I am not sure what you are looking for exactly, but can't you use CO2 emissions as a measure. As for the instrument, it depends on what you plan to measure exactly in a household. Are you trying to measure waste production, eating habits, energy usage, transportation, water use...etc.
If you can be more specific, then others and I can help more..
Sorry if my answer is not what you are looking for..
Behavioural change by households is increasingly anticipated to make an important contribution to the reduction of greenhouse gasses (GHG) and other emissions. As a result, monitoring of the environmental impacts of consumption at the household level is necessary to evaluate current performance and to support the understanding of how initiatives for change can be implemented.
Among the goods and services that make up household consumption, food, private transport, and housing are consistently identified as the most important categories in lifecycle environmental inventories of household consumption expenditures. Particularly food is at the core of the discussion of sustainable consumption in the context of the household.
In order to aid in setting priorities for public decision making, further research is needed not only into the magnitude of the environmental impacts of food consumption but also, more importantly, into how this impact could be reduced. Specifically, it is necessary to analyse how food products are combined in more and less sustainable food patterns and how changes in these food patterns as part of modern consumption activities can reduce the environmental impact of households. This information needs to be presented at a detailed level to investigate environmental improvement opportunities from retail innovation and behavioural change. Presently such analysis is restricted by the lack of a tool to measure the environmental impact of food consumption at household level.
Thus the environmental literature has yet to propose a tool to measure environmentally sustainable food and non-food consumption at the household level, surprising as this may appear. An important explanation is the restricted availability of data on environmental impact at the household level, making existing approaches either
a) product-based, focusing on only a single aspect of the supply chain; or
b) based on stated behaviour, using survey data to determine the environmental propensity of consumers.
The latter indicators reflect the stated beliefs and habits of those included in the survey rather than their actual behaviour]. The implication is that consumers could be labelled as “environmentally concerned” whilst being heavy polluters.
Against this background Panzone et al. (2013) present an indicator of sustainable household consumption: the Environmentally Sensitive Shopper (ESS) index, the structure of which is summarised in Figure 1. Compared with existing alternatives (e.g., the ecological footprint or the carbon footprint), this indicator has several innovative aspects. First, it avoids the hypothetical bias mentioned above because it is based on revealed consumer preferences. Second, the design combines insights from different disciplines, in particular economics, sociology, and sustainability science). Finally, this index focuses specifically on the consumption of households, whose emissions are a crucial component for sustainability targets: while suppliers effectively emit GHG, the demand side plays a major role not only during consumption, but also requesting the production of GHG to fuel their consumption process.
The article discusses the methodology and data basis of the ESS index and presents its use through a pilot application for the UK, where a large share of the environmental footprint of households is attributed to food purchases .
Panzone, L.A., A. Wossink and D. Southerton (2013) An environmental index to measure progress towards more sustainable household food consumption using supermarket data, Ecological Economics 94: 44-55.
Promoting sustainable consumption among young consumers has become a key priority, you may can calculate the quantity usage, then energy equivalent for each item and then GHG emission.