Uncertainty Shocks In A Model Of Effective Demand

Uncertainty Shocks In A Model Of Effective Demand Susanto Basu Boston College NBER Brent Bundick Boston College Preliminary

Can Higher Uncertainty Reduce Overall Economic Activity? Many think it is an important driver of the current downturn I ve been emphasizing uncertainties in the labor market. More generally, I believe that overall uncertainty is a large drag on the economic recovery. Narayana Kocherlakota, November 22, 21 What s critical right now is not the functioning of the labor market, but the limits on the demand for labor coming from the great caution on the side of both consumers and firms because of the great uncertainty of what s going to happen next. Peter Diamond, October 31, 21

Transmission of Uncertainty to Macroeconomy Typical Partial Equilibrium Models Increased uncertainty Reduces consumption (through precautionary saving) Increased uncertainty Reduces investment (through real options effect) Intuitive Economy-Wide Effects Increased uncertainty Reduces consumption & investment Increased uncertainty Reduces total output, hours Y = C + I (+... ) Do these intuitive partial-equilibrium results hold in general equilibrium?

Flexible Price Model Intuition - Elastic Labor Supply W t L S (λ t ) L D (K t, Z t ) N t

Flexible Price Model Intuition - Elastic Labor Supply W t L S (λ t ) L D (K t, Z t ) N t

Previous Literature Most general-equilibrium models of uncertainty cannot produce simultaneous drops in output, consumption, investment, & hours worked Examples: Bloom, Floetotto, & Jaimovich (29), Chugh (21), Gourio (21), Gilchrist, Sim, & Zakrajšek (21) [for KPR utility] Several of these papers suggest that a simple representative-firm model cannot explain why uncertainty might be contractionary

Effects of Uncertainty with Demand-Determined Output How to restore primacy of reasoning from Y t = C t + I t? Our solution: Abandon short-run neoclassical assumption of full employment Examine uncertainty shocks in model where output is demand-determined in the short run (the Effective Demand of the title) Introduce endogenously-varying markups We do so by assuming nominal price rigidity Allows us to address the effects of uncertainty shocks at zero lower bound

Sticky Price Model Intuition (I) Labor demand for firm facing nominal rigidities: W t P t = 1 µ t Z t F 2 (K t, Z t N t ) µ t : Markup of price over marginal cost With sticky prices, precautionary working lowers wages & raises µ t Reduces labor demand, so Y t and N t may fall Specific example of general mechanism in Basu and Kimball (23)

Sticky Price Model Intuition (II) W t L S (λ t ) L D (K t, Z t ) N t

Sticky Price Model Intuition (II) W t L S (λ t ) L D (K t, Z t ) N t

A Mechanism with Broad Applicability Example: How can bad news about the future lead to declines in current activity in simple DSGE models? Bad news shifts labor supply outward: same analysis applies We know ways to get this result in (complex) neoclassical models Examples: Beaudry-Portier (27) & Jaimovich-Rebelo (29) If we think nominal rigidity is necessary to explain the estimated effects of monetary shocks, then we should use the same model to examine effects of other shocks

We Show Increased uncertainty lowers Y, C, I, & N when prices are slow to adjust Same shock raises Y, I, and N in the same model with flexible prices Uncertainty can be associated with future technology or demand We calibrate the model to reproduce the increase in uncertainty about future stock returns in the Great Recession Model predicts demand uncertainty shocks are quantitatively significant Effects are noticeably larger if monetary policy doesn t lower interest rates (for example, if constrained by the zero lower bound)

Model Summary New-Keynesian sticky price model with capital Shares features with models of Ireland (23, 21) & Jermann (1998) Household holds equity shares and one-period risk-free bonds Firms owns capital stock, issue debt, & pay dividends 1st & 2nd moment shocks to technology & discount factors (demand) All shocks are persistent, transitory, and independent

Representative Household Household maximizes lifetime utility from consumption and leisure { } max E t β s Ct+s 1 σ (1 N t+s ) η(1 σ) a t+s 1 σ s= Subject to budget constraint C t + P E t P t S t+1 + 1 R R t B t+1 = W ( t D E N t + t P t P t + P t E ) S t + B t P t Stochastic process for preference (demand) shocks ln(a t ) = ρ a ln(a t ) + σ a t ε a t ε a t N(, 1) ln(σ a t ) = (1 ρ σ a)ln(σ a ) + ρ σ aln(σ a t 1) + σ σa ε σa t ε σa t N(, 1)

Representative Goods-Producing Firm (I) Firm owns capital stock K t (i) & employs labor N t (i) Quadratic cost of changing nominal price P t (i) φ P 2 [ ] 2 Pt (i) ΠP t 1 (i) 1 Y t Cobb-Douglas production function subject to fixed costs Y t (i) = K t (i) α [Z t N t (i)] 1 α Φ Adjustment costs to changing rate of investment ( K t+1 (i) = (1 δ)k t (i) + I t (i) 1 φ I 2 ( ) ) 2 It (i) I t 1 (i) 1

Representative Goods-Producing Firm (II) Firm i chooses N t (i), K t+1 (i), I t (i), and P t (i) to maximize cash flows { ( β s ) ( ) } λ t+s Dt+s (i) max E t s= Definition of firm cash flows [ D t (i) Pt (i) = P t P t λ t P t+s ] 1 θ Y t W t N t (i) I t (i) φ P P t 2 [ ] 2 Pt (i) ΠP t 1 (i) 1 Y t Firm issues 1-period bonds to finance fraction of capital stock each period B t+1 (i) = νk t+1 (i) Bonds earn 1-period real risk-free rate R R t

Representative Goods-Producing Firm (III) Total cash flows divided between payments to debt or equity Payments to equity D E t (i) P t = D t(i) P t ( ν K t (i) 1 Rt R K t+1 ) Leverage does not affect firm value or optimal firm decisions (Modigliani & Miller (1963) theorem holds) Equity becomes more volatile with leverage

Aggregation All users of final output assemble the final good Y t using the range of varieties Y t (i) in a CES aggregator [ 1 Y t = Aggregate production function Stochastic process for technology ] θ Y t (i) θ 1 θ 1 θ di Y t = K α t (Z t N t ) 1 α Φ ln(z t ) = ρ z ln(z t ) + σ z t ε z t ε z t N(, 1) ln(σ z t ) = (1 ρ σ z)ln(σ z ) + ρ σ zln(σ z t 1) + σ σz ε σz t ε σz t N(, 1)

Monetary Policy & National Income Accounting Nominal interest rate rule ln(r t ) = ρ R ln(r t 1 ) + (1 ρ R ) (ln(r) + ρ π ln(π t /Π) + ρ y ln(y t /Y t 1 )) National income accounting Y t = C t + I t + φ P 2 ( ) 2 Πt Π 1 Y t

Model Calibration and Solution Calibrate model parameters to estimates of Ireland (23, 21) Set fixed cost of production Φ to eliminate steady-state pure profits Calibrate leverage ratio =.45 Interested in determining impact of uncertainty shocks under two cases: 1. Flexible Prices (φ P = ) 2. Sticky Prices (φ P = 16) Solve model using 3rd-order approximation to policy functions of model Need 3rd-order or higher approximation to study uncertainty shocks

Second Moment Technology Shock with Flexible Prices 4.5 x 1 3 Output 1.5 x 1 3 Consumption.2 Investment 4 1 3.5 3 2.5 2 1.5 1.5.5 1 1.5 2.15.1.5.5 2.5 4 8 12 16 2 3 4 8 12 16 2 4 8 12 16 2 1.5.5 Markup 6 x Hours Worked 1 3 5 4 3 2 1 45 4 35 3 25 2 15 1 5 Volatility of Technology Flexible Prices 1 4 8 12 16 2 1 4 8 12 16 2 4 8 12 16 2

Second Moment Preference Shock with Flexible Prices.16 Output 4 x 1 3 Consumption.7 Investment.14 2.6.12.1.8.6.4 2 4 6.5.4.3.2.2 8.1 4 8 12 16 2 1 4 8 12 16 2 4 8 12 16 2 1 Markup 2 x 1 3 Hours Worked Volatility of Preference Shock 9 Flexible Prices 8.5.5 15 1 5 7 6 5 4 3 2 1 1 4 8 12 16 2 5 4 8 12 16 2 4 8 12 16 2

Second Moment Technology Shock with Sticky Prices (I).5 Output.5 Consumption.2 Investment.5.1.15.2.5.1.15.2.25.3.15.1.5.5.1.15.25 4 8 12 16 2.35 4 8 12 16 2.2 4 8 12 16 2.5.4.3.2.1 Markup.1.5.5.1.15.2.25 Hours Worked Volatility of Technology 45 Sticky Prices 4 Flexible Prices 35 3 25 2 15 1 5 4 8 12 16 2.3 4 8 12 16 2 4 8 12 16 2

Second Moment Technology Shock with Sticky Prices (II).1 Inflation.5 Nominal Interest Rate Real Interest Rate.1.2.3.4.5.1.15.2.25.3.1.2.3.4.5 4 8 12 16 2.35 4 8 12 16 2.5 4 8 12 16 2.5 Real Wage.1 Rental Rate of Capital Volatility of Technology 45 Sticky Prices 4 Flexible Prices.5.1.15.2.25.3.1.2.3.4.5 35 3 25 2 15 1.35.6 5.4 4 8 12 16 2.7 4 8 12 16 2 4 8 12 16 2

Second Moment Preference Shock with Sticky Prices (I).5 Output.5 Consumption.2 Investment.1.5.1.15.2.25.5.1.15.2.1.2.3.3.25.4.35 4 8 12 16 2.3 4 8 12 16 2.5 4 8 12 16 2.5.4 Markup.5.5 Hours Worked Volatility of Preference Shock 9 Sticky Prices 8 Flexible Prices 7.3.2.1.15.2.25 6 5 4 3.1.3 2.35 1 4 8 12 16 2.4 4 8 12 16 2 4 8 12 16 2

Second Moment Preference Shock with Sticky Prices (II).1 Inflation.5 Nominal Interest Rate Real Interest Rate.5.5.5.5.1.15.1.1.2.15 4 8 12 16 2.15 4 8 12 16 2.25 4 8 12 16 2.5 Real Wage.1 Rental Rate of Capital Volatility of Preference Shock 9 Sticky Prices 8 Flexible Prices.5.1 7.1.15.2.25.2.3.4.5 6 5 4 3.3.6 2.35.7 1.4 4 8 12 16 2.8 4 8 12 16 2 4 8 12 16 2

Uncertainty Shock Calibration Increased uncertainty can reduce Y, C, I, & N under sticky prices What is a reasonable-sized uncertainty shock in the data? What does model predict for an uncertainty shock of this size? Use VIX as measure of aggregate uncertainty VIX is forward-looking measure of S&P 5 return volatility

VIX & VIX-Implied Uncertainty Shocks 55 VIX Annualized S&P 5 Return Volatility 5 45 4 35 3 25 2 15 1 199 1992 1994 1996 1998 2 22 24 26 28 21 VIX Implied Uncertainty Shocks Estimate 4 reduced-form AR(1) model for quarterly VIX Vt D Standard Deviations 3 ln(v D 2 1 Results: V D = 2.4% ρ V =.83 σ V D =.19 ε V D t t ) = (1 ρ V )ln(v D ) + ρ V ln(v D t 1) + σ V D ε V D t, ε V D t N(, 1) : 1VIX-implied uncertainty shock 2

VIX & VIX-Implied Uncertainty Shocks 55 VIX Annualized S&P 5 Return Volatility 5 45 4 35 3 25 2 15 1 199 1992 1994 1996 1998 2 22 24 26 28 21 4 VIX Implied Uncertainty Shocks 3 Standard Deviations 2 1 1 2 199 1992 1994 1996 1998 2 22 24 26 28 21

Uncertainty Shock Calibration How do we calibrate the size and persistence of the 2nd moment shocks? Use 3rd-order perturbation method to generate model-implied VIX Household Euler equation for equity holdings: {( ) ( βλt+1 Dt+1 /P t+1 + P E )} 1 = E t+1/p t+1 t λ t Pt E /P t Return on equity R E t+1 D t+1/p t+1 + P E t+1/p t+1 P E t /P t Model-implied VIX V M t ( ) = 1 4 V ar t R Et+1

Uncertainty Shock Calibration Model-implied VIX has AR(1) law of motion in volatility shocks ˆV M t =... + η σa ˆσ a t 1 + η εa ε σa t + η σz ˆσ Z t 1 + η εz ε σz t Reduced-form AR(1) model for quarterly VIX V t ˆV D t =.83 ˆV t 1 D +.19ε V D t Calibrate size of uncertainty shocks in model to match VIX-implied results ε σa t = 1 Model-implied VIX 19% ε σz t = 1 Model-implied VIX 19% Set persistence of uncertainty shocks such that η σa = η σz =.83

Quantitative Implications of Uncertainty Shocks Did uncertainty play a role in the Great Recession? 3+ standard deviation VIX-implied uncertainty shock in Fall of 28 Little evidence of change in the volatility of technology shocks (Fernald (21) using Basu, Fernald, & Kimball (26) methodology) 3 standard deviation uncertainty shock to demand in model Peak drop in output of.9 percentage points Results suggest uncertainty contributed to severity of Great Recession

Uncertainty or Financial Market Disruptions? A false choice A financial market disruption is an event, which can have multiple effects Most analysis has focused on first-moment effects (higher cost of capital, tighter borrowing constraints, etc.) We analyze likely effects of the concurrent rise in uncertainty Increased uncertainty might also be due to financial disruptions

Uncertainty Shocks, Monetary Policy, & ZLB Monetary authority follows conventional active interest rate rule.1 Inflation.2 Nominal Interest Rate.3 Real Interest Rate.5.5.1.15.2.25.2.4.6.8.1.12.14.2.1.1.2.3.3 4 8 12 16 2.16 4 8 12 16 2.4 4 8 12 16 2 Helps stabilize economy by offsetting 2nd moment preference shock Real Wage Rental Rate of Capital Volatility of Preference Shock 9 Unconstrained 8.1.2 Constrained What if monetary authority is constrained by zero lower 7 bound on.2.4 6 nominal interest rates?.3.4 Preliminary results.5.6.8 1 5 4 3 2

Second Moment Preference Shock at ZLB (I) Output Consumption Investment.1.2.3.4.5.1.15.2.25.3.35.4.1.2.3.4.5.6.5 4 8 12 16 2.45 4 8 12 16 2.7 4 8 12 16 2.8.7.6.5.4.3.2.1 Markup.1.2.3.4.5.6 Hours Worked Volatility of Preference Shock 9 Unconstrained 8 Constrained 7 6 5 4 3 2 1 4 8 12 16 2.7 4 8 12 16 2 4 8 12 16 2

Second Moment Preference Shock at ZLB (II).1 Inflation.2 Nominal Interest Rate.3 Real Interest Rate.5.5.1.15.2.25.2.4.6.8.1.12.14.2.1.1.2.3.3 4 8 12 16 2.16 4 8 12 16 2.4 4 8 12 16 2.1.2.3.4.5.6 Real Wage.2.4.6.8 1 1.2 Rental Rate of Capital Volatility of Preference Shock 9 Unconstrained 8 Constrained 7 6 5 4 3 2 1.7 4 8 12 16 2 1.4 4 8 12 16 2 4 8 12 16 2

Conclusions Under reasonable assumptions, uncertainty can decrease Y, C, I, & N Effect is quantitatively significant, and is even larger if monetary policy is constrained from responding, as during the Great Recession Idea that good shock to marginal cost can reduce labor demand is a mechanism with broad applicability Modeling 2nd-moment shocks complements other work on crisis Uncertainty may explain some observed changes in asset prices and risk premia during the crisis