Social desirability bias for survey questions on race

Social desirability bias is the tendency for individuals to avoid answering survey questions in a way that might be looked upon unfavourably by others. It often impacts questions on issues such as race, religion and immigration. Looking at data from the CBS/NYT poll that I mentioned in my last post, I discovered quite an interesting example of social desirability bias. The poll included the following question on race relations in the US:

In recent years, do you think too much has been made of the problems facing black people, too little has been made, or is it about right?

I recoded the variable so that respondents answering "too much" were distinguished from those answering either "about right" or "too little". Crucially, the poll also included the race of the interviewer for each individual respondent. Thus, I investigated social desirability bias by examining the effect of having a black interviewer on white respondents' answers to the above question on race relations. 

The table below shows coefficients from linear probability (i.e., OLS) models of believing that too much has been made of the problems facing black people. The sample is restricted to whites (who in any case comprised the vast majority of respondents). The value in the left-hand column indicates that whites with a black interviewer were 15 percentage points less likely to answer "too much" than whites with a white interviewer. And the values in the other columns indicate that this effect remains unchanged when controlling for a range of socio-demographic characteristics. 

15 percentage points is arguably a fairly large difference. Indeed, 38% of whites with a white interviewer answered "too much", whereas only 23% of whites with a black interviewer did so.