Gender Differences in Negotiation have been in debate for a long time. There has been lots of work from psychologists, and empirical work by Linda Babcock. However, I always felt that a controlled economic style experiment was missing. Recently, I became aware of two such attempts.
The first is a lab experiment by Mary Rigdon The Role of Social Information on Gender Differences in Negotiation: Her abstract reads: "There is a consensus that there is a gap between male and female wages. This paper investigates whether this is due to a negotiation gap, and what mechanisms can alleviate it, by examining whether females ask for less in a controlled bargaining setting that accurately models relevant
aspects of negotiating over a starting salary. The results are stark: females ask for less, and earn
less than males. Providing social information eliminates the negotiation gap, and more importantly,
the wage gap." She focuses on women asking for less, in a setting where everyone negotiates (one could think of that as the intensive margin)
The second is a paper by Andreas Leibbrandt and John List "Do Women Avoid Salary Negotiations? Evidence from a Large Scale Natural Field Experiment", their abstract reads as: "One explanation advanced for the persistent gender pay differences in labor markets is that women avoid salary negotiations. By using a natural field experiment that randomizes nearly 2,500 job-seekers into jobs that vary important details of the labor contract, we are able to observe both the nature of sorting and the extent of salary negotiations. We observe interesting data patterns. For example, we find that when there is no explicit statement that wages are negotiable, men are more likely to negotiate than women. However, when we explicitly mention the possibility that wages are negotiable, this difference disappears, and even tends to reverse. In terms of sorting, we find that men in contrast to women prefer job environments where the ‘rules of wage determination’ are ambiguous. This leads to the gender gap being much more pronounced in jobs that leave negotiation of wage ambiguous." It seems they focus on the extensive margin of Negotiation.
I want to also mention the very nice paper by Marco Castillo, Ragan Petrie, Maximo Torero and Lise Vesterlund, "Gender Differences in Bargaining Outcomes: A Field Experiment on Discrimination" whose abstract reads "We examine gender differences in bargaining outcomes in a highly competitive and commonly used market; the taxi market in Lima, Peru. We find that men face higher initial prices and rejection rates. To explain the inferior treatment of men we conduct an experiment where passengers send a signal on valuation before negotiating. The signal eliminates gender differences and the response is shown only to be consistent with statistical discrimination. In separating the role of statistical and taste-based discrimination within the market, we address the concern that discrimination may be implicit." One of the nicest field experiments on Discrimination.