This paper studies behavior patterns among theater attendees in the process of ticket purchasing. Since the theater attempts to balance between a high occupancy and affordable prices, the purpose of the study is to reveal the effects of changes in prices on attendance. This project is conducted conjointly with the Perm Tchaikovsky Opera and Ballet Theater. Data are taken from the sales information system of the theater for four seasons 2011-2012/2014-2015. The data are disaggregated to the level of the seating area and performance and consist of the attendance rate, the set of prices and the performance characteristics. The research explores the determinants of demand using a censored quantile regression which accounts for the heterogeneity of effects on different levels of attendance rates and censoring. We estimate the parameters of the demand function and show that the aggregated demand is elastic by price, at the same time the elasticity varies across different seating areas. Moreover, demand for the more popular seats and performances is less elastic.

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This paper investigates the distribution of relative credit losses given mortgage default for loans provided by a major government-sponsored creditor in a local area. We use borrower's individual and loan-level data on residential mortgages originated in the period 2008-2012. Our numerical analysis indicates that mortgages bunching at certain Loan-to-Value ratios (LTV) led to a discontinuity in relative credit loss given mortgage default. Through regression analysis, we demonstrate discrete jumps in the approximated historical credit losses generated by loans with a high LTV ratios and find thresholds allowing the segmentation of loans according their credit risk. In addition, our results suggest that mortgage insurance is a potentially valuable instrument for compensation for expected loss in certain risk segments.

Many economic applications including optimal pricing and inventory management requires prediction of demand based on sales data and estimation of sales reaction to a price change. There is a wide range of econometric approaches which are used to correct a bias in estimates of demand parameters on censored sales data. These approaches can also be applied to various classes of machine learning models to reduce the prediction error of sales volume. In this study we construct two ensemble models for demand prediction with and without accounting for demand censorship. Accounting for sales censorship is based on the idea of censored quantile regression method where the model estimation is splitted on two separate parts: a) prediction of zero sales by classification model; and b) prediction of non-zero sales by regression model. Models with and without accounting for censorship are based on the predictions aggregations of Least squares, Ridge and Lasso regressions and Random Forest model. Having estimated the predictive properties of both models, we empirically test the best predictive power of the model that takes into account the censored nature of demand. We also show that machine learning method with censorship accounting provide bias corrected estimates of demand sensitivity for price change similar to econometric models.

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