Developing Interaction Shrinkage Parameters for the Liu Estimator — with an Application to the Electricity Retail Market

Abstract

In this article we examine multicollinearity in the standard OLS interaction-term model—a problem often disregarded by practitioners and in previous research. As a remedy we propose a number of new shrinkage parameters based on the Liu (Commun Stat 22:393–402, 1993) estimator. Using Monte Carlo simulations, we evaluate the robustness of all models for different data-generating processes under varying conditions such as altered sample sizes and error distributions. In the simulation study it is demonstrated that the Liu estimator, which is robust to multicollinearity, systematically outperforms the traditionally applied OLS approach. The simple reason is that interaction models by definition always induce substantial multicollinearity, which in turn distorts the inference of OLS. Conversely, the Liu estimator is robust against multicollinearity in interaction-term models. The advantages of our Liu-based method are also demonstrated in practice when examining the efficiency of the Swedish power retailing market. By the use of this unique data set we find strong evidence of positive asymmetric price transmission effects. Increases in Nord Pool electricity wholesale spot prices lead to immediate and full increases in the electricity retail prices, but decreases in Nord Pool prices are not completely passed down or are delayed before being passed down to consumers. This finding suggests evidence of inefficient and unjust wealth transfers from consumers to retailers in the Swedish power market.

Appendix

See the Tables 2, 3.

Table 2 Results when $u_i \sim N\left( {0,\sigma ^{2}} \right)$

Table 3 Results when $u_i \sim N\left( {0.5,\sigma ^{2}} \right)$