Exchange Rates: Two Stylized Facts and Yet Another (Consequent) Puzzle

My colleague, Charles Engel, has a new paper entitled The Real Exchange Rate, Real Interest Rates, and the Risk Premium, in which he tries to identify what characteristics an exchange rate model must possess in order to explain two stylized facts.

…The well-known interest parity puzzle in foreign exchange markets finds … the high interest rate country tends to have the higher expected return in the short run. The second stylized fact concerns evidence that when a country’s relative real interest rate rises above its average, its currency tends to be stronger than average in real terms.

The first stylized fact pertains to forward rate bias, or equivalently the fact that ex post uncovered interest parity doesn’t hold, discussed in these posts [1] [2]. Engel sums up the results of the paper:

This paper produces evidence that confirms these empirical regularities for the exchange rates of the G7 countries (Canada, France, Germany, Italy, Japan and the U.K.) relative to the U.S. However, these findings, taken together, constitute a previously unrecognized puzzle regarding how cumulative excess returns or foreign exchange risk premiums affect the level of the real exchange rate. Theoretically, a currency whose assets are perceived to be risky prospectively — looking forward from the near to the distant future — should be weaker, ceteris paribus. The evidence cited implies that when a country’s relative real interest rate is high, the country’s securities are expected to yield an excess return over foreign securities in the short run; but, because the high-interest rate currency tends to be stronger, over longer horizons the foreign asset is expected to yield an excess return. This behavior of excess returns in the foreign exchange market poses a challenge for conventional theories of the foreign exchange risk premium.
In brief, when one country’s interest rate is high, its currency tends to be stronger than average in real terms, it tends to keep appreciating for awhile, and then depreciates back toward its long-run value. But leading models of the forward-premium anomaly do not account for the behavior of the level of the real exchange rate: they predict that the high-interest rate currency will be weaker than average in real terms and appreciate over both the short- and long-run. A risk-based explanation for the empirical regularities requires a story of some sort of reversal of the risk premium – the securities of the high-interest rate country must be relatively riskier in the short-run, but expected to be less risky than the other country’s securities in the more distant future. It may be difficult to rationalize this pattern by focusing on the risk premium required by a single agent in each economy, as many theoretical models do. Instead, a full explanation may require interaction of more than one type of agent and perhaps also requires introducing some sort of “stickiness” in the financial markets — delayed reaction to news, slow adjustment of expectations, liquidity constraints, momentum trading, or other sorts of imperfections.

The entire paper is here.

5 thoughts on “Exchange Rates: Two Stylized Facts and Yet Another (Consequent) Puzzle

  1. ppcm

    I wished,I never read this post and its attachment, 50 pages of plain maths and few words to explain.
    Integrating the interest rates differential,inflation and current accounts as the keystone of currencies valuation
    Aknowledging the long pervasive currencies foreign exchange overshooting phenomenon.
    Assuming the risk factor (current account deterioration is embedded in the interest rate) The existence of markets auto stabilization through exchange rates mechanism Home vs foreign.
    Aknowledging the existence of the carry trade foreign exchange,interest rates (assuming the supply interest rates,currencies to be elastic revisited in 2008 as it drove to the subsequent central banks currencies swaps)
    Assuming the sample of foreign exchange participants as representative.
    To conclude with either a market anomaly or implicitly the existence of markets participants mis behavior.
    These hereunder graphs may test the validity of the assumptions ( there should be more exhaustive comparison and not with Europe euro only where the manufacturing process was to offer no risk premium, no interest rates differential)
    Risk premium or auto stabilization through interest rates?
    Balance on Current Account (BOPBCA) Please note, the balance of current account starts to deteriorate in 1990 (the currencies overshooting may be long)
    Risk premium?
    10-Year Treasury Constant Maturity Rate (DGS10)
    Auto stabilization?
    Please note as the US current account deteriorates,the USD is appreciating
    U.S. / Euro Foreign Exchange Rate (DEXUSEU
    Is the sample of foreign exchange participants testifying for a market in large?
    OCC derivatives report 3Q 2010
    The foreign exchange markets auto stabilization ?
    BIS Triennal central banks survey
    Should my understanding be correct the currencies misalignment is left open.

  2. 2slugbaits

    I’m not an economist and I’ll admit that even as an interested amateur this isn’t an area of economics that I follow all that closely, but there was much in this paper that left me totally confused. I always thought that the stylized fact from the standard model was that deficits or higher economic activity put upward pressure on interest rates, which then put upward pressure on currency as investors demanded more currency in order to buy higher return assets. So to the extent that this standard model explains the co-movements of short term interest rates and currency rates I don’t see how this is described as a risk premium. The risk was always understood to be the longer term risk of currency depreciation due to the likelihood of inflation resulting from sustained deficit spending or strong economic activity.
    The discussion on stationarity of the exchange rates left my head spinning. For example, I found this sentence confusing:
    We present evidence here that favors the hypothesis of no unit root in the real exchange rate.
    Huh? Is that a typo? Most of the unit root tests in Table 1 show that you cannot reject the null, which favors the hypothesis of accepting a unit root. Also, the timeframe in Table 1 includes the German reunification, which suggest using something like a Lutkepohl & Saikkonen cointegration test with shift dummy to account for a structural break.
    The paper also says that the choice of the price index and the weights assigned to its components isn’t terribly important. But didn’t you recently post some work suggesting that exchange rates should be adjusted to unit labor costs? A rise in unit labor costs suggests a rise in core inertial inflation, which would add to investor risk; but a rise in headline CPI would not necessarily signal added long term risk.
    Finally, the paper says:
    An investment that involves rolling over short term assets has different risk characteristics than holding a long-term asset. Hence we coin the phrase “prospective” real interest differential to avoid the trap of calling tR the long-term real interest differential.
    I thought the usual way of handling this was to use a Mean-in-GARCH so as to adjust the mean return of the long-term asset.

  3. Menzie Chinn

    2slugbaits: These are useful questions. There are many “standard” models floating around. In policy and journalistic discussions, an ad hoc model based on flows of capital drive rates. But since the late 1970’s, we’ve relied mostly on asset-based models that focus on stocks. The risk premium in the more modern (optimizing) models is a function of the correlation of relative returns with (essentially) consumption changes.

    On the unit root issue, one can interpret the same statistical results in different ways. However, stylized facts change with the sample period, and the large reversions in 2008-09 seem to have induced more evidence of stationarity. Structural breaks tend to make unit root tests fail to reject, so the fact that the DF-GLS test rejects the unit root null would not change the interpretation.

    Regarding the appropriate deflator for real exchange rates, it depends on what question one is considering. For “competitiveness”, I think ULC-deflated is better. In considering a representative consumer/asset holder model, a consumer-based basket is more appropriate.

    Regarding the long term interest rate vs. discounted short term, I think the point is he didn’t want to have to model the term premium.

  4. 2slugbaits

    Yes, I agree that including a structural break makes it more likely that one could reject the null. Similarly with seasonal dummies, although I cannot think of any intuitive reason why there would be seasonal factors in exchange rates.
    As to the long run stability of stationarity tests, this is a huge practical problem. In my own work on stationarity of the failure of high dollar value components on Army weapon systems I’ve found that if you recursively test for unit roots in the data (e.g., test at 100 observations, then again at 101, then 102, etc.), what you’ll find is that there are prolonged periods of each. And this pattern can be very different depending on which information criterion you use to determine the lag length. I see where your colleague used BIC, which has the advantage of parsimony, but I’m finding that AIC and FPE tend to be a little better at identifying turning points in stationarity. I have no idea why and it may just be an artifact of the data, but over literally thousands of recursive unit root tests this pattern is pretty clear.

  5. Bruce Krasting

    Possibly I miss something. The author speaks about the forward market for currencies and the fact that the forward market is a poor indicator of the future.
    Let’s be clear.The forward rate has nothing to do with expectations about where currencies will be on a relative basis at some point in the future.
    The forward is ALWAYS the interest differential between the two currencies at the time the observation is made.
    I wrote about this recently in regard to silver. Silver had just gone backward. (futures less than cash) I explained why this was bullish.
    I used real examples of the AUSUSD spot and one year to make a point. That should make the case here. The forward market is just the flip side of the swaps.
    note: First part is on point the second somewhere in the clouds. If you want to discuss this my email is in the blog.

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