On the applicability of maximum likelihood methods: From experimental to financial data - Sven Thorsten Jakusch (Goethe University Frankfurt, SAFE - Sustainable Architecture for Finance in Europe, 2017)
This paper addresses whether and to what extent econometric methods used in experimental studies can be adapted and applied to financial data to detect the best-fitting preference model. To address the research ques- tion, we implement a frequently used nonlinear probit model in the style of Hey and Orme (1994) and base our analysis on a simulation study. In detail, we simulate trading sequences for a set of utility models and try to identify the underlying utility model and its parameterization used to generate these sequences by maximum likelihood. We find that for a very broad classification of utility models, this method provides acceptable outcomes. Yet, a closer look at the preference parameters reveals several caveats that come along with typical issues attached to financial data, and that some of these issues seems to drive our results. In particular, deviations are attributable to effects stem- ming from multicollinearity and coherent under-identification problems, where some of these detrimental effects can be captured up to a certain degree by adjusting the error term specification. Furthermore, additional uncertainty stemming from changing market parameter estimates affects the precision of our estimates for risk preferences and cannot be simply remedied by using a higher standard deviation of the error term or a different assumption regarding its stochastic process. Particularly, if the variance of the error term becomes large, we detect a tendency to identify prospect theory as utility model provid- ing the best fit to simulated trading sequences. We also find that a frequent issue, namely serial correlation of the residuals, does not seem to be an im- portant issue. However, we detected a tendency to prefer nesting models over nested utility models, which is particularly prevalent if rank-dependent utility and exponential power utility models are estimated along with expected utility with constant relative risk aversion utility models.
Keywords: 330; Utility Functions; Model Selection; Parameter Elicitation