The Epidemiology of Macroeconomic Expectations. Chris Carroll Johns Hopkins University

Transcription

1 The Epidemiology of Macroeconomic Expectations Chris Carroll Johns Hopkins University 1

2 One Proposition Macroeconomists Agree On: Expectations Matter Keynes (1936) Animal Spirits Keynesians (through early 70s) Adaptive Expectations Rational Expectations Models RBC Models RE plus flexible prices, perfect competition, optimization Dynamic New Keynesian Models RE plus imperfect competition, sticky prices 2

3 Almost No Modeling Of Actual Empirical Expectations Data! Michigan Survey conducted since 50s, Conference Board since 70s lots of objective questions A few papers testing rationality of various inflation forecasts Croushore (2001): No evidence against rationality of professional forecasters forecasts Household forecasts not as good Souleles (2001): Highly significant demographic differences in forecasts of macro vars 3

4 This Paper Tests and rejects rationality of household forecasts of inflation Proposes to replace rational with epidemiological expectations Typical HHs get their views from the news media, the sources of infection Not everybody reads every news story (infection rate is < 100 percent) News media get their views by talking to forecasters Forecasters views are rational 4

5 A Model of Household Inflation Expectations Not a complete DNK macromodel See Mankiw and Reis (2001a,b) HH expectations matter because they should affect wage contracts HHs are willing to sign; wages are 2/3 of expenses, so wages => prices 5

6 Epidemiology 101 SIR framework susceptible infected recovered Simplest case is common source Classic example: Legionnaire s disease Everybody not infected is susceptible Constant per-period prob of infection p N t = p S t No recovery lim t 2 Sick = p + p( 1 p) + p( 1 p) +... Sick t t = p ( 1 p) = t s= 0 1 s 6

7 Reinterpretation News stories: sources of infection Each period fraction λ encounter news article, become infected with that period s rational forecast News stories at t contain a forecast of inflation rate at t+1, N t [π t+1 ] the Fed is anticipating further disinflation from most recent report Population-mean expectations will be given by: M t [π t+1 ] = λn t [π t+1 ]+(1 λ) {λn t 1 [π t+1 ]+(1 λ)(λn t 2 [π t+1 ]+...)} 7

8 Equation Not Unique to This Paper Identical to equation used for expectations dynamics in Mankiw and Reis (2001a,b) M&R motivate it by suggesting that either info costs or processing costs make people update only occasionally Further back, it is very much like the Calvo (1983) specification of price dynamics 8

9 Simplifications Derivation implicitly assumed: Newspapers print forecasts for future periods out to People have perfect recall Simplifying assumptions: People believe that inflation has a fundamental component that follows random walk Actual inflation is fundamental plus a transitory shock π t = π f t + ɛ t π f t+1 = π f t + η t+1 π f t+2 = π f t+1 + η t

10 Augmented Dickey- Fuller Tests Lags Degrees of Freedom ADF Test Statistic This table presents results of standard Dickey-Fuller and Augmented Dickey-Fuller tests for the presence of a unit root in the core rate of inflation (results are similar for CPI inflation). The column labelled Lags indicates how many lags of the change in the inflation rate are included in the regression. With zero lags, the test is the original Dickey-Fuller test; with multiple lags, the test is an Augmented Dickey Fuller test. In both cases a constant term is permitted in the regression equation. The sample is from 1959q3 to 2001q2 (quarterly data from my DRI database begin in 1959q1. In order to have the same sample for all three tests, the sample must be restricted to 1959q3 and after.) One, two, and three stars indicate rejections of a unit root at the 10 percent, 5 percent, and one percent thresholds. RATS code generating these and all other empirical results is available at the author s website. Table 1: Dickey-Fuller and Augmented Dickey-Fuller Tests for a Unit Root in Inflation 10

11 The Evolution of Average Expectations M t [π t,t+4 ] = λn t [π t,t+4 ]+(1 λ)m t 1 [π t 1,t+3 ] M t [π t,t+4 ] = λn t [π t,t+4 ]+(1 λ)m t 1 [π t,t+4 ] These assumptions allow us to derive the first equation above Not in M&R Without these assumptions, the second equation obtains Roberts (1998) proposed the first equation, but without microfoundation M was population-mean inflation expectations; Michigan survey asks a question about expectations of inflation over the next year 11

12 What is N? Whatever people get from the News But newspaper stories on inflation usually quote forecasters about the outlook for future inflation So it s plausible that what readers glean is what forecasters think What forecasters think is measured quarterly by the Survey of Professional Forecasters For notational clarity, call SPF forecast as of time t S t 12

13 Sniff Tests Dependent Variable: π t,t+4 Constant π t 4,t 1 M t [π t,t+4 ] S t [π t,t+4 ] DW Stat R (0.526) (0.145) (0.204) (0.323) (0.153) (0.161) (0.545) (0.152) (0.261) (0.241) Dependent Variable: π t+4,t π t 2,t 1 Constant M t [π t,t+4 ] π t 2,t 1 S t [π t,t+4 ] π t 2,t 1 DW Stat R (0.158) (0.140) (0.131) (0.140) (0.189) (0.239) (0.219) 13

14 Granger Causality S Granger-causes M M does not Granger-cause S 14

15 15Baseline Results Estimating Mt[πt,t+4] = α0 + α1st[πt,t+4]+α2mt 1[πt 1,t+3]+ α3pt[πt 5,t 1]+ ɛt Eqn α0 α1 α2 α3 Durbin- Test R2 Watson StdErr p-value Memo: α0 =0 (0.19) α1 + α2 = 1 (0.09) (0.08) α1 =0.25 (0.07) (0.07) α0 =0 (0.20) (0.08) (0.09) α1 + α2 + α3 =1 (0.09) (0.08) (0.05) α3 =0 (0.27) (0.08) (0.11) (0.05) α2 + α3 = 1 (0.04) (0.05) Mt[πt,t+4] is the Michigan household survey measure of mean inflation expectations in quarter t, St[πt,t+4] is the Survey of Professional Forecasters mean inflation forecast; Pt is the published inflation rate for the most recent one-year period. All equations are estimated over the period 1981q3 to 2000q2 for which both Michigan and SPF inflation forecasts are available. All standard errors are corrected for heteroskedasticity and serial correlation using a Newey-West procedure (a Bartlett kernel) with four lags. Results are not sensitive to the choice of lags.

16 Implications M&R (2001a,b) work out implications if λ=0.25 Dynamics are much more plausible than those of the standard DNK model Fed Funds shocks do not cause instant large changes in inflation Costless disinflations are not feasible over medium run 16

17 Pushing the Model If people get their views from news stories, we should expect λ to depend on the intensity of news coverage about inflation Constructed index of number of front-page stories in NYT and Washington Post including the root inflation* 17

18 Inflation Rate vs News Coverage 18

19 Michigan vs SPF Forecasts 19

20 Statistical Evidence GAPSQ t =(M t S t ) 2 GAPSQ t = α 0 + α 1 NEWS t Estimating GAPSQ t = α 0 + α 1 NEWS t Sample α 0 α 1 D-W Stat R2 1981q3-2000q (0.26) (0.50) 1982q3-2000q (0.25) (0.46) Durbin- Q-Test Eqn Sample λ Watson p-value 1 All obs (0.066) 2 NEWS t > mean(news) (0.176) 3 NEWS t < mean(news) (0.077) 20

21 Extension to Unemployment Expectations Empirical evidence finds these are highly correlated with spending, esp. on durable goods Unemployment is also highly serially correlated, so same logic should lead to same estimating equation 21

22 Problem Michigan UE question is not about unemployment rate over the next year, but whether U will rise or fall Solution: Regress U t,t+4 - U t-4,t = γ 0 + γ 1 MU t Define M t [U t,t+4 ]= γ 0 + γ 1 MU t +U t-4,t Proceed as before using this definition of M t [U t,t+4 ] 22

23 Results: The Same! Durbin- Test Eqn α0 α1 α2 α3 R2 Watson StdErr p-value Memo: α0 =0 (0.29) α1 + α2 = 1 (0.07) (0.07) α1 =0.25 (0.07) (0.07) α0 =0 (0.18) (0.07) (0.07) α1 + α2 + α3 =1 (0.07) (0.09) (0.05) α3 =0 (0.18) (0.07) (0.09) (0.06) Estimating Mt[Ut,t+4] = α0 + α1st[ut,t+4]+α2mt 1[Ut 1,t+3]+ α3pt[ut 5,t 1]+ɛt Results: The Same! 23

24 Robustness Heterogeneity in λ Allowing people to learn from each other as well as news Allowing for neighborhood effects More likely to learn from someone close to you in some social space than from random person in population 24

25 Heterogeneous λ Population of P agents Each draws a λ from λi ( λ, λ) Each period, each agent i updates with probability λ i News series is actual inflation rate from 1960q1 to beginning of SPF in 1981q3, SPF afterwards Mean HH expectations calc d 25

26 Estimate Baseline Equation on Sim Data Estimating M t [π t,t+4 ]=α 1 S t [π t,t+4 ]+α 2 M t 1 [π t 1,t+3 ]+ɛ t λ Durbin- Range α 1 α 2 R2 Watson StdErr [0.25,0.25] (0.000) (0.000) [0.00,0.50] (0.010) (0.009) [0.20,0.30] (0.000) (0.000) [0.15,0.35] (0.001) (0.001) 26

27 The Cross Section of Inflation Expectations 27

28 Adding Memory Errors π f [ π ]ƒ Ψ f tt, + 4 t t, t+ 4 it, i = S log Ψ ~ N( 025,. ) 28

29 Social Learning Allow for person-to-person spread of inflation news in addition to infection from media Any two i,j in the pop can meet With probability p, news travels from person with more recent news to person with less recent Need to impose direction, because otherwise swapping info has no effect on agg dynamics 29

30 Baseline Equation Still Works Well Prob. of Durbin- Test Social Exchange α0 α1 α2 R2 Watson StdErr p-value p = α1 + α2 =1 (0.003) (0.003) α0 =0 (0.008) (0.006) (0.006) p = α1 + α2 =1 (0.001) (0.001) α0 =0 (0.004) (0.002) (0.002) Estimating Mt = α0 + α1st + α2mt 1 + ɛt Baseline Equation Still Works Well 30

31 Local Interactions You are closer to some people than others in a social sense More likely to communicate with them Simple way to capture is to imagine people distributed across a landscape, and communication occurs between neighbors 31

32 Details Agents distributed over a 500x500 lattice, one agent at each lattice point Fraction η of agents are wellinformed - learn new forecasts from the forecasters with 0 lag Others obtain news solely from neighbors (all 8 of them) News travels in concentric circles from well informed guys 32

33 33Estimating Baseline Equation Estimating Mt = α0 + α1st + α2mt 1 + ɛt Up-to-date Durbin- Test Agents α0 α1 α2 R2 Watson StdErr p-value η = α1 + α2 =1 (0.025) (0.035) α0 =0 (0.003) (0.001) (0.001) η = α1 + α2 =1 (0.017) (0.027) α0 =0 (0.005) (0.001) (0.001) Mt is the mean value of inflation expectations across all agents in the simulated population; St is the actual annual inflation rate from 1960q1 to 1981q2, and the SPF inflation forecast from 1981q3 to 2000q2. Estimation is restricted to the simulation periods corresponding to 1981q3 to 2000q2 for which actual SPF data are available. All standard errors are corrected for heteroskedasticity and serial correlation using a Newey-West procedure (a Bartlett kernel) with four lags. Results are not sensitive to the choice of lags.

34 Conclusions Empirical HH expectations data reject rationality very strongly Epidemiological expectations work remarkably well Empirical macro behavior is much more consistent with this model than with RE Next step Household micro data Explore macro consequences of deviations from common source 34