Research Papers

Non-parametrically estimating preferences in presence of strategic reports: Application to college admissions:

Paper develops preference estimation approach that translates strategically altered reported ordinal preferences into true cardinal revealed preferences. Empirical example looks at the data on college applications by Turkish high school graduates and backs out the distribution of preferences in the population for the different university programs without imposing any distributional assumptions. Each student upon passing the unified examination and knowing their scores as long as the history of acceptance scores at all of 3000+ programs across the Turkey, is free to submit ranked list of up to 24 programs. Allocation mechanism ensures that conditional on reported preferences, each applicant gets his most desirable program that still has seats left after allocating all higher ranked applicants. Students have preferences for the programs differentiated by university and major. For example, one may prefer biology engineering in Sabancı university to computer engineering in Bilkent university to economics in Istanbul university. The student may consider dozens of other programs as well. Some of these programs the student may have a shot at with his exam scores, other may be virtually impossible to get into for him, but the space on the allowed list of reported preferences is limited, so, he has to skip the more desirable, but unreachable programs. Thus, the reported preference deviates from the true preferences the lower the placement score of an applicant is. We use the data on joint distribution of exam scores and submitted preferences to uncover the distribution of cardinal preferences (e.g. utility of studying biological engineering in Sabancı is twice as large as computer engineering in Bilkent which is tree times as large as economics in Istanbul university).

Numerical Algorithm for Inverting the Pure Characteristics Model of Demand

This paper proposes and implements the solution concept of inverting Pure Characteristics Model of demand via Pseudo-Newton algorithm in Knitro solver. The PCM model studied here ha very attractive theoretical properties in application to demand estimation in markets where share of each individual product is small (units of percents). Small market shares make the use of the classic empirical IO model (a.k.a. BLP) overfit the market shares at the expense of substitution patterns. Berry and Pakes in their seminal paper of 2007 proposed a new demand system that would balance the fit of the observed market shares and counter-factual market shared making predictions coming out of this model more accurate and useful for policy analysis, predictions and anti-trust. The application of the model was halted by sheer complexity of inverting the model i.e. backing out the underlying parameters from the observed data. This paper shows how to harness the power of the modern nonlinear optimization libraries combined with insightful initial guesses and bootstrapping out of flat Jacobian regions to reliably and precisely solving for the inversion problem.

Risky intensity peaks resulting from nonlinear holographic imaging.

This is my first academic work done as a result of my undergraduate research project at General Physics Institute of Russian Academy of Sciences. it develops computational and theoretical techniques to predict the occurrence of hot spots in downstream of the powerful lasers used to ignite thermonuclear reaction in small balls containing hydrogen isotopes. The risk comes from nonlinear imaging of physical obstructions in glass used to magnify the power of the radiation in laser amplifier. This is caused by so called nonlinear response of medium to powerful radiation, which is the same phenomenon that causes such effects as auto-focusing and doubling of of frequency of radiation. The downside of this phenomenon in laser systems like the ones we studied is that a minuscule flaw in one glass cal cause dramatic consequences in downstream glass panels that can break all of them, which follows by lengthy repairs of the whole laser channel that can cost upwards from a couple dozen million dollars. We develop theoretical and computational framework for computation of maximally allowed impurities and aberrations in glass used in these amplifiers, which allows to proof the amplifier from the operational defects caused by nonlinear imaging.

Conferences

• 12th Annual EGSC, Washington University, 2017
• International IO Conference, 2020 (canceled)
• ZICE conference, Zurich, 2016