Assuming only two factors is evidently a major simplification. Labour, for example,
comes in many different skill types and immigration may change the skill composition
if the skill mix in the immigrant inflow is unlike that in the native labour force. If the
economy needs to change the mix of skills employed within industries then native skill
types which compete closely with those dominant in the immigrant inflow may see falls
in wages relative to other skill types. To the extent that marginal tax rates on these
labour types differ then this will have consequences for tax receipts. Dustmann et al.
(2012) provide some evidence that immigration to the UK puts modest downward
pressure on wages in parts of the distribution where immigrants are concentrated,
especially at the lowest end, while raising wages elsewhere. While interesting, the
implied tax effects are not plausibly large relative to the effects that will be found by a
simple accounting approach.