No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Structural Change in the Forward Discount: Implications for the Forward Rate Unbiasedness Hypothesis
Abstract
It is a well-accepted empirical result that forward exchange rate unbiasedness is rejected in tests using the “differences regression” of the change in the logarithm of the spot exchange rate on the forward discount. We model the forward discount as an AR(1) process and argue that its persistence is exaggerated due to the presence of structural breaks. We show using a stochastic multiple break model that the forward discount persistence is substantially less if one allows for multiple structural breaks in the mean of the process. We argue that these breaks could be identified as monetary shocks to the central bank's reaction function. Using Monte Carlo simulations, we show that if we do not account for structural breaks that are present in the forward discount process, the forward discount coefficient in the “differences regression” is severely biased downward, away from its true value of 1.
... Another consensus view implies that the lack of structural changes in the data generating process may have been accompanied by the failure for the forward exchange rate to be the unbiased predictor of the future spot exchange rate (Kutan and Zhou 2003). To evaluate the impacts of unaccounted structural changes on the forward premium, Sakoulis et al. (2010) model the forward premium as a simple AR(1) process with multiple structural breaks. Their results indicate that the persistence of forward premium is a result of unaccounted structural breaks. ...
... Allowing for structural changes in a linear regression model, Sakoulis et al. (2010) provide evidence supportive of structural breaks' role in explaining the high persistence of the forward premium, which in turn leads to the forward premium bias. However, the literature has yet definitively to resolve the puzzle. ...
... Looking at 16 futures-spot basis as well as the forward premium in the exchange rate market, Coakley et al. (2011)'s findings point to a rejection of the unbiasedness hypothesis when considering multiple breaks in the mean. Moreover, Chen and Yu (2011) find results contrary to Sakoulis et al. (2010), where high persistence property is detected in the forward premium when the structural breaks are incorporated in the regression. The inconclusive findings lead to an analysis for whether or not the existence of structural changes provides bias-free coefficients of the forward premium regression. ...
This study investigates whether the ignored structural break causes the forward premium non-stationary. This paper proposes to test for the presence of unit root with multiple structural breaks. We find that, as long as the dynamic lag structure is specified, the forward premium exhibits a non-stationary process even if structural breaks are accounted for and points to no evidence of moving toward stationarity. Given our findings, the structural change model seems less robust in explaining the forward premium puzzle.
... This sub-section emphasizes the role of monetary policy in explaining the UIP puzzle. Sakoulis, Zivot, and Choi (2010) described the forward premium anomaly using the presence of structural breaks. They present evidence that structural breaks inflate the presence of the forward discount. ...
... Where the factors that contribute to risk premium has been identified as exchange risk, default risk or crash risk (Burnside, 2013;Coudert & Mignon, 2013;Nagayasu, 2014;Aysun & Lee, 2014), currency risk, stock variance risk (Zhou & Londono, 2017), consumption growth risk (Burnside, 2011;Lustig & Verdelhan, 2011;Lustig & Verdelhan, 2007;Paol & Sondergaard, 2016), liquidity (Chu, 2015) and volatility (Li, Ghoshray, & Morley, 2012). Another possible explanation for the puzzle goes through rational learning (Moran & Nono, 2018), Peso-Problem (Lothian, Pownall, & Koedijk, 2013;Rabitsch, 2016) and monetary policy interventions (Guender, 2014;Sakoulis, Zivot, & Choi, 2010). Further, the existence of excess returns is rationalized using market inefficiency. ...
Uncovered interest rate parity (UIP), is one of the crucial relations in macroeconomics and international finance, widely used in the model's construction and their analytical work. However, empirical regularities in UIP referred to as "Forward Premium Puzzle", has posed a significant challenge to open-economy models. Thus, the purpose of the study is to identify the possible explanation of the forward premium puzzle. The research has identified five distinct and coherent themes (solutions) using thematic analysis of literature review, namely, risk premium, monetary policy, rational learning and peso-problem, market inefficiency, and lastly, covered interest rate parity. The researcher can use these thematic classifications to understand the operations of the global financial market. Similarly, the identified solutions can help investors in the assessment of their investment strategies such as the risk premium implies returns obtained at the expense of assuming high risk. Thus, investors should question whether average returns received from an investment are above normal on a risk-adjusted basis.
... These results are interpreted as evidence of the forward premium anomaly. To explain this puzzle, recent studies have suggested that the right and left side of Eq. (3) do not have the same statistical properties (see Baillie and Bollerslev (1994); Choi and Zivot (2007) and Sakoulis et al. (2010), among others). For instance, several studies have found that although the spot returns are stationary, I(0), the forward premium is highly persistent. ...
... However, they found evidence of long memory in volatilities. Sakoulis et al. (2010) argued that long memory modeling requires a relatively high number of observations to provide reliable estimates of an integration order between 0 and 1. Coakley et al. (2011) found that high persistence and the long memory property are detected in the forward discount in commodity futures markets over the period 1990-2009. Baillie and Bollerslev (2000) found that long memory behavior can be observed in the forward premium series. ...
... These results are interpreted as evidence of the forward premium anomaly. To explain this puzzle, recent studies have suggested that the right and left side of Eq. (3) do not have the same statistical properties (see Baillie and Bollerslev (1994); Choi and Zivot (2007) and Sakoulis et al. (2010), among others). For instance, several studies have found that although the spot returns are stationary, I(0), the forward premium is highly persistent. ...
... However, they found evidence of long memory in volatilities. Sakoulis et al. (2010) argued that long memory modeling requires a relatively high number of observations to provide reliable estimates of an integration order between 0 and 1. Coakley et al. (2011) found that high persistence and the long memory property are detected in the forward discount in commodity futures markets over the period 1990-2009. Baillie and Bollerslev (2000) found that long memory behavior can be observed in the forward premium series. ...
This paper contributes to the empirical literature on the forward premium anomaly by investigating possible statistical explanations for this puzzling phenomenon in the energy market. To this end, time series of spot and different forward maturities for West Texas Intermediate (WTI) crude oil and Reformulated Gasoline Blendstock for Oxygen Blending (RBOB) traded on the New York Mercantile Exchange (NYMEX) over the period 1986–2018 are used. The statistical properties of the spot and forward premium time series are examined by using unit root tests with structural breaks and a long memory process. The time-varying slope coefficient of regressing spot returns on the lagged forward premium is then estimated via the rolling sample technique and the state space model using the Kalman filter. The empirical results provide strong support for the presence of multiple structural breaks and long memory in the forward premium of the crude oil and RBOB energy time series in contrast to the spot returns series, which are stationary. The results also show evidence for time-varying beta coefficients for all the energy maturities considered. Overall, there is strong evidence for the forward premium anomaly with a larger negative slope parameter for the crude oil compared to the regular RBOB gasoline. The rejection of the forward rate unbiasedness hypothesis suggests that the futures price cannot play a significant role in price discovery.
... First, we provide evidence that for each country, the FDP is particularly strong and statistically significant for a short period of less than 2 years which falls between the late 1970s and 1980s. While complementing previous studies showing that the FDP is particularly prevalent in the 1980s, such as Choi and Zivot (2007), Sakoulis et al. (2010), or Lothian and Wu (2011), our results significantly narrow both the time frame and the number of break points in the data. ...
... The dates of the shifts are reported inLafrance (1998) and Nikolsko-Rzhevskyy (2011).5 Sakoulis et al. (2010) andKim et al. (2017) consider shocks to US monetary policy in the early 1980s as the main driver of the violation of UIRP, whileMoon and Velasco (2011) attribute the changes in forecasting techniques-from fundamentalist to chartist-to the strong predictability of foreign excess returns in the USA during the 1980s. ...
In this paper we argue that major shifts in monetary policy regimes can help explain the forward discount puzzle. We hypothesize that shifts by central banks from destabilizing regimes—when the Taylor principle is violated—to stabilizing regimes—when a central bank follows a Taylor-type rule—can cause violations of uncovered interest rate parity. Following the shift is an adjustment period when the forward discount puzzle clearly appears, as forecasters gradually update their expectations, eventually restoring parity. We test this hypothesis using four major currencies: the Canadian dollar, German mark, and the British pound, against the US dollar. Results indicate that the evidence for the forward discount puzzle becomes significantly weaker after allowing for an adjustment period of as little as 18 months. These results are robust to different specifications, such as the use of different maturities or base currencies, and also hold for the New Zealand dollar and the Swedish krona, two smaller, but independent currencies.
... For example, Jeon and Seo (2003) reported a breakdown of a cointegrated relationship between spot and forward exchange rates during the 1997 Asian crisis but an immediate recovery soon after this event. Similarly, Sakoulis et al. (2010) argued that the forward rate puzzle is attributable to the lack of consideration of shifts in their analysis of the forward rate unbiasedness hypothesis. In this connection, we employ panel unit root tests which have more statistical power than univariate tests and take account of premium-speci…c regime shifts. ...
... These impacts on the forward premiums are discussed as more permanent than the Asian crisis, but do not have a persistent impact on the CIRP relationship. Thus, our …ndings complement the analysis of the forward rate unbiasedness theory by Sakoulis et al. (2010), and imply that the increased nonstationarity of forward premiums resulting from such historical events is part of the explanation of the forward premium puzzle. HK-8.20E-05-3.50E-04-6.57E-04-9.19E-04-1.48E-03-1.76E-03-1.85E-03 ...
... The AR (1) coefficients of basis 1 and basis 2 are significantly positive and much smaller than the AR (1) coefficient of basis f. When we model basis f by AR (2), all point estimates of the ‡ Sakoulis et al. (2010) argue that the persistence of the forward discount is exaggerated because of the presence of structural breaks. However, there are no structural breaks in the AR process for the futures basis and forward basis. ...
This paper investigates the predictive performance of the futures basis in directly forecasting currency spot returns and compares it with that of the one-month forward basis. We consider the settle prices of both front-month and nearby-month continuous futures contracts and find that the futures basis exhibits statistically and economically significant in-sample and out-of-sample forecasting power, which clearly exceeds that of the well-known forward basis. The empirical results show that spot returns correspond negatively to both the front-month futures basis and nearby-month futures basis. Furthermore, the futures basis reveals substantial economic value for investors in terms of sizable and tangible portfolio gains, which are consistent with statistical measures. The difference in the forecasting ability of the futures basis and forward basis can be explained by the level of exposure to the time-varying risk premium. Finally, we find that impacts of the futures basis on spot returns vary with time and experienced substantial structural changes during the Global Financial Crisis.
... When monetary policy is implemented in a non-similar way, learning about shifts is harder, and the updating process for expectations is much slower. This result is consistent with those reported in Sakoulis, Zivot, and Choi (2010), who find that structural breaks in the forward discount process as a consequence of changes in monetary policy objectives of the central banks of different countries lead to a significant downward bias for the forward discount coefficient in the Fama regression. ...
This paper provides a theoretical discussion of the forward premium anomaly. We reformulate the well-known Lucas (1982) model by allowing for the existence of monetary policy regimes. The monetary supply is viewed as having two stochastic components: (a) a persistent component that reflects the preferences of the central bank regarding the long-run money supply or inflation target, and (b) a transitory component that represents short-lived interventions. To generate agents' forecasts, we consider two scenarios: (a) consumers can distinguish the permanent and the transitory components of the money supply (complete information), and (b) consumers face a signal-extraction problem to disentangle permanent and transitory components of the money supply (incomplete information). We simulate the model from a careful estimate of the parameters involved in the model. Numerical simulations reveal that, under complete information, forward unbiasedness cannot be rejected at conventionally significant levels. However, when learning about monetary policy is incorporated, the forward bias can be reproduced without artificially assuming an unreasonable degree of risk aversion.
... Representative studies include Hodrick and Srivastava (1986), Froot and Frankel (1989), Maynard (2006), Frankel and Poonawala (2010), and the papers surveyed in MacDonald and Torrance (1989), Lewis (1995) and Engel (1996). 2 Some researchers have recently made important headway in explaining the puzzle. In this connection, Sakoulis, Zivot and Choi (2010), found that, by allowing for multiple structural breaks in the forward discount process, they are able to account for some of the forward premium puzzle. Additionaly, Baillie and Kilic (2006) and Sarno, Valente and Leon (2006) provided evidence indicating that nonlinearities may explain the puzzle while Bollerslev (1994, 2000) and Maynard and Phillips (2001) suggested that, if the forward discount is a fractionally integrated process while the return on the exchange rate is stationary, this may help account for the puzzle. ...
Empirical studies often report a negative relationship between the difference in the spot exchange rate and the forward premium, violating the forward-rate unbiasedness hypothesis. Using standard regression on a sample of ten exchange rates, we obtain both positive and negative coefficients. We argue that the negative coefficients could arise as a result of the non-linearities in the relationship and misspecification. As an alternative to the standard regression, we use a time-varying-coefficient technique that estimates bias-free coefficients and, thus, should provide better estimates of the link between spot and forward rates. Our findings strongly support the forward rate unbiasedness hypothesis. All the parameters are very close to unity and significant.
The forward premium anomaly, which refers to the empirical failure of the uncovered interest parity (UIP), has been primarily examined by the forward premium regression of [Fama, E. (1984). Forward and spot exchange rates. Journal of Monetary Economics, 14(3), 319–338. https://doi.org/10.1016/0304-3932(84)90046-1]. Some studies apply the rolling-window regression to capture the time-varying coefficient on the forward premium, with difficulty in statistically testing the deviation of the coefficient from the UIP over time. We follow [Baillie, R., & Kim, K. (2015). Was it risk? Or was it fundamentals? Explaining excess currency returns with kernel smoothed regressions. Journal of Empirical Finance, 34, 99–111] to apply the simultaneous inference procedure to the Korean Won-US Dollar spot and forward exchange rates by estimating the time-varying coefficient from the kernel-smoothed local-linear regression and constructing the uniform confidence band to test the local deviation. We find that, while the UIP is not rejected from the baseline regression, the simultaneous inference shows that the deviation from the UIP is mainly observed during the early 2000s and 2010s. Time-variation of the forward premium coefficient tends to be significantly affected by economic uncertainties such as the interest rate, inflation, and stock return volatilities in Korea and US.
This paper develops two time-varying parameter uncovered interest parity (TVP-UIP) models and studies their validity in both developed and emerging countries. Compared to the traditional models, TVP-UIP models can successfully capture dynamic relationships and help to explain the UIP puzzle. Empirical results show that the coefficients vary substantially over time and the UIP relationship can be regarded as a dynamic equilibrium process especially in emerging economies. The UIP hypothesis holds in several periods and can be significantly affected by specific major events, such as the financial crises and the recovery policies in response to it, or the US monetary policy changes. The time-varying risk premium attracts great concern in the literature but only plays a limited role in this case. Moreover, the failure of UIP in some periods can be attributable to the persistence inherent in the data, which leads to a long-lasting re-establishment of the UIP relationship after a shock.
This paper investigates possible structural changes in the persistence of the forward premium by applying the multiple structural break methodology recently proposed by Kejriwal et al. (2013). The results reveal three or four breaks over the last three decades and provide evidence of long memory within each sub regime. The estimated break dates for the persistence appear to correspond to major economic events caused by macroeconomic shocks or changes in monetary policy. We provide some implications for the forward premium anomaly: if the forward premium is strictly stationary and has long memory, in which the confidence interval includes only the stationary region, the anomaly appears to be resolved or uncovered interest rate parity tends to hold. This finding suggests that the degree of the persistence of the forward premium plays an important role in explaining the anomaly.
This article provides evidence that the forward premium involves structural changes in the trend function, which might affect the predictability of currency excess returns to be dependent on the choice of the sample period. Accounting for the shifts in trend for the forward premium reveals that currency excess returns for the Canadian dollar, Swiss franc, euro and pound against the US dollar are significantly predictable irrespective of the sample period selected. Another advantage of detrending the forward premium is that we can obtain more consistent slope coefficient estimates in the predictive regression, which enables us to make more consistent, dependable inferences about the excess return predictability.
This article extends the Lagrange multiplier (LM) cointegration test proposed by Westerlund and Edgerton (WE 2007) by allowing for an unknown number of breaks. Monte Carlo simulations provide two main results. First, a loss of power in the LM cointegration tests is detected when potential multiple breaks are ignored. Second, the modified testing procedures do not affect the asymptotic distribution and major properties of the tests of WE under the null, but noticeably increase their testing power in presence of multiple breaks. We also provide empirical applications of the proposed tests for the forward rate unbiasedness hypothesis (FRUH). The results reveal that the FRUH does hold when the effects of the multiple structural breaks are taken into account.
While a number of papers have attempted to explain the forward rate premium puzzle the issue nevertheless endures. Hall et al. (Stud Nonlinear Dyn E 17(3):265–279, 2013) argue that the standard regression approach is the cause for the empirical conundrum observed in the investigation of forward-spot relationship. In this paper we identify embedded variables to be the real cause for the miss-specification in the forward rate premium puzzle. Using the Fama (J Financ Econ 13:509–528, 1984) approach along with simulated independent and uniformly distributed data, we demonstrate the forward-spot approach to have spurious reliable forecast ability.
This study aims to determine whether forward discount represents a long memory or short memory process with multiple changes in the mean. Based on the samples of six currencies from November 3, 1986, to March 6, 1998, using Back and Pipiras's (2012, 2014) statistical procedures, our findings suggest that forward discount is a short memory process with multiple changes in the mean rather than long memory. These changes in mean are the result of an intervention by monetary authorities in the forex market. Thus, earlier findings of long memory in forward discount, as reported in the extant literature, are questionable.
This paper uses recently developed kernel smoothing regression procedures and uniform confidence bounds to investigate the forward premium anomaly. These new statistical methods estimate the local time-varying slope coefficient of the regression of spot returns on the lagged interest rate differential. Uniform confidence bands are used to test when uncovered interest parity is violated. The estimated betas in the forward premium smoothed regression are found to vary substantially over time and to be partially explicable in terms of lagged fundamentals and money growth volatilities arising from risk premium. Frequentist model averaging procedures indicate the relative importance of these variables in terms of explaining movements in the betas and hence the apparent causes of regimes where UIP fails.
In this study we analyse the issue of mean reversion in forward discount based on nonlinear framework for seven currencies. Compared to previous study, we apply a novel approach of a threshold regression (TAR) and followed by nonlinear unit root tests. This approach disentangles tbodhe issue of nonlinearity and nonstationarity in forward discount. After applying nonlinearity test, we found evidence of nonlinearities in five out of seven currencies for the forward discounts. Notably, it is found that forward discount behaves as unit root in a band and becomes mean reverting outside the band. This explains the mixed findings in earlier studies due to general assumption of linearity in forward discount.
This paper documents new results that the ability of structural breaks to explain away non-stationary long memory in the forward premium weakens considerably with higher-frequency data. For daily data, removing structural breaks does not make non-stationary long memory stationary, contrary to the evidence for monthly data reported in the recent literature. Simulating data on a daily basis, we show that using monthly data tends to overstate the importance of structural breaks, and obfuscate the true nature of persistence, in the forward premium. Our results thus corroborate earlier findings that long memory bears primary responsibility for the forward premium anomaly.
This paper makes two contributions to trying to understand the forward premium anomaly and the apparent breakdowns of Uncovered Interest Rate Parity (UIP). First, investigation of the time series properties of the forward premium reveals either four or five breaks in the last twenty three years and evidence of long memory within each sub period. In fact the forward premium is highly nonlinear and appears to defy classification as a process with a constant order of integration. The second aspect of the paper is concerned with the time varying nature of the estimate of the slope parameter when spot returns are regressed on the lagged forward premium. We compare rolling type regression estimates, with Bayesian estimation and also a new Time Varying Parameter (TVP) method that is motivated by the TVP autoregression of Giraitis et al. (2014). The procedure is a form of kernel weighted regression and delivers relatively tight standard errors on the parameter estimates. We find the existence of the forward premium anomaly with large negative beta coefficients in the 1980s and 1990s. For some currencies there is also evidence of large positive coefficients and a reversal of the forward premium anomaly after the financial crisis of 2008.
In most of the literature on transparency it has been standard to assume that central banks release truthful information when communicating with the public. However, the monetary policymaker may act strategically and misrepresent private information intending to reduce economic volatility by manipulating inflation expectations. We set up a simple model which includes misrepresentation as a possible action for the central bank and derive some testable implications. The empirical evidence from the analysis of inflation forecasts of six central banks (Brazil, Canada, England, Iceland, New Zealand, and Sweden) is consistent with the existence of strategic forecasting. (JEL E52, E58)
This paper analyzes the stationarity of forward premiums in the foreign exchange markets. Considering a wide range of countries and contract periods and taking into account cross-sectional correlations and heterogeneities in nonstationary environments, we confirmed mixed evidence of stationary forward premiums. However, mounting evidence to support the stationarity is provided when regime shifts which likely reflect the effects of the Lehman Shock and changing monetary policies are considered. Thus these events seem to have increased the nonstationary element in the premiums, and our further analysis suggests the effect of these events can be captured by interest rates, leaving the covered interest parity condition as a valid long-run concept.
This research analyzes the way agents participating in the Colombian exchange market form their expectations and how they arrive at an equilibrium price. The forward exchange rate was used as an approximation of the expected spot rate, implying the necessity to explain how its price is determined. Monte Carlo techniques and three tests of the Forward Foreign Exchange Market Efficiency Hypothesis are conducted. Six hypotheses of behavior were tested, from static to rational expectations and from risk neutrality to risk premium and/or transaction costs. Weekly data from January 1997 to January 2006 presented signs of rational and adaptative expectations, together with risk neutrality.
This note outlines the economic theory behind the theory of uncovered interest parity and some of the econometric issues involved in testing and interpretation. I illustrate some of the issues involved by estimating a rolling regression of the forward premium regression from 22 years of eight major currencies. I also conclude that Pippenger's model is not consistent with the theory of UIP and that furthermore there are severe econometric problems in estimating his model. The forward premium anomaly remains a paradox in international finance that is important and worthwhile to understand more fully.
Using Bayesian methods, we reexamine the empirical evidence from Sakoulis et al. (2010) regarding structural breaks in the forward discount for G-7 countries. Our Bayesian framework allows the number and pattern of structural changes in level and variance to be endogenously determined. We find different locations of breakpoints for each currency; mostly, fewer breaks are present. We find little evidence of moving toward stationarity in the forward discount after accounting for structural change. Our findings suggest that the existence of structural change is not a viable justification for the forward discount anomaly.
most (all?) behavior can be explained by assuming that agents have stable, well-defined preferences and make rational choices consistent with those preferences in markets that (eventually) clear. An empirical result qualifies as an anomaly if it is difficult to "rationalize," or if implausible assumptions are necessary to explain it within the paradigm. This column will present a series of such anomalies. Readers are invited to suggest topics for future columns by sending a note with some reference to (or better yet copies of) the relevant research. Comments on anomalies printed here are also welcome. The address
We provide empirical evidence that deviations from uncovered interest rate parity (UIP) display significant nonlinearities, consistent with theories based on transaction costs or limits to speculation. This evidence suggests that the forward bias documented in the literature may be less indicative of major market inefficiencies than previously thought. Monte Carlo experiments allow us to reconcile these results with the large empirical literature on the forward bias puzzle since we show that, if the true process of UIP deviations were of the nonlinear form we consider, estimation of conventional spot-forward regressions would generate the anomalies documented in previous research.
We provide empirical evidence that deviations from the uncovered interest rate parity (UIP) condition display significant nonlinearities, consistent with theories based on transactions costs or limits to speculation. This evidence suggests that the forward bias documented in the literature may be less indicative of major market inefficiencies than previously thought. Monte Carlo experiments allow us to reconcile these results with the large empirical literature on the forward bias puzzle since we show that, if the true process of UIP deviations were of the nonlinear form we consider, estimation of conventional spot-forward regressions would generate the anomalies documented in previous research. Copyright Oxford University Press Science+Business Media, Inc. 2006
FX market unbiasedness requires spot-forward cointegration with unitary vector, or a stationary forward-premium (FP). These conditions have found mixed support, which recent research explains via FP fractional integration. An alternative explanation is breaks in spot-forward cointegration regressions, so that I apply Gregory and Hansen [Gregory, A.W., Hansen, B.E., 1996a. Residual-based tests for cointegration in models with regime shifts. Journal of Econometrics 70, 99–126; 1996b. Tests for cointegration in models with regime and trend shifts. Oxford Bulletin of Economics and Statistics 58, 555–560] models to DM, Yen and Pound data, allowing for intercept, slope, and time-trend shifts. I adapt the procedure of Bai [Bai, J., 1997. Estimation of a change point in multiple regression models. Review of Economics and Statistics 79, 551–563] to sequentially search for multiple breaks, and find evidence of cointegration with “regime-and-trend shifts” for the three currencies. Cointegration-with-breaks regressions show stationary residuals and unitary slopes across regimes, consistent with long-run unbiasedness overall. Forward-premium regressions estimated for subsamples determined by cointegration-regression break dates find support for short-run unbiasedness in some regimes but not others.
In a recent paper, Baillie and Bollerslev (1989), using daily data from 1980 to 1985, identified six common stochastic trends in a vector of seven nominal exchange rates implying the existence of one cointegrating vector. Cointegration implies that (Granger) causality must run in at least one direction, that is, at least one of the exchange rates is predictable using current available information. This result has been interpreted as foreign exchange market inefficiency, by many. Another interpretation is suggested if the stationary linear combination of spot rates proxies for a time varying risk premium in some way. Then these results could be explained in a rational and risk averse market. This possibility is eliminated if the time series properties of the risk premium are incompatible with those of the error correction term. Specifically, it is demonstrated that the forward risk premium is non-stationary for the exchange rates that comprise the exchange rate cointegration relationship. In this paper, the existence of common stochastic trends in a vector of nominal exchange rates is tested over the period 1974 to 1991. The efficiency of foreign exchange markets is then tested by examining the implications of stochastic trends in the forward premium and what this means for the time series properties of a time-varying forward risk premium. (JEL F31, G14).
This paper investigates the effects of shocks to U. S. monetary policy on exchange rates. We consider three measures of these
shocks: orthogonalized shocks to the federal funds rate, orthogonalized shocks to the ratio of nonborrowed to total reserves
and changes in the Romer and Romer index of monetary policy. In sharp contrast to the literature, we find substantial evidence
of a link between monetary policy and exchange rates. Specifically, according to our results a contractionary shock to U.
S. monetary policy leads to (i) persistent, significant appreciations in U. S. nominal and real exchange rates and (ii) significant,
persistent deviations from uncovered interest rate parity in favor of U. S. interest rates.
A common finding is that the forward discount is a biased predictor of future exchange rate changes. We use survey data on
exchange rate expectations to decompose the bias into portions attributable to the risk premium and expectational errors.
None of the bias in our sample reflects the risk premium. We also reject the claim that the risk premium is more variable
than expected depreciation. Investors would do better if they reduced fractionally the magnitude of expected depreciation.
This is the same result that many authors have found with forward market data, but now it cannot be attributed to risk.
Foreign exchange returns exhibit behavior difficult to reconcile with standard theoretical models. This article asks whether
the recent findings of long swings in exchange rates between appreciating and depreciating periods affect estimates of the
foreign exchange risk premium. We demonstrate how the “peso problem” introduced by expected shifts in exchange rate regimes
can affect inferences about the risk premium in at least two ways: (1) it can make the foreign exchange risk premium appear
to contain a permanent disturbance when it does not; and (2) it can induce bias in the foreign exchange return regressions
such as in Fama (1984).
Changes in variance, or volatility, over time can be modeled using the approach based on autoregressive conditional heteroscedasticity. Another approach is to model variance as an unobserved stochastic process. Although it is not easy to obtain the exact likelihood function for such stochastic variance models, they tie in closely with developments in finance theory and have certain statistical attractions. This article sets up a multivariate model, discusses its statistical treatment, and shows how it can be modified to capture common movements in volatility in a very natural way. The model is then fitted to daily observations on exchange rates.
We introduce adaptive learning behavior into a general-equilibrium life-cycle economy with capital accumulation. Agents form forecasts of the rate of return to capital assets using least-squares autoregressions on past data. We show that, in contrast to the perfect-foresight dynamics, the dynamical system under learning possesses equilibria that are characterized by persistent excess volatility in returns to capital. We explore a quantitative case for theselearning equilibria. We use an evolutionary search algorithm to calibrate a version of the system under learning and show that this system can generate data that matches some features of the time-series data for U.S. stock returns and per-capita consumption. We argue that this finding provides support for the hypothesis that the observed excess volatility of asset returns can be explained by changes in investor expectations against a background of relatively small changes in fundamental factors.
This paper is an introduction to unit root econometrics as applied in macroeconomics. The paper first discusses univariate time series analysis, emphasizing the following topics: alternative representations of unit root processes, unit root testing procedures, the power of unit root tests, and the interpretation of unit root econometrics in finite samples. A second part of the paper tackles similar issues in a multivariate context where cointegration is now the central concept. The paper reviews representation, testing, and estimation of multivariate time series models with some unit roots. Two important themes of this paper are first, the importance of correctly specifying deterministic components of the series; and second, the usefulness of unit root tests not as methods to uncover some -true relation" but as practical devices that can be used to impose reasonable restrictions on the data and to suggest what asymptotic distribution theory gives the best approximation to the finite-sample distribution of coefficient estimates and test statistics.
We consider the time series behavior of the U.S. real interest rate from 1961 to 1986, using the methodology of Hamilton (1989), by allowing three possible regimes affecting both the mean and variance. The results suggest that the ex-post real interest rate is essentially random with means and variances that are different for the periods 1961-1973, 1973-1980 and 1980-1986. The inflation rate series also shows interesting shifts in both mean and variance. Series for the ex-ante real interest rate and expected inflation are constructed. Finally, we make clear how our results can explain some recent findings in the literature.
We investigate the existence of a time-varying risk premium in the foreign exchange market using the intertemporal asset pricing model. In this model the risk premium is due to consumption risk, which is measured by the covariance between returns and the marginal utility of money. We model this conditional covariance using Engle's (1982) ARCH model. Results are presented for three exchange rates for the 1975–1985 period. Although a time-varying risk premium is an important determinant of the expected returns, tests of IAPM restrictions show that a more flexible specification of the model is needed.
The paper decomposes GDP both in terms of level per capita and growth rate, so as to identify the sources of income differences and of economic growth for all EU27 member states. This accounting approach has multiple advantages, although a number of substantial caveats should be borne in mind when interpreting the results. In particular, the detailed accounting approach helps distinguish exogenous from policy-influenced growth drivers. The combination of lower per-hour productivity and lower labour utilisation is the cause of relatively low per capita GDP in euro area and EU15 countries, while weak productivity remains the main concern in the new member states. GDP growth rate has been broken down into 12 items, including an indicator of labour quality, based upon the composition of employment by educational attainment.
This paper investigates the power of two methodologies, the tests of Brown, Durbin, and Evans [2] and variable parameter regression, to detect several varieties of instability in the coefficients of a linear regression model. The study reported by Khan [10] on the stability of the demand for money is replicated with variable parameter regression, and his results are in part questioned and in part sharpened.
This chapter focuses on two puzzles related to international financial markets. The first puzzle concerns explanations for deviations from uncovered interest parity or, equivalently, excess returns on foreign relative to domestic deposits. The chapter considers various explanations for the puzzle. First, under standard assumptions about rational expectations, ex post excess returns just equal the market's true expected excess returns plus a forecast error that is unpredictable ex ante. The second puzzle is called “home bias,” the phenomenon that domestic investors hold too little of their portfolios in foreign assets. The chapter considers this puzzle with the two models used to examine the foreign exchange risk premium. Both models suggest that domestic investors hold too little of their wealth in the form of foreign assets. The first type of model, based upon CAPM, implies that domestic investors should hold foreign assets in their portfolio in a fraction that depends upon their degree of risk aversion, among other variables. The second type of model, based upon complete markets, gives predictions about consumption risk-sharing.
In a recent paper, Bai and Perron (1998) considered theoretical issues related to the limiting distribution of estimators and test statistics in the linear model with multiple structural changes. In this companion paper, we consider practical issues for the empirical applications of the procedures. We first address the problem of estimation of the break dates and present an efficient algorithm to obtain global minimizers of the sum of squared residuals. This algorithm is based on the principle of dynamic programming and requires at most least-squares operations of order OOT 2 for any number of breaks. Our method can be applied to both pure and partial structural change models. Second, we consider the problem of forming confidence intervals for the break dates under various hypotheses about the structure of the data and the errors across segments. Third, we address the issue of testing for structural changes under very general conditions on the data and the errors. Fourth, we address the issue of estimating the number of breaks. Finally, a few empirical applications are presented to illustrate the usefulness of the procedures. All methods discussed are implemented in a GAUSS program.
We examine the ability of the standard intertemporal asset pricing model and a model of noise trading to explain why the forward foreign exchange premium predicts the future currency depreciation with the ‘wrong’ sign. We find that the intertemporal asset pricing model is unable to predict risk premia with the correct sign to be consistent with the data. The noise-trader model, while highly stylised, receives fragmentary support from empirical research on survey expectations.
A theory of testing under non-standard conditions is developed. By viewing the likelihood as a function of the unknown parameters, empirical process theory enables us to bound the asymptotic distribution of standardized likelihood ratio statistics, even when conventional regularity conditions (such as unidentified nuisance parameters and identically zero scores) are violated. This testing methodology is applied to the Markov switching model of GNP proposed by Hamilton (1989). The standardized likelihood ratio test is unable to reject the hypothesis of an AR(4) in favour of the Markov switching model. Instead, we find strong evidence for an alternative model. This model, like Hamilton's, is characterized by parameters which switch between states, but the states arrive independently over time, rather than following an unrestricted Markov process. The primary difference, however, is that the second autoregressive parameter, in addition to the intercept, switches between states.
Both state-space models and Markov switching models have been highly productive paths for empirical research in macroeconomics and finance. This book presents recent advances in econometric methods that make feasible the estimation of models that have both features. One approach, in the classical framework, approximates the likelihood function; the other, in the Bayesian framework, uses Gibbs-sampling to simulate posterior distributions from data. The authors present numerous applications of these approaches in detail: decomposition of time series into trend and cycle, a new index of coincident economic indicators, approaches to modeling monetary policy uncertainty, Friedman's "plucking" model of recessions, the detection of turning points in the business cycle and the question of whether booms and recessions are duration-dependent, state-space models with heteroskedastic disturbances, fads and crashes in financial markets, long-run real exchange rates, and mean reversion in asset returns.
The estimation of ARFIMA models by approximate maximum likelihood estimation methods, reveals the forward premia for the currencies of Canada, Germany and the UK vis-à-vis the US dollar, to be well described by a fractionally integrated process. These models imply that all the forward premia are mean reverting, although their autocorrelations are quite persistent. This degree of persistence has led other studies to erroneously conclude that the forward premia contains a unit root. (JEL C22, E31).
We analyze the evidence for long memory and structural changes in the five G7 countries' forward discount. We establish evidence for long memory by estimating the long memory parameter without allowing for structural breaks. We also document evidence for multiple structural breaks in the mean of the forward discount. We then adjust for structural changes in the forward discount rate and re-estimate the long memory parameter. After removing the breaks, we still find evidence of stationary long memory in each country's forward discount.
The forward premium anomaly refers to the widespread empirical finding that the slope coefficient in the regression of the change in the logarithm of the spot exchange rate on the forward premium is invariably less than unity, and often negative. This “anomaly” implies the apparent predictability of excess returns over uncovered interest rate parity (UIP), and is conventionally viewed as evidence of a biased forward rate and/or of evidence of a time-varying risk premium. This paper presents a stylized model that imposes UIP and allows the daily spot exchange rate to possess very persistent volatility. The model is calibrated around realistic parameter values for daily returns and the slope coefficient estimates in the anomalous regressions with monthly data are found to be centered around unity, but are very widely dispersed, and converge to the true value of unity at a very slow rate. This theoretical evidence is shown to be consistent with the empirical findings for the monthly sample sizes typically employed in the literature. Hence, the celebrated unbiasedness regression does not appear to provide as much evidence as previously supposed concerning the possible bias of the forward rate.
The theoretical and empirical econometric literatures on long memory and regime switching have evolved largely independently, as the phenomena appear distinct. We argue, in contrast, that they are intimately related, and we substantiate our claim in several environments, including a simple mixture model, Engle and Smith's (Rev. Econom. Statist. 81 (1999) 553–574) stochastic permanent break model, and Hamilton's (Econometrica 57 (1989) 357–384) Markov-switching model. In particular, we show analytically that stochastic regime switching is easily confused with long memory, even asymptotically, so long as only a “small” amount of regime switching occurs, in a sense that we make precise. A Monte Carlo analysis supports the relevance of the theory and produces additional insights.
This paper shows that occasional breaks generate slowly decaying autocorrelations and other properties of I(d) processes, where d can be a fraction. Some theory and simulation results show that it is not easy to distinguish between the long memory property from the occasional-break process and the one from the I(d) process. We compare two time series models, an occasional-break model and an I(d) model to analyze S&P 500 absolute stock returns. An occasional-break model performs marginally better than an I(d) model in terms of in-sample fitting. In general, we found that an occasional-break model provides less competitive forecasts, but not significantly. However, the empirical results suggest a possibility such that, at least, part of the long memory may be caused by the presence of neglected breaks in the series. We show that the forecasts by an occasional break model incorporate incremental information regrading future volatility beyond that found in I(d) model. The findings enable improvements of volatility prediction by combining I(d) model and occasional-break model.
Previous empirical study on the effects of monetary policy shocks in small open economies has generated puzzling dynamic responses in various macroeconomic variables. This paper argues that these puzzles derive from an identification of monetary policy that is inappropriate for such economies. To remedy this, it is proposed that a structural model be estimated to explicitly account for the features of the small open economy. Such a model is applied to Canada with tightly estimated results overall. The dynamic responses to the identified monetary policy shock are consistent with standard theory and highlight the exchange rate as a transmission mechanism.
Forward exchange rate unbiasedness is rejected in tests from the current floating exchange rate era. This paper surveys advances in this area since the publication of Hodrick's (1987) survey. It documents that the change in the future exchange rate is generally negatively related to the forward discount. Properties of the expected forward forecast error are reviewed. Issues such as the relation of uncovered interest parity to real interest parity, and the implications of uncovered interest parity for cointegration of various quantities are discussed. The modeling and testing for risk premiums is surveyed. Included in this area are tests of the consumption CAPM, tests of the latent variable model, and portfolio-balance models of risk premiums. General equilibrium models of the risk premium are examined and their empirical implications explored. The survey does not cover the important areas of learning and peso problems, tests of rational expectations based on survey data, or the models of irrational expectations and speculative bubbles.
Standard spot return/forward premium regressions have long been known to provide a strong rejection of unbiasedness. However, due to the strong autocorrelation in the forward premium, which shows estimated autoregressive roots close and in some cases statistically indistinguishable from one, recent literature has cast doubt on the finite sample accuracy of these tests. In fact, finite sample size distortion has now come to be considered as one of several possible explanations behind the forward premium puzzle. In order to pursue this possibility further, we revisit the unbiasedness hypothesis using more appropriate inference procedures. In particular, rather than relying on standard stationarity-based asymptotics, we model the forward premium as a near-unit root process and then test unbiasedness using the bounds tests of Cavanagh et al. (1995) [Cavanagh, C.L., Elliott, G., Stock, J.H., 1995. Inference in models with nearly integrated regressors. Econometric Theory 11, 1131-1147.], which are explicitly designed to provide accurate size under near-unit root assumptions. To summarize our empirical findings, confidence intervals on the largest root confirm uncertainty regarding the stationarity/nonstationarity of the forward premium. However, estimates of the error correlation suggest only modest simultaneity bias. Consequently, we can still reject unbiasedness at the 5% level, even when using appropriately sized bounds tests. This evidence tends to suggest that the forward premium puzzle is more robust than previously imagined. It would be interesting in further work to explore to what extent such conclusions extend to alternative characterizations of the persistence in the forward premium, such as long-memory and structural break models.
A generic intertemporal asset pricing model is applied in an international setting to generate a (possibly time varying) risk premium in the market for forward foreign exchange. The model is fitted and statistical tests of its general specification are performed. These specification tests provide weak evidence against the model.
There is a general consensus that forward exchange rates have little if any power as forecasts of future spot exchange rates. There is less agreement on whether forward rates contain time varying premiums. Conditional on the hypothesis that the forward market is efficient or rational, this paper finds that both components of forward rates vary through time. Moreover, most of the variation in forward rates is variation in premium, and the premium and expected future spot rate components of forward rates are negatively correlated.
Many economic models imply that ratios, simple differences, or “spreads” of variables are I(0). In these models, cointegrating vectors are composed of 1's, 0's, and —1's and contain no unknown parameters. In this paper, we develop tests for cointegration that can be applied when some of the cointegrating vectors are prespecified under the null or under the alternative hypotheses. These tests are constructed in a vector error correction model and are motivated as Wald tests from a Gaussian version of the model. When all of the cointegrating vectors are prespecified under the alternative, the tests correspond to the standard Wald tests for the inclusion of error correction terms in the VAR. Modifications of this basic test are developed when a subset of the cointegrating vectors contain unknown parameters. The asymptotic null distributions of the statistics are derived, critical values are determined, and the local power properties of the test are studied. Finally, the test is applied to data on foreign exchange future and spot prices to test the stability of the forward–spot premium.
The hypothesis that forward prices are the best unbiased forecast of future spot prices is often presented in the economic and financial analysis of futures markets. This paper considers the hypothesis independently of its implications for rational expectations or market efficiency and in order to stress this fact, the term "speculative efficiency" is used to characterize the state envisaged under the hypothesis. If a market is subject to efficient speculation, the supply of speculative funds is infinitely elastic at the forward price that is equal to the expected future spot price. The expected future spot price is a market price determined as the solution to the underlying rational expectations macroeconomic model. Although the paper is primarily concerned with testing this hypothesis in the foreign exchange market, the methodology introduced in the paper is of general application to all futures markets.
This paper presents new empirical evidence on the effects of monetary policy shocks on U.S. exchange rates, both nominal and real. Three measures of monetary policy shocks are considered: orthogonalized shocks to the Federal Funds rate, the ratio of Non Borrowed to Total Reserves and the Romer and Romer (1989) index. Using data from the flexible exchange rate era, we find that expansionary shocks to U.S. monetary policy lead to sharp. persistent depreciations in U.S. nominal and real exchange rates as well as to sharp. persistent increases in the spread between various foreign and U.S. interest rates. The temporal pattern of the depreciation in U.S. nominal exchange rates following a positive monetary policy shock is inconsistent with simple overshooting models of the type considered by Dornbusch (1976). We also find that U.S. monetary policy was less volatile under fixed exchange rates than under floating exchange rates. Finally, we find less evidence that monetary policy shocks had a significant impact on U.S. real exchange rates under the Bretton Woods agreement.
In a recent paper, Bai and Perron ( 1998 ) considered theoretical issues related to the limiting distribution of estimators and test statistics in the linear model with multiple structural changes. In this companion paper, we consider practical issues for the empirical applications of the procedures. We first address the problem of estimation of the break dates and present an efficient algorithm to obtain global minimizers of the sum of squared residuals. This algorithm is based on the principle of dynamic programming and requires at most least‐squares operations of order O ( T ² ) for any number of breaks. Our method can be applied to both pure and partial structural change models. Second, we consider the problem of forming confidence intervals for the break dates under various hypotheses about the structure of the data and the errors across segments. Third, we address the issue of testing for structural changes under very general conditions on the data and the errors. Fourth, we address the issue of estimating the number of breaks. Finally, a few empirical applications are presented to illustrate the usefulness of the procedures. All methods discussed are implemented in a GAUSS program. Copyright © 2002 John Wiley & Sons, Ltd.
Using both semiparametric and parametric estimation methods, this paper corroborates earlier findings of fractionally integrated behaviour in the forward premium. Two new explanations are also proposed to help reconcile earlier conflicting empirical evidence on the time series properties of the forward premium. Traditional regression approaches used to test the forward rate unbiasedness hypothesis are then evaluated, including regression in levels, in returns (Fama's, 1984, regression), and in error-correction format. Interesting statistical and|or interpretive implications are found in all three cases. For example, the predictions of the appropriate nonstandard limit theory are consistent with many of the standard empirical results reported from Fama's regression, including the commonly occurring, yet puzzling negative correlations between spot returns and the forward premium. It is suggested that the principal failure of unbiasedness, may be due instead to the difference in persistence between these two series. Copyright © 2001 John Wiley & Sons, Ltd.
Using the Kalman filter, we obtain maximum likelihood estimates of a permanent-transitory components model for log spot and forward dollar prices of the pound, the franc, and the yen. This simple parametric model is useful in understanding why the forward rate may be an unbiased predictor of the future spot rate even though an increase in the forward premium predicts a dollar appreciation. Our estimates of the expected excess return on short-term dollar-denominated assets are persistent and reasonable in magnitude. They also exhibit sign fluctuations and negative covariance with the estimated expected depreciation.
Markov switching (MS) models raise a problem known as testing hypotheses when a nuisance parameter is not identified under the null hypothesis. The author shows that the asymptotic distribution theory used for testing in presence of such a problem appears to work also for MS models, even though its validity can be questioned because of identically zero scores under the null estimates. Assuming the validity of this distribution theory, he derives the asymptotic null distribution of the likelihood ratio (LR) test for various MS models. Monte Carlo experiments show that the LR asymptotic distributions approximate the empirical distributions very well. Copyright 1998 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.
This paper shows how a simple univariate stationary nonlinear process has an autocorrelation function suggesting that the underlying process has a long memory, although that is not the case. The conclusion is that just considering linear properties of a process may be misleading.
This paper presents a survey of two basic puzzles in international finance. The first puzzle is the `predictable excess return puzzle.' The returns on foreign currency deposits relative to domestic currency deposits should be equalized based upon uncovered interest parity. However, not only do researchers find that deviations from uncovered interest parity are predictable ex ante, but their variance exceeds the variance in expected exchange rate changes. In the paper, I describe different explanations of this phenomenon including the view that excess returns are driven by a foreign exchange risk premium, peso problems or learning, and market inefficiencies. While the research to date has been able to better define the `predictable excess return puzzle' and to suggest the most likely directions for future progress, no one explanation has provided a full answer to the puzzle. The second puzzle is the `home bias puzzle.' Empirical evidence shows that domestic residents do not diversify sufficiently into foreign stocks. This evidence is clear whether looking at models based on portfolio holdings or outcomes of consumption realizations across countries. In this paper, I examine several possible explanations including non-traded goods and market inefficiencies, although even after considering these possibilities, the puzzle remains.
This paper reviews recent research that grapples with the question: What happens after an exogenous shock to monetary policy? We argue that this question is interesting because it lies at the center of a particular approach to assessing the empirical plausibility of structural economic models that can be used to think about systematic changes in monetary policy institutions and rules. The literature has not yet converged on a particular set of assumptions for identifying the effects of an exogenous shock to monetary policy. Nevertheless, there is considerable agreement about the qualitative effects of a monetary policy shock in the sense that inference is robust across a large subset of the identification schemes that have been considered in the literature. We document the nature of this agreement as it pertains to key economic aggregates.
We consider a deterministically trending dynamic time series model in which multiple structural changes in level, trend, and error variance are modeled explicitly and the number, but not the timing, of the changes is known. Estimation of the model is made possible by the use of the Gibbs sampler. The determination of the number of structural breaks and the form of structural change is considered as a problem of model selection, and we compare the use of marginal likelihoods, posterior odds ratios, and Schwarz's Bayesian model-selection criterion to select the most appropriate model from the data. We evaluate the efficacy of the Bayesian approach using a small Monte Carlo experiment. As empirical examples, we investigate structural changes in the U.S. ex post real interest rate and in a long time series of U.S. real gross domestic product.
This paper addresses a new interpretation to the appearance, in the early 1980s, of systematic errors in forecasting the dollar exchange rate. Following a change in the process of a fundamental variable, market participants revise their beliefs about the process using Bayes' Rule. Since the market does not immediately recognize the change, forecast errors are, on average, wrong during a period when the market is rationally learning. For conservative parameter values, the learning behavior of the dollar exchange rate in the early 1980s appears consistent with about half of the dollar's underprediction implied by the forward market. Copyright 1989 by American Economic Association.
The unit root hypothesis is examined allowing a possible one-time change in the level or in the slope of the trend function. When fluctuations are stationary around a breaking trend function, standard tests cannot reject the unit root, even asymptotically. Consistent tests are derived and applied to the Nelson-Plosser data set (allowing a change in level for the 1929 crash) and to the postwar quarterly real GNP series (allowing a change in slope after 1973). The unit root hypothesis is rejected at a high confidence level for most series. Fluctuations are stationary. The only persistent "shocks" are the 1929 crash and the 1973 oil price shock. Copyright 1989 by The Econometric Society.
This paper studies the properties of maximum likelihood estimates of co-integrated systems. Alternative formulations of such models are considered including a new triangular system error correction mechanism. It is shown that full system maximum likelihood brings the problem of inference within the family that is covered by the locally asymptotically mixed normal asymptotic theory provided that all unit roots in the system have been eliminated by specification and data transformation. This result has far reaching consequences. It means that cointegrating coefficient estimates are symmetrically distributed and median unbiased asymptotically, that an optimal asymptotic theory of inference applies and that hypothesis tests may be conducted using standard asymptotic chi-squared sets.
This paper develops the statistical theory for testing and estimating multiple change points in regression models. The rate of convergence and limiting distribution for the estimated parameters are obtained. Several test statistics are proposed to determine the existence as well as the number of change points. A partial structural change model is considered. The authors study both fixed and shrinking magnitudes of shifts. In addition, the models allow for serially correlated disturbances (mixingales). An estimation strategy for which the location of the breaks need not be simultaneously determined is discussed. Instead, the authors' method successively estimates each break point.