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I think of inflation as a generalized increase in the price levels of a basket of goods and services.

I should add that my understanding presumes that inflation should be measured in the same currency as that in which the goods and services that make up the basket are listed and sold in the market, e.g. when measuring inflation in France, the basket price is in Euros not in US dollars or rupees.

Measuring inflation for a currency in which few if any goods are listed in, such as Bitcoin, seems erroneous as there is not Bitcoin-denominated basket anywhere in the world.

Am I onto something here?

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The answer depends on what inflation we are talking about since the definition you mention in your question is not the only type of inflation in use. There are several different inflations used by economists. When economists talk about inflation without qualification we mean inflation of goods and services, as you mention in your question, but beside that in economics we have concepts such as asset price inflation, or even house price inflation etc.

In principle, you can view bitcoin as a speculative asset not as a currency Baur et al (2018), there is actually not clear consensus on what bitcoin is because it has some characteristics of speculative asset. If you decide to view bitcoin as an asset, and construct some price index for price of an asset (what would be bitcoin exchange rate if you want to view it as a currency) then you can call change in that price index 'bitcoin price inflation', the same way as some call change in the housing price index house price inflation.

If we are talking about inflation more specifically about just goods and services inflation, then you cannot talk about bitcoin inflation, but note you cannot talk about USD or euro or pound inflation either (even if I seen people loosely talking about USD inflation, it is a misnomer).

Inflation is by definition (see Mankiw Principles of Economics pp 13):

an increase in the overall level of prices in the economy

In turn economy is by definition (ibid, pp 5):

Whether we are talking about the economy of Los Angeles, the United States, or the whole world, an economy is just a group of people dealing with one another as they go about their lives.

Hence inflation is about measuring change in prices in an economy (which could even be a household or just some region) and it does not matter how prices are quoted. As a matter of fact inflation is completely unitless quantity (in fact even CPI change of which gives you inflation is itself unitless, but if you would measure inflation observing growth in actual prices the units would still cancel out).

Consequently, it is misnomer to talk about USD or euro or bitcoin or any other currency inflation. Euro is good example to illustrate this. The 'euro inflation' in France is different than 'euro inflation' in Euro-area and 'euro inflation' in Portugal. You can see that yourself by looking at Eurostat's inflation statistics for both EU and individual Euro-zone members (see Eurostat here). Heck, as Eurostat shows you can even calculate inflation for EU and not whole EU even uses the same currencies. More properly you should be talking not about USD, euro or bitcoin inflation but about inflation of USA, Euro-zone and so on. Inflation in USA is measured by change in CPI derived from prices quoted in USD because that is the official currency of US economy, but if half of USA are would use different currency you would still be able to calculate inflation for USA. Moreover, if you want to measure inflation of goods and services in some economy (e.g. some community of people) where people use bitcoin you can do that as well, although again it would be misnomer to call it bitcoin inflation, it would be inflation of that economy (and again the economy could be as small as you want).

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