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Seemingly Unrelated Regression A researcher wants to document the gender patterns of unpaid work (i

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Seemingly Unrelated Regression

A researcher wants to document the gender patterns of unpaid work (i.e. non-paid household production activities like cooking or cleaning) and examine how it interacts with paid work (i.e. activities to earn an income) and spare time (i.e. personal care activities, household care activities or leisure time). She has access to Time Use Surveys (TUS) that provides information on how people allocate their time in a given day. The random sample contains information on 200 individuals. We consider the following model:

PaidWork_1i = α₀ + α₁female_1i + α₂married_1i + α₃child_1i + α₄schooling_1i + u_1i (1) UnpaidWork_2i = β₀ + β₁female_2i+ β₂married_2i + β₃child_2i + u_2i                                      (2)

SpareTime3i = γ₀ + γ₁female_3i + γ₂age_3i + u_3i                                                                                                           (3)

where

female: takes value 1 if individual i is a woman. married: takes value 1 if individual i is married. child: the number of children aged 0-6 years.

schooling: takes value 1 if individual i goes to school

age: the age of individual i in years.

 

?_kk

k = l, i = j

?_kl

k ≠ l, i = j

0

k = l, i ≠ j

0

k≠l, i ≠ j

Consider the following stochastic hypotheses :

E(u_1i) = E(u_2i) = E(u_3i) = 0  "i

 

 

E(U_kiU_lj) =

 

 

 

where subscripts k, l refer to equations and subscripts i, j to individuals. For instance, E(u_kiu_ij) is equal to zero for different individuals (i ≠ j) in the same equation (k = l).

1.  Write the model as :

y_m = X_mb_m + u_m   m = 1,2,3

Give the content and dimensions of y_m, X_m, b_m, u_m.

Then, regroup as:

y = Xβ + u                                           (5)

Give the content and dimensions of y. X, β, u.

2.  Calculate E(u) and E{uu'). Give the content and dimensions of each matrix.

3.  Propose an estimation method for the model and justify your choice. Describe in details the steps of the estimation method.