Executive pay has been the poster child for everything that’s wrong with capitalism. Chief executive officers are paid millions, while some of their employees make minimum wage. Bonus targets often tempt executives to take short-term actions that mortgage their company’s future.

But change is afoot. A rapidly growing trend is for executive pay to be tied not only to financial numbers, but to environmental, social and governance (ESG) targets as well. Two recent studies found that 51% of large U.S. companies and 45% of leading U.K. firms use ESG metrics in their incentive plans.

The rationale seems obvious. First, many advocates have claimed that good ESG practices will boost a company’s bottom line, so incentivizing ESG performance also will improve financial performance. This may be why even private-equity investors have started to mandate ESG targets.

Second, it is commonly believed that rewarding performance is the best way to ensure performance. Conversely, if a company won’t pay for an outcome, that is a telltale sign that it doesn’t actually care about it. Companies are making grand promises about diversity, decarbonization and resource usage—but these promises are hollow if they don’t affect CEO pay.

As an ESG advocate, I should applaud this trend. But as essayist H.L. Mencken is often paraphrased: Every complex problem has a solution that is simple, direct, plausible—and wrong. And this may be the case with ESG targets.

Let’s start with the second argument—that rewarding performance ensures performance. The evidence shows that paying for targets encourages executives to hit those targets. But it doesn’t necessarily encourage them to improve performance. The crux of the problem is that you can’t measure many of the performance dimensions that you care about—“not everything that counts can be counted,” as stressed by sociologist William Cameron (and commonly misattributed to Albert Einstein). For example, paying executives to meet earnings benchmarks leads many of them to cut research and development to do so.

Importantly, the problem of “hitting the target, but missing the point” occurs for any target—whether financial or nonfinancial. Binary thinking often equates “financial” with “short-term” and “nonfinancial” with “long-term.” But nonfinancial targets can be short-termist. Paying teachers according to test scores encourages them to teach to the test even at the expense of teaching students to develop critical thinking skills. Rewarding CEOs according to average employee pay may encourage them to outsource or automate low-paid jobs, or focus on salary rather than meaningful work, skills development and working conditions.

These unintended consequences might be even worse for ESG than financial targets. One challenge is that, for financial performance, only a couple of measures might be relevant. But ESG performance is multifaceted. Companies have a responsibility to many stakeholders—employees, customers, suppliers, the environment, communities and taxpayers—and for each stakeholder, many dimensions are relevant. Either the contract includes only a couple of ESG measures and the CEO ignores others, or it includes most of them and the contract becomes so complex that it loses any motivational effect.

A second problem is measurement. For a financial target such as earnings-per-share, there’s consensus on how to measure it. But that isn’t the case for an ESG metric. Should ethnic diversity be captured by the number of minorities on the board, in senior management, or in the workforce—or other factors such as the ethnic pay gap, or the proportion of minorities who get promoted from each level? Even ESG-rating agencies disagree significantly on how to measure ESG performance, so any measure might be perceived as unfair or ignore important dimensions.

Finally, let’s turn to the first rationale, which holds that boosting ESG performance will always boost financial performance. The evidence is far less conclusive than often claimed. In fact, only performance related to material ESG dimensions (those that are relevant to the company’s specific business model) ultimately pays off; boosting immaterial factors doesn’t. Thus, if ESG targets are to be used, they should be selected carefully based on materiality. Instead, they’re often a knee-jerk reaction to the demands of pressure groups or whatever issue happens to be the order of the day.

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So what’s the solution? I believe the answer is to scrap all bonuses—on both financial and nonfinancial targets—and instead pay CEOs like owners, with long-term shares they can’t sell for five to seven years and must retain beyond their departure. Since material ESG factors ultimately improve the long-term stock price, this holds CEOs accountable for material ESG issues—even if they aren’t directly measurable. Indeed, evidence shows that long-term pay plans improve not only financial performance, but ESG performance as well, and the relationship is causation, not just correlation. Long-term equity also is simple and transparent—there’s no need to decide which ESG factors to include and which to leave out, how high to set the targets, and how much extra pay to give for hitting them.

Companies should still set ESG goals and report on whether they are meeting them. A CEO already has strong reputational incentives, and intrinsic motivation, to meet a publicly announced ESG goal—so you don’t need pay to ensure a target is hit. But there’s a big jump between simply reporting on performance and linking pay to it, as the latter amplifies the risk of manipulation. As Goodhart’s Law suggests, when a measure becomes a target, it ceases to be a good measure.

Having said all that, let me offer one caveat: ESG pay targets might be appropriate in some companies if the above concerns are muted. For example, in an energy company, decarbonization is arguably much more important than any other stakeholder issue, so there is less of a concern about overweighting a single ESG factor. Moreover, there is relatively little disagreement on how to measure direct greenhouse-gas emissions.

But those are the rare exceptions. ESG targets aren’t the ubiquitous panacea often claimed. The best way to ensure that CEOs create long-term value for both shareholders and society is to pay them like long-term owners.

Dr. Edmans is a professor of finance at London Business School. He can be reached at reports@wsj.com.