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 hypothesisJEL 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
3.1 How accurate are agents’ forecasts?
It appears as an empirical regularity in the literature that the expected exchange rate does not equal the observed future rate, often missing the direction of change. For example, Wakita (1989) and Ito (1990) find industry-specific bias in expectations. In addition, Mussa (1979) and Frankel and Froot (1987) find constant under-predictions of exchange rate forecasts. Lewis (1995) finds evidence of systematic forecast errors.
This pattern is similar to the one found in Takagi (1991), for the yen–dollar exchange rate during 1985–1986. However, Fig. 2 shows that circumstances changed in 2011 and 2012 when the financial sector expected that the 1-year ahead exchange rate would remain constant or even appreciate. Figure 2 also exhibits some degree of short-term under-prediction for the 1-month ahead exchange rate, in the sense that expected appreciations were lesser in magnitude than observed appreciations (and vice versa for depreciations). Finally, the figure suggests that forecasts followed a similar pattern during the period in which Colombia enacted capital controls (May 2007–October 2008).
The information contained in Figs. 4 and 5 is further sub-categorized in Table 6, by type of financial institution. As noted, 1-month ahead forecasts (columns 3 and 4) are similar across banks, stockbrokers and pension funds. This is not the case for the 1-year ahead forecasts (columns 5 and 6), where pension funds show a better forecasting accuracy.
3.2 The forward discount and the risk premium
Forward exchange rates have been widely used in the literature, not only to test for the covered interest rate parity, but also to test for the effectiveness of sterilized foreign exchange intervention or the existence (or absence) of a risk premium. For the case of Colombia, Echavarría et al. (2008) show that the covered interest rate parity condition holds (on average) for all horizons considered, a result that is consistent with most of the international literature.
Most of the literature has found that the forward discount is not equal (on average) to the observed exchange rate change. For example, Fama (1984) and Hodrick and Srivastava (1984) assume that expectations are rational and give prominence to a risk premium in their explanation. The authors argue that the variance of the risk premium is greater than the variance of the expected depreciation. Similarly, Dominguez and Frankel (1993) show that, for imperfect substitutes, an increase in the amount of an asset results in either an increase in the expected return or an increase in the risk premium.^{13}
Intuitively, the risk premium shown in Eq. (7) can be thought of as the difference between a risk-free investment (in this case hedged by the forward rate) and a risky investment subject to unexpected exchange rate changes. Thus, in the case of risk-neutral agents, the market forward rate would equal the return’s expected value, eliminating the risk premium. If agents are risk averse, the risk premium would take on positive values to compensate for the increased uncertainty of the risky asset.
Similarly, Tables 7 and 8 report the individual components of Eq. (7) for both 1-month and 1-year ahead forecasts. Table 7 shows that the difference between the forward discount and the observed exchange rate change is relatively small for 1-month forecasts (with an average value of 0.5 % and a maximum of 1.6 % in 2004). Alternatively, Table 8 shows that this difference is large for 1-year forecasts (with an average of 8.7 % and a maximum value of 19.4 % in 2003). It also shows that 1-year forecast errors are large (average of 8.4 % and a maximum value of 19.9 % in 2004).
Individual components of the 1-year 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) | 7.8 | −11.6 | 17.4 | 2.0 | 5.8 |
2004 | 6.3 | −12.8 | 19.9 | −0.8 | 7.1 |
2005 | 3.2 | 1.6 | 5.0 | −3.5 | 6.6 |
2006 | 1.2 | −12.6 | 15.2 | −1.4 | 2.7 |
2007 | 3.2 | −6.2 | 12.2 | −2.9 | 6.1 |
2008 | 5.5 | 10.9 | −5.7 | 0.3 | 5.1 |
2009 | 4.7 | −13.4 | 16.5 | 1.7 | 3.0 |
2010 | 2.0 | −3.3 | 4.8 | 0.5 | 1.5 |
2011 | 1.1 | 0.0 | −0.5 | 3.0 | −1.9 |
2012 (Jan–Aug) | 3.2 | 0.0 | −0.7 | 3.9 | −0.7 |
Average | 3.8 | −4.9 | 8.4 | 0.3 | 3.5 |
Risk premium: \(E_{t}[\Delta S_{i,t+k}]=\beta _{0}+\beta _{1}(F_{t}^{t+k}-S_{t})+\beta _{2}\lambda (\frac{x'_{it}\beta }{\sigma })+\sum _{j}{\gamma _jD_\mathrm{{year}}}+\alpha _i+\epsilon _{it}\)
Coefficient/test | k = 1 month | k = 1 year | ||
---|---|---|---|---|
First differences | Fixed effects | First differences | Fixed effects | |
\(\beta _{0}\) | 0.00 (0.003) | −0.01*** (0.001) | −0.00 (0.003) | 0.03*** (0.005) |
\(\beta _{1}\) | 0.95*** (0.047) | 1.07***(0.041) | 0.39*** (0.035) | 0.46*** (0.034) |
\(\beta _{2}\) | 0.00 (0.003) | 0.00 (0.002) | 0.00 (0.005) | 0.00 (0.005) |
\(t: \beta _{1}=1\) | 1.30 (0.257) | 2.96* (0.089) | 294*** (0.000) | 251*** (0.000) |
\(Wald: \beta _{0}=0 \, \beta _{1}=1\) | 1.14 (0.324) | 36.9*** (0.000) | 150*** (0.000) | 126*** (0.000) |
Observations | 3611 | 4100 | 2869 | 3443 |
3.3 The risk premium and the rational expectations hypothesis
The use of forward rates to predict future spot exchange rates is based on the EMH, which precludes high above-normal profits through arbitrage in the forward market. This in turn encompasses the following joint hypothesis: (1) that expectations are formed rationally, and (2) that market participants are risk neutral. In sum, the efficient market hypothesis can fail as a result of non-rational expectations, or the existence of a time-varying risk premium, or both [see Hodrick (1987) and Engel (1996)].
Frenkel (1976) was one of the pioneers to test for the unbiasedness of forward rates as predictors of future exchange rates (both variables measured in levels). However, the non-stationarity properties of these variables presented a potential spurious regression problem, which was later addressed by Garbers (1987), Crowder (1994), Baillie et al. (1996), and Maynard and Phillips (2001).^{14}
Table 4 presents the estimated coefficients, a t test for the null hypothesis \(H_{0}:\beta _{1}=1\), and a Wald test for the joint hypothesis \(\beta _{0}=0\) and \(\beta _{1}=1\). Results are reported using both First Differences and Fixed Effects with clustered standard errors (reported in parenthesis). The Hausman test, conducted for all regressions, rejects the null hypothesis in which the unobserved time-invariant component \((\alpha _i)\) is uncorrelated with the model’s covariates.
Results are similar for all specifications considered. The null \(H_{0}:\beta _{1}=1\) and \(H_{0}:\beta _{0}=0 \cap \beta _{1}=1\) are rejected for all horizons except for 1-month forecasts using first differences. These results are somewhat different to those found by Frankel and Froot (1989) who reject the null for 1-month forecasts, but do not reject the null for 3-month, 6-month and 1-year horizons.^{16}
In addition to the presence of a risk premium, it is of interest to test for rational expectations so as to validate (or not) the use of ex-post exchange rates as proxies of exchange rate expectations. Recall that to determine if expectations are rational they must: (1) be unbiased predictors of the ex-post future exchange rate (unbiasedness), and (2) contain all useful information available at the time when they are formed (orthogonality). Although the first result alone would be sufficient to reject rational expectations, we also test for the orthogonally condition to shed additional light on whether expectations capture the impact of news and some selected fundamentals.
Unbiasedness: \(E_{t}[\Delta S_{i,t+k}]=\beta _{0}+\beta _{1}\Delta S_{t+k}+\beta _{2}\lambda (\frac{x'_{it}\beta }{\sigma })+\sum _{j}{\gamma _jD_{year}}+\alpha _i+\epsilon _{it}\)
Coefficient/test | k = 1 Month | k = 1 Year | ||
---|---|---|---|---|
First differences | Fixed effects | First differences | Fixed effects | |
\(\beta _{0}\) | 0.00 (0.001) | −0.00*** (0.001) | −0.00 (0.003) | 0.07*** (0.005) |
\(\beta _{1}\) | 0.30*** (0.011) | 0.27*** (0.011) | 0.26*** (0.022) | 0.12*** (0.018) |
\(\beta _{2}\) | 0.00 (0.003) | 0.00 (0.002) | 0.00 (0.005) | 0.00 (0.005) |
\(t: \beta _{1}=1\) | 3703*** (0.000) | 4750*** (0.000) | 1118*** (0.000) | 2509*** (0.000) |
\(Wald: \beta _{0}=0 \, \beta _{1}=1\) | 1857*** (0.000) | 2786*** (0.000) | 564*** (0.000) | 2053*** (0.000) |
Observations | 3611 | 4100 | 2869 | 3443 |
Unbiasedness (2): \(\Delta S_{t+k}=\beta _{0}+\beta _{1}E_{t}[\Delta S_{i,t+k}]+\beta _{2}\lambda (\frac{x'_{it}\beta }{\sigma })+\sum _{j}{\gamma _jD_{year}}+\epsilon _{t}\)
Coefficient/test | k = 1 month | k = 1 year | ||
---|---|---|---|---|
First differences | Fixed effects | First differences | Fixed effects | |
\(\beta _{0}\) | 0.01*** (0.001) | −0.01*** (0.001) | −0.01*** (0.001) | −0.14*** (0.004) |
\(\beta _{1}\) | 0.72*** (0.036) | 0.68*** (0.028) | 0.24*** (0.040) | 0.32*** (0.058) |
\(\beta _{2}\) | 0.00 (0.003) | 0.00 (0.003) | 0.00 (0.005) | 0.00 (0.006) |
\(t: \beta _{1}=1\) | 57.4*** (0.000) | 144*** (0.000) | 363*** (0.000) | 134*** (0.000) |
\(Wald: \beta _{0}=0 \, \beta _{1}=1\) | 41.7*** (0.000) | 96.7*** (0.000) | 205*** (0.000) | 2801*** (0.000) |
Observations | 3611 | 4100 | 2869 | 3443 |
Regarding the orthogonality condition, if agents use all available information, then any covariate should be orthogonal to the forecast error. Dominguez (1986), MacDonald and Torrance (1990) and Benassy-Quere et al. (2003) find that rejection of the null hardly ever occurs at 1-week and 2-week horizons. Rejection of the null is more frequent at the 1-month horizon, and becomes strongest when considering horizons larger than 3 months. At 1-year horizons, rejection becomes an empirical regularity.
Orthogonality condition: \(E_{t}[S_{i,t+k}]-S_{t+k} = x'_{it}\beta + \sum _{j}{\gamma _jD_{year}} +\alpha _i + \epsilon _{it}\)
Coefficient/test | k = 1 month | k = 1 year | ||
---|---|---|---|---|
First differences | Fixed effects | First differences | Fixed effects | |
Board \(Meetings_{t}\) | −0.18*** (0.012) | −0.07*** (0.007) | 0.15*** (0.034) | −0.02 (0.026) |
\(\Delta Policy\) \(Rate_{t}\) | 0.01*** (0.002) | −0.01** (0.003) | 0.00 (0.004) | −0.02** (0.009) |
Forward \(Discount_{t}\) | −0.46*** (0.051) | −0.60*** (0.041) | −0.11** (0.046) | −0.39*** (0.065) |
Exchange rate \(Changes_{t-1}\) | 0.30*** (0.013) | −0.06 (0.013) | 0.13*** (0.033) | 0.37*** (0.048) |
\(\textit{F} test:\) All \(\beta s =0\) | 201*** (0.000) | 97.7*** (0.000) | 8.33*** (0.000) | 31.1*** (0.000) |
Observations | 3575 | 4063 | 2513 | 3055 |
To our surprise, these results suggest that agents (on average) could have improved their forecasting accuracy by accounting for variation found in the forward discount, past exchange rate changes, policy meetings, or the policy rate. We note that the negative coefficient of past exchange rate changes for the 1-month horizon implies that in the short run, a depreciation leads to a systematic under-prediction of the exchange rate (opposite to 1-year horizons).
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
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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