The Poisson Method of Poverty Measurement Using Non-monetary Indicators: A Replication Study Based on Australian Data

This study revisits the Poisson-based framework to derive optimal thresholds of relative deprivation in the Australian context. Poverty measurement in developed countries mainly relies upon household income to capture those who are poor from the rest of the population. However, there is a growing recognition that the non-monetary indicators of relative deprivation can significantly improve the identification of those living in poverty. Relative deprivation is typically operationalised as not being able to afford and obtain a list of items that are considered essential in a given society. The key advantage of using such non-monetary indicators relates to its ability to directly capture the manifestations of poverty and assess people’s living standards. Yet, one salient issue is the selection of a meaningful threshold from which the deprived and the non-deprived can be separated. Following on Babones et al. (Babones et al. Social Indicators Research 126:711–726, 2016), this study replicates the Poisson method to specify an appropriate threshold value (k)—the number of missing essential items—that defines a person or household as deprived in Australia. Based on data from the 2018 Household, Income and Labour Dynamics in Australia (HILDA) survey, thresholds of k ≥ 4 for non-possession (merely lacking items), k ≥ 3 for derived deprivation (lacking and not being able to afford items), and k ≥ 3 for inferred deprivation (lacking and regarding items as essential) are suggested, respectively.


Introduction
Ongoing debates within the field of poverty research have long concerned the issue of how best to measure poverty. A credible poverty measure is vital for producing robust evidence on which to base relevant policy priorities and actions. Essentially, all poverty measures are concerned with the task of distinguishing those who are poor from the rest of the population. This classification process can be seen as comprising three distinct yet interconnected steps: the conceptualisation, operationalisation and measurement of poverty. It begins with defining what poverty is, selecting the indicator(s) on which to capture the concept as so defined, and ultimately specifying a threshold value to assign the status of poverty.
In developed countries such as Australia, poverty studies have predominantly relied on an income-based approach for measuring poverty. Implicit in the approach is the conception that low income and poverty are synonymous. While economic resources are one of the prerequisites for wellbeing, it has long been argued that income is an indirect measure of poverty which captures the potential rather than the actual life outcomes (Ringen, 1988). An undue reliance on income can lead to a narrow and partial picture of poverty, failing to fully capture the circumstances and experiences of the poor. Recent decades have thus witnessed a gradual shift in poverty research towards alternative approaches to conceptualising and measuring poverty. One such example is the relative deprivation approach pioneered by sociologist Peter Townsend (1979), which has been increasingly adopted around the world including the European Union as one of the official poverty measures (Nolan & Whelan, 2011). Under the relative deprivation approach, poverty is often operationalised as lacking basic items, such as nutritious meals and warm clothing, that are considered essential in a society (Townsend, 1979).
One major issue faced by the relative deprivation approach is the selection of an appropriate cut-off point or threshold value (k) to separate those who are poor from those who are not (Alkire & Foster, 2011a, 2011b. Where to draw an appropriate threshold has significant bearings on the empirical examination as even a small shift in the threshold can result in large increases or decreases in its poverty estimates. It is thus imperative that the selection of threshold is theoretically and empirically justified in order to produce meaningful poverty statistics and inform the policymaking process. This paper seeks to derive optimal deprivation thresholds for the Australian context. To this end, this paper examines the Poisson-based framework devised by Babones et al. (2016) to specify the number of essential items (k) that must be lacking in order to constitute relative deprivation. The first section reviews the poverty literature and surveys the conceptual paradigm underpinning the relative deprivation approach. The subsequent section outlines how non-monetary indicators are constructed and operationalised to measure relative deprivation. It then provides a brief description of the source of data, the Household, Income and Labour Dynamics in Australia (HILDA) survey and introduces the Poisson-based framework and its mechanism to capture the systemically deprived from the population. In the third section, deprivation thresholds are derived corresponding to three different concepts of non-possession, derived deprivation and inferred deprivation. Lastly, this paper concludes by estimating the nominal deprivation rates using the derived thresholds and presents a detailed breakdown of deprivation status across population sub-groups.

Measuring Poverty and Relative Deprivation
The definition of poverty has long been contested due to the ambiguities often associated with the term, leading to various approaches to poverty measurement we see today (Greve, 2019). Distinct implications arise from the definition of poverty such as the selection of relevant indicators to quantify and measure poverty. The extensive contestation of poverty measurement essentially involves negotiating and delineating the core and scope of poverty. As such, the debate between poverty measures is not merely about measures per se but also about the conceptual paradigms upon which they are based.
The lack of monetary resources has been one of the most widely accepted conceptualisations of poverty within the social sciences. While there is no single generally agreed upon definition, a low level of income is often conceived as the core element of poverty by scholars, governments, and international organisations (UNECE, 2017). For instance, the United Nations (2021) defines poverty as "the lack of income and productive resources to ensure sustainable livelihood". Smeeding (2016, p. 21) also argues that poverty entails serious economic constraints, noting that "poverty concerns itself with having too few resources".
The conceptual emphasis on economic resources can be tracked back at least to the late nineteenth century. Seebohm Rowntree's (1903) 'Poverty: A study of Town Life' and Charles Booth's (1892) 'Life and Labour of the People in London' were two of the very first studies that aimed to document the experience of the poor and understand the nature of poverty. These monumental studies laid the foundation for poverty research with the widely known tradition of using large-scale survey questionnaire and deriving a 'poverty line' to determine the presence and prevalence of poverty (O' Connor, 2016). Furthermore, the use of 'poverty line' has become the mainstream approach in policy settings as they provide a clear basis for setting the eligibility for government assistance and welfare (O' Connor, 2016).
In recent decades, there has been a notable shift toward alternative conceptual frameworks for understanding and examining poverty (Hick & Burchardt, 2016). The shift has mostly been driven by the conceptual and operational limitations of income poverty measures (Walker, 2019). As Ringen (1988) notes, if resources are the relevant means to ends, the ends themselves should be the ultimate concern of poverty research. Income measures, Ringen (1988) contends, are an indirect measure of poverty which represents the potential rather than the outcomes of the available resources. It has been argued that taking income as the sole axis for differentiating the poor from the non-poor can fail to capture the breadth of poverty that people experience (Hick & Burchardt, 2016). The key issue thus relates to the little consideration that is given to the actual living standards achieved, omitting other important non-monetary dimensions that altogether constitute poverty (OECD, 2019). Sen (2001, p. 56) also holds that resource holdings such as incomes are important in so far as they allow a person to achieve outcomes that "a person has reason to value". As Sen (2009, p. 254) writes, "the relationship between resources and poverty is both variable and deeply contingent on the characteristics of the respective people and the environment in which they live". The argument follows that even if resources were equally distributed and made available, the actual life outcomes would differ among groups of people depending on their needs (Alkire & Santos, 2011c). The individual heterogeneity and variation between means and ends, which Sen (1995, p. 100) calls "conversion factors", makes explicit the problem of using income to identify and capture people experiencing poverty.
As a refined conceptualisation is needed to reflect this complexity, deprivation-based concepts of poverty which place people's living standards at the centre of investigation received a major impetus. In particular, sociologist Peter Townsend (1979) has inspired a significant broadening of the concept of poverty, replacing the strong primacy of economic resources with a multidimensional view of deprivation. According to Townsend (1979, p. 31), "individuals, families and groups in the population can said to be in poverty when they lack the resources to obtain the types of diet, participate in the activities and have the living conditions and amenities which are customary". Here, Townsend's (1979) formulation of poverty suggests that the lack of resources impedes individuals to follow social customs and activities which are expected of them by virtue of their membership of the society (Gordon, 2006). It is thus maintained that poverty must be grasped with reference to the social context in which it is found, which entails examining more directly how monetary resources and their effects are embedded in the living conditions (Hick, 2012).
One of the seminal contributions of Townsend's deprivation approach is the incorporation of non-monetary indicators to measure the state of relative deprivation. Here, relative deprivation is neither confined to basic subsistence nor to a certain income level. As poverty manifests itself in various ways, individuals may maintain some aspects of their social lives at the expense of withdrawing completely from other forms of social association (Townsend, 1987). For example, while most households can afford textbooks and school fieldtrips for their children, people experiencing poverty are forced to make compromises such as skipping a meal to pay for these items and activities. This means capturing a full range of information on the plight of the poor to articulate what it means to be living in poverty, as well as what it is that precludes individuals to attain customary standards of living in a society (Kus et al., 2016). Townsend (1979, p. 136) initially devised a set of 60 non-monetary indicators by drawing on the everyday experience of the poor, encompassing deprivation in 11 areas including physical and mental health, housing, work conditions, social support, and family activities.
The selection of non-monetary deprivation indicators has been further refined in recent decades. In particular, the Consensual approach pioneered by Mack and Lansley (1985) has been a defining feature of deprivation research. Instead of relying solely on expert judgements and pragmatic selection of indicators, Mack and Lansley's (1985) Consensual approach relies on public reasoning, surveying the general population to identify the necessities that are customary in the society to which they belong. A status of relative deprivation is then assigned only when people lack and cannot afford the identified essentials, distinguishing personal choice from actual constraint. As such, the operationalisation of relative deprivation is generally based on checklists of items that are deemed essential by more than 50 per cent of the community (Mack & Lansley, 1985).
A substantial volume of work on relative deprivation has been carried out in the OECD countries. This can be illustrated by the adoption of deprivation indicators, alongside income poverty and low work intensity, as the main measure to monitor progress in reaching the European Union 2020 target of poverty reduction (Atkinson et al., 2002;Guio et al., 2017). The proposed nine deprivation items drawn from community opinions are as follows: unable to pay rent or utility bills; to keep home adequately warm; to cover unexpected expenses; to eat meat, fish or a protein equivalent every second day; to afford a week holiday away from home; to afford a car; to afford a washing machine; to afford a colour TV; to afford a telephone (Guio et al., 2017). In particular, the EU material deprivation rate refers to the proportion of population living in households that miss out on four or more of the nine items due to unaffordability (Nolan & Whelan, 2011).
As income poverty measures have often been criticised for employing ad hoc poverty lines which introduces arbitrariness into its measurement and analysis, the same issue can also be raised against deprivation measures that their thresholds are equally arbitrary without concrete justifications (Nolan & Whelan, 2011). For deprivation measures, the classification process involves determining the critical number of missing items above which a person qualifies as undoubtedly deprived (Gordon, 2006). While one may hold that only those who suffer from a concentration of problems or scarcities should be classified as deprived, it remains unclear as to how many deficiencies must be present in order to constitute such deprivation (Babones et al., 2016). It could be argued that missing even one socially defined necessity is an indication of relative deprivation. However, too broad a threshold can result in unrealistically high deprivation rates, whereas too restrictive a threshold can lose much relevance, leading to underestimation of poverty where only a tiny proportion of the population is regarded as deprived. Sen (1983) maintains that the concept of poverty is inherently vague and ambiguous, which means that various specifications of poverty and deprivation are possible. The conceptual underpinning of the approach has as its fundamental idea that deprivation is a form of context sensitivity (Gordon, 2006). On this dynamic account, deprivation measurement involves the translation of a set of social norms into the deprivation indicators. Its threshold essentially has flexible boundaries whose location shifts with the changing social and economic context. This context sensitivity means that deprivation is not simply descriptive but contains an evaluative component which presents itself with various nested thresholds (Brady, 2009). On this view, the very idea of establishing a fixed, static cut-off point is untenable. This thus makes an even stronger case for determining a threshold value that is grounded in sufficient theoretical and empirical bases.
In attempting to address the challenge of deriving meaningful thresholds for relative deprivation measures, Babones et al. (2016) have devised a flexible conceptual framework using properties of the Poisson distribution. The Poisson distribution is a discrete function that expresses the probability that an independent event would occur within a specified time period with a constant rate, lambda (λ) (Babones et al., 2016). It provides a useful framework to model discrete data where the variable of interest takes the value of positive integer with the likelihood of occurrence of the event being very small. In the context of deprivation measurement, the deprivation score is such a count data variable which often results in a positive skew towards the right. Here, lambda (λ) would refer to the number of items that the populations are deprived of, on average (Babones et al., 2016). This value allows for the computation of a Poisson distribution that displays the chance incidence of deprivation at each number of missing essential items (k = 0,1,2,3…) (Babones et al., 2016). In other words, the Poisson framework can demonstrate the extent to which the empirical distribution of deprivation can be modelled against the expected frequency of distribution given the population average number of deprived items. It follows that any positive deviation from the Poisson distribution would indicate an excess incidence of deprivation, capturing the size of the population that are systemically experiencing undue concentrations of deprivation (Babones et al., 2016).
Following this mismatch between the observed data and the baseline counterpart, the threshold can be determined at the number of items which the empirical incidence begins to exceed the baseline incidence expected of the given lambda (Babones et al., 2016). As such, the Poisson-based framework uses the idiosyncrasies of the data to help produce an appropriate threshold value (k) that corresponds to a particular national context (Babones et al., 2016). For example, when more households possess and can afford essential items from the list, a more restrictive deprivation threshold would be derived. Data at different points in time and context would exhibit different frequency of lambda (λ) which shapes the Poisson distribution and consequently affects the location of the threshold (Babones et al., 2016). The Poisson-based framework thus provides a useful mechanism for a systemic variation of deprivation threshold for a cross-sectional comparison and analysis.
This present study replicates the Poisson method to specify a deprivation threshold by observing the discrepancy between the number of expected cases of deprivation and the actual figure generated from the HILDA survey data. In addition to investigating the demographic profiles of deprivation in Australia, this study attempts to derive empirically meaningful thresholds that signify what it means to be deprived in the Australian context.

Data
HILDA is a nationally representative longitudinal survey of Australian households conducted annually, collecting a wide range of information on employment, health, education, and family formation (Wilkins et al., 2020). Established in 2001, HILDA provides detailed demographic and socioeconomic data about the lives of Australian population, tracking about 10,000 households across the country (Wilkins et al., 2020). The data collection takes place through face-to-face interviews in the home of the sample member, with occasional telephone interviews in instances where their situation does not allow for in-person meetings (Summerfield et al., 2019). In particular, the wealth of information provided by the survey means the pattern of deprivation can be investigated across various demographic subgroups. This paper uses the general release file of Wave 18 of the HILDA survey, for which the most recent deprivation module questionnaire was surveyed. All data used in the subsequent analysis were obtained from the Australian Department of Social Services.
The Material Deprivation module data are collected through household survey questionnaires which are administered to one or two adult members of the participating household (Wilkins et al., 2020). The module involves a suite of questions asking respondents whether they see the proposed list of items as essential for every individual in Australia that no one should have to go without (Saunders & Wong, 2012). This validation process with the general public is aimed to ensure the there is a large degree of consensus among the community and the selected items are robust and suitable for large-scale deprivation measurement and analysis (Saunders & Naidoo, 2018). As set out by Mack and Lansley (1985), only those items that are agreed by more than half of the respondents qualify as "socially perceived necessities".
The questionnaire also asks respondents whether they lacked any essential items over the past 12 months (Wilkins et al., 2020). In instances where they report not having an item, a follow-up question was asked to specify whether the absence was because they could not afford it. The inclusion of the affordability question was designed to give allowance for choice in the identification of deprivation (Mack & Lansley, 1985). That is, personal choices or preferences are set to be distinguished from the enforced lack of socially perceived necessities. As such, only those who have no choice but to go without the item are counted as deprived, with a lack of affordability being an integral part of the operationalisation. Consistent with its conceptual underpinning, the notion of affordability acts as the major criterion to establish whether individuals face deprivation, particularly bridging the gap between the available resources and needs (Saunders & Wong, 2012;Saunders, 2019). The overall deprivation score is then calculated by summing the number of missing items resulting from a lack of affordability. In particular, affordability has been assessed at the household level. That is, all members from the same household are given the same score of deprivation on the assumption that resources and essential items are equally shared.
HILDA produces a variety of weights to make adjustments for differences between the collected sample and the Australian population (Summerfield et al., 2019). In 2018, the survey sample included total 9,638 responding households with the household population weights amounting to 9.5 million (Wilkins et al., 2020). The enumerated 'person' population weights, on the other hand, summed to 24.4 million (Wilkins et al., 2020). All data results shown subsequently represent national estimates which have been generalised to the Australian population as a whole. Moreover, in addressing the issue of missing data, the HILDA survey undertakes imputations by comparing and drawing on responses from previous waves by the same respondents (Summerfield et al., 2019). While values are imputed where needed, there remains a small percentage of ambiguous or unclear survey responses, which generally consist of households stating "Don't know" or simply refusing to answer when asked about affordability of essential items (Summerfield et al., 2019). These responses have been included in the sample in order to preserve the population weights but have been treated as "item affordable" in the analysis. As such, the following results should be interpreted as a conservative estimate with a downward bias, potentially representing a lower ratio than the actual incidence.

Results
This section first applies the Consensual approach to identify the list of deprivation indicators. Using the survey responses of the 2018 deprivation module, the levels of public support have been deduced and presented in Table 1. In particular, results are applied with household population weights to be indicative of how the general public regards each item as being essential. Table 1 shows the list of 25 items that were surveyed and the corresponding levels of community support for each item. Of the 25 items listed, two items-'a week's holiday away from home each year' (40.4%) and 'buying presents for immediate family or close friends at least once a year' (42.5%)-failed to receive the majority support and were thus removed from further analysis. The remaining items were generally supported by an overwhelming majority and qualified as necessities for all Australians. For instance, the most widely supported item, 'medical treatment when needed', was regarded as essential by 99 per cent of the population. A few items such as 'a motor vehicle' (50.5%) and 'new school clothes for school-age children every year' (52.1%) have marginally passed the majority threshold, receiving support by slightly more than half of the population. In total, 23 items were identified as socially perceived necessities. For the following empirical analyses, this subset of items was selected to constitute relative deprivation indicators to measure and assess the prevalence of deprivation in 2018. Table 1 also presents the incidence rates of non-possession, derived deprivation, and inferred deprivation calculated for each essential item. Here, the rates of non-possession, that is, the percentages of individuals that did not have each item, are reported in the second column. Furthermore, the rates of derived derivation in the third column refers to the proportion of people who lacked each item because they could not afford it, while inferred derivation rates in the last column represents those who did not have the item yet regarded it as essential. Results are calculated at the individual level using enumerated population weights on the assumption that household responses represent the conditions of all family members. Among the items identified as essential, 'new school clothes for school-age children every year' (39.5%) was the most lacked item by the population. However, its low derived deprivation rate (5.0%) suggests that only a small proportion of the non-possession was due to a lack of affordability. The large difference between the two results indicates that the affordability question exerts a considerable influence on measured deprivation, differentiating personal choice from constraint. Derived deprivation rates (does not have and cannot afford) were highest for items such as 'at least $500 in savings for an emergency' (11.3%) and 'home contents insurance' (8.1%). As such, people were more likely to be deprived of the ability to fund periodic large outlays that provide protection against events of financial emergency. The consistently high inferred deprivation rates for these two items (10.7% and 11.7%, respectively) also confirms that those who lacked the items were well The first columnn is calculated using household population weights, while the remaining columns used enumeratedpopulation weights aware of their importance yet still missed out, potentially signifying financial hardships where they were only just able to make ends meet. The Poisson-based framework is applied to all three operationalisations of deprivation: non-possession, derived deprivation and inferred deprivation. The first application concerns identifying the threshold for non-possession. In Fig. 1, a Poisson curve is plotted using the population average number of missing items, 1.16, as the value of lambda. Against this has been plotted the empirical frequency of individuals missing 1, 2, 3, …, 8 items. While the two curves demonstrate a broadly similar trend, a heavy right tail can be observed in the empirical frequency with larger numbers of missing items. This implies that there exists an excessive number of individuals that do not possess multiple sets of essential items than would normally arise from the Poisson expectation. Table 2 presents the data plotted in Fig. 1 to estimate the cumulative incidence of excess non-possession relative to the baseline counterpart. According to the Poisson distribution, it is expected that around 2.39% of the population (584,275) will fail to possess 4 items with the value of lambda at λ = 1.1647. Yet, the actual data suggests that around 4.22% of the population (1,031,853) have reported missing 4 essential items. Importantly, such a discrepancy arises at k = 4 where the empirical distribution of non-possession surpasses the baseline incidence onwards. It follows that the k ≥ 4 threshold results in a nominal deprivation rate of 5.6 per cent, which translates into a total excessive number of 1,365,830 individuals.
Similarly, the second application compares the disparity between the number of expected cases and the actual figure of derived deprivation. Here, the mean number of items which could not be afforded by the population was 0.4575 item. Following the same logic, a Poisson model with lambda, λ = 0.4575 has been plotted against the empirical incidence of derived deprivation in Fig. 2. Again, the Poisson model of derived deprivation provides a close approximation of the empirical observation. In particular, the excess in the empirical distribution relative to the Poisson model appears at the threshold of k ≥ 3. Data for empirical incidence of deprivation and the Poisson modelled frequency are displayed in  Table 3. Looking closely, the Poisson distribution estimates 246,705 individuals (around 1.01% of the population) to be deprived of 3 items at k = 3 whereas the empirical incidence shows that around 706,323 individuals (2.89% of the population) reported lacking and not being able to afford 3 essential items. As such, the cumulative incidence of derived deprivation for all values of k greater or equal to 3 (missing 3 or more items) gives a nominal deprivation rate of 5.3 per cent, which amount to an excess of 1,301,866 individuals suffering deprivation than the Poisson expectancy. Visually, the heavy right tail in Fig. 2 illustrates this positive deviation where many more people are unable to afford multiple items than could reasonably be expected, given that an average Australian goes without about 0.46 essential item from the list. In parallel with previous application, Fig. 3 plots the Poisson curve for inferred deprivation against the empirical distribution. Inferred deprivation, as previously noted, captures those who lacked item(s) but regarded them as essential. This is used to infer the existence of enforced deprivation which may have not been reflected by the affordability question. The Poisson-based framework is also applied to compare the empirical incidence of inferred deprivation with the baseline counterpart. From the HILDA data, the lambda which denotes the population average of inferred deprivation score was found to be 0.5474. As displayed in Fig. 3, the mismatch between the empirical frequency and the baseline frequency also begins to occur at k ≥ 3. The heavy right tail is again indicative of the existence of excessive deprivation that is not expected from the modelled occurrence. Table 4 summarises the corresponding data used to plot Fig. 3. While the data shows that around 586,559 individuals (2.40% of the population) lacked 3 items for which they regarded as essential, the Poisson distribution only expects 386,423 individuals (1.58% of the population) to be so given the population average. In particular, the cumulative deviation from the baseline figure results in a nominal inferred deprivation rate of 4.1 per cent, which leads to an estimation of extra 992,635 individuals in addition to the modelled frequency.

Discussion
Summary results for each operationalisation of deprivation are presented in Table 5. The derived deprivation thresholds represent the minimal critical points above which there exist excessive individuals experiencing acute forms of deprivation. In other words, the thresholds allow one to identify the level at which the empirical concentrations of unmet need are greater than the statistical expectancy (Babones et al., 2016). Notably, three deprivation operationalisations with the derived thresholds yielded roughly similar deprivation  rates, all of which clustered under 10 per cent. It should be noted that while the results may appear relatively small in percentage point terms, the number of people impacted is substantial once extrapolated over the population. Taking the derived deprivation rate for example, it amounted to approximately 1.6 million individuals living in unacceptable conditions by the prevailing standards of community.
On the other hand, adjusted deprivation rates are calculated to estimate the nominal proportion of population living in deprivation. For example, the adjusted derived deprivation rate of 5.3% amounts to approximately 1.3 million individuals in total. The figures in Sect. 4 have shown that as the number of missing items increases, the Poisson baseline probability of deprivation approximates to nearly zero. The nominal rates essentially represent the size of this contingent, a cumulative excess that cannot be explained by statistical expectation, signifying the systemically deprived individuals in society. However, it should be emphasised that such adjustment cannot provide an exact indication of which individuals fall under the statistically expected group and which individuals belong to the excessive subset from the modelled baseline that constitutes the adjusted deprivation rate. It should also be noted that the differentiation does not imply that one group experiences 'real' deprivation while the other group does not. The purpose of differentiation lies in identifying a critical level at which the empirical observation and statistical expectation diverge. Such divergence provides a useful anchor point to disclose some underlying patterns as to where such undue concentrations of deprivation are clustered around. That is, by investigating and comparing the deprivation levels of various demographic subgroups judged under the derived thresholds.
Furthermore, as the basis for determining the relevant deprivation cut-offs stems from the idiosyncrasies of the empirical data, the optimal thresholds are neither definite nor fixed which are most likely to vary across time as the nation's living standard rises or decreases. A higher standard of living would lead to a more restrictive deprivation threshold, just as higher living standards would produce higher income poverty threshold. Table 6 lists and compares the findings between the present study and the study by Babones et al. (2016). Across different operationalisations of deprivation, Babones et al. (2016) found that each deprivation concept produced an adjusted deprivation rate around 4% from the 2011 Swiss Household Panel study sample. While the present study replicates the Poisson-based approach by Babones et al. (2016), it differs in that the empirical incidence of deprivation and its baseline counterpart are calculated using household population weights to produce estimates at a national level. In the case of derived deprivation, the Poisson-based framework returned higher deprivation rates in Australia, as well as a more restrictive threshold (higher k). As any slight changes in the empirical distributions would have a sizeable influence on the threshold derived, this in effect suggests that Switzerland fared better in contexts of nominal deprivation. (1) Non-possession (k ≥ 4) 2,117,708 8.7% 5.6% (2) Derived deprivation (k ≥ 3) 1,579,850 6.5% 5.3% (3) Inferred deprivation (k ≥ 3) 1,438,253 5.9% 4.1% Total population 24,426,215 --Based on the three deprivation thresholds derived above, Table 7 calculates the rates of deprivation alongside two income poverty estimates. It uses relative poverty lines set at 50 per cent and 60 per cent of the median disposable income. Recognising the economies of scale in consumption which vary with household size and composition, income estimates are equivalised using the modified OECD scale. The scale assigns a value of 1 to the first adult in the household, 0.5 to each additional adult member, and 0.3 to every child present in the household scale (OECD, 2019). As such, a family of two adults and one dependent child would have an equivalence scale of 1.8, meaning that they would need an income 1.8 times that of a single-person household to reach a similar standard of living. In particular, the median equivalised income for a single person household amounted to $49,485 in 2018, calculated by Wave 18 HILDA statistical report (Wilkins et al., 2020). Implicit in the estimation is that all resources are pooled and shared equitably among the same household members.
Based on proxies for socioeconomic characteristics, the decomposition of sub-groups sets to disclose the underlying patterns of deprivation and reveal how different sub-groups fared in terms of living standards. Within each comparison category, the prevalence of relative deprivation was most pronounced among younger age groups, single parent families, the unemployed, people with long-term health conditions, public renters and Indigenous Australians. These sub-groups constitute the severely deprived which should be of the target population for policymakers. In particular, the three operationalisations of relative deprivation-non-possession, derived deprivation, inferred deprivation-tended to result in similar levels of nominal deprivation with the identified thresholds.
An important observation is that deprivation estimates differed greatly to the income poverty rate for certain sub-groups, especially for the Aboriginal Australians and Torres Strait Islanders, which further highlights the limitation of capturing poverty solely in terms of income. As presented in Table 7, while income poverty was severe for those aged 65 and above, they reported comparable or lower levels of deprivation to the population average. One potential explanation to this discrepancy is the ownership of assets (Saunders 2019). It may be that older adults were able to finance their living standards by drawing upon monetary resources other than income. As revealed in Table 7, private and public renters are at substantially higher risks of multiple deprivation in comparison to outright owners, highlighting the dominant role of existing assets and wealth. It follows that the poverty rates amongst the aged could have been inflated under the income-based measures. However, one might also argue that the low deprivation rates are artefacts of adaptive preferences whereby chronically deprived elderly people have adapted to their living circumstances over time, regarding the lack of possession as a lack of desire. What is clear from the analysis, though, is that deprivation measures do not necessarily capture the income poor as deprived, nor proxy the trends of income poverty. As outlined above, the merit of deprivation measures lies in having a direct bearing on the living standards of people across their demographic characteristics as indicated by the levels of deprivation they face. The evidence is particularly suited to inform important social policy issues such as where to direct policy attention on adequacy grounds, improving the levels of social support to demographic groups who require further assistance.

Conclusion
The study replicated the Poisson-based framework of Babones et al. (2016) to derive meaningful thresholds of relative deprivation in Australia. It has explored some key implications of the deprivation paradigm including the ways in which its non-monetary indicators are constructed, surveyed, and implemented to produce alternative poverty statistics to the income-based measure. While the income-based approach has been used as a prominent basis for the most widely quoted headline figures on poverty, its conceptual and methodological limitations to measuring poverty have been highlighted throughout the paper.
The deprivation approach has the great merit of directly measuring poverty by looking into the living standards achieved by individuals and households. It presents a clear approximation of a person's standard of living by facilitating a sociological account of poverty, substantially complementing the statistical and analytical armoury for mapping the poverty profile. Indeed, empirical data has shown that the incorporation of the deprivation metric reveals a different pattern and composition of poverty in Australia.
However, like the critique of income poverty lines, it has often been raised that the choice of deprivation threshold should also not be taken for granted. It requires explicit rationale and justification where the conceptual and empirical bases for setting its threshold value are provided. In attempting to address the arbitrariness associated with the selection of threshold, this study replicated the design of Babones et al. (2016) using the 2018 data from the HILDA survey. Based on the properties of the Poisson distribution, thresholds of k ≥ 4 for non-possession (merely lacking items), k ≥ 3 for derived deprivation (lacking and not being able to afford items), and k ≥ 3 for inferred deprivation (lacking and regarding items as essential) are suggested, respectively.
The deprivation thresholds represent the cut-off points where the scale of nominal deprivation experienced by the population can be identified. The Poisson-based framework is particularly helpful in discerning the size of extensive deprivation by considering the baseline occurrence expected of the idiosyncrasies of empirical data. In other words, the nominal estimate reflects the existence of systemic deprivation for which urgent public policy attention should be devoted. Such a specification informs where to concentrate policy focus and mobilise public resources to alleviate poverty. The evidence directs attention to those currently experiencing severe deprivation such as public renters who were about five times more likely to be deprived than average, as well as lone parent households who were about three times more likely to experience multiple deprivation than an average household. As such, a strong motivation for using the derived thresholds lies in the ability to capture this subset from the population to merit priority in prescribing and targeting poverty alleviation policies.
Another important insight from the analysis is that the deprivation measure alters the composition of the poor to that indicated by the conventional income measure. As discussed, an undue reliance on a single poverty measure should be avoided when the evidence suggests that alternative poverty measures capture different subgroups of people as poor and deprived. This is not to suggest that income measures are no longer useful but that one should caution against the reliance, as it is very likely that each poverty measure paints an incomplete picture of the lived experiences of the poor. As such, one can benefit greatly from collating and comparing the poverty statistics from multiple poverty measures. The triangulation of results is much more likely to produce robust understandings of poverty and relevant policy implications.
Moreover, future studies are needed to reconcile the diverse, sometimes competing insights. In particular, the mismatch between income poverty and deprivation can be investigated from combining multiple data sources on expenditure, wealth, and deprivation to synthesise a more complete picture of people's living standards. Future research could also take the shift from a static, cross-sectional measurement to a longitudinal analysis of poverty and deprivation. By following the trajectories of people's living conditions over time, a more dynamic understanding of the persistence of poverty can be obtained. One important conclusion is the need to think reflexively about the results and particularly the poverty thresholds used in poverty measures. As illustrated throughout the paper, the ambiguous nature of poverty means that researchers invariably make choices, working with assumptions that are not necessarily sensible given the data. The selection of threshold can often be pragmatic and authoritative in that there exists no explicit rationale and justification behind it. This means that poverty statistics can easily be manipulated to exhibit a decline or increase in poverty, producing a total that is acceptable from a political perspective. In this regard, poverty measures can conceal as much as they reveal about the severity of the problem, depending precisely on what one is most anxious to capture. It is thus imperative to scrutinise how the poverty results have come about and its underlying methodologies.
Poverty lingers, even in rich countries. The relative deprivation approach is valuable in that its conceptual paradigm moves beyond the realm of income to frame poverty in multidimensional and sociological terms. In this regard, the relative deprivation approach represents a step towards a more dynamic understanding of poverty where the causal processes at work can be better apprehended. In addition to investigating the demographic profiles of deprivation in Australia, the central aim of this paper has been replicating the Poissonbased framework of Babones et al. (2016) to derive empirically meaningful deprivation thresholds that capture the deprived in Australia. To attain more ambitious poverty reduction goals, the key will be to continue scrutinising and improving poverty measures including the thresholds employed. The study ultimately sought to advance the development of this perspective in poverty research.
Funding The author did not receive any funding from any organisation for the submitted work.
Data Availability This paper uses unit record data from the Household, Income and Labour Dynamics in Australia (HILDA) Survey conducted by the Australian Government Department of Social Services (DSS).

Conflict of interest
The author also has no competing interests in any material discussed in this article. The findings and views reported in this paper, however, are those of the author and should not be attributed to the Australian Government, DSS, or any of DSS' contractors or partners. https:// doi. org/ 10. 26193/ 3QRFMZ Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.