W HEN THOMAS PHILIPPON moved from France to America in 1999 to begin a P h D in economics, he found a consumer paradise. Domestic flights were dazzlingly cheap. Household electronics were a relative bargain. In the days of dial-up modems Americans, who were charged a flat rate for local calls, paid far less than Europeans to get online. But over the past two decades, Mr Philippon writes in “The Great Reversal”, this paradise has been lost. Europeans now enjoy cheap cross-continent flights, high-street banking, and phone and internet services; Americans are often at the mercy of indifferent corporate giants. Perking up their economy might mean cutting those giants down to size.

Much that has happened to the American economy since the 1990s has not been to the typical worker’s advantage. Growth in output, wages and productivity has slowed. Inequality has risen, as have the market share and profitability of the most dominant firms. Economics journals are packed with papers on these trends, many of which argue that the dominance of big firms bears some blame for other ills. Between 1987 and 2016 the share of employment accounted for by firms with over 5,000 employees rose from 28% to 34%. Between 1997 and 2012, this newspaper reported in 2016, the average share of revenues accounted for by the top four firms in each of 900 economic sectors grew from 26% to 32%.

Two rival stories vie to explain the rise in concentration. One is that domestic competition has been weakened by lax antitrust enforcement, anticompetitive practices and regulatory changes friendly to powerful firms. This is Mr Philippon’s view. Some economists reckon, though, that concentration is rising because of the success of superstar firms—highly innovative and productive companies that have shoved aside unfit competitors. Either explanation could account for the size and persistent profitability of industry-dominating companies. But the implications of each for future growth—and policy—differ greatly. Which is right?

If concentration is caused by ultra-productive firms outcompeting weaker rivals, then investment ought to rise as those firms scale up to exploit their competitive edge. Investment, however, has been disappointing across the American economy. In the 1990s a statistic called Tobin’s Q (a measure of a firm’s market value relative to the cost of replacing its assets, named after an economist, James Tobin) closely tracked rates of net investment. A high Tobin’s Q indicates that future profits are likely to be high relative to the cost of expanding production. That suggests leading firms should scale up or see a flood of investment by competitors seeking to divert part of that profit stream. In this millennium, however, investment has lagged behind what one would expect, given the level of Tobin’s Q across the economy. A finer-grained analysis shows that the most concentrated sectors account for nearly all the investment shortfall. The change could be caused in part by a shift in investment from tangible capital, such as buildings and machines, to harder-to-measure intangible capital, such as intellectual property, brand value and firm culture. Superstar firms may invest more in intangible capital. But accounting for intangibles, says Mr Philippon, narrows but does not close the investment gap.

Then there is productivity. If concentration is mainly caused by the triumph of superstar firms, it should be rising. Here the data are murkier. The authors of “The fall of the labour share and the rise of superstar firms”, a forthcoming paper in the Quarterly Journal of Economics, find a clear link between size and productivity (bigger firms are more productive) and between industry concentration and patenting (which they use as a proxy for innovation). But the relationship between concentration and measures of productivity is less clear, particularly outside manufacturing. Mr Philippon, on the other hand, finds a positive and statistically significant relationship between concentration and productivity in the 1990s but not more recently. What seems clear is that even as concentration has risen across the economy over the past two decades, the rate of productivity growth has not. If superstar firms are indeed a force for concentration, their unique capabilities have not translated into broader gains for the American economy.

Few economists—or Americans—would deny that there are problems with competition in certain sectors, including health care, finance, telecoms and air travel. The most heated arguments about corporate power, however, concern tech giants. They have not, for the most part, used their market power to raise prices; on the contrary, much of what they provide to consumers is free. The most aggressive invest heavily and eke out rather modest profit margins. Comparisons with Europe are not very helpful, since the continent has mostly failed to produce big and innovative rivals to Google, Apple and Amazon. Would it really be wise for America to carve up its tech champions?

The harder they fall

As Mr Philippon notes, economic power is not all that matters. America’s tech giants have gobbled up competitors and spent lavishly on political donations and lobbying. There is no guarantee that superstars, having achieved dominance, will defend it through innovation and investment rather than anti-competitive behaviour. And even if large platform firms are perfectly efficient, economically speaking, Americans might worry about their influence over communities, social norms and politics.