Analysis of obligation-to-sales ratio

[JNing0]

There might be a problem in the analysis of obligation-to-sales ratio. We should use the same control group in each tercile so that we can compare results across terciles. Specifically, we divide the treatment group, i.e., the small businesses into three subgroups based on their obligation-to-sales ratio. The control group should consists of all large businesses. We run three diff-in-diff analysis. We use the same control group in all analysis and vary the treatment group across the bottom, middle, and top terciles. This way we will be able to compare the results across terciles.

We should also check the parallel-trend assumption between the control group and each treatment tercile group.

When running the ratio analysis for large businesses that receive contract financing, we should do the same thing. We should divide only the treatment group based on the obligation-to-sales ratio and use all small businesses as the control group.

[vibhuti6]

Hi Jie, thanks for sharing this. I understand the first point you make -- that we divide the treatment group (e.g., small businesses) into three categories based on terciles.

So my interpretation is that we run the following regression:

Delay = a + SmallBusiness₁+SmallBusiness₂+SmallBusiness₃+AfterQP + SmallBusiness₁ x AfterQP+ SmallBusiness₂ x AfterQP+ SmallBusiness₃ x AfterQP + e

where

• SmallBusiness_i = 1 if the firm is a small business and its ratio is in the i-th tercile
• AfterQP = 1 if the quarter is after quickpay was implemented

But I am not entirely sure what you mean by running three diff-in-diff analysis. Could you please clarify if I am misinterpreting something here? Thanks!

[JNing0]

Hi Vibhuti, I meant the DiD tercile analysis. My understanding is that you ran DiD analysis for the bottom, middle, and top terciles separately and each tercile has a different control group, correct? For example, in the DiD analysis for the bottom tercile, according to the table here, the treatment group consists of 5,237 small-business contracts and the control group consists of 2,927 large-business contracts.

This approach creates a problem if we want to compare the treatment effect across terciles because the control group changes. What I meant is that we pool all large businesses together and use it as the control group for different terciles of the small businesses. So we need to redo the DiD analysis for the bottom, middle, and top terciles to be able to interpret the results.

[vibhuti6]

Hi Jie, thanks for clarifying and sorry for the slow response.

Yes, the current analysis compares small and large businesses within the same tercile.

Just to confirm, based on your suggestion, we should run the following: Delay = a + SmallBusiness + AfterQP + SmallBusiness x AfterQP + e for three subsamples. Each subsample i contains small businesses in the i-th tercile, and all large businesses. Is this correct?

As you point out, we should also check for the parallel trends in this case because the firms (and, by extension, the contracts they hold) could be quite different in these subsamples.

[JNing0]

Yes, this is correct. And we will do the same things in the tercile analysis on large businesses who receive contract financing. The control group is all small business contracts and we vary the treatment group across terciles of large businesses with financing. We also need to check the parallel-trend assumption. Because we use a fixed control group, the parallel-trend assumption requires that all terciles of the treatment group have the same trend as the control group before treatment. So they only respond to the treatment differently.

[vibhuti6]

Thanks, Jie -- I will run this analysis and get back to you.

[vibhuti6]

Hi Jie, I have updated the results pages (here and here) for this analysis.

I have also added two wiki pages to plot parallel trends for different subsamples: here and here. I will continue to update these pages further. Thanks.