The Difference-in-Differences (DiD) statistical method has now been in use for almost 30 years. see: ‘Using the Longitudinal Structure of Earnings to Estimate the Effect of Training Programs‘ by Orley Ashenfelter; David Card, The Review of Economics and Statistics, Vol. 67, No. 4. (Nov., 1985), pp. 648-660. (page 5 in the .pdf).
And the Difference-in-Differences (DiD) method was extended, in 1994, with the addition of the the Difference-in-Difference-in-Differences (DiDiD) technique. See: Jonathan Gruber : ‘The Incidence of mandated Maternity benefits’ The American Economic Review, Vol. 84, No. 3 (Jun., 1994), pp. 622-641 (page 7 in the .pdf)
Improbable will of course attempt to inform readers if and when the Difference-in-Difference-in-Difference-in-Differences method makes an appearance.
Further extensions of the Did and DiDiD : In 1998, the Difference-in-Differences (DiD) method was extended by Heckman, J., Ichimura, H., Smith, J. and Todd, P. ‘Characterizing selection bias using experimental data’, Econometrica, Vol. 66, pp. 1017–1098. (page 25 in the .pdf) to include the Conditional Difference-in-Differences (CDiD) method.
And in 2011 the Difference-in-Difference-in-Differences (DiDiD) method, like the Difference-in-Differences (DiD) method before it, also received a conditional extension, the Conditional Difference-in-Difference-in-Differences (CDiDiD) paradigm. see: Buscha, F., Maurel, A., Page, L. and Speckesser, S. (2012), ‘The Effect of Employment while in High School on Educational Attainment: A Conditional Difference-in-Differences Approach.‘ Oxford Bulletin of Economics and Statistics, 74: 380–396. (page 7 in the .pdf).
Note: Statistically speaking, not everyone is 100% convinced of the accuracy of some DiD applications. See: from 2003, Bertrand, M.; Duflo, E.; Mullainathan, S. ‘How Much Should We Trust Differences-in-Differences Estimates?‘. Quarterly Journal of Economics 119 (1): 249–275 (page 18 in the .pdf)
“Our study suggests that, because of serial correlation, conventional DD standard errors may grossly understate the standard deviation of the estimated treatment effects, leading to serious over-estimation of t-statistics and significance levels. Since a large fraction of the published DD papers we surveyed report t-statistics around 2, our results suggest that some of these findings may not be as significant as previously thought if the outcome variables under study are serially correlated. In other words, it is possible that too many false rejections of the null hypothesis of no effect have taken place.”
BONUS: ‘Difference in Indifference’ in: ‘Intermediacy: extracting vitality from intersecting borderlines’ (page 11 in the .pdf)
“Ordinary is ordinary. Indifferent is indifferent. Too many differences are likely to turn into indifference. Minute difference in indifference is far more extra-different than exhaustive extra-ordinary.”