Are exchange rates disconnected from macroeconomic variables? Evidence from the factor approach

Abstract

We use factor-augmented predictive regressions to analyze the relation between nominal exchange rates and macroeconomic variables. Using a panel of 121 US macroeconomic time series, we estimate eight factors through principal component analysis. Those estimated factors have significant predictive power and can substantially improve the predictive power of purchasing power parity through both in-sample and out-of-sample analyses. The estimated macroeconomic factor, which co-moves with US stock market variables, has strong predictive power for nominal exchange rate fluctuations in the short run, while estimated factors, co-moving with interest rate spreads, government-issued bond yields and employment variables, have strong predictive power in the long run. Moreover, optimal factors selected by the BIC in the out-of-sample analysis differ greatly depending on the time points when forecasts are made. Finally, we show that factors extracted from a panel of 121 US time series data and those extracted from a panel of 215 Korean macroeconomic series together can predict a substantial portion of movements in the Korea–US bilateral exchange rate.

1 Introduction

Since Meese and Rogoff (1983) questioned the ability of macroeconomic variables to forecast exchange rates, many economists have investigated this issue. Although numerous macroeconomic models have been proposed and examined empirically, the empirical findings on the relation between exchange rates and macroeconomic variables differ greatly depending on the selected macroeconomic variables, sample periods, countries, length of forecast horizons, econometric methodologies, and other factors. For example, while Mark (1995) and Chinn and Meese (1995) report that variables based on the monetary model with flexible prices have significant predictive power for future exchange rate changes, Kilian (1999) and Berkowitz and Giorgianni (2001) show that those results are not robust for extended sample periods. Later, however, Park and Park (2013) argue that those variables have strong ability to predict future exchange rate movements through the time-varying cointegration approach.

We address the literature’s inconsistent and controversial results on the forecasting ability of macroeconomic variables by employing the factor-augmented predictive regression framework. Specifically, we use a panel of 121 monthly macroeconomic variables in the USA to determine the relation between exchange rates and macroeconomic variables. The factor approach, developed by Stock and Watson (2002) and Bai and Ng (2002, 2006), enables us to extract latent factors from the underlying panel of variables and test whether those latent factors have significant predictive power for future exchange rate movements. This factor approach can be particularly effective in examining the relation between exchange rates and macroeconomic data in several ways. First, previous studies have used a few selected macroeconomic variables and reported controversial results, but the factor approach enables us to avoid arbitrary decisions on the selection of macroeconomic variables. Instead, we can utilize information contained among the large number of macroeconomic data without causing a dimension problem due to a large number of predictors. Second, factors estimated from a large number of macroeconomic data are less noisy and have better explanatory power than individual time series data. [See Stock and Watson (2002) and Moench (2008)].

Using the advantages of the factor approach, we apply the factor-augmented predictive regression framework to 26 economies’ bilateral US dollar exchange rates.¹ We find that estimated factors from a panel of US macroeconomic data have significant predictive power for future nominal exchange rate changes, even without accounting for non-US counterpart economies. The predictive power of those factors is particularly pronounced when the estimated factors are combined with the real exchange rate in both in-sample and out-of-sample analyses. Moreover, we show that individual factors’ predictive powers differ over forecasting horizons, implying that different macroeconomic information is needed to forecast nominal exchange rate changes over different forecast horizons. After identifying the US macroeconomic variables co-moving with those estimated factors, we find that the factor co-moving with US stock market variables has greater predictive power for nominal exchange rate changes over short horizons, whereas the factors covarying with interest rate spreads, government-issued bond yields, and employment variables in the USA are selected more frequently as significant factors over long horizons. Moreover, the optimal factors selected by the BIC in the out-of-sample analysis differ greatly depending on the time points when forecasts are made. These findings echo Cheung and Chinn (2001), who report that the list of important macroeconomic variables and models in currency traders’ mind to understand movements in exchange rates shifts over time. Moreover, the findings can explain why previous studies provide conflicting results, even when a large panel of macroeconomic variables is stably related with exchange rate fluctuations. Finally, we add estimated factors from a panel of Korean time series variables as well as estimated US factors in the predictive regression and show that factors from Korea and USA together predict a substantial portion of movements in the Korea–USA bilateral exchange rate, confirming the connection between macroeconomic variables and exchange rates.

Our study is similar to Ludvigson and Ng (2009, 2010) and Jurado, Ludvigson, and Ng (2015) in the sense that latent factors are extracted from a large number of macroeconomic variables, but it is also different in the sense that those factors are used to forecast bilateral US dollar exchange rate changes instead of bond returns or to measure uncertainty. Similarly to Engel, Mark, and West (2014) and Greenway-McGrevy et al. (2018), we apply the factor approach in predicting exchange rates. Unlike those studies, however, we estimate factors from a panel of US macroeconomic data and/or a panel of Korean macroeconomic series instead of a panel of exchange rate data.

The rest of this paper is organized as follows: Section 2 presents our econometric methodology. Data sources and estimated factors from a large set of macroeconomic series are presented in Sect. 3. The results of an in-sample analysis are shown in Sect. 4. Section 5 provides evidence from an out-of-sample analysis. Section 6 presents the results of the predictive regression with factors estimated from a panel of Korean time series as well as estimated US factors. Finally, concluding remarks are offered in Sect. 7.

2 Econometric methodology

Although the exchange rate is a macroeconomic variable monitored by policymakers and economists, its movements are not well explained by other macroeconomic variables, and its impact on other macroeconomic variables also seems limited. This phenomenon has been reported by many studies since Meese and Rogoff (1983) and is named the “exchange-rate disconnect puzzle” by Obstfeld and Rogoff (2001). In this literature, a standard approach to assessing whether nominal exchange rate changes are predictable by macroeconomic variables uses the following predictive regression:

$$ \Delta^{h} s_{i,t + h} = \beta_{0,i} + \beta_{i,h}^{\prime } X_{t} + \varepsilon_{i,t + h} $$

(1)

where $s_{i,t}$ denotes the log of the nominal exchange rate between the currency of country $i$ and US dollars, $\Delta^{h} s_{i,t + h} \equiv s_{i,t + h} - s_{i,t}$, and $X_{t}$ denotes a vector of macroeconomic predictors.

$X_{t}$ in Eq. (1) usually consists of a few macroeconomic variables, depending on the underlying model. However, this approach could be restrictive because the relation between exchange rates and macroeconomic variables depends on the selected macroeconomic variables, sample periods, forecast horizons, and other decisions. Furthermore, Cheung and Chinn (2001) find from a survey of US foreign exchange traders that the importance foreign exchange traders attach to macroeconomic fundamentals varies over time. Observing the unstable relation between exchange rates and a few selected macroeconomic series, we seek to address whether macroeconomic series have significant predictive power for future exchange rate changes utilizing a large number of macroeconomic variables together. However, when the number of macroeconomic series (denoted by $N$) is greater than the number of time periods (denoted by $T$), this approach with a large number of variables is not feasible in the conventional regression approach.² To overcome this problem, we assume the following factor structure for US macroeconomic variables:

$$ x_{j,t} = \lambda_{j}^{\prime } F_{t} + e_{j,t} $$

(2)

where $x_{j,t}$ is an individual series contained in $X_{t}$, $F_{t}$ is a $r \times 1$ vector of common factors, $\lambda_{j}$ is a corresponding $r \times 1$ vector of factor loadings, and $e_{j,t}$ is an idiosyncratic error. $e_{j,t}$ can be serially correlated and weakly correlated across series, as in Stock and Watson (2002).

We estimate $F_{t}$ using the principal component analysis (PCA). Bai and Ng (2002) and Stock and Watson (2002) show that the space spanned by $F_{t}$ can be consistently estimated by $\hat{F}_{t}$ (an estimate of $F_{t}$ by PCA) as both $N$ and $T \to \infty$. We employ the information criterion (${\text{IC}}_{2}$) developed in Bai and Ng (2002) to determine the number of factors. When we apply ${\text{IC}}_{2}$ to the panel of 121 macroeconomic series, we find eight factors over the full sample.³ Having obtained these factors, we run the following predictive regressions for 26 economies to check whether the estimated factors from US macroeconomic data are helpful in forecasting nominal exchange rates:

$$ \Delta^{h} s_{i,t + h} = \alpha_{0,i} + \alpha_{F,i,h}^{\prime } \hat{f}_{t} + \alpha_{Z,i,h}^{\prime } Z_{t} + \varepsilon_{i,t + h} $$

(3)

where $\hat{f}_{t}$ denotes an estimate of $f_{t}$, a subset of $F_{t}$, and $Z_{t}$ is a vector of the observable predictor. We run regression Eq. (3) both without $Z_{t}$ and with $Z_{t}$ in the empirical analysis. When we include $Z_{t}$, we use the real exchange rate to represent Purchasing Power Parity (PPP) fundamentals, which are reported to have the strongest predictive power among macroeconomic models in Engel, Mark, and West (2008). Moreover, PPP fundamentals are also expected to reflect the relative macroeconomic conditions between US and non-US economies. Since the factors that are pervasive in the panel of US macroeconomic series are not necessarily important for forecasting $\Delta^{h} s_{i,t + h}$, $f_{t} \subset F_{t}$. Although we use $\hat{f}_{t}$ instead of true $f_{t}$ in Regression (3), Bai and Ng (2006) show that the bias arising from the error-in-variable problem disappears asymptotically and that (up to a rotation) the least squares (LS) estimate of $\alpha_{F,i,h}^{\prime }$ is consistent and asymptotically normal as $N,T \to \infty$ and $\sqrt T /N \to 0$. Hence, we apply the LS estimation to Eq. (3) to examine the predictive power of factors from the US macroeconomic variables on a panel of bilateral US dollar rates.

3 Data and latent factors from US macroeconomic series

3.1 Data

Nominal exchange rate data for 26 countries are obtained from International Financial Statistics (IFS).⁴ Nine currencies that switched to the euro at the beginning of 1999 are rescaled using bilateral euro rates to avoid discontinuity for those currencies. The consumer price indices (CPI) of the associated countries are also taken from IFS. After removing bilateral US dollar rates, 121 macroeconomic series are obtained from Federal Reserve Economic Data-Monthly Databases (FRED-MD), a macroeconomic dataset managed by the Federal Reserve Bank of St. Louis.⁵ This dataset mimics the coverage of the “Stock–Watson dataset” which is constructed primarily from Global Insights Basic Economics Database and used in many studies such as Stock and Watson (2002, 2006), Ludvigson and Ng (2009) and Jurado, Ludvigson, and Ng (2015). The advantage of FRED-MD database is that the large macroeconomic panel dataset is publically accessible and updated in real time. The database contains information about various aspects of the US economy, such as real output, income, employment, consumer spending, housing market condition, inventories, money stock, interest rates and spreads, stock market indicators, and price indices. This database shares the same predictive content as that in the so-called Stock–Watson dataset as demonstrated by McCracken and Ng (2016). For those reasons, we use the FRED-MD database excepting for exchange rate variables. All of the macroeconomic data are standardized prior to estimation. The sample period covers January 1973 to December 2015, which is dictated by the availability of the panel of macroeconomic variables.

3.2 Latent factors from US macroeconomic series

We apply PCA to 121 macroeconomic series to estimate the latent factors, the number of which is determined by ${\text{IC}}_{2}$. This criterion selects eight factors from the series under investigation, consistent with the results in Ludvigson and Ng (2009) and Jurado, Ludvigson and Ng (2015). The factors that are pervasive in the panel of US macroeconomic series are not necessarily selected by the BIC in the predictive regression of exchange rate changes. Because of this possibility, we should favor a conservative approach in selecting the number of factors, in the sense of including possibly more factors than the true number of pervasive factors but not fewer. The factors in excess will be trimmed by the BIC in the predictive regression. Hence, we check the number of factors using alternative criteria such as ${\text{IC}}_{1}$ in Bai and Ng (2002), edge distribution (ED) in Onatski (2010), and eigenvalue Ratio (ER) in Ahn and Horenstein (2013). The number of factors estimated by ${\text{IC}}_{1}$ is also eight, whereas ED and ER indicate that the number of factors is six and three, respectively. These pieces of evidence suggest that the number of factors selected by ${\text{IC}}_{2}$ is not too few but satisfies the conservative approach.

Autocorrelation coefficients and cumulative $R^{2} {\text{s}}$ for these eight factors are reported in Table 1. The factors exhibit some, but not extreme, persistence. $\hat{F}_{2t}$ exhibits the highest autocorrelation (0.77) among the eight factors. $\hat{F}_{1t}$ explains 17%, the largest fraction, of the total variation in the macroeconomic dataset. The eight factors together can explain more than 52% of the total variation in the 121 macroeconomic series.

Table 1 Descriptive statistics for estimated factors

Factor analysis is often criticized for making it difficult to give an economic meaning to the estimated factors. To mitigate this problem, we regress each of the 121 US macroeconomic series on each of those eight factors and obtain $R^{2} {\text{s}}$. Based on the obtained $R^{2} {\text{s}}$, we identify which macroeconomic variables are closely related with those factors. Figures 1 and 2 plot each of the eight factors together with those closely related macroeconomic series. As shown in the top panel of Fig. 1, $\hat{F}_{1t}$ moves closely with various measures indicating US employment conditions, while $\hat{F}_{2t}$ varies tightly with interest rate spreads (both credit spreads and long-run term spreads). $\hat{F}_{3t}$ and $\hat{F}_{4t}$ are related with prices and government-issued bond yields (i.e., interest rates), respectively. $\hat{F}_{5t}$ shares components with short-term interest rate term spreads. Although it is difficult to relate one economic sector to $\hat{F}_{6t}$, $\hat{F}_{6t}$ seems to covary with stock market variables and investment variables. $\hat{F}_{7t}$ co-moves with stock market variables, and $\hat{F}_{8t}$ is generally correlated with measures of money supply.

Fig. 1

Estimated factors and related macroeconomic series: $\hat{F}_{1t}$–$\hat{F}_{4t}$

Fig. 2

Estimated factors and related macroeconomic series: $\hat{F}_{5t}$–$\hat{F}_{8t}$

4 Predictive regression: in-sample analysis

4.1 Optimal factors versus PPP

Utilizing the estimated factors from the panel of US macroeconomic series, we first run a predictive regression (3) without including any observable predictor (i.e., without $Z_{t}$). For each country and for each horizon (1 month, 3 months, 6 months, 12 months, and 24 months), we select the subset of eight factors that minimizes the BIC criterion and regress nominal exchange rate changes on those selected factors. Note that the factors that are important for the total variation of a macroeconomic series do not necessarily have the best ability to forecast $\Delta^{h} s_{i,t + h}$. Hence, the factors selected by the BIC criterion do not need to be $\hat{F}_{1t}$ or $\hat{F}_{2t}$. Figure 3 shows the frequencies at which each factor has been selected for each horizon. $\hat{F}_{7t}$, which is closely related with US stock market variables, is selected at overwhelming frequencies for the 1-month horizon, In addition, $\hat{F}_{8t}$ co-moving with US money supply measures is quite frequently chosen for the 1-month horizon, but other factors are selected more frequently as the horizon increases. This pattern suggests that factors with strong predictive power for nominal exchange rate movements differ across horizons. $\hat{F}_{7t}$ and $\hat{F}_{8t}$ play an important role in predicting exchange rates in the short run. For longer horizons such as 1 and 2 years, however, $\hat{F}_{1t}$, $\hat{F}_{4t}$, $\hat{F}_{5t}$ and $\hat{F}_{7t}$ which are related to US real economic activity such as employment conditions, interest rate spreads and stock market variables, become important in explaining exchange rate changes.⁶ In contrast with $\hat{F}_{1t}$, $\hat{F}_{4t}$, $\hat{F}_{5t}$, $\hat{F}_{7t}$ and $\hat{F}_{8t}$, $\hat{F}_{3t}$, related to the price sector, is rarely selected as an optimal factor in the predictive regression. Table 2 shows adjusted $R^{2}$ from $\Delta^{h} s_{i,t + h} = \alpha_{0,i} + \alpha_{F,i,h}^{\prime } \hat{f}_{t} + \varepsilon_{i,t + h}$. Although the predictive power of the factors estimated from the US macroeconomic series to explain bilateral exchange rate movements differ greatly across counterpart countries, the predictive power as measured by adjusted $R^{2}$ generally increases with the forecast horizon. The magnitude of the predictive power is substantial: the average adjusted $R^{2}$ ranges from 1.1% at a 1-month horizon to 20% at a 2-year horizon.

Fig. 3

Selected frequencies of macroeconomic factors in predictive regressions with macroeconomic factors only. This figure shows the selected frequencies of macroeconomic factors when the predictive regression has estimated macroeconomic factors only

Table 2 Adjusted $R^{2}$ from factor-augmented predictive regressions: optimal macroeconomic factors only

To compare the predictive power of the optimal factors chosen by the BIC with that of PPP, the following predictive regression, with only the real exchange rate, is run:

$$ \Delta^{h} s_{i,t + h} = \gamma_{0,i} + \gamma_{0,i,h} q_{i,t} + \varepsilon_{i,t + h} $$

(4)

where $q_{i,t}$ is the real exchange rate between country $i$ and USA. Comparing Table 2 with the PPP columns in Table 3, we note that the optimal factors selected by the BIC show much better forecasting ability than PPP shows at a 1-month horizon in terms of adjusted $R^{2}$. For a 1-month horizon, adjusted $R^{2} {\text{s}}$ improve in 20 out of 26 countries when the optimal factors from the US macroeconomic series (instead of the real exchange rate) are used in the predictive regression. This result is notable because we use factors from the US macroeconomic variables only, without considering any of the variables from counterpart countries. Possibly due to this limit, however, PPP shows better performance in predicting nominal exchange rate changes at three- and 6-month horizons. The gap in adjusted $R^{2} {\text{s}}$ between PPP and the optimal factors becomes smaller as the horizon grows, and the optimal factors show almost equal predictive power when the horizon reaches the 2-year threshold.

Table 3 Adjusted $R^{2}$ from factor-augmented predictive regressions: PPP only and PPP and optimal factors

4.2 Optimal factors and PPP

Next, we run the predictive regression (3) with optimal factors and an observable predictor. The chosen $Z_{t}$ in regression (3) is $q_{i,t}$. We select $q_{i,t}$ as the observable predictor for several reasons. Engel, Mark, and West (2008) report that PPP has the strongest ability to forecast exchange rate changes among alternative models. We also intend to check whether the optimal factors from the US macroeconomic series have additional predictive power for nominal exchange rate movements after controlling for $q_{i,t}$ as well as a synergy effect with $q_{i,t}$ in forecasting nominal exchange rate fluctuations. Finally, the real exchange rate might account for the economic status of non-US counterpart countries in bilateral exchange rates.

Again, optimal factors are determined by the BIC criterion; the frequencies selected are shown in Fig. 4 for each horizon. The pattern is quite similar to that in Fig. 3. $\hat{F}_{7t}$ (co-moving with US stock market variables) is overwhelmingly the most frequently chosen at the 1-month horizon. However, $\hat{F}_{5t}$ (co-moving with US interest rate short-term spread variables), $\hat{F}_{4t}$ (covarying with US interest rates), and $\hat{F}_{1t}$ (correlated with US employment conditions) become more frequently chosen at 1- and 2-year horizons. Moreover, $\hat{F}_{3t}$ (related to US price indices) is rarely selected at any horizon, implying that US price sectors have limited relationships with exchange rate fluctuations.

Fig. 4

Selected frequencies of macroeconomic factors in predictive regressions with macroeconomic factors and PPP. This figure shows the selected frequencies of macroeconomic factors when the predictive regression has estimated macroeconomic factors and the real exchange rate

The adjusted $R^{2} {\text{s}}$ of the predictive regression with optimal factors and $q_{i,t}$ are presented in Table 3, along with those of the predictive regression with $q_{i,t}$ only. As shown in Table 3, the optimally chosen factors improve the adjusted $R^{2} {\text{s}}$ substantially. The adjusted $R^{2} {\text{s}}$ from all countries examined except Thailand improve with the inclusion of the optimal factors at a 1-month horizon. At a 2-year horizon, improvement in the adjusted $R^{2}$ can be observed in all countries: adjusted $R^{2}$ increases an average of 20–32% at this horizon. Switzerland shows a remarkable improvement in adjusted $R^{2}$ in Table 3 when US macroeconomic factors are combined with PPP in the predictive regression compared with the adjusted $R^{2}$ of the predictive regression with factors only in Table 2. This might imply that the relative economic condition between Switzerland and the US captured by PPP as well as the US macroeconomic factors are important in forecasting the dynamics of the bilateral exchange rate between Switzerland and the US. Overall, the results in Table 3 suggest that US macroeconomic variables have substantial predictive power for future nominal exchange rate movements in addition to the PPP relation.

When $\sqrt T$ is comparable to $N$, a bias may appear for the slope coefficients in the predictive regression, as discussed in Bai and Ng (2006). Hence, bias-corrected slope coefficients for the real exchange rate and optimal factors in predictive regressions for the 1-month horizon are provided in Appendix Table 9.⁷ Consistent with the finding in Ludvigson and Ng (2010) that the bias is quite small for large N and T, the bias-corrected slope coefficients and t-statistics are slightly changed. We also report test results for the hypothesis that all coefficients of macroeconomic factors in the predictive regressions are zero. As shown in Table 4, the null hypothesis is generally rejected at the conventional significance level; for example, the null hypothesis is rejected at the 5% significance level for 20 countries at 2-year horizons. These results suggest that US macroeconomic factors are generally significant predictors of nominal exchange rates.⁸,⁹

Table 4 Joint test results of macro factors in factor-augmented PPP model

5 Predictive regression: out-of-sample analysis

In addition to the in-sample analysis, we conduct an out-of-sample analysis, a standard way to evaluate forecasting ability since Meese and Rogoff (1983). The initial sample period for the first forecast covers January 1973 to December 1987 where $1 =$ January 1973 and $t_{0} =$ December 1987. The out-of-sample analysis is conducted as follows. First, we estimate US macroeconomic factors and factor loadings during the initial period using the panel of macroeconomic variables for $t = 1,2 \ldots t_{0} - h$. Then, we select optimal factors in the predictive regression using the BIC criterion for the initial period. With the optimal factors and the real exchange rate, we make a forecast for $s_{{t_{0} + h}} - s_{{t_{0} }}$, and calculate a forecast error. We repeat these steps to predict $s_{{t_{0} + 1 + h}} - s_{{t_{0} + 1}}$ recursively after adding the next one-period observations of the real exchange rate and US macroeconomic data to our dataset at $t_{0} + 1$. That is, factors are estimated again from PCA using series for $t = 1,2, \ldots ,t_{0} + 1 - h$, optimal factors are selected by the BIC criterion, and forecasts are made with selected optimal factors and the real exchange rate at $t_{0} + 1$ for $s_{{t_{0} + 1 + h}} - s_{{t_{0} + 1}}$. This process continues until the end of the sample period. Forecast horizons are the same as those for the in-sample analyses.

The optimal factors selected by the BIC differ not only across horizons but also across time points when the forecasts are made. The finding that optimal factors vary across time points is similar to the report in Cheung and Chinn (2001) that foreign exchange traders’ ranking of important macroeconomic variables shifts over time. Consistent with the results of the in-sample analysis, Fig. 5 also shows that $\hat{F}_{7t}$ is the factor selected most frequently at a 1-month horizon. As the forecast horizon increases, however, the frequency of the selection of $\hat{F}_{7t}$ decreases, and $\hat{F}_{1t}$ and $\hat{F}_{2t}$ are the factors chosen most frequently at a 2-year horizon. Unlike the results of the in-sample analysis, $\hat{F}_{3t}$ is also selected with some frequency in the out-of-sample analysis. This result also implies that US stock market variables are important in forecasting exchange rate changes in the short run, while variables indicating employment conditions and interest rate spreads make greater contributions in long-run predictions.

Fig. 5

Selected frequencies of macroeconomic factors in out-of-sample predictive regressions with PPP. This figure shows the selected frequencies of macroeconomic factors by the BIC when the predictive regression has estimated macroeconomic factors and the real exchange rate in the out-of-sample analysis

We compare the predictive power of the predictive regression augmented with the factors and PPP with that of the random walk model or PPP only. Clark and West (2007) statistics are employed for the evaluation of the predictive powers of the competing models. When the random walk model is compared, for example, the Clark–West adjusted U-statistics can be written as follows:

$$ \tilde{U}_{i,h}^{{\left( {F,R} \right)}} = \frac{{P^{ - 1} \mathop \sum \nolimits_{t = 1}^{P} \left( {\Delta^{{\hat{h}}} s_{i,t + h}^{F} - \Delta^{h} s_{i,t + h} } \right)^{2} - P^{ - 1} \mathop \sum \nolimits_{t = 1}^{P} \left( {\Delta^{{\hat{h}}} s_{i,t + h}^{F} - \Delta^{{\hat{h}}} s_{i,t + h}^{R} } \right)^{2} }}{{P^{ - 1} \mathop \sum \nolimits_{t = 1}^{P} \left( {\Delta^{{\hat{h}}} s_{i,t + h}^{R} - \Delta^{h} s_{i,t + h} } \right)^{2} }} $$

(5)

where superscript F indicates the factor-PPP augmented model, superscript R is a random walk model, and P is the number of forecasts. The null hypothesis is that the two competing forecasting models have an equal mean squared prediction error, whereas the alternative hypothesis is that the larger model (the factor-PPP augmented model) has a smaller mean squared prediction error. Due to the possible serial correlation among forecast errors, Newey–West standard errors are employed for the test. According to Bai and Ng (2006), factor estimation yields a contribution at order $N^{ - 1}$ to the variance of the prediction error. It means that a large $N$ allows better estimation of the factors, which would result in smaller prediction uncertainty. Since we use a large panel of macroeconomic variables, we conjecture that the prediction uncertainty arising from the factor estimation would be small.

Table 5 shows the Clark–West adjusted U-statistics against the random walk model. Bold font numbers indicate that the null hypothesis of the equal mean squared prediction error is rejected at a 10% or higher significance level. The factor-PPP augmented model shows a smaller mean squared prediction error than the random walk model in all countries except Thailand at a 1-month horizon. Moreover, the difference is significant in 20 out of 26 countries. As the horizon increases, a similar pattern continues, and the factor-PPP augmented model has a significantly smaller mean squared prediction error than the random walk model in all countries but Portugal at a 2-year horizon.

Table 5 Out-of-sample analysis: optimal factors and PPP versus random walk

We also test the equal predictive accuracy between the factor-PPP augmented model and the PPP model in Table 6. As shown in the first column of Table 6, the factor-PPP augmented model outperforms the PPP model in 23 countries out of 26 at a 1-month forecast horizon. Among those 23 countries, the adjusted Clark–West adjusted U-statistics is significant in 18 countries. At three- and 6-month horizons, the adjusted Clark–West U statistics are significantly smaller than one in approximately half the countries. However, the rejection rate increases with the horizon again, and the null hypothesis is rejected at a 10% or higher level in 18 countries at a 2-year horizon.

Table 6 Out-of-sample analysis: optimal factors and PPP versus PPP

6 Forecasting exchange rate with US macroeconomic factors and domestic macroeconomic factors

We have shown that US macroeconomic factors have substantial predictive power for bilateral exchange rates with or without conditioning on PPP. In examining the predictive ability of US macroeconomic factors, we have not considered the economic conditions of counterpart economies. It would be interesting to evaluate the forecast ability of macroeconomic factors extracted not only from a panel of US macroeconomic series but also from a panel of a counterpart economy’s macroeconomic series to examine the connection between the exchange rate and macroeconomic variables. We thus run the following regression:

$$ \Delta^{h} s_{i,t + h} = \alpha_{0,i} + \alpha_{F,h}^{\prime } \hat{f}_{t} + \alpha_{dF,i,h}^{\prime } \widehat{df}_{i,t} + \varepsilon_{i,t + h} $$

(6)

where $\widehat{df}_{i,t}$ denotes an estimate of the macroeconomic factors from a large panel of time series data for the counterpart economy.

Due to data accessibility issues, we examine regression (6) using the Korea–US bilateral exchange rate, a panel of macroeconomic data for Korea, and a panel of macroeconomic data for the US. A total of 215 macroeconomic series of Korea are obtained from the dataset managed by the Bank of Korea (BOK) and the National Statistical Office.¹⁰ The large macroeconomic dataset constructed for Korea contains information on various aspects of the Korean economy, such as domestic construction, industry production, inventory, sales, unemployment, housing market, export, import, monetary base, interest rates, price indices, and stock market indices. The list of 215 macroeconomic variables in Korea is provided in Table 10 in Appendix.

Because exchange rates in Korea became completely floating from January 1998, we focus on the period between January 1998 and December 2015. Over this period, four macroeconomic factors are estimated from the 215 macroeconomic series for Korea. $\widehat{DF}_{i,t1t}$ has a high correlation, at almost one, with the export value index; $\widehat{DF}_{2t}$ is positively correlated with domestic construction orders; $\widehat{DF}_{3t}$ has a positive correlation with the market interest rate (the yield on CD); and $\widehat{DF}_{4t}$ co-moves with the shipment index by industry and the index of mining and manufacturing industrial products.

Optimal factors among the estimated Korean and US factors are selected by the BIC in the predictive regression. Table 7 compares the results from the predictive regressions with the real exchange rate only, with US macroeconomic factors, and with US and Korean macroeconomic factors. As shown in Table 7, the predictive regressions with US macroeconomic factors have lower adjusted $R^{2}$ than in the PPP model at all horizons. When Korean macroeconomic factors are added, however, the adjusted $R^{2}$ improves substantially for all horizons, implying that the macroeconomic variables from both economies have significant predictive power for movements in the bilateral exchange rate. Similar to the results in previous sections, the factors chosen by the BIC differ across horizons. For example, $\widehat{DF}_{4t}$, co-moving with the shipment index by industry and the index of mining and manufacturing industrial products in Korea, is often selected over short horizons, while $\widehat{DF}_{3t}$, related to the market interest rate, replaces $\widehat{DF}_{4t}$ at long horizons. Consistent with Chen and Tsang (2013) who show that yield curves have good predictive power for nominal exchange rate movements, factors related with US interest rates and Korean interest rates ($\hat{F}_{2t} , \hat{F}_{5t}$, and $\widehat{DF}_{4t}$) have significant coefficients from the 6-month horizon and on.

Table 7 Predictive regression with macroeconomic factors from Korea and the US: in-sample analysis

Finally, we compare the out-of-sample performance of Eq. (6) with that of the random walk model and the PPP in Table 8. We employ the Clark–West adjusted U-statistics to test the null hypothesis of the equal predictability between Eq. (6) and the random walk model and the Diebold–Mariano test statistics to test the same null hypothesis between Eq. (6) and PPP.¹¹ As shown in Table 8, Eq. (6) shows more accurate predictability than the random walk at all horizons, and those differences are significant at the 5% level. In the comparison between Eq. (6) and PPP, Eq. (6) shows slightly better performance at 1-month, 3-month, and 2-year horizons, although the null of equal forecast ability cannot be rejected. We then add the real exchange rate to Eq. (6) and compare out-of-sample predictive power between Eq. (6) augmented with the real exchange rate and the random walk model and PPP. As shown in the last two panels of Table 8, the addition of the real exchange rate greatly enhances the predictive power of Eq. (6). As a result, Eq. (6) augmented with the real exchange rate shows significantly more precise out-of-sample predictive power than the random walk model or the PPP at all horizons according to the Clark–West adjusted U-statistics.

Table 8 Predictive regression with macroeconomic factors from Korea and the US: out-of-sample analysis

7 Conclusion

Many studies in international finance have tried to relate exchange rates to macroeconomic variables. Some have succeeded in finding a significant relation between the two, whereas others have not. We use a large panel of US macroeconomic series to see whether bilateral US dollar exchange rates are explained by US macroeconomic variables. Utilizing the factor-augmented predictive regression, we find that factors extracted from US macroeconomic data have significant predictive power for fluctuations in the nominal exchange rate and can substantially improve the predictive power of the PPP through both in-sample and out-of-sample analyses. Furthermore, factors estimated from the large panels of Korean and US macroeconomic variables show excellent predictive power for movements in the Korea–US bilateral exchange rate. Overall, this evidence strongly suggests that the exchange rate is not disconnected from a large panel of macroeconomic variables.

Moreover, we find that the factors frequently chosen to predict short-run movements in the exchange rate are not necessarily the factors most often selected to predict long-run movements in the exchange rate and that optimal factors selected by the BIC in the out-of-sample analysis differ greatly depending on the time points when the forecasts are made. These findings can explain why the few macroeconomic variables selected in previous studies have sensitive forecast abilities depending on the sample period, forecast horizon, and other conditions. The findings suggest that, even if there is a stable relation between the exchange rate and a large panel of macroeconomic variables, that relation cannot be clearly seen between the exchange rate and a few selected variables as the sample period or forecast horizon changes. This might be due to the finding in Cheung and Chinn (2001) that currency traders use different models and macroeconomic variables over time to understand exchange rate movements, or due to the consequence of the scapegoat effect described in Bacchetta and Van Wincoop (2013). Further investigation in this direction would be an interesting future research project.

Appendix

See Tables 9 and 10.

Table 9 Results of factor-augmented predictive regression: 1-month horizon

Table 10 List of Korean macroeconomic variables