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 growth | Standard 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 Terms | Offset in quarters | ||||
---|---|---|---|---|---|

0 | 1 | 2 | 3 | 4 | |

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 Terms | Offset in quarters | ||||
---|---|---|---|---|---|

0 | 1 | 2 | 3 | 4 | |

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.

**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 terms | Offsets | |||
---|---|---|---|---|

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 terms | Offsets | |||
---|---|---|---|---|

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.