Abstract
This paper presents a version of the proportionally calibrated almost ideal demand system (PCAIDS) model, useful for merger simulations, which can be econometrically estimated using price data for two firms in a market. PCAIDS is therefore seen as a set of restrictions to be imposed in an econometric estimation, and not only as a pure calibration method. The proposed model is applied to a database of the Argentine gasoline market, and its results are compared to the ones obtained with other alternative specifications.
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Notes
Another difference between PCAIDS and AIDS is that PCAIDS suppresses the real expenditure term when estimating demand equations. The inclusion of this term is one of the distinguishing characteristics of the original AIDS specification. See Deaton and Muellbauer (1980).
The logic of PCAIDS, for example, implies that if own-price elasticities are negative, then cross elasticities are always positive and smaller in absolute value, as well as other desirable properties of demand parameters.
For example, if we have data on the evolution of market shares along time or about differences among market shares in different geographic regions or groups of buyers, that information is not used when PCAIDS is used as a calibration method. That calibration is exclusively based on a “photograph” of average market shares at a certain point in time.
For a more developed explanation of the PCAIDS assumptions and their implications on the matrix of price coefficients, see the appendix in Epstein and Rubinfeld (2002). For an additional exposition of the PCAIDS model, and some possible extensions that allow incorporating more flexible demand specifications, see Epstein and Rubinfeld (2004).
This advantage does not hold if we estimate Eq. (20) as part of a system of demand and supply equations, since in that case the two prices (or at least one of them) become endogenous variables.
These figures correspond to the period 1998–2000. In December 2001 the majority of the shares of Eg3 was bought by the Brazilian firm Petrobras, which since then has been replacing the brand Eg3 by its own one.
In the other nine provinces (Formosa, Jujuy, Mendoza, Misiones, Salta, Santa Cruz, Santiago del Estero, Tierra del Fuego and Tucumán), either there is at least one major national brand that is not present or there is a regional brand which is largest than at least one major national brand.
We also imposed the restriction that, in each equation, the income elasticity be such that the sum of all the elasticities (own-price, cross-price and income elasticity) added up to zero.
Running a joint Wald test of the restrictions that all the own-price elasticities are the same and all the cross-price elasticities are same, for example, produces a chi-square statistic equal to 132.7046, whose probability value is essentially zero. Running an F test using the sum of the square residuals with and without the restrictions produces an F statistic equal to 21.463317, whose probability value is 0.000411.
In this case we were not able to run a joint Wald test of the restrictions, since the restrictions implied by the PCAIDS model are not linear equations of the coefficients produced by the full AIDS model.
OLS was used for this estimation (instead of SUR or 2SLS) because it referred to a single equation, and all its right-hand side variables can be considered exogenous in the context of a demand estimation.
These numbers are evaluated at the average market shares of the firms that appear on Table 1. This occurs because the PCAIDS model generates price elasticities that are functions of those market shares.
We also ran a version of this system of regressions that allowed for different c ypf coefficients in each of the three equations of the system. When we performed a Wald test of the hypothesis that those three coefficients were equal, we obtained a chi-square coefficient of 0.0662, whose probability value is 0.967442. This implies that the null hypothesis cannot be rejected at any reasonable level of significance.
Running a Wald test of the hypothesis that “c avg=−0.284380”, for example, generates a chi-square coefficient equal to 0.366557, whose probability value is equal to 0.544887.
I thank an anonymous referee for having suggested this hypothesis.
References
Deaton A, Muellbauer J (1980) An almost ideal demand system. Am Econ Rev 70:312–326
Epstein R, Rubinfeld D (2002) Merger simulation: A simplified approach with new applications. Antitrust Law J 69:883–919
Epstein R, Rubinfeld D (2004) Merger simulation with brand-level margin data: extending PCAIDS with nests. Advances in economic analysis and policy 4, issue 1, article 2
Hausman J, Leonard G (1997) Economic analysis of differentiated products mergers using real world data. George Mason Law Rev 5:321–346
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Acknowledgements
I am grateful to Andrés Chambouleyron, Baldev Raj and Pablo Spiller for their comments. I am also especially grateful to an anonymous referee, whose comments helped to improve the paper considerably. The remaining errors, of course, are exclusively imputable to me.
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Coloma, G. Econometric estimation of PCAIDS models. Empirical Economics 31, 587–599 (2006). https://doi.org/10.1007/s00181-005-0033-6
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DOI: https://doi.org/10.1007/s00181-005-0033-6