Is there any variable commonly used as a proxy for the inflation target set by the Central Bank? I have been asiggned to estimate a monetary policiy rule à la Taylor for my macroeconometrics class. There are no explicit inflation targets stated by the Central Bank (of the country I am the estimating the model for (Costa Rica)) for a part of the period whose data I must use. I would like to know if there is some variable commmonly used as an aproximation of proxy of the inflation target chosen by the Central Bank. Any help, commentary or reference to any bibliography is deeply aprecciated. Thank you.
Actually Costa Rica publishes inflation target. See the graph below provided by IMF where the inflation target is given by orange band (it is completely normal to target range rather than precise number):



There are no proxies that can be just lifted from statistics that I know of but there are ways how to discover how central banks set monetary policy even if it is not public.

For example, you can start with specifying some possible rules that central bank could be following (e.g. Taylor rule etc.) and afterwards you can conduct an econometric analysis that can show you how much the central bank behavior matches the 'guessed' monetary policy rule. Or alternatively you can deduce it from case studies of central bank's decisions. There are actually many ways how to do this and it is beyond the scope of stack exchange to provide extensive overview of them all.
Commonly used variables to do this are the interest rates that central bank sets, wider interest rates, inflation itself, inflation expectations, money supply aggregates and many more. Have a look at the literature below. However, there is no simple proxy as far as I know.
Examples of such empirical papers include Castroa, (2011); Bec, Salem, &amp; Collard, (2002); Bernanke, and  Mishkin (1992); McGouldrick, (1984). Of course, the list is not exhaustive I tried to include diverse range of papers on this topic. You should have look at the sources cited therein and do additional search based on the keywords you find.