Peter Wechselberger () Stefan Lang () Winfried J. Steiner ()
Abstract
We discuss inference for additive models with random scaling factors. The additive effects are of the form (1+g)f(z) where f is a nonlinear function of the continuous covariate z modeled by P(enalized)-splines and 1+g is a random scaling factor. Additionally, monotonicity constraints on the nonlinear functions are possible. Our work is motivated by the situation of a retailer analyzing the impact of price changes on a brand's sales in its orange juice product category. Relating sales to a brand's own price as well as to the prices of competing brands in the category, we estimate own- and cross-item price response functions flexibly to represent nonlinearities and irregular pricing effects in sales response. Monotonicity constraints are imposed so that a brand's own price is inversely related and the prices of competing brands are directly related to the number of items sold, as suggested by economic theory. Unobserved store-specific heterogeneity is accounted for by allowing the price response curves to vary between different stores.
Download Info
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. In case of further problems read
the IDEAS help
page. Note that these files are not on the IDEAS
site. Please be patient as the files may be large.
Publisher Info
Paper provided by Faculty of Economics and Statistics, University of Innsbruck in its series Working Papers with number
2007-27.
Did you know? You can include your works in the database easily by uploading them on the Munich Personal RePEc Archive (MPRA) if you do not have access to an institutional RePEc archive.