Essays on corporate DB pension plans and on cointegrated time-series and panel models

Managing Sponsor Risk in Pension Plans: Dynamic Strategies vs. Pension Assurance: Defined-benefit (DB) pension funds, often underfunded, rely on the legal obligation of their sponsor to secure pension rights for individuals. Because that guarantee is risky, ways must be found to secure the pension promises. This paper is the first to identify the optimal pension fund portfolio, taking into account the riskiness of the sponsor’s guarantee, both with and without external insurance against the sponsor’s riskiness. I show that such Pension Indemnity Assurance (PIA) facilitates the implementation of the optimal strategy even in a First-Best, complete markets setting. I also study the optimal design of PIA taking into account risk-shifting incentives in pension plans. The optimal PIA is a non-redundant asset and contract that reduces the risk-shifting incentives from each party to the pension contract and fully mitigates sponsor risk.

Improving the finite-sample estimators of cointegrated panel models: Though ordinary least square (OLS) estimates are super-convergent with cointegrated variables, their finite-T bias can be large in the presence of endogenous feedback. Fully modified OLS (FMOLS) are the modern and parsimonious tools to measure the long-run [cointegrating] slope between integrated variables in the presence of weak endogeneity, and correct the first-order OLS bias to the extent necessary
to provide a nuisance parameter-free asymptotic distribution: in FMOLS, because the first-stage OLS estimator is consistent, the second-stage asymptotically successfully removes the nuisance parameters. Yet FMOLS nests in T-asymptotic and the finite-T situation is not studied. This paper studies properly the impact of the first-step bias and of its correction in the FMOLS setting, as follows:
• I establish that due to the reliance on biased residuals from the first-step OLS regression, FMOLS asymptotically leave an O(h=T) fraction of the OLS bias, where h is the selected bandwidth.
• I introduce a correction for the residual O(h=T) FMOLS bias, thus also improving the ability to rely on non-parametric techniques in panels.
• I establish the maximal size at which N can grow simultaneously to T for the tests statistics of panel group-mean of time-series estimators to be asymptotically nuisance parameter-free.
In the scenarios reviewed by previous research, my finite-T FMOLS fares compared to its asymptotic estimator, but size distortions increase with the width of the panel.

Finite-T panel cointegration : Though ordinary least square (OLS) estimates are super-convergent with cointegrated variables, their finite-T bias can be large in the presence of endogenous feedback. Fully modified OLS (FMOLS, see Phillips and Hansen, 1990 or Pedroni, 2001), or conditionally unbiased FMOLS (FT-FMOLS, see Sender, 2013) are the modern and parsimonious tools to measure the long-run [cointegrating] slope between integrated variables in the presence of weak endogeneity, yet they nest in T-asymptotic, and the application of time-series estimators in panel data results in distortions in the size of the associated test-statistics that increase with the width of the panels. An open question is thus whether, in the presence of weak endogeneity of un unknown form, one can extract information from the panel dimension so as construct estimators with better finite-T properties, and testable hypothesis. The contribution of this paper is to show that in a large-N setting and possibly small-T setting, one can use the information content of the cross-section (under the assumption of homogenous feedback) to build virtually bias-free estimators. As it happens, the gain in precision from the panel data allows for the use of a more flexible and testable weight structure than that embedded in kernels used in nonparametric estimates. Variance is also better estimated, which results in markedly more accurate size statistics compared with existing estimators (OLS, FMOLS or even FT-FMOLS). In the scenarios reviewed by previous research, panel estimators bring not only large improvements with wide panels, but also, perhaps surprisingly, even when the panel width is as small as 20, empirically even in the presence of cross-section heterogeneity.