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Legislative Productivity and Presidential Approval
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effects, also known as ‘macro’ effects or ‘level 2’ effects, are the effects of national
variables on the entire population. There are two ways in which national variables can
impact approval, which is measured in individuals. A ‘main effect’ is an effect that
impacts everyone equally. An interactive effect (or a ‘cross-level interaction’) is one that
has different effects on different people. In the tables presented here, I have separated
out the individual effects, main effects and interactive effects. These are actually all part
of the same models; they have been broken up to simplify presentation of the results as
much as possible.
Table 3 presents the aggregate-level coefficients for the variables of interest.
16,17
Readers should note that these are the main effects coefficients of models that include
interactive effects. As many of these interactions are statistically significant, we must use
the main effects estimates from these models, to avoid omitted variable bias, which can
16
Jarvis (2003) presents an in-depth examination of the relationships among the measures of ‘productivity.’
Not only does multicollinearity present a problem, but the few effective degrees of freedom make hypothesis testing with the saturated models difficult. Furthermore, pairs of variables (Bills Passed and Landmark Legislation, Issues Passed and Gridlock) are, in fact, necessarily related, as they are constructed from the same measures. For instance, inclusion of both Issues Passed and Gridlock in a model is identical to including the (here excluded) Issues Failed measure instead of either variable. To avoid the confusion that this entails, these highly related measures were only included together in a fully saturated model. In general, we can think of the saturated model as the strictest possible test of statistical significance, as an estimated coefficient must be nearly 3 times as large as the estimated standard error of the coefficient to be considered statistically significant at the p <.05 level, as compared to the ‘rule of thumb’ of 2 for more degrees of freedom. Seeking to both find robust results and results that are meaningful (for what does it mean to control for Issues Passed in estimating the effect of Bills Passed, which must deal with at least one issue?), I have chosen to discuss only these unsaturated models. The results of more saturated models are available upon request, and I have included one of the simpler permutations in the tables in this paper as an example (Model 5).
17
One of the measures of productivity discussed in Jarvis (2003) is Bills Failed, Edwards, Barrett and
Peake’s (1997) measure of the number of bills that met Mayhew’s criteria for inclusion in his original dataset but failed to pass. This measure was not included here because it is only available until 1996, and the degrees of freedom lost in this case are precious. However, one interesting note is that the coefficient interaction of Bills Failed with education is generally negative and significant, indicating that more highly educated people are more aware of what has not been done and are unhappy about it than are less educated people (see ‘cross-level interactions’).
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| | Authors: Jarvis, Matthew. |
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effects, also known as ‘macro’ effects or ‘level 2’ effects, are the effects of national
variables on the entire population. There are two ways in which national variables can
impact approval, which is measured in individuals. A ‘main effect’ is an effect that
impacts everyone equally. An interactive effect (or a ‘cross-level interaction’) is one that
has different effects on different people. In the tables presented here, I have separated
out the individual effects, main effects and interactive effects. These are actually all part
of the same models; they have been broken up to simplify presentation of the results as
much as possible.
Readers should note that these are the main effects coefficients of models that include
interactive effects. As many of these interactions are statistically significant, we must use
the main effects estimates from these models, to avoid omitted variable bias, which can
16
Jarvis (2003) presents an in-depth examination of the relationships among the measures of ‘productivity.’
Not only does multicollinearity present a problem, but the few effective degrees of freedom make
hypothesis testing with the saturated models difficult. Furthermore, pairs of variables (Bills Passed and
Landmark Legislation, Issues Passed and Gridlock) are, in fact, necessarily related, as they are constructed
from the same measures. For instance, inclusion of both Issues Passed and Gridlock in a model is identical
to including the (here excluded) Issues Failed measure instead of either variable. To avoid the confusion
that this entails, these highly related measures were only included together in a fully saturated model. In
general, we can think of the saturated model as the strictest possible test of statistical significance, as an
estimated coefficient must be nearly 3 times as large as the estimated standard error of the coefficient to be
considered statistically significant at the p <.05 level, as compared to the ‘rule of thumb’ of 2 for more
degrees of freedom. Seeking to both find robust results and results that are meaningful (for what does it
mean to control for Issues Passed in estimating the effect of Bills Passed, which must deal with at least one
issue?), I have chosen to discuss only these unsaturated models. The results of more saturated models are
available upon request, and I have included one of the simpler permutations in the tables in this paper as an
example (Model 5).
17
One of the measures of productivity discussed in Jarvis (2003) is Bills Failed, Edwards, Barrett and
Peake’s (1997) measure of the number of bills that met Mayhew’s criteria for inclusion in his original
dataset but failed to pass. This measure was not included here because it is only available until 1996, and
the degrees of freedom lost in this case are precious. However, one interesting note is that the coefficient
interaction of Bills Failed with education is generally negative and significant, indicating that more highly
educated people are more aware of what has not been done and are unhappy about it than are less educated
people (see ‘cross-level interactions’).
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