A credibility theory for automobile bonus systems

Summary

This paper deals with the problem of designing experience rating systems of the bonus type, commonly used in automobile insurance. On the basis of a simple model the mean squared deviation between a policy's expected claim amount and its premium in the nth insurance period as n→∞, is taken as a measure of the efficiency of a bonus system. It is shown that to any set of bonus rules (which determines the bonus class transitions of the policies), there is an optimal premium scale, which coincides with the one proposed by Pesonen in 1963. Thus the problem of choosing an efficient bonus system reduces to choosing efficient bonus rules. Examples are given of comparison between different bonus rules. In one example the present Norwegian bonus system is compared to alternative systems. Comments are made on earlier papers on bonus systems. The credibility theoretic foundation is laid in a separate section.     

Estimation and decomposition of inefficiency when producers maximize return to the outlay: an application to Norwegian fishing trawlers

This paper deals with estimation of a production technology where endogeneous choice of input and output variables is explicitly recognized. In particular, we assume that producers maximize return to the outlay (RO). For simplicity and tractability we start with a Cobb–Douglas transformation function with multiple inputs and outputs and show how the first-order conditions of RO maximization can be used to derive an estimating equation which is nothing but a partial input productivity equation. This equation does not suffer from the econometric endogeneity problem although the output and input variables are endogenous. First, we consider the case where producers are fully efficient allocatively but technically inefficient. The model is estimated using a single equation stochastic frontier approach. The model is then extended to allow allocative inefficiency and it is estimated as a system using generalized method of moment. Algebraic expressions are derived to decompose the effect of technical and allocative inefficiencies on RO. We also consider translog specifications that are estimated as (1) a single equation frontier model as well as (2) a system. We use a panel of Norwegian fishing trawlers data to estimate the model. Outputs are different species caught while inputs are labor and vessel size. We also control for number of days of operation, age of the vessel and year effects. Empirical results show that the average rate of RO is reduced by about 20 to 30 % due to technical inefficiency. On the other hand, average allocative efficiency is found to be about 78 %. The average overall efficiency is found to be around 60 %.     

Overdeterminacy and Endogenous Cycles: Trygve Haavelmo's Business Cycle Model

The econometrician Trygve Haavelmo pursued a research programme in macroeconomic theory that was highly original for its time. We present his macro model for an economy with deregulated financial markets and a policy determined interest rate path. Disequilibria arise in the interface between asset markets and the real economy. A mismatch between the marginal return to capital and investors' required rate generates endogenous switching between recession and full employment regimes. Haavelmo regarded the ‘switching mechanism’ as a substitute for liquidity constraints, and together with his ideas of price dynamics, there is a clear Keynesian and Wicksellian influence on his macroeconomic theorizing.     

Macroeconomic Stability or Cycles? The Role of the Wage‐Price Spiral

We formulate a small and stylised dynamic macroeconomic model, and study how different specifications of the supply side affect the model's dynamic properties. The wage‐price equilibrium‐correction model (ECM) and the Phillips curve model (PCM) that both can be used to represent the supply side of a New Keynesian macro model, are synthesised in a generalised model of the wage‐price spiral. We show that the choice of ECM or PCM has implications for the long‐run stability of the macro model, without need of a NAIRU. We also find that the range of theoretically admissible dynamics is wide. For example, both the ECM and PCM may display endogenous cyclical fluctuations in inflation and unemployment, showing that even simple structures can give rise to complex dynamics. In practice that may entail that forecasting the effects of shocks and policy changes is difficult even in the best of circumstances.     

HAZARDS IN IMPLEMENTING A MONETARY CONDITIONS INDEX

Some recent studies have suggested constructing a Monetary Conditions Index (or MCI) to serve as an indicator of monetary policy stance. The central banks of Canada, Sweden and Norway all construct an MCI and (to varying degrees) use it in conducting monetary policy. Empirically, an MCI is calculated as the weighted sum of changes in a short-term interest rate and the exchange rate relative to values in a baseline year. The weights aim to reflect these variables’ effects on longer-term focuses of policy — economic activity and inflation. This paper derives analytical and empirical properties of MCIs in an attempt to ascertain their usefulness in monetary policy. An MCI assumes an underlying model relating economic activity and inflation to the variables in the MCI. Several issues arise for that model, including its empirical constancy, cointegration, exogeneity, dynamics and potential omitted variables. Because of its structure, the model is unlikely to be constant or to have strongly exogenous variables, yet constancy and exogeneity are critical for the usefulness of an MCI. Empirical analyses of Canadian, Swedish and Norwegian MCIs confirm such difficulties. Thus, the value of an MCI for conduct of economic policy is in doubt.     

On Bonus and Bonus Prognoses in Life Insurance

The surplus on a life insurance policy is defined, at any time during the term of the contract, as the difference between the second order retrospective reserve and the first order prospective reserve. General principles for redistribution of the systematic part of the surplus as bonus are formulated, and various special bonus schemes are discussed. Techniques for forecasting future bonuses are worked out in an extended model with stochastic experience basis. Numerical illustrations are provided.     

Plant Exit, Vintage Capital and the Business Cycle

Despite the large literature on plant exit behavior, little attention has been paid to the vintage capital theory as an alternative hypothesis to learning. Learning models predict that exit rates decrease with plant age and the vintage capital theory predicts that exit rates increase with the age of capital. We use a panel of Norwegian manufacturing plants and construct an index of capital age to distinguish between the effects on exit rates. The empirical results imply that there is both a learning effect and a vintage capital effect. We also find that exit rates depend on the business cycle, and increase in severe downturns.