Introduction

The European Union (EU) recognizes the need to reduce the heat demand of existing buildings, as reflected in efforts such as the “nearly zero-energy buildings initiative” (European Commission, 2014) and the “European Green Deal” (European Commission, 2019). As old buildings are generally not energy-efficient, energy retrofits offer substantial energy-saving potentials. Increasing the retrofit rate has also long been recognized as necessary for achieving national climate protection goals (Holm et al., 2018; McKenna et al., 2013). Despite the availability of government funding, e.g., as in Germany through the KfW, known as the world’s largest development bank, little progress has been made. To increase retrofit efforts in the building sector, the German government, among others, introduced a carbon tax and additional funding for retrofits in 2021. An increase in funding applications is evident, but the impact of the new conditions on the retrofit rate is not yet known and, moreover, the funding landscape has already been substantially changed again in 2022. Furthermore, additional changes are expected in the near future.

In order to design effective and evaluate existing funding frameworks, it is important to know relevant barriers for building owners. This makes it possible to estimate under what circumstances a significant increase in retrofit rates can be expected. Surveys have been conducted to understand the decision-making process of building owners regarding retrofits. Many reasons have been identified which prove to be highly individual depending on the situation of the owner (e.g., age or missing awareness) and the building (Renz & Hacke, 2016; Stieß & Dunkelberg, 2013; Wasser et al., 2020). To further analyze the decision-making process, it is important to distinguish between refurbishment, rehabilitation, and retrofitting (the terminology is based on suggestions in Shahi et al., 2020), whereby rehabilitation and retrofitting can be partial measures of a refurbishment. While the cause for refurbishments is often the rehabilitation and therefore to fix technical issues (e.g., replacement of windows, painting of walls, renewal of the roof), the purpose of energy retrofits is the reduction of energy consumption and energy costs. Energy retrofits can be considered as an investment option when not required by law, such as in Germany when major roof or facade work is done during repairs. This distinguishes them in the decision-making process from rehabilitation measures that may be considered necessary. In addition, the relevance of economic aspects has been found to be very important for the decision-making of building owners (Renz & Hacke, 2016).

The two main economic barriers are economic feasibility and high investment costs. Furthermore, many owners see the economic feasibility of retrofits as problematic or at least doubtful (Renz & Hacke, 2016; Weiß & Pfeifer, 2020). And indeed, amortizing the full investment costs of refurbishments (costs for rehabilitation and energy retrofit) through energy savings is very unlikely within a reasonable timeframe. For example, Streicher et al. (2020) found that only 3% of the potential energy retrofits in Switzerland would be feasible when considering the full investment costs. At the same time, it is often claimed that energy retrofits are economically feasible. This discrepancy results from the calculation of the costs to be amortized. In case of retrofits that are carried out at the same time as technically necessary rehabilitation measures, only additional costs of the retrofit measures and not the substantial costs for rehabilitation (e.g., renewal of roof, replacement of windows with identical energy characteristics) are applied. In this case, theoretically, only the additional costs need to be amortized through energy cost savings, since the rehabilitation costs are necessary anyway (Weiss et al., 2012; Weiß & Dunkelberg, 2010).

However, if the owner chooses between a refurbishment with energy retrofits and no refurbishment, there are no costs at all associated with the latter case. Although the two statements on economic feasibility do not contradict each other, they can lead to confusion in the decision-making process when statements by experts and laypersons are considered and compared. This is a problem because expert knowledge must be regarded as trustworthy and consistent with the views of people in the personal environment (Stieß & Dunkelberg, 2013). The different statements can lead to doubts about the measures and mistrust of the experts, which can lead to a reluctance to seek advice from energy consultants and ultimately to fewer retrofits. In addition, it becomes clear that the need for rehabilitation is decisive for retrofits. Sartori et al. (2016) conclude: “Many energy efficiency measures are cost efficient only if performed when a building is undergoing a deep renovation in any case.”

The refurbishment rate, and in particular the rehabilitation rate, is therefore crucial, as it has a decisive influence on economic feasibility. Surveys have also shown that the retrofit rate falls behind the theoretical rate derived from the rehabilitation cycle, which is a result of the theoretical useful life of building components (Weiß & Dunkelberg, 2010; Diefenbach et al., 2010). In Sandberg et al. (2016), the model described in Sartori et al. (2016) is applied to 11 EU countries and theoretical rehabilitation rates (in Sandberg et al., 2016: renovation rates) calculated. The theoretical rehabilitation rates are in a range of 0.6–1.6%/a (Germany 1.3%/a 2015, 1.4%/a 2030, 1.5%/a 2050). This means that the theoretical rehabilitation rates are significantly lower than targeted retrofit rates for the modernization of the residential building stock in the EU. Building owners also often overestimate the condition of their building and will not refurbish (Diefenbach et al., 2010; Weiß & Dunkelberg, 2010). Since owners also question the economic viability, there is a tendency to delay refurbishments as long as possible. As a result, the retrofit rate is below the potential of theoretical rehabilitation cycles and a backlog of rehabilitation measures is created.

Besides increasing the retrofit rate, the question arises as to which retrofit concept is consistent with the climate protection goals. Bürger et al. (2017) concludes that the KfW55 (KfW, 2022) efficiency class is considered a model refurbishment concept in line with the national climate goals of Germany. Since the overarching goal is to reduce CO2 emissions, it is not intuitive to focus on efficiency classes, which are primarily measured by the efficiency of the building envelope. On the other hand, low consumption levels are needed so that climate-neutral supply technologies can be used, many of which operate at low temperatures (e.g., cold local heating networks & heat pumps). Thus, achieving efficiency classes with retrofits is not the goal itself, but the means to achieve the goals.

One potential solution that could lead to increased retrofit rates is the creation of attractive economic conditions. However, it is much more difficult to create attractive economic conditions if there are no buildings in need of rehabilitation with potentially high energy savings. Therefore, if it is possible to increase retrofit rates, the more difficult task is to maintain them at a high level until the entire building stock is brought up to the required standard.

Aim of the research

The aim of this paper is to develop a framework as a baseline model for the evolution of the size and energy efficiency status of national building stocks under varying economic conditions. This is intended to analyze the impact of policies and ultimately answer the question of which measures can potentially lead to the achievement of national climate goals in the building stock. The focus in this paper is on a modular framework, which allows for easy application, comparison, and improvement of individual modules. It is intended to be expanded in subsequent research with a calibrated national energy balance and endogenous functions to assess the influence of economic conditions on the energy retrofit rates. For the time being, the economic conditions are compressed and represented by a single black-box variable. This variable will be replaced in subsequent research to integrate the economic environment in more detail. The idea is to reduce combinations of different parameters into one key indicator (e.g., high material costs and low interest rates vs. low material costs and high interest rates).

As explained above, the link between the theoretical rehabilitation rate and the economic framework conditions is considered essential. The theoretical rehabilitation rate should be incorporated into the model with an ability to influence the resulting retrofit rates by changing economic conditions. The underlying assumption here is that poor economic conditions lead to increased procrastination and good conditions lead to early action. The black box variable can be used as a simplified exogenous parameter to simulate improving or deteriorating economic conditions. This is to be done against the background of the respective deviation from the current and theoretical refurbishment/rehabilitation cycle.

As a basis for the simulation of the transformation process of the building stock, decisive parameters of the residential building stock are also to be modeled endogenously. Living space is chosen as the model’s underlying scale variable used to capture the energy efficiency and the economic conditions of different building age classes and building types. Therefore, the development of living space per building class and building type has to be modeled for the period under consideration. For this purpose, the rates of new construction, deconstruction and retrofit, and thus the transition to a new energy class are modeled endogenously.

Literature review building stock models

There are already many scientific publications dealing with the modeling of the building stock. On an international level, approaches such as in Sartori et al. (2016) and Sandberg et al. (2016) are worth mentioning, which use renovationFootnote 1 rates based on the rehabilitation cycle. Due to the prominent role for economic feasibility mentioned in the introduction, we see this as a crucial driver in models. In order to derive guidelines for policy making, an integration of the influence of economic framework conditions on the retrofit rates would be an important extension.

In addition, there are approaches that model retrofit rates endogenously through economic evaluation (e.g., Giraudet et al., 2012). However, the use of LCC for decision-making is viewed critically because the economic calculation is modeled in more detail than corresponds to the reality of conventional building owners. According to Gossen and Nischan (2014), economic feasibility is very important, but is not studied in detail. In many cases, building owners only make a rough assessment of the economics before the retrofit and the actual savings that occur afterwards are neither observed nor quantified (Gossen & Nischan, 2014). Also, the link to the economically important criterion of the rehabilitation cycle is missing in Giraudet et al. (2012). The fact that the tenant-landlord problem emerges as a decisive barrier from the results is viewed skeptically as well, since it is not reflected in the retrofit rates under consideration (higher retrofit rates in multifamily buildings than in single-family buildings in Cischinsky & Diefenbach, 2018). Instead, we see higher retrofit rates in multifamily buildings that are mainly rented out, which can be explained by:

  • Extensive experience of the owners with retrofits and lower costs, especially in the case of companies (Michelsen, 2016).

  • In Germany, only 6% of the buildings are not owned by owner-occupiers and private landlords (Cischinsky & Diefenbach, 2018). The decision-making process of the latter has similarities to that of owner-occupiers (März, 2019), and 25% of these landlords also live in the same buildings as their tenants (Weiß et al., 2018).

In addition, research has been published that is specifically related to the residential building stock in Germany (e.g., Bründlinger et al., 2018; Bürger et al., 2017; Diefenbach et al, 2016; Jochum et al., 2015; McKenna et al., 2013; Steinbach, 2016; Steinbach et al., 2021; Stengel, 2014). In Stengel (2014), for example, an agent-based simulation model is presented that describes the decision-making process (of the owners/agents) in great detail. However, we also see a clear disadvantage in such approaches, which lies in the level of detail itself. All kinds of information are needed, and assumptions have to be made. Therefore, the model becomes sensitive towards the amount of chosen assumptions, which also must be predicted within the observation period, and we would suggest to use such models rather for short observation periods and for the estimation of short-term effects of distinct policies. As the number of input projections in models result in high uncertainties, Slavkovic et al. (2022) recommends “…that modelling frameworks should allow a high degree of flexibility in testing different evolution values in a simplified manner, so that the sensibility of results to particular parameters can be identified.”

Many studies (e.g., Bründlinger et al., 2018; Bürger et al., 2017; Jochum et al., 2015) and many building stock model results (e.g., Sandberg et al., 2016; Sartori et al., 2016) show significantly higher deconstruction rates than seen in national statistics. Sartori et al. (2016) consider that the average lifetime of buildings should be higher, so that there is less demolition activity in the model. Instead, we recommend modeling deconstruction activities based on demand. Otherwise, longer lifetimes would also lead to longer refurbishment cycles. This would also be consistent with the concern that fewer buildings should be replaced since deconstruction and new construction have a higher environmental impact than deep refurbishments.

In Camarasa et al (2022), global building stocks are examined and show no compliance with climate targets. Also, none of the publications mentioned above show measures with which the climate goals for building stocks are achieved. Instead, cost-optimized scenarios (Steinbach et al., 2021) and trend projections are examined. Thus, it remains important to answer and investigate which measures promise long-term success for achieving the climate goals of national building stocks.

Modelling and methods

The model was developed on the basis of a literature review and the evaluation of the development of key factors of the residential building stock since 1990. The literature review was used to identify key patterns and relationships characteristic of the residential building stock, from which basic equations were developed to describe the parameters. These equations were finalized by evaluating past developments. Finally, the equations were validated by comparing them with other scenario analyses and forecasts. The following section summarizes the key characteristics of the model.

Model characteristics

Living space is used as the underlying variable determining the size of the building stock. The assumptions for the development of living space are based on a population-induced growth factor and a base-growth factor, which can be translated into higher space demand in square meter per capita. Deconstruction and new construction are modelled on the basis of housing demand forecasts. This differs from other approaches where models are based on building lifetimes. The latter approach tends to overestimate the deconstruction rate, leading to inaccurate estimates.

The energy performance gap is addressed using consumption-adjusted building models. These models consider realistic energy use patterns and help bridge the gap between predicted and actual energy performance. By incorporating actual consumption data, a more accurate representation of building energy efficiency can be achieved, allowing for a more realistic calculation of energy cost savings and therefore a better conclusion on the economic benefit.

The retrofit rate is considered to be an important core statement and is defined by a modular equation. The equation therefore offers the flexibility to improve and change individual aspects and makes the provisional use of an exogenous variable for the economic framework in this equation more practicable. The rehabilitation cycle plays a central role in the refurbishment decision, as it has a significant impact on economic feasibility and is often the reason for a refurbishment and energy retrofit. Therefore, a rehabilitation is a valuable opportunity to introduce long-term energy-saving measures. Accordingly, the rehabilitation cycle is an elementary part of the endogenous retrofit calculation. To simplify the complex economic conditions associated with construction projects for the time being, a black box approach is used. In this approach, the complicated economic factors are embedded in a simplified framework and summarized in a single variable. In addition to simplification, this approach is also intended to improve comparability and thus reduce sensitivity to parameter assumptions.

The current version of the model focuses on the thermal envelope of the building and does not include heating systems in the retrofit rates.

Modelling approach

The development of functions defining the parameters is carried out using the German residential building stock as an example. The basis for this are the past developments since the 1990s, official statistics and studies on the condition of the residential building stock (e.g., destatis, 2019a; Cischinsky & Diefenbach, 2018; dena, 2016). The mathematical functions are based on the assumptions explained above (cf. the “Model characteristics” section) and are developed by evaluating past trends in the key building parameters. While the form of the function is developed in terms of the theoretical dependencies, the parameters are chosen to match measured data from past years and current conditions (e.g., population-driven and increased space demand per capita of living space). Figure 1 shows an overview of the modelling approach and the central model functions.

Fig. 1
figure 1

Scheme of the modeling approach (corresponding section in this paper)

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German residential building stock

The TABULA web database (IWU, 2017) provides energy conditions for different building types, subdivided into building age-relevant periods with three states per type (initial state, standard retrofit, ambitious retrofit). For the initial state, the as-built conditions were chosen, whereby a replacement with two-pane windows was assumed for very old buildings. Table 1 provides an overview of the archetype building models used and the implemented energy consumption by building age class and retrofit standard. Energy consumption was statistically adjusted from demand values to consumption values to account for the energy performance gap.Footnote 2 Extensive examples of the underlying retrofit packages are available online in the TABULA web database (IWU, 2017).

Table 1 Energy demand adjusted to consumption values of archetype buildings for Germany based on TABULA web database (IWU, 2017); SFH, single-family houses; TH, terraced houses; MFH, multi-family houses; energy demand without efficiency of the heating system
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The latest data about the building stock is taken from the 2018 update of the Microcensus 2014 of the Federal Statistical Office of Germany (destatis, 2019a). According to this, the number of dwellings in Germany in 2018 amounts to 42,235,402 dwellings with 3.88 billion \({{\text{m}}}^{2}\) of living spaceFootnote 3 in 19,053,216 residential buildings (destatis, 2019a). For the breakdown into building age classes, information can be taken from the results of the Microcensus 2014 (destatis, 2016), the first IWU data survey (Diefenbach et al., 2010), and the data survey for 2016 (cut-off date December 31, 2016) (Cischinsky & Diefenbach, 2018). For the modeling of the building stock, the data set according to Cischinsky and Diefenbach (2018) is used, since this uses the building age classes as in TABULA and is the most recent of the three data sets mentioned. Since the data collection corresponds to the situation at the end of 2016, the years 2017 and 2018 were supplemented using the data in destatis (2019a). The added residential buildings are added into the 2016 + group, extending it to 2018. Deconstruction up to the start date 2019 is evenly distributed across the space weight and subtracted from the building age classes up to 1978. This assumes that primarily older buildings are deconstructed. The results are shown in Fig. 2.

Fig. 2
figure 2

Percentage breakdown of German building stock by building age class for 2018 (own calculation based on data survey (Cischinsky & Diefenbach, 2018) and update for 2018 (destatis, 2019a))

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The breakdown between residential buildings and dwellings needs to be further refined as residential buildings and dwellings have a wide range of sizes. For example, a single-family house with 150 \({{\text{m}}}^{2}\) of living space or more counts as one dwelling, as does a one-bedroom apartment in the city with 30 \({{\text{m}}}^{2}\) or less. Therefore, further division into building types like single-family houses/two-family houses (SFH/TFH) and multi-family houses (MFH) is necessary.

Figure 2 and Table 2 show the underlying distribution of living space in the building stock by building age class and building type.

Table 2 Living space distribution of the building stock by building age class and building types for 2018 (own calculation based on Cischinsky & Diefenbach, 2018, and dena, 2016)
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Living space development

The development of living space is used as the central defining parameter for modeling the building stock. The course of the living space consumption is to be modeled as a function of the population growth. For the population growth, the population forecast from destatis (2019b) is adopted. A proportional influence of the population growth on the living space consumption cannot be inferred from the past developments due to the building boom after German reunification. Other building stock models often use direct proportional population impact with an increasing factor for living space per capita (e.g., Yang et al., 2022). From the past trends in construction, deconstruction, living space, and population, it is concluded that the impact of population growth is reduced and delayed. Moreover, it shows a sluggish behavior of housing construction and a “base” growth of the residential building stock. The latter also occurred when the population declined and was then characterized by higher proportions of SFH (cf. low ratio of dwellings per building in 2002–2012; Fig. 2), which feature higher proportions of living space per capita. Still, the development of the building stock, as well as new construction, deconstruction or the ratio of SFH to MFH, is a result of changing demographic, cultural, legal, construction, and economic conditions which are very hard to predict. Changing ratios have also been observed in the past (cf. Fig. 2). The impact of population growth is slightly lagged by considering the last 3 years. An additional base growth independently from the population development is also considered (cf. Eq. 1). For a more realistic influence of the population growth onto the housing demand, natural growth and growth through migration should be divided, as migration results in direct housing demand while this is not so much the case with natural growth. However, since population forecasts and especially migration are difficult to predict and imprecise, a split view is not taken.

$${{l}}{{s}}\left({{n}}\right)={{{b}}{{g}}}_{{{n}}}+{{{p}}{{g}}{{f}}}_{{{n}}}\times \left(\frac{1}{3}\times \left[\frac{{{{P}}}_{{{n}}-2}-{{{P}}}_{{{n}}-3}}{{{{P}}}_{{{n}}-3}}+\frac{{{{P}}}_{{{n}}-1}-{{{P}}}_{{{n}}-2}}{{{{P}}}_{{{n}}-2}}+\frac{{{{P}}}_{{{n}}}-{{{P}}}_{{{n}}-1}}{{{{P}}}_{{{n}}-1}}\right]\right);\left[{\%}/{a}\right]$$
(1)
ls(n):

Living space development in year n [%]/[a]

bgn:

Base growth [%]/[a]

pgfn:

Population growth factor [%]/[a]

Pn:

Population in year n [capita]

With a base growth (\(b{g}_{2018}\)) of 0.7 and the population growth factor (\(pg{f}_{2018}\)) of 0.75, the function value fits the current situation and the expected high rate of new construction very well, despite a stagnant or even declining population.

The increase in living space predicted by Eq. 1 for the period 1995–2018 corresponds to the real trend minus the statistical adjustment in 2010 (− 200,000 m2) and the effects of the building boom after German reunification (− 100,000 m2). In addition, different trends can be seen mainly between 2010 and 2018. The forecast is more pronounced due to significant population changes. The real course is much more sluggish and corresponds to a slow trend of the forecast values. If the effects of the construction boom (years 1995–2000) and the statistical adjustment (2010) are excluded, the following average values result for Eq. 1 = 0.74%/a (2001–2018), while the actual course was 0.72%/a (2001–2018 without 2010).

A smoothing function is applied to the results of Eq. 1 to overcome the jumping influences of the population forecast interpolation.Footnote 4 For the years 2016–2018, the actual living space and after 2018 the results of the function (Eq. 1) are used. The resulting development when keeping the factors (\(b{g}_{2018}\) and \(pg{f}_{2018}\)) constant at 0.7 and 0.75 is shown in Fig. 3 in comparison to the population forecast. Although the graphs show a significant decline in the period from 2020 to 2050, the living space continues to grow.

Fig. 3
figure 3

Function results for \({{l}}{{s}}\left({{n}}\right)\) with \({{b}}{{{g}}}_{2018-2050}\) = 0.7, \({{p}}{{g}}{{{f}}}_{2018-2050}\) = 0.75 and population forecast

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New construction and deconstruction

New construction and deconstruction are modeled as a function of the living space and therefore both depending on the expected demand rather than the theoretical lifetime of buildings. In the past, the ratio of new construction to deconstruction has varied steadily. Interestingly, the ratio of new construction to deconstruction correlated very well with the ratio of SFH to MFH (cf. Fig. 4). The correlation also has causality, because when housing demand is low, SFH continue to be built and a greater number of buildings are deconstructed. In addition, when housing demand is high, new construction and the share of MFH increase due to economic interests. Thus, the correlation also shows a common dependence on demand and provides a reason to model deconstruction as a function of demand (in this case represented through the expected living space development).

Fig. 4
figure 4

Comparison of new construction ratio SFH/MFH to deconstruction/new construction (data from destatis, 2019a)

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Given the volatile nature of the construction sector, it is questionable to what extent the factor of 10 (cf. left and right y-axis in Fig. 4) will still apply in future years. Nevertheless, the correlation provides a very good basis for modeling and is thus used to model new construction and deconstruction (see Eqs. 2 and 3).

$${{N}}{{C}}\left({{n}}\right)=\frac{{{L}}{{{S}}}_{{{n}}{{e}}{{w}}}\left({{n}}\right)}{1-\frac{{{s}}{{f}}{{{h}}}_{{{n}}{{e}}{{w}}}\left({{n}}\right)}{10\times \left(1-{{s}}{{f}}{{{h}}}_{{{n}}{{e}}{{w}}}\left({{n}}\right)\right)}};\left[{{m}}^{2}/{a}\right]$$
(2)
$${{D}}{{C}}\left({{n}}\right)=\frac{{{s}}{{f}}{{{h}}}_{{{n}}{{e}}{{w}}}\left({{n}}\right)}{10\times \left(1-{{s}}{{f}}{{{h}}}_{{{n}}{{e}}{{w}}}\left({{n}}\right)\right)}\times {{N}}{{C}}\left({{n}}\right);\left[{{m}}^{2}/{a}\right]$$
(3)
$$sfh_{new}\left(n\right)=1-0.78\times\frac{ls\left(n\right)}{1\lbrack\%/\mathrm a\rbrack}\left[-/-\right]$$
(4)
NC(n):

New construction in year n [m2/a]

DC(n):

Deconstruction in year n [m2/a]

LSnew(n):

∆Living space in year n [m2/a]

lS = s(n):

Living space development in year n [%]/[a]

sfhnew(n):

Share of SFH in new construction in year n [-/-]

The ratio of SFH to new construction is also modeled as a function of the living space, based on the current ratio. Equation 4 is designed only for the expected range of \(ls\left(n\right)\) 0–1.0%/a for Germany in the model. The results of the parameter modeling for the residential building stock forecast are given in Fig. 5.

Fig. 5
figure 5

Overview of living space parameters in the trend scenario in the model

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Energy retrofit rate

The modeling of the retrofit activities is mainly performed by two parts, which are determined individually per building type and building age class. The first part reflects the rehabilitation/refurbishment demand of a building age class and is represented through the refurbishment factor (\(ref{m}_{i,j} ,\) calculated with Eq. (5)). The refurbishment factor is determined using the year of construction (ConYear) and the service life or lifetime (cf. SL in Eq. (5)), the latter being the decisive parameter. For the two oldest building age classes (up to 1948) the refurbishment factor is reduced on the premise that many of these buildings have already been refurbished in the past without energy retrofits. The refurbishment factors are multiplied by 0.3 (before 1918, \(ref{m}_{i,1}\)= 1.35) and 0.5 (1919–1948, \(ref{m}_{i,2}\)= 1.11) to obtain refurbishment factors comparable to those of the building age classes 1949–1957 (\(ref{m}_{i,3}\)= 1.69) and 1958–1968 (\(ref{m}_{i,4}\) = 1.14) in the base year. Technically, this means that buildings from these building classes are shifted by two building classes to account for these refurbishments.

$$refm_{i,j}(n)=\frac1{SL_{i,j}^2}\times\left(n-ConYear_{i,j}\right){}^2$$
(5)

In addition to the refurbishment demand, the influence on the speed of retrofits is modeled through an additional factor, the economic factor (\({ecof}_{i,j}\left(n\right)\)). This factor is intended to reflect the influence of economic conditions on retrofit rates as the model is expanded and is currently an exogenous parameter. A numerical value of this factor less than 1 reduces the retrofit rate below the theoretical speed of the refurbishment cycle. In combination, these are the determining parts for the retrofit activities per building class and building type. The respective deep retrofit rate (retrofit rate) is given by Eq. 6. The additional factors \(mref\), \(SLf\), and \(po{t}_{i,j}\left(n\right)\) represent the theoretical mean refurbishment rate, a service life factor, and the potential share of not yet modernized buildings in the building age class. The mean refurbishment rate (\({mref}_{i,j}\)) is intended to represent the mean rate for the applied lifetime in Eq. 6 (e.g., 0.01818 for 55 years) and thus the steady rate when considering > 1 deep refurbishments in the observation period. In the trend scenario, the mean refurbishment rate is substituted with numerical values corresponding to the average current retrofit ratesFootnote 5 of buildings classes up to 1978. Thus, they are used on the one hand to weight the retrofit rates of SFH/TH to MFH, and on the other hand, they can be used to determine the expected current state/value for \({ecof}_{i,j}\left(n\right)\). The service life (\(S{L}_{i,j}\)) is set at 55 years for all building types and classes due to the consideration of deep retrofit equivalents and is thus intended to represent the expected service life of the most durable building component, the exterior facade.

$${{{r}}{{e}}{{t}}{{r}}{{o}}{{f}}{{i}}{{t}}}_{{{i}},{{j}}}\left({{n}}\right)=\mathrm{S}\mathrm{L}\mathrm{f}\times {{m}}{{r}}{{e}}{{f}}\times {{r}}{{e}}{{f}}{{{m}}}_{{{i}},{{j}}}\left({{n}}\right)\times {{{e}}{{c}}{{o}}{{f}}}_{{{i}},{{j}}}\left({{n}}\right)\times {{p}}{{o}}{{{t}}}_{{{i}},{{j}}}\left({{n}}\right)$$
(6)

with: i = 1: [SFH], 2: [TH], 3: [small MFH], 4: [large MFH] j = 1–12 respective building class

$$\begin{array}{c}{{{m}}{{r}}{{e}}{{f}}}_{{{i}},{{j}}}=\frac{1}{{{S}}{{{L}}}_{{{i}},{{j}}}}\end{array}$$
(7)

The service life factor (\(SLf\)) can be used to adjust the amount of retrofitted buildings at the end of their service life. With \(SLf\)=2 and \(S{L}_{i,j}\)=55 years, 48% of the buildings are retrofitted after 55 years and the maximum of the retrofit function is also located at 55 years (= \(S{L}_{i,j}\)). In conclusion, the \(SLf\) and \({mref}_{i,j}\) may be used to form the shape/profile of the retrofit curves, improving the modular and accessible approach of the model (Fig. 6).

Fig. 6
figure 6

Characteristic line of the service life factor

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The expected mean refurbishment rate is used in the trend scenario for the weighting of EFH/MFH and is set to numeric values that correspond to the average current deep retrofit rates of old buildings (\({{{m}}{{r}}{{e}}{{f}}}_{1+2,{{j}}}=0.01268, {{{m}}{{r}}{{e}}{{f}}}_{3+4,{{j}}}=0.01615; 1.268 [\mathrm{\%}/{\text{a}}]\mathrm{ SFH}, 1.615 [\mathrm{\%}/{\text{a}}]\mathrm{ MFH})\). The theoretical \({mref}_{i,j}\) can be calculated with Eq. 7.

$${{\text{pot}}}_{{\text{i}},{\text{j}}}\left({\text{n}}\right)=\left(1-{{\text{RETF}}}_{{\text{i}},{\text{j}},\mathrm{ n}=0}\right)-{\int }_{0}^{{\text{n}}-1}{{\text{retrofit}}}_{{\text{i}},{\text{j}}}\left({\text{n}}\right){\text{dn}}$$
(8)

In combination with a successive reduction of the remaining fraction of non-modernized buildings (\(po{t}_{i,j}\left(n\right)\), cf. Eqs. 6 and 8), this results in a kind of normal distribution.

Scenarios

The target energy efficiency class of the deep retrofits is specified through the deep retrofit concepts from TABULA (cf. Table 1). TABULA specifies a standard and an ambitious retrofit. The proportions are set at 35% ambitious and 65% standard retrofits and, for comparison, a maximum scenario of 100% ambitious retrofits. As a result from literature (Metzger et al., 2019; dena, 2016), a deep retrofit share of 33.5% (\(RET{F}_{i,j<6, n=0}\)) for building age classes before 1978 and 15% (\(RET{F}_{i,j=\mathrm{6,7},n=0})\) for classes from 1979 to 1994 is assumed for the year 2018.

The model is used for different values of \({ecof}_{i,j}\left(n\right)\) which represent different assumptions. The settings of \({ecof}_{i,j}\left(n\right)\) used in the scenarios are shown in Fig. 7. In the trend scenario (scenario a), the currently observed retrofit rates are used to determine \({ecof}_{i,j}\left(n=0\right)\) (which may be translated as economic conditions at the beginning of 2019) via the theoretical mean refurbishment rate (\({{{m}}{{r}}{{e}}{{f}}}_{{{i}},{{j}}}=0.01818\); cf. Fig. 7). A closer look at the increase of \({{\text{ecof}}}_{{\text{i}},{\text{j}}}\left({\text{n}}\right)\) in scenarios c and d shows that \({{\text{ecof}}}_{3+4,{\text{j}}}\left({\text{n}}\right)\) increases faster than \({{\text{ecof}}}_{1+2,{\text{j}}}\left({\text{n}}\right)\). This is explained by the fact that changing conditions have the same percentage effect. The assumption here is that changes in the economic framework conditions have the same percentage effect on each building class. Accordingly, the economic factors remain constant to each other in percentage terms, unless this is explicitly taken into account in any measures (e.g., increase in subsidies explicitly for SFH).

Fig. 7
figure 7

Economic factor setup in scenarios a–d

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In scenario b, the economic factor is set to a static 1, which is associated with retrofit rates in line with the assumed refurbishment/rehabilitation cycle. This means an increase in comparison to the trend scenario and may be translated with an assumed backlog of refurbishment demand.

For scenarios c and d, two different progressions are shown to exemplify how the retrofit rates react to an improvement of \({ecof}_{i,j}\left(n\right)\). In scenario c, the initial values of \({ecof}_{i,j}\left(n=0\right)\) are equal to the trend scenario to simulate the economic conditions at the start of the observation period. In 2023 and 2031, a significant increase is assumed. Scenario d uses a continuous approach, where the economic conditions are again set equal to the trend scenario and afterwards continuously improving at a constant rate (cf. Fig. 7).

A closer look at the increase of \({ecof}_{i,j}\left(n\right)\) in scenarios c and d shows that \({ecof}_{3+4,j}\left(n\right)\) increases faster than \({ecof}_{1+2,j}\left(n\right)\). This is explained by the fact that changing conditions have the same percentage effect. The assumption here is that changes in the economic framework conditions have the same percentage effect on each building class. Accordingly, the economic factors remain constant to each other in percentage terms, unless this is explicitly taken into account in any measures (e.g., increase in subsidies explicitly for SFH).

Results

The unfavorable economic conditions assumed in the trend scenario (\({ecof}_{i,j}\left(n=0\right)\) <1) lead to peaks of the different normal distributions for \({retrofit}_{i,j}\left(n\right)\) at 59.5 to 64 years (depending on the type SFH vs. MFH). The reduced values of the economic factor shift the maximum value to later years. The retrofit rates for the different building age classes (green, orange and blue lines in Fig. 8) and the average total retrofit rate (black line in Fig. 8) in the trend scenario are shown in Fig. 8a. With the given setting of parameters, the result is exactly within the expected range. On the one hand, this is due to the reduction of the pre-war building age classes and certainly also to the incorporation of the average retrofit rates in old buildings for SFH and MFH in \({mref}_{i,j}\). This flattens the curves and simulates a slight refurbishment backlog accordingly. This remedies itself in the model with a delay of a few years (59.5 to 64 instead of 55 years) by a growing need for refurbishment expressed by the refurbishment factor (\(ref{m}_{i,j}\left(n\right)\)). In the trend scenario, the growing number of buildings in need of refurbishment results in a slight increase in the retrofit rate up to a maximum value of 1.068% in 2032.

Fig. 8
figure 8

Retrofit rates total and per building age class (BAC); retrofit rates refer in each case to total BAC or total residential building stock including new construction. (a) Trend scenario, (b) theoretical refurbishment cycle, (c) improvement of conditions in 2023 and 2031, (d) continuously improving conditions

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The total retrofit rate in each case refers to the total quantity of the residential building stock including the newly constructed buildings. Accordingly, a nearly constant retrofit rate results in growing absolute numbers. The peak in 2032 is also due to the high number of buildings constructed in the post-war period. Although these buildings are already being rehabilitated and partially also retrofitted, in the model only the 1949–1957 building age class reached the peak in retrofit activity by 2019. Since the same deep retrofit share of 33.5% (for the year 2018) is assumed for the old buildings from before 1978, this results in shares of buildings still potentially in need of rehabilitation (\(po{t}_{i,j}\left(n\right)\)) that deviate from the normal distribution. Accordingly, the maximum value for the 1949–1957 building age class (see about 1.9%/year in Fig. 8a) is increased because a smaller proportion is assumed to be already retrofitted than would be the case if the maximum value were normal. Correspondingly, this would be more pronounced for the pre-war buildings. This, however, is suppressed by the aforementioned reduction in the refurbishment factor for these building age classes. The opposite is true for the 1969–1978 building age class, where the assumed share of 33.5% is higher than expected.

If \({ecof}_{i,j}\left(n\right)\) is raised to 1 and \({mref}_{i,j}\) kept at 0.01818 (mean rate at 55 years), this results in maximum values of 0.01818 at a building lifetime of 55 years and represents the speed of the theoretical refurbishment cycle under the given parameters. The same is true for other corresponding combinations of \({mref}_{i,j}\) and the service life at which \(ref{m}_{i,j}\) reaches the value of 1.Footnote 6 This setting of parameters is shown in Fig. 8b. Improved economic conditions for retrofits are simulated in the two scenarios c and d with the start conditions of the trend scenario. In the first, an exogenous increase of \({(ecof}_{i,j}\left(n\right)\)) in 2023 and additionally in 2031 is assumed (cf. Fig. 7). The result is shown in Fig. 8c. This scenario indicates that even when improving the conditions for retrofits, the retrofit rate will decrease rapidly afterwards, as the refurbishment cycle is not affected. Therefore, the amount of potential buildings with demand for refurbishment will continuously decrease. In scenario d, a linear increase is assumed for \({(ecof}_{i,j}\left(n\right)\)) (cf. Fig. 7). The scenario d reaches a maximum increase for \({ecof}_{i,j}\left(n\right)\) that is significantly higher than in scenario c in 2050 and still the retrofit rates decrease steadily after their maximum in 2035 (1.92%/a).

The results for the retrofit shares and final energy demands for two different proportions of ambitious retrofits (35% and 100%) in 2050 are listed in Table 3. It should be noted that the maximum proportion of buildings that can be retrofitted is assumed to be 95%, as a proportion of 5% is assumed to be listed buildings with no significant potential for improvement. However, the deconstruction of listed buildings is theoretically possible.

Table 3 Result scenario (a–d) deep retrofitted shares in 2050 and \(\Delta\) final energy 2030/2050
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Discussion

The model presented in this paper is intended as a framework basis for building stock models that take into account the economic factors that influence retrofit rates in different countries. Therefore, \({ecof}_{i,j}\left(n\right)\) is currently an exogenous set parameter that weights the effort needed to influence the retrofit rates. The numerical values of \({ecof}_{i,j}\left(n\right)\) set to increase the retrofit rates in the scenarios have yet to be translated into corresponding economic conditions. This could be done through a function that weights the influence of the economic conditions and is the subject of further research.

The simulation is based on deep retrofits, which do not reflect the typical behavior of all building owners. Currently, building components such as windows and roofs are retrofitted much more frequently than others, and the refurbishment cycle in particular varies due to the different lifetimes of building components. The estimated lifetime is a decisive parameter and tries to capture the lifetime of the entire building system. But all lifetimes depend on the type of component, the quality and weather conditions. Therefore, even within groups of building components, a wide range of lifetimes can be observed. Although it would theoretically be possible to model retrofit rates on the component-level with the given equations, it is unclear to what extent an increased level of detail would also lead to more precise results. This would break down the inaccuracy of different lifetimes at the building level to a number of components. In the case of windows alone, this can amount to 10–60 years (cf. Ritter, 2011). In addition, building components, such as windows, consist of different components, which themselves have very different lifetimes and can partly be replaced even without renewing the windows.

The model assumes only one deep retrofit per building. Necessary refurbishments in already retrofitted buildings are then assumed to be equivalent to maintaining the energy level and are therefore not taken into account. Accordingly, when comparing the results with other building stock models, it must be considered which construction measures are included in the retrofit rate.

The \({ecof}_{i,j}\left(n\right)\) factor includes economic barriers as well as other barriers, as other barriers cannot be extracted with the available data. However, according to the literature, economic barriers are the most important. Nevertheless, it should be explicitly noted that organizational or psychological factors are also included. These can be, for example, insufficient information, difficulties related to refurbishments, synergies (e.g., tenants moving), etc. In a broader sense, however, these can also be considered economic factors. However, a reliable assessment of these extended factors would require larger empirical research.

Added value of the model

Essentials such as the need for rehabilitation are defined, while the economic framework conditions are treated as a “black box” variable in this paper. This is subject of further research, but the methodology presented demonstrates clear advantages. In fact, the economic framework and its impact on decision-making are highly intricate and vary across countries. Incorporating additional levels of detail typically results in inaccuracies due to underlying assumptions. In addition, each current framework condition must be specifically forecast for the observation period (e.g., interest rates, energy prices, construction costs, owner mindset, owner experience, owner distribution over time, owner income, national and EU regulatory frameworks). More detailed models are therefore only as accurate as the assumptions they make. Thus, short forecast horizons or a large number of scenario variants are necessary to keep the power of detailed models high.

By treating the refurbishment/rehabilitation cycles and economic influences separately, inaccuracies in these areas can be analyzed separately. In particular, the aggregated form of economic conditions in a black box variable also allows for the comparison of different economic conditions in further research. For example, the effect of low interest rates combined with high construction costs could be compared to high interest rates with low construction costs.

On the reliability of the model:

The profile of retrofitting rates in steady state (without historical deviations) is very similar to that observed in Sartori et al. (2016) (cf. Fig. 4 in Sartori et al., 2016). The results are also in good agreement with existing and historical retrofitting rates when \({ecof}_{i,j}\left(n\right)\) is set as in the trend scenario. Therefore, the question of reliability largely depends on the translation of economic conditions into \({ecof}_{i,j}\left(n\right)\), as well as on the setting of the lifetime.

Conclusion and outlook

The framework presented in this paper is a simple and effective means to model the size and status of residential building stocks. In particular, the model can be linked to TABULA for energy balances in 20 European countries. It is based on population growth, living space, service life assumptions, and a set of endogenous parameters. By adjusting these parameters, the model can be applied to other national building stocks or further improved. The model accurately captures the evolution of the German building stock and responds well to changes in parameters. It is useful for modeling the size and retrofit actions of building stocks and for deriving appropriate conditions for increasing retrofit rates also in other countries. Additional parameters could be incorporated.

The model shows that an increase in the retrofit rate to 2%/a or even 3 to 4%/a is unrealistic, as this would require refurbishments with very poor economic feasibility, assuming that retrofits are only economically viable when rehabilitation measures are pending. The scenarios with increased retrofit rates reach 1.92%/a max and already lead to sound retrofit rates for the older building age classes. Attempting to deeply retrofit the younger building age classes (1995 +) would require significant improvements in conditions, as these buildings offer less energy savings potential and generally have much less need for refurbishment. The final energy results for 2030 (cf. Table 3) show that high short-term final energy savings from energy retrofits are unlikely in Germany. Even scenarios with increased retrofit rates generate only minor savings (< 13%, cumulative 2018–2030). To improve this, the energy performance gap could be addressed or levers like heat pumps may be used, which require less energy by using environmental energy. The energy performance gap can in turn be addressed by trying to operate and use current buildings as efficiently as possible. Therefore, buildings (especially those with higher energy quality) have a potential that can be utilized without construction measures, but with appropriate user behavior.

In conclusion, it is necessary to increase the retrofit rate to realistic levels by focusing on the current weak points of buildings. Weak points are the retrofit rates of the facade and basement (ceiling) and, in particular, unsuited heating systems. Since the most promising heating system for residential buildings from today’s perspective, the heat pump, often requires energy retrofits for efficient use, the targeted replacement of the heating systems is strongly linked to the retrofit rates. Deep retrofits or gradual retrofits suited for the installation of heat pumps therefore appear to be essential for the modernization of heating systems. In any case, retrofits should be so attractive that refurbishment occasions are in fact used for (eventually deep) retrofits. Sartori et al. (2016) describe it as follows: “These figures should give a clear impression of the inertia in the building stock and the risk of lock-ins, and therefore a clear understanding of how precious an occasion renovation is for introducing long lasting energy conservation measures.” Otherwise, the important window of opportunity, i.e., the need to refurbish a building, could be wasted with measures such as painting the exterior wall. In addition, it is recommended to improve user behavior in order to increase the hidden efficiency potential in buildings to a reasonable level without structural measures.

Refurbishment and retrofit activities are affected by growing costs and uncertainties. In the face of high construction and rising financing costs, targeted funding programs and reliable subsidy terms are becoming increasingly important.