Question

Describe Censored data and truncated data, and how it relates to finance.

Answer 1

Censored Data

Censored data have unknown values beyond a bound on either end of the number line or both. It can exist by design. When the data is observed and reported at the boundary, the researcher has made the decision to restrict the range of the scale.

An example of a lower censoring boundary is the recording of pollutants in our water. The researcher may not care about (or instruments may not be able to detect) the level of pollutants if it falls below a certain threshold (e.g., .005 parts per million). In this case, any pollutant level below .005 ppm is reported as “<.005 ppm.”

An upper censor could be placed on temperature in a science experiment. Once the temperature goes above x degrees the scientist doesn’t care. So s/he measures it as “>x”.

Data can be censored on both ends as well. Income could be reported as “<$20,000” if the actual is below $20,000 and reported as “ >$200,000” if above that level.

There are potential censored data not created by design. Test scores or college admission tests are examples of censored data not created by design, but by the actual bounds. A student cannot score above 100% correct no matter how much better they know the topic than other students. These are bounded by actual results.

Truncated Data

Truncation occurs when values beyond a boundary are either excluded when gathered or excluded when analyzed. For example, if someone conducting a survey asks you if you make more than $100,000, and you answer “yes” and the surveyor says “thanks but no thanks”, then you’ve been truncated.

Or if a number of arrests is measured from police records, then everyone with 0 arrests will, by definition, be excluded from the sample.

Excluding cases from a data set at a preset boundary has the same effect. Creating models on middle income values would involve truncating income above and below specific amounts.

So to summarize, data are censored when we have partial information about the value of a variable—we know it is beyond some boundary, but not how far above or below it.

In contrast, data are truncated when the data set does not include observations in the analysis that are beyond a boundary value. Having a value beyond the boundary eliminates that individual from being in the analysis.

In truncation, it’s not just the variable of interest that we don’t have full data on. It’s all the data from that case.