The “Efficiency Wage” is a New Keynesian theory aimed to highlight a so-called market failure. Gregory Mankiw describes the theory as follows :
There are various theories about how wages affect worker productivity. One efficiency-wage theory holds that high wages reduce labor turnover. Workers quit jobs for many reasons—to accept better positions at other firms, to change careers, or to move to other parts of the country. The more a firm pays its workers, the greater their incentive to stay with the firm. By paying a high wage, a firm reduces the frequency of quits, thereby decreasing the time spent hiring and training new workers.
What we must understand here is that not all firms should have an incentive to pay a wage above the equilibrium level. An efficiency wage would make a particular job attractive relative to the other options. And this statement holds true unless all firms decide (in unison) to increase wages. An efficiency wage, simply put, is incentive only when wages in firms A, B and C increase relative to wages in firms X, Y and Z.
A second efficiency-wage theory holds that the average quality of a firm’s workforce depends on the wage it pays its employees. If a firm reduces wages, the best employees may take jobs elsewhere, leaving the firm with less-productive employees who have fewer alternative opportunities. By paying a wage above the equilibrium level, the firm may avoid this adverse selection, improve the average quality of its workforce, and thereby increase productivity.
This is the core of the theory. Gregory Mankiw did not specify it, but we know that the theory says something like this : “all firms would pay a wage above the equilibrium level and this would increase unemployment level”. But the biggest problem with the main assumption of the efficiency-wage theory is to infer that people would prefer to starve themselves to death by staying voluntarily unemployed just on the basis that their wages are not incentive enough to put them to work. In the real, non-keynesian world people could not resist a cut in their wages nor they would try to free ride when unemployment is becoming high. That is to say, workers would be more productive, not less, when unemployment is high. A further blow to the theory is the fact that firms have different size. This imply that some industries can pay a higher wage than other industries can.
As for the third assumption :
A third efficiency-wage theory holds that a high wage improves worker effort. This theory posits that firms cannot perfectly monitor the work effort of their employees and that employees must themselves decide how hard to work. Workers can choose to work hard, or they can choose to shirk and risk getting caught and fired. The firm can raise worker effort by paying a high wage. The higher the wage, the greater is the cost to the worker of getting fired. By paying a higher wage, a firm induces more of its employees not to shirk, and thus increases their productivity.
There seems to be little evidence of this. As Knez and Simester (2001) show, Continental Airlines succeeded to overcome the adverse selection phenomenon, thanks to the mutual monitoring :
III. Free Riding and Mutual Monitoring
In this section, we argue that, despite its size, Continental exploited the benefits of mutual monitoring, thus mitigating the free-riding problem. […]
Free Riding and Mutual Monitoring in Large Firms
An incentive scheme like Continental’s is expected to raise efforts only if the additional likelihood of receiving the bonus is sufficient to compensate employees for working harder. Formally, an individual employee deciding whether or not to work hard will do so if and only if bg > c, where b describes the value of the bonus, g denotes the incremental likelihood that the bonus is paid when the employee works hard, and c represents the amount required to compensate an employee for additional effort. Because a single employee has a negligible influence on overall performance, we expect g to be very small. It is this observation that makes the apparent success of Continental’s bonus scheme so surprising. In general, we expect g to be a decreasing function of firm size (n) because overall firm performance is less sensitive to the actions of individual employees in large firms.
By paying all employees a bonus based on satisfaction of a common goal, Continental’s incentive scheme introduces externalities between the efforts of employees and the welfare of their colleagues. Choice of low effort by any employee not only reduces the probability that he or she will receive the bonus, it also affects the likelihood that other employees will receive the bonus. This creates incentives for employees to monitor their colleagues and encourage them to work harder. Mutual monitoring (sanctioning) can take on two forms. First, there is peer pressure in the form of direct sanctioning of co-workers who do not work hard, together with peer pressure generated by the feeling of shame from not working as hard as colleagues (Kandel and Lazear 1992).  Second, an employee may sanction a co-worker by reporting low effort to management. Either way, mutual monitoring is an additional penalty imposed on co-workers who work below (or above) the effort norm established by the group.
There are two reasons to doubt that mutual monitoring will support a high effort norm. First, to the extent that it is costly to monitor and sanction co-workers, there is an incentive to free ride on the monitoring and sanctioning efforts of other co-workers. Moreover, just like the first-order free-rider problem, the larger the group the greater the second-order free-rider problem. Hence, the likelihood of effective mutual monitoring is decreasing in both the size of the group and cost of the mutual monitoring. Second, Continental’s employees were geographically dispersed, restricting direct interactions and preventing them from observing the efforts of employees at other locations. Both reasons have been used previously to support forceful predictions that mutual monitoring will not occur in large firms. 
Mutual Monitoring within Continental’s Autonomous Work Groups
The presence of autonomous work groups mitigates the second-order free-rider problem by reducing group size. This makes monitoring more feasible and limits the opportunity to free ride on the monitoring and sanctioning efforts of colleagues. Furthermore, there are reasons to believe that the structure of airport operations dramatically reduces the cost of monitoring. Ramp and gate employees typically work alongside each other performing overt tasks: pushing out or waving in aircraft, loading and unloading baggage, and greeting and boarding passengers. As a result, they are well placed to observe the performance of fellow team members. Moreover, tasks are standardized and rotated, so employees have a common understanding of what behavior distinguishes high and low effort.  For example, employees unloading baggage from a cart have also spent time inside the hold and can recognize whether delays are due to unusually heavy baggage or neglect by an employee in the hold. Finally, the organization of employees into groups ensures repeated interactions with the same colleagues, revealing habitual (rather than isolated) behavioral patterns.
We might expect that working repeatedly alongside the same colleagues would aggravate sanctioning costs by increasing the cost of damaging social relationships. However, Coleman (1990) argues that in the general context of group norms, sanctioning need not be costly if there is consensus that a high effort “norm” has been violated. Consensus reduces the costs of sanctioning for several reasons. First, it provides social support to the individual that implements the sanction. Second, it may lead to sanctions implemented at the group level (e.g., ostracism from the group’s social interaction). Third, it may increase the likelihood of managerial sanctions against the violator. Finally, the mere knowledge that other group members will discuss a norm violator’s behavior may ensure compliance with the norm. 
Some of the factors that facilitate monitoring also facilitate consensus. Regular interaction with the same employees provides ample opportunity for information about poor performance to be disseminated. Because the work process is standardized, there is a common and accurate interpretation of poor performance. Finally, a high degree of interdependence between group members causes the costs of norm violation (low effort) to be shared. Interdependence is introduced both by the bonus itself (everyone cares about joint output) and the nature of the ramp and gate operations. A flight cannot depart until the entire ramp and gate activities have been performed, so that poor performance by one employee can negate good performance by the rest of the group. For example, maintenance or fueling delays will prevent a flight from leaving on time, even if passengers and baggage are loaded and the plane is otherwise ready to leave. Similarly, if the flight crew is slow to complete their preflight checks, passengers cannot be boarded despite the completion of catering and cleaning activities.
The nature and organization of the gate and ramp activities appear to support our claim that monitoring and sanctioning within Continental’s work groups were feasible and may not have been costly. Conditional on a work group agreeing to adopt a high effort norm, consensus that an employee is performing poorly will develop quickly and support sanctioning. Although formal evidence of sanctioning and monitoring is hard to collect, we did learn of several examples that offer further support for our claim.
As a part of our initial data-gathering exercise we interviewed the CEO, the COO, three supervisors, five ramp and gate employees, and airport managers at three of Continental’s airports (including its largest hub). Four of the ramp and gate employees were interviewed as a focus group. We asked questions concerning the overall structure of operations and observed the process of performing ramp and gate activities. We also posed a series of open-ended questions directed at identifying perceived changes in employee behavior and the reasons for these changes.  Care was taken to avoid leading questions, especially concerning the bonus scheme. The responses and anecdotes that follow are firsthand accounts of employee, supervisor, and airport manager experiences.
A consistent response from the focus group discussion was the emergence of a team orientation that had been absent prior to 1995. We were concerned that employees were reciting the new corporate “mantra” and so asked for explicit examples of employees behaving “more like a team.” We were told that after introduction of the scheme, employees began initiating their own performance reviews whenever airport operations caused a flight to be delayed. These meetings, which were neither attended nor sponsored by managers, focused on identifying sources of delay. Employees also began contacting colleagues who had called in sick, to ask whether any assistance was needed. According to the employees, these calls enabled them to monitor whether the absences were due to valid illnesses. 
We also heard several examples of employees sanctioning each other, including employees being summoned from break rooms by colleagues, employees being chastised for leaving their stations, and gate agents climbing into aircraft holds to identify and help overcome sources of delay. In one example, employees themselves initially attempted to improve a colleague’s performance by providing additional training and reallocating his tasks. When this did not resolve the problem, they reported the situation to management, which (after further opportunities to improve) led to that employee’s dismissal. An increase in the use of social sanctions was apparently particularly noticeable during the pilots’ industrial action in May and June of 1995. The industrial action had a dramatic effect, resulting in rankings of eighth and tenth in on-time performance for May and June (respectively).  Gate and ramp employee reacted strongly, directly confronting pilots who were causing delays and withdrawing cooperation such as access to break rooms and recommendations for dining and ground transportation.
During the focus group the employees volunteered the bonus scheme as an important factor influencing changes in their own behavior. One employee stated that the bonus plan proved that management was serious, and another employee admitted, in a somewhat embarrassed tone, that $65 was an attractive incentive. These sentiments appeared to be shared by the other employees.
The New Keynesian efficiency-wage theory, thus, fails at every level.