 1.51 0.82 1.41 0.52 0.87 −1.16
Mother’s education 0.90 −1.1 1.28 0.02 1.71 1.30 1.56 0.85 1.30 0.09 0.88 −1.17
Family’s socio-economic status 0.92 −1.17 1.26 −0.02 1.56 1.03 1.58 1.11 1.32 0.19 0.93 −1.14
Time-variant predictors:
Home-ownership 1.02 −1.13 1.34 −0.38 1.40 −0.23 1.75 0.57 1.27 −0.54 2.23 1.71
Mother’s hours worked 3.79 −0.56 4.05 −0.35 7.03 2.03 4.17 −0.26 3.85 −0.51 4.05 −0.35
Father’s smoking 3.56 −0.79 4.39 −0.31 8.32 1.98 4.52 −0.24 3.97 −0.55 4.79 −0.08
Weighted means
Scheme 1b −1.11 −0.08 1.22 0.42 −0.16 −0.29 −1.11
Scheme 2c −1.14 −0.05 1.22 0.42 −0.15 −0.29 −1.14
  1. a

    The PRESS statistic is not a mean absolute difference but a standardised measure of the distance between the observed and predicted values. Smaller values are better.

  2. b

    Time-invariant predictors given a weight of 1/5 each, time-variant predictors given a weight of 1/3 each. Other characteristics were each given a weight of 1.

  3. c

    Means by predictor variables given a combined weight of 1 with the time-invariant predictors each given a weight of 0.1 and the time-variant predictors each given a weight of 1/6. Other characteristics were each given a weight of 1.

Table 2
Mean absolute differences (MAD) (smaller is better) and standardised mean absolute differences (SMAD) (more negative is better) between simulated and observed data for age 10.
OLS-LDV RE RE-AR (1) Hybrid FE System GMM DPM
Data Characteristic MAD SMAD MAD SMAD MAD SMAD MAD SMAD MAD SMAD MAD SMAD
PRESS statistica 0.41 −0.31 0.38 −0.48 0.81 1.94 0.39 −0.46 0.32 −0.82 0.49 0.12
Overall distributions 1.46 −0.83 2.77 −0.07 6.25 1.95 2.85 −0.02 1.96 −0.54 2.04 −0.49
Means across time 0.50 −1.42 0.69 −0.05 0.70 −0.01 0.93 1.66 0.64 0.23 0.73 −0.41
Within-child correlations (dynamism) 0.09 −1.45 0.23 0.85 0.24 0.92 0.23 0.82 0.14 −0.46 0.15 −0.68
Within-child standard deviations 0.76 −1.75 1.07 −0.27 1.38 1.19 1.13 0.02 1.27 0.14 1.16 0.66
Time-invariant predictors:
Gender 0.66 −1.26 1.05 0.15 1.11 0.4 1.32 1.14 1.21 0.74 0.69 −1.17
Breast-feading 1.49 −0.88 1.77 −0.26 2.75 1.93 1.94 0.12 1.68 −0.45 1.67 −0.46
Father’s education 0.79 −1.49 1.26 0.03 1.57 1.04 1.44 0.6 1.47 0.72 0.97 −0.91
Mother’s education 0.78 −1.4 1.35 0.2 1.70 1.18 1.54 0.71 1.40 0.33 0.92 −1.01
Family’s socio-economic status 0.78 −1.46 1.06 −0.21 1.35 1.08 1.28 0.75 1.26 0.65 0.92 −0.82
Time-variant predictors:
Home-ownership 0.77 −0.67 0.97 −0.47 1.24 −0.19 1.29 −0.15 0.92 −0.52 3.42 2.00
Mother’s hours worked 4.67 −0.58 4.77 −0.49 7.44 1.88 4.88 −0.39 4.45 −0.78 5.72 0.35
Father’s smoking 4.29 −0.81 4.80 −0.49 8.23 1.71 4.83 −0.47 4.52 −0.67 6.68 0.72
Weighted means
Scheme 1b −1.10 −0.07 1.18 0.34 −0.24 −0.09
Scheme 2c −1.12 −0.04 1.19 0.36 −0.26 −0.12
  1. a

    The PRESS statistic is not a mean absolute difference but a standardised measure of the distance between the observed and predicted values. Smaller values are better.

  2. b

    Time-invariant predictors given a weight of 1/5 each, time-variant predictors given a weight of 1/3 each. Other characteristics were each given a weight of 1.

  3. c

    Means by predictor variables given a combined weight of 1 with the time-invariant predictors each given a weight of 0.1 and the time-variant predictors each given a weight of 1/6. Other characteristics were each given a weight of 1.

Table 3
Mean absolute differences (MAD) (smaller is better) and standardised mean absolute differences (SMAD) (more negative is better) between simulated and observed data for age 11.
OLS-LDV RE RE-AR (1) Hybrid FE System GMM DPM
Data Characteristic MAD SMAD MAD SMAD MAD SMAD MAD SMAD MAD SMAD MAD SMAD
PRESS statistica 0.54 −0.01 0.43 −0.65 0.82 1.55 0.43 −0.65 0.36 −1.05 0.69 0.81
Overall distributions 1.87 −0.93 3.70 0.2 6.32 1.81 3.67 0.18 2.37 −0.63 2.37 −0.63
Means across time 0.50 −1.42 0.69 −0.05 0.70 −0.01 0.93 1.66 0.73 0.23 0.64 −0.41
Within-child correlations (dynamism) 0.09 −1.45 0.23 0.85 0.24 0.92 0.23 0.82 0.15 −0.46 0.14 −0.68
Within-child standard deviations 0.76 −1.75 1.07 −0.27 1.38 1.19 1.13 0.02 1.16 0.14 1.27 0.66
Time-invariant predictors:
Gender 0.57 −1.5 1.13 0.27 1.14 0.33 1.26 0.71 1.38 1.11 0.76 −0.92
Breast-feading 1.84 −1 2.14 −0.22 2.99 1.93 2.21 −0.04 2.10 −0.32 2.09 −0.35
Father’s education 0.83 −1.58 1.33 0.07 1.65 1.08 1.40 0.29 1.57 0.85 1.09 −0.71
Mother’s education 0.93 −1.4 1.65 0.3 1.97 1.07 1.72 0.48 1.79 0.63 1.06 −1.08
Family’s socio-economic status 0.86 −1.66 1.06 −0.57 1.38 1.22 1.22 0.31 1.26 0.55 1.19 0.16
Time-variant predictors:
Home-ownership 1.04 −0.79 1.57 −0.4 2.16 0.04 1.78 −0.24 1.34 −0.57 4.71 1.96
Mother’s hours worked 5.17 −0.45 5.06 −0.52 8.79 1.9 5.13 −0.48 4.70 −0.76 6.35 0.31
Father’s smoking 5.42 −0.88 5.90 −0.51 8.22 1.26 5.96 −0.47 5.65 −0.70 8.27 1.30
Weighted means
Scheme 1b −1.10 −0.06 1.09 0.28 −0.27 0.05
Scheme 2c −1.10 −0.03 1.09 0.34 −0.30 0.01
  1. a

    The PRESS statistic is not a mean absolute difference but a standardised measure of the distance between the observed and predicted values. Smaller values are better.

  2. b

    Time-invariant predictors given a weight of 1/5 each, time-variant predictors given a weight of 1/3 each. Other characteristics were each given a weight of 1.

  3. c

    Means by predictor variables given a combined weight of 1 with the time-invariant predictors each given a weight of 0.1 and the time-variant predictors each given a weight of 1/6. Other characteristics were each given a weight of 1.

Table 4
Mean absolute differences (MAD) (smaller is better) and standardised mean absolute differences (SMAD) (more negative is better) between simulated and observed data for age 12.
OLS-LDV RE RE-AR (1) Hybrid FE System GMM DPM
Data Characteristic MAD SMAD MAD SMAD MAD SMAD MAD SMAD MAD SMAD MAD SMAD
PRESS statistica 0.65 0.19 0.48 −0.74 0.82 1.05 0.48 −0.73 0.42 −1.06 0.86 1.29
Overall distributions 2.00 −1.1 3.72 0.37 5.23 1.66 3.68 0.33 2.61 −0.58 2.48 −0.69
Means across time 0.50 −1.42 0.69 −0.05 0.70 −0.01 0.93 1.66 0.73 0.23 0.64 −0.41
Within-child correlations (dynamism) 0.09 −1.45 0.23 0.85 0.24 0.92 0.23 0.82 0.15 −0.46 0.14 −0.68
Within-child standard deviations 0.76 −1.75 1.07 −0.27 1.38 1.19 1.13 0.02 1.16 0.14 1.27 0.66
Time-invariant predictors:
Gender 0.78 −1.49 1.18 0.18 1.09 −0.18 1.31 0.76 1.45 1.33 0.99 −0.61
Breast-feading 1.92 −0.62 1.95 −0.52 2.76 1.94 2.06 −0.19 1.88 −0.73 2.17 0.13
Father’s education 0.92 −1.71 1.16 −0.37 1.46 1.25 1.25 0.11 1.33 0.56 1.26 0.16
Mother’s education 1.03 −1.57 1.31 −0.22 1.67 1.53 1.42 0.33 1.38 0.11 1.32 −0.18
Family’s socio-economic status 1.04 −1.09 1.01 −1.32 1.26 0.97 1.17 0.16 1.18 0.27 1.26 1.01
Time-variant predictors:
Home-ownership 1.44 −0.49 1.51 −0.44 1.75 −0.29 1.76 −0.29 1.38 −0.52 5.43 2.03
Mother’s hours worked 5.14 −0.57 5.30 −0.44 8.14 1.82 5.29 −0.44 4.78 −0.85 6.45 0.48
Father’s smoking 7.48 −0.71 7.80 −0.48 9.13 0.51 7.86 −0.43 7.49 −0.71 10.88 1.82
Weighted means
Scheme 1b −1.06 −0.11 0.94 0.28 −0.30 0.25
Scheme 2c −1.08 −0.05 0.95 0.34 −0.32 0.16
  1. a

    The PRESS statistic is not a mean absolute difference but a standardised measure of the distance between the observed and predicted values. Smaller values are better.

  2. b

    Time-invariant predictors given a weight of 1/5 each, time-variant predictors given a weight of 1/3 each. Other characteristics were each given a weight of 1.

  3. c

    Means by predictor variables given a combined weight of 1 with the time-invariant predictors each given a weight of 0.1 and the time-variant predictors each given a weight of 1/6. Other characteristics were each given a weight of 1.

Table 5
Mean absolute differences (MAD) (smaller is better) and standardised mean absolute differences (SMAD) (more negative is better) between simulated and observed data for age 13.
OLS-LDV RE RE-AR (1) Hybrid FE System GMM DPM
Data Characteristic MAD SMAD MAD SMAD MAD SMAD MAD SMAD MAD SMAD MAD SMAD
PRESS statistica 0.78 0.25 0.56 −0.75 0.83 0.5 0.56 −0.73 0.52 −0.93 1.08 1.66
Overall distributions 1.98 −1.43 3.82 0.6 4.39 1.23 3.78 0.56 3.20 −0.09 2.49 −0.87
Means across time 0.50 −1.42 0.69 −0.05 0.7 −0.01 0.93 1.66 0.73 0.23 0.64 −0.41
Within-child correlations (dynamism) 0.09 −1.45 0.23 0.85 0.24 0.92 0.23 0.82 0.15 −0.46 0.14 −0.68
Within-child standard deviations 0.76 −1.75 1.07 −0.27 1.38 1.19 1.13 0.02 1.16 0.14 1.27 0.66
Time-invariant predictors:
Gender 0.74 −1.65 1.32 0.22 1.12 −0.42 1.40 0.48 1.68 1.36 1.26 0.01
Breast-feading 1.81 −0.38 1.68 −0.75 2.52 1.67 1.73 −0.61 1.69 −0.72 2.21 0.78
Father’s education 0.86 −1.39 0.98 −0.72 1.27 0.81 1.11 −0.06 1.12 −0.01 1.37 1.37
Mother’s education 0.93 −0.62 0.87 −0.85 1.36 1.08 1.01 −0.27 0.89 −0.78 1.45 1.43
Family’s socio-economic status 1.09 −0.26 0.89 −1.08 1.32 0.74 1.01 −0.57 1.03 −0.48 1.54 1.63
Time-variant predictors:
Home-ownership 1.07 −0.48 1.07 −0.48 1.46 −0.24 1.28 −0.36 1.09 −0.47 5.15 2.03
Mother’s hours worked 5.27 −0.79 5.57 −0.56 7.98 1.3 5.60 −0.54 5.40 −0.69 7.95 1.27
Father’s smoking 5.79 −0.51 5.75 −0.53 8.22 0.7 5.83 −0.5 5.07 −0.88 10.23 1.71
Weighted means
Scheme 1b −1.06 −0.11 0.94 0.28 −0.30 0.25
Scheme 2c −1.08 −0.05 0.95 0.34 −0.32 0.16
  1. a

    The PRESS statistic is not a mean absolute difference but a standardised measure of the distance between the observed and predicted values. Smaller values are better.

  2. b

    Time-invariant predictors given a weight of 1/5 each, time-variant predictors given a weight of 1/3 each. Other characteristics were each given a weight of 1.

  3. c

    Means by predictor variables given a combined weight of 1 with the time-invariant predictors each given a weight of 0.1 and the time-variant predictors each given a weight of 1/6. Other characteristics were each given a weight of 1.

Table 2
t-values from paired t-tests (df=29) comparing the absolute differences (between the simulated and observed percentiles of the distribution of reading scores). Values greater than 2.46 indicate (unadjusted) significance at the .01 level.
Percentile
Comparison 10th 25th 50th 75th 90th
OLS-LDV – RE −31.08 −19.56 −28.23 −24.00 −14.27
OLS-LDV – RE-AR(1) −9.90 −18.06 −17.57 −8.52 −6.81
OLS-LDV – Hybrid −2.11 0.11 2.12 −1.35 −0.61
OLS-LDV – System GMM DPM 1.45 −10.74 −22.55 −7.51 −8.31
OLS-LDV – FE −29.93 −9.64 −6.25 −29.91 −13.54
RE – RE-AR(1) −2.63 −2.30 1.66 1.75 −3.02
RE – Hybrid 2.41 9.73 25.19 8.85 2.46
RE – System GMM DPM 11.01 −0.14 12.25 9.27 −2.54
RE – FE 20.03 9.72 3.66 31.28 10.41
RE-AR(1) – Hybrid 14.97 13.80 27.01 22.03 10.03
RE-AR(1) – System GMM DPM 30.17 5.88 14.38 26.04 10.18
RE-AR(1) – FE 3.34 10.18 16.87 6.51 3.00
Hybrid – System GMM DPM 11.02 0.92 5.88 5.89 0.31
Hybrid – FE 2.72 −8.57 −18.00 −4.00 −3.29
System GMM DPM – FE −31.08 −19.56 −28.23 −24.00 −14.27
Table 2
t-values from paired t-tests (df=29) comparing the absolute differences (between the simulated and observed means of reading scores). Values greater than 2.46 indicate (unadjusted) significance at the .01 level.
Age
Comparison 9 10 11 12 13
OLS-LDV – RE −1.84 −1.95 −3.48 −0.90 −1.83
OLS-LDV – RE-AR(1) −1.85 −1.65 −3.75 −1.04 −2.31
OLS-LDV – Hybrid −3.39 −3.59 −4.38 −3.43 −3.07
OLS-LDV – System GMM DPM 1.80 0.21 −2.02 −1.49 −2.69
OLS-LDV – FE −1.53 −2.34 −3.70 −1.38 −2.05
RE – RE-AR(1) −0.05 1.98 −1.10 −0.28 −0.74
RE – Hybrid −3.47 −2.94 −1.75 −2.64 −1.98
RE – System GMM DPM 2.16 2.12 1.38 −0.77 −1.75
RE – FE 0.96 −0.75 −1.87 −1.57 −1.15
RE-AR(1) – Hybrid −3.43 −3.13 −1.32 −2.44 −1.72
RE-AR(1) – System GMM DPM 2.18 1.80 1.68 −0.71 −1.56
RE-AR(1) – FE 0.91 −1.55 −1.12 −1.07 −0.38
Hybrid – System GMM DPM 3.65 3.63 2.56 1.05 −0.76
Hybrid – FE 3.54 2.09 0.78 1.79 1.16
System GMM DPM – FE −1.85 −2.38 −2.02 0.29 1.52
Table 3
t-values from paired t-tests (df = 29) comparing the absolute differences (between the simulated and observed percentiles of the distribution of child-specific correlations between current and lagged reading scores). Values greater than 2.46 indicate (unadjusted) significance at the .01 level.
Percentile
Comparison 10th 25th 50th 75th 90th
OLS-LDV – RE −37.88 −82.01 −93.94 −89.52 −83.17
OLS-LDV – RE-AR(1) −30.27 −44.09 −55.95 −62.67 −61.41
OLS-LDV – Hybrid −40.68 −88.06 −96.87 −87.17 −78.17
OLS-LDV – System GMM DPM −14.53 −13.64 −13.83 −13.49 −12.42
OLS-LDV – FE −14.39 −83.70 −111.84 −104.30 −95.05
RE – RE-AR(1) −14.68 0.23 22.05 40.07 47.60
RE – Hybrid 2.32 2.40 2.45 2.49 2.21
RE – System GMM DPM 3.64 33.06 65.29 75.15 72.97
RE – FE 52.68 51.85 49.02 46.74 44.81
RE-AR(1) – Hybrid 14.35 0.36 −18.04 −30.84 −34.43
RE-AR(1) – System GMM DPM 10.04 25.17 40.75 48.78 49.55
RE-AR(1) – FE 34.24 24.66 14.86 4.77 −2.32
Hybrid – System GMM DPM 3.50 34.37 69.56 75.74 71.70
Hybrid – FE 51.39 48.19 44.55 41.19 37.90
System GMM DPM – FE 9.43 −14.40 −47.04 −63.95 −67.09
Table 4
t-values from paired t-tests (df = 29) comparing the absolute differences (between the simulated and observed percentiles of the distribution of within-child standard deviations of reading scores). Values greater than 2.46 indicate (unadjusted) significance at the .01 level.
Percentile
Comparison 10th 25th 50th 75th 90th
OLS-LDV – RE −9.99 −7.43 −7.45 10.71 7.70
OLS-LDV – RE-AR(1) 6.32 1.89 −12.79 −22.29 −17.18
OLS-LDV – Hybrid −10.20 −7.87 −7.97 9.05 8.06
OLS-LDV – System GMM DPM −8.23 −5.83 −1.88 −11.14 −13.73
OLS-LDV – FE −9.84 −5.31 −2.92 0.78 −0.01
RE – RE-AR(1) 41.95 42.88 −23.07 −24.19 −15.65
RE – Hybrid −2.70 −2.81 −2.74 −4.01 0.82
RE – System GMM DPM 3.10 2.52 6.10 −16.29 −15.82
RE – FE −0.02 9.12 9.48 −5.53 −19.46
RE-AR(1) – Hybrid −31.43 −22.63 8.32 24.63 16.44
RE-AR(1) – System GMM DPM −10.40 −6.09 11.37 6.68 4.14
RE-AR(1) – FE −35.78 −26.65 20.58 9.90 8.05
Hybrid – System GMM DPM 3.54 3.13 6.71 −14.82 −16.49
Hybrid – FE 2.17 7.17 8.74 −3.88 −13.89
System GMM DPM – FE −3.12 −0.91 −1.21 6.90 6.82
Table 5
t-values from paired t-tests (df = 29) comparing the absolute differences (between the simulated and observed mean reading scores by gender). Values greater than 2.46 indicate (unadjusted) significance at the .01 level.
Gender
Comparison Girls Boyx
OLS-LDV – RE −3.97 −3.21
OLS-LDV – RE-AR(1) −3.75 −4.12
OLS-LDV – Hybrid −4.51 −3.65
OLS-LDV – System GMM DPM −2.48 −1.64
OLS-LDV – FE −5.08 −4.03
RE – RE-AR(1) 0.97 −0.91
RE – Hybrid −2.88 −0.98
RE – System GMM DPM 2.22 1.52
RE – FE −3.70 −3.81
RE-AR(1) – Hybrid −2.44 0.07
RE-AR(1) – System GMM DPM 1.71 2.30
RE-AR(1) – FE −2.16 −0.98
Hybrid – System GMM DPM 3.35 1.85
Hybrid – FE 1.12 −1.13
System GMM DPM – FE −3.41 −2.84
Table 6
t-values from paired t-tests (df = 29) comparing the absolute differences (between the simulated and observed mean reading scores by duration of breast-feeding). Values greater than 2.46 indicate (unadjusted) significance at the .01 level.
Breast-feeding Duration (months)
Comparison 0 3 6 9 12
OLS-LDV – RE −0.35 −2.91 −1.63 −5.11 −0.45
OLS-LDV – RE-AR(1) −2.99 −4.71 −3.66 −4.12 −3.40
OLS-LDV – Hybrid −2.15 −2.66 −2.87 −4.09 −1.10
OLS-LDV – System GMM DPM −2.89 −2.52 −2.01 −4.44 −1.10
OLS-LDV – FE −0.33 −2.46 −2.96 −4.79 −0.96
RE – RE-AR(1) −3.08 −3.82 −3.46 −0.95 −2.69
RE – Hybrid −2.76 −1.43 −2.58 3.03 −1.26
RE – System GMM DPM −2.07 −0.09 −0.91 0.93 −0.09
RE – FE −0.04 −0.12 −2.42 0.05 −1.61
RE-AR(1) – Hybrid 0.64 2.70 1.78 1.97 2.44
RE-AR(1) – System GMM DPM 0.52 2.42 1.73 1.61 2.82
RE-AR(1) – FE 2.74 3.00 2.53 0.88 1.88
Hybrid – System GMM DPM −0.10 0.57 0.43 −0.10 0.49
Hybrid – FE 2.38 1.20 0.87 −2.05 −0.10
System GMM DPM – FE 1.95 0.04 0.01 −0.89 −0.47
Table 7
t-values from paired t-tests (df = 29) comparing the absolute differences (between the simulated and observed mean reading scores by father's education at the child's birth). Values greater than 2.46 indicate (unadjusted) significance at the .01 level.
Father’s education
Comparison Tertiary Secondary None
OLS-LDV – RE −3.39 −2.57 −2.37
OLS-LDV – RE-AR(1) −5.48 −4.60 −2.30
OLS-LDV – Hybrid −3.19 −3.14 −3.59
OLS-LDV – System GMM DPM −4.01 −2.57 −1.27
OLS-LDV – FE −4.96 −2.38 −2.83
RE – RE-AR(1) −3.49 −3.00 −0.10
RE – Hybrid −0.38 −0.79 −3.00
RE – System GMM DPM 0.38 0.55 0.65
RE – FE −4.00 0.17 −1.61
RE-AR(1) – Hybrid 3.59 2.01 −2.10
RE-AR(1) – System GMM DPM 3.24 3.47 0.67
RE-AR(1) – FE 0.26 2.65 −0.59
Hybrid – System GMM DPM 0.55 0.96 2.07
Hybrid – FE −2.62 0.86 1.97
System GMM DPM – FE −2.54 −0.43 −1.03
Table 8
t-values from paired t-tests (df = 29) comparing the absolute differences (between the simulated and observed mean reading scores by mother's education at the child's birth). Values greater than 2.46 indicate (unadjusted) significance at the .01 level.
Mother’s education
Comparison Tertiary Secondary None
OLS-LDV – RE −6.45 −0.29 −2.34
OLS-LDV – RE-AR(1) −6.12 −3.75 −3.28
OLS-LDV – Hybrid −4.41 −2.06 −3.56
OLS-LDV – System GMM DPM −3.33 −2.50 −0.42
OLS-LDV – FE −7.30 0.12 −2.20
RE – RE-AR(1) −2.01 −4.99 −1.28
RE – Hybrid 0.79 −2.13 −2.76
RE – System GMM DPM 2.81 −1.62 1.36
RE – FE −3.19 0.97 0.06
RE-AR(1) – Hybrid 2.57 2.54 −1.27
RE-AR(1) – System GMM DPM 5.07 2.15 1.95
RE-AR(1) – FE 0.66 4.18 1.06
Hybrid – System GMM DPM 2.17 −0.06 2.67
Hybrid – FE −2.45 2.72 2.64
System GMM DPM – FE −3.92 2.02 −1.34
Table 9
t-values from paired t-tests (df = 29) comparing the absolute differences (between the simulated and observed mean reading scores by family's socio-economic status at the child's birth). Values greater than 2.46 indicate (unadjusted) significance at the .01 level.
Socio-economic status
Comparison Professional Clerical Semi-skilled
OLS-LDV – RE −2.90 −0.90 0.34
OLS-LDV – RE-AR(1) −4.91 −2.14 −2.62
OLS-LDV – Hybrid −2.41 −2.75 −1.37
OLS-LDV – System GMM DPM −3.18 −1.14 −1.70
OLS-LDV – FE −4.24 −1.22 0.09
RE – RE-AR(1) −2.34 −2.12 −3.34
RE – Hybrid 0.00 −3.11 −2.46
RE – System GMM DPM 0.13 0.16 −1.90
RE – FE −3.99 −1.24 −0.46
RE-AR(1) – Hybrid 2.31 −1.35 1.06
RE-AR(1) – System GMM DPM 2.46 1.29 0.55
RE-AR(1) – FE −0.30 1.18 2.84
Hybrid – System GMM DPM 0.11 2.10 −0.48
Hybrid – FE −2.50 2.51 1.83
System GMM DPM – FE −2.19 −0.52 1.71
Table 10
t-values from paired t-tests (df = 29) comparing the absolute differences (between the simulated and observed mean reading scores by home-ownership status). Values greater than 2.46 indicate (unadjusted) significance at the .01 level.
Home-ownership status
Comparison Owned Rented
OLS-LDV – RE −4.37 −0.56
OLS-LDV – RE-AR(1) −4.74 −3.13
OLS-LDV – Hybrid −4.72 −1.70
OLS-LDV – System GMM DPM −4.57 −7.86
OLS-LDV – FE −3.93 0.52
RE – RE-AR(1) −1.13 −4.04
RE – Hybrid −2.20 −2.74
RE – System GMM DPM −2.40 −7.80
RE – FE −0.59 2.66
RE-AR(1) – Hybrid −1.83 1.12
RE-AR(1) – System GMM DPM −2.00 −6.59
RE-AR(1) – FE 0.12 4.75
Hybrid – System GMM DPM −0.81 −7.30
Hybrid – FE 1.63 3.87
System GMM DPM – FE 2.13 8.07
Table 11

t-values from paired t-tests (df = 29) comparing the absolute differences (between the simulated and observed mean reading scores by number of hours worked per week by the mother).

The values of working hours chosen at which to compute the significance tests were the minimum (0 hrs, also the 10th and 25th percentiles), mean (16 hrs), 75th percentile (27 hours), and 90th and 95th percentiles (both 40 hrs), for the distribution of mother's working hours at age 11.

Values greater than 2.46 indicate (unadjusted) significance at the .01 level.

Mother’s Hours Worked (hours per week)
Comparison 0 16 27 40
OLS-LDV – RE −3.05 −4.92 4.61 −2.85
OLS-LDV – RE-AR(1) −4.95 −8.76 1.44 −6.15
OLS-LDV – Hybrid −4.15 −3.22 4.51 −3.18
OLS-LDV – System GMM DPM −4.11 −4.30 −1.35 −4.52
OLS-LDV – FE −2.78 −4.31 3.26 −2.57
RE – RE-AR(1) −4.54 −7.13 −5.52 −3.86
RE – Hybrid −3.32 1.02 −0.95 −1.29
RE – System GMM DPM −2.10 0.47 −5.83 −2.89
RE – FE 0.60 −0.90 −2.07 0.23
RE-AR(1) – Hybrid 1.63 7.43 5.58 1.87
RE-AR(1) – System GMM DPM 0.31 6.53 −2.63 −1.68
RE-AR(1) – FE 3.56 6.24 3.37 3.26
Hybrid – System GMM DPM −0.50 −0.03 −5.73 −2.22
Hybrid – FE 2.70 −1.94 −1.73 1.34
System GMM DPM – FE 2.35 −0.82 4.07 2.86
Table 12

t-values from paired t-tests (df = 29) comparing the absolute differences (between the simulated and observed mean reading scores by number of hours worked per week by the mother).

The values of cigarettes chosen at which to compute the significance tests were the minimum (0 cigarettes, also the 10th, 25th, and 75th percentiles and the median), mean (4 cigarettes), and the 90th and 95th percentiles (both 20 cigarettes) for the distribution of number of cigarettes smoked per day by the father-figure at age 11. Values greater than 2.46 indicate (unadjusted) significance at the .01 level.

Father’s Smoking (cigarettes per day)
Comparison 0 4 20
OLS-LDV – RE −3.20 −5.84 −0.03
OLS-LDV – RE-AR(1) −3.62 −6.38 −0.18
OLS-LDV – Hybrid −4.33 −5.50 −1.36
OLS-LDV – System GMM DPM −6.99 −1.60 −6.97
OLS-LDV – FE −3.02 −3.51 −1.91
RE – RE-AR(1) −1.42 −5.41 −0.24
RE – Hybrid −2.69 −0.63 −2.72
RE – System GMM DPM −4.60 1.81 −7.37
RE – FE −1.06 0.51 −2.47
RE-AR(1) – Hybrid −2.03 5.17 −1.46
RE-AR(1) – System GMM DPM −4.47 5.56 −7.67
RE-AR(1) – FE 0.11 4.33 −1.49
Hybrid – System GMM DPM −2.77 2.16 −6.86
Hybrid – FE 1.74 0.72 0.15
System GMM DPM – FE 3.88 −1.13 6.95
Table 3
Exogeneity tests for predictors for OLS-LDV, RE, RE-AR(1), and FE models.
OLS-LDV RE an RE-AR (1) FE
C statistic: x2(1) p Under-identification Test Rejecteda Cragg-Donald Wald F C statistic: x2(1) p Under-identification Test Rejecteda rk statisticb C statistic: x2(1) p Under-identification Test Rejecteda rk statisticb
Age 6.93 .0085 Yes 13.60 2.67 .1021 Yes 10.47
Age squared 4.83 .0280 No 0.71 4.76 .0291 No 1.49
Time-invariant:
Father’s education – tertiary 0.53 .4273 Yes 5.90 0.05 .8202 No 1.75
Father’s education – secondary 0.01 .9324 Yes 9.85 0.44 .5062 Yes 2.24
Breast-feeding 0.96 .3263 Yes 28.94 0.31 .5777 Yes 7.23
Mother’s education – tertiary 0.67 .4125 Yes 18.96 5.94 .0148 Yes 5.27
Mother’s education – secondary 0.78 .3766 Yes 24.78 4.87 .0273 Yes 5.77
Socio-economic status – professional 0.80 .3702 Yes 36.90 4.30 .0382 Yes 8.30
Socio-economic status -clerical 1.43 .2297 Yes 30.21 6.29 .0122 Yes 5.13
Gender – male 1.94 .1637 Yes 3.20 3.00 .0831 No 0.51
Time-variant:
Father’s smoking 0.00 .9615 Yes 41.87 0.12 .7262 Yes 10.14 0.27 .6052 Yes 12.10
Home-ownership 1.24 .2664 Yes 97.35 4.03 .0447 Yes 16.51 0.24 .6278 Yes 6.96
Mother’s working hours 5.64 .0175 Yes 67.08 10.81 .0012 Yes 26.95 0.25 .6190 Yes 20.41
  1. a

    Kleibergen-Paap rk LM test. Rejection based at the .05 level.

  2. b

    Kleibergen-Paap rk Wald F test.

Table 2
Exogeneity tests for predictors for the hybrid model.
C statistic: x2(1) p Under-identification Test Rejecteda rk statisticb
Age 0.80 .3726 Yes 8.03
Age squared 3.19 .0741 No 1.15
Time-invariant:
Father’s education – tertiary 0.00 .9863 No 1.60
Father’s education – secondary 0.37 .5457 Yes 2.25
Breast-feeding 0.44 .5063 Yes 7.08
Mother’s education – tertiary 4.76 .0291 Yes 4.62
Mother’s education – secondary 4.12 .0423 Yes 5.29
Socio-economic status – professional 3.45 .0633 Yes 7.31
Socio-economic status -clerical 5.28 .0216 Yes 4.20
Gender – male 2.48 .1153 No 0.48
Father’s smoking means 1.50 .2200 Yes 5.84
Home-ownership means 3.89 .0486 Yes 14.23
Mother’s working hours means 9.16 .0025 Yes 18.47
Time-variant:
Father’s smoking deviation score 1.95 .1627 Yes 6.36
Home-ownership deviation score 0.57 .4524 Yes 3.34
Mother’s working hours deviation score 7.05 .0079 Yes 11.05
  1. a

    Kleibergen-Paap rk LM test. Rejection based at the .05 level.

  2. b

    Kleibergen-Paap rk Wald F test.

Table 3
Glossary of variable names and labels used in stata code.
Variable name Variable label
burt Burt reading score
agecent Age centred
agecentsq Age centred squared
gender Gender
meduc1 Indicator variable for mother having tertiary education at the child’s birth
meduc2 Indicator variable for mother having secondary education at the child’s birth
feduc1 Indicator variable for father having tertiary education at the child’s birth
feduc2 Indicator variable for father having secondary education at the child’s birth
ses1 Indicator variable for family’s socio-economic status to be professional at the child’s birth to
ses2 Indicator variable for family’s socio-economic status to be clerical at the child’s birth to
breast Duration of breast-feeding
mhrswrk Average number of hours worked per week by the mother
homeown Indicator variable for owning the home
fsmoke Average number of cigarettes smoked per day by the father
ga Gestational age
single Indicator variable for child living in a single-parent family
welfare Indicator variable for child’s family receiving a benefit
fhrswrk Average number of hours worked per week by the father
chpar Indicator variable for whether the child experienced a change in parents in the last year
kids Number of children in the household
chres Number of changes in residence over the last year
pregalc Average number of alcoholic drinks consumed per week during pregnancy
bw Birth weight
single0 Indicator variable for the child being born into a single-parent family
accom Indicator variable for the child living in a detached house
fage Father’s age at the child’s birth
pregsmk Average number of cigarettes smoked per day during pregnancy
overcrowd Indicator variable for the child living in over-crowded conditions
mage Mother’s age at the child’s birth
msmoke Average number of cigarettes smoked per day by the mother
id Individual child id

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