Empirical Similarity: estimation, multivariate extensions, and applications

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Economists aim to describe reality with formal decision rules which postulate specific causal relationships validated empirically by econometric analysis. However, sometimes there is no appropriate decision rule at hand, but only some experienced cases defined as a set of conditions, acts and their outcomes. Then a case-based decision should resemble successful decisions in those experienced cases which are similar to the current case. The empirical similarity (ES) approach provides econometric framework for case-based decisions and presumes that the variable of interest is a sum of historical outcomes weighted by similarities of current and previous cases. Hence, the ES weights are time-varying and determined by nonlinearly by exogenous variables which allows to reveal the principles of case-based decision making directly from the data. Its application has already provided useful insights in experimental economics, modeling real estate prices, predicting volatilities on financial markets or evaluating legal juridical decisions. However, there are still some unresolved econometric issues as well as interesting applications which we will address in this project.In the theoretical part of the project we are going to analyse, first, which properties of empirical data are suitable for applying ES technique and what happens if the underlying assumptions are violated. Second, estimation instability of existing ES models hinders their application in many important problem settings. Our objective is to propose regularization techniques for stabilizing ES estimation procedure as well as to provide results about variable selection and dimension reduction issues. Third, the current theoretical results focus on univariate data whereas multivariate ES (MES) models are required for decisions characterized by vectors of variables. We aim to develop MES models with a particular attention paid to model selection, inferences and robust estimation.Further, in the empirical part of the project we are going to apply the ES concept to research problems in economics and finance. We plan to investigate whether monetary policy of the US Federal reserve implemented by adjustments of the nominal interest rate is driven by formal rules or primarily by experience relying on case-based arguments. Then, we are going to consider technical analysis as a nonparametric approach to asset pricing from the ES perspective. We focus on recognition of price patterns and measuring similarities between different patterns in order to get information about future prices. Next, we will consider various portfolio selection strategies and determine the weights of different strategy by means of ES approach.Summarizing, the project will cover a set of theoretical problems and potential applications of the promising ES approach which is the econometric setting for case-based decisions contrasted to formal rule-based modeling.