SPATIAL-WC ECONOMET · SPATIAL AND WORST-CASE ECONOMETRIC TECHNIQUES, WITH APPLICATION TO MANAGEMENT MODELLING

Final Activity Report Summary - SPATIAL-WC ECONOMET (spatial and worst-case econometric techniques, with application to management modelling)

The work carried out during this project was concerned with several lines of research. The first focused on worst-case econometrics, the second was devoted to statistics and econometrics for spatial data and the last one considered management modelling applications. Several research papers were submitted for publication in international peer-refereed journals and some were in progress by the time of the project completion. All research results gave rise to the following manuscripts: 1. ‘Worst-case estimation and asymptotic theory for models with unobservables’, with Mercedes Esteban-Bravo. This paper proposed a worst-case approach for estimating econometric models containing unobservable variables. Limiting theory was obtained and a Monte Carlo study of finite-sample properties was conducted. An economic application was also included. The manuscript keywords were unobservable variables, robust estimation, minimax optimisation, M-estimators and GMM estimators. The manuscript was submitted by the time of this report. 2. ‘Automatic nonparametric spectral density estimation for multilateral spatial processes’. This paper considered the nonparametric estimation of spectral densities for second order stationary spatio-temporal processes. We prove uniform consistency and asymptotic normality when the smoothing number was estimated from the sampled data. The paper keywords were spatial data, multilateral samples, edge effect, nonparametrics, spectral density and smoothing number. The paper was submitted by the time of the project completion. 3. ‘Nonparametric prediction for spatial data in the frequency domain: extrapolation and interpolation’. This paper considered the nonparametric prediction of second order stationary random fields using linear filters based on spectral analysis. We discussed extrapolation and interpolation problems and derived the asymptotic properties of the proposed estimators. The considered approach allowed data to spread in some or all space directions. The relevant keywords were random fields, spectral analysis, nonparametrics, prediction and interpolation. The paper was submitted by the time of this report. 4. ‘Spatial density in retailing and its impact on business performance’, with Mercedes Esteban-Bravo and J. M. Mugica. In this paper we offered an efficient and strong competition measurement which captured the interdependent nature of spatial relationships. We considered a spatial density metrics based on spatial point processes and nonparametric statistics. Our results confirmed that retail density had an impact on economic performance. Furthermore, this methodology outperformed the results inferred from data aggregated by a conventional postcode partitioning. The submitted paper keywords were retailing, spatial competition, spatial point process models and nonparametric estimation. 5. ‘Optimal duration of magazine promotions’, with Mercedes Esteban-Bravo and J. M. Mugica. On the basis of the expected economic return associated with dynamic response to stimuli, we determined the ideal length of marketing events using dynamic programming optimisation and applied the model to a complex promotion event. Relevant keywords were optimal duration of promotion events, Markovian process and dynamic programming. This paper was forthcoming in Marketing Letters by the time of the project completion. 6. ‘The value of a ‘free’ customer’, with Sunil Gupta and Carl Mela. The purpose of this paper was to develop an analytical model that would help us assess customer value in the presence of direct and indirect network effects. The paper keywords were indirect network effect, customer relations management and customer valuation. The theoretical results were completely established and an empirical application was considered by the time of the project completion. We expected to write up the results and submit the paper for its publication in the near future.

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