Empirical Macroeconomics

Transcription

1 Empirical Macroeconomics Francesco Franco Nova SBE April 22, 2013 Francesco Franco Empirical Macroeconomics 1/15

2 From Keynes to Friedman The amount of aggregate consumption mainly depends on the amount of aggregate income Keynes 1936 The relationship proved to be unstable across households and proportional over time Friedman (1957) PIH and Modigliani (1956) LCH provided a straightforward explanation Francesco Franco Empirical Macroeconomics 2/15

3 PIH In the PIH that we saw in the first part C = Y P.Nowcurrent income Y = Y T + Y P.ItisfairtoassumethatY T has mean zero and is uncorrelated with Y P. Consider now the regression C i = a + by i + e i using our assumptions we have that b OLS = Cov(Y, C) Var(Y ) = Var(Y P ) Var(Y P )+Var(Y T ) a OLS = C b OLS Ȳ =(1 b OLS )Ȳ P Francesco Franco Empirical Macroeconomics 3/15

4 The random walk hypothesis Hall s extension of the PIH predicts that when output declines unexpectedely, consumption declines only by the amount of the fall in permanent income. The empirical literature has focused on testing if predictable changes in income produce predictable changes in consumption. (The hypothesis of excessive sensitivity) Francesco Franco Empirical Macroeconomics 4/15

5 Hall the RWH implies that no information available attime t 1 can be used to forecast the change in consumption from t 1 to t Hall followed this approach and was unable to reject the RWH when using lagged C or Y.(butstockpricespredicted changes in consumption) Francesco Franco Empirical Macroeconomics 5/15

6 Campbell Mankiw CM test an alternative hypothesis: a fraction behaves simply (Keynesian) and the other follows the PIH C t C t 1 = (Y t Y t 1 )+(1 ) e t = Z t + v t where Z t and v t are surely correlated. Theory tells us that any variable that is known at time t 1isuncorrelatedwiththe residual. They find a between 0.4 and0.5 in function of the specification departures from RW PIH appears important Francesco Franco Empirical Macroeconomics 6/15

7 Shea s test using micro data Shea focuses on households in the PSID with wage-earners covered by long-term union contracts: the wage increases and indexations in contracts cause income growth to have an important predictable component. The regression of consumption growth on a measure of expected wage growth gives a coe cient of 0.89 (but significance is small). Another departure from RWH. Francesco Franco Empirical Macroeconomics 7/15

8 Shea s test using micro data Shea also controls fror liquidity constraints: divide the households according to wheter they have liquid assets. The coe cient is the same in the two groups. split the low wealth sample between expected change in wage is positive or negative. he finds if increase a coe cient of 0 and of 2.24 if decreases. The opposite of what liquidity constraints would suggest Francesco Franco Empirical Macroeconomics 8/15

9 Discussion many authors have focused on government policies that cause predictable income movements, tipycally reject PIH when predictable income changes are very large an periodic (seasonal) PIH come back Liquidity constraints: impact of changes in the credit limit of households credit cards (instrument) B it = b 0 L it + b 1 L it b 12 L it 12 + a Õ X it + e it the sum of b is They split the sample if utilization rate is above 90% the sum of b s is It remains positive for lower utilization rates but with a much smaller elasticity. Francesco Franco Empirical Macroeconomics 9/15

10 Risk Consider the Euler equation C t = fl E t Ë1 2 È 1 + rt+1 i Ct+1 where is the coe cient of RRA. Define gt+1 c = C t+1 C t express the previous equation E Ë (1 + r i )(1 + g c ) È = 1 + fl 1. You can Francesco Franco Empirical Macroeconomics 10/15

11 Risk Take a second order Taylor approximation E Ë r iè Ó Ë E [g c ] E r iè Ô E [g c ]+Cov(r i, g c ) + 1 Ó Ô 2 ( + 1) (E [g c ]) 2 + Var(g c ) ƒ fl when time is continuous E # r i$ E [g c ] and (E [g c ]) 2 drop. Francesco Franco Empirical Macroeconomics 11/15

12 Risk The approximated Euler equation becomes E Ë r iè ƒ fl + E [g c ]+ Cov(r i, g c ) 1 2 ( + 1)Var(g c ) and comparing two assets E Ë r iè E Ë r jè = Cov(r i, g c ) Cov(r j, g c ) = Cov(r i r j, g c ) Mehra and Prescott show that it is di cult to reconcile with observed returns on bonds and stocks as the implied is around 25...This is known as the equity-premium puzzle. Francesco Franco Empirical Macroeconomics 12/15

13 Equity Premium puzzle Figure : US equity premium Francesco Franco Empirical Macroeconomics 13/15

14 Equity Premium puzzle Figure : G4 equity premium Francesco Franco Empirical Macroeconomics 14/15

15 Equity Premium puzzle Table 4. U.S. Economy Sample Statistics, Statistic Value Risk-free rate, R f Mean return on equity, E(R e ) Mean growth rate of consumption, E(x) Standard deviation of growth rate of consumption, s(x) Mean equity premium, E(R e ) R f Figure : Calibration Francesco Franco Empirical Macroeconomics 15/15