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  • Correcting for selectivity and omitted variable problems in discrete time event history analysis

    Apologies for cross-listing.

    Dear all,

    I am trying to examine the effect of family ownership on the deactivation of offshore companies in the Panama Papers data leak. Unfortunately, for some of the companies, ownership information is not available because of the use of bearer shares, enabling beneficial owners to maintain their full anonymity. This is a case of NMAR.
    Furthermore, I don't have data to capture the size of offshore companies in the network - which may cause omitted variable problems. To correct for the selectivity effect arising from missing ownership information and for omitted variable problems arising from data unavailability on company size, I am using gsem in Stata/MP 15.1.

    This is the list of my covariates:

    familiar_shareholders - family-owned company (binary variable)
    age - company's age (quantitative variable)
    llc - legal form: llc vs. corporation (binary variable)
    connected_exits_L1 -the number of deactivations of tied offshore companies in the ownership network between the beginning of the prior year and time t (quantitative variable)
    degree centrality (quantitative variable)
    closeness centrality (quantitative variable)
    betweenness centrality (quantitative variable)
    local clustering (quantitative variable)
    inter_incorporations_L1 - number of incorporations by the focal company's intermediary at t-1 (quantitative variable)
    inter_deactivations_L1 - number of deactivations by the focal company's intermediary at t-1 (quantitative variable)
    jur_deactivations_L1 - number of deactivations in the focal company's jurisdiction at t-1 (quantitative variable)
    jur_incorporations_L1 - number of incorporations in the focal company's jurisdiction at t-1 (quantitative variable)
    post_tiea - country-jurisdiction dyad under a tax information exchange agreement (binary variable)
    i.year - year fixed effects (binary variables)
    i.count_jur_dyad - country-jurisdiction dyad fixed effects (binary variables)
    bearer - bearer shares, causing familiar_shareholders = . (binary variable)

    I am assuming that the probability of deactivation depends on a time-varying latent variable L1 (representing size), which also affects family ownership and the presence of bearer shares. In particular, family ownership is affected by L1, other exogenous covariates, and conditional on the absence of bearer shares - I am using another latent variable L2 to correct for selection. The presence of bearer shares is affected by L1, L2, and other exogenous covariates. I am using weights (k2k Coarsened Exact Matching (CEM) approach) to match family and non-family owned offshore companies in the sample based on their network positioning (degree, closeness, betweenness, clustering), legal form, and incorporation year.

    The Stata code I am using is:

    Code:
     gsem (deactivation <- i.familiar_shareholders connected_exits_L1 degree closeness_adj betweenness_adj clustering age i.llc inter_incorporations_L1 inter_deactivations_L1 jur_deactivations_L1 jur_incorporations_L1 i.post_tiea i.year L1, probit) ///
     (familiar_shareholders <- L1 L2 age inter_incorporations_L1 inter_deactivations_L1 jur_deactivations_L1 jur_incorporations_L1 i.post_tiea i.year, probit) ///
     (bearerother <- L1 L2@1 age inter_incorporations_L1 inter_deactivations_L1 jur_deactivations_L1 jur_incorporations_L1 i.post_tiea i.year, probit) [iweight=jc_k2k_matched_cem], var(L1@1 L2@1) nolog
    I had to remove country-jurisdiction dyad fixed effects from the model because I was receiving the following error message:
    Code:
     Grid search failed to find values that will yield a log likelihood value.
    The model has been running for 15 hours. Since I will have to run it several times to test my hypotheses, I was wondering whether you could provide me with any suggestions on how to simplify the model while still correcting for endogeneity and selectivity issues.

    Thank you for considering my request.
    Best regards,
    Ambra
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