<p>The authors of this paper (<a href="http://andrewleigh.org/pdf/GunBuyback_Panel.pdf" rel="nofollow noreferrer">http://andrewleigh.org/pdf/GunBuyback_Panel.pdf</a>) appear to be essentially regressing the change in the death rate to the change in guns from a gun buy back in Australia, at the state level: $\Delta$death rate involving guns= $\Delta$guns + $\epsilon$</p>

<p>Specifically, they state on page 16 of the pdf:</p>

<blockquote>
  <p>In this paper, we ask whether firearm deaths dropped proportionately
  more in states where relatively more firearms were bought back. If
  the gun buyback itself was effective in reducing firearm-related
  deaths, then this would imply that states where more firearms were
  removed from the population should have seen a greater reduction in
  firearm death rates than the Australian average</p>
</blockquote>

<p>On page 17 (of the pdf) it states the following:</p>

<blockquote>
  <p>For the purposes of our empirical strategy, what matters is that differences in buyback rates were not correlated with other factors that
  might have affected gun deaths. In particular, we are concerned
  about two potential confounders. First, if differences in buyback
  rates were driven by pre-existing gun ownership rates and if the
  relationship between gun ownership and gun deaths is non-linear, this
  could lead to a spurious correlation. However, although a non-linear
  relationship is theoretically plausible, we have been unable to locate
  any studies supporting such a theory.</p>
</blockquote>

<p>I <em>think</em> the concern that the differences in buy back rates were driven by pre-existing gun ownership is because if this was the case (and given that we assume that pre-existing gun ownership could also impact the change in deaths) we would have confounding.  <strong>Is this correct?</strong></p>

<p><strong>But I don't understand the concern that the relationship is non-linear?</strong></p>

<p>Can anyone explain the econometric issues?</p>

<p>ADD 1: </p>

<p>I was also interested in page 17 where this is stated. I wanted to link what I read in a paper with the textbook econometrics. <strong>Is this an example of the authors arguing that if they find drivers of why the gun buy back rates differ between states, that is not the death rates, that this is evidence that there is no reverse causation?</strong></p>

<blockquote>
  <p>Second, our empirical strategy relies on the assumption that the
  state- level gun buyback rate is exogenous with respect to firearms
  death rates. It is thus important to consider the various factors that
  might explain why the buyback rate varied across states.</p>
</blockquote>

<p>ADD 2:</p>

<p>The final model used is on page 26 of the pdf. I am a little confused by it but what I think they are doing is the following (I note there is data and stata code <a href="https://dataverse.harvard.edu/dataset.xhtml?persistentId=hdl:1902.1/21943" rel="nofollow noreferrer">HERE</a> but I dont know how to read stata): I believe the change in guns (gun buy back) here is the difference in average guns pre and post 1997 and thus is a constant value for a given state, repeated for each records for a state in the data (each state as multiple records, one for each year).</p>

<p><a href="https://i.sstatic.net/EIIXr.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/EIIXr.png" alt="enter image description here"></a></p>

CC BY-SA 3.0
2015-10-05T15:50:25.703Z
Clarifications : 1) Is the data cross-sectional or panel? 2) Is the core equation formed with or without a constant term? 3) What are the units of measurement for "change in death rate" and "change in guns"? Are we talking levels, percentages, is the specification in logarithms?
Alecos Papadopoulos
CC BY-SA 3.0
2015-10-05T16:11:40.717Z
Cross posting is not encouraged in SE. It would perhaps be better to choose one among the two, and if you don't get what you are looking for, ask for your question to be migrated to the other (migration is done my the moderators).
Alecos Papadopoulos
CC BY-SA 3.0
2015-10-06T13:19:35.130Z
Alecos, I deleted the cross validated question. I also added to this question describing what I think the model is....
B_Miner
CC BY-SA 3.0
2015-10-07T16:55:57.110Z
The more I read the paper the more confused I become. I will respond to your question, but it may take a few days.
Alecos Papadopoulos
CC BY-SA 3.0
2015-10-07T20:36:11.853Z
Thanks Alecos I appreciate your help very much! I want to start reading papers and learning more about econometrics. Perhaps I picked a confusing one to start.
B_Miner
CC BY-SA 3.0
2015-10-07T21:23:41.943Z
Start with papers published in empirical econometrics journals.
Alecos Papadopoulos
CC BY-SA 3.0
2015-10-08T00:13:31.063Z
OK. I am def interested in this one still though
B_Miner
<econometrics><regression>
Explanation of paper's econometric assumptions
B_Miner
# Explanation of paper's econometric assumptions

(Asked by: username_0 on 2015-10-05)

The authors of this paper (<http://andrewleigh.org/pdf/GunBuyback_Panel.pdf>) appear to be essentially regressing the change in the death rate to the change in guns from a gun buy back in Australia, at the state level: $\Delta$death rate involving guns= $\Delta$guns + $\epsilon$

Specifically, they state on page 16 of the pdf:

> In this paper, we ask whether firearm deaths dropped proportionately
> more in states where relatively more firearms were bought back. If
> the gun buyback itself was effective in reducing firearm-related
> deaths, then this would imply that states where more firearms were
> removed from the population should have seen a greater reduction in
> firearm death rates than the Australian average

On page 17 (of the pdf) it states the following:

> For the purposes of our empirical strategy, what matters is that differences in buyback rates were not correlated with other factors that
> might have affected gun deaths. In particular, we are concerned
> about two potential confounders. First, if differences in buyback
> rates were driven by pre-existing gun ownership rates and if the
> relationship between gun ownership and gun deaths is non-linear, this
> could lead to a spurious correlation. However, although a non-linear
> relationship is theoretically plausible, we have been unable to locate
> any studies supporting such a theory.

I *think* the concern that the differences in buy back rates were driven by pre-existing gun ownership is because if this was the case (and given that we assume that pre-existing gun ownership could also impact the change in deaths) we would have confounding. **Is this correct?**

**But I don't understand the concern that the relationship is non-linear?**

Can anyone explain the econometric issues?

ADD 1:

I was also interested in page 17 where this is stated. I wanted to link what I read in a paper with the textbook econometrics. **Is this an example of the authors arguing that if they find drivers of why the gun buy back rates differ between states, that is not the death rates, that this is evidence that there is no reverse causation?**

> Second, our empirical strategy relies on the assumption that the
> state- level gun buyback rate is exogenous with respect to firearms
> death rates. It is thus important to consider the various factors that
> might explain why the buyback rate varied across states.

ADD 2:

The final model used is on page 26 of the pdf. I am a little confused by it but what I think they are doing is the following (I note there is data and stata code [HERE](https://dataverse.harvard.edu/dataset.xhtml?persistentId=hdl:1902.1/21943) but I dont know how to read stata): I believe the change in guns (gun buy back) here is the difference in average guns pre and post 1997 and thus is a constant value for a given state, repeated for each records for a state in the data (each state as multiple records, one for each year).

[![enter image description here](https://i.sstatic.net/EIIXr.png)](https://i.sstatic.net/EIIXr.png)

**Tags:** econometrics, regression

> **Comments:**
> **username_1**: Clarifications : 1) Is the data cross-sectional or panel? 2) Is the core equation formed with or without a constant term? 3) What are the units of measurement for "change in death rate" and "change in guns"? Are we talking levels, percentages, is the specification in logarithms?  
> **username_1**: Cross posting is not encouraged in SE. It would perhaps be better to choose one among the two, and if you don't get what you are looking for, ask for your question to be migrated to the other (migration is done my the moderators).  
> **username_0**: Alecos, I deleted the cross validated question. I also added to this question describing what I think the model is....  
> **username_1**: The more I read the paper the more confused I become. I will respond to your question, but it may take a few days.  
> **username_0**: Thanks Alecos I appreciate your help very much! I want to start reading papers and learning more about econometrics. Perhaps I picked a confusing one to start.  
> **username_1**: Start with papers published in empirical econometrics journals.  
> **username_0**: OK. I am def interested in this one still though  

---

## 0 answers

