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I have a certain law as my (non-binary) treatment variable (range: 0-2) at the state level which takes on different values based on whether it prohibits altogether (2), limits (1), or allows the unlimited (0) flow of money to political candidates as campaign contributions.

And there are many such laws, for example, contributions from individuals to political candidates (CFIC), contributions from PACs to political candidates (CFPC), etc., that I am using to delineate the effect of these laws on my outcome variable.

In a simple regression framework, I can use each of these laws individually or by adding them up (e.g., CFIC + CFPC -> taking on values from 0 to 4) as my independent variable. This much is straightforward.

The tricky part begins when my treatment variable (non-binary standalone laws or a sum of laws) have the following Generalized DiD kind of a setting:

  1. Late and early adopters i.e. staggered adoption
  2. Treatment status switches between 0 1 2 for some states - from 0 to 2 or 1 to 2 or 2 to 1 or 1 to 0, etc. (analogous to changing of treatment status from 0 to 1 in one year and then from 1 to 0 after some years)
  3. No specific control groups/states (except for only 2 out of 50 US states)

A similar application of DiD with varying treatment intensity or non-binary treatment can be found here: Difference in Differences Model Specification with Year-Quarter Effects (treatment non-binary)

In summary, I need help with applying generalized DiD in a non-binary treatment setting.

Thank you in advance.

Table 1: enter image description here

Table 2: enter image description here

Table 3: enter image description here

Table 4: enter image description here

Ahmed Chaudhry
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  • Welcome. So you're investigating *more than one* law/policy, each with its own intensity structure? – Thomas Bilach Apr 07 '21 at 00:27
  • I realized my previous question wasn't entirely clear. Suppose you have a policy introduced in a subset of U.S. states and not others. The treatment variable may take on values from 0–2, where each step up the ladder is a different level of intensity; I assume 0 represents the *absence* of campaign contributions. But in your setting, is each shift in intensity the result of the same law or do some states enact completely new laws which affect contributions? If you could provide further clarification that would be helpful. – Thomas Bilach Apr 07 '21 at 02:01
  • There are many different kinds of laws on campaign contribution across the US states which regulate the flow of contributions from donors to political candidates. Donors can be categorized as individuals, labor unions, corporations, and political actions committees (PACS) (there are other donor categories as well but for my analysis, these are most relevant). So for each of the donors, a different law exists. For example, consider these laws: - contributions from individuals to candidates - contributions from labor unions to candidates - contributions from PACs to candidates – Ahmed Chaudhry Apr 08 '21 at 02:24
  • For example, consider these laws: - contributions from individuals to candidates - contributions from labor unions to candidates - contributions from PACs to candidates - contributions from corporation to candidates Different states may have a subset of these laws in place or all of them enacted. – Ahmed Chaudhry Apr 08 '21 at 02:32
  • As for range is concerned, I mistyped in earlier in my post and now I have corrected it. The correct form is that if a state allows unlimited contribution from a particular donor to candidates then it is coded as 0. If it limits the amount to some $ figure, then it takes the value of 1, and if a state prohibits contributions from a particular donor then I have a value of 0. – Ahmed Chaudhry Apr 08 '21 at 02:37
  • So higher values indicate stricter laws. Each of these individual laws affects my outcome variable. But also, they may have some aggregated effect too. I can do a principal component analysis and construct an index to measure the aggregate effects, this is one way of doing it. But I have seen quite a few authors just simply adding up the laws to capture the aggregated effect, e.g., contributions from PACs to candidates + contributions from corporations to candidates + ... + .. And again higher values indicate the presence of a stricter set of laws in a Sate. – Ahmed Chaudhry Apr 08 '21 at 02:43
  • Ideally, what I would want to do is to model a generalized DiD for each of the laws separately, and then, if possible, do a robustness check with the aggregated additive index. I hope this clears up the situation. Thank you for responding! – Ahmed Chaudhry Apr 08 '21 at 02:47
  • So let's look at one law/policy at a time. Suppose we have a law/policy shock within a subset of U.S. states affecting *individual* donors only. In New Jersey, for example, they may completely prohibit contributions. For this one law/policy in New Jersey, may restrictions change over time? – Thomas Bilach Apr 08 '21 at 16:36
  • Yes, that is how it works. I have added three tables in my original post for reference purposes. They show the distribution of different values of specific laws with respect to the US states. – Ahmed Chaudhry Apr 09 '21 at 17:33
  • So in the pre-period, aren’t states starting at different levels of intensity? Is it possible to see one treated state and one untreated state? Put differently, can I see states’ observations *over time* before and after one law goes into effect? – Thomas Bilach Apr 09 '21 at 17:47
  • Yes, some states start at different levels of intensity (Another table - Table 4 - is added to the original post above). And there are a few states which actually start at a higher intensity and then lowers the intensity over the sample time, and then raise the intensity again, in other words, these states opt-out and then opt-in the laws. As for seeing the observation over time before and after the law goes into effect, the general answer is Yes, there are a significant number of states for which we can observe this. – Ahmed Chaudhry Apr 10 '21 at 00:40

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