Reduced form models that explain total exports with real effective exchange rates (REERs) are widely used in applied policy work, but their analytical structures are only loosely based on international trade theory. Incorrect aggregation of theory-consistent bilateral trade equations implies that estimations performed on aggregate data lead to bias in the underlying elasticties. Models calibrated with these elasticities will have predictions at odds with the implication of their bilateral counterparts.
This paper shows that the standard REER approach constitutes an approximation, which holds only for small changes, and causes an aggregation bias. We propose a new alternative regression specification that produces unbiased estimates. In our specification, aggregate exports are a function of the real exchange rate (RER) and foreign demand deflated by the destination-specific price index all denominated in an international currency as postulated by the dominant currency paradigm. If prices are set in the producer or the local currency, the estimation of the aggregate elasticities without bias is only possible if exchange rate pass-through is complete. To reveal the importance of theory-consistent aggregation for parameter inference, we resort to theoretical model simulations and quantify the magnitude of the aggregation bias in standard REER regressions.
Our simulation results show that aggregation bias in standard REER regressions is substantial (around 10 percent) and increases with measurement errors. The fact that many macroeconomic models are calibrated with these elasticities has important policy implications. The predictions of these models exaggerate the response of exports and, by extension, output following an exchange rate shock. Calibrating these models with elasticities estimated from our new estimation equation with variables denominated in the dominant international currency (ie, US dollar) improves the model's fit and results in predictions consistent with microeconomic behavior in bilateral trade equations.
This paper shows that real effective exchange rate (REER) regressions, the standard approach for estimating the response of aggregate exports to exchange rate changes, imply biased estimates of the underlying elasticities. We provide a new aggregate regression specification that is consistent with bilateral trade flows micro-founded by the gravity equation. This theory-consistent aggregation leads to unbiased estimates when prices are set in an international currency as postulated by the dominant currency paradigm. We use Monte-Carlo simulations to compare elasticity estimates based on this new "ideal-REER" regression against typical regression specifications found in the REER literature. The results show that the biases are small (around 1 percent) for the exchange rate and large (around 10 percent) for the demand elasticity. We find empirical support for this prediction from annual trade flow data. The difference between elasticities estimated on the bilateral and the aggregate levels reduce significantly when applying an ideal-REER regression rather than a standard REER approach.
JEL classification: F11, F12, F31, F32
Keywords: trade elasticity, real effective exchange rate, gravity equation, dominant currency paradigm, aggregation bias
Read the full paper at: https://www.bis.org/publ/work786.htm