<blockquote>
<p>If yes, then how does this square with the general point that
causality/exclusion cannot generally be established with statistical
tests...</p>
</blockquote>
<p>It seems to me that &quot;[exogeneity of IV] cannot generally be established with statistical tests&quot; does not imply that it cannot be tested in specific cases. In this (very specific) context, the exogeneity claim rests on absence of serial correlation, which in principle can be tested as a null.</p>
<blockquote>
<p>Or, is it merely a diagnostic that may be used as a secondary
argument along with primarily qualitative arguments for exclusion?</p>
</blockquote>
<p>I would agree with you there. A non-rejection of the no-serial correlation null is by itself insufficient to establish exogeneity.</p>
<p>(If, hypothetically, the null hypothesis is presence of serial correlation, then yes, but such tests seems statistically unfeasible.)</p>

CC BY-SA 4.0
2020-10-08T04:23:22.067Z
Michael, many thanks for your reply.  I hope you would not mind me asking your level of expertise with this family of estimators (e.g., published research on these models, used them in published research, carefully read original papers), etc.  From your response, it seems that you have at the very least, carefully read the papers and thought about the underlying assumption.
Here is my rather rudimentary engagement with these models (as I only see them used very occasionally in my field): I read about them in texts by Cameron & Trivedi, Badi Baltagi (and Stata manuals).
Student
CC BY-SA 4.0
2020-10-08T04:37:43.097Z
Michael, additionally, may I ask if you have a recommendation for an accessible, succinct, and *accurate* reading on the AB test within this family of IV models.
Student
CC BY-SA 4.0
2020-10-08T03:00:37.043Z
2020-10-08T03:00:37.043Z
Michael
<p>I am an applied researcher and occasionally come across papers that have panel data and that use dynamic models with both a fixed-effects term and lagged DV (or multiple autoregressive terms):</p>
<p><span class="math-container">$y_{it} = \beta_0 + B_1X_{it}+\alpha y_{i(t-1)}+\delta D_{it} + \lambda_i + \gamma_t + \epsilon_{it}$</span></p>
<p>where <span class="math-container">$i$</span> denotes the panel unit and <span class="math-container">$t$</span> denotes the time dimension.  The parameter of interest is <span class="math-container">$\delta$</span> and <span class="math-container">$D_{it}$</span> denotes a binary treatment.  When the number of time periods is small, such a model cannot be estimated using OLS because of Nickell's bias.</p>
<p>One approach I have seen people use is to employ higher lags as instruments.  The identifying assumption is usually stated as no serial correlation between higher-order error terms.</p>
<p>Is it correct to take this assumption of no serial correlation as the exclusion restriction, i.e., the IV affects the final outcome only through the instrumented variable? If yes, then how does this square with the general point that causality/exclusion cannot generally be established with statistical tests such as the Arellano Bond Test, which statistically tests for the null hypothesis of &quot;no autocorrelation,&quot; and proceeds if there is a failure to reject the null for higher orders?</p>
<p>In Mostly Harmless Econometrics (book), Angrist &amp; Pischke write (p. 245):</p>
<blockquote>
<blockquote>
<p>The problem here is that the differenced residual, <span class="math-container">$\Delta \epsilon_{it}$</span>, is necessarily correlated with the lagged dependent variable, <span class="math-container">$\Delta Y_{i(t-1)}$</span>, because both are a function of <span class="math-container">$\epsilon_{i(t-1)}$</span>. Consequently, OLS estimates of (5.3.6) are not consistent for the parameters in (5.3.5), a problem first noted by Nickell (1981). This problem can be solved, though the solution requires strong assumptions. The easiest solution is to use <span class="math-container">$Y_{i(t-2)}$</span> as an instrument for <span class="math-container">$\Delta Y_{i(t-1)}$</span> in (5.3.6).10 But this requires that <span class="math-container">$Y_{i(t-2)}$</span> be uncorrelated with the differenced residuals, <span class="math-container">$\Delta \epsilon_{it}$</span>. This seems unlikely, since residuals are the part of earnings left over after accounting for covariates. Most people’s earnings are highly correlated from one year to the next, so that past earnings are also likely to be correlated with <span class="math-container">$\Delta \epsilon_{it}$</span>. If <span class="math-container">$\epsilon_{it}$</span> is serially correlated, there may be no consistent estimator for (5.3.6).</p>
</blockquote>
</blockquote>
<p>Angrist &amp; Pischke make no reference to the Arellano Bond Test to establish the validity/exclusion of the IV.  Instead, they make qualitative arguments as I generally see with IV models used for other types of data generation processes.</p>
<p>Does the Arellano Bond (AB) Test really establish exclusion/validity?  Or, is it merely a diagnostic that may be used as a secondary argument along with primarily qualitative arguments for exclusion.  If the AB test is merely a diagnostic, how should one evaluate research studies that assert identification on the basis of the AB test?  (i.e., the AB test fails to reject the null of &quot;no autocorrelation&quot; but qualitatively, one may have reasons to believe that there should be a correlation but the current sample does not show it).</p>
<p>NOTE: Slightly edited version cross-posted on <a href="https://stats.stackexchange.com/questions/490747/skepticism-about-the-claims-of-instrument-variable-validity-exclusion-through-a">https://stats.stackexchange.com/questions/490747/skepticism-about-the-claims-of-instrument-variable-validity-exclusion-through-a</a></p>

<econometrics><time-series><paneldata><instrumental-variable><causal-inference>
Skepticism about the claims of instrument variable validity/exclusion through a statistical test—the Arellano-Bond Test
Student
# Skepticism about the claims of instrument variable validity/exclusion through a statistical test—the Arellano-Bond Test

(Asked by: username_0 on 2020-10-06)

I am an applied researcher and occasionally come across papers that have panel data and that use dynamic models with both a fixed-effects term and lagged DV (or multiple autoregressive terms):

$y\_{it} = \beta\_0 + B\_1X\_{it}+\alpha y\_{i(t-1)}+\delta D\_{it} + \lambda\_i + \gamma\_t + \epsilon\_{it}$

where $i$ denotes the panel unit and $t$ denotes the time dimension. The parameter of interest is $\delta$ and $D\_{it}$ denotes a binary treatment. When the number of time periods is small, such a model cannot be estimated using OLS because of Nickell's bias.

One approach I have seen people use is to employ higher lags as instruments. The identifying assumption is usually stated as no serial correlation between higher-order error terms.

Is it correct to take this assumption of no serial correlation as the exclusion restriction, i.e., the IV affects the final outcome only through the instrumented variable? If yes, then how does this square with the general point that causality/exclusion cannot generally be established with statistical tests such as the Arellano Bond Test, which statistically tests for the null hypothesis of "no autocorrelation," and proceeds if there is a failure to reject the null for higher orders?

In Mostly Harmless Econometrics (book), Angrist & Pischke write (p. 245):

> > The problem here is that the differenced residual, $\Delta \epsilon\_{it}$, is necessarily correlated with the lagged dependent variable, $\Delta Y\_{i(t-1)}$, because both are a function of $\epsilon\_{i(t-1)}$. Consequently, OLS estimates of (5.3.6) are not consistent for the parameters in (5.3.5), a problem first noted by Nickell (1981). This problem can be solved, though the solution requires strong assumptions. The easiest solution is to use $Y\_{i(t-2)}$ as an instrument for $\Delta Y\_{i(t-1)}$ in (5.3.6).10 But this requires that $Y\_{i(t-2)}$ be uncorrelated with the differenced residuals, $\Delta \epsilon\_{it}$. This seems unlikely, since residuals are the part of earnings left over after accounting for covariates. Most people’s earnings are highly correlated from one year to the next, so that past earnings are also likely to be correlated with $\Delta \epsilon\_{it}$. If $\epsilon\_{it}$ is serially correlated, there may be no consistent estimator for (5.3.6).

Angrist & Pischke make no reference to the Arellano Bond Test to establish the validity/exclusion of the IV. Instead, they make qualitative arguments as I generally see with IV models used for other types of data generation processes.

Does the Arellano Bond (AB) Test really establish exclusion/validity? Or, is it merely a diagnostic that may be used as a secondary argument along with primarily qualitative arguments for exclusion. If the AB test is merely a diagnostic, how should one evaluate research studies that assert identification on the basis of the AB test? (i.e., the AB test fails to reject the null of "no autocorrelation" but qualitatively, one may have reasons to believe that there should be a correlation but the current sample does not show it).

NOTE: Slightly edited version cross-posted on <https://stats.stackexchange.com/questions/490747/skepticism-about-the-claims-of-instrument-variable-validity-exclusion-through-a>

**Tags:** econometrics, time-series, paneldata, instrumental-variable, causal-inference


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## 1 answers

### Answer by username_1 on 2020-10-08. Score: 2

> If yes, then how does this square with the general point that
> causality/exclusion cannot generally be established with statistical
> tests...

It seems to me that "[exogeneity of IV] cannot generally be established with statistical tests" does not imply that it cannot be tested in specific cases. In this (very specific) context, the exogeneity claim rests on absence of serial correlation, which in principle can be tested as a null.

> Or, is it merely a diagnostic that may be used as a secondary
> argument along with primarily qualitative arguments for exclusion?

I would agree with you there. A non-rejection of the no-serial correlation null is by itself insufficient to establish exogeneity.

(If, hypothetically, the null hypothesis is presence of serial correlation, then yes, but such tests seems statistically unfeasible.)

> **Comments:**
> **username_0**: username_1, many thanks for your reply.  I hope you would not mind me asking your level of expertise with this family of estimators (e.g., published research on these models, used them in published research, carefully read original papers), etc.  From your response, it seems that you have at the very least, carefully read the papers and thought about the underlying assumption. Here is my rather rudimentary engagement with these models (as I only see them used very occasionally in my field): I read about them in texts by Cameron & Trivedi, Badi Baltagi (and Stata manuals).  
> **username_0**: username_1, additionally, may I ask if you have a recommendation for an accessible, succinct, and *accurate* reading on the AB test within this family of IV models.  

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