Introduction PE1 PE2 GE Monetary Policy and Redistributional Channel Adrien Auclert Presented By Ding Dong Department of Economics, HKUST HKUST Macro Group Adrien Auclert Presented By Ding DongDepartment of Economics, HKUST Monetary Policy and Redistributional Channel 1 / 46
Introduction PE1 PE2 GE MP Transmission Mechanisms 2 Classics Channels of MP: Interest Rate Channel i ↓ ⇒ r ↓ (with sticky price) ⇒ c ↑ ( Euler Equation ) Exchange Rate Channel i ↓ ⇒ ε ↓ ⇒ NX ↑ ⇒ Y ↑ ⇒ C ↑ Asset Price Channel 1 ( q-theory & life-cycle theory ) i ↓ ⇒ equity > debt ⇒ equity price ↑ ⇒ wealth ↑ ⇒ c ↑ Credit Channel Bank Lending Channels i ↓ ⇒ bank’s lending ⇒ firm’s borrowing Balance Sheet Channels (BG, 1995) i ↓ ⇒ balance sheet improves ⇒ cost of borrowing ↓ 1 Iacaviello (2005) etc. also explore the real estate price channel. 2 Ireland, 2005. The New Palgrave Dictionary of Economics, Second Edition Adrien Auclert Presented By Ding DongDepartment of Economics, HKUST Monetary Policy and Redistributional Channel 2 / 46
Introduction PE1 PE2 GE Highlight of This Paper Monetary expansions: increase real income (from labor/capital) raise inflation lower real interest rates NOT everyone is equally affected by these changes. working hours and capital ownership is unlikely to be equal unexpected inflation revalues nominal balance sheets. → nominal creditors lose and nominal debtors gain. lower R doesn’t necessarily benefit asset holders → duration and measurement of assets and liabilities matter Adrien Auclert Presented By Ding DongDepartment of Economics, HKUST Monetary Policy and Redistributional Channel 3 / 46
Introduction PE1 PE2 GE Highlight of This Paper Channels of MP on consumption: Interest Rate Channel* un-hedged interest rate exposure , URE Earning Heterogeneity Channel* Fisher Channel* net nominal position , NNP Income Channel Substitution Channel Exchange Rate Channel closed economy Asset Price Channel secondary effect through dY, dP and dR *redistribution channels of mp Adrien Auclert Presented By Ding DongDepartment of Economics, HKUST Monetary Policy and Redistributional Channel 4 / 46
Introduction PE1 PE2 GE Outline Introduction Conventional transmission channels of MP Highlight of this paper Partial Equilibrium Models PE 1: Complete Market, Perfect Foresight PE 2: Incomplete Market, Uninsured Idiosyncratic Risk General Equilibrium Model Aggregation Results Re-distributional Channels Sufficient stats: Redistribution elasticity of consumption Conclusion Adrien Auclert Presented By Ding DongDepartment of Economics, HKUST Monetary Policy and Redistributional Channel 5 / 46
Introduction PE1 PE2 GE PE Model 1 Complete Market No Uncertainty Separable preference over c and n Perfect foresight over P and W Adrien Auclert Presented By Ding DongDepartment of Economics, HKUST Monetary Policy and Redistributional Channel 6 / 46
Introduction PE1 PE2 GE UMP of Agent (1) with No Financial Asset � β t { u ( c t ) − v ( n t ) } max t s . t . P t c t = P t y t + W t n t where Py is endowed income, aka claimed profit; Wn is wage income. Adrien Auclert Presented By Ding DongDepartment of Economics, HKUST Monetary Policy and Redistributional Channel 7 / 46
Introduction PE1 PE2 GE UMP of Agent (1) with No Financial Asset At period 0, � β t { u ( c t ) − v ( n t ) } max t � � s . t . c t = ( y t + w t n t ) t � 0 t � 0 where w=W/P is real wage rate. Adrien Auclert Presented By Ding DongDepartment of Economics, HKUST Monetary Policy and Redistributional Channel 8 / 46
Introduction PE1 PE2 GE UMP of Agent (2) with Real Bond � β t { u ( c t ) − v ( n t ) } max t � s . t . P t c t + t q t + s ( t b t + s ) P t + s = P t y t + W t n t + s � 1 � ( t − 1 b t ) P t + t q t + s ( t − 1 b t + s ) P t + s s � 1 where t q t + s is time-t (real) price of real zero coupon bonds that mature at time t+s, and t b t + s is the quantity purchased. Define 0 q t ≡ q t Adrien Auclert Presented By Ding DongDepartment of Economics, HKUST Monetary Policy and Redistributional Channel 9 / 46
Introduction PE1 PE2 GE UMP of Agent (2) with Real Bond At period 0, � β t { u ( c t ) − v ( n t ) } max t � � � s . t . q t c t = q t ( y t + w t n t ) + q t ( − 1 b t ) t � 0 t � 0 t � 0 Adrien Auclert Presented By Ding DongDepartment of Economics, HKUST Monetary Policy and Redistributional Channel 10 / 46
Introduction PE1 PE2 GE UMP of Agent (3) with with Real and Nominal Bond � β t { u ( c t ) − v ( n t ) } max t � � s . t . P t c t + t Q t + s t B t + s + t q t + s t b t + s P t + s = P t y t + W t n t + s � 1 s � 1 � � ( t − 1 B t ) + t Q t + s t − 1 B t + s +( t − 1 b t ) P t + t q t + s t − 1 b t + s P t + s s � 1 s � 1 (1) where t Q t + s is time-t price of nominal zero coupon bonds that mature at time t+s, and t B t + s is the quantity purchased. Adrien Auclert Presented By Ding DongDepartment of Economics, HKUST Monetary Policy and Redistributional Channel 11 / 46
Introduction PE1 PE2 GE Aside: No Arbitrage Condition At period t, with 1 dollar: The nominal return to nominal bonds that mature at period t+s: 1 t Q t + s The nominal return to real bonds that mature at period t+s: 1 P t + s t q t + s P t No Arbitrage Condition (Fisher Equation): t Q t + s = ( t q t + s ) P t (2) P t + s Adrien Auclert Presented By Ding DongDepartment of Economics, HKUST Monetary Policy and Redistributional Channel 12 / 46
Introduction PE1 PE2 GE Aside: Real Flow Budget Constraint Nominal (Q replaced by q): ( t q t + s ) P t � � P t c t + t B t + s + t q t + s t b t + s P t + s = P t y t + W t n t + P t + s s � 1 s � 1 ( t q t + s ) P t � � ( t − 1 B t )+ t − 1 B t + s +( t − 1 b t ) P t + t q t + s t − 1 b t + s P t + s P t + s s � 1 s � 1 Real: 1 P t + s � � c t + ( t q t + s ) t B t + s + t q t + s t b t + s = y t + w t n t + P t + s P t s � 1 s � 1 t − 1 B t 1 P t + s � � + ( t q t + s ) t − 1 B t + s +( t − 1 b t )+ t q t + s t − 1 b t + s P t P t + s P t s � 1 s � 1 Adrien Auclert Presented By Ding DongDepartment of Economics, HKUST Monetary Policy and Redistributional Channel 13 / 46
Introduction PE1 PE2 GE UMP of Agent (3) with with Real and Nominal Bond At period 0, � β t { u ( c t ) − v ( n t ) } max t q t [( − 1 b t ) + ( − 1 B t � � � s . t . q t c t = q t [ y t + w t n t ] + )] ≡ ω P t t � 0 t � 0 t � 0 � �� � � �� � ω F : financial wealth ω H : human wealth (3) Message: Financial assets with same financial wealth deliver same solution to UMP. ⇒ The composition of balance sheet is irrelevant. Question: Is the composition relevant after a shock? Adrien Auclert Presented By Ding DongDepartment of Economics, HKUST Monetary Policy and Redistributional Channel 14 / 46
Introduction PE1 PE2 GE Aside: MP Shock in NK Models A stylized NK model with no uncertainty and investment features: log ( c t c ) = log ( c t +1 ) − σ ( i t − log ( P t +1 ) − ̺ ) (4) ¯ c ¯ P t log ( P t ) = β log ( P t +1 P t ) + κ log ( c t c ) (5) P t − 1 ¯ i t = ̺ + φ π log ( c t c ) + ε t (6) ¯ Now consider a one-time monetary shock: ε 0 < 0; and ε t = 0 ∀ t � = 0 (7) where ¯ x is steady state value of x; ̺ = 1 /β − 1 is steady state real interest rate; σ is the elasticity of substitution; κ is f(parameter). Adrien Auclert Presented By Ding DongDepartment of Economics, HKUST Monetary Policy and Redistributional Channel 15 / 46
Introduction PE1 PE2 GE Aside: MP Shock in NK Models The solution features: c t = ¯ i t = ̺ ; P t = P t − 1 t ∀ t � 1 solving it backward, impact on i and c is one-shot ( i 0 ↓ , c 0 ↑ ); 1 i 0 = ̺ + ε 0 1 + κσφ π log ( c 0 σ c ) = − ε 0 ¯ 1 + κσφ π Impact on P is immediate and permanent ( P t ↑ ): log ( P 0 κσ P ) = − ε 0 ¯ 1 + κσφ π Adrien Auclert Presented By Ding DongDepartment of Economics, HKUST Monetary Policy and Redistributional Channel 16 / 46
Introduction PE1 PE2 GE Aside: MP Shock in NK Models Given that wage w t = v ′ ( c 1 / 1 − α ) t u ′ ( c t ) → The impact on wage is one-shot ( w 0 ↑ ). Given that capital rent v ′ ( c 1 / 1 − α α α ) 1 − α w t c 1 / 1 − α c 1 / 1 − α t ρ t = = t t 1 − α u ′ ( c t ) → The impact on capital return is one-shot ( ρ 0 ↑ ). Given that claimed profit v ′ ( c 1 / 1 − α α ) c 1 / 1 − α t π t = c t − w t n t − ρ t k = c t (1 − ) t 1 − α u ′ ( c t ) → The impact on claimed profit is one-shot ( π 0 ↑ ). Adrien Auclert Presented By Ding DongDepartment of Economics, HKUST Monetary Policy and Redistributional Channel 17 / 46
Introduction PE1 PE2 GE Aside: MP Shock in NK Models Given that q 0 = Q 0 = 1, and P t = P 0 for t � 1, 1 q t = Q t = Π t − 1 β t − 1 s =0 s Q t = 1 + i 0 where the first equation utilizes no arbitrage condition that P 0 Q t = q t P t Define R=1+i, we have that for t � 1. dq t = dQ t = − dR 0 , q t Q t R 0 → The impact on nominal and real state prices is permanent, starting from t=1. Adrien Auclert Presented By Ding DongDepartment of Economics, HKUST Monetary Policy and Redistributional Channel 18 / 46
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