At the 2015 conference of the Journal of Accounting Research, the editors set up a paper and panel discussion about structural estimation. Structural estimation is an estimation procedure that recovers the estimated equations from a formal economic model, often but not always with an explicit reference to utility maximization. Setting such a panel is courageous, given that very little such work exists in accounting at this date. The panel included several distinguished empiricists and econometricians (but, surprisingly, no theory), and generally concluded that it is a worthwhile method to explore.
However, I am afraid that lack of perspective about structural estimation might lead to the wrong conclusion about its place within the literature, by giving a misleading impression about what the method can deliver. The two econometricians on the panel, Peter Reiss and Christian Hansen, were both very, very clear that structural estimation does not magically grant identification in the sense of a randomized trial or field experiment. Endogeneity is a problem of lack of information in the data, and cannot be addressed using a more sophisticated technique, should it be instrumental variables or structural estimation.
The role and place of structural estimation lies much closer to reduced-form papers that provide ‘consistent evidence with a model’ as in Theory and Evidence papers. By noting that many theoretical predictions appear to be consistent with data, the reader of such a paper earns some confidence that the model is correctly reflecting the underlying data-generating process; of course, with more risky predictions being satisfied by the data, confidence in the model increases. With this approach, we can never be absolutely sure whether some other endogenous effect might be actually driving the results but there is, clearly, some revision in the reader’s posterior belief.
Structural estimation works in the same manner, but at a much more extreme degree. The procedure forces the researchers to explicitly use all the assumptions made in the theory, including its implied functional forms or moment restrictions. This makes for very, very risky predictions, because structural estimates try to predict not only directions of the effects (as in Theory and Tests) but also magnitudes. A structural model that explains data provides a greater degree of confidence in a theory. In this light, structural estimation is a companion to carefully-crafted reduced-form evidence and, indeed, works with the same scientific approach. Then, its success in accounting will, very probably, be tied to its ability to tie into the extensive empirical literature, and structural estimation should not be marketed, as I heard, as a ‘revolution’.
Unfortunately, the novelty of the technique has created a lot of confusion by some who have never used it, do not know much about it and (this appears to be a constancy in our area) still feel like they should talk about it. A young panelist at the conference stated that structural estimation is very difficult, takes two years to even estimate, and any small change in an assumption would take six months to implement; in fact, he noted, the technique will not pick up until there is a PROC STRUC available. Of course, this comment is stupid and does not refer to any survey of the literature in economics, finance or marketing.
First, structural estimation relies on relatively simple strategic interactions and, unlike theory work, does not require a complete solution of a game, or the derivation of its many properties, since the computer will do the work. Most applied structural estimation is done in Matlab and relies on far fewer lines of code or commands that the typical data cleaning in SAS. As to math, most programs rely on basic matrix algebra, not advanced mathematical concept, and the Matlab automatically provides many optimization routines, just like SAS or Stata will do for statistical analysis. Second, the vast majority of structural models run between an hour and a month, and those based on closed-form moments restrictions are usually on the low end of this range; there are exceptions of course, but those exceptions exist also in reduced-form analysis using, for example, gigantic datasets in physics or computer science. If the estimation takes longer, it can usually be run parallelized (with a single extra command) or, for the lazy researcher like me, can be run by Amazon for an extra fee. Third, many changes, if they do not involve complete generalizations of the model, can be addressed with a simple tweak to the code, as in the case of regression. And, no, the point of structural estimation is to adapt the estimation to the institutional and economic context: there will never be a PROC STRUCT that will create a structural model on demand.
So let us say it: structural estimation will not recover all the answers from endogenous data, will not replace reduced-form statistical analysis (or randomized experiments) but: it is fresh and has great potential to add to the body of knowledge. It is also nascent in accounting, which means that it is, at a point, where the barriers to entry are small because we are writing the very first, simple, such estimations. In my own work, for example, the structural estimation of the Dye model for sporadic (non-sticky) forecasters only requires a few lines of code on Matlab or Stata, essentially solve one non-linear equation, as compared with pages of Stata to clean up the data. The barrier to entry is coding, not mathematics, and empirical researchers have the right skill set to do it, a lot more than theorists (theorists have the motivation, that counts as well though). This makes structural estimation a great place to start for any empiricist with interests in trying something new and different, opening up an area ripe with the unexplored.
If you are structural estimation curious, consider the following further readings:
Earnings management and earnings quality: theory and evidence, by A. Beyer, I. Guttman and I. Marinovic
Causal inference in accounting research, by D. Larker, I. Gow and P. Reiss
Competition in the Audit Market: Policy Implications, by J. Gerakos and C. Syverson
Identifying Accounting Quality, by V. Nikolaev
How often do managers withhold information?, by J. Bertomeu, I. Marinovic and P. Ma
Are Top Management Teams Compensated as Teams? A Structural Approach, by C. Li
Measuring Intentional GAAP Violations: A Structural Approach, by A. Zakolyukina