## _wp0696

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---

### I. INTRODUCTION
- UIP (uncovered interest parity) provides a relationship between:
  - the interest rate on an asset denominated in one country's currency,
  - the interest rate on a similar asset denominated in another country's currency,
  - and the expected rate of change in the spot exchange rate between the two currencies.
- Historical context and development:
  - Keynes (e.g., 1923: pp. 115-39) emphasized forward exchange trading after World War I.
  - Nineteenth-century literature largely focused on spot rates; Walther Lotz (1889) an exception.
  - Forward trading gave rise to covered interest parity (CIP), relating domestic-foreign interest differentials to the percentage difference between forward and spot rates.
  - UIP builds on CIP by postulating the forward rate equals the expected future spot rate under market forces.

### II. BASIC CONCEPTS
- Investor choices at time t:
  - Hold domestic asset yielding own rate r_t between t and t+1.
  - Hold foreign asset yielding r*_t, converting at spot s_t, accumulating s_t(1+r*_t) foreign units at t+1, then reconverting.
- Covered Interest Parity (CIP) condition (as stated):
  - (1) 1+r, = St( 1+rZ' )/ft .
  - If (1) did not hold, riskless arbitrage opportunities would exist.
- Uncovered Interest Parity (UIP) postulate (as stated):
  - (2) l+r, = E, [s, (l+r - )/s,+, I = st (l+r' - ) E, (Us,+,).
- Approximations and manipulations:
  - CIP implies (manipulated form presented in text).
  - First approximation for values of l+r, in the vicinity of 1 is noted.
  - Jensen's inequality caveat leading to approximation:
    - (5) r" - rt 2 E, [(st+, - s,)/s,l = (Erst+, - s,)/s,.
- Role of UIP:
  - Adds dynamics to CIP by linking observed variables at t to expected spot at t+1.
  - If valid at all horizons, observed spot and term structures could infer expected future spot path (Porter, 1971).
  - UIP central to debate on official intervention effectiveness: if UIP valid short-term, intervention cannot change spot relative to expected future spot without changing interest rates.

### III. EMPIRICAL EVIDENCE
- CIP evidence and limitations:
  - CIP abstracts from credit risks, capital controls, explicit taxes.
  - Interviews at large banks show CIP used as a trading formula; Eurocurrency rate differentials used to set forward/spot quotes and deposit spreads (Herring and Marston, 1976; Levich, 1985).
  - Taylor (1989) dataset (1967–1987) on bid-offer rates for multiple maturities found no unexploited profit opportunities in calm periods; arbitrage opportunities occurred during turbulence and increased with maturity length.
  - Deviations from CIP systematically related to effective taxes from capital controls and non-currency-specific risk premiums (Dooley and Isard, 1980).
- UIP testing methodology:
  - UIP harder to test because market expectations of future exchange rates are not directly observable.
  - Joint testing usually assumes rational expectations: future realization equals time-t expectation plus an error uncorrelated with information at t.
  - Leads to representation (as in text):
    - (7) st+l - s, = rt - r’ + ut+1
  - Regression specifications commonly used:
    - (8) and (9) st+[ - st = b,, + bl (rt - r”) I + ut+1 (form and numbering preserved from source).
- Empirical findings and issues:
  - Two empirical issues distinguished:
    - Size of prediction errors: interest differentials explain only a small proportion of subsequent exchange rate changes; suggests changes driven by unexpected information or “news.”
    - Systematic bias (unbiasedness tests): testing whether slope = 1 and intercept = 0.
      - Tests based on equation (8) often support slope = 1.
      - Tests based on equation (9) soundly reject slope = 1 for horizons of a year or less.
      - Conflict resolved in favor of (9) findings because (8) is not a legitimate regression equation.
  - Horizon dependence:
    - Strong rejection of unbiasedness at horizons up to one year.
    - Evidence more favorable to unbiasedness at horizons of five to twenty years; pooled industrial-country data with nonoverlapping five- to twenty-year averages yield slope coefficients in (9) insignificantly different from unity.

### IV. DOES PREDICTION BIAS REFUTE THE UIP ASSUMPTION?
- Interpretations of short-horizon prediction bias:
  1. Reject UIP but keep rational expectations: systematic bias reflects required risk premiums for holding uncovered foreign positions (risk aversion, omitted variable problem).
  2. Abandon rational expectations: market participants not fully rational.
  3. Explanations consistent with UIP and rational expectations:
     - Peso problem (Rogoff 1980; Krasker 1980): prolonged forward discount before anticipated devaluation leads to biased predictors over finite samples (example: Mexican peso 1976).
     - Simultaneity bias (Isard 1988; McCallum 1994): monetary authorities adjust short-term interest rates in response to exchange movements, biasing estimates if not modeled simultaneously.
     - Incomplete information with rational learning (Lewis 1988, 1989): repeated mistakes by rational agents can produce bias akin to peso problem.
     - Rational bubbles (self-fulfilling prophecies) possible but considered empirically implausible by most economists (Mussa, 1990).

### V. WHERE THINGS STAND
- Indirect tests via survey data:
  - Since UIP not directly testable, survey expectations collected since early 1980s have been used.
  - Studies show average survey forecasts deviate considerably from prevailing forward rates (Frankel and Froot, 1987; Takagi, 1991; Chinn and Frankel, 2002) — apparent evidence against UIP if averages are meaningful.
- Modeling pragmatic considerations:
  - Intertemporal open-economy models require linking current spot to expected future spot.
  - Abandoning UIP depends on ability to model the deviation (exchange risk premium = forward rate minus expected future spot).
  - Early portfolio-balance models (Dooley and Isard, 1983) explain only a small portion of exchange risk premium variation (Tryon, 1983; Boughton, 1987).
  - More sophisticated behavioral hypotheses relate exchange and credit risks to macroeconomic and political conditions of issuer countries (Dooley and Isard, 1983; Isard, 1988); casual evidence supportive but formal tests difficult.
- Practice in macroeconomic modeling:
  - Many models continue to impose UIP or UIP adjusted by an exogenous exchange risk premium.
  - Models imposing UIP and fully model-consistent expectations struggle to replicate observed macro behavior; thus models often treat exchange rate expectations as not completely rational.
  - Common practice: treat exchange rate expectations (and inflation expectations) as having both forward-looking (model-consistent) and backward-looking components.
- Final assessment:
  - Regardless of UIP's ex ante usefulness, there is abundant evidence that expected changes in spot exchange rates are generally dominated by unexpected changes.
  - Therefore, UIP alone provides a very inaccurate framework for predicting ex post exchange rate changes.

*Source — _wp0696 - References*

### References .............................................................................................................

### References

### I. INTRODUCTION
- UIP (uncovered interest parity) provides a relationship between:
  - the interest rate on an asset denominated in one country's currency,
  - the interest rate on a similar asset denominated in another country's currency,
  - and the expected rate of change in the spot exchange rate between the two currencies.
- Historical context:
  - Keynes (e.g., 1923: pp. 115-39) emphasized forward exchange trading after World War I.
  - Nineteenth-century literature largely focused on spot rates; Walther Lotz (1889) an exception.
  - Forward trading gave rise to covered interest parity (CIP), which relates domestic-foreign interest differentials to the percentage difference between forward and spot rates.
  - UIP builds on CIP by postulating the forward rate equals the expected future spot rate under market forces.

### II. BASIC CONCEPTS
- Investor choices at time t:
  - Hold domestic asset yielding own rate r_t between t and t+1.
  - Hold foreign asset yielding r*_t, converting at spot s_t, accumulating s_t(1+r*_t) foreign units at t+1, then reconverting.
- Covered Interest Parity (CIP) condition (as stated):
  - (1) 1+r, = St( 1+rZ' )/ft .
  - If (1) did not hold, riskless arbitrage opportunities would exist.
- Uncovered Interest Parity (UIP) postulate (as stated):
  - (2) l+r, = E, [s, (l+r - )/s,+, I = st (l+r' - ) E, (Us,+,).
- Approximations and manipulations:
  - CIP implies (manipulated form presented in text).
  - First approximation for values of l+r, in the vicinity of 1 is noted.
  - Jensen's inequality caveat leading to approximation:
    - (5) r" - rt 2 E, [(st+, - s,)/s,l = (Erst+, - s,)/s,.
- Role of UIP:
  - Adds dynamics to CIP by linking observed variables at t to expected spot at t+1.
  - If valid at all horizons, observed spot and term structures could infer expected future spot path (Porter, 1971).
  - UIP central to debate on official intervention effectiveness: if UIP valid short-term, intervention cannot change spot relative to expected future spot without changing interest rates.

### III. EMPIRICAL EVIDENCE
- CIP evidence:
  - CIP abstracts from credit risks, capital controls, explicit taxes.
  - Interviews at large banks show CIP used as a trading formula; Eurocurrency rate differentials used to set forward/spot quotes and deposit spreads (Herring and Marston, 1976; Levich, 1985).
  - Taylor (1989) dataset (1967–1987) on bid-offer rates for multiple maturities found no unexploited profit opportunities in calm periods; arbitrage opportunities occurred during turbulence and increased with maturity length.
  - Deviations from CIP systematically related to effective taxes from capital controls and non-currency-specific risk premiums (Dooley and Isard, 1980).
- UIP testing issues:
  - UIP harder to test because market expectations of future exchange rates are not directly observable.
  - Joint testing usually assumes rational expectations: future realization equals time-t expectation plus an error uncorrelated with information at t.
  - Leads to representation (as in text):
    - (7) st+l - s, = rt - r’ + ut+1
  - Regression specifications commonly used:
    - (8) and (9) st+[ - st = b,, + bl (rt - r”) I + ut+1 (form and numbering preserved from source).
  - Two empirical issues distinguished:
    - Size of prediction errors: interest differentials explain only a small proportion of subsequent exchange rate changes; suggests changes driven by unexpected information or “news.”
    - Systematic bias (unbiasedness tests): testing whether slope = 1 and intercept = 0.
      - Tests based on equation (8) often support slope = 1.
      - Tests based on equation (9) soundly reject slope = 1 for horizons of a year or less.
      - Conflict resolved in favor of (9) findings because (8) is not a legitimate regression equation.
  - Horizon dependence:
    - Strong rejection of unbiasedness at horizons up to one year.
    - Evidence more favorable to unbiasedness at horizons of five to twenty years; pooled industrial-country data with nonoverlapping five- to twenty-year averages yield slope coefficients in (9) insignificantly different from unity.

### IV. DOES PREDICTION BIAS REFUTE THE UIP ASSUMPTION?
- Interpretations of short-horizon prediction bias:
  1. Reject UIP but keep rational expectations: systematic bias reflects required risk premiums for holding uncovered foreign positions (risk aversion, omitted variable problem).
  2. Abandon rational expectations: market participants not fully rational.
  3. Explanations consistent with UIP and rational expectations:
     - Peso problem (Rogoff 1980; Krasker 1980): prolonged forward discount before anticipated devaluation leads to biased predictors over finite samples (example: Mexican peso 1976).
     - Simultaneity bias (Isard 1988; McCallum 1994): monetary authorities adjust short-term interest rates in response to exchange movements, biasing estimates if not modeled simultaneously.
     - Incomplete information with rational learning (Lewis 1988, 1989): repeated mistakes by rational agents can produce bias akin to peso problem.
     - Rational bubbles (self-fulfilling prophecies) possible but considered empirically implausible by most economists (Mussa, 1990).

### V. WHERE THINGS STAND
- Indirect tests via survey data:
  - Since UIP not directly testable, survey expectations collected since early 1980s have been used.
  - Studies show average survey forecasts deviate considerably from prevailing forward rates (Frankel and Froot, 1987; Takagi, 1991; Chinn and Frankel, 2002) — apparant evidence against UIP if averages are meaningful.
- Modeling pragmatic considerations:
  - Intertemporal open-economy models require linking current spot to expected future spot.
  - Abandoning UIP depends on ability to model the deviation (exchange risk premium = forward rate minus expected future spot).
  - Early portfolio-balance models (Dooley and Isard, 1983) explain only a small portion of exchange risk premium variation (Tryon, 1983; Boughton, 1987).
  - More sophisticated behavioral hypotheses relate exchange and credit risks to macroeconomic and political conditions of issuer countries (Dooley and Isard, 1983; Isard, 1988); casual evidence supportive but formal tests difficult.
- Practice in macroeconomic modeling:
  - Many models continue to impose UIP or UIP adjusted by an exogenous exchange risk premium.
  - Models imposing UIP and fully model-consistent expectations struggle to replicate observed macro behavior; thus models often treat exchange rate expectations as not completely rational.
  - Common practice: treat exchange rate expectations (and inflation expectations) as having both forward-looking (model-consistent) and backward-looking components.
- Final assessment:
  - Regardless of UIP's ex ante usefulness, there is abundant evidence that expected changes in spot exchange rates are generally dominated by unexpected changes.
  - Therefore, UIP alone provides a very inaccurate framework for predicting ex post exchange rate changes.

*Italic: Source — _wp0696 - References*

### REFERENCES

### _wp0696 - REFERENCES

### Econometric tests and empirical assessments of exchange rate models
- Boughton, J.M.. 1987. “Tests of the Performance of Reduced-Form Exchange Rate Models,“ Journal c?f’I?ltenl~ltiorlcrl Economics. Vol. 23. pp. 41-56.
- Levich, R.M., 1985, “Empirical Studies of Exchange Rates: Price Behavior, Rate Determination and Market Efficiency,” in R.W. Jones and P.B. Kenen (eds.), Hundbook qf Intc~rrzationcrl Economics, Vol. 2 (Amsterdam: North Holland), pp. 979- 1040.
- Mussa. M., 1979, “Empirical Regularities in the Behavior of Exchange Rates and Theories of the Foreign Exchange Market,“ Ccrrrzegie-Roclzester Conference Series on Public Policy, Vol. 11, pp. 9-57.
- Mussa. M., 1990, ”Exchange Rates in Theory and Reality,“ E.s.su~.s irz Zrltenzatio~~rl Firzunce No. 179 (Princeton: International Finance Section, Department of Economics, Princeton University).
- Meese, R.A., 1989, “Empirical Assessment of Foreign Currency Risk Premiums,” in C.C. Stone (ed.), Financial Risk: Theon, Evidence and Iw~plications (Boston: Kluwer), pp. 157-80.
- Krasker, W.S.. 1980. “The Peso Problem in Testing the Efficiency of Forward Exchange Markets.” Journal of Monetcrn Economics, Vol. 6, pp. 269-76.
- Lewis, K.K., 1989, “Changing Beliefs and Systematic Rational Forecast Errors with Evidence from Foreign Exchange,” Anwrican Economic Revien,, Vol. 79, pp. 621-36.
- Lewis, K.K., 1988, “The Persistence of the ‘Peso Problem’ when Policy is Noisy,” Journal of Interncrtiorzcrl Money unrl Filzance, Vol. 7, pp. 5-21.

### Interest parity, forward markets, and term structure
- Chinn, M.D., and Meredith. G., 2004. “Monetary Policy and Long Horizon Uncovered Interest Parity,“ IMF Staff Papers, Vol. 51, pp. 409-30.
- Dooley, M.P., and Isard, P., 1980, “Capital Controls, Political Risk and Deviations from Interest-Rate Parity,” Jo~lrncrl of Political Econom?>, Vol. 88. pp. 370-84.
- Dooley, M.P., and Isard, P., 1983, ”The Portfolio-Balance Model of Exchange Rates and Some Structural Estimates of the Risk Premium.” IMF StyfPcprs, Vol. 30, pp. 683-702.
- Dooley, M.P., and Isard, P., 1991, ”A Note on Fiscal Policy, Investment Location Decisions, and Exchange Rates.” Jmrtzd c~fl~~tenzution~l Money nnd Finance, Vol. 10, pp. 161 -68.
- Herring. R.J., and Marston, R.C., 1976, “The Forward Market and Interest Rates in the Eurocurrency and National Money Markets,” in C.H. Stern, J.H. Makin, and D.E. Logue (eds.), Elrrocurrencies and the International Monetary System (Washington: American Enterprise Institute), pp. 139-63.
- Porter, M.G., 1971. “A Theoretical and Empirical Framework for Analyzing the Term Structure of Exchange Rate Expectations.” ZMF Stujf’Pclpers, Vol. 18, pp. 61 3-42.
- McCallum, B.T., 1994, “A Reconsideration of the Uncovered Interest Parity Relationship,” Jolrrnul of Moneran Economics, Vol. 33, pp. 105-32.
- Rogoff. K.. 1980, “Tests of the Martingale Model for Foreign Exchange Futures Markets,” in Essays 011 E.xpectatiot1s cuzd E.xcllcn~ge RLIte Volntility (doctoral dissertation; Cambridge, Massachusetts: Massachusetts Institute of Technology).

### Exchange rate expectations, surveys, and news
- Chinn, M.D., and Frenkel, J.A., 2002. “Survey Data on Exchange Rate Expectations: More Currencies. More Horizons, More Tests.” in W. Allen and D. Dickinson (eds.), MonetcRn Policy> Ccqital Flow:s, c1nd Fim~nci~rl Market Der~e1opment.s in ~111 Ercr of Fin~~rzcinl Glob~di;~tion: Es.scr?w in Honorrr c?fMu.x Fn (London: Routledge). pp. 145-67.
- Frankel, J.A.. and Froot, K.A.. 1987, “Using Survey Data to Test Standard Propositions Regarding Exchange Rate Expectations.” Anzerican Econornic Review, Vol. 77, pp. 133-53.
- Frenkel, J.A., 1981, “Flexible Exchange Rates, Prices and the Role of ‘News’: Lessons from the 1970s.” Jo~rrnal qf Politicwl Economy. Vol. 89, pp. 665-705.
- Takagi. S., 1991, “Exchange Rate Expectations: A Survey of Survey Studies,” ZMF Stqf Pczpers, Vol. 38, pp. 156-83.
- Taylor. M.P., 1989, “Covered Interest Arbitrage and Market Turbulence,” Economic Jozrrnul, Vol. 99, pp. 376-91.
- Krasker, W.S.. 1980. “The Peso Problem in Testing the Efficiency of Forward Exchange Markets.” Journal of Monetcrn Economics, Vol. 6, pp. 269-76.
- Porter, M.G., 1971. “A Theoretical and Empirical Framework for Analyzing the Term Structure of Exchange Rate Expectations.” ZMF Stujf’Pclpers, Vol. 18, pp. 61 3-42.

### Market microstructure, intervention, and policy-related studies
- Flood, R.P., and Taylor, M.P., 1997, “Exchange Rate Economics: What’s Wrong with the Conventional Macro Approach‘?’’ in J.A. Frankel, G. Galli, and A. Giovannini (eds.), The Microstructure of Foreign Exchunge Murkets (Chicago: University of Chicago Press), pp. 261-94.
- Henderson, D.W.. and Sampson S., 1983. “Intervention in Foreign Exchange Markets: A Summary of Ten Staff Studies,” Federal Reserve Bulletin (November), pp. 830-36.
- Tryon, R.W., 1983, “Small Empirical Models of Exchange Market Intervention: A Review of the Literature,” Staff Studies 134 (Washington: Board of Governors of the Federal Reserve System).
- Dooley, M.P., and Isard, P., 1983, ”The Portfolio-Balance Model of Exchange Rates and Some Structural Estimates of the Risk Premium.” IMF StyfPcprs, Vol. 30, pp. 683-702.
- Isard. P., 1978, ”Exchange-Rate Determination: A Survey of Popular Views and Recent Models,” Princeton Studies in International Finance, No. 42 (Princeton: International Finance Section. Department of Economics, Princeton University).
- Isard. P., 1988, “Exchange Rate Modeling: An Assessment of Alternative Approaches,” in R.C. Bryant, D.W. Henderson. G. Holtham, P. Hooper. and S.A. Symansky (eds.), Empiricul Mcrcroecorzor?lic..s,fi,r lnterclependetzt Ecorzomies (Washington: Brookings Institution), pp. 183-201.

### Historical, theoretical, and foundational texts
- Einzig, P., 1962. The Histon! qf Foreign Exchcrnge (London: Macmillan).
- Keynes, J.M., 1923. A Truct on Monetnry R&-tn (London: Macmillan).
- Lotz, W., 1889, “Die Wahrungsfrage in Ostesreich-Ungarn,” Schmollers Juhrhuch, Vol. 13, pp. 34-35.
- Isard. P., 1995. Esc~hnnge Rcrte Economics (Cambridge: Cambridge University Press).
- Meese, R.A., 1989, “Empirical Assessment of Foreign Currency Risk Premiums,” in C.C. Stone (ed.), Financial Risk: Theon, Evidence and Iw~plications (Boston: Kluwer), pp. 157-80.

*Source: _wp0696 - REFERENCES (PDF chapter/section).*

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