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The computer analysis found that federal agencies awarded more than 190,000 contracts and spent more than $16.3 billion since 2002 on the various efforts — an average of about $1.5 billion annually.

That total, however, does not include the amounts spent each year by the various military services on the hundreds of flyovers they stage with aircraft to wow audiences at sporting events. The Pentagon doesn’t know how much is spent on those efforts, because it doesn’t track the costs.

The biggest spenders among the agencies were the Pentagon, and the departments of the Treasury and of Health and Human Services. The spending on the ads, marketing and image-making appears to have peaked under President George W. Bush in 2008 at nearly $2 billion, and has fallen under President Obama to $1.3 billion in 2011, the last year with full spending records available.

Though most ad and communications campaigns were months or years in the making, federal agencies frequently skipped bargain shopping that would have gotten taxpayers the best deal. At least 30 percent of the advertising, marketing and communications contracts were awarded without full and open competition, the review found.

Not all of the contractors can be publicly tracked. The government — especially the Defense and State Departments — hires many foreign firms for advertising, marketing or communications work, and refuses to disclose their names.

About $161 million over the past decade was awarded to “miscellaneous foreign contractors” for contracts ranging from a Fourth of July fireworks show to sculptures for embassies to expenditures for the newspaper “Baghdad Now,” the investigation found.

Sometimes, different federal agency campaigns offered conflicting messages. For instance, the Health and Human Services Department was spending millions crafting and placing ads encouraging Americans to eat healthier and be more fit, while the U.S. Agriculture Department was spending tens of millions pitching wines, popcorn, hard liquor and chocolates to foreign markets.

The value of the government’s $1.5 billion-a-year outside messaging machine lies in the eye of the beholder.

“Advertising is one of the more effective ways of [recruitment] … advertising is one of the two resources that you can turn on and off easier,” said James Dertouzos, a former economist with RAND Corp. who published a 2009 study that concluded the Army’s ads were effective in attracting new recruits, but could be made even more effective.

Mr. Coburn has sought to shine light on the Agriculture Department’s Market Access Program, which since 1999 has doled out more than $2.1 billion to help American agriculture companies pitch their products in foreign markets. He issued a report this summer questioning why the government was using tax dollars to assist large agribusinesses and its industry trade groups — such as California winemakers, almond growers, candy and popcorn manufacturers and distillers — in competing overseas, when combined they had billions of dollars in annual revenues.

“Despite the billions of dollars in taxpayer funds, little, if any, data exist to show how the program has had any significant impact on American agriculture’s total share of global exports,” Mr. Coburn declared in his report. “The time has come to debate whether the federal government should be in the business of promoting private market goods to foreign buyers.”

The Republican senator may have found an ally in the Obama administration, which has tried to cut MAP and declared in its 2011 budget-savings proposal that the program’s “economic impact is unclear, and it does not serve a clear need.”

While bipartisan sentiments to rein in advertising and marketing spending appear to be rising, the actual job of making cuts is complicated by politics. Big contractors, major agribusinesses, trade lobbies and even NASCAR have their protectors in Congress, and thus far they have been fairly effective in warding off major cuts. And then there’s the added challenge of determining what constitutes advertising and marketing.

The Congressional Research Service’s Kevin Kosar noted in an April 2012 report that there is no official definition for what constitutes federal advertising and no central authority for approving such expenditures. He also noted that the intention of the ad often determines the public’s perception of its value.

“Americans have long been of mixed mind about advertising. On the one hand, advertising is beneficial insofar as it provides information. On the other hand, advertising (be it private or governmental) often attempts to persuade individuals to alter their behaviors,” Mr. Kosar wrote. “Unease with advertising can be magnified if the advertiser is the government, especially if an advertisement conflicts with widely held beliefs about government.”