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NTU Management Review Vol. 34 No. 1 Apr. 2024

3.3 Estimation Strategy
First, we estimate equation (1) for the full sample using feasible generalized least
27
squares (FGLS) with a panel-specific AR (1) autocorrelation structure. We include year
dummies in the model to control for exogenous economic factors related to reserving

28
decisions that change over time and have not otherwise been controlled for in the model.
Chow tests are conducted to determine whether it is appropriate to pool weak and
healthy insurers in the same regression. Accordingly, equation (1) also is estimated for the
subsamples of weak versus healthy insurers. We define weak insurers as insurers that have
failed four of the Insurance Regulatory Information System (IRIS) ratio tests (e.g., see
Gaver and Paterson, 2004; Petroni, 1992) and classify all other insurers as “healthy.”
29

4. Data and Sample Selection

In this section we discuss the sources for the data used in our analyses and sample
selection criteria, which includes the Propensity Score Matching process.

27 The Breusch-Pagan Lagrangean multiplier tests suggest that fixed/random effects models are pre-
ferred to a pooled cross-sectional model with no unit or time effects. Hausman tests indicate that fixed
effects are preferred to random effects models. However, full fixed effects models assume the error
term is normally distributed and homogeneous. Modified Wald tests reject the null hypothesis that
there is no existence of group-wise heteroscedasticity (p < 0.0001). Wooldridge (2010) tests indicate
serious autocorrelation exists in our panel data. Beaver and McNichols (1998) report positive serial
correlation in reserve errors indicating multi-period reserve management. Grace and Leverty (2012)
also report heteroscedasticity and serial correlation in their sample. Therefore, the assumptions for
fixed effects are not met for our data. FGLS estimation with autocorrelation controls for serial cor-
relation and group wise heteroscedasticity is commonly used to deal with these problems (Grace and
Leverty, 2012). We have to drop some firms from the FGLS estimation because they are present for
only one year of the sample period. This reduced the sample by 112 observations.
28 Exogenous economic factors include unexpected inflation and changes in court attitudes and jury ver-
dicts which are out of management control (Petroni, 1992). Gaver, Paterson, and Pacini (2012) doc-
ument that the P-C insurance industry as a whole over-reserved from 1993 to 1997, under-reserved
from 1998 to 2002, and returned to over-reserving from 2003 to 2004. Reserve errors for our sample
by year are -0.0108, -0.0298, -0.0346, -0.0261, -0.0034, 0.0162, 0.0296, 0.0346, 0.0348, 0.0322,
0.0305, and 0.0286 from 1999 to 2010, respectively.
29 The IRIS system consists of twelve financial ratio tests. Insurers with four test results outside of the
NAIC prescribed boundaries are scrutinized more rigorously than other insurers. The degree of scru-
tiny; however, varies by state. For an excellent discussion of these ratio tests, see Gaver and Paterson
(2004).

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