Keynesianism

Consumption smoothing and the balanced budget multiplier
                In some of the debate following this post, and then this, there often seems to be a big distinction drawn between models based on consumption smoothing, and the old fashioned balanced budget Keynesian multiplier. Even Paul Krugman felt it necessary to say that he ‘never said a word about the balanced budget multiplier’. Now of course the models are different. However I want to suggest that in the context of fiscal expansion in a recession caused by demand deficiency, the balanced budget multiplier story can be retold in a manner consistent with consumption smoothing.
                The most basic model of consumption smoothing involves two periods. Let period 1 be a demand deficient recession, and so output is determined in a Keynesian manner by aggregate demand. Period 2, which is much longer, is Classical, and nothing changes in period 2. (If having a two period model of unequal lengths is a worry, think of period 2 as being divided into a large number of sub-periods of equal length to period 1, but where every sub-period is Classical.) We keep monetary policy neutral by assuming the real interest rate is constant. Optimising consumers will then spend a fixed proportion of their permanent income in period 1: that is consumption smoothing. Let’s call this proportion c, which could be quite small. There is no investment, and the economy is closed.
                The government now increases government spending by G in period 1 only, and taxes rise by the same amount in period 1. The ‘direct’ or ‘first round’ effect is that consumption in period 1 falls by less than G, because the impact of higher taxes on consumption is smoothed via permanent income. That is as far as I needed to go in my ‘Mistakes’ post to make the point I wanted to make. However it is obviously not the end of the story, because higher output implies higher income. What happens to output eventually (call the answer Y)? Well consumption rises/falls by Y-G times the fixed proportion c, so we solve Y=G+c(Y-G), which of course implies Y=G, a multiplier of one. This is not only the same result as given by the Keynesian balanced budget multiplier, but the mechanics are identical. Consumption does not change at all: higher period 1 income offsets the higher taxes. We do not need to worry about any knock on effects in period 2, because permanent income ends up unchanged. So the simple Keynesian balanced budget multiplier need not be considered some ancient fossil that we are forced to teach undergraduate students, but a simple expression of what consumption smoothing implies in a particular context.
                We could get to the same result using consumption smoothing alone, by noting that consumption in period two is tied down by (classical) Y and permanent G. Second period consumption and the Euler equation then fixes period 1 consumption, as real interest rates are unchanged by assumption. So any change in government spending in period 1 leads to an equal increase in output.
Woodford, in section 2 of the paper noted by Krugman and myself, does something with similarities to this, but with more elegance. My period 2 becomes the steady state, a steady state in which (given the usual assumptions) the real interest rate equals the rate of time preference. With real interest rates fixed at this value in all periods, consumption is equal in all periods, so any temporary change in government spending leads to an equal temporary change in output. We get a multiplier of one. With this benchmark, it is then intuitive to see how the multiplier will fall if real interest rates are not constant but rise. Equally, if we are at a zero lower bound, the multiplier will be greater than one because higher output generates inflation, which reduces real rates.