Questions on code to "Bargaining over Babies"

Forums Questions on specific programs Questions on code to "Bargaining over Babies"

This topic contains 1 reply, has 2 voices, and was last updated by Fabian Kindermann August 30, 2021 at 2:54 pm.

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  • #1944

    Shengzhi Mao
    User

    Dear Fabian,

    Recently, I’m learning the codes of your paper “Bargaining over Babies: Theory, Evidence and Policy Implications” and meet some questions about the codes. Maybe other people would also have these questions in the future, so I guess it might be better to ask them here instead of writing you private emails.
    The questions come from the code “wage_distribution.f90”. In specific, in the function moment_eq(p), we have:

    moment_eq = exp(log(com_p) - sigma*(Phi_LFP - sigma/2d0))*(1d0-normalCDF(Phi_LFP - sigma))/com_LFP - com_w

    while in the upper lines (51-54),

        ! set parameters of the log normal distribution
        sigma  = p
        mu     = log(com_p) - sigma*normalCDF_Inv(1d0-LFP_without)
        mu_log = exp(mu + sigma**2/2d0)

    the mu_log is
    exp((log(com_p) - sigma*normalCDF_Inv(1d0-LFP_without)) + sigma**2/2d0), which is different from

    exp(log(com_p) - sigma*(Phi_LFP - sigma/2d0))*(1d0-normalCDF(Phi_LFP - sigma))/com_LFP in the function moment_eq(p).

    The first question is why the mu_log is given by
    exp((log(com_p) - sigma*normalCDF_Inv(1d0-LFP_without)) + sigma**2/2d0).

    Moreover, are the values of com_p(=p_cost=0.358) and LFP_without(=/62.59615d0, 80.49617d0/) from fertdec.f90 already be given here? Thus only the sigma is unknown here?

    However, in the paper, just below Table 6, you write “These four target moments (Women’s Labor Force Participation) help pin down the dispersion of women’s wages σ_{w,e}, the labor market participation cost p_c, and the cost of market-based child care w_y.” So I thought sigma should not be estimated alone as you did in wage_distribution.f90?

    The second question is why in the moment_eq, you add
    (1d0-normalCDF(Phi_LFP - sigma))/com_LFP,
    which is confusing to me.

    Thank you very much!

    Best wishes,
    Shengzhi Mao

    #1950

    Fabian Kindermann
    Moderator

    Dear Shengzhi,

    this is an excellent questions, but it will take some time to explain this. What we are doing here is to simultaneously calibrate the (education specific) mean and the variance of the wage distribution. We are doing so to achieve the following goals: We want

    1. the labor force participation rate of women without children to match the data
    2. the mean wage !!! of the employed women without children !!! to be equal to 1 for the lower educated and 1.5 for the higher educated.

    The labor force participation rate is equal to the likelihood that the wage is larger than the participation cost. From this we get a closed form for the mean. In the function moment_eq we then calculate the mean wage of employed women as E(w | w >= p_c). This brings us to the equation from which we can determine the standard deviation.

    If you drop me your email address privately, then I can send you a quick write-up of this.

    Best,
    Fabian

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