# Hicksian complementarity and perturbed utility models

Research Article

First Online:

- 3 Downloads

## Abstract

This paper studies aggregate complementarity without price or income variation. We show that for a class of utility functions, variation in non-price observables allows one to recover a measure of complementarity similar to Hicksian complementarity. In addition, the entire Slutsky matrix can be recovered up to scale without price variation. We then examine aggregate complementarity in latent utility models used in discrete choice, bundles, and matching. We show that classical linear instrumental variables can recover Hicksian complementarity for the special case of quadratic utility.

## Keywords

Hicksian complementarity Demand Instrumental variables## JEL Classification

D01 D11 C10## Notes

## References

- Allen, R., Rehbeck, J.: Latent complementarity in bundles models. Available at SSRN 3257028, (2019a)Google Scholar
- Allen, R., Rehbeck, J.: Identification with additively separable heterogeneity. Econometrica
**87**(3), 1021–1054 (2019b)CrossRefGoogle Scholar - Allen, R., Rehbeck, J.: Revealed stochastic choice with attributes. Available at SSRN 2818041 (2019c)Google Scholar
- Amir, Rabah, Erickson, Philip, Jin, Jim: On the microeconomic foundations of linear demand for differentiated products. J. Econ. Theory
**169**, 641–665 (2017)CrossRefGoogle Scholar - Arora, A.: Testing for complementarities in reduced-form regressions: a note. Econ. Lett.
**50**(1), 51–55 (1996)CrossRefGoogle Scholar - Athey, S., Stern, S.: An empirical framework for testing theories about complimentarity in organizational design. Technical report, National Bureau of Economic Research (1998)Google Scholar
- Blackburn, D.: Online piracy and recorded music sales. Working paper, (2004)Google Scholar
- Chambers, C.P., Echenique, F.: Supermodularity and preferences. J. Econ. Theory
**144**(3), 1004–1014 (2009)CrossRefGoogle Scholar - Chiappori, P.-A., Salanié, B.: The econometrics of matching models. J. Econ. Lit.
**54**(3), 832–61 (2016)CrossRefGoogle Scholar - Choo, E., Siow, A.: Who marries whom and why. J. Polit. Econ.
**114**(1), 175–201 (2006)CrossRefGoogle Scholar - Farrell, J., Shapiro, C.: Antitrust evaluation of horizontal mergers: an economic alternative to market definition. BE J. Theoret. Econ.
**10**(1), 1–41 (2010)Google Scholar - Feng, G., Li, X., Wang, Z.: On substitutability and complementarity in discrete choice models. Oper. Res. Lett.
**46**(1), 141–146 (2018)CrossRefGoogle Scholar - Fosgerau, M., de Palma, A. Monardo, J.: Demand models for differentiated products with complementarity and substitutability. Available at SSRN 3141041, (2018)Google Scholar
- Fox, J.T., Yang, C.H., David, H.: Unobserved heterogeneity in matching games. J. Polit. Econ.
**126**(4), 1339–1373 (2018)CrossRefGoogle Scholar - Fudenberg, D., Iijima, R., Strzalecki, T.: Stochastic choice and revealed perturbed utility. Econometrica
**83**(6), 2371–2409 (2015)CrossRefGoogle Scholar - Galichon, A., Salanié, B.: Cupid’s invisible hand: Social surplus and identification in matching models. Available at SSRN 1804623, (2015)Google Scholar
- Gentzkow, M.: Valuing new goods in a model with complementarity: online newspapers. Am. Econ. Rev.
**97**(3), 713–744 (2007)CrossRefGoogle Scholar - Gibson, M., Shrader, J.: Time use and labor productivity: the returns to sleep. Rev. Econ. Stat.
**100**(5), 783–798 (2018)CrossRefGoogle Scholar - Heckman, J.J., Vytlacil, E.: Structural equations, treatment effects, and econometric policy evaluation 1. Econometrica
**73**(3), 669–738 (2005)CrossRefGoogle Scholar - Hicks, J.R., Allen, R.G.D.: A reconsideration of the theory of value. Economica
**1**(1934), 52–176 (1934)CrossRefGoogle Scholar - Hofbauer, J., Sandholm, W.H.: On the global convergence of stochastic fictitious play. Econometrica
**70**(6), 2265–2294 (2002)CrossRefGoogle Scholar - Howard, D.H.: Rationing, quantity constraints, and consumption theory. Econometrica
**45**(2), 399–412 (1977)CrossRefGoogle Scholar - Lancaster, K.J.: A new approach to consumer theory. J. Polit. Econ.
**74**(2), 132–157 (1966)CrossRefGoogle Scholar - Manzini, P., Mariotti, M., Ülkü, L.: Stochastic complementarity. Econ. J.
**129**(619), 1343–1363 (2018)CrossRefGoogle Scholar - McFadden, D.L., Fosgerau, M.: A theory of the perturbed consumer with general budgets. Technical report, National Bureau of Economic Research, (2012)Google Scholar
- McFadden, D.: Econometric models of probabilistic choice. In: Manski, C.F., McFadden, D. (eds.) Structural Analysis of Discrete data with Econometric Applications. MIT Press, Cambridge (1981)Google Scholar
- Milgrom, P., Shannon, C., et al.: Monotone comparative statics. Econometrica
**62**(1), 157–180 (1994)CrossRefGoogle Scholar - Novak, S., Stern, S.: Complementarity among vertical integration decisions: evidence from automobile product development. Manag. Sci.
**55**(2), 311–332 (2009)CrossRefGoogle Scholar - Oberholzer-Gee, F., Strumpf, K.: The effect of file sharing on record sales: an empirical analysis. J. Polit. Econ.
**115**(1), 1–42 (2007)CrossRefGoogle Scholar - Rieskamp, J., Busemeyer, J.R., Mellers, B.A.: Extending the bounds of rationality: evidence and theories of preferential choice. J. Econ. Lit.
**44**, 631–661 (2006)CrossRefGoogle Scholar - Rob, R., Waldfogel, J.: Piracy on the high c’s: music downloading, sales displacement, and social welfare in a sample of college students. J. Law Econ.
**49**(1), 29–62 (2006)CrossRefGoogle Scholar - Samuelson, P.A.: Complementarity: an essay on the 40th anniversary of the Hicks-Allen revolution in demand theory. J. Econ. Lit.
**12**, 1255–1289 (1974)Google Scholar - Schennach, S., White, H., Chalak, K.: Local indirect least squares and average marginal effects in nonseparable structural systems. J. Econ.
**166**(2), 282–302 (2012)CrossRefGoogle Scholar - Topkis, D.M.: Minimizing a submodular function on a lattice. Oper. Res.
**26**(2), 305–321 (1978)CrossRefGoogle Scholar - Varian, H.R.: Microeconomic Analysis. WW Norton, New York (1992)Google Scholar
- Vives, X.: Nash equilibrium with strategic complementarities. J. Math. Econ.
**19**(3), 305–321 (1990)CrossRefGoogle Scholar - Zentner, A.: Measuring the effect of file sharing on music purchases. J. Law Econ.
**49**(1), 63–90 (2006)CrossRefGoogle Scholar

## Copyright information

© Society for the Advancement of Economic Theory 2019