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Alternative Explanations



Comparison of party terms

When variation in a variable, X, is highly correlated with variation in another variable, Y, there are five possible explanations (This summary is paraphrased from Applied General Statistics, by Frederick E. Croxton and Dudley J. Crowden -- Prentice Hall, New York, 1955.):
1) The variation in X causes the variation in Y,
2) The variation in Y causes the variation in X,
3) There is a third variable, Z, which causes the variation in both X and Y,
4) Causation moves in more than one direction,
5) The correlation is due to chance.



Explanation 5 is highly unlikely. The six Republican terms each saw less growth than the average Democratic term. That, by itself, would only occur one time out of 64 by chance. The t-test is statistically more sophisticated. It would give us:

Party:Number of terms Mean growthStandard Deviation
Democratic 5 17.35% 3.70%
Republican 6 11.66% 1.16%

The pool standard deviation is 2.61%
Which makes the standard error 1.58%
The t value is (17.35-11.66)/1.58, or 3.59

For 9 degrees of freedom and a 1% significance level, the critical t value is 3.25. So, if the conditions of the t test were met, the probability of this resulting from chance would be less than 1%.

Unfortunately, the t test is strictly valid only when the underlying population has normal distribution. It is hard to even state what the underlying population is -- the growth of the economy in all possible four-year periods? -- let alone demonstrate that it has a normal distribution.


Holding explanation 4 in abeyance for the moment, explanation 3 in our problem would be some mood or other influence which led to both the election of a Democratic president and a rapid expansion of the economy.

Explanation 2 can not hold in pure form for our particular problem. The increase in RGDP over a term cannot determine the party of the president inaugurated at the beginning of the term. Causation flows with time. There might, however, be some premonition about the increase in RGDP over the next four years which influenced the election of the president.

Either explanation 2 or explanation 3,. though, requires causation through the popular vote. Does anyone really think that any Supreme Court justice in 2000 was saying, "I think we're heading for low growth; let's put Bush in"? Thus, we can check both explanations by considering the relationship of the popular vote to economic growth.

It seems somewhat perverse to do actual correlations with a yes/no series like whether a party won the presidency, but it is perfectly possible. In the following table, I've taken the ratio of the Democratic presidential popular vote to the Republican presidential popular vote. Both are in thousands, as reported by Statistical Abstract of the United States.

Election Year Democratic Vote Republican Vote Ratio D/R
1960 34,327 34,108 1.006
1964 43,130 27,178 1.587
1968 31,275 31,785 0.984
1972 29,170 47,170 0.618
1976 40,831 39,148 1.043
1980 35,484 43,904 0.808
1984 37,577 54,455 0.690
1988 41,809 48,886 0.855
1992 44,909 39,104 1.148
1996 47,402 39,199 1.209
2000 50,992 50,455 1.011

Now, let's compare those popular vote ratios with the party in the white House and with growth in RGDP.

Election Year Ratio D/R W H Subsequent Growth (%)
1960 1.006 1 19.86
1964 1.587 1 21.81
1968 0.984 0 12.38
1972 0.690 0 10.62
1976 1.043 1 13.67
1980 0.808 0 12.63
1984 0.690 0 15.98
1988 0.855 0 8.81
1992 1.148 1 13.53
1996 1.209 1 17.67
2000 1.011 0 9.56

The coefficients of linear correlation are:
Vote ratio to WH:.... 0.726
Vote ratio to growth: 0.627
WH to growth:........ 0.706


Since the economic growth is more strongly correlated with the party in the White House than with the popular vote, it is obviously irrational to argue that the first correlation is somehow a result of the second. The argument in the other direction is far less clear. When we look at the "residuals," the vote ratio and the economic growth with the correlation witht he party in the White House removed, we see q correlation of 0.234. That is far less strong, but it is something.



There is also a possible explanation 6, the correlation is determined by a deliberate selection. (Take any long-enough sequence; then it will have a subsequence which exhibits any pattern one wishes.) This is not a case of deliberate selection; the terms reported are all the terms covered by the latest edition of The Economic Report of the President, and the Bush-appointed Council of Economic Advisors might be trusted to not select their reporting period to demonstrate this phenomenon. Also, longer series are available, although with more arithmetic involved. From Quarterly Data,

Republican Terms% Gain
1953 - 56 13.46%
57 - 60 10.90
69 - 72 12.38
73 - 76 10.62
81 - 84 12.63
85 - 88 15.68
89 - 92 8.81
2001 - 04 9.56
------
Mean 11.79
Standard Deviation 2.31

Democratic Terms% Gain
1949 - 52 21.01%
61 - 64 19.86
65 - 68 21.81
77 - 80 13.67
93 - 96 13.53
97 - 2000 17.87
------
Mean 17.96
Standard Deviation 3.63



This concludes the consideration of actual alternative explanations for the statistically significant difference between the growth of the economy during Democratic and Republican administrations. However, experience tells me that partisans suggest that one should ask one or another different question instead of the one that gives the results they don't like.


7) Why didn't I put in a year's lag?
That's fair. After all, The president isn't inaugurated until January of the first year that I'm considering. Then a budget is passed -- which had been submitted by the previous administration, but may be modified by the new one. This budget doesn't take effect until October of the first year, and can be assumed to have most of its consequences still later.
In fact, the results after a year's lag are only slightly less dramatic than the results previously given.:

Democratic Terms% Gain
62-'65 24.65%
66-'69 18.00
78--81 11.39
94-'97 15.54
98-2001 13.64
--- ---
Mean 16.65
Standard deviation 5.09%

Republican Terms% Gain
70-'73 15.30%
74-'77 9.42
82-' 85 14.40
86-'89 15.32
90-'93 7.90
2002-'05 12.54
--- ---
Mean 12.48
Standard deviation 3.17%


Still, no Republican term experiences growth as great as the average Democratic term, and only one Democratic term experiences growth as small as the average Republican term. The standard deviations are somewhat greater; which makes the claim that this is the true measure unlikely.

The data are available in finer detail from the St. Louis Federal Reserve. Quarterly Data. This enables us to calculate this table of the 4-year growth starting (and ending) in later quarters:

Republican TermsOffset in quarters
0 1234
1953 - 56 13.46% 12.61% 11.32% 10.70% 10.65%
57 - 60 10.90 9.81 9.67 9.63 11.25
69 - 72 12.38 13.25 14.19 14.70 15.30
73 - 76 10.62 9.44 8.93 9.19 9.42
81 - 84 12.63 13.40 13.59 13.57 14.40
85 - 88 15.68 15.90 15.89 15.75 15.32
89 - 92 8.81 8.54 8.32 7.93 7.90
2001 - 04 9.56 10.04 10.86 11.75 12.58
- - - - - -
Mean 11.79 11.63 11.59 11.65 12.10
Standard deviation 2.31 2.54 2.71 2.79 2.77

Democratic TermsOffset in quarters
01234
1949 - 52 21.01% 22.48% 24.78% 26.55% 27.22%
61 - 64 19.86 21.75 23.00 24.01 24.65
65 - 68 21.81 21.55 20.80 19.84 18.00
77 - 80 13.67 13.25 13.64 12.43 11.39
93 - 96 13.53 13.88 14.33 15.04 15.54
97 - 2000 17.87 17.12 16.04 14.79 13.64
- - - - - -
Mean 17.96 18.34 18.63 18.78 18.41
Standard deviation 3.63 4.16 4.91 5.64 6.28


(The Calculation is change from one year's RGDP to one four years later. The year's RGDP represents the average of the annualized RGDP for the four quarters of the year.)

A Republican partisan would prefer a four-quarter offset, just as a Democratic partisan would prefer one of two or three quarters. The standard deviation, however, increases monotonically. Still, the distinctions aren't all that great. The question of whether the party of the president influences the current economic growth has been determined; the question of when it exerts its influence is far less clear. For more on this question see Annual Results .



8) How about the previous administration?
It turns out that party of the previous administration has little effect compared with the party of the present administration. Compare the means of the following four groups:

Republicans following Democrats:...11.5%
Republicans following Republicans: 11.8%
Democrats following Democrats:..... 19.8%
Democrats following Republicans:... 15.7%

Since none of these group has more than three members, these results are not statistically significant.
.



9) How about an eight-year lag, the administration before the previous administration?
This is more plausible in one sense. After all, most Republican administrations were eight years after a Democratic administration and all the Democratic administrations we are considering were eight years after a Republican administration. How can we tell whether the lower growth during Republican administrations isn't the result of the mismanagement of the economy eight years previously?

One way is the Annual pattern during Republican administrations . It is much less plausible that a lag of eight years should influence the contrast in growth between the second and fourth years of an administration than that it should influence the growth over the entire period. But let's compare the two cases of Republican administrations eight years after Republican administrations (middle column), elections of 1980 and 1988, with those of Republicans eight years after Democrats (left column) and Democrats eight years after Republicans (right column).

Republican 8 years after Democrat Republican 8 years after Republican Democrat 8 years after Republican
Mean growth 12.82% 10.72% 17.35%
Growth in
Yr 2 less than in Yr 4 4/4 2/2 0/5
Yr 3 less than in Yr 4 4/4 2/2 3/5

Clearly, the middle column resembles the left-hand column closely, and the right-hand column very slightly. Treating the growth over the four-year period and the patterns of relative growth as separate issues, we can say that the likelihood of any single period's meeting either of the listed criteria simply by chance is 1/2 (ignoring the quite small likelihood of any of the stated inequalities of being met by an equality). Then the likelihood of two different periods' meeting both criteria is 1/16. That the growth across the period of two out of seven periods should be the two lowest by chance is even less likely -- 1/21.. Since both these chances would have to be true to hold the hypothesis of the causation from eight years previously, that hypothesis may be rejected as having less probability than three in one thousand.


10) What about Congress?
Congress passes the actual budget. Doesn't the makeup of Congress have some effect?
The partisan makeup of Congress had little detectable effect. From the beginning of the period studied here (1960) until 1994, the House of Representatives was controlled by Democrats. It has been controlled by Republicans since. The Senate has seen somewhat more change, resulting in a split Congress for a fifth of that time.

Not only does that record not give enough data points for a statistically significant analysis, the information available suggests that the economic significance is low. Of the two presidential terms entirely within the period of Republican Congressional control, one had the second lowest growth and the other the third highest growth of the entire set of eleven terms.

This concludes the consideration of the alternative explanations for differences in growth over presidential terms.


Years within a Republican term


11) Can the pattern of growth during the different years of a Republican presidential term be caused by chance?
This is highly unlikely. Analysis of variance yields the following tables:

Republican termsOffsets
Election Year +1 +2 +3 +4
1968 3.09% 0.17% 3.36% 5.29%
1972 5.76 -0.50 -0.19 5.33
1980 2.52 -1.94 4.52 7.19
1984 4.13 3.47 3.38 4.13
1988 3.54 1.88 -0.17 3.33
2000 0.75 1.60 2.70 4.22
- - - - -
Mean 3.30 0.78 2.27 4.91
Standard Deviation 1.67 1.92 1.98 1.35

The mean for all years is 2.81% growth per year.

Analysis of Variance Table

Source of variability Degrees of Freedom Sums of squares Mean sums of squares F
Treatment 3 54.5 18.17 5.93
Error 20 61.23 3.06

As the critical F value for 3 and 20 degrees of freedom and 1% probability is 4.9, this concentration of growth has less than 1% likelihood of occurring by chance. Since the F-test -- like the t-test -- has strict validity only if the underlying population has normal distribution, it might not be applicable here. A cruder test would be that the growth in neither the second nor the third year in any term is as great as the average of growth in the fourth years. Either one of these has only a 1/64 chance of occurring. Put together, they may be likelier than the product -- 1/4000 -- but much less likely than one in 64.



12) Isn't this behavior typical of both parties?
Why don't I look at the Democrats, too? I did. Growth under Democratic administrations follows a different pattern, and one with much less reliability.

Democratic termsOffsets
Election Year +1 +2 +3 +4
1960 2.33% 6.06% 4.38% 5.81%
1964 6.42 6.52 2.52 4.82
1976 4.62 5.57 3.16 -0.23
1992 2.67 4.02 2.50 3.70
1996 4.50 4.18 4.45 3.66
- - - - -
Mean 4.11 5.27 3.40 3.55
Standard Deviation 1.66 1.12 0.96 2.29

The mean for all years is 4.08% growth per year.

Analysis of Variance Table

Source of variability Degrees of Freedom Sums of squares Mean sums of squares F
Treatment 3 10.76 3.59 0.71
Error 16 40.74 2.55


Since the critical F value for 3 and 16 degrees of freedom and 10% probability is 2.462, there is better than one chance in ten that this could occur by pure chance. Also, the mean of the fourth year is actually lower than the mean of the entire set -- and, therefore, lower than the mean of the other years combined.