Finite sample inference in multivariate instrumental regressions with an application to Catastrophe bonds*

Abstract

We propose exact exogeneity tests and weak-instruments-robust tests on factor loadings for a system of regressions with possibly non-Gaussian disturbances. Our methodology is valid in finite samples and accounts for common cross-sectional factors. Analytical invariance results are derived, with companion simulation studies. Finally, a total-effect parameter is introduced that embeds the unobservable endogeneity factor. Proposed tests are applied to assess whether Catastrophe bond mutual funds co-move with financial markets. Significant risk premiums are detected globally and over time, although they are less pervasive from a domestic currency perspective. Findings underscore the importance of instrumenting and assessing direct and total effects.

Keywords:

• Catastrophe bond mutual funds
• endogeneity
• finite-sample multivariate test
• instrumental variable test
• weak instruments
• zero-beta asset

JEL CLASSIFICATION:

• C1
• C3
• C58

Notes

1 See Anderson and Rubin (1949).

2 See Durbin (1954), Wu (1973), Hausman (1978).

3 A general definition of a block of simultaneous equations is given by Anderson (2006).

4 In 2017 for example, $30 billion USD of CBs were outstanding with a nearly 60% share of all new bond issues captured by CBMFs (Aon Benfield, 2017a; Artemis, 2017). In addition, CBs accounted for nearly 30% of global funding of property catastrophe reinsurance obtained from alternative channels (Aon Benfield, 2017b).

5 We used a similar argument in the Appendix to prove invariance. Here we also need to recall that $M(X_1)M(X)=M(X)M(X_1)=M(X).$

6 n = 25 or 49 correspond to common applications with Fama-French portfolios in asset pricing.

7 Our paper does not aim to take a stand on pandemic bonds specifically but the bonds and funds we study cover extreme mortality and life risks.

8 For instance, in a low interest rate environment investors” reaching for the yield” may find CBMFs that offer attractive returns more appealing. Investors may be also more interested in CBMFs with a riskier composition. Reinsurance companies are also subject to systematic risks.

9 The division into sub-periods is based on dates from the National Bureau of Economic Research.

10 Descriptive statistics are reported in the Appendix.

11 As a robustness check, we used VWRETD expressed in foreign currency, along with the same exchange rates as described above. Results reveal no change in our empirical evidence using that alternative.

Additional information

Funding

This work was supported by the Social Sciences and Humanities Research Council of Canada, Natural Sciences and Engineering Research Council of Canada and the Chaire RBC en innovations financières.