*2.1. Bottom-Up Approach*

We use a bottom-up energy demand model covering all EU countries. In this model, the EU electricity consumption and sale prices of dishwashers, washing machines, and washer dryers are based on the related energy e fficiency technological improvements, which are estimated while using an engineering approach.

The technological improvements that were triggered by the implementation of the new regulations have an e ffect on the sales price of the appliances as well as in the electricity consumption of the overall stock at EU level. The sales price of each machine is estimated based on the manufacturing costs, manufacturers and retailers' mark-ups, the value added tax, and, wherever appropriate, the additional costs of the improvement options that are added to the basic models to achieve a better energy e fficiency and, therefore, a better energy e fficiency label classification. The manufacturing costs are provided by the manufacturers and assumed to decrease over time according to the experience curve [27], experience gained by the manufacturer in producing the machines. This correction is applied to the sale prices beyond 2015.

The annual electricity consumption of the overall stock at the EU level is estimated based on the average unitary electricity consumption of one appliance. Data regarding the energy consumption of the appliances are based on the performance data provided by the manufacturers, data from consumer surveys on how the appliances are used, and the evolution of technology. This unitary electricity consumption also depends on the sales distribution over the energy e fficiency classes of the year when the appliance is purchased. The annual market share of each energy e fficiency class is based on the historical data series and the influence that labelling has on the investment decisions of consumers, directing preference towards more energy e fficiency appliances [28].

The way that this bottom-up model calculates the energy consumption is similar to that used by Yilmaz et al. [6], as both models estimate the number of replaced machines throughout a Weibull distribution. However, Yilmaz et al. [6] disregard the e ffect of the users when using the appliances and assumed the testing program energy consumption as the average value. For a complete description of the calculations and the assumptions that were considered in this bottom-up stock model, see [15,16].

A variety of studies have addressed the rebound e ffects for appliances, including an increase in operation hours, appliance size, or ownership rate [11,29,30]. The direct rebound e ffect related to dishwashers, washing machines, and washer dryers has been estimated to be negligible. The most recent user surveys [10,13] report that consumers remain using these appliances in the same way, regardless of their energy e fficiency class, and this behavior has been stable in the last years. For example, the annual number of cycles of use of the appliances is stable and it mainly depends on the household

size. The laundry load has remained constant through the last years at approx. 3.4 kg laundry/cycle, and the number of washing machines per household has remained constant, which indicates a saturated market.
