Exchange Rates and Uncovered Interest Differentials: The Role of Permanent Monetary Shocks. Stephanie Schmitt-Grohé and Martín Uribe

Transcription

1 Exchange Rates and Uncovered Interest Differentials: The Role of Permanent Monetary Shocks Stephanie Schmitt-Grohé and Martín Uribe Columbia University December 1, 218

2 Motivation Existing empirical work assumes that monetary shocks come in only one type: temporary disturbances. However, temporary monetary shocks are not the only conceivable type of monetary shock. As shown in recent work by Uribe (218) permanent monetary policy shocks, i.e., shocks to long-run inflation expectations, are at least as important as transitory monetary policy shocks for explaining the dynamics of changes in output, inflation, and the nominal interest rate in the United States. Motivated by this finding the present paper estimates the effects of monetary policy shocks on exchange rates within an empirical framework that distinguishes transitory from permanent monetary shocks. 2

3 This paper finds that: permanent monetary shocks explain the majority of short-run movements in nominal exchange rates. there is no exchange-rate overshooting in response to monetary shocks, suggesting that existing overshooting results may be the consequence of confounding permanent and transitory impulses. transitory tightenings cause deviations from uncovered interestrate parity in favor of domestic assets, whereas permanent tightenings cause deviations in favor of foreign assets. 3

4 Previous related literature 4

5 Dornbusch (1976): Exchange Rate Overshooting UIP: (1 + i t ) = (1 + i t) ( ) St+1 S t Money demand: M t P t = L(i t, Y ) Long-run neutrality: P t = S t P t i t = domestic nominal interest rate. i t = foreign nominal interest rate. S t = domestic currency price of one unit of foreign currency. M t = domestic money supply. P t = domestic price level. Experiment: A contractionary monetary shock, M. 5

6 Empirical Evidence on Exchange Rate Overshooting A large number of papers has tested the validity of Dornbusch s overshooting result conditional on monetary shocks. Two findings emerge: 1.) A monetary tightening causes an appreciation of the domestic currency with an overshooting effect either on impact (Kim and Roubini, 2; Faust and Rogers, 23; Kim, Moon, and Velasco, 217) or with a delay (Eichenbaum and Evans, 1995; Scholl and Uhlig, 28). Main difference across these papers is how the monetary policy shock is identified. 2.) UIP, conditional on a monetary shock, fails, contradicting a key assumption of Dornbusch s model. Specifically, a domestic tightening generates excess returns on domestic assets. 6

7 The key innovation in the present paper is to allow for 2 types of monetary disturbances, temporary and permanent ones. 7

8 Empirical Model The following variables are assumed to be nonstationary y t π t i t ɛ t i t = log of real US output US inflation US interest rate change in dollar exchange rate foreign interest rate stationary, but unobservable, variables: ŷ t ˆπ t î t ˆɛ t î t y t X t π t Xt m i t Xt m ɛ t Xt m + Xt m i t Xm t. 8

9 AR(L) in latent variables ŷ t ˆπ t î t ˆɛ t î t X m t z m t X t z t X m t = B(L) = ρ ŷ t 1 ˆπ t 1 î t 1 ˆɛ t 1 î t 1 X m t 1 z m t 1 X t 1 z t 1 X m t 1 + C + ψ X m t z m t X t z t X m t where Xt m = permanent monetary shock; zt m = transitory monetary shock; X t = permanent nonmonetary shock; z t = transitory nonmonetary shock; and Xt m = foreign permanent monetary shock. Innovations νt i iid N(,1), for i = 1,...,5, ρ and ψ are diagonal 5 5 matrices. (To simplify the exposition constants are omitted.) ν 1 t ν 2 t ν 3 t ν 4 t ν 5 t, 9

10 5 Observables and corresponding observation equations (1) y t y t y t 1, time difference of domestic real output. (2) r t i t π t, interest-rate-inflation differential. (3) i t i t i t 1, time difference of domestic nominal rate. (4) ɛ t ɛ t ɛ t 1, time difference of devaluation rate. (5) i t i t i t 1, time difference of foreign nominal rate. We then have the following observation equations: y t = ŷ t ŷ t 1 + X t r t = î t ˆπ t i t = î t î t 1 + Xt m (1) ɛ t = ˆɛ t ˆɛ t 1 + Xt m Xt m i t = î t î t 1 + Xm t 1

11 Measurement Errors o t = y t r t i t ɛ t i t + µ t (2) where µ t is a 5-by-1 vector of measurement errors distributed i.i.d. N(, R), with R diagonal. 11

12 Let Ŷ t ŷ t ˆπ t î t ˆɛ t î t ; u t X m t z m t X t z t X m t ; ν t ν 1 t ν 2 t ν 3 t ν 4 t ν 5 t Assuming a lag length of L months, the empirical model can be written as Ŷ t = L i=1 B iŷt i + Cu t (3) u t = ρu t 1 + ψν t (4) 12

13 State Space Form Let ξ t Ŷ t Ŷ t 1. Ŷ t L+1 u t Then the system composed of equations (1), (2), (3), and (4) can be written as ξ t+1 = Fξ t + Pν t+1 o t = H ξ t + µ t, where the matrices F, P, and H are known functions of B i, i = 1,... L, C, ρ, ψ, and R. 13

14 To estimate the effects of temporary and permanent monetary shocks on the real exchange rate, e t, e t ln(s t P t )/P t we replace the change in the depreciation rate with the level of the real exchange rate, that is, we replace ɛ t with ɛ r t e t e t 1, in Ŷt and o t. 14

15 Estimation The model to be estimated then is ξ t+1 = Fξ t + Pν t+1 ; with ν t iid N(, I), o t = H ξ t + µ t ; with µ t iid N(, R), The state vector ξ t is latent. The arrays F, P, H, R are what we want to estimate. The vector o t is observable. The model is estimated using Bayesian techniques. The Kalman filter is used to evaluate the likelihood function. 15

16 Identification Assumptions 1. Output (y t ) is cointegrated with the permanent nonmonetary shock (X t ). 2. Inflation (π t ) and the nominal interest rate (i t ) are cointegrated with the permanent monetary shock (X m t ). 3. The foreign nominal interest rate (i t ) is cointegrated with the foreign permanent monetary shock (Xt m ). 4. The depreciation rate (ɛ t ) is cointegrated with (X m t X m t ). 5. A transitory monetary shock that increases the interest rate (z m t ) has a nonpositive impact effect on inflation and output: C 12, C

17 Prior Distributions Parameter Distribution Mean. Std. Dev. Main diagonal elements of B 1 Normal.95.5 All other elements of B i, i = 1,..., L Normal.25 C 21, C 31, C 55 Normal -1 1 C 12, C 22 Gamma 1 1 All other estimated elements of C Normal 1 ρ ii, i = 1,2,3,5 Beta.3.2 ρ 44 Beta.7.2 ψ ii, i = 1,...,5 Gamma 1 1 R ii [ Uniform, var(o t) 1 Note. The lag length, L, is assumed to be 6 months. ] var(o t ) 1 2 var(o t )

18 The Data Domestic country: U.S.; Foreign country: U.K. or Japan Monthly: 1974:1 218:3. y t = U.S. industrial production (Source: OECD MEI) P t = U.S. CPI index (Source: OECD MEI) i t = Federal Funds rate (Source: FRB) S t = $ or $ nominal exchange rate (Source: FRED) i t = Official bank rate (Source: BOE) or Call rate (Source: BOJ) P t = U.K. or JP CPI index (Source: OECD MEI) 18

19 Foreign Country: United Kingdom Impulse responses to permanent U.S. interest rate shocks (X m t ) and to transitory U.S. interest rate shocks (z m t ) 19

20 Impulse Responses to Permanent and Transitory U.S. Monetary Shocks Foreign country is the United Kingdom Permanent US Interest-Rate Shock Permanent US Interest-Rate Shock Permanent US Interest-Rate Shock Permanent US Interest-Rate Shock US Interest Rate, i t 1 Dollar-Pound Nominal Exchange Rate, S t 6 Dollar-Pound Real Exchange Rate, e t 2 Uncovered Interest Rate Differential, i t i t ɛ t+1 1 percent per year.5 percent 4 2 percent percent per year Transitory US Interest-Rate Shock Transitory US Interest-Rate Shock Transitory US Interest-Rate Shock Transitory US Interest-Rate Shock US Interest Rate, i t 1.5 Dollar-Pound Nominal Exchange Rate, S t.5 Dollar-Pound Real Exchange Rate, e t 1 Uncovered Interest Rate Differential, i t i t ɛ t percent per year 1.5 percent.5 percent 1 2 percent per year Solid lines: posterior mean estimates from MCMC chain of length 1 million. Broken lines: asymmetric 95-percent Sims-Zha error bands. 2

21 Observations on the figure: responses of exchange rate and covered interest rate differential to temporary and permanent monetary shocks are of opposite sign. no overshooting of the nominal exchange rate, neither for permanent nor for transitory shock (contrary to related literature). In response to permanent monetary shock (Xt m ), short-run response of nominal exchange rate larger than that of the real exchange rate, whereas in response to temporary monetary shock (zt m ), short-run response of nominal and real rate of similar magnitude. (That is, no Mussa puzzle for permanent monetary shocks.) 21

22 Impulse Responses of U.S. Inflation and Output to Permanent and Transitory U.S. Monetary Shocks: United Kingdom 5 Permanent US Interest-Rate Shock US inflation rate, π t.4 Transitory US Interest-Rate Shock US Inflation Rate, π t percent percent Permanent US Interest-Rate Shock US output, y t.5 Transitory US Interest-Rate Shock US output, y t percent 1.5 percent

23 Observations on the figure Transitory tightening causes contraction in output and a fall in inflation (consistent with extensive existing literature on the effects of transitory monetary policy shocks, see, for example, Christiano, Eichenbaum, and Evans (25)) Permanent tightening causes an immediate increase in inflation and an expansion in aggregate activity (i.e., there is a neo-fisher effect) as first documented in Uribe (218). 23

24 Results obtained when the foreign country is taken to be the United Kingdom continue to hold when the foreign country is assumed to be Japan. 24

25 Impulse Responses to Permanent and Transitory U.S. Monetary Shocks: Foreign country is Japan Permanent US Interest-Rate Shock Permanent US Interest-Rate Shock Permanent US Interest-Rate Shock Permanent US Interest-Rate Shock US Interest Rate, i t.8 Dollar-Yen Nominal Exchange Rate, S t 1 Dollar-Yen Real Exchange Rate, e t 1.5 Uncovered Interest Rate Differential, i t i t ɛ t+1.5 percent per year percent 5 percent 1.5 percent per year Transitory US Interest-Rate Shock Transitory US Interest-Rate Shock Transitory US Interest-Rate Shock Transitory US Interest-Rate Shock US Interest Rate, i t 1.5 Dollar-Yen Nominal Exchange Rate, S t 5 Dollar-Yen Real Exchange Rate, e t Uncovered Interest Rate Differential, i t i t ɛ t+1 4 percent per year 1.5 percent 5 percent 1 2 percent per year Solid lines: posterior mean estimates from MCMC chain of length 1 million. Broken lines: asymmetric 95-percent Sims-Zha error bands. 25

26 Observations on the figure: responses of exchange rates and covered interest rate differentials to temporary and permanent monetary shocks are of opposite sign. permanent tightening leads to depreciation of the dollar in the short run and excess returns in favor of yen assets whereas temporary tightening leads to appreciation of the dollar and excess returns in favor of dollar assets. no overshooting of the nominal exchange rate, neither for permanent nor for transitory shock 26

27 Impulse Responses of U.S. Inflation and Output to Permanent and Transitory U.S. Monetary Shocks: Foreign country is Japan 2 Permanent US Interest-Rate Shock US inflation rate, π t 2 Transitory US Interest-Rate Shock US Inflation Rate, π t percent percent Permanent US Interest-Rate Shock US output, y t Transitory US Interest-Rate Shock US output, y t.5 percent 1.5 percent

28 Observations on the figure As for the case in which the foreign country is the UK, we find that: transitory tightening causes contraction in output and a fall in inflation (consistent with conventional wisdom) permanent tightening causes an immediate increase in inflation and an expansion in aggregate activity (i.e., there is a neo Fisher effect) as in Uribe (218) 28

29 The Importance of Permanent Monetary Shocks for Exchange Rates Forecast Error Variance Decomposition at Horizon 36 months A. United Kingdom y t π t i t ln S t ln e t i t UID ermanent Monetary Shock, Xt m ransitory Monetary Shock, zt m ermanent Nonmonetary Shock, X t ransitory Nonmonetary Shock, z t ermanent Foreign Monetary Shock, Xt m B. Japan y t π t i t ln S t ln e t i t UID ermanent Monetary Shock, Xt m ransitory Monetary Shock, zt m ermanent Nonmonetary Shock, X t ransitory Nonmonetary Shock, z t ermanent Foreign Monetary Shock, Xt m Notes. Uncovered interest rate differential (UID)= i t i t ɛ t+1. y t, U.S. output growth; π t, U.S. inflation; i t, the Federal Funds rate; ln S t, dollar-pound or dollaryen nominal exchange rate; ln e t, the dollar-pound or dollar-yen real exchange rate; i t, U.K. or Japanese nominal interest rate; ɛ t ln(s t /S t 1 ), devaluation rate. 29

30 Observations on the table: Permanent monetary shocks (Xt m and Xt m ) are the main drivers of the level of the nominal exchange rate even in the short run,.37 and.58 at 36 months and.23 and.26 at 12 months (not shown). The U.S. permanent monetary shock (X m t ) accounts for the majority of the forecast-error variance of U.S. inflation, 82 and 84 percent, and for a significant fraction of the variance of the federal funds rate, 35 and 57 percent, which is consistent with Uribe s (218) estimates of a quarterly closed economy model on U.S. and Japanese data. The U.S. temporary monetary shock (zt m ) explains little of the FEV of the dollarpound or dollar-yen nominal exchange rate, inflation, or the nominal interest rate. By contrast, Eichenbaum and Evans (1995) find that 19 and 22 percent of the forecast-error variance of the dollar-pound and dollar-yen nominal exchange rates at horizons 31 to 36 months are due to monetary shocks. (At horizon 12 months, we find that zt m explains 23 % of the FEV of i t.) Monetary shocks play a modest role in accounting for movements in the real exchange rate, consistent with findings of Clarida and Gaĺı (1994). (CG:.4% percent of FEV of the level of the real $- exchange rate at a horizon of 12 quarters.) 3

31 2 18 Cointegrated Monetary Policies? Federal Funds Rate UK Bank Rate Japanese Call Rate percent per year

32 Observations on the figure: U.S. and U.K. policy rates seem to share a common permanent component. (ADF test p-value =.49) This is less so the case for U.S. and Japan. (ADF test p-value =.123) Accordingly, we next consider a variant of the empirical model that assumes that the federal funds rate and the U.K. bank rate are cointegrated. 32

33 Model with only one permanent monetary shock: X m t+1 z m t+1 X t+1 z t+1 X m t+1 Xm t+1 = ρ X m t z m t X t z t X m t X m t + ψ ν 1 t+1 ν 2 t+1 ν 3 t+1 ν 4 t+1 ν 5 t+1. The assumption that Xt m Xt m is stationary induces stationarity in both the interest rate differential, i t i t, and the devaluation rate, ɛ t ln(s t /S t 1 ). o t = y t r t i t ɛ t i t i t + µ t, 33

34 Impulse Responses to Permanent and Transitory U.S. Monetary Shocks Under Cointegrated U.S. and U.K. Monetary Policies Permanent US Interest-Rate Shock Permanent US Interest-Rate Shock Permanent US Interest-Rate Shock Permanent US Interest-Rate Shock US Interest Rate, i t 1 Dollar-Pound Nominal Exchange Rate, S t 1.5 Dollar-Pound Real Exchange Rate, e t 1 Uncovered Interest Rate Differential, i t i t ɛ t+1.5 percent per year percent 1.5 percent.5 percent per year Transitory US Interest-Rate Shock Transitory US Interest-Rate Shock Transitory US Interest-Rate Shock Transitory US Interest-Rate Shock US Interest Rate, i t 1.5 Dollar-Pound Nominal Exchange Rate, S t 1 Dollar-Pound Real Exchange Rate, e t Uncovered Interest Rate Differential, i t i t ɛ t+1 3 percent per year 1.5 percent 1 2 percent 1 2 percent per year Solid lines: posterior mean estimates from MCMC chain of length 1 million. Broken lines: asymmetric 95-percent Sims-Zha error bands. 34

35 Observations on the figure: By construction, the response of the level of the nominal exchange rate to a permanent U.S. tightening is now bounded. As in the baseline case we find: the nominal and real exchange rates depreciate in response to a permanent tightening and appreciate in response to transitory trightening. There is no exchange-rate overshooting. The uncovered interest-rate differential moves in favor of U.S. assets in response to a temporary tightening but against U.S. assets in response to a permanent tightening. 35

36 Kim, Moon, and Velasco (JPE, 217) argue that a feature of the Volcker era was delayed exchange rate overshooting. The present paper, by contrast, argues that once one allows for both transitory and permanent monetary shocks, the overshooting effect, instantaneous or delayed, disappears altogether. The next figure shows that our finding of no overshooting are robust to truncating the sample in December of 1987, the last year of Paul Volcker s Fed chairmanship. 36

37 No Delayed Exchange Rate Overshooting During the Volcker Era 1 Permanent US Interest-Rate Shock Dollar-Pound Nominal Exchange Rate, S t 2 Transitory US Interest-Rate Shock Dollar-Pound Nominal Exchange Rate, S t 8 percent 6 4 percent Permanent US Interest-Rate Shock Dollar-Yen Nominal Exchange Rate, S t 4 Transitory US Interest-Rate Shock Dollar-Yen Nominal Exchange Rate, S t 4 2 percent percent Baseline model estimated on the 1974:1-1987:12 sample. 37

38 Conclusions The innovation of the present paper is to allow for permanent and transitory monetary shocks. Estimation on monthly post-bretton- Woods data from the United States, the United Kingdom, and Japan shows that: permanent monetary shocks explain the majority of short-run movements in nominal exchange rates. there is no exchange-rate overshooting in response to monetary shocks, suggesting that existing overshooting results may be the consequence of confounding permanent and transitory impulses. transitory tightenings cause deviations from uncovered interestrate parity in favor of domestic assets, whereas permanent tightenings cause deviations in favor of foreign assets. 38

39 Extras 39

40 Forecast Error Variance Decomposition at Horizons between 12 and 48 months: United Kingdom y t π t i t ln S t ln e t i t uid Permanent Monetary Shock, Xt m Horizon 12 months Horizon 24 months Horizon 36 months Horizon 48 months Transitory Monetary Shock, zt m Horizon 12 months Horizon 24 months Horizon 36 months Horizon 48 months Permanent Nonmonetary Shock, X t Horizon 12 months Horizon 24 months Horizon 36 months Horizon 48 months Transitory Nonmonetary Shock, z t Horizon 12 months Horizon 24 months Horizon 36 months Horizon 48 months Permanent Foreign Monetary Shock, Xt m Horizon 12 months Horizon 24 months Horizon 36 months Horizon 48 months Note. uid= i t i t ɛ t+1. 4

41 Forecast Error Variance Decomposition at Horizons between 12 and 48 months: Japan y t π t i t ln S t ln e t i t uid Permanent Monetary Shock, Xt m Horizon 12 months Horizon 24 months Horizon 36 months Horizon 48 months Transitory Monetary Shock, zt m Horizon 12 months Horizon 24 months Horizon 36 months Horizon 48 months Permanent Nonmonetary Shock, X t Horizon 12 months Horizon 24 months Horizon 36 months Horizon 48 months Transitory Nonmonetary Shock, z t Horizon 12 months Horizon 24 months Horizon 36 months Horizon 48 months Permanent Foreign Monetary Shock, Xt m Horizon 12 months Horizon 24 months Horizon 36 months Horizon 48 months Note. uid= i t i t ɛ t+1. 41

42 The State Space Representation Now including the constants, which were omitted earlier. Ŷ t y t X t E(y t X t ) π t Xt m E(π t Xt m) i t Xt m E(i t Xt m) ɛ t Xt m + Xt m i t Xm t E(ɛ t Xt m + X m E(i t Xm t ) t ) ; u t X m t E( X m t ) z m t X t E( X t ) X m t z t E( X m t ) Ŷ t = L i=1 B iŷt i + Cu t ξ t [ Ŷ t u t = ρu t 1 + ψν t Ŷ t 1... Ŷ t L+1 u t ] ξ t+1 = Fξ t + Pν t+1 o t = A + H ξ t + µ t 42

43 V = 5, number of variables included in the vector Ŷ t, S = 5, number of shocks in the vector ν t, L = 6, number of lags. B [B 1 B L ]; F = B Cρ [ IV (L 1) V (L 1),V ] V (L 1),S S,V L ρ ; P = Cψ V (L 1),S ψ A = [ E( X t ) E(i t π t ) E( Xt m) E( Xm t Xt m ) E( Xt m ) ] H = [ M ξ V,V (L 2) M u ], M ξ = ; M u = Prior for the elements of the matrix A: Normal, mean(o t ), standard deviation, var(ot ), where T denotes the sample length, 531 months. T 43

44 Observation equations in model with only one permanent monetary shock y t = ŷ t ŷ t 1 + X t r t = î t ˆπ t i t = î t î t 1 + X m t ɛ t = ˆɛ t + X m t X m t i t i t = î t î t + Xm t X m t. Note that only the last two observation equations differ from their baseline counterparts. 44

45 Cross-Country Evidence on the Long-Run Fisher Effect Long-Run Averages of Inflation and Nominal Interest Rates 15 1 Average of it in percent Average of π t, in percent 25 OECD countries. Average sample period is 1989 to

46 Eichenbaum and Evans, QJE 1995 Three definitions of a monetary shock are considered: 1. Orthogonalized innovations to the log of the ratio of nonborrowed reserves to borrowed reserves (NBRX). 2. Orthogonalized innovations to the federal funds rate. 3. The Romer-Romer (1989) index of monetary contractions. We will present their results for identification scheme 2, orthogonalized innovations to the federal funds rate, as all three schemes give qualitatively very similar results. 46

47 Sample Monthly data from 1974:1 to 199:5. Five exchange rates (s t ): Yen, Deutsche Mark, Lira, French Franc, and UK Pound, where s t denotes the log of the U.S. dollar price of one unit of foreign currency. The log of the real exchange rate is defined as s R t = s t + p t p t, where p t and p t denote the logs of the consumer price indices in the foreign country and the United States, respectively. VAR: 7 variables: log of U.S. industrial production (Y ), log of U.S. consumer price index (P), log of foreign industrial production (Y ), foreign interest rate (i ), federal funds rate (i), log of nonborrowed-to-borrowed reserve ratio (N BRX), and the nominal (or real) exchange rate (s or s R ). 47

48 VAR Specification Ordering of the VAR: [Y, P, Y, i, i, NBRX,s (or s R )] Identification of monetary policy shock, Cholesky decomposition. VAR includes 6 lags. Monthly data from January 1974 to May 199. Error bands of impulse responses: ±1 standard deviation in width. 48

49 The next slide shows the impulse response to a U.S. monetary policy shock, specifically a tightening of 6 basis points. It is Figure 3 of Eichenbaum and Evans (QJE 1995). Row 1: Impulse response of U.S. federal funds rate, i Row 2: Impulse response of foreign interest rate, i Row 3: Impulse response of real exchange rate, s R Row 4: Impulse response of log of nominal exchange rate, s Row 5: Impulse response of uncovered interest rate differential, i t i t + s t+1 s t Columns are: Japan, Germany, Italy, France, and the United Kingdom 49

50 5

51 Main Findings of Eichenbaum and Evans (QJE, 1995) 1. A contractionary shock to U.S. monetary policy leads to persistent and significant appreciation in nominal and real U.S. exchange rates. 2. The maximal impact of a monetary shock on exchange rates does not occur contemporaneously but about 36 months after the monetary policy shock. This finding supports a broader view of overshooting, delayed overshooting. 3. A contractionary U.S. monetary policy shock induces a systematic and persistent departure from uncovered interest parity with excess returns in favor of U.S. assets. 51