*One of David Ricardo’s foundational assertions was the law of one price. That tradeable goods will cost the same, when their transport costs are included, in different places. The insight being that if they weren’t then people would buy in one, sell in the other, thereby equalising prices. A reasonable corollary to this idea is that exchange rates should move based upon purchasing parity or interest rate parity. The second is because people can move their money, just like anything else, to arbitrage between prices – here, the interest rate. The other because, well, that’s what arbitrage will do, equalise those PPP exchange rates. Not wholly, not perfectly, but roughly enough.*

As it turns out, 201 years later, Ricardo is still right. amazing for a Dead White Guy:

Nominal exchange rate dynamics and monetary policy: Uncovered interest rate parity and purchasing power parity revisited

Yossi Saadon, Nathan Sussman 31 October 2018

Global integration has increased rapidly over recent decades, leaving basic theories of exchange rate equilibrium ripe for reconsideration. This column tests two such theories – purchasing power parity and uncovered interest rate parity – using the case of the advanced, small open economy of Israel and the US. The results show that when the necessary conditions are met, the purchasing power parity and uncovered interest rate parity relationships continue to hold in the short run.

The effectiveness of monetary policy and its impact have been debated since the onset of the Global Crisis. Forbes (2018)recently emphasised the increasing impact of global factors on domestic inflation and the Phillips curve. Meanwhile, central banks became increasingly concerned with developments in their economies’ exchange rates. Some intervened in foreign exchange markets to defend their currencies against appreciation. Increasing global economic integration and the increasing preoccupation with exchange rates call for revisiting the basic theories of exchange rate equilibrium: purchasing power parity (PPP) and uncovered interest rate parity (UIP).

PPP and UIP are nominal exchange rate equilibrium conditions. The basic PPP relationship relates to the currentaccount and states that in competitive international markets, the price of a tradable good sold at home should equal its price abroad multiplied by the exchange rate. The UIP relationship relates to the capital account and states that if capital flows are free and exchange rates are flexible, the nominal interest rate on a domestic bond should equal the interest rate of a comparable foreign bond plus the expected change in the nominal exchange rate over the duration of the bond.

The PPP relationship gained worldwide notoriety with The Economist’s Big Mac index. The empirical validity of the PPP and UIP relationship was tested in a variety of specifications and samples. A survey by Taylor and Taylor (2006) concluded that the PPP holds in the ‘long run’ and that short-term deviations tend to revert to it. Chinn (2004) provides evidence that UIP also holds in the ‘long run’, when tested with long maturity bonds. Engel (2016) recently documented that UIP does not hold for short-term interest rates. Owing to transaction costs, taxes, and other frictions, PPP is often stated in terms of rates of change. Under rational expectations, this means that the expected change of the nominal exchange rate equals the difference between domestic and foreign expected inflation rates.

PPP and UIP equilibrium conditions are appealing because they are based on a fundamental assumption – namely, the absence of arbitrage. Hence their popularity in textbooks. However, they require conditions that are hard to fulfil. PPP and UIP require perfect competition in traded goods, and the UIP condition also needs deep financial markets and free capital flows. To jointly test the dynamics of nominal exchange rates related to the current and capital accounts, we also require flexible exchange rates. These conditions limit the cases that can be used to examine the validity of these textbook economic conditions. We are looking for small (financially) advanced open economies with flexible exchange rates.

## Testing for PPP and UIP in an advanced small open economy

Our empirical strategy calls for selecting data that match as closely as possible the assumptions behind these no-arbitrage conditions. In particular, we need forward-looking data, rather than the often-used backward-looking data. Our contribution is to use data from Israel, a small, advanced, and open economy that can be considered a price taker in global consumer goods and financial markets. Because of its history of high inflation, short-term inflation-indexed bonds are traded in a relatively deep market. This allows us to use forward-looking 12 months’ market-based breakeven inflation rates. These are publicly available from the Bank of Israel. In Figure 1, we demonstrate that the backward-looking inflation differential differs substantially from the forward-looking differential. This difference underscores the importance of using forward-looking inflation differentials to anchor the expected change in the exchange rate. The Bank of Israel issues a 12-month nominal bill (the Makam). We used this to compute the interest rate differential with a 12-month constant maturity US Treasury bill. Fortunately, nominal yields for 12 months differed substantially during the financial crisis (see Figure 2). This allows us to exploit a longer time series in a period when yields on 12-month US Treasuries did not vary much.

**Figure 1 **Forward and backward looking expected inflation differential between Israel and the US, 1996–2018

*Sources*: Backward looking PPP: Israel: 12 month percent change in CPI all items, 2016=100, Not seasonally adjusted (CBS), US: CPI for All Urban Consumers: All Items, Index 1982-1984=100, Not Seasonally Adjusted (FRED) Forward looking PPP: Israel: 12 months breakeven inflation rate, Bank of Israel. U.S: Michigan consumer survey, FRED.

**Figure 2 **The yield on 1-year BOI bond yield and 1-year US Treasury bond yield, 1996–2018

*Sources*: Israel, Bank of Israel. U.S. 1 Year constant maturity treasury bill, FRED.

## PPP and UIP hold in an advanced small open economy

We estimated the relationship between the percentage change in the Israeli new shekel and the US dollar over a 12-month period as a function of the 12 months’ inflation expectations differential between Israel and the US prevailing at the beginning of the period. We used both OLS and two-stage least squares. We were not able to reject the hypothesis that relative PPP, based on forward-looking inflation expectations, holds. The coefficient of the expected inflation rate differential is equal, as in the theory, to one. Similar to findings in the literature, estimating this equation using actual inflation, we can reject the hypothesis of relative PPP. To test for convergence to equilibrium we estimated a vector error correction model for the relative PPP relationship. We found that following a shock, it takes on average a year for the exchange rate to revert to its equilibrium level.

The second step was to estimate the UIP relationship. We regressed the spread between Bank of Israel bills and US Treasuries on the expected change in the exchange rate. A variety of specifications show that UIP holds with a coefficient of one. This result was obtained by estimating a simple OLS regression of the interest rate differential on the forward change in the exchange rate. To test whether the PPP and UIP are jointly determined, we estimated the UIP relationship substituting the expected change in exchange rates with the expected inflation differential (from the PPP equation). Finally, we estimated the joint equilibrium conditions using two-stage least squares estimation. The PPP relationship was the first stage, and the UIP relationship was the second stage. Again, we obtained a coefficient of one. Figure 3 shows the results of this estimation. Estimating a vector error correction equation for the UIP relationship, we find that the exchange rate reverts to the equilibrium relationship within a year. It is noteworthy that the Bank of Israel’s foreign exchange interventions did not significantly affect these dynamics directly.

**Figure 3 **Actual vs a UIP forecast of the equilibrium depreciation, Israel 1996–2018

*Notes*: Actual deprecation: 12 months ahead change in N.I.S to $US exchange rate. Equlibrium exchange rate based on a 2sls regression of the UIP condition: 12 months ahead change in the exchange rate on the yield differential between Israel and U.S 12 month bills, instrumented by 12 months ahead difference between Israel and US expected inflation rates.

Plantin and Shin (2018) argue that deviations from UIP produce balance sheet effects that can potentially destabilise the economy. We tested whether the deviations from the equilibrium UIP relationship have an impact on the portfolio and other investments’ account of the balance of payments. We found that non-residents invest more in Israel when the exchange rate deviates below that implied by UIP; this can be viewed as destabilising. Residents, on the other hand, react in the opposite direction and do not seem to coordinate with the destabilising forces (Figure 4). We found that the reaction of non-residents to deviations is faster than that of residents. The interaction of both types of investors suggests that net investment flows are not affected by the deviations from UIP. We found that balance sheet effects were insignificant perhaps owing to free capital flows and the stabilising activity of Israeli institutional investors.

**Figure 4 **Balance sheet effects of deviations from UIP, Israel 1997–2018

## Policy implications

Using data from Israel, we show that the PPP and UIP equilibrium relationships hold in the short run when necessary conditions for their existence are met. The restrictions include price-taking behaviour, international goods and financial markets integration, and the existence of a market for inflation expectations for the short run. The necessary conditions for the existence of PPP and UIP are more likely to be met in the future for more economies; this can be inferred from the rising correlation of inflation rates among developing economies. The increase in global market integration is partly driven by technological innovations. One such innovation is international online shopping, with an example being the share of Amazon’s revenue out of OECD GDP (Figure 5). Market integration is reflected more broadly in the rising share of trade in services as a percentage of trade in goods (Figure 6). Indeed, in a recent study Cavallo et al. (2018) analyse prices of individual goods from online platforms and present evidence supporting PPP. Finally, financial deepening is manifested in the rising prevalence of defined contribution pension funds that invest globally and also in an increase in the prevalence of inflation swaps in financial markets of small developed economies.

**Figure 5 **Amazon’s revenue to OECD GDP

*Sources*: OECD and www.statista.com/statistics/273963/quarterly-revenue-of-amazoncom

**Figure 6 **Share of service exports of total exports, G7 1999–2017

*Sources*: OECD balance of payments dataset

The existence of short-term UIP and PPP implies that, given price stickiness and flexible exchange rates, monetary policy in small advanced open economies has an important role in smoothing shocks through expenditure switching channels as in the classic Mundell-Fleming model. We also found that despite substantial short-term deviations, nominal exchange rates are anchored by the monetary regime through inflation expectations and the corresponding short-term interest rates. Credible inflation targeting, therefore, anchors the exchange rate. In the absence of balance sheet effects, foreign exchange interventions directlyaffect only the dynamics of the exchange rate. Monetary policy can also affect the dynamics of the exchange rate through its impact on short-term interest rates and inflation expectations. In particular, monetary policy errors may lead to deviations of the exchange rate and inflation that could undermine financial stability and destabilise the economy. The indirectrole of foreign exchange interventions (at the effective lower bound) in maintaining the credibility of the inflation target, and minimising balance sheet effects, is left for future research.