There were many good comments, raising a number of issues that require clarification on my part.
First, there is a significant distinction between public and private corruption, but the latter is a source of inefficiencies. Indeed, although the aggregate economic impact of private corruption is no doubt much smaller than that of public corruption, there is actually less ambiguity about the inefficiency of private corruption. In a standard case of commercial bribery, a buyer for a firm accepts a bribe from a supplier to buy some input from that supplier rather than another. The result is to increase the buying firm's costs, which is both a private and a social harm. Some public corruption, however, can be efficient because it circumvents inefficient laws. Private firms will rarely impose inefficient rules.
This may clarify the sense, confusing to one of the commenters, in which I used "victimless" to describe the crime of bribery. I placed the word in quotation markets in my original posting as here because there are of course victims. But the victims tend to be members of society at large, none of whom has an incentive to complain to the authorities. The bribe giver and bribe taker are unlikely to complain; in that respect the bribe giver is different from the victim of a crime like robbery, who is eager to complain.
A cost of public corruption that I neglected to mention is that it advantages insiders, i.e., people who know whom to bribe, how much to pay and in what form, etc. So people invest in becoming insiders, and the investment represents an added cost of transactions that has on average no economic benefit. This moreover can help us to see why, as I pointed out in my original posting, bribery tends to be more common among immigrant groups. Newly arrived immigrants have difficulty assimilating to their new society so they fall back on personal and business networks within their immigrant community, where they do not face a language or other cultural barrier. In effect they bypass many of the established transactional systems in their new society in favor of systems more suitable to their circumstances. Instead of dealing comfortably with strangers, they base transactions on trust, personal and family contracts, and ethnic solidarity--in other words on methods of transacting that are different from that of impersonal markets--and this facilitates bribery when some members of the network become officials.
Some comments suggest that Becker and I neglect the role of personal values of honesty and integrity in limiting the amount of bribery in a society. Such values are indeed important influences on behavior. But the interesting question is where they come from. We believe they come largely from social and family structures strongly influenced by economic factors, such as immigrant status.
One commenter suggested that bribery is egalitarian, because contracts favor the rich and bribery does not. I think this is mistaken. Contracts often involve asymmetric resources and information, as in the typical consumer transaction, but in a competitive market the net transactional benefit is to consumers because competition forces price down to (or at least close to) cost. Since the cost of a good may be much less than its value (i.e., how much the consumer could be forced to pay for it in the absence of competition), consumer transactions generate consumer surplus, which is to say a net value, above cost.
What is true is that bribery tends to be more common in poor societies. But that is not because bribery benefits the poor, but because bribery is one of the factors that makes a society poor!
Finally, some comments raise the question whether donations by business or other organizations or groups to political campaigns should be considered a form of bribery. There is certainly an analogy, since these donations involve giving money to politicians, many of whom are already officials, in the hope of obtaining some favor to which the donor would not otherwise be entitled. But the differences between this type of "corruption" and conventional bribery are sufficiently great to warrant treating the political donations as a separate issue. The differences include: (1) the pecuniary benefit to the recipient of the donation is indirect, as the money is not being used for his personal consumption but for his political campaign; (2) the recipients are nonincumbent candidates as well as officials, and without access to private donations it would be difficult to challenge an incumbent; (3) more broadly, the alternatives to private financing of political campaigns are fraught with problems; (4) the donations go largely to finance political advertising, which has some social value; and (5) there is no direct quid pro quo.