The Mussa puzzle and the optimal exchange rate policy

Oleg Itskhoki, Dmitry Mukhin 17 January 2022

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What is the most convincing evidence that monetary shocks affect real outcomes? When Nakamura and Steinsson (2018) surveyed prominent macroeconomists, “the three most common answers were: the evidence presented in Friedman and Schwartz (1963) regarding the role of monetary policy in the severity of the Great Depression; the Volcker disinflation of the early 1980s and accompanying twin recession; and the sharp break in the volatility of the US real exchange rate accompanying the breakdown of the Bretton Woods System of fixed exchange rates in 1973”.  This third fact, famously documented by Mussa (1986), is especially appealing as it relies on a simple and clear identification of the causal real effect from a shift in monetary policy: a large and discontinuous change in the nominal exchange rate process makes it hard to attribute the increased volatility of the real exchange rate to any other factors (see Figure 1).1

Figure 1 Nominal and real exchange rates

Note: monthly log changes, US vs the rest of the world (defined as G7 countries except Canada plus Spain), with the red vertical line identifying the end of the Bretton Woods system of fixed exchange rates.

Figure 2 Inflation and consumption growth

Note: monthly inflation and quarterly consumption growth rates for G7 countries except Canada plus Spain. 

What is missing from this narrative, however, is that there was no simultaneous change in the properties of other macro variables – neither nominal like inflation, nor real like consumption and output (Baxter and Stockman 1989, Flood and Rose 1995, and Figure 2). One could interpret this as an extreme form of neutrality, where a major shift in the monetary regime, which increases the volatility of the nominal exchange rate by an order of magnitude, does not affect the equilibrium properties of any macro variables, apart from the real exchange rate. In fact, this is a considerably more puzzling part of the larger set of ‘Mussa facts’ summarised in Figures 1 and 2. In a recent paper, we argue that this evidence points to a particular unconventional transmission mechanism of monetary policy and has important normative implications for both open and closed economies (Itskhoki and Mukhin 2021b). 

Why can’t sticky prices resolve the puzzle?

The conventional wisdom among both academic researchers and policymakers is that the Mussa puzzle points to the importance of nominal rigidities (Monacelli 2004). Indeed, sticky prices and wages imply that inflation adjusts sluggishly and ensure that the real exchange rate closely co-moves with the nominal exchange rate. However, this interpretation misses the second half of the picture: a change in equilibrium exchange rate volatility requires a change in monetary policy, which under sticky prices must be accompanied by changing properties of output, consumption, and other real variables. With nominal rigidities, monetary policy has a direct effect on consumption, investment, and GDP. Therefore, this argument does not rely on trade openness and the nature of import price stickiness, which mute the exchange rate pass-through at the border; thus, it applies even for relatively closed economies such as the US importing goods in domestic currency.2 

Financial channel of monetary policy

We propose an alternative framework where monetary non-neutrality arises due to financial market segmentation with local agents borrowing and saving in domestic currency and all international capital flows intermediated by risk-averse arbitrageurs (Jeanne and Rose 2002, Gabaix and Maggiori 2015). The model features liquidity demand shocks in international asset markets, which our earlier work shows to be essential in explaining the exchange rate disconnect from macroeconomic fundamentals under a floating regime and resolve a variety of associated exchange rate puzzles, including the Meese-Rogoff, purchasing power parity (PPP), Backus-Smith and forward premium puzzles (Itskhoki and Mukhin 2021a).3 

A change in the exchange rate regime, and the associated change in nominal exchange rate volatility, determines the quantity of risk faced by intermediaries when participating in international financial transactions, in particular in currency carry trades. Greater nominal exchange rate volatility discourages intermediation and results in larger equilibrium interest rate gaps across countries under the floating regime.4 In contrast, a lower nominal exchange rate volatility under the peg encourages intermediation, shielding real exchange rates from financial shocks. As a result, a change in the monetary regime has real consequences via the financial market, even when prices are fully flexible, thus affecting the volatility of both nominal and real exchange rates simultaneously. This mechanism is consistent with larger deviations from the uncovered interest rate parity (UIP) and more distorted international risk sharing, as measured by the Backus-Smith correlation, after the breakdown of Bretton Woods (see Figure 3).

Figure 3 Risk premia and risk sharing before and after the end of Bretton Woods

Note: The left panel displays Fama regression coefficient from an OLS regression of nominal exchange rate depreciation on interest rate differential (monthly data; 1960-72 for Peg and 1973-90 for Float); departures from +1 and, in particular, negative Fama coefficients identify large UIP deviations. The right panel displays the Backus-Smith correlation between relative consumption growth and real exchange rate depreciation (annual data; 1960-71 for Peg and 1973-89 for Float); efficient international risk sharing implies that this correlation must be positive and large. The figures display results for individual countries against the US, and RoW stands for G7 countries without Canada plus Spain. Negative Fama coefficients and negative Backus-Smith correlations suggest high international risk premia and low international risk sharing, respectively (Itskhoki and Mukhin 2021b). 

Importantly, a credible commitment to a peg encourages intermediaries to absorb most of the shocks in financial markets confronting the monetary authority with little need to compromise between inflation and exchange rate stabilisation. As a result, the model is consistent with a dramatic change in exchange rate volatility unaccompanied by any comparable change in macroeconomic volatility, whether nominal or real. Instead, macroeconomic outcomes are primarily shaped by fundamental macroeconomic forces, such as productivity and aggregate demand shocks, and in turn are largely insensitive to volatility in the international financial market and in the resulting exchange rate volatility.

Policy implications

This new interpretation of the Mussa puzzle fits well with the growing evidence supporting the transmission of monetary shocks via financial markets (e.g. Rey 2018, Kalemli-Ozcan 2020) and has several important policy implications. In particular, it points to a fundamental trade-off faced by monetary authorities in open economies, namely, a floating exchange rate regime improves allocations in the product market by facilitating international expenditure shifting in response to macroeconomic shocks (Friedman 1953), yet it may result in excessive exchange rate volatility in response to financial shocks, which limits the extent of international risk sharing. 

In general, a combination of two policy instruments – conventional interest rate policy and foreign exchange (FX) interventions – is required to achieve the efficient allocation, as we show in Itskhoki and Mukhin (2022). The latter policy tool is highly effective under segmented financial markets, but might be subject to several additional restrictions. In particular, inability to have negative foreign reserves, risks associated with expanding the central bank's balance sheet, and limited ability to disentangle financial and fundamental shocks make the first best policy infeasible.

When FX interventions are not feasible and the central bank is limited to solely setting the interest rate, there exists a special case when this policy can simultaneously achieve the optimal outcome in the product market and implement efficient risk sharing internationally. We refer to it as an open-economy counterpart to the celebrated ‘divine coincidence’ in the closed economy. In particular, this special case obtains when the real exchange rate supporting the first-best allocation in the product market is constant. In this case, the monetary authority should fully stabilise the nominal exchange rate using exchange rate targeting, which simultaneously ensures stable domestic inflation and eliminates the output gap. 

More generally, however, the optimal policy faces a trade-off and must deviate from exclusive inflation and output gap targeting in order to partially stabilise the nominal exchange rate. Because financial market expectations are the key determinant of the risk premium, the credibility of monetary policy plays a central role: it is not possible to improve international risk sharing without reputation and commitment. Without credible commitment, the policy should focus exclusively on the domestic goal of stable inflation.

These policy implications are not limited to an open economy environment. The ability of a peg to stabilise the risk premium on the carry trade raises the question of whether monetary policy can and should partially stabilise the volatility of risk premia in other financial markets, including equity and long-term debt. How such policies affect the economy and whether they are desirable are important questions for future research.

References

Baxter, M and A C Stockman (1989), “Business cycles and the exchange-rate regime: Some international evidence,” Journal of Monetary Economics 23(3): 377–400. 

Flood, R P and A K Rose (1995), “Fixing exchange rates A virtual quest for fundamentals,” Journal of Monetary Economics 36(1): 3–37. 

Friedman, M (1953), “The case for flexible exchange rates,” Essays in Positive Economics 157(203): 33. 

Gabaix, X and M Maggiori (2015), “International Liquidity and Exchange Rate Dynamics,” The Quarterly Journal of Economics 130(3): 1369–1420.

Itskhoki, O and D Mukhin (2021a), “Exchange Rate Disconnect in General Equilibrium,” Journal of Political Economy 129(8): 2183–2232.

Itskhoki, O and D Mukhin (2021b), “Mussa Puzzle Redux,” NBER Working Paper No. 28950.

Itskhoki, O and D Mukhin (2022), “Optimal Exchange Rate Policy,” working paper. 

Jeanne, O and A K Rose (2002), “Noise Trading and Exchange Rate Regimes,” The Quarterly Journal of Economics 117(2): 537–569. 

Kalemli-Ozcan, S (2020), “US monetary policy, international risk spillovers, and policy options,” VoxEU.org, 16 January.

Monacelli, T (2004), “Into the Mussa puzzle: monetary policy regimes and the real exchange rate in a small open economy,” Journal of International Economics 62(1): 191–217. 

Mussa, M L (1986), “Nominal exchange rate regimes and the behavior of real exchange rates: Evidence and implications,” Carnegie-Rochester Conference on Public Policy 25(1): 117–214. 

Nakamura, E and J Steinsson (2018), “Identification in Macroeconomics,” Journal of Economic Perspectives 32(3): 59–86. 

Rey, H (2018), “The global financial cycle,” EEA-FBBVA Lecture Interview 2016.

Endnotes

1 The break-up of the Bretton Woods system is indeed a unique natural experiment. First, it constituted a large discontinuous break in the monetary regime from a near-perfect system of fixed exchange rates to a pure float between the US dollar and other major currencies. Second, the Bretton Woods system was more credible and persistent than most alternative pegs. Third, the breakup of the Bretton Woods system featured two large regions and multiple countries, as opposed to isolated small open economies which typically enter and exit pegs as part of a broader domestic policy shift.

2 While real business cycle models are consistent with this neutrality of macroeconomic variables in Figure 2, these models cannot explain the changing behavior of the real exchange rate in Figure 1 – the origin of the Mussa puzzle.

3 The Meese-Rogoff puzzle emphasizes the lack of even contemporaneous correlations between exchange rates and macroeconomic fundamentals, either nominal or real. Exchange rates are also an order of magnitude more volatile than macroeconomic aggregates such as consumption, output, and inflation. Purchasing power parity (PPP) puzzle emphasizes that the real exchange rate closely tracks the nominal exchange rate at most frequencies and in particular exhibits a similarly large volatility and persistence, without a clear pattern of mean reversion to purchasing power parity even in the medium run. The Backus-Smith puzzle and the Forward premium puzzle, or the violation of the uncovered interest rate parity (UIP), emphasize the lacking relationships between exchange rates and consumption growth and interest rate differentials, respectively, which are implied by the conventional equilibrium conditions in the financial market.

4 Interest rate gaps across countries, or more precisely across funding currencies, are called uncovered interest rate parity (UIP) deviations and are a common feature in the data, giving rise to profitable, yet risky, carry trades.

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Topics:  Exchange rates Monetary policy

Tags:  Mussa puzzle, floating exchange rate regime, exchange rate policy, sticky prices

Professor of Economics at University of California, Los Angeles, CEPR Research Affiliate

Assistant Professor of Economics, London School of Economics and CEPR Research Affiliate

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