Tutorial 9: (Women) labour force participation

In this exercise, we are going to learn:

  1. How households decide on their labour supply
  2. How the family size affect the latter
  3. Estimate the effects of having children on women labour participation

Theoretical approach of labour supply

Consider an individual who derives her utility from consuming a good \(c\) and leisure \(l\). The good comes at price \(p=1\), it is the numéraire. Utility function is:

\[ U(c,l) = c^\alpha \times l^{1-\alpha} \]

The individual earns a labour wage \(w\). The number of hours worked is denoted \(h\), hence the labour income is \(wh\). She also obtains a lump-sum benefit from the government \(y\). Hence, her total income is \(wh + y\). There is a fixed number of hours \(T\) in each day, such that \(T = l+h\).

  1. What are the two constraints? Can you express the budget constraint as a function of leisure \(l\), consumption, and total amount of time \(T\) only?
  2. Write down the maximization problem and the associated Lagrangian.
  3. Solve the maximization program to find \(c^\star\) and \(h^\star\).

We are now going to proceed to some comparative statics, i.e. we are going to twist some parameters to understand the partial equilibrium effects.

  1. How does \(h^\star\) evolve with wage? With the lump-sum benefit?

Now, we are going to assume that the individual has a positive number of children \(n>0 \in \mathbb{N}\). Then, she must allocate a fixed number of hours to take care of their children. Each child requires \(K\) hours of childcare, hence the total number of hours is \(nK\). In practice, it reduces the number of hours available to leisure and work.

  1. How does it affect labour supply? Is there a threshold upon which the mother stops providing labour?

Empirical approach

The theoretical prediction is that mothers might drop out the labour force because they have children. We are going to estimate this effect.

  1. Open the dataset lfs_women.csv.
Variable Description
idmen Household ID
obs Household member position in the HH
mne1 Number of children
nag Age
nsexe 1 if male
same_sexe 1 if first two children have the same gender
hh_twin_after 1 if second born are twins
ndiplo Scale from 1 to 9, high skilled from 5 to 9
ntravail 1 if the individual is working
ntpp 2 if the individual is working full time

For the sake of time, the dataset has been already cleaned. We can directly move to the estimation.

  1. Write a model with the labor force participation on the left hand side: we want to identify the effect of being the mother (of a large family) on labor force participation.
  2. Create the relevant variables.
  3. Run this model. Interpret the sign and magnitude of coefficients.
  4. Is there endogeneity? Which variables would you include to tackle it?
  5. Add household fixed effects. Why part of endogeneity do they tackle?
  6. Is there any endogeneity left?
  7. A first potential instrument for large families is the presence of twins among the second born children. Why? Discuss the validity of this instrument.
  8. Run the corresponding IV regression. Interpret the type of treatment effect obtained and the results.
  9. An alternative instrument is to have two first children of the same gender. Why? Discuss the validity of this instrument.
  10. Run the corresponding IV regression. Interpret the type of treatment effect obtained and the results