Quantitative Easing in a Small Open Economy: An International Portfolio Balancing Approach

Transcription

1 Quantitative Easing in a Small Open Economy: An International Portfolio Balancing Approach Serdar Kabaca Bank of Canada November 6, 27 Central Bank Macroeconomic Modelling Workshop The views expressed are those of the author, not necessarily those of the Bank of Canada.

2 International Portfolio Balancing Portfolio balancing channel of QE: A fall in the stock of long-term gov t bonds lowers yields below the expected path of short-term rates; i.e., term premium. Tobin (969): Relative asset supply matters.. In the case of SOE, a large pool of substitutes exist. SOE term premia highly co-move with the global one, albeit not perfectly.

3 Main Question: What I do How stimulatory can QE be in small open economies? To what extent does domestic term premium deviate from global term premium after a QE shock? Effects through exchange rate? Method: SOE-DSGE model with nominal and real rigidities ST and LT portfolios including domestic and foreign bonds Imperfect substitution between these assets (preferred habitat) Main finding: SOE term premium: a combination of the global term premium and an excess premium that depends on home-foreign asset substitution. CA and US bonds are estimated to be highly substitutable, esp at longer maturities - QE is less effective on rates. High substitution at longer (shorter) maturities implies a larger (smaller) exchange rate response.

4 Illustration of QE in an SOE The slope of relative demand curve represents the degree of substitution between assets.

5 Literature Review Portfolio balance models: Tobin (969), Hau and Rey (24), Blanchard, Ostry, Ghosh and Chamon (2), Blanchard, Giavazzi, and Sa (2), Beenstock and Longbottom (98), Vayanos and Vila (29). Preferred Habitat DSGE models: Closed economy: Andres, Lopez-Salido and Nelson (24), Chen, Curdia and Ferrero (22), Harrison (22). Open economy: Alpanda and Kabaca (2), Chin, Filippeli, and Theodoridis (2), Adler, Lama, and Medina (27). Financial Intermediation DSGE models: Getler and Karadi (2), Dedola, Karadi and Lombardo (23), Cespedes, Chang and Velasco (26). Empirical evidence against UIRP : Bekaert and Hodrick (993), Engel (996), Froot and Thaler (99), Chinn and Meredith (24), Chinn and Quayyum (22), Valchev (24)

6 Model Summary Small-open economy DSGE model (Monacelli, 2; Gali and Monacelli, 2; Justiniano and Preston, 2) with an exogenous foreign bloc. Nominal rigidities: price-setters domestic producers and retail firms. Real rigidities: (habit formation) in consumption. Imperfect substitution among assets through portfolio adjustment costs in preferences (Andres et. al, 24) Introducing long-term bonds: Perpetuities that cost q L and pay an exponentially decaying coupon κ s at period s +. R L,t = /q L,t + κ Both home and foreign assets are internationally traded. However, home assets are negligible part of foreign portfolio. SOE cannot alter world asset prices (R*, R L exogenous). Bond supply: Controlled by gov t through budget constraint. QE shock: Change in the supply of long-term bonds relative to short-term. Closing the model: Home goods and asset external demand function.

7 Households Problem [ max E t β τ t ε d n +ϑ ] τ t log [c τ ζc τ ] ξ n + ϑ Θt τ=t ( ) s.t. Θ t = ξa γa A 2 S,t + ξ ( ) ( ) S γs B 2 HS,t + ξ 2 L γ L q L,t B HL,t 2 γ a A L,t 2 γ S e tb FS,t 2 γ L e tql,t B FL,t where A S,t = B HS,t + e tb FS,t and A L,t = q L,t B HL,t + e tq L,t B FL,t.

8 Households Problem [ max E t β τ t ε d t log [cτ ζc n +ϑ ] τ τ ] ξ n + ϑ Θt τ=t s.t. c t + B HS,t P t + etb FS,t ( + ε cr t ) + q L,tB HL,t P t P t Wt n t + R t B HS,t P t P t e t ( + κql,t + P t + etr t B FS,t P t + ) B FL,t + profits tax, ( + ε dr t ) + etq L,t B FL,t P t ( ) + κql,t BHL,t P t ( + ε cr t )( + ε dr t )

9 Long-term rate at home: where T t = Home and Global Term Premium ) R L,t = ( κrl E t ( κ { ) s R t+s + R L s= ξ a ) (âl,t â S,t + γ a( γ a) ( ζ) c a T t+s } ξ ( L q L,t + b HL,t rer t q L,t ( γ b ) FL,t a)γ L ξ S ( bhs,t rer t b ) FS,t + ˆε dr t. γ aγ L A similar relationship can be written for the global term premium and portfolios and then combined with the above equation to get: T t = T t + ξ [ L q L,t + b HL,t ( rer t + q L,t Υ + b )] FL,t ξ S [ bhs,t ( rer t + b )] FS,t Υ 2 where Υ = ( γ a)γ L ( γ L ) and Υ 2 = γ aγ S ( γ S ). Note that T t = T t when ξ S = ξ L =.

10 Modified UIP: Exchange Rate in the Model E t dt+ = R t R t Combining with T t T t : R L,t e e R L,t ( ζ) c a ξ S [ bhs,t ( rer t + b )] FS,t + ˆε cr t Υ 2 E t dt+ = R t R t ( ζ) c + ( T t T t a ) ( ζ) c ξ [ L q L,t + b HL,t ( rer t + q L,t }{{} a Υ + b )] FL,t + ˆε cr t UIP deviations - costs of adjusting home and foreign asset ratio. Under ZLB, QE depreciates the currency only if ξ S >. FX rate depends on short-term rate and term premium differentials, as well as relative long-term bond holdings. Summary of QE effects on the domestic term premium and the exchange rate Higher ξ S : Higher term premium and higher depreciation Higher ξ L : Higher term premium but lower depreciation

11 Consolidated budget constraint: R t π t Policy and BoP b S,t + R L,tq L,t b L,t = tax t + b S,t + q L,t b L,t π t Government controls the supply of LT bonds: q L,t b L,t = Γε b t b S,t ε b t follows an AR() process. ( ) bs,t +q Tax policy: tax t = Ξy L,t b τb L,t b S +q L b L ε τ t Conventional Monetary Policy: Taylor Rule Balance of Payments: ( rer tb FS,t rertr t b ) ( FS,t πt + rer tql,t b FL,t rertr L,t q L,t b ) FL,t πt ( b FS,t R ) ( t b FS,t ql,t bfl,t R ) L,tq L,t b FL,t = p h,t cf,t rer t rer tπ t rer t rer rertc f,t tπ t ()

12 Closing the model External demand for home goods: ( P cf f,t,t = P t ) λ c c t 2 External demand for home short-term bonds: bfs,t ( ) Rtε cr η S t = b rer t Rt S,t E td t+ 3 External demand for home long-term bonds: q L,t bfl,t ( R e L,t ε cr ) η L t = q L,tb rer t Rt e L,t E td t+ 4 Foreign bloc: VAR(2) of ŷ, π, R, R L, b S, q L b L

13 Parameters Table : Calibrated parameters Parameter Value Explanation Discount factor, β.98 matching the st.-st. interest rate (. %, quarterly) Home share (short), γ S.93 st-st ratio of home bonds in short-term portfolio Home share (long), γ L.92 st-st ratio of home bonds in long-term portfolio Short share, γ a.42 st-st ratio of short-term bonds in overall portfolio Coupon, κ.98 calibrated matching the average duration of bonds ( years) Home biasness, γ c.7 matching the st-st ratio of imports-to-gdp (3 %)

14 Parameters Table : Estimated parameters - portfolio Prior Posterior Parameter Density Mean Std Median Mean Std ST-LT portfolios, adj. cost ξ a G H-F Short-term bonds, adj. cost ξ S G H-F Long-term bonds, adj. cost ξ L G...3e-.3e- 2.e-8 Prior mean for ξ a: Model matches US QE effects in a closed economy setup. Prior means for ξ S and ξ L : SOE QE is at least as effective as in closed economy. Observables (Canada): GDP, inflation, Overnight rate, GDP deflator, real exchange rate, yr yield, relative supply between long- and short-term government bonds over 99Q-2Q4. Observables (US, VAR): GDP, GDP deflator, FFR, yr yield, long- and short-term government bond supply.

15 QE Shock. Term premium. Long-term rate.4 GDP 4 Inflation Policy rate Baseline Large economy QE shock (Long-term outstanding) Short-term Canadian bond outstanding CAD depreciation RER Trade balance.3 Real exports Real imports Home LT Bond Holdings Home ST bond holdings US LT bond holdings US ST bond holdings Non-residents' short-term CAD holdings

16 Trade-off: term premium and the exchange rate. Term Premium. Long-term Rate GDP 2 Inflation Policy rate Baseline Higher ξ l QE shock (Long-term outstanding) Short-term Canadian bond outstanding CAD Depreciation RER Real exports Home LT Bond Holdings Home ST Bond Holdings US LT Bond Holdings US ST Bond Holdings Non-residents' short-term CAD holdings

17 Sensitivity on H-F bond substitution in short-term maturities Term Premium Long-term Rate GDP 6 Inflation Policy rate ξ s = Baseline ξ s = QE shock (Long-term outstanding) Short-term Canadian bond outstanding CAD Depreciation RER Real exports Home LT Bond Holdings Home ST Bond Holdings US LT Bond Holdings US ST Bond Holdings Non-residents' short-term CAD holdings

18 Domestic debt market: Closed vs. Open. Term premium. Long-term rate.6 GDP 4 Inflation Policy rate Baseline Domestic debt market closed QE shock (Long-term outstanding) Short-term Canadian bond outstanding CAD depreciation RER Real exports Home LT bond holdings Home ST bond holdings US LT bond holdings US ST bond holdings

19 Concluding Remarks In a SOE model with preferred habitat, QE is effective only when domestic and foreign assets are not perfect substitutes. The substitution between home and foreign assets is estimated to be high, implying a smaller QE effect in a SOE than in a large economy. However, lower substitution at shorter maturities could imply significant exchange rate response. Ignoring foreigners access to domestic debt market could mistakenly make the policy look more effective.

20 Without ZLB commitment. Term premium. Long-term rate GDP. Inflation.3 Policy rate Baseline Without ZLB commitment QE shock (Long-term outstanding) Short-term Canadian bond outstanding CAD depreciation RER Real exports Home LT bond holdings Home ST bond holdings US LT bond holdings US ST bond holdings Non-residents' short-term CAD holdings

21 Alternative ways to introduce imperfect substitution Financial intermediaries that collect one-period deposits from households at rate R A, financed by investments in short- and long-term government debt in a similar fashion as in Harrison (2). [ max E t R tb HS,t (i) + e trt B FS,t (i) + ( ) ) ] + κq L,t BHL,t (i) + e t ( + κql,t B FL,t (i) ( ) R t A a S,t (i) 2 ( ) ( ) A t + γ a a L,t (i) b HS,t (i) γ S rer tb FS,t (i) q L,t b HL,t (i) + γ a rer tql,t b FL,t (i) 2 In a similar fashion as in Alpanda and Kabaca (2), portfolios enter in a CES specification: [ ] max E β t n t (i) +ϑ υ t log [c t (i) ζc t ] + ξ a log a t (i) ξ n + ϑ Θt t= [ a t (i) = γ λa a [ as,t (i) ] λa λa + ( γ a) λa [ al,t (i) ] ] λa λa λa λa 3 Portfolio adjustment costs in household s budget constraint back

22 Log-linearizing external asset demand since a S,t = b HS and a L,t = q L,t b HL : E t dt+ = R t R t ( ) β R π β R π λ S ( [ b FS,t rer t + b )] HS,t E t dt+ = R e L,t ( ) e β R π R L,t β R π λ L [ q L,t + b ( FL,t rer t + q L,t + b )] HL,t back

23 Estimated Parameters Prior Posterior Parameter Density Mean Std Mode Median Mean Std % 9 % ST-LT portfolios, adj. cost ξa G H-F Short-term bonds, adj. cost ξs G H-F Long-term bonds, adj. cost ξl G...e-.3e-.3e- 2.e-8.2e-.4e- Inverse Frisch elas. ϑ G Habit ζ B Calvo domestic prices θh B Calvo import prices θf B Indexation domestic prices ςh B Indexation import prices ςf B Elas. H-F goods λ G Taylor rule, smoothing ρ B Taylor rule, inflation rπ G Taylor rule, output ry G Taylor rule, output growth rδy G Taylor rule, nominal exchange rate rd G Elas. in tax policy τb G Pers. productivity ρz B Pers. preferences ρd B Pers. cost-push imports ρf B Pers. country risk premium ρcr B Pers. duration risk premium ρdr B Pers. bond supply ρb B Pers. tax ρτ B Std. productivity σz IG Std. preferences σd IG Std. cos-push imports σf IG Std. country risk premium σcr IG Std. duration risk premium σdr IG Std. bond supply σb IG Std. tax στ IG Std. monetary policy σr IG back

24 Short-term US Bond Holdings by Canadians

25 Foreign Currency Deposits in Canada back

26 Bayesian IRFs Term premium -3 Long-term rate GDP Inflation Policy rate.6 RER -. Real imports.4 Real exports Long-term Canadian bond outstanding Short-term Canadian bond outstanding back