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Does no arbitrage in the FX market have any implications for purchasing power parity (PPP) tests? To be more specific, suppose you have currencies A, B and C and you can form three currency pairs (exchange rates) AB, BC and AC. Only two of those can be independent of each other. Suppose you run a test on each currency pair to see whether or not PPP holds and only two of the tests indicate a PPP relationship. Is this result consistent with a no-arbitrage FX market? I would lean towards a yes, but I am not entirely sure.

Pavel Filip
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    Is that mathematically possible? If two PPP relationships hold then a good in country A costs the same as the good in country B, and similarly for B versus C, then surely the good costs the same in A and C ? – dm63 Mar 31 '24 at 13:31
  • @dm63 I didn't realize that. Thank you. – Pavel Filip Mar 31 '24 at 18:45

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