The claim that women leaders are better at fighting the novel coronavirus has overtaken the Internet.

For pundits and even some economists, the connection seems obvious. New Zealand Prime Minister Jacinda Ardern led her country through 102 days without any new cases, while President Trump still denies public health concerns and promotes controversial therapies.

But it’s not so simple. We find no consistent relationship between gender and pandemic outcomes. That’s because not all women leaders have the same policy powers — and because containing the virus requires action on several fronts, from public health to the economy. Women’s leadership matters for the pandemic, but not always in ways you might expect.

Here are five things political science tells us about women leaders and the pandemic.

1. Pandemics change what people value in their leaders

Nearly all the world’s chief executives are men. This means that stereotypically masculine qualities such as strength, aggression and assertiveness become synonymous with being a president or a prime minister. Women politicians often work harder to prove they are up to the job, because they don’t match traditional ideas about how leaders should look or act.

But the pandemic changes what citizens value in their leaders. Women leaders displaying stereotypically feminine traits such as compassion make citizens feel protected and cared for, one study explains. Empathy is suddenly more valuable than bluster. Celebrating feminine leadership styles helps counter ideas that women are unfit to be presidents or prime ministers.

2. Women leaders are no better than men at containing viral spread

One study examined 132 countries and found no relationship between executive gender and the timing of stay-at-home orders, school closures or public information campaigns. Another study of U.S. governors found no relationship between women governors and early shelter-in-place measures. And citizens do not comply more readily with emergency orders issued by women than those issued by men.

These studies focus on women who head the government, like a prime minister or governor. A different paper suggesting that women-led countries have lower mortality rates included countries where women serve as heads of state — roles that are symbolically important but have little policy power.

Research by one of us, Jennifer Piscopo, compared women and men heads of government across the 37 OECD countries, and found that the relationship between women leaders and lower coronavirus death rates is probably coincidental.

Instead, the critical factor distinguishing countries’ response to covid-19, the disease caused by the virus, is what political scientists call “state capacity”: countries’ ability to govern effectively, efficiently and fairly. High-capacity countries have strong bureaucracies, little corruption, greater income equality and more trust in government.

Today, high-capacity countries are more likely to elect women executives. That’s why it seems that women leaders are doing a better job fighting the virus. But when women and men govern high-capacity countries, coronavirus mortality rates are similar.

3. Women politicians prioritize the pandemic’s social consequences

The pandemic’s consequences go beyond infection and mortality rates. Across the globe, millions of people have lost jobs, and governments face higher demands for emergency relief to help people get by.

Research shows that women politicians are more likely to prioritize social policies like welfare, health care and child care. This seems to be holding true during the pandemic.

A study by one of us, Kendall Funk, examined Democratic women mayors in large U.S. cities. Women mayors were focused not just on viral spread but also on how the pandemic would affect vulnerable communities. Women mayors created policies to tackle food insecurity, homelessness and child care. Consistent with research showing that women leaders are often more collaborative than men, the women mayors shared their strategies, enabling other cities to replicate these much-needed programs.

Women mayors’ ethnicity and race also shapes their priorities. Latina and Black mayors who are women created programs to reduce covid-19’s effects on people of color. Examples include Tucson Mayor Regina Romero’s Somos Uno Resiliency Fund or Chicago Mayor Lori Lightfoot’s Racial Equity Rapid Response Team.

4. The economic crisis may be bad news for women leaders

The pandemic has triggered a worldwide recession. That means gender stereotypes about women as poor economic managers come into play.

Together with Magda Hinojosa, we studied how voters’ economic outlook affects the number of women congressional candidates, using data from 18 Latin American countries over eight years. When voters are unhappy with their countries’ economic performance, parties run fewer women candidates. Other research examining 68 countries over 30 years concluded that economic crises reduced women’s presence in parliament.

These findings counter the oft-mentioned idea that economic crises create opportunities for women leaders. Stereotypes about women as more honest and less corrupt, or ideas about women as fresh faces, might benefit some women — but their rise to power in these circumstances has serious downsides: in stepping into a precarious situation, they are often set up to fail.

That’s because people judge women executives more harshly in polls than men. Even when women and men govern during similar crises, women leaders have shorter tenures and lower approval ratings overall. Men politicians might weather financial storms, while women chief executives and legislators more quickly find themselves out of a job.

5. Studying gender requires careful research

Knowing whether women leaders are better at fighting covid-19 requires comparing women and men in the same type of political office. It also means understanding that a leader’s gender does not have the same consequences for pandemic containment as it does for social policy.

Well-designed research on gender and leadership offers two big conclusions.

First, gender stereotypes shape how voters and commentators view women leaders, but gender stereotypes cut both ways. Celebrating women’s greater empathy and competence may elevate women now, but setting the bar even higher for women leaders can lead to outsize criticism as a pandemic persists.

Second, women leaders may matter for enhancing social protection more than containing viral spread. Countries with effective governments, strong bureaucracies and high levels of trust mount effective coronavirus responses, whether led by women or men. But women leaders may spend more time bolstering government capacity, especially by investing in the social programs necessary to protect those hardest hit.

Jennifer M. Piscopo (@Jennpiscopo) is associate professor of politics at Occidental College.

Kendall Funk (@Kendallfunk12) is assistant professor of political science at Arizona State University.