Messing around with DW-Nominate and Bond Returns

Over the past year and a half I have spent most of my time at the Fed working with yields data from U.S. Treasuries. Before the Fed I spent most of my time at LSE working with political data. Specifically, a dataset called DW-Nominate. I won’t do it a full service here, but it’s a measure of partisanship within the U.S. congress. It is a formalization of our heuristic classifications. We ‘know’ Hillary Clinton is further ‘to the left’ than Ted Cruz, but how are we actually identifying that? It doesn’t work too well to identify it on specific policies, as even just 8 years ago both her and Obama were against gay marriage, which no longer is reconcilable with ‘the left.’ Poole and Rosenthal identified it by using multi-dimensional scaling to simultaneously find the ‘ideal point’ of a legislator on a single dimension, as a function of their legislative voting records, and who they vote with most. As a result a legislator, who is always voting with other legislators on ‘the left’ and not with legislators on ‘the right’ of the dimension, will be classified farther to the left.  This has allowed for each congress (in this case the House) to have its measure of partisanship estimated, based on where in the dimension the average winning vote occurs. It also has allowed for a measure of partisanship, which is a measure of disagreement amongst legislators.

The yields data from U.S. treasuries are the most fundamental indicator of the present and future of the U.S. economy.  The pricing of the yield curve is related to the expectations of the U.S. interest rate and real economic activity. For example, steepness of the curve is a great indicator of future recessions, due in large part to how monetary policy affects the yield.  From this data I have constructed an excess return series, based on a function written by an economist I work for, which is the average of the additional return that can be achieved from buying an N-year bond, and selling it at N-1 years, when compared to just buying a 1 year bond. What this identifies is the time-varying risk premium in the term structure, which reflects investor’s demands for a risk premium to compensate them for interest rate risk. For example, if an investor buys a 5-year bond and sells it a year later, he takes the risk that rates rose in the interim period, which means he might realize a loss (when compared to the counterfactual of having just bought a 1-year bond). For this he requires an additional risk.

I always was curious if there was a way to identify a political risk premium in the term structure of yields, so I ran a series of regressions using the DW-nominate measures of partisanship, and political polarization. While the results were a little interesting, they appear to be null results.  I won’t entirely give up on the general thesis that there is a relationship between political polarization and the U.S. economy, but I have at least proven to myself that identifying that relationship will be much more challenging than simply throwing time-series at a regression. With that said, I’ve documented a snippet of the resulting graphs below, as well as my code.

plot2Chart 1: This chart is a benchmark, and graphs the fitted values of a regression of excess returns on the first three principal components. The theoretical idea behind this is that the term structure of yields should include all knowable future information on the U.S. economy, including the time-varying risk premium. So for another variable to meaningfully contribute, it must add above and beyond these three principal components. The R2 for this regression is 0.17


Chart 2: this chart is a regression of excess returns on only the two political variables, without including the principal components. What this regression specifically asks, as an example, is standing at the end of a 2-year congressional term and looking back at the dynamics of that legislative body, what amount of the future time-varying risk premium can I predict? Despite reaching a statistically significant result, and having an R2 of 0.11, the economic significance of this chart does not look meaningful.


Chart 3: This chart asked the same question as before, but assumed the investor was able to have perfect foresight of what the dynamics of the legislative body would be in the coming two years, essentially allowing him to predict the future and use it for his investment today.  The R2 and significance essentially remain the same as chart 2, but the variation at least looks slightly more interesting, but still pretty unconvincing.


Chart 4: This combines the two political variables with the first three principal components in the black line, and compares it to the benchmark of only the first three principal components in the red line. Statistically the R2 here is 0.26 vs. the benchmark value of 0.17, and the additional variables are significant.

I’m not convinced this represents any meaningful causal relationship outside of some historical idiosyncratic patterns. It is possible there are some deep latent factors in the U.S. and the world, which relate or drive increasing political polarization and variation in the time varying risk-premium. But absent any strong theoretical connection, I can’t bring myself to buy any of the significance.  There are also no meaningful reasons to prefer one model specification over another. For example, instead of excess returns I could have used the slope of the yield curve, and I could experiment with lags or forwards of explanatory variables without running against any theoretical reason to prefer one over the other (I tried lots of these, without results much different from what I achieved here).  And given all this freedom to try varying models, I could surely find a tight fit eventually, by luck.

In addition, the sample size of data on each congress is not particularly large, with only around 30 unique points for the entire sample (compared to the daily yields data).

Messy R Code:

DW-Nominate data from