Accommodating price dynamics in semiparametric sales response models

In marketing research, the modeling of demand is one of the key factors in the value-to-customer concept
for predicting sales and setting prices, and thus constitutes an important determinant of price management.
Sales or price response functions build the basis for the analysis of price effects based on aggregate data, and
in the context of retail sales data they are often embedded into a promotional context, where the pricing
for products is usually accompanied by non-price promotional activities. The analysis of store-level data
has several advantages over household data in terms of availability, representativeness and processability,
but it may also suffer from, e.g., aggregation biases and difficulties to disentangle certain (dynamic) effects
which have their origin at the more disaggregate household level. Particular challenges in this context are
the specification of the functional form of the relationship between sales and (own and competitive) prices
and the accommodation of heterogeneity in marketing effects across different stores of a retailer, where
the first challenge can be addressed by nonparametric estimation techniques (e.g., using splines) and the
latter by hierarchical modeling approaches. The importance of accounting for functional flexibility and store
heterogeneity has been emphasized in several related studies, but the additional use of dynamic variables
as a third related issue has not yet been incorporated. A dynamic perspective on brand sales can help
to understand multi-period relationships between prices and sales, which in turn affects sales predictions,
related pricing decisions and (optimal) expected profit calculations. Therefore, the topic of price dynamics
is in the center of this dissertation, and the three included studies contribute to closing this research gap.
In the first study, the focus is on price-change or reference price effects in semiparametric sales response
models. Its theoretical motivation is based on adaptation-level theory and prospect theory. The former states
that the perceived value of a new stimulus (here: the price of a product) results from the comparison with an
already known ‘adaptation level’ (here: a reference price), while the latter suggests that the value function
for evaluating the difference between price and reference price is convex for losses (positive difference) and
concave for gains (negative difference). To verify this assumption in aggregate sales data, we model reference
price effects on brand sales using a semiparametric approach. We consider differences between current price
and reference price in absolute and relative terms, compare the results with parametric benchmark models
in an empirical study, and find that accounting for that kind of price dynamics (largely) improves the out-ofsample
model performance. Gain and loss effects turn out to be highly asymmetric, which demonstrates an
important advantage of the semiparametric approach: its flexibility allows us to capture such asymmetries
without prior knowledge of their existence and without the need to use separate covariates for gains and
losses as necessary in parametric models. Furthermore, the study reveals partly very complex nonlinearitites
for gain effects that in addition turn out larger than loss effects, which is not in line with prospect theory.
In the second study, we combine a semiparametric heterogeneous sales response model with a dynamic
pricing approach by incorporating one-week lagged prices. We further estimate several nested benchmark
models in an empirical study to be able to compare dynamic vs. static model alternatives as well as flexible
vs. parametric and heterogeneous vs. homogeneous models in terms of their predictive capabilities. In this
context, we introduce a scoring rule for probabilistic forecasts to the marketing literature and find that the
more complex models are able to outperform their simpler counterparts in most cases. Moreover, we apply a
dynamic programming approach for price optimization. We examine the resulting price paths and compare
the various model alternatives with regard to optimized profits and expected losses. While optimized prices
from static models closely follow (variable) costs, the incorporation of a lagged price variable leads to a
distinct hi-lo pattern with partially large price discounts, depending on the extent of consumers’ price
sensitivity in a considered store. The comparison of observed, predicted, and optimized profits further
confirms that over- and underestimations of sales can be avoided by imposing reasonable price and sales
constraints in the dynamic program, while leading to higher optimal profits compared to the currently
observed pricing strategy.
In the third study, we develop a semiparametric reparametrization approach with dynamic price effects.
In particular, we propose a sales response model with a flexible nonparametric own-price effect, with the
possibility to scale this price effect to the individual store level by accounting for unobserved cross-sectional
store heterogeneity and/or to the time dimension by accommodating time-dependent effects (operationalized
as price-change effects in subsequent weeks). In an empirical study, we show that the proposed new
reparametrization approach can provide more accurate sales predictions, particularly when compared to
a model that ignores price-change effects (i.e., the time dimension in our data), and even when crosssectional
store heterogeneity is considered. Interestingly, the accommodation of substantial price decreases
greatly improves the predictive performance of the model, whereas the consideration of corresponding price
increases does not or is clearly of minor importance. Lastly, we find a strong underestimation of price
elasticities in weeks with substantial price cuts as well as a (less dramatic) overestimation in case of high
prices when not accommodating for the price-change effects.