He makes some fair points, but this passage strikes me as somewhat obtuse:
The suggestion in the obituaries that he united free-market economists with other conservatives is especially misleading. Free-market economists have always been on a different track from the kind of political and social conservative that Buckley exemplified. He was a friend of free markets, but on moral grounds rather than because he thought the market a more efficient method of allocating resources than the government, though he thought that also.
The conservative economic movement has had two major streams, which are convergent. One is the Austrian school, whose best-known exemplar was Friedrich Hayek ... The other stream, largely independent of the Austrian, originated with maverick economists, such as Milton Friedman, Aaron Director, and George Stigler, who at the height of the 1930s depression, when free-market economics was in the dog house and the Soviet Union's collectivist economy was widely admired including among economists, had the temerity (like Hayek) to argue that collectivist regulation of the economy was inferior to leaving the regulation of economic activity to the market ...
... The movement received virtually no hearing during the 1960s, the era of the "Great Society" programs of Lyndon Johnson. However, the stagflation of the 1970s exposed the failure of conventional “liberal” (in the welfare-state sense) policies, promoted increased acceptance of free-market economics, and stimulated the deregulation and privatization movements, which began in the Clinton Administration and expanded in the Reagan and (first) Bush Administration, continuing into the Clinton Administration, notably with welfare reform.
All this had nothing to do with William Buckley. Most of the causes dearest to his heart were unrelated to economic policy, such as his belief about the proper strategies for defending against the Soviet Union, expelling Soviet agents from the federal government, or defeating our current enemies ...
Buckley may not have united free-market economists with conservatives (though I think even that assertion is open to question), but he certainly united free-market economics with conservatism, and that marriage had a considerable impact on the developments that Posner claims Buckley had "nothing to do with." In the 1970s as today, debates over economic policy - or any policy question - aren't just settled on questions of efficiency and growth maximization; they're settled in public arguments where questions of morality play a not-insignificant role. And by wedding conservatives (and others) to the idea that the free market might be not only morally defensible but actually morally superior to socialism, Buckley helped make free-market economics seem politically as well as theoretically appealing - and that made an enormous difference to its eventual success.
See also Gary Becker's thoughts.