Identifying the private-information horizon and completing the Twitter-sentiment test of the exchange-rate disconnect

Gholampour and van Wincoop (2019) estimated the information structure of a dispersed-private-information model of exchange-rate determination from the sentiment of 44,568 opinionated Euro-dollar tweets, and showed that the estimated model reproduces the classic Meese–Rogoff out-of-sample forecasting benchmarks that define the exchange-rate disconnect puzzle. However, the result hinges on a private-information horizon $T$ that the Twitter moments cannot discriminate (the examined values of 20, 60 and 240 trading days are all statistically acceptable, and the simulated benchmarks vary materially with $T$), on the assumption that tweets express unbiased beliefs, and on evidence from a single currency pair and language. The objective is to complete this empirical validation: pin down $T$ from data or establish that available moments cannot identify it, robustify the disconnect conclusions to modeled tweeting motives, and extend the structural estimation to at least one further currency pair or language.

Background

The exchange-rate disconnect puzzle, documented by Meese and Rogoff (1983), is the empirical finding that structural exchange-rate models based on observed macroeconomic fundamentals (money supplies, output, and similar aggregates) do not outperform a naive random-walk forecast of exchange rates at short or medium horizons. The standard summary statistic is the mean-squared-error (MSE) ratio: the out-of-sample forecast error of a fundamentals-based model divided by that of a random walk, so a ratio near or above one means the fundamentals model adds nothing. Later empirical studies refined the benchmark: Cheung, Chinn and Garcia Pascual (2005) at quarterly frequency, Cerra and Saxena (2010) at annual frequency, and the survey by Rossi (2013); disconnect at horizons up to several years is robust.

One theoretical candidate explanation is dispersed private information. Bacchetta and van Wincoop (2006) built a noisy rational-expectations model — a model in which traders infer information from the equilibrium exchange rate itself, so prices aggregate others' signals imperfectly — in which traders hold heterogeneous private signals about future fundamentals and unobservable portfolio-balance (noise) shocks also move the exchange rate. Because traders cannot perfectly separate the two, exchange-rate movements become largely disconnected from observed fundamentals, potentially generating the Meese–Rogoff facts. The mechanism is hard to test directly, since private beliefs are by construction unobservable.

Gholampour and van Wincoop (2019) proposed social media as an observable proxy for private beliefs. They classified opinionated tweets about the Euro/dollar rate into positive, negative and neutral views using a custom lexicon of foreign-exchange trader jargon, aggregated them into a daily Twitter Sentiment Index, and matched 11 moments of this index (its variance, cross-sectional disagreement, forward correlations and directional-prediction moments at 20–60 trading-day horizons, and its contemporaneous correlation with exchange-rate changes) to the corresponding moments of the Bacchetta–van Wincoop model. The structural parameters — the precision of private signals ($\sigma_v$), the volatility of noise shocks ($\sigma_b$), and the persistence of noise ($\rho_b$) — were estimated by Simulated Method of Moments (SMM), i.e., by choosing parameters so that simulated model moments match the data moments. The horizon $T$ over which agents are assumed to hold private information about future fundamentals was fixed rather than estimated, at values of 20, 60 and 240 trading days. With parameters estimated at $T=240$, simulations of the model, subjected to the same out-of-sample rolling-regression forecasting exercises as the empirical studies, reproduce short-horizon MSE ratios near one and long-horizon ratios consistent with the empirical ranges.

Several gaps in this evidence remain unresolved. The horizon $T$ is not identified: all three examined values are statistically acceptable, yet the disconnect conclusions depend on it — matching short-horizon benchmarks requires $T$ at least as large as the forecast horizon, and under the Cheung methodology at the five-year horizon the simulated MSE ratio is 0.24 when $T=20$, far below the empirical range of 0.9 to 3.22. Tweets are assumed to express the sender's true beliefs; reputational, market-manipulation, or selective-participation motives could bias the index, and the paper offers only indirect evidence that such bias is small. The evidence covers one currency pair (EUR/USD) and English-language tweets only, and information acquisition and the act of tweeting are exogenous to the model. The question is whether the private-information mechanism survives these gaps.

Problem Statement

Complete the empirical test of dispersed private information as a quantitative explanation of the exchange-rate disconnect, along the dimensions left unresolved by the evidence in Gholampour and van Wincoop (2019). The single scientific objective is to determine whether the private-information mechanism, once its free parameters — above all the private-information horizon $T$ — are identified from data rather than assumed (or the inability of the Twitter-sentiment moments to identify them is established), still reproduces the empirical Meese–Rogoff MSE-ratio benchmarks, and whether that conclusion is robust to how and why people tweet and to at least one further currency pair and/or language. Concretely, this objective spans three dimensions:

1. Identification of the horizon: estimate $T$ with enough precision that the disconnect conclusion no longer rests on an unidentified parameter across the examined 20-to-240 trading-day range, or demonstrate formally that the class of Twitter Sentiment Index moment conditions used in the estimation cannot identify $T$, stating which additional observable moments would.
2. Tweeting motives: allow expressed sentiment to differ from true beliefs (reputation, attempted market influence, or selective tweeting when opinions are strong), addressing the direction and size of the induced bias in the information-structure parameters and whether the disconnect conclusions survive it.
3. External validity: extend the structural estimation to at least one additional currency pair and/or language, which includes constructing and validating the corresponding foreign-exchange lexicon, and report whether the estimated information structure and the model's ability to reproduce empirical MSE-ratio benchmarks carry over.

Extensions the paper also suggests — endogenous information acquisition, communication through social media within the model, and a direct out-of-sample forecasting exercise on a longer sample — may accompany this work but are not part of the stated objective.

References

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