Bad News in the Great Depression, the Great Recession, and Other US

Bad News in the Great Depression, the Great Recession, and Other U.S. Recessions: A Comparative Study

Jean-Paul L’Huillier and Donghoon Yoo∗

February 2016

Abstract

In economic recessions consumption usually drops in tandem with other aggregate quantities as output or employment. Following the permanent income hypothesis, these drops can be rationalized by the idea that consumers have pessimistic views about their long-run income. Using a standard signal-extraction model, we show that this pessimism can be due either to a persistent fall of aggregate productivity before and during the recession (signaling a future decline of income), or to other negative information unrelated to fundamentals, which we label “bad news”. We classify U.S. recessions (from 1919 to 2015) according to a bad news index that reﬂects this negative information. We ﬁnd that both the Great Depression and the Great Recession score highest in this index. The index is such that we can rule out that this is due merely to the length or the depth of these recessions. Instead, these two recessions are similar in that both were aggravated by a wave of pessimism about future income which cannot be related to contemporaneous fundamentals.

Keywords: recessions; permanent income hypothesis; news and noise.

∗Einaudi Institute for Economics and Finance, Via Sallustiana, 62, 00187 Rome, Jean- [email protected]; and University of Lausanne, Quartier UNIL-Dorigny, 1015 Lausanne, [email protected]. We would like to thank Daniele Terlizzese, Robert Waldmann, and participants at the conference “Large-scale Crises: 1929 vs 2008” for helpful comments.

1 1 Introduction

Aggregate consumption fluctuations not only depend on economic fundamentals but are also heavily affected by swings of consumers’ perceptions of the current and future state of the economy. Originally advanced by Pigou (1927) and Keynes (1936), and later rejuvenated by Beaudry and Portier (2004), the expectation- driven business cycle hypothesis suggests that fluctuations could arise due to expectations about future fundamentals. The purpose of this paper is to examine the role of consumers’ perceptions about the state of the economy on the behavior of consumption in the Great Recession and in the Great Depression, the two large scale crises over the last century and to compare them with the experiences of other U.S. recessions. Following Blanchard, L’Huillier, and Lorenzoni (2013), we base our inference on the permanent income hypothesis, allowing for noisy signals about future income, which in the model is determined by productivity. Consumers and firms decide their current spending by solving a signal extraction problem. The signal extraction problem involves two types of information. First, there is productivity, composed of a permanent and transitory component. Second, there is a noisy signal about the permanent component of productivity. A shock to the signal is able to influence beliefs about the future level of income and thereby distort agents’ expectations. Our key point of departure from Blanchard et al. (2013) is the classification of the sample into periods of “bad” news and periods of “good” news beyond the information conveyed by fundamentals (that is productivity). This means, for a given period, we compute the behavior or consumption warranted by the observation of productivity and compare it with the actual realized level of consumption. If the realized level of consumption is below (above) the one warranted by productivity, this is evidence that consumers received bad (good) news about the future through the signal.1 Based on this simple idea, we study whether U.S. recessions are mostly driven by persistent falls in productivity (letting consumers infer that their income will fall in the future and thereby triggering a recession), or whether they are driven by other information that cannot be explained by looking at the

1Notice that this is diﬀerent from just a negative (positive) signal (using the notation in Blanchard et al. 2013, st < 0 (st > 0)).

2 dynamics of productivity alone. We perform this exercise on each recession in isolation and compute a bad news index for each. This allows us to compare recessions on this dimension. Our investigation requires an initial technical step which is to show that our decomposition of Bayesian inference into the beliefs obtained by the observation of productivity alone, and beliefs obtained by the observation of the signal afterwards is equivalent to the inference obtained by the usual updating using both signals simultaneously. Our second step in the paper is to proceed to estimation. We estimate a simple permanent income consumption model on U.S. quarterly data from 1919 to 2015. Consistent with previous work (Blanchard et al. 2013; L’Huillier 2012; Yoo 2015), we find that consumers’ belief updating and consumption spending respond more to noisy information than to observed productivity at high frequencies. We then estimate the shocks to productivity and to the signal using a Kalman smoother. This reveals that an overwhelming majority of the Great Depression and the Great Recession are associated with consumers receiving bad news about the state of the economy. Of the fourteen quarters of the Great Depression, only one period is associated with consumers receiving good news, and during the Great Recession, consumers always received bad news about the state of the economy. This implies that during these two episodes noisy information worsened the economic slowdown. Interestingly, not all recessions are so clearly related to consumers receiving bad news about the state of the economy. In fact, in some recessions consumers actually receive good news about future fundamentals. Our main finding in this paper is that the Great Depression and the Great Re- cession are the two recessions associated with the highest amount of bad news. We establish this result by constructing a bad news index based on a (standardized) sum of the bad news received in each recession. Table 1 shows U.S. recessions ranked according to this index. We find that the Great Depression and the Great Recession are have a similar score in our bad news index. Also, they are different from other U.S. recessions because all other recessions did not feature such a high amount of drops in consumption that one cannot explain with fundamental information. Several other works have claimed that the Great Depression and the Great Recession are similar in many dimensions. For instance, Gallegati, Gatti, Gaffeo,

3 Table 1: Standardized News Index for U.S. Recessions

Recession Dates Duration Standardized News

Great Recession 2007:Q4–2009:Q2 7 -0.0220 Great Depression 1929:Q3–1933:Q1 15 -0.0207 Early 1990s (Gulf War) 1990:Q3–1991:Q1 3 -0.0180 Double-dip Recession (Volcker) 1980:Q1–1982:Q4 12 -0.0154 1937–38 1937:Q2–1938:Q2 5 -0.0119 Oil Crisis 1973:Q4–1975:Q1 6 -0.0103 1920–21 1920:Q1–1921:Q3 7 -0.0087 1953–54 1953:Q2–1954:Q2 5 -0.0085 Monetary Recession of 1960–61 1960:Q2–1961:Q1 4 -0.0075 Recession of 1958 1957:Q3–1958:Q2 4 -0.0062 1926–27 1926:Q3–1927:Q4 6 -0.0012 Dot-com Bubble 2001:Q1–2001:Q4 4 0.0010 1948–49 1948:Q4–1949:Q4 5 0.0016 Recession of 1969–70 1969:Q4–1970:Q4 5 0.0025 1923–24 1923:Q2–1924:Q3 6 0.0048 1945 1945:Q1–1945:Q4 4 0.0292

Notes: Recessions start at the peak of a business cycle and end at the trough. The duration is in quarters. and Gallegati (2015) stress credit booms as a lead-variable for big crises, Cao and L’Huillier (2015) emphasize the technological booms preceding crises, Anderson, Bordo, and Duca (2015) suggest that sharp increases in risk premia and declines in M2’s velocity were notable feature of the onset of the two large scale crises; Fratianni and Giri (2015) highlight the importance of tight money triggering the crises, of sudden arrest in capital flows inducing balance-of-payments crises, and of the impacts driven by a banking crisis among others; Bianchi (2015) documents similarities between these rare events by examining the behavior of financial mar- kets with a Markov-switching vector autoregression (MS-VAR). Our contribution to this body of work is to emphasize yet another dimension in which these two important U.S. recessions are similar, mainly that it is difficult to rationalize the associated drops in consumption by appealing to contemporaneous fundamentals, and this more than in other U.S. recessions. This paper closely follows a revival in macroeconomic models with imperfect information initiated by Mankiw and Reis (2002), Woodford (2003), Hellwig (2005),

4 Bacchetta and van Wincoop (2006), among others. Within this literature, we follow a body of empirical papers using signal extraction in DSGE models, see Lorenzoni (2009), Boz, Daude, and Durdu (2011), Barsky and Sims (2012), and other papers cited above. Methodologically, we attempt to disentangle contribu- tions of multiple signals by sequential filtering, in order to more closely examine the respective role of each signal on consumption fluctuations. Rest of the paper is organized as follows. Section 2 discusses the information structure and the model. This is followed by the solution of the model in Section 3, discussing consumers’ and the econometrician’s filters. Section 4 estimates the model and studies the empirical implications. Section 5 concludes.

5 2 The Model

2.1 Productivity Processes and Information Structure

Consider a “news and noise” information structure (Blanchard et al. 2013), where productivity at (in logs) is the sum of a permanent component xt and a transitory component zt:

at = xt + zt

Consumers do not observe these components separately. The permanent component follows a randomly changing trend due to a permanent shock:

∆xt = ρx∆xt−1 + εt (1)

The transitory component follows the stationary process:

zt = ρzzt−1 + ηt

The coeﬃcients ρx and ρz are in [0, 1), and εt and ηt are i.i.d. Gaussian (per- 2 2 manent and transitory productivity) shocks with variances σε and ση. Similar to Blanchard et al. (2013), we assume that

ρx = ρz ≡ ρ (2) and that the variances satisfy the following restriction,

2 2 2 ρσε = (1 − ρ) ση (3) to ensure that the univariate process for at is a random walk, that is

E[at+1|at, at−1, ...] = at (4) which satisﬁes the following conditions:

2 2 2 σ = (1 − ρ) σu (5)

2 2 ση = ρσu (6)

6 In addition to providing analytical convenience, this random walk property of productivity is broadly in line with actual aggregate labor productivity data.

Besides observing productivity level at, consumers also receive a noisy signal about the permanent component of productivity:

st = xt + νt

2 where νt is an i.i.d Gaussian (noise) shock with mean zero and variance σν. Methodologically, this noisy signal provides an additional source of information for consumers about the permanent component of productivity which can eventu- ally help the econometrician make inferences about the (unobserved) productivity trend by looking at the behavior of consumption. This model (implicitly) allows for a timing structure where there are two infor- mational subperiods. Thus, it is worthwhile to explicitly state consumers’ information set at diﬀerent times within a given period. First, the consumers’ information set at time t, It, includes current productivity, at, a noisy signal, st, and lagged information, It−1:

It = (at, st, It−1)

2 where I0 = (a0, s0). For a given variable χt, we deﬁne consumers’ expectations about the variable with information at time t as follows:

χt|t = E [χt|It] where E is the expectation operator. Similarly, since our focus is on separating the role of the noisy signal on consumption ﬂuctuations from that of productivity, we also consider consumers’ expectations about the variable χt with current productivity and lagged information:

χt|at = E [χt|Ωt] where Ωt is the information set including current productivity and lagged infor-

2Throughout the paper, we use the terms expectations and beliefs interchangeably.

7 mation:

Ωt = (at, It−1)

This implies Ωt ⊂ It and Ωt ∪ st ≡ It.

2.2 Consumption

In this economy, consumption is the only endogenous variable and the behavior of consumption is described by a random walk. Speciﬁcally, we assume that the consumers’ Euler equation is given by

ct = E[ct+1|It] (7)

The supply side is drastically simpliﬁed such that there is no capital and output is fully determined by the demand side where consumption is the only component of demand. Speciﬁcally, output in logs is equal to consumption in logs such that

yt = ct

and the labor input nt adjusts to produce output yt given current productivity at:

3 yt = at + nt

In addition, output returns to its natural level in the long run:

lim t[ct+j − at+j] = 0 (8) j→∞ E

From (7) and (8), we obtain

ct = lim t[at+j] (9) j→∞ E

Thus, consumption depends on consumers’ expectations about long-run productivity.4

3 This implies that the production technology in level is given by Yt = AtNt. 4Blanchard et al. (2013) show that this consumption model is the limit case for a standard New Keynesian model with Calvo pricing in which the frequency of price adjustment goes to zero. Similarly, Cao et al. (2016) show that it is the limit case of a small open economy RBC

8 3 Solving the Model

According to Equation (9), consumers form beliefs about long-run productivity and choose spending: Solving the model involves a signal extraction problem as consumers are to estimate (unobserved) permanent productivity components by processing information (to forecast long-run productivity). This is because long- run productivity is driven by permanent shocks and not by transitory ones to productivity. In this paper, we attempt to solve this signal extraction problem by assuming that consumers sequentially update beliefs and disentangle consumers’ beliefs updated with productivity from the ones updated with the noisy signal. Updating beliefs sequentially and simultaneously do not make any difference in terms of the end-of-period beliefs as all shocks in the model are assumed to be Gaussian. In addition, solving the model sequentially has one distinct advantage: We would be able to identify the contribution of two sources of information on consumption fluctuations separately. This results from a one-to-one mapping from consumers’ beliefs to consumption spending. For the sake of our analysis, we assume that there are two subperiods at time t such that at subperiod 1, consumers observe productivity variable at and at subperiod 2, consumers observe a noisy signal st. Consumers then choose spending at the end of subperiod 2. Figure 1 depicts the timing of belief updating and consumption spending at a given time t. The solution of the model, which can be obtained using the standard Kalman filter, solves consumption as a function of current and lagged beliefs about the permanent productivity and three shocks in the model - a permanent productivity shock (), a transitory productivity shock (η), and a noise shock (ν). First, as shown in (9), consumption depends on consumers’ beliefs about long- run productivity and using the definition of productivity in the long-run, we have consumption as a function of consumers’ contemporaneous beliefs about current and lagged permanent productivity:

1 c = x − ρx (10) t 1 − ρ t|t t−1|t model when the interest rate becomes insensitive to changes in debt holdings.

9 Figure 1: Timing of Belief Updating and Consumption

time t − 1 beliefs: E[x|Ωt] beliefs: E[x|It] consumption: ct t

Notes: Beliefs are ﬁrst updated with productivity at and then with the noisy signal st. Consumption ct is determined with full information It.

where xt|t and xt−1|t represent consumers’ beliefs about current and lagged permanent productivity, respectively. Appendix A discusses the derivation of the consumption equation (10).

Second, the dynamics of consumers’ expectations (xt|t and xt−1|t) can be obtained by solving the consumers’ Kalman filter. The novelty of our approach is that we attempt to disentangle the effects of two different signals, productivity

(at) and a noisy signal (st), on consumption fluctuations by updating beliefs sequentially. With the sequential belief updating consumers first update beliefs with current productivity at = xt + zt and then with a noisy signal st = xt + νt. It should be noted that reversing the order of the sequence does not alter consumers’ consumption choices as the exogenous shocks are assumed to be i.i.d Gaussian processes. 0 Now, let the state vector be xt = (xt, xt−1, zt) and the consumers’ beliefs in the last period (t − 1) be denoted by xt−1|t−1. Thus, at the first subperiod of time t (when consumers’ information set include only productivity at), by updating beliefs, we have

xt|at = Axt−1|t−1 + H(at − at|t−1) (11)

Kalman gain for observing productivity at, and A and H depend on the underlying parameters of the model.

Similarly, conditional on beliefs xt|at by updating beliefs with the noisy signal, we get

xt|t = xt|at + G(st − st|at ) (12)

0 where xt|t = (xt|t, xt−1|t, zt|t) is the consumers’ beliefs with full information

10 It (having access to an additional information st) and G is the Kalman gain of observing the noisy signal st which also depends on the underlying parameters of the model. Appendix B contains further details on consumers’ ﬁltering. Since the aim of this paper is to study the role of noisy signals in explaining consumption dynamics, we consider the level of spending consumers would have chosen with the information set Ωt, denoted here by ct|at :

1 c = x − ρx (13) t|at 1 − ρ t|at t−1|at

The interpretation is straightforward such that without observing a noisy signal st, consumers choose spending as a function of their beliefs about the current and lagged permanent productivity with the information set Ωt.

Similarly, consumption changes due to the noisy information deﬁned as ∆ct|st is given by:

1 ∆c = G1 − ρG2 s − x (14) t|st 1 − ρ t t|at where G1 and G2 are the first and the second components of G and respectively represent the gains of observing noisy signals on xt and xt−1. Equation (14) implies that an amount of consumption changes that cannot just be explained by fundamental information depends not only on a standardized news, the second-term of the right-hand side, but also on relative precision of such noisy information, which is reflected on the first-term of the right-hand side. In addition, it suggests whenever an observed noisy signal st is greater than xt|at , consumers’ beliefs about a permanent component xt updated with productivity observation, ∆ct|st would be positive and vice versa. Intuitively, when consumers receive good information about the state of the economy, they would be willing to increase spending and this corresponds to st > xt|at . It is also easy show that

5 ct = ct|at + ∆ct|st (15)

5 Using (13) and (14), we have

1  1 2  ct = xt|a − ρxt−1|a + G − ρG st − xt|a  1 − ρ t t t

11 Since we are interested in consumption changes, we also use ∆ct|at , consumption changes from the last period due to productivity observation:

∆ct|at = ct|at − ct−1

and from (11) and the deﬁnition of ct−1, we get

1 ∆c = H1 − ρH2 a − x (16) t|at 1 − ρ t t|t−1 where H1 and H2 are the ﬁrst and the second components of H and respectively represent the gains of observing productivity on xt and xt−1. Similar to (14),

Equation (16) indicates that whenever productivity at is greater than xt|t−1, the last period’s forecast on the permanent component, ∆ct|at would be positive and vice versa. Same reasoning holds here: When consumers receive good information compared to a benchmark (in this case, the last period’s estimate on xt), they would increase spending such that ∆ct|at > 0. Thus, we have disentangled consumption ﬂuctuations into the ones due to changes in actual productivity and the ones due to observed noisy signals and it is also straightforward to show that

∆ct = ∆ct|at + ∆ct|st (17)

Because the consumption variable is in logs, Equation (17) implies that we can easily decompose the rate of consumption growth into two sub-components.

3.1 News

The following deﬁnitions on belief updating are useful for our purposes.

Deﬁnition 1 (Bad news) Signals that consumers receive are regarded as bad- news when a noisy signal st is smaller than beliefs revised with productivity, xt|at : st < xt|at . from which using (12), we can show that consumption is a function of beliefs on permanent productivity as in (10).

12 Deﬁnition 2 (Good news) Similarly, signals are regarded as good news when a noisy signal st is greater than beliefs revised with productivity: st > xt|at .

The implication of above deﬁnitions can be best observed from (14). As pre- viously discussed, given that G1 > ρG2, receiving good news (st > xt|at ) implies that consumers choose to spend more than they would have just by observing productivity (ct > ct|at ). Similarly, when consumers receive bad news (st < xt|at ), consumers consume less than they would have consumed without observing the 6 noisy signal (ct < ct|at ). Giving a proper interpretation on what exactly these good and bad news mean requires careful reasoning. For example, bad news does not necessarily mean a short-term negative demand shock. Blanchard et al. (2013) suggest that a negative (positive) noise shock can be interpreted as a negative (positive) demand shock.

However, even with a positive noise shock, νt > 0, bad news can still arise as long as consumers’ beliefs about the fundamental after observing productivity is sufficiently high. When a substantial increase in productivity is observed, a positive demand shock does not necessarily generate good news. The definitions of good and bad news in this model, thus, are relative concepts. Figure 2 depicts the (linear) relationship between the types of news, a noisy signal, and a belief updated with productivity. The higher the belief updated with productivity (xt|at ), the larger a noisy signal has to be to deliver good news. Granted, if, ex-ante, consumers had a higher expectation about the future (a large positive xt|at ), outside information must be really good (a larger positive value of st) in order for the consumers to adjust their belief about the future upward.7 While providing good intuition, the bad and good news defined here do not fully quantify the nature of such news for a given recession since they are binary indicators. Thus, for a better quantification, we create a news index as follows.

Deﬁnition 3 (A standardized bad news index) Assume that a recession lasts

6Yoo (2015) also use the similar definitions to distinguish the types of news consumers receive when information is not only noisy but also ambiguous. 7 While we define the types of news in terms of the noisy signal st, we could as well define the news types with productivity at. Specifically, whenever productivity at is greater than consumers’ beliefs updated with the noisy signal xt|st , we would consider it good news and vice versa. However, since our aim is to study the role of noisy information on consumption fluctuations, we decide that it would be more intuitive to define the news types as illustrated above.

13 from time t to t + j, a standardized news index (for the recession) is given by

Pt+j s − x News Index = i=t i i|ai j + 1

When the index takes a large negative value, it implies that large drops in consumption experienced during recessions cannot be explained with fundamental information conveyed by a fall in aggregate productivity. On the other extreme, a large positive value of the index indicates that a fall in aggregate productivity accounts for the drop in consumption.

Figure 2: The Types of News

Good News

xt|at

Bad News

Notes: If st > xt|at , a noisy signal delivers good news. On the contrary, when st < xt|at , a signal disseminates bad news to consumers.

14 4 Results

We adopt the solution procedure described in the last section and proceed to estimate the model. Given consumers’ filtering discussed in Appendix B, we can represent the dynamics of the model in a state-space form with the appropriate observation equations, which in this case contains a productivity variable at and a consumption variable ct. In our model, consumers’ expectations become part of the unobserved state vector of the econometrician. The econometrician’s Kalman filter is used to construct the likelihood function and to estimate the model’s parameters. Appendix C contains detailed derivation of the econometrician’s filtering. Following Blanchard et al. (2013), our estimations include the demeaned first differences of the logarithm of labor productivity ∆at and those of the logarithm of per-capital consumption ∆ct. The simplicity of the model above allows to extract a significant amount of information using only these two series, which at the same time allows us to overcome important data limitations regarding the period of the Great Depression (i.e. it would difficult or just not be possible to estimate a medium-scale DSGE for this period.) The model is estimated through maximum likelihood. Productivity is assumed to follow random walk as in (4) and we estimate ρ, σu, and σν. The standard deviation of the shocks to productivity σ and ση are recovered from the estimated

ρ and σu according to (5) and (6). Our aim is to use a Kalman smoother to estimate the shocks to the permanent component of productivity, the temporary component, and the signal. Given the long sample use, we need to split it in several periods so that our estimates are not polluted by low-frequency shifts in the series. We report the results for three periods, one including the Great Depression (1919:Q1-1951:Q4), another including the Great Recession (1976:Q1-2015:Q1), and another the recessions happening in 1950s–1970s.8 We then compare the results for the two large scale crises and other recessions in the sample.

8An alternative approach would be to remove a ﬂexible trend from the series, as for instance in Garcia-Cicco, Pancrazi, and Uribe (2010).

15 4.1 The Great Depression

For the Great Depression, we construct the series for productivity by taking the log of per capita GDP (real GDP divided by the labor input) where the real GDP was obtained from the Gordon-Krenn data (Y) and the labor input series was taken from Kendrick (1961), Appendix A, Table XXIII, 2nd column (“Per- sons Engaged”). The consumption series is similarly obtained by taking the log of per capital consumption (real consumption expenditure divided by the total population) where the real consumption expenditure was also obtained from the Gordon-Krenn data (CD+CND+CS) and the population data was taken from the Historical National Population Estimates of the U.S. Census Bureau. The Reces- sion Indicators for the United States represents the periods of recession deﬁned by the NBER. The sample is from 1919:Q1–1951:Q4.

0.15

noisy signal updated belief -0.15 1920 1925 1930 1935 1940 1945 1950

Figure 3: Smoothed Belief and Noisy Signals: 1919Q1-1951Q4

Notes: Shaded areas indicate U.S. recessions. When a belief updated with productivity xt|at is greater than a noisy signal st, it delivers bad news.

0.1

with noisy signal with productivity -0.1 1920 1925 1930 1935 1940 1945 1950

Figure 4: Consumption Changes: 1919Q1-1951Q4

Notes: Shaded areas indicate U.S. recessions. The ﬁgure disentangles the consumption growth due to changes in aggregate productivity and to other negative information unrelated to fundamentals (news).

16 Table 2: Parameter Estimates, U.S. 1919-1951

Parameter Description Value s.e. ρ Persistence productivity 0.9750 0.0107 σu Std dev. productivity 0.0240 0.0011 σ Std dev. permanent shock (implied) 0.0006 - ση Std dev. transitory shock (implied) 0.0237 - σν Std dev. noise shock 0.0259 0.0153

Notes: σ and ση are obtained with the random walk assumption of productivity from (3). As they are indirectly recovered, no standard errors are given.

Table 2 reports the estimation results. The results show that the persistent productivity parameter is estimated at 0.975. Since the permanent and transitory productivity components are assumed to have the same persistence, both components are estimated to be very persistent. Due to the high persistent productivity process, the standard deviation for permanent productivity shocks is very small. On the contrary, the standard deviation for noisy shocks is estimated to be large at 2.59%. In order to examine the contribution of each signal on consumption ﬂuctua- tions in more detail, we consider two measures of consumption changes from the previous section: We obtain smoothed estimates of consumption changes due to productivity observations, ∆ct|at , and consumption changes due to noisy signal observations, ∆ct|st . Figure 3 shows the smoothed estimate of permanent productivity with the information set including current productivity at and the smoothed noisy signals st. Given the high persistence of productivity processes, consumers’ beliefs are very persistent. On the contrary, since the noisy signals are driven by a random noise shock, they are much less persistent. Second, we observe that there are extended periods in which consumers receive the same types of news. For example, during most of the early and mid 1920’s, consumers received good news about the permanent state of the economy whereas the period of World War II are mostly associated with consumers receiving bad news.

17 noise shocks are an important source of consumption volatility.9

4.2 The Great Recession

For the sample including the Great Recession, consumption variable is constructed by taking the first difference of the logarithm of the ratio of NIPA consumption to population whereas productivity variable is constructed by taking the first difference of the logarithm of the ratio of GDP to employment. Real personal consumption expenditure (PCECC96), real gross domestic product (GDPC1), employment (LNS12000000Q), and population (LNS10000000Q) series are from 1976:Q1 to 2015:Q1 and were taken from the U.S. Bureau of Economic Analysis for the first two series and from the U.S. Bureau of Labor Statistics for the next two series. In addition, the Recession Indicators for the United States represents the periods of recession defined by the NBER.10 Table 3 reports the estimation results. Similar to the results for the Great Depression, productivity processes are estimated to be very persistent at ρ = 0.957 and the standard deviation for permanent productivity shocks is very small. In addition, the standard deviation for noisy shocks is estimated at 1.39%.

Table 3: Parameter Estimates, US 1976-2015

Parameter Description Value s.e. ρ Persistence productivity 0.9572 0.0080 σu Std dev. productivity 0.0061 0.0003 σ Std dev. permanent shock (implied) 0.0003 - ση Std dev. transitory shock (implied) 0.0060 - σν Std dev. noise shock 0.0139 0.0042

Notes: σ and ση are obtained with the random walk assumption of productivity from (3). As they are indirectly recovered, no standard errors are given.

Figure 5 shows the smoothed estimates of permanent productivity with the information set including current productivity at and the smoothed noisy signals st. From the mid 1980’s and the early 1990’s to around the year 2000, consumers

9For example. Blanchard et al. (2013) demonstrate that noise shocks explain a substantial portion of short-term consumption ﬂuctuations. 10The only exception is the early 1980’s recession. We combine two recessions occurred in the early 1980’s to better characterize W-shaped recession.

18 mostly received good news about the permanent state of the economy whereas the late 2000’s are mostly associated with consumers receiving bad news.

Figure 6 shows the smoothed estimates of ∆ct|at and ∆ct|st . Similar to the results from the ﬁrst sample, consumption changes due to observing noisy signals,

∆ct|st , exhibits a higher volatility in comparison to consumption changes due to observing productivity, ∆ct|at .

0.1

noisy signal updated belief -0.1 1980 1985 1990 1995 2000 2005 2010 2015

Figure 5: Smoothed Belief and Noisy Signals: 1976Q1-2015Q1

Notes: Shaded areas indicate U.S. recessions. When updated belief with productivity xt|at is greater than the noisy signal st, the signal delivers bad news.

0.015

-0.005

with noisy signal with productivity -0.025 1980 1985 1990 1995 2000 2005 2010 2015

Figure 6: Consumption Changes: 1976Q1-2015Q1

Notes: Shaded areas indicate U.S. recessions. The ﬁgure disentangles the changes in consumption by belief updating with productivity and with the noisy signals.

However, it should be noted that relatively large changes in consumption due to noisy signal does not tell the whole story. For example, the eﬀects of observing two signals do not always go in the same direction. In the sample, approximately half the time, they move in the opposite directions. In other words, conditional on productivity observation, consumers on average have been equally likely to receive good and bad news.

19 4.3 Estimation Results for Other Recessions

This section summarizes the estimation results for the period of 1949-1969, where there are five recessions. Two estimations are conducted, one from (1949:Q1– 1968:Q4) and the other from (1969:Q1–1979:Q4). Consumption variable, as before, is constructed by taking the first difference of the logarithm of the ratio of NIPA consumption to population. Similarly, productivity variable is calculated by taking the first difference of the logarithm of the ratio of GDP to employment. Real personal consumption expenditure (PCECC96), real gross domestic product (GDPC1), and employment (LNS12000000Q) employment series are from 1949Q1 to 1979:Q4 and were obtained from the U.S Bureau of Economic Analysis for the first two series and from the U.S. Bureau of Labor Statistics for the last series. Population series was obtained from Blanchard et al. (2013), originally from the U.S. Bureau of Labor Statistics. Table 4: Parameter Estimates, US 1949-1979

1949–1968 1969–1979 Parameter Description Value s.e. Value s.e. ρ Persistence productivity 0.8630 0.0448 0.7372 0.0734 σu Std dev. productivity 0.0109 0.0007 0.0090 0.0009 σ Std dev. permanent shock (implied) 0.0015 - 0.0023 - ση Std dev. transitory shock (implied) 0.0101 - 0.0077 - σν Std dev. noise shock 0.0103 0.0047 0.0090 0.0039

Notes: σ and ση are obtained with the random walk assumption of productivity from (3). As they are indirectly recovered, no standard errors are given.

Table 4 reports the estimation results. The results show that the persistent productivity parameter is estimated at 0.863 and 0.737 respectively, which is com- parably less persistent than the ones estimated in two other periods. Also, the standard deviation for permanent productivity shocks are estimated somewhat larger at 0.15% and 0.23%.

4.4 Recessions Comparison

We now focus speciﬁcally on the recessions in the sample. Recessions are associated with signiﬁcant drops in output and the question is whether we are able

20 to identify an empirical regularity in the recessions in terms of the types of news that consumers have received.11 Table 5 shows some summary statistics of U.S. recessions in different periods. Table 6 indicates that vast majority of the two large scale crises in the sample, the Great Depression and the Great Recessions, are associated with consumers’ receiving bad news about the state of the economy. In fact, of the fourteen quarters of the Great Depression, only one period was associated with consumers receiving good news. Furthermore, during the Great Recession, consumers always received bad news. It shows that during these two historical episodes, the noisy information that consumers received worsened the economic slowdown. Specifically, computing ∆ct|st shows that by observing noisy signals consumption declined more than one percent (1.41%) per quarter on average during these large scale crises.12 Ta- ble 7 shows that these two large scale crises are associated with strong drops in consumption. We already ranked recessions according to the news index above (in Table 1). The Great Depression and the Great Recession are the two recessions having the lowest index value, indicating that the drops in consumption are the ones most difficult to explain using productivity. This is not due simply to the fact that the cumulated consumption drop in those recession was larger. There are some exam- ples of this. For instance, during the 1973-1975 Oil Crisis consumption dropped at least as much as during the Great Recession.13 Also, the index is standardized in the sense that it is an average of the bad/good news received during the whole length of the recession, and thus this finding is not due to the fact that these recession were long. Some other recessions strongly feature bad news as well, as for instance the recession in the early 1990s. A related paper here is Blanchard (1993), which associates this recession to a drop in demand. It is also important to emphasize that not all recessions are related to consumers receiving bad news about the state of the economy. Of all the recessions in

11This model is drastically simpliﬁed such that consumption is the only endogenous variable. But as argued by Blanchard et al. (2013), it is still a decent approximation to analyze ﬂuctuations, and this allows us to overcome some data limitations mentioned above. 12Bad news delivered from observing noisy signal account for 1.70% and 0.82% of consumption declines per quarter on average during the Great Depression and the Great Recessions. 13Cumulated consumption drop was 4.07% in the 1973–1975 Oil Crisis and 4.03% in the Great Recession.

21 Table 5: Summary Statistics

Variable Description Mean Std Obs

1919Q1-1951Q4 Full Sample

∆ct|at Consumption changes with at 0.00016 0.0066 131

∆ct|st Consumption changes with st 0.00062 0.0200 131 Recessions

∆ct|at Consumption changes with at -0.00178 0.0072 48

∆ct|st Consumption changes with st -0.00487 0.0190 48 Non-Recessions

∆ct|at Consumption changes with at 0.00127 0.0061 83

∆ct|st Consumption changes with st 0.00379 0.0201 83

1952Q1-1975Q4 Full Sample

∆ct|at Consumption changes with at -0.00055 0.0058 95

∆ct|st Consumption changes with st 0.00031 0.0066 95 Recessions

∆ct|at Consumption changes with at -0.00410 0.0052 24

∆ct|st Consumption changes with st -0.00357 0.0077 24 Non-Recessions

∆ct|at Consumption changes with at 0.00065 0.0055 71

∆ct|st Consumption changes with st 0.00161 0.0056 71

1976Q1-2015Q1 Full Sample

∆ct|at Consumption changes with at 0.00007 0.0027 156

∆ct|st Consumption changes with st -0.00003 0.0056 156 Recessions

∆ct|at Consumption changes with at -0.00159 0.0031 23

∆ct|st Consumption changes with st -0.00497 0.0079 23 Non-Recessions

∆ct|at Consumption changes with at 0.00019 0.0025 133

∆ct|st Consumption changes with st 0.00082 0.0047 133

Notes: Obs refers to the number of observations in the sample. We take a period to represent a quarter and the results are obtained from the demeaned series. the sample, if we remove the Great Depression and the Great Recession, about 40%

22 Table 6: News in the Great Depression and the Great Recession

29Q4 30Q1 30Q2 30Q3 30Q4 31Q1 31Q2 31Q3 31Q4 32Q1 News: ------32Q2 32Q3 32Q4 33Q1 08Q1 08Q2 08Q3 08Q4 09Q1 09Q2 News: - - - + ------

Notes: The signs - and + respectively denote bad and good news in a given quarter.

(29 out of 73 recession quarters) of time-periods consumers received good news. This suggests that not all recessions are associated with consumers having pessimistic beliefs about the state of the economy. Sometimes optimistic consumers (by receiving good news) adjust beliefs upward, even though permanent productivity drops. A clear example is the post-World War II recession. Another is the dot-com bubble recession of the early 2000s, in which aggregate investment falls strongly but consumption was rising together with the housing boom. We observe, however, that this is not the case for the two large scale crises in the sample. As Equation (14) suggests, from Table 7 we now observe that relative precision of such noisy signals matter. For example, the standardized bad new index for the Great Depression is higher than the one for the 1937-38 recession. However, as the relative precision of noisy signals in the 1937-38 recession (0.82) is greater than the Great Depression (0.37), consumption dropped more by observing noisy signals, which are not related to fundamental information, in the 1937-38 recession than in the Great Depression.

5 Conclusion

In this paper, we have focused on the relative contribution of productivity and noisy information on consumption ﬂuctuations in the permanent income model of consumption. This allows us to examine how much drops in consumption during recessions can be attributed to a persistent fall of aggregate productivity (fundamental information) or to other negative information unrelated to fundamentals, which we label “bad news”. Our results document that a large amount of consumption drops in the Great Depression and the Great Recession, cannot just be

23 Table 7: Consumption Changes in Recessions

Recession Dates Duration Average ∆ct|st

Great Depression 1929:Q3–1933:Q1 15 -1.70% 1937–38 1937:Q2–1938:Q2 5 -0.98% Great Recession 2007:Q4–2009:Q2 7 -0.82% 1920–21 1920:Q1–1921:Q3 7 -0.71% Early 1990s (Gulf War) 1990:Q3–1991:Q1 3 -0.67% 1953–54 1953:Q2–1954:Q2 5 -0.64% Oil Crisis 1973:Q4–1975:Q1 6 -0.61% Recession of 1958 1957:Q3–1958:Q2 4 -0.47% Double-dip Recession (Volcker) 1980:Q1–1982:Q4 12 -0.38% Monetary Recession of 1960–61 1960:Q2–1961:Q1 4 -0.14% 1926–27 1926:Q3–1927:Q4 6 -0.10% Dot-com Bubble 2001:Q1–2001:Q4 4 0.04% 1948–49 1948:Q4–1949:Q4 5 0.13% Recession of 1969–70 1969:Q4–1970:Q4 5 0.15% 1923–24 1923:Q2–1924:Q3 6 0.39% 1945 1945:Q1–1945:Q4 4 2.40%

Notes: Recessions start at the peak of a business cycle and end at the trough. The fourth column, Average ∆ct|st denotes the average consumption changed due to observing noisy signals in a given recession. explained by drops in actual aggregate productivity and that bad news heavily inﬂuenced agents’ pessimistic views about future income and reduced spending.

24 References

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25 Garcia-Cicco, J., R. Pancrazi, and M. Uribe (2010). Real Business Cycles in Emerging Countries? American Economic Review 100 (5). Hellwig, C. (2005). Heterogeneous information and the welfare eﬀects of public information disclosures. Mimeo, UCLA. L’Huillier, J.-P. (2012). Did the US consumer overreact? A test of rational expectations. Economics Letters 116 (2), 207–209. Lorenzoni, G. (2009). A theory of demand shocks. American Economic Re- view 99 (5), 2050–84. Mankiw, G. and R. Reis (2002). Sticky information versus sticky prices: a pro- posal to replace the New Keynesian Phillips curve. Quarterly Journal of Economics 117 (4), 1295–1328. Pigou, A. (1927). Industrial Fluctuations. MacMillan. Woodford, M. (2003). Interest and prices. Princeton University Press. Yoo, D. (2015). Ambiguous information, permanent income, and consumption ﬂuctuations. Mimeo.

26 A Consumption

Permanent income consumers choose consumption as a function of their beliefs about the long-run productivity:

ct = lim t [at+j] j→∞ E

Using the fact that productivity at is sum of two components xt and zt, we have

ct = lim t [xt+j + zt+j] j→∞ E where the right-hand side can simply be written as

lim t [xt+j + zt+j] = lim t [∆xt+j + ∆xt+j−1 + ··· + ∆xt+1 + xt + zt+j] j→∞ E j→∞ E

Taking out the last two terms on the right-hand side, we have:

j j j+1 lim t [xt+j + zt+j] = lim t ρ ∆xt+1 + ρ ∆xt + ··· + ∆xt+1 + lim t [xt] + lim t ρ zt j→∞ E j→∞ E j→∞ E j→∞ E from which, by using the deﬁnition of Et [xt] and the fact that ρ < 1, we get the following simpliﬁcation:

j lim t [xt+j + zt+j] = ρ lim t 1 + ρ + ··· + ρ ∆xt + xt|t j→∞ E j→∞ E

Therefore, consumers choose consumption spending as a function of their beliefs about current and lagged permanent productivity as follows:

ρ lim Et [at+j] = Et [∆xt] + xt|t j→∞ 1 − ρ ρ = x − x + x 1 − ρ t|t t−1|t t|t 1 = x − ρx 1 − ρ t|t t−1|t

27 B Consumers’ Kalman Filter

Consider the following dynamic system:

xt = Axt−1 + BVt

st = C1xt + D1Wt

0 0 and xt = (xt, xt−1, zt) , Vt = (t, 0, ηt) , Wt = νt, D1 = 1,

1 + ρ −ρ 0 1 0 0 h i     A =  1 0 0 ,B = 0 0 0 ,C1 = 1 0 0 0 0 ρ 0 0 1

Conditional on xt|at from (11), using (12) consumers’ end-of-period beliefs xt|t are:

xt|t = xt|at + G(st − xt|at )

= [I − GC1]xt|at + Gst (18)

where G is the gain of observing new information st.

From (11) consumers’ beliefs updated with current productivity xt|at are:

xt|at = Axt−1|t−1 + H(at − at|t−1)

= [I − HC2]Axt−1|t−1 + Hat (19) where H is the Kalman gain for observing productivity,

at = C2xt + D2Wt

0 h i and xt = (xt, xt−1, zt) , Wt = νt, C2 = 1 0 1 , D2 = 0.

Substituting xt|at from (19) into (18), we represent a vector of consumers’ expectations as follows:

xt|t = [I − GC1][I − HC2]Axt−1|t−1 + [I − GC1]Hat + Gst (20)

We can also show that beliefs updated sequentially and beliefs updated simul-

28 taneously are the same in terms of beliefs updated at the end of period and (in terms of) consumption spending.14

B.1 Kalman Gains

With sequential ﬁltering to obtain the Kalman gains G and H requires properly computing the time-invariant predicted covariance Pt|t−1 using the following Ric- cati recursion (by solving for Pt|t−1 = Pt+1|t):

2 where A, C1, C2, are from the model, Σ is the covariance matrix for Vt, R1 = σν, and R2 = 0. Then, we can compute the Kalman gains G and H:

−1 0 h 0 i H = Pt|t−1C2 C2Pt|t−1C2 + R2 0 0 −1 G = Pt|at C1 C1Pt|at C1 + R1

C Sequential Filtering for the Econometrician

The econometrician’s information set does not include noisy signals; instead, she observes consumption which is determined according to (10). Thus, she extracts consumers’ beliefs using all available information with the following Kalman ﬁlter such that given lagged beliefs, consumers’ beliefs updated with current productivity

14Changing the sequence of ordering to noisy signal and productivity does not aﬀect anything in terms of end-of-sequence beliefs updated and consumption spending decisions.

29 xt|at is given by

 x  x  x  t|at t−1|t−1 h i t−1 x  = A x  + H 1 + ρ −ρ −ρ x  + H + Hη (21)  t−1|at   t−2|t−1  t−2 t t

zt|at zt−1|t−1 zt−1

Similarly, conditional on xt|at , xt|t is given by

 x   x  x  t|t t|at h i t−1 x  = x  + G 1 + ρ −ρ 0 x  + G + Gη + Gν (22)  t−1|t  t−1|at   t−2 t t t

zt|t zt|at zt−1

E Denoting xt to represent the state vector of the econometrician where

E 0 xt = (xt, xt−1, zt, xt|t, xt−1|t, zt|t)

E and xt follows

E E 0 xt = Qxt−1 + R(t, ηt, νt) (23)

The matrices Q and R, which depend on the underlying parameters of the model, are given respectively by " # A 0 Q = QA

" # B R = R where Q, R, and A are given by " # 1 + ρ −ρ ρ Q = B 1 + ρ −ρ 0

" # " # " # 1 + ρ 0 0 1 + ρ 0 0 1 + ρ 0 0 R = B + B + B 1 + ρ 0 0 1 + ρ 0 0 1 + ρ 0 0

30 h i h i A = I − HC2 I − GC1 A

As the econometrician observes productivity and consumption, the observation equation reads as

E (at, ct) = T xt (24) where " # 1 0 1 0 0 0 T = 0 0 0 1/ (1 − ρ) ρ/ (1 − ρ) 0 Thus, econometrician’s ﬁltering can be solved with (21), (22), (23) and (24).

D Other Mathematical Notes

D.1 Equation (15)

From (11) and (12), we have

such that ct = ct|at + ∆ct|st .

15 We also use the fact that st|at = xt|at .

31 D.2 Equation (16)

From (11) and using the fact that

1 c = x − ρx t−1 1 − ρ t−1|t−1 t−2|t−1 we have

1 ∆c = x − ρx + x − ρx t|at 1 − ρ t|at t−1|at t−1|t−1 t−2|t−1

Since, from (9), we have