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Let's say that we have longitudinal panel data. Rows are unique by date and individual. Columns consist of characteristics of the individuals on the given date as well as a dependent variable.

My ultimate objective is to perform a cross-sectional regression as well as a panel regression as there appears to be a time-series effect as well.

The characteristics for an individual are a constant for each quarter. So if I observe one value in the quarter I can successfully impute to remaining values in the quarter.

However, there are some individuals which are completely missing the values for one characteristic.

When I construct a bivariate chart with equal frequency binning of the characteristic on the x-axis and the dependent on the y-axis (see below), I observe a monotonic relationship. Also, I have grouped all missings in the NA bin on the far-right.

Bivariate chart with characteristic binned on x-axis; missings in far-right bin

Since the height of the NA bin is similar to the height of the 6th bin I would like to impute the missings to values in the 6th bin (for example, by imputing NA's to sampled values from the 6th bin ensuring imputation is constant within each quarter). What makes this challenging is that there is dependency structure (i.e. the characteristic of an individual in today's quarter tends to persist into the next quarter).

Can I simply impute missings to sampled values from the 6th bin (by quarter), or do I need to impute (somehow) by quarter AND by instrument to preserve the dependency relationship in the characteristic across time?

By "somehow" it's not clear how you would perform an imputation that preserves the dependency structure without already having a panel model at the ready. Perhaps I could impute via multiple regression using the other inputs for each time slice.

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This isn't really an "answer" but I'm not allowed to comment yet...just wanted to point you to these notes on missing data from NBER. Econometricians (non-financial, at least) seems relatively wary of imputing data, so the first section discusses assumptions under which your estimates using the "selected sample" (i.e., observations where you have values for all the covariates) aren't biased. Sections 2 and 4 discuss ways to try correcting if it is biased. Section 3 discusses imputation, and the needed assumptions. There are also ways to conservatively construct bounds on your estimator (Charles Manski's research), but that doesn't sound like what a Quant Guy would want =)

Some other questions/comments
* does the text above the graph mean you have 166,382 observations with a missing value? and that 17.52% of your obs have a missing value?
* I assume there's some variance in the second covariate conditional on "NA", so I wouldn't just stick them all into bin 6 if some of them have values 5e-04 (etc.), unless you know a priori that all "NA" map to the same bin. (You could show the same graph but with a box plot instead, to give us an idea.)
* if you have "NA" in one quarter, do you usually have "NA" for every quarter (for that individual), or are you more often just missing one quarter out of many? you mentioned high persistence in the characteristic, so I was wondering if it might be more accurate to impute based on the previous/next quarter values instead of the other covariate
* what sort of panel data model are you running? Might help in thinking about how your ultimate results will depend on the imputation method you use (although sensitivity tests are probably even better than just "thinking"!).

Hope some the reference notes (and questions) help some!
Dave

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  • $\begingroup$ Thanks David! 1) yes, the % missing is 17% and 166,382 are missing. Since the characteristics are a constant for a quarter I am really performing 166,382 / 13 weeks observations. (Each row is unique by week). 2) Great point on checking the variance of NA bin vs. bin 6. Will do. 3) Usually it is the case that the prior quarter, current quarter, and next quarter is missing. More specifically, I should state that there is high persistence although the characteristic does evolve quarter-to-quarter and is not static. 4) was thinking fixed effects panel but need to do more analysis before decision. $\endgroup$
    – Ram Ahluwalia
    Commented Aug 5, 2011 at 17:39
  • $\begingroup$ Two more comments: i) this was in the notes I linked, but I think missing at random (MAR) is a key idea. maybe for you values are just randomly missing, but usually they're not--e.g. survey data in India more likely missing for more distant/rural households in my friend's project. ii) above all, I'd check any final estimate with imputation against the estimate you get when dropping the obs with missing values--though even that is biased if MAR is not true (as the notes discuss), so unfortunately no easy way out w/o MAR! $\endgroup$
    – David M Kaplan
    Commented Aug 9, 2011 at 15:25
  • $\begingroup$ Oops, I was imprecise with MAR versus missing completely at random (MCAR)...I assume the notes do a more precise job! $\endgroup$
    – David M Kaplan
    Commented Aug 9, 2011 at 15:54

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