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In practice, quantitative easing (QE) in a currency union, such as the one implemented by the European Central Bank (ECB) in the Euro Area, follows guidelines arising from the capital key, which allocates country-specific long-term government bond purchases by GDP and population weights. This paper analyzes the optimal allocation of long-term government bond purchases within a currency union using a two-region DSGE model where regions are asymmetric with respect to portfolio characteristics. QE affects government asset prices in three ways: 1) it directly lowers the term premium component of long-term yields, 2) term premiums spill over through portfolio rebalancing of cross-border assets within the union, 3) lower outstanding government debt held by private agents lowers the risk premium on these assets. An optimal quantitative easing policy under discretion does not only reflect different region sizes, but is also a function of parameters dictating imperfect substitutability between assets, the extent of price rigidities, and other dimensions of heterogeneity across regions.
