A Scenario Model for the Generation of Waste

2. Methodology

The model developed may be seen as a satellite to ADAM, where the endogenous variables are the amount of waste apportioned by fraction and primary source in ISAG and the explanatory variables are relevant waste generating economic activity variables in ADAM. The method followed is to individually examine the ISAG fractions and primary sources and for each of these categories evaluate which activity variables in ADAM explain the associated generation of the waste. As no exact information is available on which economic activities generate specific amounts of waste, the coupling between economic activities and waste generation is subject to some uncertainty. The explanatory variables used, which represent our best estimates, should thus be viewed solely as indicator variables (not firmly established relationships). An important feature of the coupling to variables in ADAM is that forecasts of the amount of waste may be based on official economic forecasts. The methodology used implies that the level of aggregation is determined by the ISAG categories and not by the economic activities. Normally in economic models, coupling would be made by ascribing amounts of waste to individual activity variables in the economic model. Given the ISAG sources, however, this is not practical as it would be necessary to subdivide the ISAG sources according to more detailed economic activities. The uncertainty associated with such a subdivision would be fairly great. (The primary sources in ISAG are: Households, Institutions, Trade and services, Manufacturing, Building/construction and Sewage Plants.)[1]

In general in the model, waste from households is linked to categories of private consumption in constant prices [2], while waste from Trade and services, Manufacturing etc., Building/construction, etc. is linked to the production in constant prices by the relevant branches. Waste from waste water treatment plants is exogenous. Moreover, waste is generally linked to the present levels of consumption or production. Waste from durable goods may alternatively be linked to past consumption. However, this would require a scrapping curve for durable goods, which is not available. The model therefore implicitly assumes that present purchases of durable goods replace old goods that will be scrapped. This is a simplified assumption, which is questionable for some durable goods, however, as waste is generally generated within the same year as the consumption or production of the goods.

The coupling of waste to private consumption and production by branches is parallel to the method used in Nagelhout, D. et al. (1990) and Bruvoll, A. and Spurkland, G. (1995). However, in Bruvoll, A. and Ibenholt, K. (1997), which puts forward a waste model linked to the Norwegian MSG-EE model, it is argued that instead of production, the relevant explanatory variable for waste from enterprises is the material inputs. According to a material balance perspective, it is argued that in a production process the physical amount of material inputs ends up either in the product or as waste. In economic models like MSG-EE, where the ratio between material inputs and production may change (due to technical changes or substitution between material inputs and other production factors), material inputs may be argued to be the relevant explanatory variable. In ADAM, however, material inputs are Input/Output-determined and are a constant share of production in the individual branches, i.e. material inputs and production change proportionally. Therefore, for projections the result is not affected by whether material inputs or production are used as the explanatory variable. From a theoretical point of view, and taking into account that the modelling in ADAM may be changed, material inputs may be preferred as the explanatory variable, however in the present model production is used as the explanatory variable.

Mathematically, the relationship between the amount of waste and the explanatory variable may be formulated in numerous ways. In generalised terms, the basic equation used in the present model is:

(Eq. 1)

where

	is the amount of waste for fraction f and source s in year t and the base year t0. (For a few fractions and sources, the waste is further disaggregated according to ISAG types and supplementary information.)
	is the explanatory variable for fraction f and source s in year t and t0 (One or more activity variables in ADAM.)
	is an amount of waste added to the present waste category in year t. The amount may be either positive or negative
	is a proportionality factor between changes in the amount of waste and the explanatory variable
	is a time dependent coefficient allowing for shifts in the relation

As an example, if is the amount of paper and cardboard (fraction f) from households (source s), the explanatory variable will be the private consumption of other non-durable goods in ADAM (the ADAM variable fCi "other non-durable goods in constant prices"), i.e. the amount of waste of paper and cardboard collected from households is assumed to follow development in the private consumption of other non-durable goods.

When =1.0, changes in the amount of waste are proportional to changes in the explanatory variable. When =0.5, a 1% increase in the explanatory variable implies a 0.5% increase in the amount of waste. One reason why may differ from 1.0 is that changes in the explanatory variable may imply changes in the weighting of waste generating components of the explanatory variable.

is a time series of coefficients normalised to 1.0 in the base-year. If changes over time, so does the waste coefficient (the ratio between the amount of waste and the explanatory variable). Assuming =1.0, the waste coefficient in period t is the product of and the coefficient in the base-year, i.e.

.

If is changed 5% from the base-year t₀ to year t, the waste coefficient also changes 5%. may change due to waste policies, changes in the physical content of the explanatory variable, changes in the weighting of waste generating components of the explanatory variable, or changes in the habits of waste generating agents, for instance changes in the packaging of goods.

The amount may be positive or negative and is added to the waste of this category. Often the amount is waste transferred from one category of waste to another.

Assuming that (Eq.1) reduces to:

(Eq. 2)

where is a constant waste coefficient calculated for the base year

i.e. the waste coefficient is constant. This is the assumption made in the above mentioned Norwegian and Dutch models, and the assumption made in the first version of the present model. However, in order to facilitate the incorporation of future evaluations of waste policies and changing waste coefficients, the equations are formulated as Eq. 1, with 1996 being the base-year t₀. When sufficiently long time series for the amount of waste are available and assuming that the development of can be described by some regular trend, the coefficients for the regular trend and may be estimated using time series analyses. At present, data for the amount of waste are only available for the years 1994 to 1996 and it is not possible to estimate the coefficients with these data alone. However, the assumption of constant waste coefficients is analysed in Chapter 4 using the data for 1994 to 1996.

Another extension of the model could be to express the explanatory variables in tonnes instead of in constant prices. Statistics Denmark is presently developing National Accounts in tonnes, which provides coupling between production in constant prices and in tonnes. For calculating amounts of waste, production or material input expressed in tonnes appears to be a more suitable explanatory variable than when expressed in constant prices. The ratio between the variable in tonnes and in constant prices may differ between branches and for a number of reasons may change over time.

Finally, for the model to be a comprehensive waste and environmental model it also needs to encompass modelling of waste management, waste generation from management facilities (waste from secondary sources) and the environmental effects of different management alternatives. As ISAG contains data on management facilities and waste from secondary sources, some basic information is available. Taking base year management shares (defined from ISAG) and adopted waste policies as the starting point and defining future management capacities and shares, it should be possible to calculate waste generation from secondary sources and the environmental effects of management alternatives. Modelling of these aspects is beyond the scope of the present model, however.

2. In economic models, the development of variables measured in constant prices is interpreted as the development in real or physical quantities.