T HE Z ERO L OWER B OUND AND E NDOGENOUS U NCERTAINTY Michael Plante Federal Reserve Bank of Dallas Alexander W. Richter Federal Reserve Bank of Dallas Nathaniel A. Throckmorton College of William & Mary The views expressed in this presentation are our own and do not necessarily reflect the views of the Federal Reserve Bank of Dallas or the Federal Reserve System.
I NTRODUCTION • Considerable interest in understanding the relationship between uncertainty and economic activity • Several recent papers find a negative relationship in the data using various measures of uncertainty • DSGE literature uses stochastic volatility shocks to model uncertainty, which typically reduce economic activity • Literature primarily focuses on how economic activity responds to changes in specific types of uncertainty • This paper examines how recent events affected uncertainty and its correlation with real GDP growth P LANTE , R ICHTER , AND T HROCKMORTON : T HE ZLB AND E NDOGENOUS U NCERTAINTY
F INDING IN THE D ATA • Measures of uncertainty: ◮ Time-varying VAR with stochastic volatility ◮ Stock Market Volatility ◮ Survey-based forecast dispersion ◮ Macro uncertainty index from Jurado et al. (AER, 2015) • A stronger negative correlation between real GDP growth and uncertainty emerged in the data in 2008Q4 • Theory: ZLB constraint contributed to the stronger negative correlation because it restricts the ability of the central bank to stabilize the economy P LANTE , R ICHTER , AND T HROCKMORTON : T HE ZLB AND E NDOGENOUS U NCERTAINTY
T ESTING OUR T HEORY • Estimate a nonlinear DSGE model with a ZLB constraint ◮ Small-scale new Keynesian model ◮ Habit persistence, interest rate smoothing ◮ Preference, growth, and monetary policy shocks • Create a data-driven, forward-looking uncertainty measure ◮ Expected volatility of real GDP growth forecast errors • Results from our estimated model: ◮ Correlations with GDP growth near the values in the data ◮ Strong positive correlation between uncertainty measures ◮ Cross correlations with leads/lags of GDP growth indicate uncertainty arises due to what is happening in the economy P LANTE , R ICHTER , AND T HROCKMORTON : T HE ZLB AND E NDOGENOUS U NCERTAINTY
Relationship between Economic Activity and Uncertainty P LANTE , R ICHTER , AND T HROCKMORTON : T HE ZLB AND E NDOGENOUS U NCERTAINTY
VAR WITH S TOCHASTIC V OLATILITY • Following Primiceri (2005), we estimate a time-varying VAR with stochastic volatility using Bayesian methods: y t = b t + B 1 ,t y t − 1 + B 2 ,t y t − 2 + A − 1 t Σ t ε t , t = 1 , . . . , T � ′ , ε ∼ N (0 , 1) , � where y t = GDP Growth Inflation T-Bill 1 0 0 σ 1 ,t 0 0 , . A t = α 21 ,t 1 0 and Σ t = 0 σ 2 ,t 0 α 31 ,t α 32 ,t 1 0 0 σ 3 ,t • Calculate the correlation between real GDP growth and the standard deviation of the shock to output ( σ 1 ,t ) for each draw from the posterior distribution from 1986Q1-2014Q2 P LANTE , R ICHTER , AND T HROCKMORTON : T HE ZLB AND E NDOGENOUS U NCERTAINTY
TVP VAR E STIMATED V OLATILITY 1.5 1.1 ZLB period 1 1 Real GDP Growth (Data) 0.5 0.9 Volatility (Model) 0 0.8 -0.5 0.7 -1 0.6 -1.5 0.5 -2 0.4 -2.5 0.3 1988 1992 1996 2000 2004 2008 2012 P LANTE , R ICHTER , AND T HROCKMORTON : T HE ZLB AND E NDOGENOUS U NCERTAINTY
R EAL GDP VS . E STIMATED V OLATILITY Pre-ZLB Sample ZLB Sample Differences (1986Q1-2008Q3) (2008Q4-2014Q2) (ZLB - Pre-ZLB) Federal Funds Rate − 0 . 24 ** − 0 . 60 *** − 0 . 35 * Federal Funds Rate + − 0 . 21 * − 0 . 57 ** − 0 . 34 * Financial Uncertainty Shadow Rate − 0 . 24 ** − 0 . 60 *** − 0 . 35 * 10-Year T-Bill Rate − 0 . 25 ** − 0 . 61 *** − 0 . 35 * Real Rate − 0 . 23 * − 0 . 59 *** − 0 . 36 * P LANTE , R ICHTER , AND T HROCKMORTON : T HE ZLB AND E NDOGENOUS U NCERTAINTY
A LTERNATIVE M EASURES OF U NCERTAINTY • Real GDP is our main measure of economic activity ◮ Also examine industrial production • Popular measures of uncertainty: ◮ CBOE VXO index ◮ SPF real GDP forecast dispersion ◮ BOS forecast dispersion ◮ Jurado, Ludvigson, and Ng (JLN) Macro Uncertainty • Quarterly data: 1986Q1-2014Q2 • For each measure, calculate correlations with GDP growth P LANTE , R ICHTER , AND T HROCKMORTON : T HE ZLB AND E NDOGENOUS U NCERTAINTY
A LTERNATIVE U NCERTAINTY M EASURES VXO BOS FD 2 60 1 40 0 -1 20 -2 -3 0 1986 1990 1994 1998 2002 2006 2010 2014 1986 1990 1994 1998 2002 2006 2010 2014 SPF FD JLN 0.9 1.3 0.7 1.1 0.5 0.9 0.3 0.1 0.7 1986 1990 1994 1998 2002 2006 2010 2014 1986 1990 1994 1998 2002 2006 2010 2014 P LANTE , R ICHTER , AND T HROCKMORTON : T HE ZLB AND E NDOGENOUS U NCERTAINTY
RGDP G ROWTH VS . U NCERTAINTY VXO BOS FD SPF FD JLN Pre-ZLB Sample − 0 . 09 − 0 . 19 ** − 0 . 08 − 0 . 45 *** (1986Q1-2008Q3) ZLB Sample − 0 . 72 *** − 0 . 70 *** − 0 . 47 ** − 0 . 73 *** (2008Q4-2014Q2) Difference − 0 . 64 *** − 0 . 51 *** − 0 . 39 ** − 0 . 29 ** (ZLB − Pre-ZLB) Fisher z-transformation—tests whether the pre- and post-Great Recession correlations are significantly different: • 1% level: VXO and BOS FD • 5% level: SPF FD and JLN P LANTE , R ICHTER , AND T HROCKMORTON : T HE ZLB AND E NDOGENOUS U NCERTAINTY
IP G ROWTH VS . U NCERTAINTY VXO BOS FD SPF FD JLN Quarterly Data Pre-ZLB Sample − 0 . 11 − 0 . 19 ** − 0 . 26 *** − 0 . 64 *** (1986Q1-2008Q3) ZLB Sample − 0 . 74 *** − 0 . 59 *** − 0 . 61 *** − 0 . 78 *** (2008Q4-2014Q2) Difference − 0 . 62 *** − 0 . 40 ** − 0 . 34 ** − 0 . 14 (ZLB-Pre-ZLB) Monthly Data Pre-ZLB Sample − 0 . 10 * − 0 . 13 ** − − 0 . 41 *** (1986Q1-2008Q3) ZLB Sample − 0 . 50 *** − 0 . 38 *** − − 0 . 54 *** (2008Q4-2014Q2) Difference − 0 . 40 *** − 0 . 25 ** − − 0 . 13 (ZLB-Pre-ZLB) P LANTE , R ICHTER , AND T HROCKMORTON : T HE ZLB AND E NDOGENOUS U NCERTAINTY
Theoretical Model P LANTE , R ICHTER , AND T HROCKMORTON : T HE ZLB AND E NDOGENOUS U NCERTAINTY
N EW K EYNESIAN M ODEL The representative household chooses { c t , n t , b t } ∞ t =0 to maximize expected lifetime utility given by ∞ � ˜ β t [log( c t − hc a t − 1 ) − χn 1+ η E 0 / (1 + η )] , t t =0 where ˜ β 0 ≡ 1 and ˜ β t = � t j =1 β j for t > 0 subject to c t + b t = w t n t + i t − 1 b t − 1 /π t + d t Optimality implies w t = χn η t ( c t − hc a t − 1 ) , 1 = i t E t [ q t,t +1 /π t +1 ] , where q t,t +1 ≡ β t +1 ( c t − hc a t − 1 ) / ( c t +1 − hc a t ) is the pricing kernel. P LANTE , R ICHTER , AND T HROCKMORTON : T HE ZLB AND E NDOGENOUS U NCERTAINTY
N EW K EYNESIAN M ODEL • Firm optimality condition: � π t � π t +1 � π t π = 1 − θ + θw t � � π t +1 y t +1 � ϕ π − 1 + ϕE t q t,t +1 − 1 ¯ ¯ z t ¯ π π ¯ y t • Production Function y t = z t n t • Monetary policy rule ı, i ∗ i t = max { ¯ t } gc t − 1 )) φ c ) 1 − ρ i exp( ν t ) , t − 1 ) ρ i (¯ π ) φ π ( c t / (¯ i ∗ t = ( i ∗ ı ( π t / ¯ where i ∗ is the notional interest rate. P LANTE , R ICHTER , AND T HROCKMORTON : T HE ZLB AND E NDOGENOUS U NCERTAINTY
N EW K EYNESIAN M ODEL • Resource constraint: π − 1) 2 / 2] y t = y gdp c t = [1 − ϕ ( π t / ¯ t • Discount factor ( β ) follows an AR(1) process β ) ρ β exp( ε t ) β t = ¯ β ( β t − 1 / ¯ • Technology ( z ) follows a random walk: z t = z t − 1 g t g ) ρ g exp( υ t ) g t = ¯ g ( g t − 1 / ¯ • Exogenous state variables: β t , g t , ν t • Endogenous state variables: c t − 1 , i ∗ t − 1 • Policy functions: c t , π t P LANTE , R ICHTER , AND T HROCKMORTON : T HE ZLB AND E NDOGENOUS U NCERTAINTY
C OMPETITIVE E QUILIBRIUM Consists of sequences of quantities { ˜ λ t , ˜ c t , ˜ y t } ∞ t =0 , prices { w t , i ∗ t , π t } ∞ t =0 , and shocks { β t , g t } ∞ t =0 that satisfy: ˜ λ t = ˜ c t − h ˜ c t − 1 /g t y η t ˜ w t = χ ˜ ˜ λ t 1 = i t E t [ β t +1 (˜ λ t / ˜ λ t +1 ) / ( g t +1 π t +1 )] � π t � π t +1 � ˜ � � π t λ t � π t +1 y t +1 ˜ ϕ π − 1 π = 1 − θ + θ ˜ w t + ϕE t β t +1 − 1 ˜ ¯ ¯ ¯ π π ¯ y t ˜ λ t +1 π − 1) 2 / 2]˜ ˜ c t = [1 − ϕ ( π t / ¯ y t c t − 1 )) φ c ) 1 − ρ i exp( σ ν ν t ) t − 1 ) ρ i (¯ π ) φ π ( g t ˜ i ∗ t = ( i ∗ ı ( π t / ¯ c t / (¯ g ˜ g ) ρ g exp( ε t ) g t = ¯ g ( g t − 1 / ¯ β t = ¯ β ( β t − 1 / ¯ β ) ρ β exp( υ t ) P LANTE , R ICHTER , AND T HROCKMORTON : T HE ZLB AND E NDOGENOUS U NCERTAINTY
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