Underwriting Profits: Are the Data Consistent with “Rationally Priced” Insurance Cycles? - Leng, Chao-chun; Venezian, Emilio (Assurances et gestion des risques / Insurance and Risk Management, 2003)
Cummins and Outreville (1987) suggested that the cyclical nature of insurance profits might result from the combination of insurance prices created in an environment of rational expectations with lags in information and in profit reporting. Their theoretical model predicts the autoregressive properties of underwriting profits. They interpret the model as an AR2 process, and from this, they derive the range of cycle lengths and conclude that the hypothesis is in general agreement with the empirical results they present. This paper looks in more detail at empirical tests of this “rational pricing with lags” model of insurance cycles. We find the predicted cycle lengths are often not in the same range as most of the observed cycle lengths. The predicted joint range of the two AR2 coefficients is fairly restricted and the empirical data seem to be away from this region. The values of R2 predicted by the theory are lower than most of those observed empirically. We show that under the Cummins and Outreville hypothesis, the autocorrelation coefficients at lags of three or more should be zero. Data by line of insurance from the United States for the periods 1960 to 1980 and 1973 to 1997, from Europe for the years 1955 to 1979, and from Asia for various periods show that this consequence of the model is contrary to the empirical evidence.