### Introducing and studying state-dependence

Many political scientists think about the possibility that outcomes are path-dependent, or that the power of X to change Y depends on a contextual factor Z. But in my reading of the literature, not very many (quantitative) political scientists are thinking about the possibility that path dependence changes the association between X and Y.

Jackie Demeritt and I have put together a couple of papers about this idea, which we call state-dependence. The concept is pretty simple: the marginal effect of $x_{t}$ on $y_{t}$ depends on the current state of the system, $y_{t-1}$. (It’s also true, as a consequence of Young’s theorem, that the relationship between $y_{t}$ and $y_{t-1}$ depends on $x_{t}$.)

I think that this idea is already pervasive in the thinking of social scientists, but not necessarily recognized as such and translated into an appropriate empirical model. For example, economists have known for years that the effect of monetary policy ($x_{t}$) on growth ($y_{t}$) depends on the current state of the economy ($y_{t-1}$): the Fed is really good at using interest rates to control inflation and growth during boom times, but terrible at using interest rates to decrease unemployment/increase growth  during recessions. The problem is so well-known that it comes with its own analogy: interest rates are like a string, good at “pulling” down an overheated economy but bad at “pushing” up a depressed one.

Our first paper works out the methodological implications of this idea, proposes an accompanying empirical model, verifies that this model works at detecting and modeling state-dependence, and then does a quick example application to presidential approval ratings and macroeconomic performance. In brief, we find that simply interacting the lagged dependent variable with the independent variable of interest works:

$y_{t} = \beta_{0} + \beta_{1}*y_{t-1} + \beta_{2}*x_{t} + \beta{3}*y_{t-1}*x_{t}$

Furthermore, the statistical significance of $\beta_{3}$ is a decent dispositive indicator of state dependence. The standard techniques for presenting marginal effects in interaction models are accurate and effective at presenting the nature and degree of state-dependence in the DGP. There are far more details in the paper, including the surprising fact that this model creates latent interaction among all the variables of the model, and I hope you’ll check it out.

The second paper applies our state-dependence model to the question of whether “naming and shaming” by international human rights groups (e.g., the UN Commission on Human Rights) actually hurts foreign aid receipts for the condemned state. Somewhat surprisingly, we find evidence that condemnation tends to reinforce pre-existing relationships in the international network. That is, weak ties that are mostly humanitarian and symbolic become weaker (aid from these relationships falls) and strong ties that are based on mutual political benefit become stronger (aid from these relationships stays the same or rises). Although obviously not much can be made out of our one finding (actually two findings, since we verify the relationship in two different data sets), that’s a pretty interesting statement about the role that morality plays in international politics.

I hope you’ll find some time to take a look at our papers and offer us helpful feedback!