RDP 2016-05: Trade Invoicing Currency and First-stage Exchange Rate Pass-through 3. Regression Analysis

In this section we use a regression framework to examine the relationship between invoice currency and exchange rate pass-through. Ideally, we would make use of price-level data to examine pass-through. In the absence of these data, we estimate the following panel regression using two-digit SITC-level data at a quarterly frequency:

where:

• Δp_i,t is the log difference of the import price index for two-digit SITC division i
• is the share of imports in two-digit SITC division i invoiced in Australian dollars
• Δe_{i,t − j} is the log difference of the import trade-weighted exchange rate index for two-digit SITC division i, constructed as described in Section 2.3
• is the pass-through coefficient for Australian dollar-invoiced goods at horizon j, and analogously for for foreign currency-invoiced goods
• ΔGDP_{t − j} is the quarterly log difference of Australian real GDP
• α_i are SITC division fixed effects, which allow for different average growth rates of prices across SITC divisions (our results are almost identical if we exclude the fixed effects).

We include quarterly GDP growth to control for domestic economic conditions, as in Gopinath et al (2010). We also tried including quarterly CPI inflation, or non-tradeable CPI inflation (and lags) alongside GDP growth. Doing so made no difference to our results. Using time fixed effects to control for aggregate-level variables instead of GDP growth is discussed in Appendix A.

We exclude four mostly homogenous-good SITC divisions from the regression because there is no reason to expect invoice currency should affect pass-through for flexible-price goods. (Table 2 lists the SITC divisions for which we have data, and the four that we exclude.) Excluding these four, the two-digit SITC divisions for which we have data cover a little over 60 per cent of all goods imports, based on trade weights for the September 2014 import price index.

Note that we do not need data on the price of Australia's imports in the source country to understand the role of invoicing currency. In the model developed by Gopinath et al (2010), the choice of whether to invoice in the local or the producer currency is determined only by the unconditional covariance of exchange rate shocks and firms' desired prices over the duration for which prices are expected to be fixed. In other words, because the cost of goods in the exporter's home country is unaffected by the decision to invoice exports in the local or the producer currency, we do not need information on the price of goods in exporters' home currencies to understand invoicing behaviour.

Figure 7 shows the estimated cumulative change in import prices following an exchange rate change for Australian dollar-invoiced and foreign currency-invoiced goods, out to a seven-quarter horizon. The red line plots the cumulative sum of the estimated coefficients out to horizon h, and the purple line does the same for the coefficients . Figure 8 shows the raw coefficients.

In the first quarter following an exchange rate change, pass-through for foreign currency-invoiced goods is immediate and complete, and close to zero for Australian dollar-invoiced goods. This is consistent with prices being sticky in their currency of invoice. At longer horizons, once firms have had time to reset prices, pass-through remains close to complete for foreign currency-invoiced imports. We believe two years is a long enough period to expect firms to have reset prices because Gopinath and Rigobon (2008) document that median duration before import prices are changed is 11 months.^[8] Although we find evidence of more-than-complete pass-through for foreign currency-invoiced goods, we believe this finding is unlikely to be economically meaningful.

Strikingly, for Australian dollar-invoiced goods, pass-through is statistically indistinguishable from zero even after two years. Our central estimate is that pass-through is just 14 per cent after two years. The confidence intervals are wide, which probably reflects the fact that we have relatively aggregated data and can only exploit invoicing currency variation across the 19 SITC divisions for which we have data. Moreover, our sample is relatively short, comprising 16 years of data. Nonetheless, we can reject pass-through of more than 50 per cent for Australian dollar-invoiced goods at the 95 per cent level of statistical significance. Our results are robust to different exchange rate measures and to the use of period-average invoice currency shares by two-digit SITC division; see Appendix A for details.

Because we use two-digit SITC-level data rather than price-level data, our results could be affected by aggregation bias. There are two ways aggregation might affect our pass-through coefficients. First, if prices remain unchanged for two or more years this will bias our long-run pass-through estimates. For foreign currency-denominated imports the bias is towards a coefficient of 1 (i.e. a finding of pass-through of 100 per cent), because pass-through for foreign currency-invoiced trade is mechanically 100 per cent over the duration that the foreign currency price is unchanged. For Australian dollar-invoiced trade the bias in our estimate of pass-through coefficients is towards zero. Assuming that import prices are reset on average approximately every 11 months (Gopinath and Rigobon 2008) and that the hazard rate of price changes is constant (the Calvo model), around 10 per cent of prices will remain unadjusted after two years. An estimated dynamic stochastic general equilibrium model for Australia implies that import prices are reset on average every three quarters (Jääskelä and Nimark 2011), slightly more frequent than reported by Gopinath and Rigobon (2008) for the United States. Thus, although this bias may marginally affect our exact estimate of pass-through, we do not believe it is likely to be large enough to substantially change the qualitative story.

Second, we would ideally use fixed-weight price indices that abstract from substitution among goods in response to price changes. At lower levels of aggregation, index weights are fixed between irregular sampling reviews, but at higher levels of aggregation index reweighting occurs annually. Nonetheless, substitution among goods at higher levels of aggregation is likely to be low given the quite different nature of the goods (e.g. road vehicles and furniture). Reassuringly, aggregation bias did not appear to materially affect pass-through estimates in the US data used by Gopinath et al (2010) – their results using aggregate- and price-level data are largely the same.

Footnote

Gopinath and Rigobon use the same import price data as Gopinath et al (2010). [8]