There’s an old joke about an economist, an engineer and a biologist stranded on a desert island. They become increasingly worried that they might starve to death. And then they discover an unopened can of beans. The biologist suggests waiting until erosion eats away at the metal. The engineer suggests building a device from the rocks on the island to break open the can. The economist says, "Let’s assume we have a can opener".

Last week Treasury was forced to release a report (pdf) under the Freedom of Information Act showing the advice it had given the federal government about the potential costs of its proposed carbon tax. The report’s conclusion, based on the economic models adopted by Treasury, was that the carbon tax would result in a gross "cost" to Australian households of $16.60 per week.

New Matilda readers would be correct to be a little bit cautious of accepting the outcomes of such modelling exercises on face value. To butcher a phrase, there are lies, damned lies, and economic models.

Modelling is useful; it allows us to abstract from an increasingly complex world so we can ask questions and see how the answers to these questions may play out in the real world, given a set of assumptions. Making good use of modelling, therefore, requires a good understanding of the assumptions behind those models and recognising what their assumptions mean.

Before unpacking the assumptions behind Treasury’s carbon tax model, let’s take a brief look at what the Cabinet briefing paper actually said.

The $16.60 per week figure bandied about by the Opposition and media pundits is based on modelling a carbon price of $30 per ton. The final price may be higher or lower with the costs to households varying accordingly, especially after rebates are taken into account. The four areas of household spending most affected by carbon pricing — electricity, gas, petrol prices and food — will only rise by $4.20, $2.20, $3.60 and $1.70 respectively. So long as a carbon price is part of a suite of measures to address climate change, there is a strong argument that this is a small price to pay to remove the subsidy that effectively currently exists for carbon-intensive industries. In any event, according to Treasury, the carbon price will result in a less than 1.5 per cent increase in CPI.

Onwards to the models themselves and what they assume about the way in which the Australian economy functions.

The model used by Treasury is the PRISMOD price input-output model. The model provides a very detailed representation of the Australian economy and is based on the pioneering work of Wassily Leontief, the Russian-American economist who was awarded the Nobel Prize in 1973.

PRISMOD creates a model of the economy such that each industry is presumed to demand "inputs" from a number of other industries in fixed proportions. These inputs are then used to create an output. For example, let’s say it takes two litres of water, three oranges and four pieces of plastic to make one unit of juice. If only one unit of juice is demanded, then the juice industry will demand two litres of water, three oranges and four pieces of plastic. If the demand for juice doubles to two units, then the juice industry will demand four litres of water, six oranges and eight pieces of plastic. This increase in demand for water, oranges and plastic will also flow on to the inputs for each of those industries resulting in multiplier effects across the economy.

PRISMOD is a fairly simple model. The simplicity is achieved through its assumption that industries demand inputs in fixed proportions, regardless of the price of those inputs. As a result, the dynamics of how a change in relative prices of inputs may force firms to substitute between inputs is not modelled at all. Returning to our example, consider that the price of water skyrockets relative to oranges. In this situation, because oranges contain a bit of water, to produce the same amount of juice it is possible to reduce (up unto a point) the amount of water being used by substituting it with oranges. This substitution allows for the reduction in overall costs because firms use less of the now more expensive inputs. This substitution effect and its resultant impact are not accounted for in PRISMOD; PRISMOD estimates do not take into account that an increase in the price of water may spur innovation, in the form of new recipes of orange juice that use less water or none at all.

PRISMOD is also a static model of the Australian economy. It can make no comment on the longer term dynamics of the impact of a carbon price and how the economy adjusts to a carbon price. The estimates also say nothing about the costs to the actual welfare of consumers in terms of the levels of consumption or overall GDP.

There are other more sophisticated models, known as general equilibrium models, that are able to capture the dynamics of demand and prices that allow firms and consumers to substitute between goods in response to price changes. These models take the next step and ask the question of what would happen to demand and overall consumer welfare if consumers and firms were allowed to respond to price increases by altering their relative demand for goods. General equilibrium models come in many varieties and each makes its own assumptions. That said, general equilibrium models have been used to explicitly model the effect of carbon policy on consumptions levels and, by extension, standards of living.

The Garnaut Review used general equilibrium modelling for its assessments of the impact of a carbon price and emissions targeting, showing that overall per capita income in Australia would continue to increase. While the growth in income is predicted to be 55 per cent as opposed to the 67 per cent if the carbon emissions target of 450 parts per million is not reached, a 55 per cent increase is, by any account, substantial.

But even general equilibrium models fall short of being able to accurately "predict" the long impact of carbon pricing on the Australian economy because they do not explicitly model the development of new technologies and how it may respond to prices. Though substitution itself can be thought of as a form of technological change, the models do make assumptions about the path of increases in the overall rate of technological development. In particular, they do not adequately account for how firms may respond to a carbon price by investing in new technologies that may result in a dramatic reduction in the costs of abatement. This is because it is extremely difficult to model the development of future technologies.

Perhaps the biggest assumption behind all of these models is that the Australian economy operates along purely neoclassical lines, characterised by profit- and utility-maximising agents and diminishing marginal returns. This is obviously not necessarily representative of how most of us operate in reality.

The limited predictive capacity of economic models does not mean that they should be dismissed outright. Modelling is a useful intellectual exercise that can help us think about an increasingly complex world and to help us get a sense of the direction in which we are heading, but they should not be used as crystal balls. Without a clear understanding of the assumptions underpinning economic models, the numbers they throw out are close to meaningless.

What we do know from Treasury modelling of a carbon price set at $30 per ton is that it will increase prices of goods and services by $16.60 per week for an average Australian household if the relative and absolute quantities of goods and services demand by households stays the same, and if businesses pass on prices to consumers as if all production processes were essentially frozen.

The responsible use of this type of modelling is to ask the question of how industries and consumers may respond to this change in prices by adjusting their behaviour, rather than making an assessment of the hip-pocket impact of the tax on Australians.

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