2.1 General model features
The
DYNK model describes the interlinkages between 74
NACE1 industries as well as the consumption of five household income groups (quintiles) by 47 consumption categories (
COICOP2) in the Austrian economy.
The modelling approach bears some similarities with DSGE (Dynamic Stochastic General Equilibrium) models, as it explicitly describes an adjustment path towards a long-run equilibrium. This feature of dynamic adjustment towards equilibrium is most developed in the consumption block and in the macroeconomic closure via a fixed short- and long-term path for the public deficit. The term “New Keynesian” refers to the existence of a long-run full employment equilibrium, which will not be reached in the short run due to institutional rigidities. These rigidities include liquidity constraints for consumers (deviation from the permanent income hypothesis), wage bargaining (deviation from the competitive labour market) and an imperfect capital market. Depending on the magnitude of the distance to the long-run equilibrium, the reaction of macroeconomic aggregates to policy shocks can differ substantially.
DYNK is an input-output model in the sense that it is demand-driven, as all what is demanded is produced. The price block in
DYNK is similarly elaborated as in a
CGE (
Computable General Equilibrium) model, with user-specific prices and a proper account of margins, taxes less subsidies, and import shares that are different for each user. Besides the price block, also other parts of the DYNK model, in particular the labour market block, have similar specifications as a dual
CGE model (see for example Conrad and Schmidt [
5] or Löfgren et al. [
6]). The dual model is based on price and cost functions instead of production functions and therefore these models in a certain sense are also “demand-driven”, especially if constant returns to scale do not allow for price setting on the supply side.
For more comprehensive descriptions of the DYNK model, see for instance Kratena and Sommer [
7], Sommer and Kratena [
8] or Kirchner et al. [
9].
2.2 Integrating prosumer activities in the household module
For the analysis of prosumer activities, both the demand and supply side of DYNK are expanded. On the supply side, the cost structure of the input-output sector “energy” (NACE sector D35), which comprises the generation and distribution of electricity, natural gas and district heat, has been disaggregated into natural gas supply/distribution (D35B), district heat supply/distribution (D35C) and the sector that generates and provides public electricity (D35A) in a special evaluation by Statistics Austria. The electricity sector has then been further disaggregated into subsectors comprising 10 electricity generation technologies (such as gas power plants, PV, wind and hydro) as well as electricity trade and distribution (i.e. grid operation).
On the demand side, the module of the private households has been expanded. The module on households in DYNK comprises investment behaviour in durable commodities, such as own houses, vehicles and electric appliances. We expand this approach by a new type of durables—“energy supply and storage appliances”—allowing to simulate the economic impacts and the increasing role of prosumers in the electricity system and assessing impacts of these developments on different household groups.
A special evaluation of the microcensus “Energy Consumption of Private Households” by Statistics Austria [
10] shows that whether or not a household commands over a PV system depends mainly on two factors: (1) the type of building (single-family house, SFH, vs. multi-family house, MFH) and (2) the income level. Households with higher incomes are more likely to have a PV system installed than low-income households. The building type is even more decisive: Irrespective of the household income level, in multi-family houses the proportion of households with a PV system is significantly lower than in single-family or two-family houses. This reflects i.a. existing legal provisions (especially the requirement of majority voting for the installation of a PV system on the roof or façade of a multi-family building). For modelling prosumer activity, the household sector in
DYNK was therefore split up into ten types, differentiating between single-/double and multi-family houses on the one hand and five household income groups (quintiles) on the other hand. The corresponding consumption and income data for the ten household types was derived from Statistics Austria’s Household Budget Survey.
The investment decisions of the different household groups were added to the consumption block and are modelled as follows. The highest household income group (quintile 5) behaves according to the Permanent Income Hypothesis (PIH) and does not face liquidity constraints [
11]. Its stock of photovoltaic (including storage
3) appliances in period
t,
KPV,t, is optimal and grows by taking into account the relationship (
β) between the price of electricity (
pel,t) and the interest rate
rt plus all shocks
e from previous periods
t and the adjustment to these shocks with parameter
α:
$$\Updelta \mathrm{logK}_{PV{,}t}=\mu +\beta log\left(\frac{p_{el{,}t}}{r_{t}}\right)+\sum _{\tau }\alpha \varepsilon _{\tau }$$
(1)
For all other household income groups this equation of PIH consumers describes the development of some optimal stock
\({K}_{PV{,}t}^{*}\)to which these households attempt to adjust, given their liquidity constraints. Due to these constraints, the development of real disposable income ∆log(
YDt/
Pt) drives their investment in photovoltaic (including storage) appliances. The subsidy offsets the liquidity constraints completely at a subsidy rate (
tr) of 1, so that we get for the investment function of households in quintile 1 to 4:
$$\Updelta \mathrm{logK}_{PV{,}t}=\begin{cases} \mu +\gamma log\left(\frac{YD_{t}}{P_{t}}\right)+\varepsilon _{t}{,}whentr< 1\\ \Updelta log{K}_{PV{,}t}^{* }{,}whentr=1 \end{cases}$$
(2)
The data set, which is a special evaluation by Statistics Austria of a large cross-section data set, did not allow for an econometric estimation of the parameters β, μ and γ. Therefore, we calibrated β according to the assumption of rational behaviour where any increase in electricity prices is fully compensated by additional consumer capacity leaving the costs of energy services unchanged. The parameters μ and γ were calibrated to reproduce the allocation of PV investments across household groups in the base year.
The new household structure has then been integrated into the adapted DYNK model and the household variables (income, consumption structures) have been linked to relevant variables of the new disaggregated electricity sector in the adapted DYNK.