In defense of reduced form models

This post is for economists in the sense that I freely use jargon and technical concepts of the discipline. If you can’t get past the first sentence, don’t worry about it, and just skip this post. (If you need something good to read, here’s a recommended post from the archives. It’s about Medicare Advantage, circa 2009. Though it is slightly dated, the main concepts remain relevant.)

A slightly different version of the following appears in a forthcoming paper by me, Roger Feldman, and Steve Pizer. If you need to defend reduced form models using HHIs as a measure of market structure, cite this as:

Frakt AB, Pizer SD, and Feldman R, “The Effects of Market Structure and Payment Rates on Private Medicare Health Plan Entry,” forthcoming in Inquiry.

A working paper version is available on SSRN.


There is an ongoing debate about the strengths and limitations of both structural and reduced form models in empirical industrial organization (IO) (Angrist and Pischke 2010, Nevo and Whinston 2010). I’m not going to take a side in that debate. However, I raise the existence of it to point out that it is by no means settled in the broad economics community that either paradigm is preferred for all applications. In this post I explore the strengths and limitations of both types of models, though largely defend the reduced form approach while acknowledging it is not necessarily ideal in all cases.

Recent work on health care markets has used both structural and reduced form approaches: Maruyama (2011), Starc (2010), and Lustig (2010) using structural models and Dafny et al. (2009), Danfy (2010),  Schneider et al. (2008), Shen et al. (2010), Moriya et al. (2010), and Bates and Santerre (2008) using reduced form models. Structural models of entry have been applied in health care (most recently by Maruyama (2011)) and, for decades, to problems in non-health industries as well (e.g., Berry 1992, Seim 2006). Many of the reduced form models employ the Herfindahl-Hirschman Index (HHI) as an independent variable (Dafny et al. 2009, Bates and Santerre 2008, Schneider et al. 2008, Shen et al. 2010, Moriya et al. 2010). Although these are ad hoc, Gaynor and Town (2011) write that “one can think of them as attempting to capture the impacts of relative bargaining power on price, using buyer and seller HHIs as proxies for bargaining power.”

Though there are strengths of structural models, which I’ll get to, one limitation is tractability. For some applications, they cannot be applied for this reason. For instance, Mazzeo (2002) examined entry into motel markets by firms endogenously choosing high, medium, or low quality.  This approach requires firms to choose only one product type in each market and it becomes intractable with more than three types.  If one considers, for example, applying such an approach to the Medicare market of health plans, this intractability becomes a barrier. Although that market has only three main types of products a firm could offer — CCPs (coordinated care plans, like HMOs or PPOs), PDPs (stand alone prescription drug plans), and PFFS (private fee-for-service) plans — Mazzeo’s approach cannot be applied because firms may enter with one of seven configurations (CCP only, PDP only, PFFS only, CCP-PDP, CCP-PFFS, PFFS-PDP, or CCP-PDP-PFFS).

A fundamental distinction between the structural models espoused by practitioners of new empirical IO and the reduced form models coming from the structure-conduct-performance (SCP) paradigm is in the type of assumptions required. Structural modelers correctly point out that market structure is endogenous. In entry models, for instance, concurrent market structure is, in essence, the dependent variable. As an alternative to including market structure (even if lagged and/or instrumented) as an independent variable, structural models instead impose assumptions about the nature of competition between firms. Evaluating the validity of those assumptions requires a substantial research program, sometimes including access to exogenous data on markups (Nevo 2001).

The reduced form SCP approach, on the other hand, permits one to be agnostic about the underlying game and, thereby, to avoid any game-theoretic assumptions (Gaynor and Town 2011). Naturally, the trade off is that one is not estimating fundamental parameters associated with a game. In addition, one must justify the use of HHI on the right-hand side. In particular, one must defend one’s instruments for HHI. However, this is not qualitatively different from a problem faced in structural models that include (instrumented) price as an independent variable. In both contexts, instruments must be defended as reflective of exogenous factors and excludable from the second stage.

When valid instruments for HHI can be found, they may reflect unobserved factors affecting market structure. For example, in the case of health plan entry such factors might include local marketing organizations or longstanding provider networks.  When those factors shift, they affect HHI and entry. By putting (instrumented) HHI on the right-hand side, one gains some insight into the aggregate effects of those factors.  This is a less precise insight than might be gained from a more detailed structural model, but with the advantages of weaker assumptions and simpler interpretability and econometric methodology. In addition, despite its shortcomings, HHI remains an important market measure for policy. The antitrust agencies still use it to inform their analysis of markets for anticompetitive mergers (DoJ and FTC 2010). Consequently, there are both practical empirical and policy relevancy rationales for use of HHIs in a reduced form framework.

Further Reading from TIE


Angrist J and Pischke S. The Credibility Revolution in Empirical Economics: How Better Research Design is Taking the Con out of Econometrics. The Journal of Economic Perspectives 2010;24(2).

Berry S. Estimation of a Model of Entry in the Airline Industry. Econometrica 1992;60(4); 889-97.

Bates L, Santerre R. Do health insurers possess monopsony power? International Journal of Health Care Finance and Economics 2008;8; 1-11.

Dafny L, Duggan M, Ramanarayanan S. Paying a Premium on Your Premium? Consolidation in the U.S. Health Insurance Industry. National Bureau of Economic Research Working Paper No. 15434; 2009; October.

Dafny L. Are health insurance markets competitive? American Economic Review 2010;100;1399-1431.

Gaynor M and Town R. Competition in Health Care Markets. Chapter for the Handbook of Health Economics, Volume 2. T. McGuire, M.V. Pauly, and P. Pita Barros, Editors 2011.

Lustig J. Measuring welfare losses from adverse selection and imperfect competition in privatized Medicare. Unpublished manuscript, Boston University 2010.

Maruyama S. Socially Optimal Subsidies for Entry: The Case of Medicare Payments to HMOs. International Economic Review 2011;52(1).

Mazzeo M. Product Choice and Oligopoly Market Structure. RAND Journal of Economics 2002;33(2); 221–42.

Moriya A, Vogt W, and Gaynor M. Hospital prices and market structure in the hospital and insurance industries. Health Economics, Policy and Law 2010;5; 459-479.

Nevo A. Measuring Market Power in the Ready-to-Eat Cereal Industry. Econometrica 2001;69(2); 307-342.

Nevo A and Whinston M. Taking the dogma out of econometrics: Structural modeling and credible inference. Journal of Economic Perspectives 2010;24(2).

Schneider J, Li P, Klepser D, Peterson N, Brown T, and Scheer R. The effect of physician and health plan market concentration on prices in commercial health insurance markets. International Journal of Health Care Finance and Economics 2008;8:13-26.

Seim K. An Emperical Model of Firm Entry with Endogenous Product-Type Choices. RAND Journal of Economics 2006;37(3); 619-40.

Shen Y, Wu V, and Melnick G. Trends in hospital cost and revenue, 1994-2005: How are they related to HMO penetration, concentration, and for-profit ownership? Health Services Research 2010;45(1); 42-61.

Starc A. Insurer pricing and consumer welfare: Evidence from Medigap. Unpublished manuscript, Harvard University 2010.

U.S. Department of Justice (DoJ) and the Federal Trade Commission (FTC). Horizontal Merger Guidelines. August 19, 2010.

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