Do ability tests predict maximal more than typical job performance? I have often read that ability tests are indicative of what people "can do", but that job performance also depends on what people "will do".

For example, Ackerman and Beier (2012) wrote that:


  There is a fundamental mismatch between what is measured by extant
  intelligence tests and the criteria one is most interested in, when
  predicting job-related performance measures, that is, the mismatch
  between typical and maximal behaviors. ... Although assessments of
  what someone can do will serve as an assessment of the upper bound of
  a person’s performance on the day that the applicant is assessed, I–O
  psychologists and managers are most interested in what the applicant
  will do on a day-to-day basis on the job—that is, the individual’s
  typical performance.


Thus, my questions are:


What is the  correlation between maximal job performance and typical job performance?
To what extent do ability tests predict maximal performance more than typical performance?


I'm interested in learning about empirical studies that have tested these ideas. I also imagine that findings will vary based on factors related to the work setting, and so forth (e.g., some work environments permit greater variability in discretionary effort). Also, presumably the degree to which ability-performance correlations differ between typical and maximal will be greater where the correlation between typical and maximal is lower. I'm also interested in understanding more about the methodological challenges associated with operationalising typical and maximal performance.

References


Ackerman, P. L., Beier, M. (2012) The problem is in the defition: g and intelligence in I-O psychology. Industrial and Organizational Psychology, 5 149–188.
The distinction between maximum and typical performance was originally established by Sackett et al. (1988), and since then, how to predict either and their relation to one another seems to have been a very active area of research. In fact, there is a prohibitively large literature on the matter for a full review.
Fortunately, your questions were recently addressed comprehensively, along with other inquiries about the relationship between typical and maximum performance, in the December 2007 issue of Human Performance. To start, one paper by Barnes and Morgeson (2007) which provides support for Ackerman and Beier's claim, in its descriptive sense, that typical performance is that which is of interest to employers, which found that compensation was predicted by typical performance and intra-individual performance variability, but not by maximum performance. I suspect the claim was made in a prescriptive sense, though, so let's continue and see where the evidence takes us.
In the same issue, Marcus et al. (2007) reported support for the long-standing claims that measures of cognitive ability, such as g, serve as predictors of maximum performance, whereas measures of personality serve as predictors of typical performance. Tables provided in this paper also suggest, to me, that a meaningful correlation between typical and maximum performance may be tricky or impossible to elicit, as does another paper in the same issue of the journal.
This paper, by Mangos et al. (2007), suggests that job performance in an ecologically valid setting tends to be characterized by a mixture of need for typical and maximum performance, which I think makes life somewhat difficult for Ackerman and Beier's claim about what IO psychologists and managers are interested in, in the prescriptive sense, with respect to performance. Methodologically, it is not clear how we ought to dissociate the two, and theoretically, it is not clear why we would want to.
In conclusion, based on this special issue on the matter, it seems the simplest answer to your question about ability tests and maximum performance is that ability test scores seem to account for a large amount of the observed variance. With respect to your question about the correlation between maximum and typical performance, it unfortunately appears the answer to your question is complex and not readily summarized.
References

Barnes, C. M., &amp; Morgeson, F. P. (2007). Typical performance, maximal performance, and performance variability: Expanding our understanding of how organizations value performance. Human Performance, 20(3), 259-274.
Mangos, P. M., Steele-Johnson, D., LaHuis, D., &amp; White III, E. D. (2007). A multiple-task measurement framework for assessing maximum-typical performance. Human Performance, 20(3), 241-258.
Marcus, B., Goffin, R. D., Johnston, N. G., &amp; Rothstein, M. G. (2007). Personality and cognitive ability as predictors of typical and maximum managerial performance. Human Performance, 20(3), 275-285.
Sackett, P. R., Zedeck, S., &amp; Fogli, L. (1988). Relations between measures of typical and maximum job performance. Journal of Applied Psychology, 73(3), 482.