State-Dependent Pricing and the Paradox of Flexibility Luca Dedola and Anton Nakov ECB and CEPR May 24 Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 / 28
Policy rates in major economies have been constant for years US UK EA 6 6 5 5 4 3 2 5 4 3 2 4 3 2 26 27 28 29 2 2 22 23 24 26 27 28 29 2 2 22 23 24 26 27 28 29 2 2 22 23 24 JP.6.5.4.3.2.. 26 27 28 29 2 2 22 23 24 SW 2.8 2.4 2..6.2.8.4. 26 27 28 29 2 2 22 23 24 CA 5 4 3 2 26 27 28 29 2 2 22 23 24 Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 2 / 28
In theory leading to amplification of shocks Recent literature shows that ZLB leads to the amplification of shocks: Eggertsson and Krugman (22): paradoxes of thrift, toil, and flexibility Woodford (2), Christiano, Eichenbaum, Rebelo (2): fiscal multiplier is large at ZLB Erceg and Linde (24), Del Negro et al. (23), Kiley (24)... Mechanism: If it = i, then c t = γ T k= E tπ t+k + c t+t γ (E t p t+t p t ) Gt C t provided monetary policy implies that the price level at exit exceeds the current price level Then Y t G t > Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 3 / 28
The paradox of flexibility The paradox of flexibility : with i t = i increasing price or wage flexibility leads to a larger response of cumulative inflation and larger amplification I.e. it leads to a deeper recession and deflation when hit by a deflationary shock (Eggertsson and Krugman) Also leads to a larger government spending multiplier (Christiano et. al., Erceg and Linde) Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 4 / 28
What role for the form of nominal price rigidities? These papers all assume Calvo price setting Ohanian (22): Results depend on price rigidity in Calvo model, but incentives to change prices rise during turbulent/crisis periods In general the details of price setting at the micro level may matter a great deal for the dynamics of aggregate variables E.g. in a fixed menu cost model a la Golosov-Lucas (27) a strong selection effect makes the price level a lot more flexible than in a Calvo model with the same average frequency of adjustment Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 5 / 28
This paper Looks at the effects of a shock to government spending when the nominal interest rate is held constant for T periods Across three pricing models: Calvo, fixed menu cost, and encompassing model Encompassing model is smoothly state-dependent (Costain and Nakov, 2): adjustment probability is a smoothly increasing function of the adjustment gain We look at different monetary policy rules with/without CIR Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 6 / 28
Main finding With constant interest rates SDP can produce even larger amplification than Calvo The surprising results at the ZLB are a feature of sticky prices, not just an artifact of Calvo. Firm idiosyncratic shocks also affect aggregate price flexibility and amplification (Vavra, 22) Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 7 / 28
A very large literature ZLB/constant rate in (large) DSGE models Normative analyses Empirical studies about amplification at ZLB We do not pretend to say anything about what happened in reality; we only try to shed light on a theoretical mechanism Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 8 / 28
Outline of the talk Introduction 2 Model 3 Results 4 Conclusions Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 9 / 28
Model: added ingredients Model is a two-step deviation from textbook New Keynesian model: Idiosyncratic shocks State-dependent pricing We focus on dynamics under a constant interest rate for T periods (anticipated shocks to Taylor rule, Gaĺı 22) Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 / 28
Model: households The household s period utility is C γ t γ χn+ψ t + ψ + log(m t/p t ) Consumption is a CES aggregate of differentiated products { C t = } ɛ C ɛ ɛ ɛ it di The household s nominal period budget constraint is P it C it di + M t + Rt B t = W t N t + M t + T t + B t Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 / 28
Model: household optimality conditions Households choose C it, N t, B t, M t to maximize expected utility, subject to the budget constraint Optimal consumption across the differentiated goods C it = (P t /P it ) ɛ C t [ P ɛ it di P t ] ɛ Optimal labor supply, consumption, and money use χct γ Nt ψ = W t /P t [ ( )] = βr t E t P t C γ t+ / P t+ Ct γ M t /P t = C γ t R t / (R t ) Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 2 / 28
Model: monopolistic competitor firms Firm i produces output Y it = A it N it Productivity is idiosyncratic, log A it = ρ A log A it + ε a it, ε a it N(, σ2 a) Firm i faces demand from households, and the government, Y it = C it + G it The government s consumption basket is also a CES, { } G t = G ɛ ɛ ɛ ɛ it di Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 3 / 28
Model: monopolistic competitor firms Demand curve, Y it = (C t + G t )P ɛ t P ɛ it Period profits, U it = P it Y it W t N it Discount rate, Q t,t+ = β PtC γ t P t+ C γ t+ Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 4 / 28
Model: firm value function Value functionv (P, A, Ω) = U(P, A, Ω) + βe { Q t,t [V (P, A, Ω ) + EG(P, A, Ω )] A, Ω } where EG( ) is the expected gain from adjustment [ D(P, A EG(P, A, Ω, Ω ] ) ) λ W (Ω D(P, A, Ω ) ) D(P, A, Ω ) max P V (P, A, Ω ) V (P, A, Ω ) Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 5 / 28
Model: adjustment function λ(l) increases with the gain from adjustment L In particular, we postulate λ (L) λ ( λ) + λ (α/l) ξ where L is the relevant state With ξ, λ (L) = λ Calvo With ξ, λ (L) = {L α} Fixed menu cost Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 6 / 28
Model: adjustment function and histogram fit Density.25.2.5. Price changes: models vs data AC Nielsen FMC Calvo SSDP Probability of adjustment.9.8.7.6.5.4.3 α=.3, λ=.89 ξ=5 ξ=.5 ξ= ξ=.23 (SSDP).5.2..5.5 Size of log price changes.2.4.6.8. Loss from inaction Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 7 / 28
Model: monetary policy and government spending The monetary authority follows a Taylor rule R t R = [ (Pt ) ] φr /P φπ ( ) φr T t Rt Π where ε R t i are anticipated shocks Government spending ( ) Gt log G = ρ G log with ε G t N(, σ 2 G ). R ( Gt G i= ) + ε G t exp(ε R t i) Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 8 / 28
Calibration Discount factor β 2 =.4 Golosov-Lucas (27) CRRA γ = 2 Ibid. Elast. of subst. ɛ = 7 Ibid. Labor supply elast. ψ = Inflation target Π = AC Nielsen Inflation reaction φ π = 2 Length of CIR period T = {24, 36} Erceg and Linde (24) Persistence of G t ρ G =.9 Ibid. Persistence of A it ρ A =.9 Costain-Nakov (2) Std. dev. of A it σ A =. Ibid. State dependence ξ = {,.23, } Ibid. Fixed menu cost α =.4 Ibid. Calvo frequency λ =. Nakamura-Steinsson (28) Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 9 / 28
Preliminaries: textbook Calvo model The flexible price multiplier is (Woodford, 2) Γ = γ γ + ψ Log-linearized consumption Euler equation Phillips curve ( g t = Gt Ḡ Ȳ ; σ = γ ) : y t g t = E t (y t+ g t+ ) σ (i t E t π t+ r) π t = κ β j E t (y t Γg t ), j= where κ = ( α)( αβ)(γ + ψ)/α Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 2 / 28
Preliminaries: textbook Calvo model with Taylor rule Under a simple Taylor rule we have ( ) ( ) γ µ TR g t = (φ π ) p t lim E tp t+t T Solution ( ) φπ ρ µ TR βρ κ + φ C ( Γ) = + ( ) < φπ ρ ( ρ) γ + βρ κ + φ C Higher κ (more flexibility) leads to smaller µ TR Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 2 / 28
Results: idiosyncratic shocks + Taylor rule: FMC vs Calvo Government spending (% of Y) FMC Calvo hetero Calvo homo.5..2 Consumption (% of Y).5 Output, Y (%).3 2 3.4 2 3 2 3.5 Inflation (pp, annualized) Nominal interest rate (pp, annualized) 3 Real interest rate (pp, annualized) 2.5 2.5.5 2 3 2 3 2 3.6 Intensive margin Selection effect Interquartile range of price changes.4.4.2.5.3.2. 2 3 Months 2 3 Months 2 3 Months Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 22 / 28
Preliminaries: textbook Calvo model with CIR Dynamics under CIR/ZLB General solution γ (y t g t ) = γe t (y t+ g t+ ) + E t π t+ y t g t = y t Γg t = π t βe t π t+ κ κ ( Γ) ρ ( ρ) ( βρ) γ κρ g t + a λ t + a 2 λ t 2 Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 23 / 28
Preliminaries: Woodford s special stochastic case Focus on case = ( ρ) ( βρ) γ κρ > Then λ, λ 2 > and so setting a, a 2 = ensures a unique bounded solution: κ ( Γ) ρ y t = g t + g t = µ ZLB g t Paradox of flexibility: as κ, + then µ ZLB + Ohanian: paradox is limited to >, otherwise for larger κ, µ ZLB is not well defined due to multiplicity of equilibria Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 24 / 28
Preliminaries: Erceg and Linde s perfect foresight solution Difference equations valid only up to T ; thereafter CB follows its policy rule which determines equilibrium upon liftoff: y t = ( ) µ ZLB κ ( Γ) ρ ρβλ ρ T t g t βλ 2 g t + λ π T + + ( βλ ) γ (y T + g T + ) ( ), βλ 2 γλ T t When T sufficiently large and κ such that +, solution close to µ ZLB (ρ < λ < ) For κ larger, such that <, ρ/λ >, backward explosion The multiplier grows with T, and the Paradox of flexibility is established for any κ Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 25 / 28
Results: Calvo + idiosyncratic shocks + CIR Government spending (% of Y) 2 Consumption (% of Y) 3 Output, Y (%).5.5.5 2 2 3 2 3 2 3 Inflation (pp, annualized) Nominal interest rate (pp, annualized). Real interest rate (pp, annualized).5 2 5 4.5 6 2 3. 2 3 8 2 3 Intensive margin Selection effect Interquartile range of price changes 5.5.5.5 2 3 4 Months 2 3 4 Months.5 2 3 4 Months Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 26 / 28
Results: FMC + idiosyncratic shocks + CIR Government spending (% of Y) FMC Calvo hetero Calvo homo.5 3 2 Consumption (% of Y) 3 2 Output, Y (%) 2 3 4 2 3 4 2 3 4 5 Inflation (pp, annualized) Nominal interest rate (pp, annualized).4 Real interest rate (pp, annualized) 2 5.2 2 4 5 2 3 4.2 2 3 4 6 2 3 4 3 Intensive margin Selection effect Interquartile range of price changes 5 2 5 5 2 3 4 Months 5 2 3 4 Months 5 2 3 4 Months Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 27 / 28
Conclusions Large amplification of shocks with CIR/ZLB is present also with SDP With active monetary policy under SDP fiscal multiplier is closer to flexible-prices (smaller) than Calvo But with CIR/ZLB it can be much larger, paradox of flexibility With CIR firm-level shocks increase aggregate price level responsiveness even in the Calvo model Dedola and Nakov (ECB and CEPR) SDP and the Paradox of Flexibility 5/4 28 / 28