## 3 Results  
### Panel Data Analysis of Dynamic Pricing Schemes  
We analyze how the RTP and TOU treatment perform in terms of demand variation, in order to validate both schemes and their difference in behavior. Assuming that each household has his very own price sensitivity and energy usage patterns, a panel data regression is capable of assessing the statistical significance of the individual variables within each separate panel. It also accounts for individual-level heterogeneity, making it possible to control for variables that are not measurable, per se, across households or across time. We apply a panel data regression to measure the behavior of entities as households across time [37], allowing double-subscripts on the variables, taking cross-sections into account as well as time-dimensions. We denote:  
\[U_{i,t}=\alpha_{i}+\beta\;X^{\prime}_{i,t}+\varepsilon_{i,t} \tag{1}\] \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline _Attributes_ & **Mean** & **Median** & **Min** & **Max** & & & & \\ \hline Solar Influx & 37.74 & 1 & 0 & 259 & & & & \\ \hline \multicolumn{8}{c}{**RTP**} & \multicolumn{8}{c}{**TOU**} \\ \hline  & **Mean** & **Median** & **Min** & **Max** & **Mean** & **Median** & **Min** & **Max** \\ \hline
**Persons** & 2.63 & 2 & 1 & 6 & 2.967 & 3 & 1 & 8 \\
**Building Age** & 2.739 & 3 & 1 & 4 & 2.239 & 2 & 1 & 4 \\
**Building Size** & 158.2 & 140 & 58 & 550 & 153.5 & 123 & 50 & 600 \\
**Building Type** & 3.416 & 3 & 1 & 5 & 3.02 & 3 & 1 & 5 \\
**Heating Type** & 1.185 & 2 & 1 & 2 & 1.219 & 2 & 1 & 2 \\
**Roof Insulation** & 1.853 & 2 & 1 & 2 & 1.76 & 2 & 1 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Sample descriptors of household attributes. where the \(U_{i,t}\) is the dependent variable, representing a form of the demand of household i during the hour t of the day, with error \(\varepsilon\). In order to study how the behavior depending on treatment throughout the day, we take an hourly approach. Coefficient \(\alpha_{i}\) reflects household-fixed effects that record potential time-invariant, household-level heterogeneity related to the net electricity usage. \(\beta\) represents the vector of coefficient estimates of dimension \(N\) of explanatory variables \(X^{\prime}_{i,t}\). More information on the explanatory variables can be found in Table 1.  
We verify different behavior between the tariff schemes in two steps. First, we verify demand shifting behavior for both treatments analyzing relative electricity usage throughout the day. We set the dependent variable in (1) to electricity usage relative to total daily usage \(\overline{U}_{i,t}\), comparing daily usage across treatments. The updated coefficient estimate \(\beta\) is two-dimensional, consisting of the main effect for price and control effect for solar influx. Figure 3 visualizes the relative electricity usage and the average daily electricity price for both tariff schemes. Load shifting behavior occurs more dominantly in the RTP treatment as expected, occurring between 3 p.m. and 9 p.m., corresponding to higher prices for electricity usage. This is compensated for by relatively higher demand from late evening until late morning. Table 3 gives the differences in regression coefficients between the control and treatment groups. The results show that both dynamic electricity price schemes have a positive significant relationship with relative electricity usage. When we control for interaction effects in the single model, we find a significant negative difference in slopes for the price variable for both treatments (\(\beta=-0.16\) (\(0.31\))). We thus find that the price difference effect is smaller for RTP treatment than it is for the TOU treatment. Although counterintuitive at first, we argue that this comes from the fact that RTP behavior is less reactive to price differences around peak times, as indicated by Figure 3, finding evidence for differing load shifting behavior between both dynamic price settings. Next, we analyze what effect household attributes have on demand patterns throughout the day.