The Dynamic Deprivation Index: measuring relative socio-economic deprivation in NZ on a monthly basis

ABSTRACT

The standard measures of relative socio-economic deprivation within New Zealand are the NZDEP studies and the NZ IMD. Although both sets of studies are extremely rigorous, high quality research outputs they are only able to provide a snapshot of the national distribution of relative socio-economic deprivation at fixed points in time. The inability to express deprivation levels as an extended and current time series means that not only are policy analysts and researchers working with outdated information, but also that it is often unfeasible to associate changes in deprivation levels to specific events or policy implementations. The Dynamic Deprivation Index (DDI) assigns a deprivation score and deprivation index to each area unit in New Zealand on a monthly basis. In this paper we look to describe the methodology behind the construction of the DDI and to validate the results therein. We argue that if public bodies were to make the data they hold more easily accessible, then there is no reason why New Zealand should not be able to benefit from a measure of socio-economic deprivation that combines the sophistication of the NZDEP studies or IMD with the contemporaneousness of the DDI.

KEYWORDS:

• Dynamic deprivation index
• relative socio-economic deprivation
• New Zealand

Introduction

Townsend (1987) defines relative socio-economic deprivation as:

… a state of observable and demonstratable disadvantage relative to the local community, wider society or nation to which an individual, family or group belongs.

Quantifying this ambiguous concept is not an easy task. In New Zealand the standard measures of relative socio-economic deprivation (hereafter referred to simply as socio-economic deprivation) are the NZDEP studies produced by Crampton et al. (1998a, 1998b, 2002, 2007, 2014). Using census data from the corresponding year these studies assign a deprivation score to each moderately populated meshblock and area unit (AU) in New Zealand, the latest study (NZDEP13) being constructed from data obtained from the March 2013 census. Meshblocks and AUs are then ranked separately into deciles, known as deprivation indices, on the basis of their deprivation score. Conceptually, the higher the deprivation score / decile of a meshblock or AU the higher the level of socio-economic deprivation endured by its inhabitants. It is important to realise, however, that the NZDEP studies are aggregate, rather than individual, measures of deprivation. The deprivation scores assigned to meshblocks and AUs can, and in fact regularly do, mask considerable variations in the levels of socio-economic deprivation experienced by the individuals therein (see for instance Salmond and Crampton 2001, 2002).

The NZDEP studies are extremely rigorous, high quality research outputs. This is perhaps best evidenced by the fact that the results of these studies are associated with almost every aspect of social policy; from mental health, suicide and self-harm (Ministry of Health 2016a); to assault rates (Ward et al. 2018); to alcohol use (Ministry of Health 2015); to smoking rates (Salmond et al. 2012); to health outcomes (Ministry of Health 2016b); to problem gambling rates (Wheeler et al. 2006); to educational attainment (Shulruf et al. 2008); and even burn rates (Mistry et al. 2010). Indeed, as noted in Crampton et al. (2014), the NZDEP studies are routinely used in governmental funding formulas, by social scientists investigating the associations between socio-economic deprivation and other external variables and by community based service providers to advocate for additional resources.

More recently Exeter et al. (2017) developed the NZ Index of Multiple Deprivation (IMD), the intention of which was to provide a more nuanced measure of the multi-dimensional nature of socio-economic deprivation. The IMD breaks New Zealand up into nearly 6000 data zones (bespoke amalgamations of meshblocks) and incorporates 28 indicators of socio-economic deprivation across seven domains; employment, income, crime, housing, health, education and geographical access. In the construction of the IMD each data zone is scored against each separate domain of deprivation, the scores across each domain then being combined into an overall IMD score and rank through the use of a fixed weighting procedure whereby the weights are driven by existing literature on multiple deprivation. Herein lies a significant advantage of the IMD. Each of the seven domains of deprivation can be used either individually or in combination to measure (a particular aspect of) socio-economic deprivation. For instance, a researcher wishing to investigate the association between household over-crowding and deprivation can exclude the housing domain from the overall index in order to help avoid circularity of argument (Exeter et al. 2017).

Although the IMD is anticipated to be updated much more frequently than the NZDEP studies (every 18–24 months as opposed to after every census), both studies are only able to provide a snapshot of the distribution of socio-economic deprivation across New Zealand at fixed points in time. The consequences of this are twofold. First, as the time since the last data collection point increases distinctions emerge between the current socio-economic deprivation status of the inhabitants of each geographic region and their deprivation status as measured by the index (around 47% of AUs that appeared in both the NZDEP06 and NZDEP13 studies changed deprivation index over the inter-census period in question). As such, the indices quickly become outdated especially in communities that undergo substantial population and social change (Exeter et al. 2017). Indeed, this is a particular problem with regards to the application of government funding formulas, e.g. the current Warmer Kiwi Homes government grant which is available only to households within decile 9 and 10 meshblocks as defined by the NZDEP13 study (EECA 2018). Secondly, since levels of socio-economic deprivation cannot be presented as extended time series, it is not feasible to attempt to identify the drivers of changes in socio-economic deprivation. Whilst it may be possible to show that relative socio-economic deprivation levels within a particular area unit (or larger geographic region) changed between two consecutive iterations of the NZDEP studies or IMD, one would not know whether this change occurred gradually or whether there was a shift in deprivation levels over a more compact timeframe. In the latter case, one may be interested in attempting to determine whether the change in deprivation levels was associated with a particular policy initiative or socio-economic event. As a consequence there is a need to develop a more contemporary and dynamic measure of socio-economic deprivation within New Zealand.

However, this challenge is not unique to New Zealand. In the UK methods to measure changes in small area socio-economic deprivation levels across census years have been developed (see for instance Norman (2010); Norman (2016); Norman & Darlington-Pollock (2017)). In Italy, Landi et al. (2018) developed methods with a similar aim specific to the city of Genoa. However, all of the aforementioned studies are unable to say anything about the evolution of socio-economic deprivation between decennial census years. Indeed, the need to develop dynamic measures of socio-economic deprivation is being spurred on across the world by the growth of big data analytics. On the one hand, improvements in information technology are likely to render censuses obsolete in the foreseeable future (Ajebon & Norman 2016) depriving researchers of a frequently used source of data. On the other hand, improvements in the capture and dissemination of administrative data (i.e. data collected by public bodies) enables the possibility of developing measures of socio-economic deprivation that update at far more frequent intervals than censuses can be conducted.

In this regard, researchers at data science company DOT Loves Data (DOT) created the Dynamic Deprivation Index (DDI). The DDI uses a combination of public and proprietary data sets, containing 34 variables spanning five dimensions of deprivation (employment, support, income, education and material deprivation) and assigns a DDI Score and DDI Decile to each of the 1867 different 2017 AUs appearing within the NZDEP13 study each month. Indeed, the DDI is ‘seeded’ by NZDEP13 in the sense that the DDI Scores for Mar-13 coincide exactly with the deprivation scores given within the NZDEP13 study (after standardisation). The DDI currently runs from Mar-13 to Jun-18. However, for reasons that will become apparent, within this paper we choose to focus on the results obtained over the more restricted period from Mar-13 to Mar-18.

The purpose of this paper is to describe the methodology used within the construction of the DDI and to validate the results produced therein. From the outset we stress that we cannot hope to match the methodological rigour of the NZDEP studies or the IMD. This is because dynamic data sets that provide information pertinent to socio-economic deprivation at granular enough geographic levels are simply not made publicly available in the majority of cases. Instead, our intention is to show that if public bodies were to make the information they hold more easily available, then there is no reason why New Zealand should not be able to benefit from a measure of socio-economic deprivation that combines the sophistication of the NZDEP studies or IMD with the contemporaneousness of the DDI. This could only strengthen the ability of national and local governments to support the communities most in need and improve the quality of social science research within New Zealand.

Materials and methods

Meshblocks and area units

Meshblocks are contiguous geographical units defined by Statistics New Zealand and are the smallest geographic unit for which statistical data are publicly reported. Each meshblock borders another to form a network covering all of New Zealand’s land mass and 200 mile exclusive economic zone. Although meshblocks can vary in size considerably in rural areas, in urban areas meshblocks usually coincide with streets or city blocks. AUs are aggregations of meshblocks which in urban areas generally coincide with suburbs or parts thereof. At the time of the 2013 New Zealand Census, the median usually resident meshblock and AU populations were 78 people and 1985 people respectively. The geographic regions defined by meshblocks and AUs are updated by Statistics New Zealand on the 1st of January every year. The meshblock and AU geographies (QGIS maps) and concordance with geographies for previous years can be found on the Statistics New Zealand website (see Statistics New Zealand 2018a, 2018b).

We take this opportunity to stress that the difference between 2013AU boundaries and 2017AU boundaries is negligible. Utilising the QGIS ‘Intersection’ geometry tool we intersected the 2013AU boundaries with the 2017AU boundaries and calculated the physical area covered by the resulting intersected regions. Of the 1867 AUs that appeared in the NZDEP13 study there were only two AUs where the intersected regions covered less than 85 percent of either the corresponding 2013AU or 2017AU (581721 Saxton Island & 608700 Frankton). Indeed, there were only eight such AUs where the intersected region covered less than 95% of either the corresponding 2013AU or 2017AU. As such, in the remainder of the paper we assume that the 2013 and 2017AU boundaries are essentially the same.

NZDEP studies

The methodology used within NZDEP13 is broadly consistent with the methodologies used in the construction of previous NZDEP studies. As such, for ease of exposition, in this section we simply provide a brief description of the methodology pertaining to the construction of NZDEP13. The starting point of the NZDEP13 study was the agglomeration of 2013 meshblocks into 23751 ‘small areas’ each containing (where possible) a usually resident population of at least 100 people. The agglomeration process was conducted in such a way that each small area consisted of contiguous meshblocks each belonging to the same 2013AU. For each constructed small area, Mar-13 census data was used to determine the proportion of the population:

Table

- Aged < 65 with no home access to the internet (Communication).	- Not living in their own home (Owned home).
- Aged 18–64 receiving a means tested benefit (Income).	- Aged 18–64 without any qualifications (Education).
- With household income below a given threshold (Income).	- Aged 18–64 unemployed (Employment).
- Below a bedroom occupancy threshold (Living Space).	- Without access to a car (Transport).
- Aged < 65 living in a single parent family (Support).

Hence, the NZDEP13 study captures nine variables reflecting eight different dimensions of deprivation. After the variables had been age and sex standardised, principal component analysis was applied and a deprivation score (normalised to have a mean of 1000 and a standard deviation of 100) was assigned to each small area using the first principal component. Herein the first principal component was reported as explaining 60.7% of the variance. Each 2013 meshblock was then assigned the same deprivation score as the small area to which it belonged and ranked into deciles on the basis of this score. In contrast, each 2013AU was assigned a deprivation score by forming population weighted averages of component small area deprivation scores, before being ranked into deciles (see Crampton et al. (2014) for further details on the technical aspects of the NZDEP13 study).

Definitions of the small area boundaries used within NZDEP13 have not been made publically available. The use of this intermediate geographical level means that AU deprivation scores do not coincide exactly with population weighted averages of component meshblock deprivation scores. Nevertheless, the correspondence is very close. For each of the 2013 AUs appearing in NZDEP13, DOT constructed a modified deprivation score by forming a population weighted average of corresponding 2013 meshblock deprivation scores, setting meshblock populations at a minimum of 1. The Pearson correlation between the modified deprivation scores and actual deprivation scores was found to be equal to 0.99999 (p < 0.001). Indeed, the absolute difference between the actual and modified deprivation scores exceeded one for only twenty five AUs and exceeded two for only four AUs. Very similar results were obtained when repeating the same process for each of the previous NZDEP studies. As such, we conclude that AU deprivation scores can be very well approximated by population weighted averages of meshblock deprivation scores.

Population estimates

Using the medium usually resident population projections by age and sex constructed by Statistics New Zealand (2018c), DOT produced monthly estimates of the working population aged between 18 and 64 for each 2017AU by linearly interpolating between values for 2013 and 2018. The aforementioned projections take as their base the usually resident population as of the Mar-13 census, with the estimates for 2018 being last updated in Sep-17.

Unemployment rates, single parent support rates and means tested benefit rates

The Ministry of Social Development provided DOT with a data set detailing the number of people claiming Job Seeker Support (JSS), Single Parent Support (SPS) and all forms of Means Tested Benefits (MTB) by AU for each quarter from Sep-13 to Mar-18. Values for the number of people claiming such benefits for previous quarters could not be provided due to changes in the New Zealand benefit structure that came into effect in Sep-13. It was assumed that the number of JSS / SPS / MTB claimants in each AU was constant over the course of a quarter, i.e. if a particular AU had 100 JSS claimants in the quarter ending Dec-16, then it was assumed that there were 100 such claimants in each of the months Oct-16, Nov-16 and Dec-16.

Whilst the data for the months Jan-18 to Mar-18 was provided at a 2017AU boundary level, the data for all months up to and including Dec-17 was provided at a 2001AU boundary level. As there is considerable difference between the 2001AU boundaries and the 2017AU boundaries it was necessary to transpose the data from the 2001AU level to the 2017AU level. In order to do so, DOT used a procedure similar to that described in Exeter et al. (2017). Utilising the QGIS ‘Intersection’ geometry tool, DOT intersected the 2001AU boundaries with the 2017AU boundaries thereby effectively expressing the whole of New Zealand as a finite collection of disjoint intersected regions. For ease of exposition we refer to these regions as ‘disjoints’. By definition it is possible to express each 2001AU and each 2017AU as the union of a finite number of such disjoints. If the area covered by a disjoint constituted x% of the area covered by its parent 2017AU, then it was assumed that the disjoint contained x% of the corresponding population. In this way we were able to obtain monthly estimates of the population of each disjoint and, by summing over the relevant disjoints, within each 2001AU boundary. Benefit claimants were then distributed from 2001 AUs to component disjoints on the basis of the proportion of 2001AU boundary population contributed by each disjoint. The number of benefit claimants was then transposed to the desired geographic level by summing over all disjoints whose union formed a given 2017AU.

The number of JSS / SPS / MTB claimants within each 2017AU each month was then expressed as a rate by dividing by the corresponding working age population. If the working age population within a given AU in a particular month was less than 60, then the JSS / SPS / MTB rate for this AU was set equal to the average rate for AUs in the same decile whose working age population exceeded this threshold. This averaging process was applied to between 43 and 47 AUs depending on the month.

Ultimately, therefore, for each 2017AU each month DOT obtained estimates of the JSS / SPS / MTB rate that were directly comparable to the unemployment / single parent / means tested benefit rates used within the NZDEP13 study. Due to the aforementioned change in the New Zealand benefit structure, JSS / SPS / MTB rates had to be held fixed at Sep-13 levels for all months preceding this date. Nevertheless, the correlation between these variables for Sep-13 and the NZDEP13 deprivation scores was found to be 0.848, 0.841 and 0.793 respectively. All correlations were significant at the p < 0.001 level.

Educational attainment

It is well understood that a lack of educational attainment or formal qualifications is a key feature of socio-economic deprivation. Indeed, a plethora of studies have identified educational attainment as the primary driver of inter-generational socio-economic mobility. As Torche (2013) puts it:

… inter-generational status association is largely mediated by schooling … because factors other than parental resources account for most of the variance in schooling, educational attainment provides the most important avenue for mobility.

Within NZDEP13, this dimension of deprivation is reflected by the proportion of the population having no formal qualifications. Alternatively, within the IMD educational attainment is measured as a composite of five indicators; the proportion of people who left school before they were 17 years old; the proportion of school leavers without the equivalent of NCEA level 2; the proportion of school leavers not entering any level of tertiary study within three years of leaving school; the proportion of the population aged 15–24 not in education, employment or training; the proportion of the population without formal qualifications. The indicator of educational attainment used within NZDEP13 and the latter two indicators used within the IMD are derived from census data and are, therefore, of no use in the development of a dynamic measure of deprivation. The former three indicators used within the IMD are extracted directly from Statistics New Zealand’s IDI data repository (Statistics New Zealand 2018d), which we do not have access to. Hence, in order to incorporate this dimension of deprivation into the DDI, DOT harvested data from the Education Counts (2018) website for each school year from 2013 to 2016.¹ For each school in New Zealand the harvested data detailed the number of:

• Students enrolled;

• Students stood down, suspended or expelled;

• Students above / at / below / well below national standards in math, reading and writing (if a primary school);

• School leavers above / below NCEA level1, NCEA level2 and NCEA level3 (if a secondary school);

as at the end of the school year in December.

In order to transpose the data from a school specific (point) level to a 2017AU level, DOT first identified the 2013 meshblocks in which each school’s students were likely to reside. This was done using each school’s catchment zone geographies (where possible) and using a fixed proximity threshold from meshblock centroid to school in the case where schools did not have catchment zones. Each of the aforementioned variables was then distributed from schools to the corresponding meshblocks on the basis of 2013 meshblock school age population as expressed within the Mar-13 census (Statistics New Zealand 2013). For instance, if in a particular year a given primary school had 100 students achieving above national standards in math and a meshblock within that school’s catchment zone (or proximity threshold) constituted ten percent of the total school aged population within the catchment zone, then ten such students would be assigned from that school to that meshblock. Each variable was then summed up to a 2017AU level using the meshblock to AU correspondence files provided by Statistics New Zealand (2018b).

In this way DOT obtained yearly estimates of each of the variables listed above at a 2017AU level. These yearly variables were then linearly interpolated in order to obtain monthly variables at the 2017AU level. This interpolation process was done in such a way that the monthly variables for December always coincided exactly with the corresponding yearly variables. All variables for months post (pre) Dec-16 (Dec-13) were fixed at Dec-16 (Dec-13) levels. Finally, each month and within each 2017AU each of the aforementioned variables was expressed in proportional terms using the following example formulas:$\mathit{T}YPEA:\mathrm{\%}\text{Students Expelled}=\frac{\mathrm{\#}\text{Students Expelled}}{\mathrm{\#}\text{Students}}$ $\mathit{T}YPEB:\mathrm{\%}\text{Below NS Math}=\frac{\mathrm{\#}\text{Below NS Math}}{\mathrm{\#}\text{Above NS Math}+\mathrm{\#}\text{At NS Math}+\mathrm{\#}\text{Below NS Math}+\mathrm{\#}\text{Well Below NS Math}}$ $\mathit{T}YPEC:\mathrm{\%}\text{Below NCEA1}=\frac{\mathrm{\#}\text{Below NCEA1}}{\mathrm{\#}\text{Above NCEA1}+\mathrm{\#}\text{Below NCEA1}}$

In the rare case where denominators were equal to zero this was accounted for by setting the corresponding variables equal to zero. Table 1 below shows the Pearson correlation between each of the education variables for the month of Mar-13 and the NZDEP13 scores. As we would expect, high expulsion / suspension / stand down rates and a lack of educational attainment are associated with higher levels of socio-economic deprivation.

Table 1. Pearson correlation between March 2013 education variables and NZDEP13 scores.

Variable	Type	Correlation with NZDEP13 Score	Variable	Type	Correlation with NZDEP13 Score
% Students Expelled	A	0.272*	% Students Above NS Writing	B	−0.292*
% Students Suspended	A	0.313*	% Students At NS Writing	B	−0.468*
% Students Stood Down	A	0.324*	% Students Below NS Writing	B	0.497*
% Students Above NS Math	B	−0.449*	% Students Well Below NS Writing	B	0.576*
% Students At NS Math	B	−0.323*	% Students Above NCEA1	C	−0.432*
% Students Below NS Math	B	0.558*	% Students Below NCEA1	C	0.432*
% Students Well Below NS Math	B	0.561*	% Students Above NCEA2	C	−0.389*
% Students Above NS Reading	B	−0.447*	% Students Below NCEA2	C	0.389*
% Students At NS Reading	B	−0.134*	% Students Above NCEA3	C	−0.379*
% Students Below NS Reading	B	0.542*	% Students Below NCEA3	C	0.379*
% Students Well Below NS Reading	B	0.588*

*Significant at the p < 0.001 level.

DOT took the education variables listed in Table 1 for Mar-13, multiplied those variables found to be negatively correlated with NZDEP13 scores by a factor of minus one, performed principal component analysis on the transformed variables and associated an Education Score (standardised to have a mean of 100 and standard deviation of 10) to each 2017AU using the first principal component. The Pearson correlation between the Education Scores for Mar-13 and NZDEP13 scores was found to be equal to 0.629 (p < 0.001) with the first principal component explaining approximately 45% of the data. DOT followed the same procedure in order to associate an Education score to each AU each month from Mar-13 to Mar-18. In each iteration of the process the first principal component explained between 42% and 46% of the data.

Strictly speaking the inclusion of variables negatively correlated with socio-economic deprivation in the construction of the Education Scores (e.g. the proportion of students achieving above national standards in math), means that the Education Scores are not strict measures of deprivation. That is to say that the do not entirely represent a lack of educational attainment. Nevertheless, we decided to include these variables within the Education Scores because they were strongly correlated with deprivation levels and to prevent AUs with small student populations appearing to be overly advantaged.

Material deprivation

The fact that material deprivation reflects a particular dimension of socio-economic deprivation distinct from income has been extensively studied within the relevant literature (see for instance Beverly 2001; Slesnick 1993; Perry 2016). Indeed, Fusco et al. (2011) define material deprivation as:

… the inability to posses the goods and services and / or engage in the activities that are ordinary in socieity or that are socially perceived as necessities.

Material deprivation extends to consumer spending patterns with many researchers advocating consumption as a better measure of socio-economic deprivation than income (e.g. Meyer and Sullivan 2003). Due to its nature as a commercial enterprise, DOT has access to a large number of data sets detailing consumer spending patterns. Due to the commercial arrangements in place regarding proprietary data, the exact sources of the data cannot be specified. As a consequence, the emphasis of this section is to provide a high level overview of the outcome of using these private, proprietary data sources. We stress that in all instances data are anonymised and aggregated monthly to either a meshblock or area unit level enabling integration with other data sources within the DDI using location and time as match keys.

The data used to describe material deprivation is purchasing data that is meaningfully allocated to product categories as a natural by-product of the supplier’s processes. For the three months up to and including Mar-13, DOT calculated the proportion of purchasing activity occurring within each product category by 2017AU and correlated these proportions with the NZDEP13 scores. The results appear to align with Maslow’s Hierarchy of Needs (Maslow 1943). That is higher order needs: such as self-actualisation, esteem and social belonging do not become a priority until fundamental needs such as physiological (food, water and shelter) and safety are met. For example, art products had a correlation of −0.42 (p < 0.001) with deprivation and second hand clothing had a correlation of 0.32 (p < 0.001).

DOT took the 18 most correlated product categories, multiplied those variables found to be negatively correlated with NZDEP13 scores by a factor of minus one, performed principal component analysis on the transformed variables and associated an Initial Purchasing Behaviour Score (standardised to have a mean of 100 and standard deviation of 10) to each 2017AU using the first principal component. The Pearson correlation between the Initial Purchasing Behaviour Scores for Mar-13 and NZDEP13 scores was found to equal 0.655 (p < 0.001). Of course, the reliability of the Initial Purchasing Behaviour Score as a measure of material deprivation depends on their being a large level of purchasing behaviour activity within each AU. Imputation was used to ensure adequate coverage in areas of low purchasing activity. As such, DOT created a (final) Purchasing Behaviour Score (PUR Score) for each AU, whereby if the amount of observed purchasing activity in an area was low, the average PUR Score for AUs within the same Deprivation Index was used with the Initial Purchasing Behaviour Score being used otherwise.

It was found that the Pearson correlation between the (final) Purchasing Behaviour Scores for Mar-13 and the NZDEP13 scores was equal to 0.675 (p < 0.001), with the (final) Purchasing Behaviour Scores differing from the initial scores for only 62 out of 1867 AUs. DOT was able to assign a Purchasing Behaviour Score to each AU each month from Mar-13 onwards using purchasing behaviour data from the preceding three months following the process outlined above. In each iteration of the process the first principal component was found to explain between 27% and 33% of the data and the (final) Purchasing Behaviour Scores differed from the Initial Purchasing Behaviour Scores for between 44 and 84 AUs depending on the month under consideration.

From a theoretical perspective the inclusion of variables negatively correlated with socio-economic deprivation in the construction of the (final) Purchasing Behaviour Scores (e.g. the proportion of purchasing behaviour activity involving art) once again means that the Purchasing Behaviour Scores are not strict measures of deprivation in the sense that they do not entirely represent a lack of ability to possess certain goods and services. Nevertheless, we decided to include these variables within the construction of the Purchasing Behaviour Scores because they were strongly correlated with deprivation levels and to prevent AUs with low levels of purchasing behaviour activity from appearing to be overly advantaged.

Calculation of residuals for Mar-13

DOT combined the data sources described in the previous sections into a data set for Mar-13 detailing the JSS rate (employment), SPS rate (support), MTB Rate (income), Education Score (education), Purchasing Behaviour Score (material deprivation) and NZDEP13 Score (anchoring variable) for each of the 1867 different 2017 AUs appearing in the NZDEP13 study. The NZDEP13 scores were standardised to have a mean of 1000 and standard deviation of 100.² DOT performed principal component analysis on the above six variables in order to assign a Preliminary DDI Score to each AU using the first principal component (which explained 72% of the data). The Preliminary DDI Scores were then also standardised to have a mean of 1000 and standard deviation of 100. Finally, for each 2017AU DOT calculated a residual as the difference between the NZDEP13 score and the Preliminary DDI Score so that${\mathrm{Residual}}_{{\mathrm{AU}}_{\mathrm{i}}}={\mathrm{NZDEP}13\mathrm{Score}}_{{\mathrm{AU}}_{\mathrm{i}}}-{\mathrm{Preliminary}\mathrm{DDI}\mathrm{Score}}_{{\mathrm{AU}}_{\mathrm{i}}}\left(\mathrm{Mar}13\right).$

Calculation of Monthly Deprivation Scores

For each month from Mar-13 to Mar-18, DOT combined the data sources described in the previous sections into a data set detailing the JSS rate (employment), SPS rate (support), MTB Rate (income), Education Score (education), Purchasing Behaviour Score (material deprivation) and NZDEP13 Score (anchoring variable) for each of the 1867 different 2017 AUs appearing in the NZDEP13 study. Principal component analysis was applied to the six variables listed above and a Preliminary DDI Score (standardised to have a mean of 1000 and a standard deviation of 100) was assigned to each AU using the first principal component. The first principal component explained between 70% and 72% of the data depending upon the month in question with the corresponding weights ranging over the following minimum and maximum limits; JSS rate (0.436, 0.442), SPS rate (0.437, 0.447), MTB rate (0.411, 0.422), Education Score (0.327, 0.351), Purchasing Behaviour Score (0.315, 0.360), NZDEP13 Score (0.451, 0.460). For each month DOT then created a (final) DDI Score for each AU using the formula:${\mathrm{DDI}\mathrm{Score}}_{{\mathrm{AU}}_{\mathrm{i}}}={\mathrm{Preliminary}\mathrm{DDI}\mathrm{Score}}_{{\mathrm{AU}}_{\mathrm{i}}}+{\mathrm{Residual}}_{{\mathrm{AU}}_{\mathrm{i}}}$before standardising the DDI Scores once again to have a mean of 1000 and a standard deviation of 100. Each month AUs were ranked into deciles on the basis of their DDI Score. The addition of the residual in the construction of the DDI Scores ensures that the DDI Scores of each AU as of Mar-13 coincide exactly with the NZDEP13 scores. Conceptually, therefore, the residual compensates for the variables included within NZDEP13 that could not be incorporated into the DDI due to a lack of available data.

Transposition of NZDEP Studies to 2017AU Boundaries

To validate the results within the DDI it will be necessary to show that the level of movement of AUs between deprivation deciles over the period from Mar-13 to Mar-18 closely follows the level of movement of AUs between deprivation deciles exhibited between consecutive NZDEP studies. However, this is complicated because the AU geographies change over time and because length of time between the NZDEP06 and NZDEP13 studies was seven years as opposed to the usual five (a consequence of the 2011 Canterbury earthquake).

To navigate these problems DOT effectively created modified versions of the NZDEP studies holding AU boundaries constant at 2017 levels. Following on from an O.I.A request, Statistics New Zealand provided DOT with a set of correspondence files linking 1991 and 1996 meshblocks to 2017 AUs. These complemented the geographic correspondence files published by Statistics New Zealand (2018b) which link 2001, 2006 and 2013 meshblocks to 2017 AUs. In the worst case scenario, there were a total of 442 out of 34,841 meshblocks appearing in NZDEP91 that were assigned to multiple 2017 AUs. Indeed, only one 2013 meshblock appearing in NZDEP13 was assigned to multiple 2017 AUs. As such, DOT formed Modified NZDEP Scores for each 2017AU appearing in the NZDEP13 study for each of the years 1991, 1996, 2001, 2006 and 2013 by taking population weighted averages of component meshblock deprivation scores. Finally, DOT created Modified NZDEP Scores for each 2017AU as of Mar-11 by linearly interpolating between the corresponding Modified NZDEP Scores for 2006 and 2013. In the subsequent section it will be understood that when we refer to NZDEP91/96/01/06/11 deprivation scores or indices that we mean the Modified NZDEP Scores and indices created holding AU boundaries constant at 2017 levels.

Results & validation

Socio-economic deprivation is not an objective quantity. As such, differences in the way this multi-faceted variable is measured within different studies naturally lead to different results being produced. Consequently, any proposed measure of socio-economic deprivation must demonstrate that it does, in fact, measure that which it purports to. Crampton et al. (2014) describe two forms of validation to which a measure of socio-economic deprivation should be subjected; construct validity and criterion validity. Construct validity seeks to establish strong theoretical links between socio-economic deprivation and the variables used to measure it. In this regard, with the exception of material deprivation, the DDI incorporates variables directly comparable to variables used within either the NZDEP studies or the IMD. In contrast, criterion validity investigates how well a measure of socio-economic deprivation predicts other variables known to be associated to this phenomenon. Indeed, given that there is much evidence that smoking rates are strongly associated with socio-economic deprivation (Wilson et al. 2006; Salmond et al. 2012), the results of both NZDEP13 and the IMD are validated against data relating to the prevalence of regular smokers. However, criterion validity is something of a problem for the DDI. By means of its very purpose and design, there are very few (if any) current enough data sets against which the criterion validity of the DDI may be assessed. Nevertheless, Panel A of Figure 1 below shows the proportion of regular smokers as reported within the 2013 New Zealand census (Statistics New Zealand 2013) by NZDEP13 decile and by DDI Mar-18 decile. In both cases, the proportion of regular smokers increases monotonically as we progress from the least to most deprived deciles with a ‘flick up’ in the proportion of regular smokers being observed in the most highly deprived deciles.

Figure 1. DDI metrics.

When presented as an extended time series another criteria against which a measure of socio-economic deprivation should be assessed is that of stability. That is to say that it would certainly be undesirable to see a high proportion of AUs transitioning between different deciles each month or making large jumps between non-consecutive deciles. Given that there are 1867 AUs incorporated into the DDI, over the 60 months from Mar-13 to Mar-18 this constitutes a total of 112,020 transition points. Of these 112,020 transition points, 100,821 (90.0%) involved AUs transitioning to the same deprivation index as they were assigned in the previous month, whilst 11,081 (9.9%) involved an AU transitioning to a neighbouring deprivation decile. This information is summarised in Panel B of Figure 1.

Mobility constitutes a fourth criteria against which the DDI can be assessed. That is to say that it is important that the DDI captures a level of movement of AU scores, and movement of AUs between deprivation deciles, similar to that exhibited between previous consecutive NZDEP studies. Using the modified deprivation scores described in the previous section, DOT calculated the correlation of AU scores between consecutive NZDEP studies and compared this to the correlation observed between NZDEP13 scores and DDI Mar-18 scores. The results of this process are shown in Panel C of Figure 1. Herein, we see that the observed correlation between NZDEP13 scores and DDI Mar-18 scores is very similar to the corresponding correlations observed between consecutive NZDEP studies. We also note that the degree of such correlations appears to be generally increasing, hinting at a decreasing level of mobility of AUs within the relative deprivation scale over time. In a similar vein of thought, Panel D shows the proportion of AUs moving between deprivation deciles between consecutive NZDEP studies in comparison to the movement observed between NZDEP13 and DDI Mar-18. This should be interpreted as saying that the deprivation index of approximately 19.7% of AUs decreased by one between Mar-13 and Mar-18, compared to say 19.6% between NZDEP91 and NZDEP96. In general the level of movement of AUs observed between NZDEP13 and DDI Mar-18 is very similar to that observed between previous NZDEP studies.

Indeed, population is a key determinant of the degree of change in socio-economic deprivation levels exhibited by AUs over time. That is to say that lowly populated AUs are more sensitive to socio-economic stimuli than more heavily populated ones and, therefore, more likely to exhibit movement in their relative positions. This is demonstrated in Panel F of Figure 1. Herein, we see a monotone decreasing relationship between the average population of AUs and their absolute level of movement between consecutive NZDEP studies. For instance, the average population of AUs moving four or more deprivation deciles between two consecutive NZDEP studies is always far lower than the average population of AUs remaining in the same deprivation decile. Indeed, this relationship is also evident in terms of the movement of AUs between deprivation deciles between NZDEP13 and DDI Mar-18.

The fifth criteria against which we may assess the DDI is that of inertia. We use the term ‘probability of inertia’ to describe the probability that an AU belonged to same deprivation decile within consecutive NZDEP studies. The probability of inertia, broken down by deprivation decile, is shown in Panel E of Figure 1. There are two features to note here. First, the probability of inertia increases as we progress from AUs in the middle of the deprivation distribution to AUs at the extremes of the distribution; a phenomenon more widely referred to in the literature as ‘stickiness at the ends’ (Urahn et al. 2012). Indeed, the probabilities of inertia exhibited between NZDEP13 and DDI Mar-18 preserve this pattern. Secondly, the probability of inertia for any given decile appears to be generally increasing over time, again hinting at decreasing levels of AU mobility within the relative deprivation scale.

Agency is the final criteria against which we may assess the DDI. The concept of agency is that when presenting deprivation as an extended time series it should be possible to determine the drivers of changes in deprivation levels. Indeed, it is possible to correlate the change in JSS / SPS / MTB rates, Education Scores and Purchasing Behaviour Scores between Mar-13 and Mar-18 to the changes in the DDI Score observed over this period. The results of this process are shown in Table 2 above. In essence, Table 2 indicates that changes in the JSS / SPS / MTB rates are more highly associated to changes in DDI Score than changes in either the Purchasing Behaviour Score or the Education Score. Table 2 also shows associated regression coefficients. The results here should be interpreted as saying that, on average, a one percent increase in the unemployment rate is associated with a change of 9.30 in DDI Score whereas a unit increase in Purchasing Behaviour Score is associated with an increase of 1.85 in DDI Score.

Table 2. Associations between change in DDI input variables and change in DDI Score between Mar-13 and Mar-18.

DDI input variable	Correlation with change in DDI Score	Regression coefficient (no intercept)	R^2
Change in JSS Rate	0.653*	9.30*	0.416
Change in SPS Rate	0.608*	9.34*	0.279
Change in MTB Rate	0.550*	12.52*	0.303
Change in PUR Score	0.433*	1.85*	0.187
Change in EDU Score	0.355*	1.83*	0.125

*Significant at the p < 0.001 level.

Continuing in this regard, Panel H of Figure 1 shows that whilst the correlation between (actual) NZDEP13 scores and JSS rates has been decreasing over time the correlation between DDI Scores and JSS rates has been maintained. Indeed, similar divergences are observed with respect to the SPS and MTB rates, although this is to be expected given that these variables are internal to the model.

To conclude this section we make two final remarks. First, Panel G of Figure 1 shows the distribution of NZDEP13 scores and DDI Mar18 scores, as well as their cumulative distributions (which are virtually identical). Secondly, each month DOT creates a DDI Score for each Territorial Authority (TA) by forming population weighted averages of component AU DDI Scores. Of particular interest in this regard is Tauranga City, which has exhibited significant socio-economic improvement over the period from Mar-13 to Mar-18. Indeed, Figure 2 below shows the change in deprivation index observed for each AU in the Tauranga City TA over this period. We posit that the socio-economic improvement exhibited within the Tauranga City TA over this period may well have been influenced by economic factors such as the expansion of the port and migration (Champion 2018).

Figure 2. Changes in deprivation deciles for AUs within Tauranga City.

Discussion & conclusion

Within this study we have assigned a DDI Score and DDI Decile to each of the 1867 different 2017 AUs appearing in NZDEP13 each month from Mar-13 to Mar-18. In order to do so we have used a combination of publicly available and commercially purchased data sets containing 34 variables spanning five different dimensions of deprivation; employment, support, income, education and material deprivation.

However, there are a number of methodological limitations to our approach that should be addressed. To begin with, we simply do not have access to data at as geographically granular a level as within NZDEP13 or the IMD. That is to say that whilst the aforementioned studies are constructed using meshblock level data either derived from the census or extracted from the IDI, the majority of the data used within the DDI arrives at the AU level. The consequences of this are twofold. In the first instance, we cannot extend the DDI down to meshblock level in a rigorous fashion as within the NZDEP studies (although it is possible to produce estimates of meshblock deprivation levels holding the relative positions of each meshblock within each AU constant). In addition, the fact that the data used in the DDI arrives predominantly at an AU level means that we are precluded from creating bespoke amalgamations of meshblocks to ensure minimal population levels in the same way that ‘small areas’ are constructed in the NZDEP studies or ‘data zones’ are constructed in the IMD. Whilst this is generally not a problem, the median AU population as of the 2013 census being 1985 people, as of Jun-18 there are still approximately 39 AUs incorporated into the DDI that have a population of less than 100 people (Statistics New Zealand 2018c). Due to the existence of small denominators, our results may not be reliable for such AUs. The extent to which this is also a problem for the NZDEP studies and IMD is unclear, given that both small areas and data zones are designed to be constructed from meshblocks belonging to the same AU.

Similarly, whilst the NZDEP13 study covers eight dimensions of deprivation and the IMD seven, the DDI covers only five. This is because there are simply no publicly available data sets detailing levels of internet access, household income, home ownership and vehicle ownership released between censuses for example. However, such data sets do exist or could be easily constructed by the relevant public bodies. We did experiment with incorporating the New Zealand Police Victimisation Statistics (New Zealand Police 2016) into the DDI as per the crime domain within the IMD. However, AU crime rates are only moderately to weakly correlated with deprivation levels, as reflected by the relatively low weighting the crime domain receives within the IMD. A potential reason for this is the distinction between where an offence occurs and where the perpetrator lives. Temporal effects also serve to distort the association. For instance, Ward et al. (2018) found that socio-economic deprivation was a stronger predictor of assault outside of the hours of 22:00–03:00 on weekends despite the fact that assaults occur much more frequently during these hours due to the influence of the night time economy.

Next, there were problems inherent in the data that had to be overcome. For instance, the data provided by the Ministry of Social Development (largely) had to be transposed from a 2001AU level to a 2017AU level and did not cover the months from Mar-13 to Aug-13. Furthermore, the data did not specify claimant levels by age and sex, thereby precluding the possibility of age-sex standardisation. It is worth noting, however, that whilst variables within the NZDEP studies are age-sex standardised no such process is used within the IMD. Indeed, Crampton et al. (2014) note that only 11% of small areas constructed in the NZDEP01 study changed deprivation decile (predominantly by ± 1 decile) when comparing age-sex standardised and non-age-sex standardised deprivation scores. Continuing with respect to inherent data issues, the data harvested from the Education Counts website had to be distributed from a point specific school level to a 2017AU level and did not cover any month past Dec-16. Going forwards, this will constitute more of a problem with regards to the construction of the DDI given that primary schools are no longer required to publicly disclose national standards achievement levels.

Indeed, such issues highlight the problems associated with the use of administrative data in the construction of measures of socio-economic deprivation more generally. As noted by Norman (2016) researchers have little control with regards to the collection and dissemination of data by public bodies and, in the case of benefit claimant data, changes in eligibility criteria can cause temporal comparison issues. That being said there are significant advantages to the use of administrative data sources, as opposed to census data, in the construction of such measures. These advantages include data being provided on individuals who may not normally respond to the census, no explicit reliance upon self-reported data and an increased temporal frequency of data.

Finally, the Education Scores and Purchasing Behaviour Scores assigned to each AU contain constituent elements which mean they cannot be regarded as ‘strict’ measures of deprivation (see the sections entitled Educational Attainment and Material Deprivation for details). With regards to the later, the proprietary nature of the data used to derive the Purchasing Behaviour Scores meant that we were unable to be completely transparent with regards to how this variable is constructed and low levels of purchasing behaviour meant that Purchasing Behaviour Scores had to be imputed for between 2.4% and 4.5% of AUs depending on the month in question. Furthermore, in the creation of the DDI Scores themselves NZDEP13 score was used as an input variable. We included the NZDEP13 scores in this process as an anchoring mechanism, i.e. by including this variable in the scoring procedure we ensured that the DDI Scores for Mar-18 did not deviate too much from the NZDEP13 scores and did not vary too much from month to month. If we had access to dynamic data sets detailing all the variables appearing in the NZDEP13 study then this variable could be removed from the scoring procedure altogether.

Despite these limitations there are a number of strengths to our approach. First, the DDI is a far more current measure of socio-economic deprivation levels than either the NZDEP studies or the IMD. This provides policy analysts and researchers with the possibility of using the most up to date information possible concerning the distribution of socio-economic deprivation across New Zealand.

Secondly, the DDI is a stable measure of deprivation that recovers the important latent structures observed when analysing the results of consecutive NZDEP studies, i.e. correlations between deprivation scores, movements of AUs between deprivation deciles, larger movements of more lowly populated AUs and stickiness at the ends. Moreover, the DDI Scores for Mar-18 can be seen to be more highly correlated with the JSS / SPS / MTB rate than NZDEP13 scores. Indeed, changes in DDI Scores can be associated predominantly to changes within these variables.

Furthermore, presenting socio-economic deprivation levels as an extended time series opens up intriguing avenues for new research. Herein, we offer such an example. That there is a strong link between gambling related harms and socio-economic deprivation is well understood (Adams 2004; Walker et al. 2012). The availability and adaption gambling hypotheses are such that increased gambling availability leads to increased short term participation and harm, whilst in the longer term participation rates and harm decline as people adapt to the new environment (Abbott 2017). Given that electronic gaming machines have been identified as the most harmful form of gambling (Binde et al. 2017), that the burdens of EGM related gambling fall disproportionately on more highly socio-economically deprived communities (Adams 2004) and that EGM gambling is likely to occur within close proximity of the home (Productivity Commission 1999; Rintoul et al. 2013), if the availability and adaption hypotheses hold true then it may be possible to use the DDI to show that the opening (closing) of gaming venues is associated with short term increases (decreases) in the socio-economic deprivation levels of the surrounding areas. Indeed, such effects may be picked up by the DDI due to the inclusion of the material deprivation measure of socio-economic deprivation. Short term effects such as these would not be able to be identified using either the IMD or NZDEP studies.

All in all we believe that the DDI is a meaningful and current measure of socio-economic deprivation. In this regard, we have succeeded in our objective of demonstrating that if public bodies were to make the data they hold more easily available, then there is no reason why New Zealand should not be able to benefit from a measure of socio-economic deprivation that combines the sophistication of the NZDEP studies or IMD with the contemporaneousness of the DDI.

Acknowledgements

The authors would like to express their sincere thanks to the Ministry of Social Development and Statistics New Zealand for the provision of the data sources listed within the paper.

Disclosure statement

The DDI is the intellectual property of DOT Data Ltd. The quantitative results of the DDI may be made available to researchers upon request. However, these results must not be republished or distributed to third parties without DOT Data Ltd's explicit consent.

ORCID

Adam D. Ward http://orcid.org/0000-0002-5259-2728

Notes

1 At the time of constructing this paper Education Counts had not fully released the data for the school year ending Dec-17.

2 Recall that in the construction of NZDEP13 it is the small area deprivation scores that are normalised to have a mean of 1000 and standard deviation of 100, not the AU deprivation scores which are population weighted averages of small area deprivation scores.