Being able to model the behaviour of consumption is an immensely important economic tool, as consumption accounts for between half and two-thirds of the UK's GDP each year and so is critical in evaluating the performance of the economy and predicting future economic forecasts. During this project I will layout the theory of the consumption function and then work through the process of estimating a suitable equation. Theory:

The consumption function is an expression of the relationship between consumption and income, the general rule being that as national income increases so does consumption as people have more money to spend. This theory was first put forward by John Maynard Keynes in 1936 in his The General Theory of Employment, Wages and Money. He argued that 'The fundamental psychological law... is that men are disposed as a rule and on the average, to increase their consumption as their income increases, but not by as much as the increase in their income.

'1 From this he derived the simplest of consumption functions: Where consumption, C, is equal to autonomous consumption, c0, plus disposable income, Y, multiplied by the marginal propensity to consume, c1. The marginal propensity to consume is 'the proportion of a rise in national income that goes on consumption'2 which as Keynes stated earlier is positive and yet below unity. When this equation is fitted to the data we get the equation: Ct = 13530 + 0. 9224Yt This fits with Keynes statement that m. p. c.

must be between 0 and 1 and shows that nearly all additional income is consumed. However we must decide whether it is an accurate equation to predict consumption, this can be done using statistical tests and graphically. The top graph on figure 1 compares actual consumption with consumption derived from our equation and as you can see there is a very good correlation: Fig. 1 However the bottom graph shows us the difference between our two lines and as you can see, the equation holds well until the late 1970's where large negative differences start to appear.

This is because during this period there was the oil crisis and high unemployment and so there was a lot of uncertainty in the economy. This meant that people were unsure of their future income and so consumed less. Here we have the first failing of the Keynesian consumption function, people decide how much they consume not only on what they are earning now but also what they expect to be earning in the future. These factors are obviously of importance in predicting consumption and so they need to be incorporated into our equation.

There is one small change to the equation that needs to be made before investigating the other factors that affect consumption. The last equation was in a very simple linear form and unfortunately economic models are not that basic, however trying to estimate non-linear equations is extremely difficult and so in order to by-pass the problem, the equation needs to be converted into log-linear form, where c = log(C) and y = log(Y). This changes the relationship between C and Y to: Ct = AYc1

Now c1 represents elasticity of consumption rather than the m. p. c. The consumption function need to be calculated again now as it will now have altered slightly, the change in autonomous consumption is because c0 is now derived from log (A). The function now looks as follows: ct = 0. 7273 + 0. 9403yt As mentioned earlier, consumers look to their expected lifetime income when deciding expenditure. This theory has been explored and modelled by a number of economists most notably Friedman with his Permanent Income Hypothesis (PIH).

The theory behind this is that consumers like to keep their expenditure constant over a longer period of time and so will try to average their future income and base current expenditure on that rather than their current income now. Friedman's simplest form of PIH is that consumption is a constant proportion of permanent income, in other words: Ct = kYpt Where Yp is permanent income and k is the average propensity to consume.