- Original Research
- Open Access
Great expectations? evidence from Colombia’s exchange rate survey
- Juan Jose Echavarria^{1} and
- Mauricio Villamizar-Villegas^{1}Email authorView ORCID ID profile
- Received: 8 January 2015
- Accepted: 7 July 2016
- Published: 21 July 2016
Abstract
In this paper, we use the largest exchange rate survey in Colombia to test for the rational expectations hypothesis, the presence of a time-varying risk premium and the accuracy of exchange rate forecasts. Our findings indicate that episodes of exchange rate appreciation preceded expectations of further appreciation in the short run, but were marked by depreciations in the long run. This reversal largely explains the stabilizing pattern of expectations. Additionally, we find that the forward discount differed from future exchange rate changes due to the rejection of the unbiasedness condition and to the presence of a time-varying risk premium. Finally, we find that only short run expectations were able to outperform a random walk process as well as models of extrapolative, adaptive, and regressive expectations. Long-run expectations, on the other hand, behaved poorly in terms of forecasting accuracy.
Keywords
- Exchange rate expectations
- Risk premium
- Forecasting accuracy
- Random walk
- Forward discount
- Rational expectations hypothesis
JEL Codes: C23 , C53 , C83 , F31 , F37
1 Introduction
The total currency turnover in global financial markets has dramatically increased since the end of the Bretton Woods system in the early 1970s. In fact, progressive financial innovation and deregulation have induced foreign exchange trading to exceed, by almost 20-fold, the volume of goods and services worldwide.^{1} According to Jongen et al. (2008), “It therefore seems that the foreign exchange market is a market ‘on its own’ and that this market, because of its large volume, is highly liquid and efficient.”^{2} As such, there has been a longstanding debate in the international finance literature on the main factors driving these capital flows. Nonetheless, most of the works agree that expectations play a central role in the determination of the exchange rate and for some authors, little else matters (see Woodford and Walsh (2005)).
Exchange rate expectations are generally assumed to be unbiased, homogeneous, and stabilizing. In many occasions, expectations are also assumed to be risk neutral, which overlooks potential effects brought forth by a time-varying risk premium. Namely, models that incorporate no-arbitrage conditions (such as the uncovered interest rate parity) assume that different currency-denominated assets are perfect substitutes.^{3} Consequently, the validity of results largely depends on the accuracy of these assumptions.
Paradoxically, the empirical literature has shown again and again that these assumptions do not hold. In fact, there is a long history of evidence pioneered by Frankel (1979), Dominguez (1986), and Frankel and Froot (1987) and by more recent works of De Grauwe and Grimaldi (2006) and De Grauwe and Markiewicz (2013) that show a systematic bias in exchange rate expectations. In addition, Ito (1990) and Allen and Taylor (1990) find empirical evidence of strong heterogeneity in expectations among market participants.^{4}
There are also numerous studies such as Lewis (1995), Bekaert (1996), Mark and Wu (1998), Carlson (1998), and Meredith and Ma (2002) that find statistical evidence of a currency risk premium. Authors such as Nurkse (1944), Takagi (1991), and Frankel and Rose (1994) consider expectations to be highly volatile and unstable, and state that the influence of psychological factors may at times be overwhelming. They claim that the destabilizing pattern of expectations (commonly known as “bandwagon expectations”) produce extremely volatile exchange rates which negatively affect investment and international trade, increase protectionist pressures, and hinder the development of the financial sector.
Notwithstanding, central banks still maintain a high degree of credibility on exchange rate surveys and often use them as input for their own internal forecasts.^{5} They generally argue that the use of ex-post exchange rates as a proxy for expectations has the disadvantage of assuming rational expectations instead of testing them, that is, studies that employ observed ex-post exchange rates cannot fully determine whether the evidence of a risk premium is in fact attributed to a time-varying risk or to the failure of rational expectations.
In this paper, we use a novel (and proprietary) survey conducted monthly by the Central Bank of Colombia during October 2003–August 2012 to test for the rational expectations hypothesis, the presence of a time-varying risk premium, and the accuracy of exchange rate forecasts. Our dataset (monthly frequency) is by far the largest official exchange rate survey in the country, containing a comprehensive outlook of the financial sector, with responses from nearly all pension funds, stockbrokers, and commercial banks, and while assumptions on exchange rate dynamics have been widely researched in the literature, to our knowledge there is no study applied to the Colombian case. Consequently, we shed light on the validity of several economic assumptions that relate to the nature of exchange rate behavior, using detailed and real-time data on traders, analysts, and market makers.
Our main findings indicate that episodes of exchange rate appreciation preceded expectations of further appreciation in the short run, but were marked by depreciations in the long run. In the related literature, this pattern has been referred to as an expectational twist and partially explains the stabilizing nature of expectations. For example, as explained in Jongen et al. (2008), market participants might be reacting to momentum models in the short run (i.e., chartists), while making use of equilibrium models supported by macroeconomic fundamentals in the long run (i.e., fundamentalists). Additionally, we find that the forward discount differed from future exchange rate changes due to a significant time-varying risk premium, and that both the unbiasedness and orthogonality conditions are rejected for all horizons considered. In line with most of the existing literature, these results constitute ample evidence against the efficient market hypothesis (EMH).
Finally, we set forth five competing strategies to assess how well actual expectations performed, relative to a random walk process. We find that 1-month expectations outperform a random walk process as well as models of extrapolative, adaptive, and regressive expectations. But results are almost the opposite for 1-year forecasts, where expectations do not outperform a random walk. In this last case, traders and analysts answering the survey could have improved their forecasts by incorporating information from the forward discount, past exchange rate changes, policy meetings, or the policy rate.
This paper is organized as follows. Sect. 2 describes the data and investigates the incidence and potential attrition bias due to the number of non-responses within our unbalanced panel. Section 3 reviews the accuracy of forecasts and the relative importance of rational expectations within the purview of the forward premium puzzle. Section 4 presents different models of how expectations are formed and determines their stabilizing or destabilizing nature. This section also compares agents’ forecasting accuracy with that of a random walk. Finally, Sect. 5 concludes.
2 Data
2.1 Survey data
Survey data have been widely used in the international finance literature. Examples include interest rate surveys to test for term premia as well as surveys containing stock market rates, GNP deflators, and money aggregates.^{6} Additionally, survey data on exchange rates have been widely used to test for rationality and the presence of a risk premium without having to depend on forward rates or ex-post values of exchange rates.
There are, however, obvious drawbacks of using survey data. For one, there is no guarantee that agents will disclose their true beliefs. As mentioned by Frankel and Froot (1987), “It is a cornerstone of positive economics that we learn more by observing what people do in the marketplace than what they say”.^{7} In addition, the timing of the forecast report might not coincide with the closing of the exchange rate market, which might give some agents additional hours of information in their predictions. Finally, there can be wide dispersion in the answers provided by market participants. Nevertheless, exchange rate surveys can be less problematic than other surveys (i.e., GDP, prices, etc.) since investors or analysts responding to the survey are actively involved in foreign exchange trading. They at least represent a clear improvement on the conventional methodology of assuming ex-post exchange rates as a proxy for exchange rate expectations.
Overall, between, and within variation of selected variables
Variable | Mean | St. dev | Min | Max | Observations | |
---|---|---|---|---|---|---|
1-Month forecasts | Overall | 2140 | 319 | 1600 | 2982 | N = 4100 |
Between | 267 | 1756 | 2878 | n = 90 | ||
Within | 274 | 1593 | 3047 | T = 45.6 | ||
1-Year forecasts | Overall | 2255 | 389 | 1150 | 3425 | N = 3478 |
Between | 318 | 1761 | 3063 | n = 90 | ||
Within | 329 | 1144 | 3398 | T = 38.6 | ||
Attrition dummy | Overall | 0.57 | 0.49 | 0 | 1 | N = 9630 |
Between | 0.30 | 0.02 | 0.98 | n = 90 | ||
Within | 0.39 | −0.41 | 1.56 | T = 107 | ||
1-Month forecast errors | Overall | −0.27 % | 3.71 % | −17.1 % | 16.8 % | N = 4063 |
Between | 0.86 % | −3.05 % | 1.64 % | n = 90 | ||
Within | 3.67 % | −16.1 % | 17.4 % | T = 45.1 | ||
1-Year forecast errors | Overall | 9.06 % | 12.6 % | −79.9 % | 42.3 % | N = 3090 |
Between | 6.27 % | −15.4 % | 25.3 % | n = 89 | ||
Within | 12.0 % | −80.4 % | 41.1 % | T = 34.7 |
2.2 Non-response incidence and potential attrition bias
Sample attrition can lead to biased estimates when conducting causal inference, especially when observations are not missing at random (RAM). However, when non-responses are assumed to be MAR, the attrition bias disappears albeit with an effective reduction in sample size.
Patterns of non-response
Non-responses (% of time) | Number of institutions |
---|---|
0–10 | 8 |
10–20 | 8 |
20–30 | 3 |
30–40 | 8 |
40–50 | 9 |
50–60 | 5 |
60–70 | 11 |
70–80 | 10 |
80–90 | 13 |
90–100 | 15 |
Consequently, to test for attrition bias we first estimate a probit regression model (Eq. (2)), and test whether institution-specific variables such as past expected depreciation (surveyed answers from the previous month) or the financial type (bank, stockbroker or pension fund) had a significant effect on attrition. We also consider common variables (across entities) such as past exchange rate depreciation, episodes of capital controls, the forward discount, and the emerging market bond index (EMBI).^{10} Finally, we include the central bank’s policy rate, board meetings, and exchange rate equilibrium forecasts.
Attrition probit regression
Source: authors’ calculations
Variable | |
---|---|
Past expected depreciation \(E_t[\Delta S_{i,t-k}]\), k = 1 month | −0.61 (2.228) |
Past expected depreciation \(E_t[\Delta S_{i,t-k}]\), k = 1 year | −0.14 (0.930) |
Financial type: banks, stock brokers, pension funds | 0.04 (0.085) |
Episode of capital controls (\(D_{2007{-}2008}\)) | −0.05 (0.248) |
Central bank’s policy rate | 0.015 (0.049) |
Board meeting dates | −0.06 (0.111) |
Forward discount (\(F_{t}^{t+k}-S_{t}\)) | −4.81 (6.136) |
Exchange rate equilibrium forecast | 0.41 (1.457) |
Emerging market bond index (Embi) | −0.00 (0.001) |
Accuracy of 1-month and 1-year forecasts
Institution | Median | Direction \(\Delta S_{i,t+k}\) | \(+/-\) 50 pesos | Direction \(\Delta S_{i,t+k}\) | \(+/-\) 50 pesos |
---|---|---|---|---|---|
k = 1 month (%) | k = 1 month (%) | k = 1 year (%) | k = 1 year (%) | ||
Commercial banks | 15 | 66 | 64 | 35 | 9 |
Stock brokers | 19 | 65 | 61 | 43 | 15 |
Pension funds | 5 | 65 | 66 | 49 | 20 |
Individual components of the 1-month forward discount (Eq. 3)
Year | Forward discount \(F_{t}^{t+k}-S_{t}\) | Future depreciation \(\Delta S_{t+k}\) | Forecast error \(E_{t}[S_{i,t+k}]-S_{t+k}\) | Risk premium \(rp_t\) | Expected depreciation \(E_t[\Delta S_{i,t+k}]\) |
---|---|---|---|---|---|
2003 (Oct–Dec) | 0.2 | −1.3 | 0.7 | 0.8 | −0.6 |
2004 | 0.4 | −1.2 | 1.2 | 0.4 | 0.0 |
2005 | 0.0 | −0.4 | 0.4 | 0.0 | 0.0 |
2006 | −0.3 | −0.2 | −0.3 | 0.2 | −0.5 |
2007 | 0.1 | −0.9 | 0.5 | 0.5 | −0.4 |
2008 | 0.1 | 0.9 | −2.0 | 1.2 | −1.1 |
2009 | −0.2 | −0.8 | −0.6 | 1.2 | −1.4 |
2010 | −0.4 | −0.5 | −0.2 | 0.4 | −0.8 |
2011 | −0.1 | 0.1 | −0.8 | 0.6 | −0.7 |
2012 (Jan–Aug) | −0.1 | −1.2 | 0.2 | 0.8 | −0.9 |
Average | 0.0 | −0.5 | −0.1 | 0.6 | −0.6 |
3 Forecasts, forwards and the risk premium
4 Stabilizing–destabilizing expectations
Contrary to this strand of literature, Friedman (1953) advocacy for floating exchange rates was based on the stabilizing effect of expectations, that is, if current or past appreciations of domestic currency induce agents to expect future depreciations, then they will seek to sell domestic currency, and hence, mitigate much of the current appreciation.“[Speculative] anticipations are apt to bring about their own realization. Anticipatory purchases of foreign exchange tend to produce or at any rate to hasten the anticipated fall in the exchange value of the national currency, and the actual fall may set up or strengthen expectations of a further fall ... Exchange rates under such circumstances are bound to become highly unstable, and the influence of psychological factors may at times be overwhelming”
In sum, extrapolative expectations involve forecasting with past movements of the exchange rate (past variations are used to forecast the next period’s variation). Under adaptive expectations, investors use current forecast errors to predict future exchange rates. Intuitively, if an agent expects the exchange rate to be higher than what is observed ex-post, then she will “correct” her new forecast by lessening her expectation of the next period’s exchange rate change (expectations adapt to new changes given past mistakes). Finally, regressive expectations incorporate deviations of the exchange rate with respect to a long-run equilibrium value. This process assumes that the exchange rate “regresses” (at speed \(\beta _{reg}\)) towards a long-run value which can take the form of a constant, moving average, or purchasing power parity, among others [see Dornbusch (1976)].
The processes described in Eqs. (10–12) are stabilizing when agents believe that a large appreciation (depreciation) in the past will be followed by a smaller depreciation (appreciation) in the future. In other words, when the coefficients of \(\beta _\mathrm{{ex}}\), \(\beta _\mathrm{{ad}}\), and \(\beta _\mathrm{{reg}}\) are negative and less than unity (in absolute terms). The alternative hypothesis of static expectations (i.e., random walk) will occur when coefficients are zero. In the literature, Frankel and Froot (1990a) and Cavaglia et al. (1993) find positive values for \(\beta _\mathrm{{ex}}\), \(\beta _\mathrm{{ad}}\), and \(\beta _\mathrm{{reg}}\) when considering 1-month horizons, suggesting that short run expectations carry bandwagon or destabilizing effects. However, for horizons longer or equal than 3 months, the authors find stabilizing effects.
(De)-stabilizing expectations
Type of expectation | k = 1 Month | k = 1 Year |
---|---|---|
Extrapolative \(E_{t}[\Delta S_{i,t+k}]=\beta _{0}+\beta _{1}\Delta S_{t} + \epsilon _{it}\) | \(\beta _{1}=\) −0.03** (0.013) | \(\beta _{1}=\) −0.13*** (0.015) |
Adaptive \(E_{t}[\Delta S_{i,t+k}]=\alpha _{0}+\alpha _{1}(S_{t}-E_{t-k}[S_{it}])+\nu _{it}\) | \(\alpha _{1}=\) −0.05*** (0.016) | \(\alpha _{1}=\) −0.15*** (0.017) |
Regressive \(E_{t}[\Delta S_{i,t+k}]=\gamma _{0}+\gamma _{1}(S_{t}-\bar{S_{t}})+\eta _{it}\) | \(\gamma _{1}=\) −0.05*** (0.005) | \(\gamma _{1}=\) 0.11*** (0.029) |
4.1 The random walk benchmark
There is an ample literature on the unpredictability of exchange rates, in which studies often compare the accuracy of linear models with a benchmark random walk process. Most of these studies have generally followed the methodology presented in the seminal work of Meese and Rogoff (1983) but some earlier works include those of Nelson (1972), Christ (1975), Litterman (1979) and Fair (1979).
To date, most studies have failed to reject the null hypothesis that exchange rates are unpredictable. However, some exceptions are found in the literature. Evans and Lyons (2005), for example, use order flows as a successful determinant of future exchange rates. Cheung et al. (2005) find that models that incorporate productivity differentials outperform the random walk benchmark for some periods and currencies. Gourinchas and Rey (2005) are also able to outperform a random walk with a model that uses the trade balance and the valuation of net foreign assets.^{18}
When conducting inference for nested models, it is important to control for an existing upward shift of the predicted sample errors. We account for this by following the methodology in the study by Clark and West (2006), that is, we construct MSPE-adjusted statistics in which, under the null hypothesis that models follow a martingale difference, the sample MSPE can be equal to that of the null.^{19} We thus proceed as follows: first we define our in-sample period to be from Oct 2003 to May 2005. We then estimate the corresponding models and make 1-period out of sample forecasts before rolling over the sample by one period. Finally, we construct MSPE-adjusted statistic for each model.
Out-of-sample forecasts: competing models vs. random walk
Model | 1-Month \(\left( \mathrm{MSPE}_{r}-\mathrm{MSPE}_{u}\right)\) | 1-Year \(\left( \mathrm{MSPE}_{r}-\mathrm{MSPE}_{u}\right)\) |
---|---|---|
Extrapolative | −0.0006 (0.001) | 0.18*** (0.042) |
Adaptive | −0.0004 (0.001) | 0.20*** (0.045) |
Regressive | 0.003*** (0.001) | 0.09*** (0.030) |
Forward discount | 0.003** (0.002) | 0.03** (0.016) |
Surveyed expectations | ||
All participants | 0.009*** (0.002) | 0.01 (0.013) |
Commercial banks | 0.009*** (0.002) | 0.01 (0.015) |
Stockbrokers | 0.009*** (0.002) | 0.01 (0.012) |
Pension funds | 0.009*** (0.003) | 0.00 (0.018) |
Results for 1-month forecasts show that expectations stated in the survey outperform the three models of extrapolative, adaptive or regressive expectations, and also the forward discount. In fact, they outperform the random walk, with positive and significant numbers for \((\mathrm{MSPE}_{r} - \mathrm{MSPE}_{u})\). But results are almost the opposite for 1-year forecasts in which the statistic \((\mathrm{MSPE}_{r} - \mathrm{MSPE}_{u})\) is not significant for agent’s forecasts (rows 6–9), but is significant for the case of extrapolative, adaptive, and regressive expectations, and even the forward discount. In sum, this exercise suggests that agents do exceptionally well in forecasting 1-month horizons but should reconsider their 1-year forecasts, that is, by following models presented in rows 1–4, agents can improve their forecasting accuracy.
We note that the employed loss function (MSPE) is explicitly symmetric. In other words, forecasts suffer the same loss independent of the sign of the error. To shed some light on this issue, we considered negative and positive forecast errors separately. Results are shown in Table 13 of Appendix A and show similar results, except for the case of regressive expectations (1-month forecasts are no longer significant) and the forward discount (1-year forecasts are no longer significant).
5 Conclusion
Exchange rate expectations play a key role in determining economic variables and, according to some authors like Woodford and Walsh (2005), “little else matter”. However, there is wide disagreement on the behavior of exchange rate expectations, with various implications for economic policy.
Following the practice pioneered by Dominguez (1986), Frankel (1979), and Frankel and Froot (1987), in this paper we use the largest exchange rate survey in Colombia to test for the rational expectations hypothesis, the presence of a time-varying risk premium and the accuracy of exchange rate forecasts. Our main findings indicate that episodes of exchange rate appreciation preceded expectations of further appreciation in the short run, but were marked by depreciations in the long run. Additionally, we find that the forward discount differed from future exchange rate changes due to the rejection of the unbiasedness condition and to the presence of a time-varying risk premium.
Finally, we set forth five competing strategies to assess how well actual expectations performed relative to a random walk process. We find that 1-month expectations outperform models of extrapolative, adaptive or regressive expectations and even a random walk process (with lower mean squared prediction errors). But results are almost the opposite for 1-year forecasts, where expectations do not outperform a random walk. In this last case, traders and analysts answering the survey could have improved their forecasts by incorporating information from the forward discount, past exchange rate changes, policy meetings, or the policy rate.
Ito (1990) uses biweekly panel data collected by the Japan Center for International Finance. It includes 44 financial institutions. Allen and Taylor (1990) use data from the foreign exchange market in London.
Our sample period coincides with an inflation-targeting regime adopted by the Central Bank of Colombia in 1999 after the strongest crisis of its history. Prior to this date, pre-announced exchange rate bands were established, dating back to 1994. Access to aggregate data can be obtained in the central bank’s website: http://www.banrep.gov.co.
Additional tests such as the BGLW test, found in Becketti et al. (1985), have a similar structure but assume that attritioners exit the survey “once and for all”. This assumption does not apply to our case since, as shown in Table 2, respondents exit and enter the survey multiple times.
Capital controls on inflows were enacted between May 7, 2007 and October 8, 2008 and consisted of compulsory unremunerated reserve requirements. Namely, market participants were required to deposit 40 % of inflows at the central bank during a period of 6 months without interest payments [see Echavarría et al. (2013)].
Note that \(\sigma _{12}\) corresponds to the covariance between \(\epsilon _{1it}\) and \(\epsilon _{2it}\). In addition, \(\lambda (\cdot )= \frac{\phi (\cdot )}{\Phi (\cdot )}\), where \(\phi\) and \(\Phi\) denote the pdf and cdf of a standard normal distribution, respectively.
Expectations differed from the observed 1-month and 1-year ahead rate in up to 206 pesos/dollar (September 2007) and in up to 615 pesos/dollar (June 2007), respectively.
Some of the earliest empirical findings that reject the unbiasedness of forward rates (as predictors of future spot exchange rates) include those of Levich (1979), Hansen and Hodrick (1980), Bilson (1980), Hsieh (1983), Hansen and Hodrick (1983), and Hodrick and Srivastava (1986).
Some authors, like Kaminsky and Peruga (1990) and Baillie et al. (1996), include an unobservable risk premium in their models to account for differences in statistical properties when regressing return spreads on exchange rate changes.
Seemingly Unrelated Regressions (SUR) were also considered (not reported) to allow for cross-equation contemporaneous correlations, yielding very similar results.
Two of these models are based on the Purchasing Power Parity (PPP) condition, 2 are based on Vector Error Correction (VEC) methodologies and one model uses a Hodrick and Prescott filter.
Notes
Declarations
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Authors’ Affiliations
References
- Allen H, Taylor MP (1990) Charts, noise and fundamentals in the London foreign exchange market. Econ J 100:49–59View ArticleGoogle Scholar
- Ashley, R., C. W. Granger, and R. Schmalensee (1980) Advertising and aggregate consumption: an analysis of causality. Econometrica: Journal of the Econometric Society, 1149–1167Google Scholar
- Baillie RT, Bollerslev T, Mikkelsen HO (1996) Fractionally integrated generalized autoregressive conditional heteroskedasticity. J Econom 74:3–30View ArticleGoogle Scholar
- Becketti, S., W. Gould, L. Lillard, and F. Welch (1985) The panel study of income dynamics after fourteen years: an evaluation, UCLA Economics Working Papers 361, UCLA Department of EconomicsGoogle Scholar
- Bekaert G (1996) The time variation of risk and return in foreign exchange markets: a general equilibrium perspective. Rev Financ Stud 9:427–470View ArticleGoogle Scholar
- Benassy-Quere A, Larribeau S, MacDonald R (2003) Models of exchange rate expectations: how much heterogeneity? J Int Financ Markets Inst Money 13:113–136View ArticleGoogle Scholar
- Bilson, JFO (1980) The speculative efficiency hypothesis, NBER Working Papers 0474, National Bureau of Economic Research, IncGoogle Scholar
- Carlson JA (1998) Risk aversion, foreign exchange speculation and gamblers ruin. Economica 65:441–453View ArticleGoogle Scholar
- Cavaglia S, Verschoor WF, Wolff CC (1993) Further evidence on exchange rate expectations. J Int Money Finance 12:78–98View ArticleGoogle Scholar
- Cheng TC, Trivedi PK (2015) Attrition bias in panel data: a sheep in wolf’s clothing? A case study based on the mabel survey. Health Econ 24:1101–1117View ArticleGoogle Scholar
- Cheung Y-W, Chinn MD, Pascual AG (2005) Empirical exchange rate models of the nineties: are any fit to survive? J Int Money Finance 24:1150–1175View ArticleGoogle Scholar
- Chinn M (2007) Interest rate parity 4. Entry Written for Princeton Encyclopedia of the World EconomyGoogle Scholar
- Christ CF (1975) Judging the performance of econometric models of the US economy. Int Econ Rev 54–74Google Scholar
- Christiano LJ (1989) Not the inflation forecaster’s Holy Grail, Federal Reserve Bank of Minneapolis. Quarterly Review-Federal Reserve Bank of Minneapolis 13:3Google Scholar
- Clark TE, West KD (2006) Using out-of-sample mean squared prediction errors to test the martingale difference hypothesis. J Econom 135:155–186View ArticleGoogle Scholar
- Crowder WJ (1994) Foreign exchange market efficiency and common stochastic trends. J Int Money Finance 13:551–564View ArticleGoogle Scholar
- De Grauwe P, Grimaldi M (2006) The exchange rate in a behavioral finance framework. Princeton University Press, PrincetonGoogle Scholar
- De Grauwe P, Markiewicz A (2013) Learning to forecast the exchange rate: two competing approaches. J Int Money Finance 32:42–76View ArticleGoogle Scholar
- Diebold FX, Mariano RS (1995) Comparing predictive accuracy. J Bus Econ Stat 13:253–263Google Scholar
- Dominguez K (1986) Are foreign exchange forecasts rational? New evidence from survey data. Econ Lett 21:277–281View ArticleGoogle Scholar
- Dominguez KM, Frankel JA (1993) Does Foreign-exchange intervention matter? The portfolio effect. Am Econ Rev 83:1356–1369Google Scholar
- Dornbusch R (1976) Expectations and exchange rate dynamics. J Polit Econ 84:1161–1176View ArticleGoogle Scholar
- Echavarría, JJ, Melo LF, Téllez S, Villamizar M (2013) The impact of pre-announced day-to-day interventions on the Colombian exchange rate, BIS Working Papers 428, Bank for International SettlementsGoogle Scholar
- Echavarría JJ, Vásquez D, Villamizar M (2008) Expectativas, tasa de interés y tasa de cambio: paridad cubierta y no cubierta en Colombia, 2000–2007. Ensayos Sobre Política Económica 26:149–203Google Scholar
- Engel C (1996) The forward discount anomaly and the risk premium: A survey of recent evidence. J Empir Finance 3:123–192View ArticleGoogle Scholar
- Evans MD, Lyons RK (2005) Meese-rogoff redux: micro-based exchange rate forecasting. Tech. rep, National Bureau of Economic ResearchGoogle Scholar
- Fair RC (1979) An analysis of the accuracy of four macroeconometric models. The Journal of Political Economy, 701–718Google Scholar
- Fama EF (1984) Forward and spot exchange rates. J Monet Econ 14:319–338View ArticleGoogle Scholar
- Fama EF, French KR (1988) Permanent and temporary components of stock prices. J Polit Econ 96:246–273View ArticleGoogle Scholar
- Fitzgerald J, Gottschalk P, Moffitt R (1998) An analysis of sample attrition in panel data: the michigan panel study of income dynamics. J Hum Res 33:251–299View ArticleGoogle Scholar
- Frankel JA (1979) On the mark: a theory of floating exchange rates based on real interest differentials. Am Econ Rev 69:610–622Google Scholar
- Frankel JA, Froot KA (1986) Understanding the US dollar in the eighties: the expectations of chartists and fundamentalists. Econ Rec 62:24–38Google Scholar
- Frankel JA, Froot KA (1987) Using survey data to test standard propositions regarding exchange rate expectations. Am Econ Rev 77:133–153Google Scholar
- Frankel JA, Froot KA (1989) Forward discount bias: Is it an exchange risk premium? The Quarterly Journal of Economics, 139–161Google Scholar
- Frankel JA, Froot KA (1990a) Chartists, fundamentalists, and trading in the foreign exchange market. American Economic Review, American Economic Association. 80:181–85Google Scholar
- Frankel JA, Froot KA (1990b) Exchange rate forecasting techniques, survey data, and implications for the foreign exchange market. Working Paper 3470, National Bureau of Economic ResearchGoogle Scholar
- Frankel JA, Rose AK (1994) A survey of empirical research on nominal exchange rates. Working Paper 4865, National Bureau of Economic ResearchGoogle Scholar
- Frenkel JA (1976) A monetary approach to the exchange rate: doctrinal aspects and empirical evidence. Scand J Econ 78:200–224View ArticleGoogle Scholar
- Friedman M (1953) The case for flexible exchange rates. Essays Posit Econ 1:413–437Google Scholar
- Garbers H (1987) A misspecification analysis of the relationship between spot and forward exchange rates. Eur Econ Rev 31:1407–1417View ArticleGoogle Scholar
- Gourinchas PO, Rey H (2005) International financial adjustment, NBER Working Papers 11155, National Bureau of Economic Research, IncGoogle Scholar
- Granger CWJ, Newbold P (1977) Forecasting economic time series. Academic Press, New YorkGoogle Scholar
- Hansen LP, Hodrick RJ (1980) Forward exchange rates as optimal predictors of future spot rates: an econometric analysis. J Polit Econ 88:829–853View ArticleGoogle Scholar
- Hansen LP, Hodrick RJ (1983) Risk averse speculation in the forward foreign exchange market: an econometric analysis of linear models. In: Exchange rates and international macroeconomics, University of Chicago Press, pp 113–152Google Scholar
- Heckman JJ (1979) Sample selection bias as a specification error. Econometrica 47:153–161View ArticleGoogle Scholar
- Hodrick RJ (1987) The empirical evidence on the efficiency of forward and futures foreign exchange markets, vol. 1, 1 ed, Harwood Academic Publishers GmbHGoogle Scholar
- Hodrick RJ, Srivastava S (1984) An investigation of risk and return in forward foreign exchange. J Int Money Finance 3:5–29View ArticleGoogle Scholar
- Hodrick RJ, Srivastava S (1986) The covariation of risk premiums and expected future spot exchange rates. J Int Money Finance 5:S5–S21View ArticleGoogle Scholar
- Hsieh DA (1983) Tests of rational expectations and no risk premium in forward exchange market. J Int Econ 17:173–184View ArticleGoogle Scholar
- Ito T (1990) Foreign exchange rate expectations: micro survey data. Am Econ Rev 80:434–449Google Scholar
- Jongen R, Verschoor WF, Wolff CC (2008) Foreign exchange rate expectations: survey and synthesis. J Econ Surv 22:140–165View ArticleGoogle Scholar
- Kaminsky G, Peruga R (1990) Can a time-varying risk premium explain excess returns in the forward market for foreign exchange? J Int Econ 28:47–70View ArticleGoogle Scholar
- Keim DB, Stambaugh RF (1986) Predicting returns in the stock and bond markets. J Financ Econ 17:357–390View ArticleGoogle Scholar
- Levich RM (1979) On the efficiency of markets for foreign exchange. vol. 1, Johns Hopkins University Press, 1 edGoogle Scholar
- Lewis KK (1995) Puzzles in international financial markets. In: Handbook of International Economics. ed. by G. M. Grossman and K. Rogoff, Elsevier, vol. 3 of Handbook of International Economics, chap. 37, pp 1913–1971Google Scholar
- Litterman RB (1979) Techniques of forecasting using vector autoregressions. Working Paper 115, Federal Reserve Bank of MinneapolisGoogle Scholar
- Lo AW, MacKinlay AC (1987) Stock market prices do not follow random walks: evidence from a simple specification test. NBER Working Papers 2168, National Bureau of Economic Research, IncGoogle Scholar
- MacDonald R, Taylor MP (1992) Exchange rate economics: a survey. Staff Papers-International Monetary Fund, pp 1–57Google Scholar
- MacDonald R, Torrance TS (1990) Expectations formation and risk in four foreign exchange markets. Oxford Economic Papers, pp 544–561Google Scholar
- Mark NC, Wu Y (1998) Rethinking deviations from uncovered interest parity: the role of covariance risk and noise. Economic Journal, 1686–1706Google Scholar
- Maynard A, Phillips PC (2001) Rethinking an old empirical puzzle: econometric evidence on the forward discount anomaly. J Appl Econom 16:671–708View ArticleGoogle Scholar
- McCallum BT (1994) A reconsideration of the uncovered interest parity relationship. J Monet Econ 33:105–132View ArticleGoogle Scholar
- Meese RA, Rogoff K (1983) Empirical exchange rate models of the seventies : Do they fit out of sample? Journal of International Economics, Elsevier, 14, pp 3–24Google Scholar
- Meese RA, Rogoff K (1988) Was it real? the exchange rate-interest differential relation over the modern floating-rate period. J Finance 43:933–948View ArticleGoogle Scholar
- Meredith G, Ma Y (2002) The forward premium puzzle revisited. IMF Working Papers 02/28, International Monetary FundGoogle Scholar
- Mussa ML (1979) The theory of exchange rate determination. In: Exchange rate theory and practice, University of Chicago Press, pp 13–78Google Scholar
- Nelson CR (1972) The prediction performance of the FRB-MIT-PENN model of the US economy. The American Economic Review, pp 902–917Google Scholar
- Nurkse R (1944) International currency experience: lessons of the interwar period, 4, League of NationsGoogle Scholar
- Rogoff K (2009) Exchange rates in the modern floating era: what do we really know? Rev World Econ 145:1–12View ArticleGoogle Scholar
- Takagi S (1991) Exchange rate expectations: a survey of survey studies. IMF Staff Papers 38:156–183View ArticleGoogle Scholar
- Villa M (2011) Expectativas y Estabilidad Cambiaria. Son Desestabilizadores los Especuladores en Colombia? Tech. rep., mimeoGoogle Scholar
- Villamizar-Villegas M (2015) Identifying the Effects of Simultaneous Monetary Policy Shocks. Contemporary Economic Policy. doi:10.1111/coep.12111
- Villamizar-Villegas M, Perez-Reyna D (2015) A Theoretical Approach to Sterilized Foreign Exchange Intervention. Journal of Economic Surveys. doi:10.1111/joes.12136
- Wakita S (1989) Are survey forecasts trusted? Econ Lett 29:339–344View ArticleGoogle Scholar
- West KD, Edison HJ, Cho D (1993) A utility-based comparison of some models of exchange rate volatility. J Int Econ 35:23–45View ArticleGoogle Scholar
- Woodford M, Walsh CE (2005) Interest and prices: foundations of a theory of monetary policy. Macroecon Dyn 9:462–468View ArticleGoogle Scholar