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Nominal Exchange Rate Dynamics and Monetary Policy: Uncovered
Interest Rate Parity and Purchasing Power Parity Revisited
Yossi Saadon and Nathan Sussman*
Abstract
The increasing globalization of trade in goods and services and the deepening of financial
markets have reduced frictions that may impede the PPP and UIP relationships' operation in the
short run. In this paper, we estimate the short term relative PPP and UIP relationships. Using
data from Israel, which has a deep market for inflation expectations for 12 months, we show
that relative PPP and UIP cannot be rejected. Deviations from equilibrium last less than a year.
Data from Israel’s capital account of the balance of payments shows that the deviations are not
destabilizing. Our findings suggest that greater globalization, financial deepening, and
developing a market for short-term inflation expectations contribute to monetary policy
effectiveness.
JEL codes: F3, F31, F41, G15, E52
Keywords: Purchasing power parity, uncovered interest rate parity, Exchange rates, Monetary
policy, Inflation expectations, Balance sheet effects.
* Yossi Saadon, the Bank of Israel, Nathan Sussman, the Graduate Institute Geneva and CEPR. The
views expressed in this paper do not necessarily represent the views of the Bank of Israel.
1
Introduction
Monetary policy’s effectiveness and impact have been debated since the onset of the global
financial crisis. A recent summary by Forbes (2018) emphasizes the increasing impact of global
factors on domestic inflation, the Phillips curve, and monetary policy effectiveness, especially
for advanced small open economies. Central banks have become increasingly concerned with
developments in their currency’s exchange rates, and some intervene in foreign exchange (FX)
markets to defend their currencies against appreciation. Theoretically, the standard Mundell-
Fleming model assumes that in a floating-exchange-rate regime, the domestic central bank can
control monetary aggregates, which is more conducive to achieving inflation targets and output
stabilization than under a fixed exchange rate. However, recent research has demonstrated that
various financial frictions and the dominance of the US dollar and US financial markets may
undermine monetary policy independence even with flexible exchange rates (Rey, 2016).
Recent experience from the COVID-19 pandemic shows that capital outflows from emerging
markets triggered exchange rate depreciation and increased local currency bond yields that
undermined bond domestic monetary policy response (Hofmann et al., 2020).
One salient deviation from the equilibrium conditions underpinning the Mundell-Fleming
model is the prevalence of carry-trading, which is considered one of the most profitable
strategies in foreign currency trading and constitutes a significant factor in the foreign exchange
markets of small open economies. Recently, Plantin and Shin (2018) modeled the potentially
destabilizing effects of carry-trades. Carry trading may increase the deviations from the
uncovered interest rate (UIP) relationship.
Purchasing power parity (PPP) and UIP equilibrium conditions, which underpin the standard
Mundell-Fleming model, are appealing because they are based on a fundamental assumption—
the absence of arbitrage—hence their popularity in textbooks. However, they require hard to
fulfill conditions such as perfect competition and, for the UIP condition, deep financial markets
with free capital flows. To jointly test the dynamics of nominal exchange rates related to the
current and capital account, we also require flexible exchange rates. Moreover, since these
conditions are forward-looking, short term market-based inflation expectations are required.
These conditions limit the cases that can be used to examine the validity of these textbook
economic conditions. Therefore, the extent to which market frictions undermine the UIP and
PPP operation and hence the effectiveness of monetary policy is ultimately an empirical
question.
2
In this paper, we test whether the UIP and PPP conditions hold in the short run in a market we
believe matches more closely the assumptions behind these no-arbitrage conditions. Our
contribution is to use data from Israel, an advanced small open economy that can be considered
a price taker in global consumer goods and financial markets. We chose Israel because it is
unique: short-term inflation-indexed bonds are traded in a relatively deep market because of its
high inflation history. This allows us to use forward-looking 12 months’ market-based
breakeven-inflation rates that are publicly available from the Bank of Israel. Unfortunately, data
on market-based inflation expectations for 12 months for additional advanced small open
economies are either unavailable or available for only a short sample period (Adeney, 2017).
Because of its inflation history, data from the Israeli economy also offers greater variation in
the regressors, allowing to recover the UIP or PPP coefficients with higher precision. Moreover,
the Israeli economy is an interesting test case for several other reasons: it is a small open
economy that transitioned from an emerging market to an advanced economy; significant
changes occurred in the foreign exchange market; the disinflation process came to fruition
during the sample period; there was significant intervention in the foreign exchange market
during part of the period; and as in most of the world’s economies, the consequences of the
financial crisis were dealt with an accommodative monetary policy that lowered interest rates
to almost zero. Thus, we subject our estimation to a wide variety of changes in the environment
in which exchange rates are determined.
Following a brief theoretical exposition of the joint determination of the UIP and PPP
relationship in a small open economy, we estimated the relationship between the percentage
change in the Israeli New Shekel (NIS) and the US Dollar over twelve months as a function of
the twelve months’ inflation expectations differential between Israel and the US prevailing at
the beginning of the period. We could not reject the hypothesis that relative expected PPP holds
and that the coefficient of the expected inflation rate differential is equal, as in theory, to 1.
Estimating a vector error correction equation for the relative PPP relationship, we find that
following a shock, it takes on average a year for the exchange rate to revert to its equilibrium
level.
(Figure 1, about here)
The second step was to estimate the UIP relationship: We regressed the yield difference
between BOI bonds and US treasuries on the expected change in the exchange rate. A variety
of specifications shows that UIP holds with a coefficient of 1. We obtained these results by
estimating a simple OLS regression of the interest rate differential on the forward change in the
exchange rate. Finally, we estimated the joint equilibrium conditions using two-stage least
3
squares estimation, where the PPP relationship is the first stage, and the UIP relationship is the
second stage. Again, we obtained a coefficient of 1. This estimation (Figure 1) shows that the
UIP relationship anchors the dynamics of the exchange rate. A vector error correction
estimation for the UIP relationship shows, as can be gleaned from Figure 1 that the exchange
rate reverts to the equilibrium relationship within a year.
Our results were obtained using the simplest possible specifications, and we found none of the
puzzles reported in the literature (Engel, 2016). Our aim in this paper is not to fully account for
the deviations of exchange rates from the PPP or UIP relationships nor to forecast exchange
rates. We show that we cannot reject PPP or UIP when necessary conditions for their existence
are more closely met. Namely: price-taking behavior, international goods, and financial markets
integration, and the existence of a market for inflation expectations for the short run. These
results are obtained for a wide variety of economic and policy changes, including a period when
interest rates in Israel were at the effective lower bound. The deviations from UIP are short-
lived, and we do not observe sustained deviations. Therefore, remaining frictions do not offer
carry-trade opportunities beyond the very short-run. Owing to the relatively rapid corrections,
they are highly risky.
Using balance of payments data, we can reject the hypothesis that deviations from UIP or PPP
affect net portfolio investment. We also show that some of the deviations were probably
induced by monetary policy. These findings are also corroborated when we subject the data
from Israel to the test proposed by Hofmann et al. (2020). Unlike the findings from most small
open economies and emerging markets, the US Dollar return of five-year domestic currency
bonds does not differ from the NIS return on these bonds.
We cannot reject the relative expected PPP relationship. However, this does not imply that the
exchange rate pass-through to the economy is high. It only implies that the expected pass-
through is high. Obviously, as shown in Figure 1, exchange rates are subject to high, unexpected
volatility. The pass-through from actual changes in the exchange rate will likely decrease with
this volatility (Devereux, Engel, 2002). This finding is also consistent with (Forbes, Hjortsoe,
and Neova, 2018), who show that exchange rate shocks caused by monetary policy shocks have
a greater impact on prices. Since according to our framework, monetary policy shocks affect
inflation expectations.
The main policy implication of our findings from Israel for small open economies and emerging
markets is that developing a domestic currency bond market and having a flexible exchange
rate are necessary but not sufficient conditions to allow for effective monetary policy and
4
mitigation of deviations from UIP. It is also necessary to develop a deep market for hedging
inflation, preferably with inflation-linked bonds.1 We believe that in a world with rising goods’,
services’ and financial integration and the availability of forward-looking inflation hedging
assets in small open economies, the results we obtained for Israel will become commonplace
elsewhere. Recently, Cavallo et al. (2018) showed using data from online platforms that PPP
holds quite well for these products. This provides a more positive outlook for monetary policy
in small open economies with flexible exchange rates and inflation targeting. It also opens up
another channel of increasing monetary policy effectiveness, namely ensuring the continuation
of trade liberalization of goods and services and the development of financial markets.
The paper is structured as follows. We begin with a summary of relevant literature. In Section
2, we provide the theoretical model we estimate. In Section 3, we estimate the UIP and PPP
relationships and describe the data used. In Section 4, we provide some extensions and
robustness checks. We conclude with a summary of the results and policy implications.
1. Related literature
Our paper is closely related to the extensive literature that estimates the UIP relationship. The
extensive literature does not support, for the most part, the existence of the UIP relationship,
especially for the short run.2 Moreover, many studies show a negative interest rate gap
coefficient for short-term interest rates consistent with the carry trade literature.3 Froot and
Thaler (1990) reviewed dozens of empirical studies that tested the relationship and found that
the average coefficient was -0.88. Bansal (1997) showed that the failure of UIP is more
significant for industrialized economies compared with developing economies. Bansal and
Dahlquist (2000) and Ballie and Kalic (2006) argue that the existence of the relationship
depends on whether the interest rate gap is positive or negative. A deviation from the UIP
relationship will appear when the US interest rate is higher than the local interest rate.
Chinn and Meredith (2004) assessed the UIP relationship for 5 and 10 years for the G7
countries. They found stronger support for the existence of the relationship for long-term
interest rates than short-term interest rates of 12 and three months. Their study showed that the
1 Inflation swaps are not traded in a liquid market and the quotes are generally not available to the
general public.
2 For example, Bekaert and Hodrick (1993), Engel (1996), Mark and Wu (1998), and Weber (2011),
and others. On the other hand, a few articles do find support for this relationship: Flood and Rose
(1996), Bekaert and Hodrick (2001), Baillie and Bollerslev (2000), Chaboud and Wright (2005),
Bayaert, Garcia-Solanes and Perez-Castejon (2007), Omer et al. (2013) and Tang (2011).
3 For example, MacDonald and Taylor (1992), Isard (1996), McCallum (1994), Engel (1996), and
Chinn and Meredith (2004).
5
interest rate spread coefficient was positive and closer to 1 than to 0. In another and more recent
article, Chinn and Quayyum (2012) again supported the conclusion that the UIP relationship is
valid for long-term interest rates. Coffey, Hrung, and Sarkar (2009), who refer to the 2008
financial crisis, assert that the basic assumption of UIP that the financial markets function
effectively enough to prevent arbitrage was invalid in the 2008 financial crisis. Investors during
this period, therefore, preferred to wait in currency positions until the crisis subsided.
In a recent comprehensive study, Engel (2016) reviews articles addressing UIP and discusses
the apparent contradiction between the UIP theory and the empirical findings. According to
these studies, the exchange rate of countries with a high-interest rate tends to be revalued more
than according to the interest rate spreads based on the UIP model. As found in other studies,
he also found that the real exchange rate converges to the UIP relationship over time. Engel
tested the UIP on six leading economies (Canada, France, Germany, Italy, Japan, and the UK)
in 1979–2009 compared to the US. His study showed that the exchange rate risk plays an
important role in explaining this contradiction. He includes liquidity of assets as a factor that
can explain his findings with respect to the UIP relationship. Our contribution is to test the UIP
for a small open economy rather than for large ones that may be considered market makers. We
also use short term inflation expectations obtained from financial markets rather than using
inflation expectations based on lagged inflation. Finally, while we follow Engel and emphasize
the estimation of these relationships for the short run, we use annual observations that
correspond to the maturity of the financial assets that we use, rather than convert them into
monthly maturities by taking the 12th root.4
Our paper is also related to the literature on carry-trades and the recent emphasis on exchange
rate related balance sheet effects of monetary policy instead of the more traditional expenditure
switching cannel (Plantin and Shin, 2018). Suppose that the central bank of a small open
economy raises interest rates to cool down the economy. According to the Mundell-Fleming
framework, this will result in capital inflows and appreciate the currency. However, carry
traders will lend to the high-interest rate economy. The increasing capital inflows will
counteract monetary policy by stimulating domestic investment and consumption through a
balance sheet effect. This exposes the small economy to financial instability and loss of control
over inflation. While this strategy is exposed to considerable risk (Doskov and Swinkels (2015)
and Burnside et al. (2007)), it is often pursued when there are deviations from uncovered
interest rate parity (UIP). As a result, they make the deviations from UIP greater and longer-
4 In the Robustness section we follow Engel (2016) and show our results also hold, but with lower
significance.
6
lasting (Baillie and Chang, 2011).5 Thus, under conditions outlined by Plantin and Shin (2018),
carry trading may increase the deviations from the UIP.
The theoretical and empirical analysis of carry-trading as a destabilizing activity that
undermines the effectiveness of monetary policy rests on the existence of various frictions in
markets and inappropriate monetary policy. For example, in Plantin and Shin (2018), the
destabilizing outcome is partly the result of sticky non-traded goods prices that undermine the
PPP relationship and partly the result of passive monetary policy that underestimates the
balance sheet effects of capital flows. These theoretical considerations fit well with the
empirical literature on the UIP. Our contribution is to show that when some of the frictions are
removed, we do not find sustained deviations from UIP. This suggests that the carry trade under
such circumstances is riskier.
Our paper also relates to the extensive literature on purchasing power parity (PPP). Previous
research was summarized by Taylor and Taylor (2004). They reviewed the extensive literature
on the PPP and concluded that the PPP relationship could not be rejected in the long run. More
recent research has emphasized frictions in goods markets that explain the deviations from PPP
in the short run. One example is Sarno et al. (2004), who model deviations from PPP that occur
because of non-linear frictions such as transaction costs. Another version of price stickiness
that differs by sector is found in Carvalho and Nechio (2011). Recently, Engel (2018) and Engel
and Zhu (2018) revisited the PPP puzzle (Rogoff (1996, p. 647-648)) that argues that the real
exchange rate converges very slowly (half-life of 3 to 5 years), much slower than nominal prices
and therefore contradicts PPP. Engel (2018) offers a New-Keynesian model with Calvo pricing
that is centered around sticky prices. At the same time, Cavallo et al. (2018) use micro-level
data from online shopping platforms and show strong evidence for PPP. Their results suggest
that there are empirical issues associated with price level statistics collected by national
statistical bureaus. Our results support Cavallo et al. (2018), and at the same time, we find no
puzzle in the convergence of Israel's real exchange rate with the US.
2. Theoretical Framework
Our point of departure is the existence in the long run of two classic behavioral equations: the
first is the relative purchasing power parity (PPP) equation, which states that the change in the
exchange rate is equal to the difference between the inflation rates in two economies. The
5 In practice, profits from carry trading are usually positive, although it has caused heavy losses over
short periods in the past (see Doskov and Swinkels, 2015). However, Fama (1984), Chinn & Meredith
(2004), and Frenkel & Poonawala (2010), like many others, show that the profit and loss depend on
the, country, and time period.
7
second is the uncovered interest rates parity (UIP) equation. The difference between interest
rates of similar assets in two economies is equal to the expected depreciation of the domestic
currency against the other economy's currency. Most studies UIP that used data from
industrialized countries also examined the unbiasedness hypothesis that assumes risk-neutral
individuals and a zero or constant risk premium.
Under the rational expectations assumption, the forward-looking relative PPP equation for
estimation can be written as:
(1) ( ) = +(
) + ,
where s represents the log of the exchange rate in terms of units of domestic currency to a unit
of foreign currency; represents the expected inflation rate and
the expected
inflation rate abroad. The subscript P denotes the PPP equation. The null hypothesis is that
= 1.
The UIP condition is commonly tested using Fama’s (1984) regression:
(2) ( ) = +(
) + ,
where i represents the domestic nominal interest rate; i* represents the nominal interest rate
abroad and
α
represents the constant risk premium. The subscript U denotes the UIP equation.
Under UIP, the null is that = 0 = 1.
Following Engel (2016), we define the real exchange rate as:
(3) + log(
)log
where p represents the domestic and p* the foreign price level (CPI).
The real ex-ante interest rate r is defined as:
(4) =
3. Estimation of the PPP and UIP—the case of Israel.
In this section, we present the data and the basic estimation results that support our hypothesis
that the PPP and UIP conditions cannot be rejected for Israel's case. Our sample period of
monthly observations begins in January 1996 and ends in July 2018, the latest point in time
available. During this period, there were many changes in the economic environment and
policies in Israel that make the study of the Israeli case interesting and, at the same time,
challenging for estimating the short-run PPP and UIP relationships.
8
During this period, there were three global financial crises: LTCM in 1998, the 2000 dot.com
crisis, and the global financial crisis (GFC) that began in 2008, as well as a domestic crisis of
the Second Intifada (2000-2004). During this period, there were structural changes and changes
in Israeli economic policy. The most prominent of them were the disinflation process that ended
in 2003 and the change in the Bank of Israel’s policy in the foreign exchange market in 2008.
The exchange rate regime witnessed several developments: at the beginning of our sample—
from 1996 to the end of 1997—the exchange rate operated within a band of +/- 7%. After that,
the band's width was increased to 60%, and the Bank of Israel stopped intervening in the FX
market. In 2005, the exchange rate band was officially removed. In 2008, as part of
unconventional monetary policy, the Bank of Israel started to intervene in the FX market, a
policy that is still carried out at the time of writing this paper. Finally, in September 2010, Israel
became a member of the OECD, and in that year, Israel also exited the MSCI emerging market
index and moved to the developed markets index.
3.1. Data for estimation
Our key contribution is to use forward-looking inflation expectations in the empirical
estimation of the PPP equation (1). For Israel, we use the inflation expectations for 12 months
estimated from the market for inflation-indexed bonds and the 12-month Bank of Israel nominal
bond. The data are publically available from the Bank of Israel website. For the US, we used
the Michigan survey of consumers provided by the Federal Reserve Bank of St. Louis (FRED).
Our decision to focus on Israel is driven by either the absence of market-based inflation
expectations or their very short sample size in small advanced open economies (Adeney et al.,
2017).
Many studies estimate inflation expectations from actual inflation or lagged inflation. Recently
Engel (2016) used a vector error correction model to extract inflation expectations and calculate
the ex-ante interest rate. The recourse to estimation is partly because a series of market-based
one year ahead inflation expectations (either from breakeven inflation or swaps) does not exist
or does not have a long enough history for many countries. The advantage of using data from
Israel is that we use available assets that are common knowledge and have existed for a long
time (a legacy of the high inflation era of the 1980s), rather than those estimated ex-posts by
researchers. As shown in Figure 2, there is quite a substantial difference between lagged or
actual inflation and inflation expectations. As we will show later, using expected inflation
differentials rather than actual or lagged inflation makes a significant difference in estimating
the PPP relationship.
9
(Figure 2, about here)
The interest rate differential we focus on is the one-year nominal yield spread between a 12-
month constant maturity Treasury bill (data from the Federal Reserve Bank of St. Louis
(FRED)) and the yield on the one-year Bank of Israel bill—the Makam. As Figure 3 shows,
although the yield on the US Treasury bill was almost unchanged following the onset of the
crisis, that of Israel did. This provides a variation in the spread even when the US, and later
Israel, were at the effective lower bound.
(Figure 3, about here)
As customary in the literature (Engel, 2016), we denote the expected depreciation by using
the ex-post realized annual change in the USD-NIS (Israeli New Shekel) exchange rate.
We introduce two additional variables that will be used in our robustness checks. The first is
Israel’s country risk premium. We use the Bloomberg quote of the CDS on 5-year bonds to
measure Israel’s country risk. Unfortunately, the data is available only from July 2002. Because
Israel was classified as an emerging market up to 2010, when it joined the OECD, we produced
an estimate of Israel’s CDS by using a forecast from a regression of Israel’s CDS on the EMBI
index for the period 2002 to 2007, when we have both measures. We detail this estimation in
Appendix 1. Another variable we introduce for our robustness checks is the monthly amount of
foreign exchange rate purchases made by the Bank of Israel.6
To assess the balance sheet effects of deviations from UIP or PPP, we use quarterly portfolio
investment data, and other investment data from the balance of payments account available
from the Bank of Israel.
3.2. Estimation and results
3.2.1. Estimating the PPP relationship
In this subsection, we estimate the forward-looking relative PPP: equation (1). Since inflation
expectations and the expected change in the exchange rate are determined simultaneously, the
estimation of equation (1) does not imply causality. Since we can reject the null of both
individual and common unit-roots for the variables in our sample, we can view the estimation
6 The data on monthly FX interventions is not publically available.
10
of equation (1) as the cointegrating equation.7 We then estimate an error correction model to
obtain the length of time it takes the nominal exchange rate to return to the PPP relationship.
The results show (Table 1) that the expected inflation differential coefficient is equal to 1, and
we cannot reject the hypothesis that the intercept is zero. When we estimated a vector error
correction model (VECM), we obtained that the speed of adjustment of the exchange rate to
the PPP relationship is ten months.
In theory, both variables that make up the PPP equation are endogenous. However, using the
expected inflation differential, rather than the actual inflation differential, we regress the ex-
post change in the exchange rate on the ex-ante inflation differential. This should avoid issues
of simultaneity. Nevertheless, we re-estimate the PPP equation (1) using instruments for the
difference in expected inflation between Israel and the United States. Our instruments are the
lagged actual inflation differential in the previous year, which is commonly used to estimate
inflation expectations (Engel, 2016) and the lagged Fed policy rate—which under an inflation
target regime is an indicator of the Fed’s view on inflation. The results in the bottom panel of
Table 1 show that our previous results hold. The two-stage least squares estimation enables us
to test the exogeneity assumption of the expected change in the inflation differential. We find
that though we can reject the weak instruments hypothesis, we cannot reject the hypothesis that
the expected inflation differential is exogenous.
(table 1, here)
3.2.2. Estimating the UIP Relationship
In this subsection, we estimate the Fama regression (equation (2)). As in the PPP equation
estimation, the equation does not imply causality. Since we reject the null of unit-root, we
proceed to estimate the UIP equation as a cointegrating equation. As before, we then estimate
the VECM to obtain the speed of adjustment to deviations from the UIP relationship. The results
(Table 2) show that we cannot reject the null that the coefficient of the interest rate differential
is 1 and that the intercept is equal to zero. The speed of adjustment of the exchange rate to
deviations from the UIP (results of the VECM) turns out to be seven months. It is quite natural
that the convergence of the exchange rate to financial market conditions (UIP) is faster than the
convergence to the goods market equilibrium conditions (PPP).
7 The unit root tests, detailed in Appendix 2, on the residuals of equation (1) confirms that the variables
are cointegrated.
11
For similar considerations as in the PPP equation estimation, we estimate a two-stage least
squares version of equation (2). Our instruments for the interest rate differential are Israel’s
country risk premium (captured by the CDS on 5-year bonds), and the Bank of Israel lagged
policy rate. The results in the bottom panel of Table 2 show that our previous results hold. The
two-stage least squares estimation allows us to test the exogeneity assumption of the interest
rate differential. We find that though we can reject the weak instruments hypothesis, we cannot
reject the hypothesis that the interest rate differential is exogenous.
(Table 2 about here)
3.2.3. Balance sheet effects of the impact of deviations from PPP and UIP.
In the previous subsections, we showed that relative expected PPP and UIP hold in Israel's case
and that deviations from the equilibrium relationships tend to revert within less than a year. As
Plantin and Shin (2018) argue, the deviations from UIP produce balance sheet effects that can
potentially destabilize the economy (Rey, 2016). The findings we report above suggest that for
the case of Israel, these are not major concerns. Mantzura and Shreiber (2016) recently
documented the sharp increase of foreigners’ holding of Makam bills in the wake of the opening
interest rate differential with the US in 2010 and early 2011 (Figure 3). These were coupled
with an appreciation of the currency and could be viewed as destabilizing manifestations of the
carry trade. In this subsection, we test whether the deviations from the equilibrium UIP
relationship impact the portfolio and other investments’ account of the balance of payments.
Since our balance of payments data are quarterly, we first re-estimated equation 2 to obtain the
quarterly residuals from UIP. We then estimated the following regressions of capital flows, ,
on the residual from equation (2), i=1 for investments by nonresidents, i=2 for investments by
residents, and i=3 for net flows.
(5) ,=,+,,+,
The results (Table 3) show that nonresidents invest more in Israel when the exchange rate
deviates below what UIP implies, which can be viewed as destabilizing: when interest rates in
Israel are high, and the exchange rate is appreciating (Plantin and Shin, 2018). On the other
hand, residents react in the opposite direction and do not seem to coordinate with the
destabilizing forces. Note that the reaction of nonresidents to deviations is much faster than that
of residents. The interaction of both types of investors shows that the net investment flows are
12
not affected by the deviations from UIP; we cannot reject the hypothesis that ,= 0. Granger
causality test confirms these results. In particular, we can reject the hypothesis that nonresidents
cause, in the Granger sense, the behavior of residents.8
3.2.4. Evidence for UIP from the five-year bond market
Theoretically, the issuance of domestic-currency denominated bonds in emerging economies
alleviates concerns of 'original sin' and allows monetary policy to be more effective. Recent
research by Hofmann et al. (2000a, 2000b) compares the domestic-currency rate of return on
domestic currency bonds with the US Dollar return on these bonds. They plot the two returns
against the change in the bonds' yield (in percentage points). Theoretically, when UIP holds,
there should be no difference between the rate of return in domestic and foreign currency.
Otherwise, an arbitrage opportunity exists.
The data presented in Hofmann et al. (2000a, 2000b) shows that the credit risk of bonds
fluctuates with the spot exchange rate for small open economies and emerging markets. A
deprecation of the spot exchange rate is associated with lower returns on domestic bonds when
measured in UD dollar terms than their return in domestic currency. This finding represents a
deviation from the UIP and also from the covered interest rate parity (CIP).
We reproduced Hofmann et al. (2020b) figure 1 for Israel. We used weekly data from January
2008 to July 2020. Our results show (Figure 4) Israel is unique: on average, the returns on five-
year domestic currency bonds are identical to their US Dollar return. 9 This result provides
additional evidence there are no systematic deviations from UIP in Israel. The credit risk of
domestic currency bonds is insulated from spot exchange rate shocks. The results also confirm
the absence of significant balance sheet effects we documented in the previous sub-section.
This allows monetary policy to be much more effective than in emerging market economies
and advanced small open economies.
(Figure 4 about here)
4. Extensions and robustness checks
Using the data for Israel and the US, we cannot reject the hypothesis that during the sample
period from 1996 to 2017, the PPP and UIP relationships hold and that deviations from these
8 See Table A2 for Granger causality results.
9 The slopes of the regression line are -5.86 (s.e. 0.44) for Dollar returns and -6.12 (s.e. 0.13) for
domestic currency return. Of course, the U.S Dollar returns are more volatile because the spot
exchange rate is more volatile than the bond prices.
13
conditions converge back to equilibrium within less than a year. We obtained the results using
the most straightforward specifications. We took advantage of the fact that for most of the
sample period, Israel's monetary conditions differed from those in the US. Indeed, when
monetary conditions are identical between two economies (interest rates and expected
inflation), the PPP and UIP are empirically reduced to a random walk.
In this section, we provide some extensions and robustness tests. i) We test, within the
framework of the PPP equation, whether the use of expected inflation differentials instead of
actual (lagged) rates makes a difference in our estimations. ii) Since we found the PPP and UIP
to hold, we subject our data to some of the puzzles estimated recently by Engel (2016). iii) The
Bank of Israel intervened in the FC markets as part of the unconventional monetary policy
following the GFC's onset. We will test whether FX interventions affect equilibrium conditions.
iv) We test whether monetary policy can account for deviations from PPP and UIP. v) We re-
estimate our PPP and UIP regressions using the monthly rate of change rather than annual. vi)
We use bootstrap estimations to rule out that specific episodes determine our results.
4.1. Estimating the PPP relationship with actual inflation differentials.
In this subsection, we re-estimate the PPP relationship using 1. lagged inflation differentials as
a proxy for expected inflation and 2. ex-post realized inflation and exchange rates.
The UIP conditions are essentially forward-looking, and since the expected change in the
exchange rate is what matters. Since the PPP and UIP are two sides of the same exchange rate
coin, we estimated the PPP using forward inflation differentials. Figure 2 plots the forward
versus fully adaptive expectation differentials. The difference is noticeable. While the
correlation between lagged inflation differential and forward inflation differential is quite high
(0.8), when we substitute expected inflation differential with the lagged inflation differential,
the coefficient drops from 1 to 0.55 (Table A1). This means that using lagged inflation, a Wald
test confirms that we can reject the forward-looking PPP relationship.
What about the PPP relationship in real-time? Since the actual rate of change of the exchange
rate and the actual inflation differential are determined simultaneously, we use 2SLS estimation
to test for the ‘real-time’ PPP relationship. We instrument the inflation differential with the
beginning of period lagged inflation differential, Fed, and Bank of Israel policy rates. We find
(Table A1) that ex-post PPP also holds for Israel's case vis-a-vis the US.
4.2. Testing for PPP and UIP puzzles
14
Engel (2018) and Engel and Zhu (2018) address the PPP puzzle that shows that the real
exchange rate converges to equilibrium too slowly than warranted by the PPP relationship.
Specifically, the half-life of an AR(1) process of the real exchange rate is typically longer than
three years (See also Sarno et al. , 2011). In contrast, the nominal exchange rate and relative
prices of the two economies converge much faster. They find that the real exchange rate
converges much faster for a fixed exchange rate than for flexible exchange rate economies.
Following Engel (2018), we test for the half-lives of the real exchange rate, nominal exchange
rate, and relative price levels for Israel vis-a-vis the US. We also found that the point estimate
of the real exchange rate's half-life is slightly longer (4 months) than that of the nominal
exchange rate. However, the differences obtained from the AR(1) regressions are not significant
at the 95% level (Table 4). As a robustness measure, we estimated rolling AR(1) regressions
for two-year and seven-year windows and calculated the means of the coefficients of the AR(1)
term. For the two-year rolling regressions, we cannot reject the hypothesis that the means are
similar. Moreover, the mean of the rolling AR(1) coefficient on the real exchange is no longer
the highest (bottom panel Table 4). Therefore, the evidence for a PPP puzzle is inconclusive.
(Table 4 about here)
Engel (2016) finds empirical evidence for two UIP puzzles that are contradictory in their
implications. The first is the puzzle that relatively high interest rate countries have higher
returns on short term deposits. The second puzzle is that countries with relatively high real
interest rates have a stronger real exchange rate than would be implied by UIP.
Following the notation in Engel (2016), we define excess returns, , as:
(6) ++1
The puzzle that Engel (2016) recently estimated is that excess return from investing in short
term deposits abroad are positively correlated with higher real interest rates abroad:
(7) ( ,
) > 0
Using the definition of excess returns, , from equation (6), Engel (2016) rewrites the
Fama equation as:
(8) =+(
) + ,
Our result that the UIP relationship holds suggests that we will be able to reject the first puzzle;
we find (Table 5) that the simple correlation (equation (8)) is negative, but not significantly
different than zero. Naturally, when we estimate the modified Fama regression, we find (Table
5) that we cannot reject the hypothesis that = 0.
15
(Table 5, about here)
The second puzzle documented by Engel (2016) is formally stated as excess comovement of
the stationary component of the exchange rate with respect to the ex-ante real interest rate
differential. This means that the level of the exchange rate is strongly affected by deviations for
UIP. The strong effect of the deviations on the exchange rate level implies that the higher
interest rate (riskier) country has lower ex-ante risk premiums. Engel first regresses a model of
the level of the real exchange rate (defined above, equation (3)) on the ex-ante real interest rate
(from equation 4) differential:
(9) =+(
) + ,
He finds that is positive, implying that when interest rates are higher abroad, the home
exchange rate depreciates. This is not surprising. However, the puzzle emerges when he re-
estimates (8), replacing the level of the real exchange rate as the dependent variable with the
ex-ante sum of excess return premiums relative to their unconditional mean (
). 10
(10) (
) = +(
) + ,
Engel finds that is negative, which implies that higher interest rate currencies that are riskier
have a lower ex-ante stream of risk premiums. When we estimate equation (8), we find (Table
4) that we observe the expected positive coefficient, which implies, according to UIP, that high
real interest rate economies have an appreciated real exchange rate. However, when we
estimate equation (9), we find, unsurprisingly, given our earlier results, no evidence for a puzzle
(Table 4).
4.3. Accounting for the Bank of Israel FX intervention
As part of its unconventional monetary policy, the Bank of Israel purchased $US. Overall, FX
purchases amount to more than $50 billion since 2008. The Median monthly intervention was
$500 million, with the highest amount being $4 billion in August 2009 in the midst of the global
financial crisis. In this subsection, we re-estimate equations (1) and (2) and control for FX
purchases. We use two formulations: the first uses the monthly amount purchased and amount
squared to allow for non-linearity in the effect of purchases. In the second, we use a dummy
variable for months when the Bank of Israel intervened in the FX market.11 We find (Table 6)
10 The ex ante excess premiums are calculated as the difference between the stationary component of
the nominal exchange rate (extracted using a Beveridge-Nelson decomposition) and the expected future
nominal interest rate differentials. See Engel (2016).
11 The advantage of using the dummy variable is its availability to the public.
16
that the baseline findings are essentially unchanged. The effect of purchases on the annual
change of the exchange rate is insignificant. This implies that FX purchases did not directly
affect the fundamentals of exchange rate dynamics. However, this does not rule out that FX
interventions, as part of unconventional monetary policy, could indirectly affect the nominal
exchange rate dynamics through their effect on inflation expectations.
(Table 6 about here)
4.4. Accounting for deviations from PPP and UIP
The results obtained for the expected relative PPP and UIP equations imply that for Israel, the
interest rate differential (IRD) with the US is equal to the differences in expected inflation up
to a constant and white noise. This implies ex-ante real interest rate parity. Therefore, it is
useful to look at deviations from this constant and see whether these deviations result from
deviations of the IRD from the equilibrium relationship or shocks to the differences in expected
inflation (PPP). We assume that part of the constant difference between interest rates in Israel
and the US is related to country risk measured by Israel’s CDS premium. Part of it reflects
constant lower liquidity in the Israeli bond market relative to the US. The remaining differences
can be attributed to the real interest rate difference due to the differences in demographics and
growth (Borio et al., 2017).
We estimated the following equation:
(11) (
)(
) = (
) = ++
where captures the fundamental real interest rate differential and constant liquidity premiums.
Using the Bai-Perron multiple break test, we found that the equation is stable. This result
strengthens the conclusions we draw from the separate estimates of the UIP and PPP
relationships. It also suggests that the constant term is stable over the sample period. Next, we
obtained the residuals and compared them with the IRD and PPP components. We tested for
serial correlation using the Breusch-Godfrey Serial Correlation LM test and found a strong
serial correlation. We can observe (Figure 5) that during some episodes, the residuals seem
correlated mainly with the IRD. Indeed, the correlation of the residuals with the IRD is positive
and significant. We then tested for the correlation of the residuals with the monetary policy by
correlating them with the Bank of Israel and the Fed's policy rates. We found a stronger and
17
more significant correlation of the residuals with the Bank of Israel than with the Fed policy
rates.12
(Figure 5 about here)
These findings imply that some of the deviations were the product of monetary policy. A salient
episode that shows up remarkably well in the data (Figure 5) is the Governor of the Bank of
Israel's deal with the government to lower interest rates by two percentage points in December
2001. The move, which surprised markets, necessitated raising interest rates by more than five
percentage points within six months. It is also not surprising that deviations from equilibrium
characterized the crisis period—from October 2008 to the end of 2009—. Finally, it is
interesting to note that toward the end of our sample—since the middle of 2017—we note a
significant deviation. While it is too early to see how this episode will evolve, for now, the
divergence of policy rates of the Bank of Israel and the Fed, while the difference in expected
inflation is quite stable, may suggest that either the Bank of Israel is keeping interest rates too
low or that the Fed is raising them too fast.
4.5. Testing the PPP and UIP using monthly rates of change
Engel (2016) confirmed the consensus in the literature that the UIP relationship does not hold
for the short run. He tested the relationships using monthly rates of change in the exchange rate.
We are in total agreement that testing UIP with long-term bonds as, for example, in Chinn and
Meredith (2004), involves holding period risk. However, in this paper, we emphasize that the
availability of financial assets that allows trading future inflation is crucial for the no-arbitrage
assumption to hold. The shortest liquid maturity asset we have is twelve months’ inflation
breakeven rates. It is not even clear that if such assets existed, we could define a one-month
change in the price level as inflation. Nevertheless, we follow Engel (2016) and take the 12th
root of our annual inflation expectations series and interest rates and re-estimate equations (1)
and (2).
We first estimate equations (1) and (2) for the period 1996 to 2007 and find (Table A3) that we
cannot reject the hypothesis that PPP and UIP hold, even though the significance of our results
is weakened relative to those obtained using annual data. We then estimate the equations for
the entire sample, controlling for FX interventions, and find that our results still hold.
12 Correlation coefficient of the residual with the Bank of Israel rate = 0.348.
Correlation coefficient of the residual with the Fed rate = 0.129.
18
4.6. Bootstrap Estimation
One advantage of Israel's data is that owing to its inflation experience, we have relatively, for
advanced economies, a large variation in the regressors of the UIP and PPP regressions. This
allows us to estimate the coefficients of interests more precisely. However,
it may be argued that our results may be driven by our sample choice that includes periods with
trending disinflation (Figure 2). To rule out these selection issues, and in the way of robustness,
we used bootstrap estimations. We estimated the Fama equation (equation 2) using bootstrap
technique twice: for the whole sample and a subsample of 150 observations (out of 288). We
used 100K replications and found similar results to the baseline estimation (Figure 6): the
distribution of the Fama equation's coefficient is centered around 1 for both samples.
(Figure 6 about here)
Conclusions
We have shown that for Israel, a small open economy, we cannot reject the PPP and UIP
conditions for the short run. Our results contrast with those arrived at in the literature. The
difference between our findings and those of the literature may be driven by the characteristics
of the Israeli economy and/or the data we used. Our results indicate that the existence of a
market for inflation expectations for a short duration, namely 12 months, may help anchor the
forward-looking PPP relationship. With free capital flows, the joint determination of the
exchange rate on the current account (PPP) and the capital account (UIP) may help anchor the
UIP relationship as well. Moreover, we believe that Israel is an advanced small open economy
and is essentially a price-taker, contributes to the lower frictions in the trade of goods and
services.
The finding that we cannot reject PPP and UIP for Israel suggests that monetary policy can be
quite effective. The frictions pointed out by Rey (2016) and more recently by Plantin and Shin
(2018), and Hofmann et al. (2020a, 2020b) are likely to play a smaller role: the expenditure
switching effects of monetary policy probably dominate the balance sheet effects (a la Mundell-
Fleming). We also show the absence of significant balance sheet effects of deviations from UIP
or PPP. The effectiveness of monetary policy also means that monetary policy will continue to
affect inflation expectations. Therefore, policymakers should bear in mind that policy mistakes,
through expected PPP, may destabilize the dynamics of the exchange rate and may lead to
financial instability.
19
Can we generalize from the case of Israel? To the extent that globalization proceeds and
expands to the services industry, we will see fewer frictions, especially for advanced small open
economies (Cavallo et al., 2018). This will likely increase the likelihood of finding evidence
for the PPP relationship. To the extent financial markets in small open economies evolve and
offer short term inflation swaps, the less likely it will be that arbitrage opportunities will develop
in the foreign exchange market because the expected PPP relationship will anchor the expected
exchange rate.
20
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23
Figures and Tables
Figure 1
Actual versus Forecast Equilibrium Depreciation
Israel: 1996–2018
Figure 2
Forward and Backward Looking Expected Inflation Differentials between Israel
and the US.
(1996–2018)
24
Figure 3
The Yield on 1-year Bank of Israel Bonds and 1-year US Treasury bills
(1996–2018)
Figure 4
Five-Year NIS weekly bonds return
(2008:1–2020:7)
Figure 5
-10 -5 0 5
Retrun (percent)
-.4 -.2 0.2 .4
Yield change (percentage points)
Return (ILS, percent)
Return (USD, percent)
25
Deviations from Real Interest Rate Parity, the IRD, and PPP
(1996:1–2018:5)
26
Figure 6
Bootstrap estimation results for Fama regression
Panel A: full sample (N=288) Panel B: partial sample (N=150)
Table 1 – PPP equation: ( ) = +(
) + ,
1996:1–2017:7
95% interval
95% interval
,
1.060
(-2.40
, 4.540)
0.995
(0.277
, 1.714)
-0.106
(0.022)
2SLS estimation
1.064
(-0.882
, 3.001)
0.971
(0.359
, 1.568)
Notes: OLS: 95% confidence interval based o HAC standard errors & covariance (Pre-whitening with
lags = 2 from SIC maxlags = 6, Bartlett kernel, Newey-West fixed bandwidth = 5)
VECM: no intercept or trend in CE or Var. 4 lags.
2SLS: Instruments (
), Fed policy rate lagged. Cragg-Donald F-stat: 382.
Table 2 – Fama regressions: ( ) = +(
) + ,
1996:1–2017:7
95% interval
95% interval
,
-2.032
(-6.593
, 2.528)
0.998
(0.162
, 1.835)
-0.148
(0.028)
2SLS estimation
-2.129
(-4.714
, 0.455
1.036
(0.473
, 1.600)
Notes: OLS: 95% confidence interval based o HAC standard errors & covariance (Pre-whitening with
lags = 2 from SIC maxlags = 6, Bartlett kernel, Newey-West fixed bandwidth = 5)
VECM: no intercept or trend in CE or Var. 10 lags.
2SLS: Instruments, CDS, Bank of Israel rate lagged. Cragg-Donald F-stat: 711.
27
Table 3 – Capital account regression: ,=,+,, +,
1996:Q2–2017: Q4
95% interval
95% interval
Nonresidents
875.8
(316.8
, 1434)
-83.5
(-150
, -16.8)
Residents
-1683
(-2340
, -1027)
95.8
(11.8
,179)
Net flows
-771
(-1606
, 63.5)
26.8
(-83.7
,137)
Notes: Capital account: portfolio + other investments.
OLS: 95% confidence interval based o HAC standard errors & covariance (Pre-whitening with lags =
0 from SIC maxlags = 4, Bartlett kernel, Newey-West fixed bandwidth = 4)
J=1 for nonresidents, j=3 otherwise.
28
Table 4 – Testing for the PPP puzzle
1996:1–2018:7
q
s
log(p)-log(p*)
AR(1)
95% interval
AR(1)
95% interval
AR(1)
95% interval
0.980
(0.957
, 1.004)
0.978
(0.957
, 0.998)
0.974
(0.943
, 1.006)
Rolling AR(1) regression 24 months
mean
Std. dev.
mean
Std. dev
mean
Std. dev
0.86
0.133
0.89
0.115
0.88
0.118
Rolling AR(1) regression 72 months
0.953
0.040
0.949
0.032
0.958
0.041
q, log(p)-log(p*): OLS: 95% confidence interval based o HAC standard errors & covariance (Pre-whitening
with lags = 1 from SIC maxlags = 6, Bartlett kernel, Newey-West fixed bandwidth = 5)
s: OLS: 95% confidence interval based o HAC standard errors & covariance (Pre-whitening with lags = 2 from
SIC maxlags = 6, Bartlett kernel, Newey-West fixed bandwidth = 5)
Test for equal means 24 months Anova F-test (p=0.067), Welch F-test (p=0.077)
Test for equal means 72 months Anova F-test (p=0.037), Welch F-test (p=0.0037)
Table 5 – Testing for the UIP puzzle
1966:1–2017:7
(
,
) = 0.002; = 0 0.822
Modified Fama regression (Engel, 2016):
=
+
(
) +
,
1996:1=2017:7
95% interval
95% interval
0.024
(-0.002
, 0.050)
-0.000
(-0.005 , 0.005)
Real exchange rate regression (Engle, 2016):
=
+
(
) +
,
95% interval
95% interval
-2.233
(-2.262
, -2.204)
0.006
(-0.0007 , 0.014)
OLS: 95% confidence interval based on HAC standard errors & covariance (Bartlett kernel, Newey-West fixed
bandwidth = 5)
29
Table 6 – Accounting for Bank of Israel FX interventions
1996:2–2017:7
PPP:
=
+
(
) +
+
+
,
95% interval
95% interval
0.642
(-3.494
, 4.779)
1.026
(-0.026
, 2.079)
3.303
(0.579)
-1.250
(-0.715)
=
+
(
) + _
+
,
95% interval
95% interval
_
0.249
(-4.163
, 4.660)
1.059
(-0.048
, 2.166)
2.547
(0.636)
Fama regression
:
( ) = +(
) + +
+,
95% interval
95% interval
-3.769
(-7.670
, 0.161)
1.298 (0.386 ,2.210)
5.495
(1.345)
-1.727
(-1.242)
Fama regression
:
( ) = +(
) + _+,
95% interval
95% interval
_
-5.377
(-10.682
, -0.072)
1.565 (0.670 ,2.459)
5.330
(1.595)
Notes: 2SLS: 95% confidence interval based on HAC standard errors & covariance (pre-whitening with lags
from AIC max lags, (Bartlett kernel, Newey-West fixed bandwidth = 5)
FX: monthly billions of $US purchased. D_FX: dummy for months with FX intervention.
t statistics for FX and D_FX in parenthesis,
2SLS: Instruments PPP in parentheses,
2SLS: Instruments PPP
, Fed policy rate lagged.
2SLS: Instruments UIP: CDS, Bank of Israel rate lagged.
30
Appendix
Tables
Table A1 – PPP equation alternative specifications:
1996:1-2017:7
OLS: (
) =
+
(
) +
,
95% interval
t-statistic
95% interval
0.520
(-3.752
, 4.791)
0.553
0.848
(-0.730
, 1.838)
2SLS:
=
+
(
) +
,
0.007
-(0.027
, 0.041)
1.194
1.833
(-0.089
, 2.47)
Notes: OLS: 95% confidence interval based on HAC standard errors & covariance (Pre-whitening
with lags=3 from SIC, max lags=6, Bartlett kernel, Newey-West fixed bandwidth = 5)
2SLS: 95% confidence interval based on HAC standard errors & covariance (Pre-whitening with lags
from SIC, Bartlett kernel, Newey-West fixed bandwidth = 5)
2SLS: Instruments
, Fed policy rate (t-13) Bank of Israel rate (t-13). Cragg-Donald F-
stat: 32. 8
2SLS estimated for 1977:2–2018:6.
Table A2 – Granger causality tests of deviations from PPP equations on the capital
account of the balance of payments:
1996:1-2017:7
OLS: (
) =
+
(
) +
,
Granger causality tests of , on
,
Test
F-statistic
Prob.
Nonresidents
,
does not Granger cause
,
258
2.010
0.157
,
does not Granger cause
,
258
5.313
0.022
Residents
,
does not Granger cause
,
257
0.911
0.4033
,
does not Granger cause
,
257
4.053
0.018
Notes: 1 and 2 lags used in tests, respectively.
31
Table A3 – PPP and Fama regression monthly rate of change
PPP: (
) =
+
(
) +
,
OLS: 1996:2-2007:12
95% interval
95% interval
-0.001
(-0.003
, 0.004)
1.029
(0.129
, 1.93)
PPP: (
) =
+
(
) +
+
+
,
OLS: 1996:2-2017:7
95% interval
95% interval
-0.001
(-0.003
, 0.003)
0.952
(-0.060
, 1.965)
0.006
(1.247)
-0.002
(-1.179)
Fama regression
:
( ) = +(
) + ,
2SLS: 1996:2-2007:12
95% interval
95% interval
-0.003
(-0.009
, 0.003)
1.268
(-0.079
, 2.615)
Fama regression
:
( ) = +(
) + +
+,
2SLS: 1996:2-2007:12
95% interval
95% interval
-0.005
(-0.011
, -0.000)
1.829
(0.459
,3.199)
0.009
(1.834)
-0.003
(-1.803)
Notes: 2SLS: 95% confidence interval based on HAC standard errors & covariance (pre-whitening with lags
from SIC max lags, (Bartlett kernel, Newey-West fixed bandwidth = 5)
FX: monthly billions of $US. purchased. D_FX: dummy for months with FX intervention.
t statistics in parenthesis for FX and D_FX,
2SLS: Instruments UIP, CDS, Bank of Israel rate lagged.
32
Appendix 1: Estimation of Israel’s credit risk before 2002
Data on Israel’s credit default swap (CDS) is available from Bloomberg only from July
2002. Since Israel was considered an emerging market, we regressed Israel’s CDS on
the EMBI index. We used the estimated equation to generate estimates for Israel’s CDS
before July 2002. The R squared obtained was 0.8. Figure A1below shows the actual
CDS and the estimated CDS.
Figure A1
Actual and estimated 5 CDS for Israel: 2002:07-2007:12
33
Appendix 2: Unit root tests for main variables
In this appendix, we report the results of the unit-root test on the main variables used in our
analysis: the rate of deprecation of the currency, the 12 months’ bond spread, the difference in
expected inflation, Israel’s risk premium, and FX purchases as well as the standard deviation
of the exchange rate. We find that we can reject both that series have unit root and the hypothesis
of a joint unit root process.
Table A4 – Unit root tests
Group unit root test: Summary
Series: Exchange rate depreciation, Yield spread, Expected inflation differential, 5Y CDS, FX purchases,
Std error.
Sample: 1995M 01 2018M 12
Exogenous variables: Individual effects
Automatic selection of maximum lags
Automatic lag length selection based on SIC: 1 to 13
Newey-West automatic bandwidth selection and Bartlett kernel
Method
Statistic
Prob.**
Cross-
sections
Obs
Null: Unit root (assumes common unit root process)
Levin, Lin & Chu t*
-1.94800
0.0257
6
1570
Null: Unit root (assumes individual unit root process)
Im, Pesaran and Shin W-stat
-4.93007
0.0000
6
1570
ADF - Fisher Chi-square
53.1993
0.0000
6
1570
PP - Fisher Chi-square
100.260
0.0000
6
1594
** Probabilities for Fisher tests are computed using an asymptotic Chi-square distribution. All other
tests assume asymptotic normality
