The Western media has bought into the notion that a new wave of Western boycotts against Israel is underway. But like so many trend stories, this one doesn’t stand up to scrutiny.

For Israelis, talk of boycotts brings back bad memories of the 1970s and ’80s. After the Yom Kippur War and the Arab oil embargo, scores of countries severed diplomatic relations with the Jewish state. Europe turned a cold shoulder and many of the world’s biggest companies refused to do business with it. Israel’s pariah status not only hurt the economy, it dealt a blow to the Zionist dream of normalizing the Jews by giving them their own country.

The supposed new wave of boycotts began last December when the Dutch water company Vitens severed ties with its Israeli counterpart Mekorot. Next came a loudly proclaimed boycott of Israeli universities by the American Studies Association.

Then in January, Dutch pension fund PGGM said it would sell holdings in five Israeli banks, citing their role in helping to finance construction of West Bank settlements. Denmark’s Danske Bank was reported to have sold shares in Israel’s Bank Hapoalim, and Sweden’s Nordea was threatening to do the same to two other Israeli lenders. Norway’s sovereign wealth fund was said to have begun boycotting the property developer Africa Israel Investments and its Danya Cebus subsidiary.

When SodaStream, a manufacturer of devices for making carbonated drinks at home, hired Scarlett Johansson to appear in Super Bowl ads, anti-Israel activists found a juicy target: an A-list celebrity and Oxfam ambassador endorsing a company with a plant in the West Bank. Ms. Johansson has since resigned from Oxfam. More recently it was reported that Deutsche Bank blacklisted Hapoalim, and that the Dutch company Boskalis pulled out of an Israeli port-construction tender due to boycott pressures.

These reported boycott actions even prompted an Israeli cabinet meeting in February on how to respond. There were countless editorials for and against the boycott in newspapers around the world, strategies offered up on how to stop it and speculation about who would blacklist Israel next. Some commentators suggested the boycott was driving down the value of the Israeli shekel as well as SodaStream’s share price.

But as soon as one examines these cases individually, the boycott story melts away. They are either not new, not motivated by the boycott movement or have limited impact.

For instance, Danske will maintain its banking relationship with Hapoalim. It simply stopped buying shares in Hapoalim as a default policy for its investment banking clients; if a client wants the shares, Danske will happily buy them for the account. In any case, Danske made the decision almost a year ago and announced it in September, so it could hardly be part of a boycott “wave.”

Nordea will take a few months to decide on divesting bank shares and says no other Israeli companies are candidates for its “exclusion” list. Norway’s sovereign wealth fund banned Africa Israel Investments from its portfolio nearly five years ago and was simply renewing the policy.

Deutsche Bank has excluded Hapoalim from a single investment fund it set up for a specific client; otherwise, it is doing business with Israel as usual. Boskalis says that far from dropping out of the port tender, Israel disqualified it from the bidding.

So how did this become an “exodus” from Israel, as the Financial Times headlined it in a February article?

For the Western media, the boycott and all the ideological baggage it carries makes it irresistible. But the hysterical coverage was mostly a function of laziness (almost no one was fact-checking) and ignorance (boycott stories are typically covered by political reporters who know nothing about business, trade or investment).

Even in Israel, the boycott is just too compelling a story for the facts to get in the way. For Israeli politicians on the left and their allies abroad, it serves as a useful stick for urging talks with the Palestinians. On the right, the boycott talk provides more proof that the world is arrayed against Israel and the Jews.

The true story is that after nearly 10 years of campaigning, the global BDS (boycott, divestment and sanctions) movement has not had the slightest economic impact. Its victories have consisted of coaxing a handful of pop stars and academics to cancel appearances in Israel, and winning empty, sanctimonious declarations of support from the likes of student governments, cooperative grocery stories and leftish church groups.

Far from being isolated, Israel’s exports are reaching record highs and it attracts billions of dollars in foreign investment. In the weeks that Israel was supposedly under a boycott siege, Japan’s Rakuten agreed to buy the start-up Viber for $900 million and Ireland’s Covidien sealed a deal to buy Given Imaging for $860 million. China’s Bright Food was in talks to buy control of Israel’s biggest food maker Tnuva, and IBM, Lockheed-Martin and ERM all announced plans to open research and development centers in Israel. The Jewish state became the first non-European member of the nuclear research consortium CERN and was admitted as an observer to the Pacific Alliance, a free-trade bloc of five Latin American countries.

A real boycott wave would be devastating for Israel both economically and morally. Indeed, the cost would be many times higher than it was a generation ago because the country’s economy is more reliant on international trade and cross-border investment. But for now the boycott is nothing more than a creature of the media’s imagination.

Mr. Rosenberg is the economics editor and a columnist for the Haaretz daily’s English-language edition.