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I'm reading an economics paper, where the author is using dummy variables to test for political effects on variables, such as GDP and unemployment. The model is a simple autoregressive model with nothing but a political effect dummy added.

Instead of having a 1 if left-wing party in power, 0 otherwise variable, the author has a variable defined as "takes the value of -1 during the X months of a left-wing administration, 1 during the X months of a right-wing administration and 0 otherwise.

My question is: How would you actually interpret the dummy's coefficient? The paper is very vague and talks about implications but does not refer to coefficients individually much. So if a coefficient on a lagged GDP regression for the dummy is, say -0.76, how would you interpret it?

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  • $\begingroup$ This could be a regression model with errors following an ARMA process or a so called ARIMAX model, e.g. $y_t = \phi y_{t-1} + z_t + \beta x_t$ where $x_t$ is the covariate and $z_t$ is white noise. The interpretation of $\beta$ depends on the details, so please clarify. See robjhyndman.com/hyndsight/arimax $\endgroup$ Aug 29 '16 at 16:35
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The political variable is defined for three categories: "left-wing", "right-wing", and "otherwise".

If the researcher wanted to be completely agnostic, and let the data speak the most, she would include a dummy for each category (or two categories if a constant is used). For example, the model could include a constant, a dummy equal to 1 if the government is "right-wing", and a dummy equal to 1 if the government is "otherwise". The base category, reflected by the constant, would be that the government is "left-wing". In this case, the value of the constant reflects the effect of a "left-wing" government on GDP, whereas each dummy's coefficient indicates the difference of the political ideology of the government on GDP compared with the base category, i.e. the "left-wing" government. This approach allows for political ideologies to have any effect on GDP. For example, it could be that the third category - "otherwise" - has exactly the same effect that a "left-wing" government. This is the case when it's coefficient is zero.

In the paper you mention, the author is assuming that the differential effect of political ideology on GDP between the three categories is the same. This is, that a ceteris paribus change in political ideology from "left-wing" to "otherwise", and a ceteris paribus change in political ideology from "otherwise" to "right-wing" has exactly the same effect on GDP. Even more, she is assuming that this effect has a certain order ("left-wing", "otherwise", "right-wing"). In effect, this assumption is obtained from adding restrictions on the coefficients in the agnostic model (more precisely, is assuming in the agnostic model that the coefficient in "right-wing" dummy is twice the coefficient in the "otherwise" dummy). As such, it is a more limited approach. From your question we don't whether that decision is based on a pre-test or not, but to me seems to be quite a restrictive approach, and probably unnecessary if enough degrees of freedom are available.

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  • $\begingroup$ One could accommodate both viewpoints by choice of coding. That is, by taking two contrasts -- first the contrast representing the linear restriction and second the remaining orthogonal one (which measures the difference between the middle category and the average of the other two, or in unbalanced designs perhaps a weighted version of that kind of comparison). If the first component explains most of the variation in the "agnostic" model it's close to linear, while if the second component is large, it is not. $\endgroup$
    – Glen_b
    Aug 30 '16 at 0:10

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