1 Introduction

Reducing greenhouse gas emissions is a fundamental challenge facing humanity. The EU recently adopted the so-called Green Deal (COM/2019/640), which calls for climate neutrality by 2050.Footnote 1 This means that efforts to date focused on energy producers and large CO2 emitters must be extended to households and transportation. Currently, 20% of total greenhouse emissions in the EU come from households (Eurostat, 2022) and around 30% come from the use of buildings (EEA, 2022). The planned changes will involve further improving the energy efficiency of buildings so that they use less energy. Also, the EU renovation strategy (COM/2020/662) envisages a shift toward greener solutions in buildings, improving the energy performance of buildings, and decarbonization of electricity.

In Poland, the decarbonization of households is an extremely important challenge for two reasons. First, about 60% of single-family buildings use coal for heating (Statistics Poland, 2018), which is the cheapest but also the most emissive fossil fuel. Second, coal has a 70% share in electricity generation in Poland (Energy in Poland, 2021), hence, switching to electricity cannot reduce GHG emissions. Therefore, transformation in the building sector must consist of improving the efficiency of buildings, changing the sources of heating in homes, and improving the national energy mix.

To address the policy concerns about the households' capacity to complete the clean energy transition we employed the environmental Kuznets curve on micro-level data. Several research problems are discussed in this study:

  • What is the shape of the EKC in the case of Polish households living in single-family houses?

  • What is the impact of the current energy mix and zero-carbon electricity scenario on the households’ EKC?

  • Does a house area matter in households’ EKC estimations?

  • How hidden energy poverty is embedded in households’ income-emission trajectory?

We analyze households living in single-family buildings, which are interesting for two reasons. First, detached houses represent the majority in Poland, and second, residents of single-family houses can decide on the choice of heating sources in their homes and are also responsible for their energy efficiency. In Poland, less emitting fuels are more expensive. The choice of heating source is therefore a compromise between environmental and financial factors.

Much effort is put into studying the link between income and environmental degradation, which is thoroughly reviewed in the next section of the study. To recap, in the vast majority of studies on EKC, households are considered at an aggregated level as an actor embedded in macro models (Pablo-Romero et al., 2017; Turner & Hanley, 2011). And yet, the behavior of energy consumers is heterogeneous; for example, households may apply different coping strategies, like energy under-consumptionFootnote 2 (Anderson et al., 2012; Betto et al., 2020; Kulmer & Seebauer, 2019). Our study enriches the slowly growing literature on micro-EKC that discusses the topics of energy choices and behavior (Giovanis, 2013; Bravol & Marelli, 2007). We take a step further by providing valuable household-detail insights related to the impact of energy sources on CO2 emissions, the link between the EKC shape and hidden energy poverty (Karpinska & Śmiech, 2020) embedded in the energy under-consumption strategies, characteristics of houses, and the ability to pass through the turning point, etc.

The contribution of this study is manifold. First, this study pioneers the research on the role of hidden energy poverty in households’ carbon emissions reduction. In this study, we define hidden energy poverty as a situation in which a household falls below the relative poverty line after the estimated energy consumption is deducted from the equivalised disposable income (Karpinska & Śmiech, 2020); 60% of the after-energy-cost income is adopted as a threshold. According to the data from the energy consumption survey in 2018, about 16.5% of households were in hidden energy poverty, which means that those households prefer to under-consume energy over dissatisfaction with other basic needs.

Second, we offer an effective tool for estimating the impact of zero-carbon electricity generation on the capacity of households to reach the peak of carbon emissions faster and follow the declining emissions and growing income trend afterward. Accounting for the different ways of producing electricity allows us to emphasize the importance of decarbonization for households’ emissions at the national level.

Third, this study applies a novel approach by combining a robust least-trimmed squares regression technique with the EKC framework suitable for the analysis of micro-level data, such as energy consumption in households and the household budget surveys, regularly collected by the national statistical office. We provide a feasible data-driven model for assessing the decarbonization paths of households, which is of crucial importance from a policy-making perspective.

Lastly, utilizing the EKC theory on the individual data we draw scientific and public attention to the problem of occupying spacious stand-alone houses, which compromise clean energy transition. The size of the property is correlated with income and dictates the consumption strategy. Large spaces require more energy to heat and cool. Switching to gas involves a significant increase in energy costs unless the costs are offset by the energy efficiency of the building. The socially accepted idea of possessing large single-family houses as a sign of wealth should be further debated in the context of carbon emission reduction.

The rest of the paper is structured as follows. Section 2 provides an overview of the literature on the topic. Section 3 describes the data. Section 4 explains our methodology. Section 5 discusses the results. Section 6 concludes.

2 Literature overview

There are several streams of research that we contribute to in this study. To begin with, let us mention EKC. There is a rich literature that tests the EKC hypothesis and there are multiple exhaustive reviews covering the developments in this research field (Sarkodie & Strezov, 2019; Shahbaz & Sinha, 2019), including the most recent ones (Anwar et al., 2022). Due to an overwhelming amount of research on EKC, we would like to highlight only the most crucial from the perspective of this study's findings.

Grossman and Krueger (1991) were the first to adopt the original Kuznets curve explaining the links between economic development and environmental quality instead of income and inequality put forth by Kuznets (1955). In the last 30 years, studies on energy consumption, emissions, and economic development have proliferated. Different specifications of the EKC model, i.e. with linear, quadratic, and cubic income are examined. Apart from income, a set of additional variables are included in the analysis, like industrialization (Du & Xie, 2020), urbanization (Wang et al., 2022), economic structure (Dogan & Inglesi-Lotz, 2020), demographic change (Franklin & Ruth, 2012), financial market and renewables (Maneejuk et al., 2020), etc. The list of control variables is non-exhaustive. EKC studies consider various types of emissions, but the most popular one is CO2 (Apergis, 2016; Azam & Khan, 2016). Destek et al. (2018) consider ecological footprint as a proxy for the environmental burden. The geographical context in which EKC is tested is very broad; developing and developed economies are explored with the same level of interest (Churchill et al., 2020; Sarkodie et al., 2018).

In the modified version of EKC, i.e. energy-environmental Kuznets curve (EEKC), a response variable is energy consumption, for example, consumption from transportation activities (Pablo-Romero et al., 2017), instead of environmental degradation. The EEKC has been recently advanced by Filippidis et al. (2021), who link the EEKC results with energy poverty understood as access to energy consumption.

Many authors confirm the validity of the inverted U-shaped relationships, some others also arrive at N-shaped curves when plotting the GDP against emissions (Churchill et al., 2018; Allard et al., 2018). In some studies, EKC links are not found. A carbon leakage problem and the need to account for the emissions embedded in international trade make some authors consider consumption- and production-based emissions in EKC analysis (Dong et al., 2016; Frodyma et al., 2022). The common ground for the mentioned studies is that they apply a macro-level approach and econometric modeling for single economies and regions or groups of countries.

Micro-level studies of EKC are scant but constitute a promising area of research. Chaudhuri and Pfaff (1998) laid the foundations for the micro-level EKC. They underscore the importance of household decisions in choosing energy sources. The authors draw Engel curves for clean and dirty energy sources and support the household-level EKC, in which indoor air pollution and household income are considered. The behavior of households and environmental damage is studied by Heerink et al. (2001), who emphasize the role of income (re)distribution in the EKC research. Bulte and Soest (2001) study the consumption and production decisions of rural households in developing countries following both microeconomics modeling and EKC. By contrast, Bravol and Marelli (2007) deny the micro-level grounds of EKC and claim that there is no clear relationship between the pro-environmental behavior of individuals and the national income. Giovanis (2013) uses household data, a broad set of control variables, such as family size, gender, age, social status, etc., three air pollutants, i.e. SO2, NOx, O3, to prove the validity of the EKC hypothesis. Several authors studied EKC and transport emissions of households (Cox et al., 2012; Kahn, 1998). The results are mixed, and EKC is not always supported in the micro-level analysis.

The next stream of literature we draw upon is related to hidden energy poverty and a pre-bound effect caused by households’ energy under-consumption. Energy poverty is a relatively new topic compared to the EKC analysis. Energy poverty can be defined as a lack of access to or unaffordability of essential energy services. Haffner and Boumeester (2015) stress that unaffordability of housing is usually linked to higher energy costs being the reason for income poverty and tenants' vulnerability. The latter problem is especially acute in the case of social housing (Garnham et al., 2022). In the same vein, Yang et al. (2017) consider housing wealth and income are also correlated with carbon inequality. Our primary focus is on hidden energy poverty (Karpinska & Śmiech, 2020; Meyer et al., 2018), which indicates abnormally low energy consumption. There are studies supporting the idea that households having financial constraints usually cut their energy expenditures (Barrella et al., 2022; Betto et al., 2020; Papada & Kaliampakos, 2020). In this case, the real expenditures do not reflect the actual needs of a household (Antepara et al., 2020). Sunikka-Blank and Galvin (2012) introduced the term pre-bound effect to describe a situation when the worse the thermal properties of houses are, the more restrictive space heating behavior their occupants exhibit. Improving energy efficiency in this case results in higher energy consumption and CO2 emissions (Teli et al., 2016). By contrast, the analysis by Recek et al. (2019) confirms that the main purpose of renovating buildings in households is the reduction of energy consumption, which is also positively correlated with better indoor environmental quality.

Finally, we contribute to the literature on the crucial role of buildings in emission reduction, which tends to increase from 2000 to 2020 globally (Xiang et al., 2023). Zhang et al. (2023) suggest that the decarbonization of residential buildings of the major emitters could reserve a substantial emission space. Among the factors that have an impact on carbon emissions, which are also discussed in this study are the floor area and population size (Chen et al., 2023). Yan et al. (2023) confirmed an inverted u-shape carbon Kuznets curve applied to residential buildings for most of the economies.

Based on the review above we could detect the following knowledge gaps. Firstly, few studies take a micro-level approach to households. In most cases, households are considered at the institutional aggregated level, which impedes the identification of a household's characteristics. By including micro-variables and considering two energy scenarios, we designed our study to holistically evaluate households’ progress on the way to clean energy transition. Secondly, the usage of the EKC framework to analyze hidden energy poverty issues, i.e. energy under-consumption and an accompanying pre-bound effect opens a brand-new venue of research in this field. The study supports the idea that energy under-consumption is associated with the rise in EKC due to a pre-bound effect (Galvin & Sunikka-Blank, 2016; Papada & Kaliampakos, 2020). Thirdly, our approach to residential buildings differs in many respects. We consider housing types, and floor areas and link them to carbon emissions and income of an individual household, which allows us to bring up the scientific discussion on the sustainability of a single-family ownership. This approach inherently contributes to policy solutions for multiple problems, such as emissions of households, energy poverty, and residential housing ownership.

3 Data

We derive data from two databases. One is the Household Budget Survey (HBS), and the other one is the Energy Consumption Survey (ECS). Both questionnaires were collected from households in 2018 by Statistics Poland. Most of the variables in this study come from the ECS, which is conducted once in three years. We rely on the latest available ECS file. To complement the information on energy consumption with household characteristics we merge the respective HBS and ECS files by household numbers.

The HBS contains household characteristics and expenditures on goods and services. The survey is collected each year and provides information on the level of welfare, living conditions, consumer prices, etc. The size of the sample is about 38,000 households. Statistics Poland applies the rotation procedure to ensure the sample is fully representative. In the ECS respondents have to answer 22 questions that cover 12 sections, such as (a) the usage of energy sources for different purposes (heating, water heating, cooking, etc.), (b) heating and kitchen appliances, air conditioning, mechanical ventilation (c) lightening devices and electronics (d) measuring and regulating devices (e) energy consumption (f) energy-saving, and others. The ECS sample consists of slightly more than 4000 households representing around 9.5% of the total HBS sample. Due to incompleteness, about 12% of the ECS data were removed in the cleaning procedure. To verify that the removal of these cases does not affect the representativeness of the sample we present in Table 7 the distribution of crucial socio-economic variables in the full and final samples.

Table 1 Variables
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Our target group comprises households living in single-family houses, i.e. 1676 households, which is about 47.2% of the total dataset. To verify the EKC at a household level we select two variables, income and energy expenditures per energy source, which are later used to calculate CO2 emissions. The income is disposable and is equivalised according to the OECD-modified equivalence scale, i.e. the first adult is assigned the weight of 1, the next adult is given the weight of 0.5, and children below 14 years old weigh 0.3. The procedure of income equivalisation allows for achieving a comparable income distribution among small and large households. Table 1 provides a listing of the variables used in the analysis.

The descriptive statistics of monthly equivalised disposable income in our sample, including small and large house sub-samples, are presented in Table 2. There are about 20 observations with income below 100 EUR per month. The maximum value is reported by an extreme outlier. Income is correlated with the size of the house. We have four groups of houses with a usable area of up to 50 m2, between 50 and 100 m2, between 100 and 200 m2, and above 200 m2. As a rule, big houses require more energy to heat and a higher income to maintain compared to small dwellings. Figure 1 shows that large spaces are mostly occupied by households from upper-income deciles, and vice versa. As presented in Fig. 2 there are many more old houses built before 1980 in the lower deciles. The share of houses built after 1996 increases from 9.5% in the 1st decile to 35% in the 10th decile. Modern houses are constructed according to recent energy requirements being more energy efficient and resilient (Dz. U., 2021). Figure 3 shows that the share of insulated houses gradually increases per income decile. Also, poor and affluent households differ in terms of used energy sources (see Fig. 4). Although coal is the most common source in Poland, its share decreases with income. Households from upper-income deciles can afford more expensive but less polluting fossil fuels, i.e. natural gas. The major obstacle to using natural gas as a relatively clean alternative to coal besides its price (Karpinska & Śmiech, 2021) is the poor development of the infrastructure, i.e. lack of pipelines, in some regions of Poland. In 2019 the level of connection to the gas network varied from 11.9 to 68.7% in different regions of Poland (Bogacz, 2021). The dependence on coal and other polluting fossil fuels to some extent undermines efforts aimed at reducing the environmental burden of energy usage.

Table 2 Income statistics in households occupying detached houses
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Fig. 1
figure 1

Correlation between income deciles and a house size. Notes Standardized residuals show the difference between observed and expected numbers for category pairs. The blue color shows the over-represented categories in the sample. The red color shows under-represented categories

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Fig. 2
figure 2

Age of houses per equivalised income deciles, in %

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Fig. 3
figure 3

Insulation of houses per equivalised income deciles, in %

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Fig. 4
figure 4

Expenditures on energy sources per equivalised income deciles, in %

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4 Methods

4.1 Least trimmed squares model

The data we used are provided by Statistics Poland. The surveys are representative, well-tailored, and collected based on the best standards of statistical data collection. Yet, we encounter some issues, such as seasonality and credibility of answers provided by respondents. For example, there are fractions of households in all income groups which declare no expenditure on energy. Another group declares energy expenses that exceed their income. Regardless of the reasons, errors in the data pose a challenge to statistical procedures. An optimal procedure should allow the assessment of the relationship between pollution and income for a majority of households, ignoring questionable information that does not fit the central pattern. In our case, we try to fit a regression model:

$${y}_{i}={\beta }_{0}+{\beta }_{1}{x}_{i}+{\beta }_{2}{x}_{i}^{2}+{e}_{i}, i=1,..,n$$

to n element sample that consists of observations \(({x}_{i},{y}_{i})\), where \({y}_{i}\) is the CO2 emission of i household and \({x}_{i}\) is its income. Many estimators of model parameters \(\beta =({\beta }_{0},{\beta }_{1},{\beta }_{2})\) break down when outliers are present. The outliers might be classified into three categories (Rousseeuw & Van Zomeren, 1990). A vertical outlier appears when point (\({x}_{i}, {y}_{i})\) does not follow a linear pattern of the majority of the data, but \({x}_{i}\) is not outlying. A good leverage point means that \({x}_{i}\) is outlying but \(({x}_{i},{y}_{i})\) follows the pattern of the majority. Finally, a bad leverage point appears if \({x}_{i}\) is outlying and \(({x}_{i},{y}_{i})\) does not follow the pattern of the majority.

Since OLS has a zero breakdown value i.e. any small fraction of bed observations can change the values of estimators, robust methods are proposed. The simplest approach is to remove the outliers, which are identified from the model residuals. Rousseeuw and Leroy (2005) provide several examples to show that this method is not efficient. Sensitivity analysis techniques, recommended by Belsley et al. (2005), have difficulty when outliers are clustered, and "mask" each other. A small fraction of contaminated data can also distort the results for regression M-estimators. As shown in Rousseeuw (1984) a breakdown value, in this case, is zero, as well. The generalized M-estimators by Mallows and Schweppe are also criticized in this context. To increase the breakdown value of estimators, Rousseeuw (1984) proposed two alternative methods: least median squares (LMS) and least trimmed squares (LTS). Both estimators are insensitive to changes when the data are contaminated with a significant number of outliers. Several arguments suggest that LTS outperforms the LMS estimator. First, the objective function for LTS is smoother, making it less sensitive to local effects. Second, the statistical efficiency is better in the case of LTS. Finally, the LTS estimator is asymptotically normal and has faster convergence. To obtain the LTS estimator, one has to consider the conditional squared residuals \({r}_{i}^{2}\left(\beta \right)={\left({y}_{i}-{x}_{i}\beta \right)}^{2}\), and next to order them: \({0\le r}_{(1)}^{2}\left(\beta \right){\le r}_{(2)}^{2}\left(\beta \right)\le \dots {\le r}_{(n)}^{2}\left(\beta \right)\). The objective of the LTS estimator is to minimize:

$$\sum_{i=1}^{h}{r}_{(i)}^{2}$$

which is the same as finding h-subsets with the smallest residuals from the OLS objective function. In other words, the LTS regression fits the OLS to these h points. The breakdown value of LTS equals \(h=[\frac{n+p+1}{2}]\), where \([a]\) is the integer part of a. In practice, to estimate the parameters the Fast–LTS algorithm (Rousseeuw & Van Driessen, 2006) is used. It consists of the following steps:

  1. 1.

    Set h and sample h out of the n observations. Use these observations to obtain the ordinary least squares estimator \({\widehat{\beta }}_{{H}_{1}}\).

  2. 2.

    Calculate the residuals for all n observations using the regression with \({\widehat{\beta }}_{{H}_{1}},\) i.e.,

    $$r_{i} \left( {\hat{\beta }_{{H_{1} }} { }} \right) = y_{i} - x_{i} \hat{\beta }_{{H_{1} }} , \;{\text{for}}\;i = 1, \ldots ,\;n.,$$

Next, sort the squared residuals \({0\le r}_{(1)}^{2}\left({\widehat{\beta }}_{{H}_{1}} \right){\le r}_{(2)}^{2}\left({\widehat{\beta }}_{{H}_{1}}\right)\le \dots {\le r}_{(n)}^{2}\left({\widehat{\beta }}_{{H}_{1}}\right)\)

  1. 3.

    Take the h smallest residuals from step 2, and determine the set (\({H}_{2}\)) of observations that correspond to them. Use the LS with these observations to calculate the estimator \({\widehat{\beta }}_{{H}_{2}}\).

As the objective function of LTS descends consecutively:

$$\sum_{i\in {H}_{2}}{r}_{(i)}^{2}\left({\widehat{\beta }}_{{H}_{2}}\right) \le \sum_{i\in {H}_{1}}{r}_{(i)}^{2}\left({\widehat{\beta }}_{{H}_{1}}\right)$$

Step 2 and 3 have to be alternated until the procedure converge (Rousseeuw & Van Driessen, 2006).

4.2 Hidden energy poverty and calculation of CO2 emissions

To provide more valuable policy recommendations and put the results in the social context, we include energy poverty in our analysis. Being aware of the differences between the real energy consumption in households and the level of energy usage needed to maintain a comfortable temperature inside of a house, we refer to the concept of hidden energy poverty. Energy under-consumption when combined with low income causes hidden energy poverty (Karpinska & Śmiech, 2021). In Poland the share of households in hidden energy poverty in 2018 amounted to 16.5%; households in hidden energy poverty can be found in up to 3rd income deciles; 100%, 77.3%, and 1.7% of households are affected by hidden energy poverty in the first, second and third income deciles respectively.

In this study, the pressure on the environment is approximated by CO2 emissions. Carbon dioxide is the key pollutant responsible for around 81.8% of all GHGs in Poland in 2019 (KOBIZE, 2021). Almost the same statistics are reported for the EU and the world (OECD, 2022; EEA, 2022) confirming the crucial role of CO2 gas in measuring the environmental pressure. CO2 is released during the combustion of solid fuels often used in the residential sector for heating and cooking, which is also the reason why we focus on CO2 emissions.

CO2 emissions are calculated based on the energy expenditures of households. We account for the impact of each energy source on the environment. Table 3 summarizes the coefficients used in our analysis. We rely on several technical reports that analyze the conversion of emissions coming from different energy sources. In the case of electricity, two scenarios are of primary interest. The first one is zero-emission electricity. The second one is polluting electricity produced from the Polish energy mix, i.e. 70% of coal, 20% of renewables, and 10% of natural gas. In the first scenario, we expect that electricity consumption does not affect CO2 emissions, but the amount of electricity consumption is related to household income. In the second case, we rely on the actual less-renewable electricity generation.

Table 3 Conversion of energy expenditures (in PLN) into CO2 emissions (in kg).
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Figure 5 shows histograms of the obtained CO2 emissions in two scenarios. Both distributions are right-skewed with multiple outliers in the upper quartile. The peak in the energy-mix scenario is around 5,000 kg. The distribution of CO2 in a zero-emission scenario is multi-modal, i.e. the most common values are less than 500 kg and around 4,000 kg. Equivalised CO2 emissions of less than 500 kg per year are considered inconsistent with the actual energy needs of a household. We deal with data contamination in the next section by building the LTS model.

Fig. 5
figure 5

Distribution of annual equivalised CO2 emissions (in kg) in two scenarios

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The distribution shown in Fig. 5 is also skewed, suggesting a transformation of the variable, e.g. by logarithmisation. We decided not to do this for two reasons. Firstly, the robust procedure used for parameter estimation ignores outlier observations. Secondly, the logarithm cannot be calculated for zero emission values, and other transformations could look arbitrary.

5 Results and discussion

In establishing the link between carbon dioxide emissions and household income this study relies on a robust regression method, which is preferred in the presence of contaminated data and multiple outliers.

The empirical evidence for the inverted U-shaped EKC comes from the LTS model. The LTS parameters obtained in two scenarios for 1676 households are presented in Table 4. As expected, the first income parameter takes positive values and the squared terms of income take negative values. An intercept in both scenarios differs, and under the zero-emission scenario, the emissions are initially smaller. The turning point which implies the transition from environmental degradation to environmental improvements occurs at 1700 PLN (373 EUR) in case electricity is generated from clean energy sources, and 2553 PLN (560 EUR) otherwise. As expected the peak is reached much faster in a zero-emission scenario. The turning point under the energy-mix scenario is around the mean value and slightly higher than the median equivalised disposable income per month in the sample.

Table 4 EKC parameters obtained from the LST estimator in two scenarios
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The EKC curve has a clear inverted U-shape. Figure 6 presents two curves in a zero-emission (red line) and an energy-mix (blue line) scenarios. When electricity is produced from clean energy sources the emissions are in general much lower and we observe a lot of households having zero emissions. By contrast, CO2 emissions in the energy-mix scenario are higher.

Fig. 6
figure 6

Inverted U-shaped EKC for households occupying detached houses in two scenarios, zero-emission (right-side plot) and energy-mix (left-side plot)

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To justify the adopted strategy, i.e. the estimation of the classic EKC model for the entire sample, we conduct a series of robustness checks. First, we check the cubic specification of the EKC model estimated on the same data. Figure 10 compares the results of the standard EKC model with the cubic EKC model. In this graph, the shaded area refers to households having the typical equivalent disposable income, i.e. income in the range of the first and ninth decile. As can be noted, in the case of typical households, the two models are very similar to each other, giving similar emissions for both scenarios and offering a similar trajectory of the curves. Therefore, regardless of the model adopted, for typical households, we observe an increase in emissions accompanied by an increase in income in the case of poor households and a decrease in emissions accompanied by an increase in income in the case of wealthier households.

The second robustness check consists of checking what happens if we exclude farmers and self-employed, whose relationship between CO2 emissions and income may demonstrate a different pattern, from the sample. As a part of this check, we compare the shares of these two categories of households in the data at our disposal and the entire population. The shares are identical. Moreover, we estimate the classic EKC model for the sample with and without farmers and self-employed. The results (available upon request) are similar to those obtained for the entire sample.

There are multiple underlying reasons for the EKC curve to fall after a certain level of income. In this study, we provide a plausible explanation of what may reduce carbon dioxide pressure in Polish households given their actual energy consumption.

5.1 Characteristics of houses

First, the higher income is associated with houses in much better technical condition. Modern requirements on the energy efficiency of buildings (Dz. U. 2019.0.1065) aim at the reduction of energy consumption, carbon dioxide mitigation, and dissemination of devices that generate renewable energy. The ultimate goal is achieving zero energy by combining energy self-generation and energy efficiency. The construction of nearly zero-energy buildings is still in its nascent stage in Poland and the level of public awareness leaves much to be desired. As an example, in 2018 around 28% of households either did not eliminate energy waste or did not benefit from its reduction, around 32% of households never heard about an energy audit, and 18% of households took no action to lower their energy costs (ECS). Yet, we notice that the share of insulated houses and also the share of houses built after 1996 gradually increases as income grows. Figure 7 presents the share of insulated and modern houses as well as the share of households in hidden energy poverty with income less and more than the turning point in the two scenarios. We discuss hidden energy poverty later in this section. The results of the z-test show that the difference in proportions of all three variables, i.e. insulated houses, modern houses, and hidden energy poverty, are statistically significant at a standard 5% level. In other words, the group of households located before the turning point and located after the turning point (Fig. 6) has different profiles in terms of house conditions and hidden energy poverty. Better in terms of thermal conditions houses are more common after the turning point and coincide with the falling slope of the EKC curve supporting our idea that the energy efficiency of homes helps to lessen the environmental burden. It is worth mentioning, that households may not have the possibility to further reduce energy costs due to initial under-consumption of energy or limited financial possibilities to invest in thermal modernization. This problem is discussed at the end of this section.

Fig. 7
figure 7

The share of insulated and modern buildings and the share of households in hidden energy poverty before and after the turning point in the respective scenarios. Notes The results of the two-proportions z-test confirm that the proportions of all variables are significantly different in two sub-groups, i.e. before and after the turning point

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5.2 Energy sources

Second, the higher income is linked to the change in the composition of energy sources used by households, i.e. the share of coal decreases and the share of natural gas increases. Coal is the major contributor to CO2 emissions and occupies a large portion of the structure of households’ energy expenditures. Not to mention that 70% of electricity in Poland is produced from coal according to the current country’s energy mix. The share of coal in CO2 emissions equals 77% and 80.25% in the energy-mix and zero-emission scenarios. Gas is considered the most viable alternative to coal in most Polish regions. Due to the lower pollution damage, the presence of gas in the structure of energy expenditures has a downward effect on the slope of the EKC curve ceteris paribus. The difference between the total expenditures on coal and gas in the first income decile equals 182,044 PLN (39,922 EUR). This difference is gradually decreasing and in the tenth decile, the total expenditures on gas exceed the total expenditures on coal by 3,233 PLN (709 EUR). The difference between total expenditures on both sources of energy in each income decile is represented by a shaded area in Fig. 8.

Fig. 8
figure 8

Total expenditures on coal and gas per income decile (in PLN)

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5.3 Floor area of houses

Third, the size of a heating space is also related to the ability of a household to reduce its emissions. To trace the path of the EKC for properties of a different size, we divide our sample into two major groups, i.e. relatively small and big homes. Each group is almost equally represented in the sample; we have 847 and 829 households in a small- and big-home group respectively. The LTS coefficients are presented in Tables 5 and 6. In the case of homes with a usable area of up to 100 m2, we obtain a normally behaved inverted EKC that shows a clear U-shape trajectory (Fig. 9). Our explanatory variables take usual signs; the peak is reached at 1709 PLN (375 EUR) and 1872 PLN (410.5 EUR). By contrast in the sample of big houses, the EKC line is almost flat and the turning point occurs in 2811 PLN (616.5 EUR) in the energy-mix scenario. Moreover, we observe no EKC in the zero-emission scenario. Specifically, the turning point is noted in 24,106 PLN (5,287 EUR), which is an unrealistic amount of a monthly equivalised disposable income for an overwhelming majority of households in Poland. And, we do not expect a negative sign for an income parameter and a positive for squared terms of income.

Table 5 EKC parameters obtained from the LST estimator in two scenarios for houses with a usable area of less than 100 m2
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Table 6 EKC parameters obtained from the LST estimator in two scenarios for houses with a usable area of more than 100 m2
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Fig. 9
figure 9

Inverted U-shaped EKC for households living in houses of less than 100 m2 (right-side plot) and houses of more than 100 m2 (left-side plot)

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The usable area of houses is positively correlated with income, i.e. usually the higher the income the larger the houses. It is much easier to heat small properties and switching to gas is less costly compared to large houses. Gas consumers living in smaller houses gain additional comfort related to less indoor pollution associated with gases, dirt, and dust, for less amount of money. We presume the existence of the rebound effect in the case of households with higher incomes and bigger houses. Big heating spaces complemented with a greater number of appliances harm the environment, i.e. the level of CO2 emissions is almost constant. Part of the rebound effect may be attributed to the increased energy consumption (Guerra Santin, 2013), i.e. direct rebound effect, the other part is associated with the increased demand for other goods and services (Chitnis & Sorrell, 2015). The analysis of both effects is out of the scope of the current study and should be completed in further research.

5.4 Energy under-consumption of households

Lastly, we approach the problem of actual and estimated energy consumption. This study focuses on the reported energy usage as a basis for carbon dioxide computation. We are aware of the fact that actual energy consumption might significantly differ from the amount of energy needed to maintain thermal comfort inside a house. Many households in Poland, especially those with a low income cut on energy usage to satisfy other basic needs. Figure 7 shows the distribution of hidden energy poverty before and after the turning point in two scenarios. Hidden energy poverty indicates households who will be pushed into poverty after paying bills on the estimated amount of energy. We use the relative poverty line, i.e. 60% of the annual equivalised disposable income, from which we deduct energy costs. In 2018, the energy poverty threshold was PLN 15,652.16 (EUR 3,400). The rising part of the inverted EKC is linked to energy under-consumption that is decreasing as income grows. Households consume more energy if they have more resources and this fact corresponds to growing emissions. As under-consumption is eliminated the reduction of CO2 emissions' takes place. In our case, the pre-bound effect noted for energy poor households explains why the burden on the environment increases until a certain point. Further research on households' energy consumption behavior and heating strategies can shed light on the existence of the pre-bound effect on energy consumption.

An important conclusive point to mention is the height of the inverted U-shaped EKC. The very high level of CO2 emission may signify a certain point of irreversibility. Reaching the so-called climate tipping point poses a real danger to the state of the ecosystem as advocated by environmentalists (Club of Rome, 2022). In our study, the turnaround point has a y-axis coordinate at slightly more than 5000 kg of annual equivalised CO2 emissions. This point is lower in the case of zero-emission electricity, i.e. around 3000 kg of equivalised CO2 emissions in one year. The assessment of the environmental impact suggests a new venue for future research.

6 Conclusions

Using the EKC framework and a robust least-trimmed squares regression, this study proposes a model for estimating the households’ path to carbon emissions reduction. We examine the micro-level underpinnings of EKC theory based on individual observations of households' income, housing type, housing size, presence of hidden energy poverty, and usage of energy sources. The results confirm the existence of an environmental curve in Polish households. Thus, an initial increase in income leads to an increase in emissions; a later increase in wealth usually means a decrease in emissions.

6.1 Core findings

  • This study demonstrates that besides income, which remains an important determinant of carbon emissions, several factors should be considered in the reduction of households’ carbon emissions. Among these factors are hidden energy poverty, housing size, and energy sources.

  • Lower energy expenditures and emissions are observed in low-income households, especially those characterized by hidden energy poverty. The latter could undermine policy efforts towards carbon emissions reduction. This finding is in line with several authors who study the pre-bound effect and retrofitting policies (Galvin & Sunikka-Blank, 2016; Teli et al., 2016).

  • Increased income translates into more energy-efficient homes and less carbon-intensive fuels used for heating. An exception to these results is large houses, i.e. those with an area exceeding 100 square meters. In this case, there is no evidence of EKC. Key to these results appear to be rebound effects, i.e. increased energy consumption, but also a relatively large difference in the cost of cleaner fuel (natural gas) and dirty fuel (coal).

  • These results hold for both scenarios considered, i.e., assuming that electricity consumption burdens the environment in line with the current energy mix, and in the scenario that assumes that electricity is emission-free. The second scenario, of course, shows significantly lower emissions in the household sector.

The results obtained allow us to draw some policy recommendations for Poland.

  • First, regardless of wealth level, households emit fewer greenhouse gases when electricity is produced carbon-free. Therefore, the energy transition must proceed as quickly as possible in Poland.

  • Second, the amount of emissions generated by households is correlated with the size of the homes. The effect of EKC is especially pronounced in houses of less than 100 m2. Smaller houses generally generate less pollution. Therefore, unless we can produce energy in a zero-emission way, we should prefer to have smaller houses. It seems that the Fit for 55 provisions, which are supposed to tax emissions from the household sector, may become an incentive to reduce them. At the same time, it should be remembered that a large group of poor households emits a lot of pollution.

  • Finally, lower emissions are related to an increase in the energy efficiency of homes. It is important to propose policy instruments that will accelerate the thermo-modernization of homes.

6.2 Limitations and a venue for future research

The limitations of the current study are attributed to data, which is difficult to deal with following the usual regression analysis. The computation of CO2 emissions may include marginal error attributed to the adopted conversion standards, which vary depending on the source of energy. We also consciously disregard the cubic specification of the EKC model due to inconclusive results.

Several topics remain outside the scope of this study and should be considered in future research. First, occupant behavior is crucial in predicting CO2 emissions. Household strategies are important when it comes to the choice of energy sources, making thermal modernization decisions, energy savings, etc. Second, it is interesting to estimate re- and pre-bound effects regarding the household EKC. Third, controlling for the energy efficiency of homes and appliances would provide more information on the factors that have an impact on the shape of the EKC curve. Fourth, a further examination of the height of the EKC is necessary to assess the environmental impact of the lifestyles of households.

It seems reasonable to carry out similar studies for other EU countries, looking for specific patterns, especially before the fit-for-55 package is introduced. Identification of the income level of the households with the highest CO2 emissions would allow the optimal choice of policy tools to maximize environmental benefits and reduce the size of emission charges.