海角大神

In presidential elections, relationships matter.听

For example, political scientists know that the relationship between economic conditions, the number of causalities in war, and the incumbent鈥檚 party affiliation explain the bulk of presidential election outcomes.

In the 2016 presidential election, however, there is another 鈥渞elationship鈥� worth keeping an eye on. But rather than the correlation between two variables, this relationship is of the social variety. I鈥檓 referring, of course, to the marriage of Bill and Hillary Clinton.

Pundits on the left claim that Bill Clinton is an asset to Hillary because he brings legions of faithful supporters and has a high approval rating. Pundits on the right claim that Bill Clinton is a liability because he reminds voters of the Clintons鈥� personal affairs.

But when we strip this rhetoric down to its core, both sides are making the same empirical point: As goes Bill, so goes Hillary.听

But is it true? Are the Clinton鈥檚鈥� 鈥渕arried鈥� in the minds of voters such that the opinion of one affects opinions of the other?聽

In the the first chart above, I plotted approval ratings from Gallup.com ( and ) and Pollster.com () from 1992 to 2014 and created smooth trend lines for both Clintons. According to the figure, the answer would seem to be very clearly 鈥測es.鈥� We can see that Bill鈥檚 approval rating moves up and down alongside Hillary鈥檚 approval rating.

Surprised?聽 No?聽 Let鈥檚 get a little deeper into the data.

For starters, two variables can move up and down together without being causally related. In fact, causal relationships are notoriously hard to identify in non-experimental data (see on the relationship between Nickleback, Herpes, and Obama鈥檚 vote share in 2012). Indeed, other factors could be causing the above patterns. In other words, it鈥檚 possible the above patterns are a 鈥渟purious relationship.鈥� But also, the question here is about an individual-level relationship (what happens in the minds of voters). Inferring an individual-level relationship from aggregate data can lead to what鈥檚 known as an 鈥渆cological fallacy.鈥澛�

In short, we need better data.

Fortunately, the (ANES) has been conducting surveys for every presidential election from 1948 to 2012. We can easily download the ANES data set and quickly produce some answers to this question.

Let鈥檚 explore the relationship between opinions of Bill and Hillary Clinton in 2000. Respondents鈥� opinions are measured using a 鈥渇eeling thermometer鈥� where a score of 鈥�100鈥� indicates the highest possible approval of the Clintons while a score of 鈥�0鈥� indicates the lowest possible approval. A simple regression analysis will tell us if these two variables are indeed related and whether that relationship is statistically meaningful or not. The results are in the second chart above (scroll one frame to the right).

I鈥檒l skip the boring statistical details, but basically the regression model confirms what we see in the approval data. It would seem that that there is a very strong positive relationship between opinions of Bill and Hillary Clinton (indicated by the number 0.77 in the column 鈥淐oef鈥�). We can also see that this relationship is statistically meaningful (indicated by the number 38.95 in the column 鈥渢鈥�). In sum, as Bill鈥檚 approval goes up, Hillary鈥檚 increases, and as Bill鈥檚 approval goes down, Hillary鈥檚 declines as well.

But what about all the 鈥渙ther factors鈥� that could be causing opinions of both simultaneously?聽 For example, perhaps both are caused by views of Democrats in general, raw party identification, or the performance of the economy. In the social sciences, we call these 鈥渃ontrol鈥� variables.听聽

In the third chart above, I added five control variables (opinions of the Democratic Party, opinions of the economy, a respondent鈥檚 party identification, ideology, and gender).

Among the control variables, Democrats, respondents with a favorable opinion of Democrats, and women all have higher opinions of Hillary Clinton.听 None of this is surprising, but again, it鈥檚 important to account for these relationships.

But what鈥檚 most notable about the results is the magnitude of Bill鈥檚 effect. Indeed, from the above results we can quantify Bill鈥檚 value to Hillary鈥檚 campaign (as the title of this post suggests). In particular, because the coefficient on the 鈥淏ill鈥� variable is 0.465, the model indicates that as Bill鈥檚 approval rating increases by 1 unit, Hillary鈥檚 approval increases by just under half in the same direction.听

So while it鈥檚 not a 1-to-1 relationship, Bill has a sizable effect on how people view Hillary. Moreover, we when look at the last column on the right (labeled 鈥渂eta鈥�), what we see is that Bill鈥檚 effect is larger in magnitude than any other variable in the model. So not only does Bill matter, but he matters quite a bit.

Interested in one more model? Actually, you don鈥檛 have a choice.听

For some additional context on the magnitude of Bill and Hillary鈥檚 鈥渟tatistical鈥� relationship, I wanted to see what happened if we used the same model to predict opinions Al Gore. (See the fourth chart.)

We would expect Bill Clinton to have an effect on Al Gore鈥檚 approval rating given that they shared the White House together (remember, these data were collected in 2000). And indeed, that鈥檚 what we see in the results. However, what鈥檚 notable is that the magnitude of this relationship has decreased by about 30 percent from what the same model predicts regarding Bill鈥檚 effect on Hillary (from 0.465 to 0.320). In short, the statistical relationship between Bill and Hillary鈥檚 approval ratings is larger in magnitude than the statistical relationship between Bill and his vice president.听

What鈥檚 the big takeaway? In short, yes, opinions of Bill Clinton seem to sway聽opinions of Hillary. While we can鈥檛 say definitively this is causal (for example, causality could go the other way, with opinions of Hillary could be affecting Bill鈥檚), this relationship persists even when we control for various factors. Perhaps most importantly, the effect is surprisingly large in magnitude. It would seem that Hillary earns about a half increase or decrease in her approval rating for every 1 unit change in Bill鈥檚 approval rating. In the 2016 campaign, the so-called 鈥淏ill factor鈥� would matter quite a lot. 聽

For next week鈥檚 post (Part 2):

• What happens after Bill left office? Does this relationship exist in, say, 2008?
• Does this statistical relationship translate into actual votes?
• Is Bill鈥檚 effect strongest for Democrats, Independents, or Republicans?

Jordan Ragusa publishes his Rule 22 blog at .