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Firms’ Beliefs and Learning: Models, Identification, and Empirical Evidence

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Abstract

This paper reviews recent literature on structural models of oligopoly competition where firms have biased beliefs about the primitives of the model—e.g. demand, costs—or about the strategic behavior of other firms in the market. We describe different structural models that have been proposed to study this phenomenon and examine the approaches that have been used to identify firms’ beliefs. We discuss empirical results in recent studies and show that accounting for firms’ biased beliefs and learning can have important implications on our measures and interpretation of market efficiency.

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Notes

  1. Bajari et al. (2018) study the impact of big data on firm performance by examining how the amount of data affects the accuracy of retail product forecasts. Their results show that increases in the time dimension of the data (T) improve demand forecasts, though with diminishing returns to scale. In contrast, increases in the number of products in the data (N) do not generate significant improvements in demand forecasts, which is a surprising and controversial result. They also report that the firm’s overall forecast performance—controlling for N and T—has improved over time as the result of better models and methods.

  2. Uncertainty about the next period capital stock can be associated with stochastic depreciation or with randomness in the transformation of current investment into next period productive capital. For instance, capital can follow the transition rule \(k_{t+1}=(1-\delta _{t+1})k_{t}+\gamma _{t+1}\)\(a_{t}\), where \(\delta _{t+1}\) and \(\gamma _{t+1}\) are independently and identically distributed random variables that are unknown to the firm at period t.

  3. Note that the mixing probabilities are different for each value of \(({\mathbf {x}}_{1},a_{0},{\mathbf {x}}_{0})\).

  4. Some examples of kernel functions for adaptive learning are: (i) point kernel: \(K([{\mathbf {x}} _{t},a_{t-1},{\mathbf {x}}_{t-1}]-[{\mathbf {x}}^{\prime },a,{\mathbf {x}}])\) is the indicator function \(1\{[{\mathbf {x}}_{t},a_{t-1},{\mathbf {x}}_{t-1}]=[{\mathbf {x}} ^{\prime },a,{\mathbf {x}}]\}\); (ii) Gaussian: \(\phi ([{\mathbf {x}}_{t} -{\mathbf {x}}^{\prime },a_{t-1}-a,{\mathbf {x}}_{t-1}-{\mathbf {x}}]\beta )\), where \(\phi (.)\) is the density of the standard normal, and \(\beta\) is a vector of weighting parameters.

  5. Suppose that \(b_{t-1}({\mathbf {x}}^{\prime }|a,{\mathbf {x}} )=p_{x}({\mathbf {x}}^{\prime }|a,{\mathbf {x}})\) at any point \(({\mathbf {x}}^{\prime },a,{\mathbf {x}})\) such that at period \(t-1\) the belief function is unbiased. Then, at period t the learning rule implies that \(b_{t}({\mathbf {x}}^{\prime }|a,{\mathbf {x}})-p_{x}({\mathbf {x}}^{\prime }|a,{\mathbf {x}})=\)\(\delta\)\([K([{\mathbf {x}}_{t},a_{t-1},{\mathbf {x}}_{t-1}]-[{\mathbf {x}}^{\prime },a,{\mathbf {x}}])-p_{x}({\mathbf {x}}^{\prime }|a,{\mathbf {x}})]\), which is different from zero at \([{\mathbf {x}}^{\prime },a,{\mathbf {x}}]=[{\mathbf {x}}_{t} ,a_{t-1},{\mathbf {x}}_{t-1}]\) such that convergence is not achieved.

  6. Two important exceptions are Fershtman and Pakes (2012) and Asker et al. (2016) which allow for serially correlated private information. We discuss this more general model when we describe below the concept of Experience-Based equilibrium, and in section 5.6 where we describe Asker et al. (2016).

  7. Similarly as in the single-firm model, the subindex t in the beliefs function represents the firm’s information set \({\mathcal {H}}_{it}\) and it indicates that this function can be updated over time as new information arrives.

  8. In this representation of Bayesian updating in a dynamic game, we are implicitly assuming that at every period \(t\,\)firms observe the state vector \({\mathbf {x}}_{t}\) but not necessarily the competitors’ actions at the previous period, \({\varvec{a}} _{-i,t-1}\). If they had this additional information, the Bayesian updating formula would be slightly different. Note that in many dynamic oligopoly models the endogenous state variable \(k_{it}\) is a deterministic function of \(a_{it-1}\) and \(k_{it-1}\) such that observing the sequence of realizations of \(k_{it}\) is equivalent to observing the sequence of choices \(a_{it}.\)

  9. In the literature, we find two different approaches for the specification of the behavior of Level-0 players. In empirical applications in industrial organization (Goldfarb and Xiao 2011; Hortaçsu et al. 2017), the assumption is that a level-0 firm behaves as a monopolist. However, a good number of experimental papers assume that Level-0 players behave randomly (Camerer et al. 2004; Costa-Gomes and Crawford 2006). Crawford and Iriberri (2007) consider both types of Level-0 behavior. As shown in that paper, the specification of the behavior of Level-0 players can have important implications on the model predictions.

  10. See the critique in Manski (2018) of the traditional practice of asking to make point predictions of future events, instead of asking for probabilistic beliefs. See also Potter et al. (2017) on the advantages of probabilistic survey questions.

  11. Other example of this type of data on firms’ beliefs is the survey on entrepreneurs from the French statistical office (INSEE). For new small startups, the survey ask entrepreneurs the following two questions on their beliefs: Question 1: “What is your view for the next 6–12 months?: 1. the firm will develop, 2. the firm will keep its current balance, 3. I will have to struggle, 4. I will have to shut down the firm, 5. I will sell it, 6. I do not know.”; Question 2: “Do you plan to hire in the next 12 months?: 1. yes, 2. no, 3. I do not know”. Landier and Thesmar (2009) use these data to study the relationship between entrepreneurs’ optimism (over-confidence) and the use of short-term debt finance.

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Acknowledgements

The authors would like to thank the comments and suggestions from the Editors, Victor J. Tremblay and Mo Xiao, and from the many generous colleagues who read a first version of this paper, and especially from Yonghong An, Avi Goldfarb, Xinlong Li, Matthew Osborne, Eduardo Souza-Rodrigues, and Erhao Xie.

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  1. University of Toronto and CEPR, 150 St. George Street., Toronto, ON, M5S 3G7, Canada

    Victor Aguirregabiria

  2. Boston University, 270 Bay State Road, Boston, MA, 02215, USA

    Jihye Jeon

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Aguirregabiria, V., Jeon, J. Firms’ Beliefs and Learning: Models, Identification, and Empirical Evidence. Rev Ind Organ 56, 203–235 (2020). https://doi.org/10.1007/s11151-019-09722-5

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