VOL. 7I NO. 2 THE ECONOMICS OF RECESSIONS on of the desired capital stock-still holds constant. Aggregate consumption however nd there can be substantial anticipated grows at rate y: disregarding the change in movements in investment he consumption pool is clearly not innocu- What is the empirical evidence on o? ous. If aggregate income has also a stochas E uations such as(2) have recently been tic component, then to the extent that the estimated and their results are puzzling: they expected consumption of those who start ield implausibly low values of usually consuming is different from the consump- round. 05. Such values of imply, as tion of those who stop, there will be some we have seen, very large adjustment costs anticipated change in consumption and very small anticipated or unanticipated To see whether this anticipated change movements in investment; this is hard to can be large, consider a world in which one reconcile with the actual movements of in- agent is born each period and lives for N vestment. There are reasons to believe that periods, in which r=8=0 and in which ag these estimates of are biased downwards: gregate income follows Y,=a+pY-1+e the shadow price q is usually approximated each agent receiving 1/N of aggregate in- s by the ratio of market come. We can derive the behavior of as value to replacement cost which is likely to gregate consumption C, and look at the ratio be a mediocre proxy. The market value it- of the anticipated change in C to its total self is also surprisingly volatile during the change by computing sample period This is a puzzle in itself; see Robert Shiller, 1981. )Both reasons would E(E(C+1|92)-C)2 lead to a downwards bias in if investment does not follow a mar E(C+1-C)2 tingale, where did the martingale ap- For p=l, i.e if income itself follows a mar- proximationargument of the previous fine tingale, then AN=0: aggregate consumption tion go wrong? It went wrong in assuming also follows a martingale. If on the other that the fair game property of x, implies hand, p=0, then AN is given by that the present discounted value q, follows, even approximately, a martingale. Present discounted values do not in general follow martingales: the present discounted value of an AR(I) variable for example follows also an AR(I) with the same coefficient of serial As the sum in the numerator converges but correlation. This was emphasized by Shiller the second sum in the denominator d (1979, Appendix A), but the mistake is still verges, AN tends to zero as n gets large quite frequently made This implies that the martingale approxima- tion is correct for large N. If we assume for IV. Anticipated Movements in Consumption example that agents consume for 50 years e get Aso=7 percent and the martingale The story is different for consumption. approximation is quite good. To reject the Under the life cycle hypothesis and the ad- martingale result, we therefore have to reject ditional assumptions made in Section I, some of the assumptions made in Section I individual consumption indeed follows a An obvious candidate is the implicit as- martingale. Is it true however of aggregate sumption that wealth can be negative. What consumption Can we really disregard the happens if wealth cannot be negative for an effects of the change in the consumption individual, if there are liquidity constraints? pool? Suppose, for example, that aggregate Consider an individual for whom 8=r,so ncome is deterministic and grows at rate y. that in the absence of liquidity constraints, Suppose also that r=8 so that the consump- his consumption follows a martingale. How on of each individual is constant. If we will he plan consumption if he expects to be look at the total consumption of the agents liquidity constrained? He will still never an present in two successive periods, it is ticipate to decrease his consumption: if he