Preference Shocks, Liquidity Shocks, and Price Dynamics Nao Sudo 21st April 21 at GRIPS () 21st April 21 at GRIPS 1 / 47
Directions Motivation Literature Model Extracting Shocks (BOJ) 21st April 21 at GRIPS 2 / 47
Motivation (BOJ) 21st April 21 at GRIPS 3 / 47
Motivation I Short-run determinants of price dynamics According to classical monetary business model, P t = vm t c t. Lucas (198, AER) : Quantity theory of money holds only in the long-run. Segmented market model of Alvarez., Atkeson and Edmond (29, QJE) deliver the endogenous velocity dynamics. AAE with shocks to money supply and goods supply explain only half of the velocity variation in the data. Role of other types of shocks Is there room that shocks other than those to money and goods a ect price variation? Are these other shocks quantitatively important? (BOJ) 21st April 21 at GRIPS 4 / 47
Motivation II Velocity in long run and short run 3.9 Velocity.6 Velocity Original Series Business Cycle Component 4.4 4.1.2 Level 4.2 4.3 4.4 Deviation from Trend.2 4.5 4.6.4 4.7 197 198 199 2 21 Date.6 197 198 199 2 21 Date (BOJ) 21st April 21 at GRIPS 5 / 47
Contribution I We develop a DSGE model that focus on the source of price variations. Extension of the model of AAE (29, QJE). Shocks to transaction (liquidity shocks) and shocks to preference are considered. Liquidity shock (adverse shocks to credit service) A positive liquidity shock increases money demand in all agents in the economy, causing a decline of price and an upsurge of interest rate. Preference shock A positive discount factor shock decreases the velocity of agents with much money holdings and increases that of agents with less money holdings, reducing aggregate velocity and price. It leads to a decline of interest rate. (BOJ) 21st April 21 at GRIPS 6 / 47
Contribution II We distilled the liquidity shocks and preference shocks using the Japanese data from 1971Q1 to 27Q4. We evaluate the contribution of shocks to money supply, goods supply and these two shocks. Throughout the period, about half of price variations are explained by shocks to liquidity and shocks to discount factor. In 7s and 8s, shocks to discount factor are relatively important. In 9s and s, shocks to liquidity are relatively important. (BOJ) 21st April 21 at GRIPS 7 / 47
Literature (BOJ) 21st April 21 at GRIPS 8 / 47
Related Literature I Empirical studies for money and price Analysis on frequency domain: Money supply is responsible for price variation in low frequency, but not in high frequency (Assenmacher-Wesche and Gerlach, 27, JEEA; Assenmacher-Wesche, Gerlach and Sekine, 28, JJIE). Theory of money demand Simple cash in advance constraint : Hodrick, Kocherlakota, and Lucas (1991, JPE). Inventory model of money demand: Market segmentation generates the liquidity e ect (Grossman and Weiss, 1983, AER; Lucas and Weber, 21, AER; and AAE). (BOJ) 21st April 21 at GRIPS 9 / 47
Related Literature II Liquidity shocks Shocks to the credit service provided by nancial sector and money demand: Improvement in the productivity of nancial sector makes the credit-based transaction cheaper than money-based transaction (Benk, Gillman, and Kejak, 25, JMCB, 28, REDS; Ireland, 1994, AER). Shocks to the preference Christiano, Motto and Rostagno (27, JMCB) : HH starts to accumulate currency at the expense of demand deposits and other liabilities (time deposits). Christiano, Eichenbaum and Rebelo (29, WP) : HH attaches a larger utility weight on the consumption tomorrow. (BOJ) 21st April 21 at GRIPS 1 / 47
Model (BOJ) 21st April 21 at GRIPS 11 / 47
Model: Overview I Extension of AAE (29, QJE). Endowment economy where aggregate goods Y t and aggregate money M t are exogenously supplied. There are N agents in the economy, categorized by its type s. Each type of agent consumes c t (s) and holds Z t (s) of money. N N y t (s) = Y t = C t = c t (s), s=1 s=1 N Z t (s) = M t. s=1 Agents purchase goods using money holdings in his wallet. Agents are allowed to go to the ATM once a N periods to withdraw money. (BOJ) 21st April 21 at GRIPS 12 / 47
Model: Overview II Key feature of the model N agents have di erent size of money holdings and di erent pattern of consumption expenditure. Consequently, N agents have di erent size of individual velocity. Because agents have to use money over N periods, Money held by agent 1 Money held by agent 2 Money held by agent N Z t (1) > Z t (2)... > Z t (N). Individual velocity is written as velocity of agent 1 P t c t (1) Z t (1) velocity of agent 2 < P t c t (2) Z t (2)... < velocity of agent N P t c t (N). Z t (N) The aggregate velocity changes because of the compositional e ect. (BOJ) 21st April 21 at GRIPS 13 / 47
Model: Household I Maximization problem of agent that is s = 1 at period t is written as max s.t. (i) Budget constraint in the wallet β τ log c τ (s), τ=t N 1 θ t+j P t+j c t+j (s + j) M t (1). j= (ii) Budget constraint in the ATM at period for 8τ and for all s except s = 1. B τ 1 + i τ B τ 1 + P τ y τ (s) P τ c τ (s) (1 θ τ ). (BOJ) 21st April 21 at GRIPS 14 / 47
Model: Household II Eular equation for households s = 2,...N. 1 1 β t+1 θ t+1 λ t+1 (1) = c t+1 (s + 1) c t (s) θ t P t λ t (1) π t+1. Note that λ t (1) equals to the value of a dollar in the ATM for all agents. For θ t = 1, we have β t+1 = c t+1 (s + 1). π t+1 c t (s) Because (i) agents s = 2,...N cannot access to the ATM, and (ii) transaction requires cash, slope of consumption tilted with in ation rate π t. (BOJ) 21st April 21 at GRIPS 15 / 47
Model: Aggregate variables Nominal interest rate 1 + i t 1 = β t+1 c t (1) P t. 1 + i t c t+1 (1) P t+1 Nominal interest rate re ects the price of money in the ATM market. Velocity v t vt = P t N s=1 c t (s) N s=1 M t (s). (BOJ) 21st April 21 at GRIPS 16 / 47
Model: Shocks I Money supply shock µ m t. M t = µ m t M t 1 Money supply shock is market operation 6= helicopter money. Central bank supplies newly printed money into the ATM. Goods shock µ y t. Y t = µ y t Y t 1 = N µ y t y t 1 (s). s=1 (BOJ) 21st April 21 at GRIPS 17 / 47
Model: Shocks II Liquidity shock µ θ t. θ t+1 (s + 1) = µ θ t θ t (s). It rises the transaction based on money. Preference shock µ β t. β t+1 (s + 1) = µ β t β t (s). A rise in the discount factor increases the value of consumption tomorrow, reducing that of consumption today. (BOJ) 21st April 21 at GRIPS 18 / 47
Model: Working mechanism I Suppose N = 2. Then we have M t = Money held by agent 1 Z t (1) + Aggregate velocity is written as v t = P ty t M t = P tc t (1) + P t c t (2) = 2 s=1 M t Portion of money held by agent s Z t (s) M t Note that because θ t P t c t (2) = Z t (2), θ t P t c t (1) Z t (1) = Money held by agent 2 Z t (2). velocity of agent s P t c t (s) Z t (s). θ t P t c t (1) Z t+1 (2) + θ t P t c t (1) < θ tp t c t (2) Z t (2) (BOJ) 21st April 21 at GRIPS 19 / 47
Model: Working mechanism II A negative shock to money supply increases aggregate velocity. It reduces a portion of money held by agents with low velocity. v t+1 Portion of money held by agent 1< Z t+1 (1) + Z (1) M + Z t+1 (1) + Portion of money held by agent 2> Z t (2) M + Z t+1 (1) velocity of agent 1<1 Pc (1) Z (1) velocity of agent 2 =1 Pc (2) Z (2) (BOJ) 21st April 21 at GRIPS 2 / 47
Model: Working mechanism III A positive shock to goods supply lowers aggregate velocity. It reduces velocity of agents with low velocity. v t+1 Portion of money held by agent 1 Z (1) M velocity of agent 1, < Pt+1 c t+1 (1) Z (1) P t drops to clear the market. Under our parametrization, drop of P t is larger than an increase in c t+1 (1). (BOJ) 21st April 21 at GRIPS 21 / 47
Model: Working mechanism IV A positive shock to liquidity lowers aggregate velocity. It reduces a velocity of all agents. v t+1 Portion of money held by agent 1 Z (1) M + Portion of money held by agent 2 Z (2) M velocity of agent 1, < Pt+1 c t+1 (1) Z (1) velocity of agent 2 Pt+1 c t+1 (2) Z (2) Given Z (1) and Z (2), an increase in θ t+1 reduces the expenditure. P t+1 c t+1 (1) = Z (1) θ t+2p t+2 c t+2 (2) θ t+1 P t+1 c t+1 (2) = Z (2) θ t+1 (BOJ) 21st April 21 at GRIPS 22 / 47
Model: Working mechanism V A positive shock to discount factor lowers aggregate velocity. It reduces a velocity of agent that possess higher portion of money, and increases a velocity of agent that possess smaller portion of money. Because of the composition of money holdings, the former e ect dominates the latter. v t+1 Portion of money held by agent 1 Z (1) M + Portion of money held by agent 2 Z (2) M velocity of agent 1, < Pt+1 c t+1 (1) Z (1) velocity of agent 2 Pt+1 c t+1 (2). Z (2) (BOJ) 21st April 21 at GRIPS 23 / 47
Response to a contractionary money supply shock Money 2 Nominal Interest Rate 1 1.5 2 1 3.5 4 5 1 5 5 1 15 2.5 1 5 5 1 15 2 1 Price 2 Velocity 1 1.5 2 1 3.5 4 5 6 1 5 5 1 15 2.5 1 5 5 1 15 2 (BOJ) 21st April 21 at GRIPS 24 / 47
Response to a positive goods supply shock 1 Goods.5 Nominal Interest Rate.8.6.5.4.1.2.15 1 5 5 1 15 2.2 1 5 5 1 15 2 Price Velocity.2.4.5.6.1.8.15 1 1.2.2 1.4 1 5 5 1 15 2.25 1 5 5 1 15 2 (BOJ) 21st April 21 at GRIPS 25 / 47
Response to a positive preference shock 1 Discount Factor Nominal Interest Rate.8.5.6.4 1 1.5 2.2 2.5 1 5 5 1 15 2 3 1 5 5 1 15 2.2.4.6.8 1 1.2 1.4 1.6 Price 1.8 1 5 5 1 15 2.2.4.6.8 1 1.2 1.4 1.6 Velocity 1.8 1 5 5 1 15 2 (BOJ) 21st April 21 at GRIPS 26 / 47
Response to a positive liquidity shock 1 Cash Requirement.35 Nominal Interest Rate.8.3.25.6.2.4.15.2.1.5 1 5 5 1 15 2 1 5 5 1 15 2.1.2.3.4.5.6.7.8 Price.9 1 5 5 1 15 2.1.2.3.4.5.6.7.8 Velocity.9 1 5 5 1 15 2 (BOJ) 21st April 21 at GRIPS 27 / 47
Summary of IRFs I Contractionary money supply shock: P t declines. V t and i t increase. M t is scarce while goods supply are constant, reducing P t. M t is scarce in the ATM, raising interest rate. Most of money is held by agents with higher velocity v t (s), raising V t. Positive goods supply shock (level shock): P t declines. V t and i t increase. Goods supply increases at the initial period, reverting to the steady state with persistency. M t is scarce, reducing P t. Growth rate of consumption falls. i t declines to clear the market. (BOJ) 21st April 21 at GRIPS 28 / 47
Summary of IRFs II Positive preference shock: P t and V t decline. i t decreases. Agents postpone consumption, less money prevails in the market while Y t unchanged, reducing P t. Given consumption growth rate, i t falls to clear the market. Positive liquidity shock: P t and V t decline. i t increases. M t is scarce because transaction becomes cash intensive, reducing P t. Given money supply, i t raises to clear the market. (BOJ) 21st April 21 at GRIPS 29 / 47
Simulation Linearly detrend private consumption and M2+CD to obtain the deviation of exogenous variables fy t, M t g 29Q2 τ=197q1. Feed through these observable exogenous variables into the model. Examine the portion of velocity and price variations explained by shocks to goods supply µ y t and money supply µ m t. Recover shocks to transaction µ θ t and shocks to preference µβ t, using the discrepancy between model-generated velocity Ṽ t and interest rate ĩ t, and their data counterparts. (BOJ) 21st April 21 at GRIPS 3 / 47
Baseline simulation I: Time path of Model-generated series µ y t and µ m t are feeded into the model..6 Velocity Simulated Data.5.4 Price Simulated Data.4.3.2.2 Deviation from Trend Deviation from Trend.1.1.2.2.3.4.4.6 197 198 199 2 21 Date.5 197 198 199 2 21 Date (BOJ) 21st April 21 at GRIPS 31 / 47
Baseline simulation II: Baseline Statistics Model-generated velocity and price, with money supply shocks and goods supply shocks, are highly correlated with data. Model underpredicts velocity variations throughout the period. Model underpredicts price variations before 9s and over-predicts them after 9s. It implies that other two shocks help to o set the e ect of money shocks and goods shocks. Corr, V t Corr, P t Vol, V t Vol, P t Full Sample.62.64.44.78 7s.68.63.36.62 8s.67.7.8.63 9s.59.75.76 1.49 After 2s.41.78.42 1.5 (BOJ) 21st April 21 at GRIPS 32 / 47
Recovering shocks: Methodology We have two observable shocks µ m t shocks µ t θ and µβ t. and µ y t,and two unobservable Equilibrium system of the economy is written as K t = AK t 1 + B 2 6 4 µ m t µ y t µ θ t µ β t 3 7 5, where K t is endogenous variables, such as P t and i t. We can recover µ θ t and µβ t using the discrepancy between model-generated P t and i t and the data. (BOJ) 21st April 21 at GRIPS 33 / 47
Recovering shocks II: Time path of the Two shocks.4 Discount Factor.4 Cash Requirement.3 Discount Factor Goods Supply.3 Cash Requirement Goods Supply.2.2 Deviation from Trend.1 Deviation from Trend.1.1.1.2.2.3 197 198 199 2 21.3 197 198 199 2 21 Date Date (BOJ) 21st April 21 at GRIPS 34 / 47
Recovering shocks III: Cyclicality of the Two shocks Movement of discount factor is cyclical. β t increases with Y t. Movement of cash share in payment is cyclical in the rst sub-sample period and counter cyclical in the latter sub-sample period. In 9s and s, θ t increases when Y t drops (more money is needed in the recession). Corr (Y t, β t ) Corr (Y t, θ t ) Full Sample.53.12 7s.63.34 8s.47.13 9s.26 -.31 After 2s.41 -.44 (BOJ) 21st April 21 at GRIPS 35 / 47
Contribution of Shocks in Price Variations.4.3.3.2.2.1.1.1.1.2.3 Money Goods Liquidity Preference.2.4 71 76 81 86 91 96 1 6.3 71.4 (BOJ) 21st April 21 at GRIPS 36 / 47
Contribution of Shocks in Price Variations.3.2.2.1 QE, 1Q1:6:Q3.15.1.5.1.2 Finanial Crisis, 97Q4 Money Goods Liquidity Preference.5.1.15.3 9 91 92 93 94 95 96 97 98 99 1 2 3 4 5 6 7.2 9 91.2 (BOJ) 21st April 21 at GRIPS 37 / 47
Contribution of Shocks in Velocity Variations.4.3 Money Goods Liquidity Preference.2.1.1.2.3.4 71 76 81 86 91 96 1 6 (BOJ) 21st April 21 at GRIPS 38 / 47
Contribution of Shocks in Velocity Variations.2.15 Money Goods Liquidity Preference.1.5.5.1.15 Finanial Crisis, 97Q4 QE, 1Q1:6:Q3.2 9 91 92 93 94 95 96 97 98 99 1 2 3 4 5 6 7 (BOJ) 21st April 21 at GRIPS 39 / 47
Contribution of Shocks in Interest Rate Variations.3.2.1.1 Goods Liquidity Money Preference.2.3 71 76 81 86 91 96 1 6 (BOJ) 21st April 21 at GRIPS 4 / 47
Contribution of Shocks in Interest Rate Variations.2.15.1 QE, 1Q1:6:Q3.5.5.1.15 Finanial Crisis, 97Q4 Money Goods Liquidity Preference.2 9 91 92 93 94 95 96 97 98 99 1 2 3 4 5 6 7 (BOJ) 21st April 21 at GRIPS 41 / 47
Variance Decomposition over sample period (Velocity) 1.9.8 Variance Decomposition of Velocity Variations Money Goods Liquidity Preference.7.6.5.4.3.2.1 197 198 199 2 (BOJ) 21st April 21 at GRIPS 42 / 47
Variance Decomposition over sample period (Price) 1.9.8 Variance Decomposition of Price Variations Money Goods Liquidity Preference.7.6.5.4.3.2.1 197 198 199 2 (BOJ) 21st April 21 at GRIPS 43 / 47
Variance Decomposition over sample period (Interest Rate) 1.9.8 Variance Decomposition of Interest Rate Variations Money Goods Liquidity Preference.7.6.5.4.3.2.1 197 198 199 2 (BOJ) 21st April 21 at GRIPS 44 / 47
Conclusion (BOJ) 21st April 21 at GRIPS 45 / 47
Conclusion I We develop a DSGE model that focus on the source of price variations. Extension of the model of AAE (29, QJE). Shocks to transaction (liquidity shocks) and shocks to preference are considered. Liquidity shock A positive liquidity shock increases money demand, causing a decline of price and an upsurge of the interest rate. Preference shock A positive preference shock causes delayed consumption, reducing money supply used for transaction and price level. It leads to a decline of interest rate. (BOJ) 21st April 21 at GRIPS 46 / 47
Conclusion II We distilled the liquidity shocks and preference shocks using the Japanese data. Roughly half of price variations is attributed to shocks to money supply and goods supply. The rest is explained by other two shocks. In the current sub-sampe period, role of liquidity shocks becomes increasingly important in price variations. In the current sub-sampe period, realization of liquidity shocks are counter-cyclical, helping price to go down during the recession. (BOJ) 21st April 21 at GRIPS 47 / 47