How to get the data to reproduce a published result? I'm studying published journal articles on my topic, and I'd like to reproduce their analysis.  How can I get a copy of their dataset and enough specifications to reproduce their numerical results?

In my specific case, I'm studying this work: Stecklov et al. (2005), published in Demography, and they're using PROGRESA datasets which are publicly available, but when I try to reproduce their results, all the base statistics are off by a bit, and the regressions come out a bit different.  Probably I'm just including or excluding a few different cases, but what can I do to identify the difference?
Email the author nominated for communications, and ask them for a copy of their dataset and enough specifications to reproduce their numeric results. As a backstop, ask for the specific criteria they used to exclude cases. Consider offering co-authorship on any papers that will result from your analysis, as incentive. Give them enough context about you &amp; your own work, so that they know your enquiry is serious, and that you're looking to constructively build on their work, (and not to stitch them up!)