Researchers at the University of Notre Dame who studied the 2015 emission-rigging scandal involving Volkswagen found that the fallout from the automaker's wrongdoing cost other German car makers billions of dollars in sales.

Volkswagen was exposed for bypassing U.S. emissions standards by equipping diesel-engine cars with a so-called defeat device that could detect emissions tests, adjust levels to ensure compliance and then revert to non-compliant levels after the tests were completed.

"We find that the VW scandal reduced the sales of the other German auto manufacturers.... Specifically, the overall effect on those manufacturers amounted to a decline in sales of 104,661 vehicles valued at $5.2 billion in 2016, based on the list prices in the data," the researchers wrote in a paper released by the National Bureau of Economic Research.

(Read "VW scandal: When good engineers do the wrong thing.")

For years, Volkswagen — which also owns Porsche and Audi — emphasized the value of "German engineering" in its advertisements, the researchers said. Stefan Gies, Volkswagen's head of chassis development, told Car and Driver that, in his view, "German engineering stands for precision in all that we do — precision in the design and what you feel in the car. Everything the driver touches and controls must instill this feeling of confidence and precision. We want that person to feel that they have the car under control and that it will do exactly what they desire it to do."

The reputation of German know-how led Volkswagen to top Toyota as the world's most profitable car manufacturer in 2015, listing its 2014 net profit at €2.5 billion in its annual report. The researchers noted that because vehicles by other German makes often are substitutes for Volkswagen vehicles, substitution away from Volkswagen should have increased demand for the other German makes.

However, they found that it did not do so sufficiently to overcome the negative reputation of the scandal. BMW and Mercedes, for example, were not implicated in the emissions scandal, yet their revenue took a hit. The researchers found that collective reputation matters.

In order to document changes in sentiment toward non-VW German automakers that indicate harm to their collective reputation, the researchers reviewed Twitter data from before and after the scandal broke. The data reflected a sharp spike in negative sentiment toward VW: from an average of 3 percentage points below the company's average in the pre-scandal month to an average of 26 percentage points above. There was also a statistically significant decline of 3.5 percentage points in positive sentiment toward non-VW German auto manufacturers as a result of the scandal.

"The scandal must have tarnished the reputations of the other German auto manufacturers through their association with Volkswagen, consistent with the notion of a collective reputation," the authors wrote.