The Equilibrium Nobody Costed

Salary ranges are now appearing in job postings across Canada. The case for that is usually made in terms of fairness, and the economics of what happens next is usually left out entirely. A paper in one of the discipline's leading journals fills it in.

A Note On Scope

Stated first, because this touches a live policy question and the scope is narrower than the topic.

This article reports what a body of economic research finds about wage effects. It takes no position on whether pay transparency is good policy, which depends on values this article does not adjudicate.

It is not employment, compensation, human resources or legal advice. Disclosure obligations differ by jurisdiction, are set by legislation, and are not described here. A separate article on this site covers the Ontario rules.

And it concerns average wages and bargaining. It is not an article about whether pay gaps between groups are real, which is a different question with a different literature.

Our Grades For These Claims

Applying the scheme from the first article in this series.

Grade A for the theoretical prediction. Published in Econometrica, with the abstract obtained verbatim from three independent sources including the working paper record and the authors' own institutional summaries.

Grade B for the approximately two percent decline. It is the paper's own headline empirical estimate from an event study, and we did not obtain the paper, its identification strategy or its confidence intervals.

Grade B that the effect is muted without individual bargaining power, which is a differential result within the same unobtained paper.

Grade C for the corroborating estimates from other studies, which reach us through a summary table.

Our position: the mechanism is compelling and the magnitude rests on one paper we could not read, though three independent studies in a comparison table point the same way.

A Note On Method

Everything here is verified to August 2026.

We obtained the published abstract verbatim from three independent sources[1][2][3], and separately the abstract of a 2017 working draft containing claims the published version does not[4].

We did not obtain the paper, its model, its identification strategy, its standard errors or its robustness checks.

Comparative effect sizes come from a summary table in conference materials[5], not from the underlying studies.

We did not obtain the Canadian study, which is the one a reader here would most want, and it has its own section.

All arithmetic is ours; the spillover model is invented and no source states a spillover rate.

The Paper

The citation.

Cullen and Pakzad-Hurson published Equilibrium Effects of Pay Transparency in Econometrica, 91(3), 765–802, in May 2023[6], with working paper versions circulating from at least 2017[4][1].

Its opening states the gap: "The public discourse around pay transparency has focused on the direct effect: how workers seek to rectify newly-disclosed pay inequities through renegotiations. The question of how wage-setting and hiring practices of the firm respond in equilibrium has received less attention."[2]

Two observations, ours.

That framing is the article's title. The direct effect is the one everybody models informally: a worker learns they are underpaid and asks for more.

The equilibrium effect is what happens when the employer also knows the worker will learn, and sets pay accordingly from the start. One is a story about a conversation; the other is about the policy that precedes it.

The Prediction

What the model says.

"Our model predicts that transparency reduces the individual bargaining power of workers, leading to lower average wages."[2]

Three observations, ours.

Note the direction. Most public argument for transparency assumes it raises pay for the underpaid. The model predicts it lowers the average.

Note also that this is a claim about averages, not about every worker. A prediction that the mean falls is compatible with some individuals gaining.

And it is a claim about individual bargaining power specifically, which is the qualifier that generates the paper's most useful result and which we come to below.

The Key Insight

The mechanism, in the authors' own words.

"A key insight is that employers credibly refuse to pay high wages to any one worker to avoid costly renegotiations with others under transparency."[2]

Three observations, ours.

The word credibly is doing the work. This is not a firm pretending it cannot pay. It is a firm that genuinely faces a larger bill than the raise itself.

Which reframes a familiar interaction. When a manager says I would if I could, but then I would have to do it for everyone, that has usually been read as a negotiating tactic. Under transparency the model says it is arithmetic.

And it means the constraint binds hardest where roles are most comparable, because that is where a raise is most obviously precedent-setting.

We Costed The Mechanism

Because a claim about cost can be given a number. Our own model, invented, illustrative; no source states a spillover rate and none of these figures appears in any paper.

Suppose one worker asks for an extra ten thousand dollars. Under secrecy that costs ten thousand. Under transparency, comparable colleagues learn of it and some fraction successfully renegotiate.

In a team of five with a thirty percent spillover rate, the true cost is $22,000, or 2.2 times the raise.

In a team of ten at fifty percent: $55,000, or 5.5 times.

In a team of twenty at fifty percent: $105,000, or 10.5 times.

Two observations.

The multiple scales with team size, which means the effect should be strongest in larger groups of comparable staff and weakest for genuinely unique roles.

And it makes the employer's position legible rather than villainous. A firm refusing a ten thousand dollar raise that actually costs fifty-five thousand is not being mean. It is facing a different price than the worker thinks it is.

Why The Refusal Is Credible

Following the mechanism through to the bargaining table. Ours.

Three points.

Bargaining power rests on what each side can credibly threaten. A worker's leverage is the cost to the employer of losing them.

Under transparency the employer can point to a cost of conceding that exceeds the cost of replacement, and both parties can see it. The threat to leave stops working.

And this is why the effect is about individual bargaining. The mechanism requires that pay be individually negotiated in the first place; where it is not, there is nothing for transparency to undermine.

The Empirical Test

What they did with the prediction.

"We test these predictions by evaluating the roll-out of U.S. state legislation protecting the right of workers to inquire about the salaries of their coworkers."[2]

And the result: "Consistent with our prediction, the laws lead wages to decline by approximately 2% overall, but declines are progressively smaller in occupations with higher unionization rates."[2]

A summary table records the estimate as -0.019 across 13 US states for laws establishing the right of workers to talk[5].

Three observations, ours.

The policy tested is the weakest form of transparency: not published salaries, merely the protected right to ask a colleague. That matters for how far the result generalises.

We did not obtain the paper and cannot assess the identification, the pre-trends, or the confidence interval around two percent.

And the differential result is the stronger evidence. A finding that moves in the predicted direction across the predicted subgroups is harder to obtain by chance than a single headline number.

What Two Percent Is

Putting the figure in context. Our arithmetic; the two percent is the paper's, the salary levels are invented and are not Canadian wage data.

On a salary of $55,000, two percent is $1,100 a year. On $85,000, $1,700. On $120,000, $2,400.

Across a payroll of twenty-five people averaging seventy thousand, it is about $35,000 a year in wage bill.

Three observations.

Per person this is small, and smaller than most people would notice against annual variation.

In aggregate it is a real transfer, and the honest description is that it moves from staff to the firm. An employer reading this should not file it as a saving without noticing where the saving came from.

And two percent is modest as policy effects go. It does not support a claim that transparency is ruinous, only that its sign is the opposite of what is usually assumed.

Where The Effect Disappears

The condition, which is the most actionable thing in the paper.

"In situations where workers do not have individual bargaining power, such as under a collective bargaining agreement or in markets with posted wages, greater transparency has a muted impact on average wages."[2]

Three observations, ours.

Two examples are named: collective agreements and posted wages. In both, pay is set by a schedule rather than negotiated case by case.

Which means the negative wage effect is not a property of transparency itself. It is a property of transparency imposed on a system of individual negotiation.

And that is a genuine design implication, ours: a firm moving to published bands at the same time as it publishes pay is in the muted case, not the declining one. The two changes are usually discussed separately and the model suggests they interact.

Three Other Estimates

Corroboration, reported at one remove.

A summary table of transparency studies records, alongside the -0.019 above: a study of US universities posting individual salaries at -0.016, and a further estimate for posting individual salaries at -0.014[5].

The table's own note states it is "largely replicated from" the paper under discussion, and identifies further entries drawn from studies by Baker and colleagues, Bennedsen and colleagues, and Duchini and colleagues[5].

Two observations, ours.

Three estimates clustering between -0.014 and -0.019, from different settings and policies, is a more reassuring picture than one number.

But the table is largely reproduced from the paper we are assessing, which means it is not fully independent corroboration, and we flag that rather than presenting three studies as three votes.

What The Earlier Draft Said

A 2017 version of the paper contains claims the published abstract does not, and they matter.

"By accounting for these effects, we find that increasing pay transparency shifts surplus away from workers and toward their employer. Greater transparency can also increase employment and decrease inequality in earnings."[4]

Its methods: "We isolate these effects in a theoretical equilibrium model of dynamic bargaining and in a large-scale longitudinal data analysis. We further corroborate our conclusion using an online field experiment."[4]

Three observations, ours.

Increase employment and decrease inequality is a substantial pair of benefits sitting beside the wage decline. Lower average pay with more jobs and less dispersion is a different policy picture from lower pay alone.

We report these as the earlier draft's claims and cannot tell whether they survived into the published version, because we did not obtain either paper in full.

And the draft notes it "subsumes two earlier drafts: Equal Pay for Unequal Work? and Is Pay Transparency a Good Idea?"[4], which is a useful reminder that a single citation can represent years of revised argument.

The Worst Level Is The Middle

The most counterintuitive claim we found, from the same earlier draft.

"Intermediate levels of pay transparency, achieved through a permissive environment to discuss relative pay, can exacerbate the gender pay gap by virtue of network effects. External intervention may be necessary to maintain a desirable level of transparency."[4]

Three observations, ours.

If accurate, the relationship is not monotonic. Partial transparency can be worse than either full disclosure or none.

The proposed mechanism is network effects, which we read as informal information travelling unevenly through social ties. Who you happen to know determines what you learn.

And this is the claim we would most want tested, because a permissive environment to discuss pay is precisely what most firms actually have. We report it as a working draft's claim, from a source we did not obtain in full, and grade it no higher.

The Canadian Study We Could Not Obtain

The gap most relevant to this publication's readers, stated in the body.

Reference lists identify Baker, M., Halberstam, Y., Kroft, K., Mas, A., and Messacar, D., Pay Transparency and the Gender Gap, circulated as a working paper and drawing on Canadian universities[7][5].

We did not obtain it and report no findings from it.

Two observations, ours.

This is the closest thing to Canadian evidence in the literature we surveyed, and it is the one document we would most want a Canadian employer to have.

The summary table draws figures from it, which we could have quoted without attribution to a specific finding. We have chosen not to, because a number lifted from a table without its context is exactly the practice this series has criticised elsewhere.

What This Does Not Say

Four things, stated explicitly because this topic invites overreach. Ours.

It does not say transparency is bad policy. Lower average wages with higher employment and lower dispersion is a trade-off, not a verdict, and weighing it requires values this article does not supply.

It does not say pay gaps are not real. That is a separate literature and this article makes no claim about it.

It does not give an employer a reason to resist disclosure obligations, which are set by law and are outside this article entirely.

And it does not establish that two percent is the right number. It is one paper's estimate, we did not obtain the paper, and the supporting table is largely drawn from that same paper.

What An Employer Should Take From It

The practical reading. Ours, untested.

Four points.

Decide whether you negotiate individually before you decide what to disclose. The model says the wage effect comes from transparency imposed on individual bargaining, and disappears where pay follows a schedule.

Expect precedent to become the binding constraint. Once pay is comparable and visible, the cost of any single raise includes its spillover, and on our own illustrative figures that multiple can be substantial.

Say the real reason. If a raise is refused because of precedent rather than affordability, that is now a defensible and true thing to say, and the alternative is a worker concluding they are simply not valued.

And do not treat a lower wage bill as a windfall. On this literature it is a transfer from staff, it is visible in the same data everyone else can see, and a firm that pockets it quietly has taken a position without deciding to.

What To Do

Note the direction. The model predicts transparency lowers average wages, which is the opposite of the usual assumption, and the tested laws showed about a two percent decline.

Check whether you have individual bargaining at all. The effect is muted under collective agreements and posted wages, so the wage consequence depends on your pay-setting system rather than on disclosure itself.

Cost the precedent, not the raise. On our own illustrative model a ten thousand dollar raise in a comparable team of ten can carry a five-figure spillover.

Consider bands and disclosure together. They are usually discussed separately, and the model implies they interact.

Be careful with partial transparency. A working draft claims intermediate levels can be worse than either extreme through network effects, and that describes most workplaces.

Do not read a two percent estimate as settled. We did not obtain the paper, and the corroborating table is largely reproduced from it.

Keep the wage question separate from the fairness question. This literature is about averages and bargaining, not about whether disclosure is right.

The Limits Of This Analysis

Several caveats matter. This article reports economic research on wage effects and is not employment, compensation, human resources or legal advice; disclosure obligations differ by jurisdiction and are not described here. It takes no position on whether pay transparency is good policy and makes no claim about pay gaps between groups, which is a separate literature. Everything is verified to August 2026. We obtained the published abstract verbatim from three independent sources but did not obtain the paper, its model, identification strategy, standard errors or robustness checks, and cannot assess the two percent estimate beyond reporting it. Comparative effect sizes come from a summary table whose own note states it is largely reproduced from the paper under discussion, so it is not fully independent corroboration. The claims about employment, inequality and intermediate transparency come from a 2017 working draft, and we cannot tell whether they survived into the published version. We did not obtain the Canadian study, which is the most directly relevant document for this publication's readers, and report no findings from it despite figures from it appearing in a table we did see. All arithmetic is ours; the spillover model is invented, no source states a spillover rate, and the salary levels used are illustrative and are not Canadian wage data. The applications for employers are our own reasoning, untested.

Related Reading

Employment Ontario Job Posting Rules What the disclosure rules actually require, as distinct from what the evidence says they do. Behavioural Finance The Lottery That Picks The Employee The other article on variation in decisions that nobody has measured. No. 48 Relative, Not Absolute Repetition increases liking, at one of the larger effect sizes in this series. It works better when people do not notice it. And one meta-analysis...

Frequently Asked Questions

What does the research actually find?

That transparency reduces the individual bargaining power of workers and lowers average wages, because employers credibly refuse to pay any one worker highly to avoid costly renegotiations with others. US state laws protecting the right to ask colleagues about pay were associated with wages declining about two percent.

Why would transparency lower pay?

Because a raise stops costing what it says on the letter. On our own illustrative model, a ten thousand dollar raise in a comparable team of ten with half the colleagues renegotiating costs fifty-five thousand. The employer refusing is not being mean; they face a different price.

Does it apply to every employer?

No, and this is the most useful part. The paper reports the effect is muted where workers lack individual bargaining power, such as under collective agreements or posted wages. The negative wage effect is a property of transparency imposed on individual negotiation, not of transparency itself.

Is two percent a lot?

Per person, no. On our own illustrative figures it is about $1,100 a year on a $55,000 salary. Across a payroll of twenty-five averaging seventy thousand it is roughly $35,000 annually, and the honest description is that it moves from staff to the firm.

Is partial transparency safer?

Possibly the opposite. A 2017 working draft claims intermediate transparency, achieved through a permissive environment to discuss pay, can exacerbate the gender pay gap through network effects. That describes most workplaces, and it is the claim we would most want tested.

Does this mean transparency is bad?

No. The same earlier draft reports that greater transparency can also increase employment and decrease inequality in earnings. Lower average pay with more jobs and less dispersion is a trade-off requiring values this article does not supply.

References

1. Working paper database record for Cullen, Zoe B., and Pakzad-Hurson, Bobak (2021), Equilibrium Effects of Pay Transparency, National Bureau of Economic Research working paper 28903, reproducing the abstract, on the public discourse having focused on the direct effect of how workers seek to rectify pay inequities through renegotiation while the question of how firms respond has received less attention; on the model predicting that transparency reduces the individual bargaining power of workers, leading to lower average wages; on the key insight that employers credibly refuse to pay high wages to any one worker to avoid costly renegotiations with others under transparency; on greater transparency having a muted impact on average wages where workers lack individual bargaining power, such as under a collective bargaining agreement or in markets with posted wages; on the authors testing these predictions by evaluating the adoption of U.S. state legislation protecting the right of workers to inquire about coworkers' salaries; on the laws leading wages to decline by approximately 2% overall with effects muted when workers have low individual bargaining power; and on the model reconciling effects documented in a variety of countries and contexts. Note: a working paper database record. We obtained the abstract and did not obtain the paper. ideas.repec.org
2. Institutional research summary reproducing the abstract of the same work, on the model of bargaining under two-sided incomplete information predicting that transparency reduces individual bargaining power and leads to lower average wages; on employers credibly refusing to pay high wages to any one worker to avoid costly renegotiations with others; on pay transparency having a muted effect where workers have low individual bargaining power; on the authors testing the model with an event-study analysis of U.S. state-level laws protecting the right of private sector workers to communicate salary information with coworkers; and on transparency laws empirically leading wages to decline by approximately 2%, with declines smallest in magnitude when workers have low individual bargaining power. Note: an institutional summary of the authors' own work; a second independent reproduction of the abstract. hks.harvard.edu
3. Seminar announcement reproducing the abstract, in a version stating that declines are progressively smaller in occupations with higher unionization rates. Note: a seminar listing; a third independent reproduction of the abstract, and the source for the unionization phrasing which differs slightly from other versions. events.umich.edu
4. Conference paper record for a December 2017 working draft of the same research, on the public conversation about increasing pay transparency largely ignoring its equilibrium effects such as changes in hiring, wage-setting and bargaining processes; on the authors finding that increasing pay transparency shifts surplus away from workers and toward their employer; on greater transparency also being able to increase employment and decrease inequality in earnings; on the effects being isolated in a theoretical equilibrium model of dynamic bargaining, in a large-scale longitudinal data analysis, and corroborated using an online field experiment; on intermediate levels of pay transparency, achieved through a permissive environment to discuss relative pay, being able to exacerbate the gender pay gap by virtue of network effects; on external intervention possibly being necessary to maintain a desirable level of transparency; and on the paper subsuming two earlier drafts titled Equal Pay for Unequal Work? and Is Pay Transparency a Good Idea?. Note: a 2017 working draft, not the published paper. Its claims about employment, inequality and intermediate transparency do not appear in the published abstract, and we cannot tell whether they survived revision. topcat.aeaweb.org
5. Conference supporting materials containing a summary table of pay transparency studies, recording an estimate of -0.019 for Cullen and Pakzad-Hurson (2021) covering 13 US states and the right of workers to talk; -0.016 for Obloj and Zenger (2022) covering US universities posting individual salaries; and -0.014 for a further study on posting individual salaries; with notes stating the table is largely replicated from Cullen and Pakzad-Hurson (2021), that coefficient estimates are reported from the specification with the most fixed effects, and identifying figures drawn from Baker and colleagues (2022), Bennedsen and colleagues (2020) and Duchini and colleagues (2022). Note: a summary table in conference materials, not the underlying studies. Its own note states it is largely reproduced from the paper under discussion, so it is not fully independent corroboration. topcat.aeaweb.org
6. Bibliographic record confirming Cullen, Zoë B., and Pakzad-Hurson, Bobak (2023), Equilibrium Effects of Pay Transparency, Econometrica, Econometric Society, volume 91, issue 3, pages 765–802, May; and identifying related work including Bennedsen, M., Simintzi, E., Tsoutsoura, M., and Wolfenzon, D. (2022), Do Firms Respond to Gender Pay Gap Transparency?, Journal of Finance, 77(4), 2051–2091, and Cullen, Z., and Perez-Truglia, R. (2023), The salary taboo: privacy norms and the diffusion of information, Journal of Public Economics. Note: a bibliographic record, used to confirm the journal, volume, issue, pages and date of publication. ideas.repec.org
7. Reference list in a peer-reviewed article on the influence of pay transparency, identifying Baker, M., Halberstam, Y., Kroft, K., Mas, A., and Messacar, D., Pay transparency and the gender gap, National Bureau of Economic Research working paper 25834 (2019); Mas, A., Does transparency lead to pay compression?, Journal of Political Economy, 125, 1683–1721 (2017); Bennedsen, M., Simintzi, E., Tsoutsoura, M., and Wolfenzon, D., Do firms respond to gender pay gap transparency?; and Cullen, Z. B., and Pakzad-Hurson, B., Equilibrium effects of pay transparency. Note: a reference list; citations only. We did not obtain the Canadian study and report no findings from it. nature.com

This article reports economic research on wage effects and is not employment, compensation, human resources or legal advice. It takes no position on whether pay transparency is good policy and makes no claim about pay gaps between groups. The paper discussed was not obtained; its abstract was verified across three independent sources. The comparative table used is, by its own note, largely reproduced from that same paper. All arithmetic is the authors' own; the spillover model is invented and the salary levels are illustrative rather than Canadian wage data.