Using \"Higher-Level\" Variables as Instruments — The Exogeneity Dilemma of Industry-Mean IVs and Strategies for Justification

I. Introduction: Your Reviewer Says "This IV Is Not Clean Enough"—But You See It Used in AER

You are studying the effect of corporate digital transformation on productivity. Digitalization is endogenous—high-productivity firms may be more inclined to invest in digitalization, and you cannot tell whether digitalization drives productivity or productivity drives digitalization.

You have found an ingenious instrumental variable: the average digitalization level of other firms in the same industry and same year—the industry mean (excluding the firm itself). The logic is:

• Relevance: Firms in the same industry face similar technological trends and competitive pressures—the industry's overall digitalization level is clearly highly correlated with the firm's own digitalization level. The industry mean exerts a push on individual firms—"if your peers are all digitalizing, the cost of not digitalizing rises."
• Exogeneity: The industry's overall digitalization level (after excluding the firm itself)—should not directly affect the firm's productivity, except through the channel of pushing the firm to digitalize.

You run the first stage—F = 124.6, almost perfect. You think this instrumental variable is excellent—strong relevance, data availability, and clear intuitive logic.

Then the reviewer writes the following comment:

"The author uses 'the average digitalization level of other firms in the same industry' as an instrumental variable. However, firms in the same industry share market demand, supply chain structures, policy environments, and technological changes—these industry-level common factors simultaneously affect both the industry-average digitalization and firm productivity. Even after excluding the firm itself, the industry mean may still directly affect firm productivity through channels other than digitalization—such as industry competitive dynamics, demand spillovers, and supply chain coordination. This is a classic exclusion restriction problem. The author needs to provide more thorough justification to address this concern."

You stare at this comment. You know that AER, JPE, and QJE have published numerous papers using similar strategies—industry-mean IVs, Bartik IVs, shift-share IVs—all using higher-level aggregate variables as instruments. Why can those papers get published, but when it comes to yours, the reviewer says "not clean enough"?

Because what you lack is not a new instrumental variable—but a complete framework for arguing "why the industry mean is exogenous in this specific research context."

Core message: When using higher-level variables (industry means, regional means, group means) as instrumental variables, the exogeneity argument faces a distinctive structural challenge—industry-level common factors may simultaneously affect the industry mean (IV) and the individual outcome (Y), such that the exclusion restriction cannot be automatically defended by the "exclusivity" of the data structure itself. In other words, you cannot simply claim that the IV is exogenous merely because "I used the industry mean and excluded the firm itself"—you need to additionally argue why those common factors have been controlled in your specification, will not generate bias, or even if they exist, their direction of influence does not threaten your conclusions. There are four core strategies for this argument: (1) decompose the sources of variation in the industry mean—distinguishing "good variation" (exogenous industry trends) from "bad variation" (industry demand shocks)—and use industry × year fixed effects to absorb common shocks; (2) exploit differential exposure of individuals to the industry mean rather than the industry mean itself—the core of the Bartik logic is to redefine the instrument as "initial individual characteristics × industry common trends" rather than a simple industry mean; (3) add targeted falsification tests on top of the industry-mean IV—showing that in subsamples where the X→Y path does not exist, the reduced-form effect of the IV on Y is insignificant; (4) control for industry-level confounders and demonstrate the robustness of the conclusions. Choosing a higher-level variable as an IV is essentially exploiting "group push"—but you need not only that the push is strong enough (relevance), but also that the push does not come from those common factors that would also directly push Y (exogeneity). Justifying the latter requires not more data—but more careful decomposition of variation sources and more honest falsification designs.

II. Why Are "Higher-Level IVs" Easily Questioned?—A Structural Explanation

2.1 What Counts as a "Higher-Level IV"?

In empirical work, four constructions are most common:

Their common feature: the variation in the IV comes from a "higher-level aggregation"—industry, region, or group—and identification rests on the assumption that "this aggregate variation does not affect the individual's Y (except through X)."

2.2 The Reviewer's Concern Is Not "Nitpicking"—It Is a Structural Problem

The industry-mean IV faces a structural dilemma that can be precisely stated with two equations:

Structural equation: $Y_{it} = \beta_0 + \beta_1 X_{it} + \mu_{jt} + \varepsilon_{it}$

First stage: $X_{it} = \pi_0 + \pi_1 \bar{X}_{-i,j,t} + \nu_{jt} + u_{it}$

where $\mu_{jt}$ and $\nu_{jt}$ are industry × year level common factors affecting Y and X, respectively—such as industry demand shocks, industry technological changes, and industry policy changes.

What the reviewer worries about can be precisely written as a "bad reduced form":

If the exogeneity of the IV holds, then $\bar{X}_{-i,j,t}$ affects Y only through the X channel. But if $\mu_{jt}$ exists in the Y equation (directly affecting Y) and is correlated with $\bar{X}_{-i,j,t}$ (because the industry mean naturally contains industry common factors)—then even if you exclude the firm itself, the reduced-form effect of the IV on Y contains a non-X channel.

In plain language: Industry demand rises → all firms in the industry generally increase digitalization investment → the industry mean (IV) rises. Simultaneously, industry demand rises → productivity of all firms generally rises (direct effect, not through digitalization). The association between your IV and Y is contaminated by the direct effect of the common driver "rising industry demand"—rather than a pure "IV → X → Y" causal chain.

2.3 How Does This Dilemma Differ from Classical IV?

In classical IV—such as Angrist-Krueger's "quarter of birth"—the correlation between the source of variation in Z (quarter of birth) and unobservable factors in Y (ability, family background) is logically implausible—it is "institutional design" that protects exogeneity.

In the industry-mean IV—the source of variation in Z (industry common factors) and unobservable factors in Y (part of the industry common factors) naturally overlap. Exogeneity is not protected by institutions—it is "hoped to hold." And this is precisely what the reviewer worries about: your exogeneity argument cannot be "I excluded it"—it must be "I controlled for it" or "even if it exists, it is not a problem."

III. Justification Strategy 1: Decompose Variation Sources—Distinguishing "Good Variation" from "Bad Variation"

3.1 The Industry Mean Contains Two Types of Variation

The same industry-mean IV contains two fundamentally different types of variation:

• "Good variation"—exogenous industry technology/policy trends: such as nationwide declines in digital technology costs, IT infrastructure diffusion, and rising internet penetration—these factors push digitalization across the industry, but their direct effects on firm productivity, after controlling for time trends, are weak, or at least their effects can be absorbed by year fixed effects.

• "Bad variation"—industry-level demand/supply shocks: such as the expansion of market demand in a specific industry ("new energy vehicles exploded this year")—this shock simultaneously (a) pushes digitalization investment by firms in the industry (relevance holds) and (b) directly raises firm productivity (exogeneity is violated—because the demand shock enters the Y equation directly).

Justification strategy: not to claim that "there is no bad variation in the industry mean"—but to argue that (a) the bad variation has been controlled in your model; or (b) the bad variation and good variation can be distinguished in direction; or (c) the magnitude of the bad variation is insufficient to change your conclusions.

3.2 Adding Industry × Year Fixed Effects—Absorbing "Bad Variation"

The most direct approach is to add industry × year fixed effects ($\lambda_{jt}$) to the regression:

$Y_{it} = \beta_0 + \beta_1 X_{it} + \lambda_{jt} + \text{controls} + \varepsilon_{it}$

$\lambda_{jt}$ absorbs any factor common to all firms in each industry within each year—including industry demand shocks, industry technological changes, and industry policies—whether observed or unobserved.

After adding $\lambda_{jt}$, where does your identifying variation come from?

• Not from "industry A's digitalization level in year t vs. industry B's digitalization level in year t" (absorbed by $\lambda_{jt}$).
• Rather, from differences in digitalization across firms within the same industry and same year—why, within the same industry and same year, do some firms digitalize more and others less? Your IV needs to explain precisely this "within-industry, within-year" variation.

But here a new tension arises: if you add industry × year FE, the "industry-level common component" of the industry-mean IV's variation has already been absorbed—what remains is the variation in "the mean of other firms within the same industry and year, after excluding the own firm." This remaining variation may still be correlated with the firm's market position, competitive strategy, etc.—factors that may also directly affect Y (output). The exogeneity problem shifts to "whether the within-industry, within-year differential mean still contains non-X channels of influence"—but it is at least more defensible than the original problem, because the most obvious "bad variation" (industry demand shocks) has already been absorbed.

Practical advice: explicitly show in the paper how the first stage and reduced form change with and without $\lambda_{jt}$—demonstrating that after absorbing industry common factors, the IV still has sufficient relevance, and that the direction and magnitude of changes in the reduced-form coefficient are consistent with the theoretical expectation of "removing the direct effect of industry demand shocks." If the first-stage F drops substantially after adding $\lambda_{jt}$ (from 100+ to 5–10), it indicates that most of the IV's variation comes from industry-level common variation—which is precisely the "bad variation" the reviewer worries about. You need to accept this diagnosis and discuss it candidly in the paper.

3.3 Adding Industry-Specific Time Trends

A weaker but more parsimonious alternative to industry × year FE:

$Y_{it} = \beta_0 + \beta_1 X_{it} + \gamma_j \cdot t + \delta_t + \text{controls} + \varepsilon_{it}$

This allows each industry to have its own linear (or nonlinear) time trend. It absorbs slowly evolving demand and technological changes within industries—but not discrete shocks in each year. Suitable when T is small and the number of industries is large.

IV. Justification Strategy 2: From "Industry Mean" to "Differential Exposure"—The Logic of Bartik IV

4.1 The Core Idea of Bartik IV

Bartik's (1991) instrumental variable—the "shift-share" IV—is a refined improvement over the industry-mean IV. Its construction is:

$Z_{i,t} = \sum_{s} \omega_{i,s,0} \cdot G_{s,t}$

where $\omega_{i,s,0}$ is individual i's share in industry s at a base period (typically well before the sample period), and $G_{s,t}$ is the national-level growth rate (or aggregate change) of industry s at time t.

Example: city i's employment shares by industry in 1980 ($\omega_{i,s,1980}$) × national employment growth rates by industry from 1980–2020 ($G_{s,t}$) → city i's "predicted" employment growth at time t → this "predicted" employment growth is used as an IV for the city's actual employment growth.

4.2 Why Is Bartik IV "Cleaner" Than the Industry-Mean IV?

The key difference between the industry mean and Bartik IV lies in the source of variation:

• Industry-mean IV: $\bar{X}_{-i,j,t}$—variation comes from contemporaneous industry-level factors (good and bad mixed together).
• Bartik IV: $\sum_s \omega_{i,s,0} \cdot G_{s,t}$—variation comes from the interaction of base-period shares ($\omega_{i,s,0}$, fixed before the sample period) and national trends ($G_{s,t}$, at the national rather than industry level).

Bartik IV excludes "bad variation" (contemporaneous industry demand/supply shocks) from the IV—because $G_{s,t}$ is a national trend, not an industry-specific trend. And $\omega_{i,s,0}$ is from the base period—unaffected by industry shocks during the sample period. The core of the exogeneity argument shifts to:

• Is $G_{s,t}$ (national trend) exogenous to the individual's Y?—National-level macro trends can typically be absorbed by year FE.
• Is $\omega_{i,s,0}$ (base-period share) exogenous?—The base-period share itself may be correlated with base-period Y, but it is from the base period—it does not reflect sample-period shocks.

This is why Bartik IV is more popular in empirical work than a simple industry-mean IV—not because it necessarily has stronger relevance (in fact, the first-stage F of Bartik IV is usually lower than that of industry-mean IV), but because its variation source is structurally cleaner—"bad variation" is more thoroughly excluded.

But Bartik IV has its own challenges: Goldsmith-Pinkham and Sorkin (2024) systematically show that identification in Bartik IV is essentially equivalent to GMM with base-period shares as instruments—the exogeneity argument ultimately depends on the assumption that "base-period shares are exogenous" (similar to the exclusion restriction of the industry mean). So Bartik does not circumvent the problem of the industry-mean IV—it shifts the problem from "contemporaneous industry shocks" to "initial conditions of base-period shares," but the need for exogeneity does not disappear—it is merely pushed to an earlier point in time.

4.3 What to Learn from the Bartik Logic—Constructing "Cleaner" Higher-Level IVs

Whether or not you use the specific Bartik form, the methodological lesson from Bartik is:

• Use "base-period individual characteristics that no longer change within the sample" as exposure weights to industry trends—rather than contemporaneous exposure weights that may be endogenous to Y.
• Use "higher-level common trends" (national, macroeconomic) rather than "the industry's own contemporaneous trend"—push the source of "bad variation" to a more macro level, where it is more easily absorbed by year FE.

V. Justification Strategy 3: Falsification Tests and "Unaffected Subsamples"

5.1 Falsification Tests Specific to Industry-Mean IVs

The core logic of falsification tests is: find a subsample in which the X→Y path is theoretically severed or naturally nonexistent—if the IV still predicts Y in this subsample → the IV affects Y through channels other than X → exogeneity is questionable. If the IV is significantly weakened or disappears in this subsample → this supports exogeneity.

For industry-mean IVs, the following falsification tests are particularly useful:

Test 1: Test in firms where "digitalization (X) is unlikely to affect productivity (Y)"

Some firms' productivity may be determined more by non-digitalization factors—such as natural-resource-dependent firms (mining, agriculture), highly regulated utilities, etc. In these firms, the theoretical channel from digitalization to productivity is weak or even nonexistent. In this subsample, if the IV (industry mean) still significantly predicts productivity → the IV may affect productivity through channels other than digitalization (such as industry demand shocks) → exogeneity is questionable.

Test 2: Using "lagged values of the industry mean" as a Placebo IV

If the industry-mean IV affects Y (contemporaneous productivity) only by pushing the firm's own X (contemporaneous digitalization), then the future value of the industry mean (period t+1), after controlling for the contemporaneous industry mean, should have no additional explanatory power for contemporaneous Y. Why? Because the future industry mean cannot travel back in time to push past X. If the future industry mean does predict contemporaneous Y → the industry mean contains a persistent confounding factor that directly acts on Y (such as the industry's long-run demand trend), rather than operating only through the X channel.

Specifically: $Y_{it} = \beta_0 + \beta_1 X_{it} + \beta_2 \bar{X}_{-i,j,t+1} + \lambda_{jt} + \varepsilon_{it}$

Test whether $\beta_2 = 0$. If $\beta_2$ is significantly ≠ 0 → the industry mean contains persistent confounding factors that do not operate through contemporaneous X (such as industry demand trends) → exogeneity is questionable.

Test 3: Testing in "entering/exiting" firms

Firms enter an industry at different times—some are long-standing players, others are new entrants. If the industry-mean IV operates mainly through the "industry technology trend → firm X → firm Y" channel—then for firms that have just entered the industry, the effect of the industry mean on Y should be stronger than for incumbent firms (because new entrants rely more on industry trends to set their own X). If there is no difference in the reduced form between incumbents and new entrants → this does not necessarily overturn exogeneity. But if the reduced form for incumbents is anomalously stronger than for new entrants → this suggests that the persistent confounding component of the industry mean is playing a dominant role.

5.2 Presenting Falsification Tests

In the "Instrumental Variable Validity" section of the paper, falsification tests are typically presented in table form, with each column representing a falsification test design and its results. The key wording is not "these tests prove the exogeneity of the IV," but rather "these tests fail to find evidence against the exogeneity of the IV."

VI. Justification Strategy 4: Controlling for Industry-Level Confounders—Act Before Being Challenged

6.1 Directly Including Industry-Level Control Variables

If the reviewer worries that "industry demand shocks" simultaneously affect industry digitalization and firm productivity—why not directly include industry demand shocks as control variables in the model? After including industry demand shocks in the model, the channel through which the industry-mean IV affects Y via industry demand shocks is explicitly closed.

Of course, you cannot measure all industry-level confounders—but you can measure some important ones and include them in the regression:

* Industry demand: industry total sales growth rate
* Industry competition: industry HHI index
* Industry policy: whether the industry enjoys tax incentives
* Industry technology: average number of patents in the industry
 
reghdfe y (x = iv), absorb(firm year) first
* Also include these industry-level control variables in the second-stage regression

6.2 Showing "The Conclusion Is Consistent With and Without Industry Controls"

Add industry-level control variables to your model step by step and show how the IV coefficient changes—if the IV coefficient barely changes after adding control variables → industry confounders are not the main driver; if the IV coefficient changes substantially after adding them → industry confounders play an important role, and you need to discuss this finding and its implications for your conclusions (to what extent the conclusions still hold).

This is an honest diagnostic—rather than assuming they do not exist.

VII. Justification Strategy 5: Benchmarking Against Arguments in the Existing Literature—"My Instrument Is Also Reasonable in Their Framework"

7.1 Citing Argumentative Frameworks from the Methodological Literature

The methodological literature on industry-mean IVs and Bartik IVs has seen extensive discussion over the past decade. If your IV construction is structurally similar to those discussed in this literature—cite the argumentative frameworks from these papers to support your own exogeneity argument:

• Goldsmith-Pinkham, Sorkin, and Swift (2020): Bartik IV is equivalent to GMM with base-period shares as instruments—the exogeneity argument is equivalent to the assumption that base-period shares are uncorrelated with the error term.
• Borusyak, Hull, and Jaravel (2022): Identification in Bartik IV can be equivalently stated as "national industry shocks are exogenous"—rather than exogeneity of the shares. If your IV can be restated as a structure of "exogenous shocks × differential exposure," the exogeneity argument can focus on the exogeneity of the shocks.
• Adão, Kolesár, and Morales (2019): In shift-share IV designs, standard errors should be clustered at the level of the shocks rather than the individual level—this advice also applies to industry-mean IVs (if industry demand shocks are correlated, inference should at least cluster at the industry level or use a two-way clustering framework).

7.2 Do Not Treat Citations as a Substitute—They Are Background, Not the Answer

Citing this literature is good background—but it cannot replace your exogeneity argument for your specific IV in your specific research context. Reviewers will read this methodological literature—they know that Bartik is equivalent to some form of GMM, and they know about Borusyak et al.'s restatement. You need to present your argument within their frameworks, combined with your data, your industry, and your research design.

VIII. Common Misconceptions

8.1 Misconception 1: "I Excluded the Own Firm → the Industry Mean Is Exogenous"

Excluding the own firm (leave-one-out) solves the "mechanical correlation" problem—where the firm's X simultaneously appears in the numerator of the IV (industry mean) and in X itself, generating a spurious correlation purely from the construction. But excluding the own firm does not solve the problem of "industry common shocks simultaneously affecting the industry mean and the individual's Y." Excluding the own firm is a necessary condition, not a sufficient one. It is a construction detail, not an exogeneity argument.

8.2 Misconception 2: "The First-Stage F of the Industry-Mean IV Is High → the IV Is Good"

A high F only indicates that the industry mean is strongly correlated with the individual firm's X—this never equals exogeneity. In fact, the F of industry-mean IVs is often high precisely because the industry mean contains a large amount of industry common shocks—which may be exactly the "bad variation" the reviewer worries about. A high F in this context is a double-edged sword—it is both evidence of relevance and a signal that exogeneity may not hold (if industry common shocks are at work).

8.3 Misconception 3: "I Included Industry FE → I Have Already Controlled for Industry-Level Confounders"

Industry FE controls for time-invariant industry characteristics—such as industry technology intensity and entry barriers. But it cannot control for time-varying industry shocks—such as annual fluctuations in industry demand and changes in industry policy. These are precisely the core threats facing industry-mean IVs. Adding industry FE is not enough—consider adding industry × year FE to absorb time-varying industry confounders. (But accept the reality that this may lower the first-stage F—because most of the variation in the industry mean comes from the industry × year level.)

8.4 Misconception 4: "My IV Has the Same Construction as One in AER → Therefore It Is Valid"

The same type of IV construction may have completely different sufficiency of exogeneity arguments in different research contexts. An industry-mean IV that is valid in "digital transformation" does not imply it is valid in "corporate charitable giving"—because the way, degree, and direction in which industry common shocks operate in the two contexts may be completely different. Exogeneity is research-context-specific—not methodology-specific. What validates an IV is not "it has been used before," but "you have argued, in your data and context, for its exclusion restriction in this specific relationship."

8.5 Misconception 5: "Bartik IV Solves All the Problems of the Industry-Mean IV"

Bartik IV shifts the concern about "bad variation" from "contemporaneous industry shocks" to "whether base-period shares are exogenous" and "whether national shocks are exogenous." But Bartik is not magic—it still requires an exogeneity argument. Goldsmith-Pinkham and Sorkin (2024) show that Bartik is equivalent to GMM with industry means—meaning the two methods share the same core exogeneity problem. Bartik's advantage is that it makes the exogeneity argument more feasible in the data—because the nature of base-period variables and national shocks is clearer and easier to argue than the contemporaneous industry mean. But it makes the argument more feasible—not unnecessary.

IX. Summary

Five core strategies for exogeneity arguments when using higher-level variables as instrumental variables:

1. Decompose variation sources—distinguish "good" from "bad" variation. The industry mean contains both industry technology trends (good—absorbable by year FE) and industry demand shocks (bad—simultaneously affecting IV and Y). Add industry × year FE to absorb common shocks, and show how the first-stage F changes before and after adding FE—this itself is an informative diagnostic.

2. Move from the industry mean to differential exposure—the Bartik logic. Redefine the IV as the interaction of "base-period individual characteristics × national trends" rather than the "contemporaneous industry mean." This shifts the source of IV variation from contemporaneous industry shocks (potentially endogenous) to national trends (more easily absorbed by year FE) + base-period characteristics (fixed before the sample period).

3. Design targeted falsification tests. Test the reduced form in subsamples where the X→Y path is blocked or weak—if the IV is ineffective in these subsamples but effective in the full sample → this supports exogeneity. Use the future industry mean as a Placebo IV—if the future IV still predicts contemporaneous Y after controlling for the contemporaneous IV → there are persistent confounding factors not operating through contemporaneous X → exogeneity is questionable.

4. Directly control for industry-level confounders and show robustness. Do not assume they do not exist—put them in the regression and show whether the coefficient changes after adding them. If the conclusions are stable across different sets of control variables → industry confounders are not the main driver.

5. Position your exogeneity argument within the frameworks of the methodological literature. Cite Goldsmith-Pinkham-Sorkin (share exogeneity), Borusyak-Hull-Jaravel (shock exogeneity), and Adão-Kolesár-Morales (inference level)—not merely for literature review, but to provide argumentative structure and inference methods for your specific IV within these frameworks.

One-sentence conclusion:

"Using the industry mean to leverage the individual's X—this strategy never lacks relevance. What it lacks is your ability to draw a line within the variation of the industry mean: on the left side of the line is the 'exogenous push that drives X but does not directly touch Y'; on the right side is the 'industry common shock that drives both X and Y.' Excluding the own firm is merely the prerequisite for drawing the line—it is not the line itself. To draw this line properly, you need industry × year FE to absorb the most obvious common shocks, you need the Bartik logic to push the variation source to an earlier point in time, you need falsification tests to find evidence of 'no effect' in subsamples where X→Y does not operate, and you need to put industry-level confounders directly into the model and show that they are not the driver. After doing all this—you are not claiming that your IV is a perfect exogenous instrument. You are saying: 'I have spent considerable time attacking it—it has not been broken. Based on this record, exogeneity is a more reasonable explanation than any alternative hypothesis.'"

X. Presentation Suggestions for Bilibili/WeChat Official Account

• Bilibili video: Suggest using "the two faces of the industry mean" as the core visual metaphor. Opening: a large ball representing the industry mean is cut open—the left half is blue ("good variation"—exogenous technology trends), the right half is red ("bad variation"—industry demand shocks). A line connects the blue half → X, and a line connects the red half to both X and Y. Voiceover: "The industry mean is a double-edged sword—one edge faces firm digitalization (relevance), the other edge may simultaneously face firm productivity (exogeneity threat). Excluding the own firm merely moves the blade away from yourself—but the red side is still in the sword." Act 1 "Decomposing variation": industry × year FE appears, the red half is absorbed (fades), the blue half remains. The visual shows the F statistic dropping from 124 to 18 (still strong enough). Annotation: "Industry × year FE absorbs common shocks—the IV's variation shifts from 'differences between industries' to 'differences between firms within the same industry and year.' F drops, but the remaining variation is cleaner." Act 2 "The Bartik logic": the industry mean is decomposed into two pieces—base-period shares (locked in, time-invariant) and national trends (rising smooth curve). Their product = Bartik IV. Annotation: "Bartik pushes the source of 'bad variation' from the contemporaneous industry to the national trend—and the national trend can be absorbed by year FE. It does not eliminate the exogeneity argument—it pushes the argument to a clearer, more defensible place." Act 3 "Falsification tests": three subsamples—in subsample A (resource-based firms, weak X→Y channel), the reduced form is insignificant. In subsample B (highly competitive firms, normal X→Y channel), the reduced form is significant. The visual draws a comparison between the two subsamples. Annotation: "If the IV 'does not work' where X→Y cannot operate—and 'works' where X→Y can operate—then the IV is more likely operating through X, rather than bypassing X."

• WeChat Official Account: Create a reference card for the four types of higher-level IV constructions (industry mean, regional mean, Bartik, group mean). Make the "good variation vs. bad variation" classification comparison the core infographic—with the source, example, and control strategy for each type of variation. Create a "cleanliness upgrade" diagram showing the progressive logic chain from industry mean → industry × year FE → Bartik. Create four strategy cards for the falsification test design templates (subsample, future IV, entry/exit, mechanism substitution). Create a correction card for the five common misconceptions. Create an academic background card with the "argumentative framework correspondence table" for the three methodological papers—Goldsmith-Pinkham-Sorkin, Borusyak-Hull-Jaravel, and Adão-Kolesár-Morales.

• Recommended titles:

  • Main title: "Using the Industry Mean as an Instrumental Variable—When the Reviewer Says It Is Not Exogenous Enough, How Should You Respond?"
  • Alternative title: "Excluding the Own Firm ≠ Exogeneity—The 'Good Variation' and 'Bad Variation' of Industry-Mean IVs"
  • New media title: "An Instrumental Variable with F = 124.6—Why Did the Reviewer Still Reject It?"

• Key quotes:

  "Excluding the own firm is not a guarantee of exogeneity—it merely removes a mechanical correlation. Industry demand shocks still sit between the industry mean and firm outcomes—you have only removed the spurious correlation of being affected by yourself, but you have not removed the true endogeneity of the entire industry being pushed by the same hand."

  "The high F of an industry-mean IV is a double-edged sword—it is both the relevance you need and possibly exactly the confounding you fear. Industry demand rises → industry-wide digitalization increases → your IV rises, your X rises. Industry demand rises → industry-wide output increases → your Y rises. In the association between IV and Y, how much comes from the X channel and how much from demand directly pushing Y—a high F cannot answer this question."

  "Bartik IV is not an 'upgrade' of the industry-mean IV—it is a 'variant' of the industry mean, shifting the exogeneity argument from short-term industry shocks to long-term historical conditions. It does not make exogeneity more 'true'—it merely places the problem in better light, making it easier for you to see where the weaknesses in the argument lie."

  "Falsification tests are not 'proving exogeneity'—they are 'efforts to expose endogeneity that have failed.' You test the reduced form in subsamples where X→Y cannot operate, you attack the contemporaneous model with the future industry mean—these attacks did not succeed. This does not mean your IV is perfect. But compared to not saying 'it must be perfect' and not running any tests—you are already on a more honest path."