As campaign season gets underway, inquiring minds want to know: does partisan control in Washington, DC have an effect on economic performance? This question has been asked before, using varied sets of variables, and the answers have varied accordingly. Lattice Insight has been publishing the Switkay USA Economic Vitality Index at the end of every quarter, when finalized data becomes available for the previous quarter. The components making up the index can be tracked back to the beginning of 1973, but they are not all available any earlier.

Partisan control in Washington falls naturally into 2-year time blocks: odd-numbered years followed by even-numbered years constitute one congress, between successive congressional elections. From 1973 to 2014 we have 21 such 2-year periods. In each, the White House was controlled by one of the two main political parties. Congress was controlled by one of the parties, or else control of the two houses was split. (The analysis could be refined further by examining the effect of partisan control of each house; however, control of the Senate and of the House have a moderate positive correlation, and there were too few cases of split control to justify such a division.)

The graphs above show the average performance of the Switkay USA Economic Vitality Index as a function of partisan control of the White House and of the Congress for each of the 21 2-year periods, with Democrat control on the left side of the graph and Republican control on the right side. Republican control of each branch appears to produce a positive effect on the index, and this effect is more pronounced for Congress than for the White House.

In a model including both White House and Congress, control of the White House is almost but not quite significant (p = .0668) in the presence of congressional control; control of Congress remains significant (p = .0223) even in the presence of control of the White House. Thus, as the graphs above suggest, control of Congress has more impact on the economy than control of the White House. The model including these two predictors has an R-squared of .3309, meaning partisan control can explain about 33% of the variability of the economic index. Contrary to popular opinion, there is no significant effect with divided control (p = .8831), in which it has been suggested that the economy benefits from having one party in the White House and another controlling Congress.

The 21 2-year periods are divided into 6 categories, based on control of the White House (D or R) and control of Congress (D, split, or R). The best average value for the index was 125.84, under a Republican president and a Republican Congress (2003-2006). The worst average value for the index was 64.74, under a Democrat president and split Congress (2011-2014).

How are the presidential candidates doing in the polls? Here is one way to visualize it. The rankings utilize the latest value of the smoothed average of all polls published on the Huffington Post, a more inclusive average than that published by Real Clear Politics. Each candidate is compared to the average poll share per candidate; this is 14.3% (100%/7) for the Democrats (in red), and 6.7% (100%/15) for the Republicans (in blue).

Since Biden is included in all polls, he is included in the denominator of the above fraction. If Biden is not included, the standard of comparison would be 16.7% (100%/6) for Democrats, dropping each Democrat candidate 2.4%.

Clinton and Trump hold commanding leads for the time being, although Sanders and Carson are surging. See however my previous post on Zipf's law.

The graph suggests that the lowest ranking four Democrat candidates, and the lowest ranking five (or even nine) Republican candidates could be dropped from future debates without disappointing too much of the public. These candidates are supported appreciably less than the average within their respective parties.

If you enjoy data and politics, there's little more fun than polls. The horse race in the primaries is a field ripe with statistics, which can shed light on the relative performance of the individual candidates, particularly the leaders in each party.

Zipf's law arose in linguistics, but has found applications in other areas. Zipf studied the relative frequencies of words used in a language, like English, and found that the 2nd most frequent word is used about 1/2 as much as the most frequent word; the 3rd most frequent word is used about 1/3 as much as the most frequent word, and so on. That is, word frequency is inversely proportional to word rank. A similar pattern occurs examining the populations of a country's cities, and other agglomerations.

It appears that a version of Zipf's law applies to the popularity of the presidential candidates. The leftmost dot in each graph represents the leader (currently, Trump and Clinton). The relatively large value of R-squared tells us that the model has very good predictive power.

If Zipf's law applied exactly, the coefficient of x in the regression equation would be -1 (since the graph is essentially plotted on log-log paper). The steeper slopes of the lines above is a result of the downward pull on the right side of the graphs by the lowest-ranked candidates, who are performing worse than Zipf's law would predict. It seems rather safe to predict that these candidates (Gilmore, Graham, Pataki, Jindal, and Santorum; and Chafee, Webb, and O'Malley) are unlikely to last, if only for financial reasons. When these candidates are removed from the dataset, R-squared moves closer to 1 (better predictive power), and the slope of the line moves closer to -1 (Zipf's law). (The graph doesn't include a point for Gilmore, whose poll numbers are roughly 0%, thus off the chart.)

If Zipf's law holds, the leading candidate should be polling around 100%/H_n, where H_n = 1 + 1/2 + 1/3 + ... + 1/n. (When n is large, 1/H_n can be approximated conveniently by 1/(.5772+ln (.5+n)); see the graph below.) Trump and Clinton can be expected to poll around 30% and 41% respectively; the actual numbers are 34% and 44%, a good approximation. The leading candidate should not be expected to pass 40% until there are only 6 candidates left in the race - if Zipf's law describes voter preferences accurately.

This is especially interesting because Trump's poll numbers are close to what would be expected in a 10-person race - exactly what we would have if the bottom 5 Republicans dropped out. The ceiling that some commentators attribute to Trump may be a paper ceiling through which he can rise as the other candidates drop out. In contrast, the Democrat race has only 3 viable candidates, in which case Clinton should be polling around 54%. Her relative weakness may indicate an uneasy electorate.