{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T17:22:34Z","timestamp":1774632154369,"version":"3.50.1"},"reference-count":44,"publisher":"The Econometric Society","issue":"4","license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"DOI":"10.13039\/100012296","name":"National Bureau of Economic Research","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100012296","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["QE"],"abstract":"<jats:p>We propose a demand estimation method that allows for a large number of zero\u2010 sale observations, rich unobserved heterogeneity, and endogenous prices. We do so by modeling small market sizes through Poisson arrivals. Each of these arriving consumers solves a standard discrete choice problem. We present a Bayesian IV estimation approach that addresses sampling error in product shares and scales well to rich data environments. The data requirements are traditional market\u2010level data as well as a measure of market sizes or consumer arrivals. After presenting simulation studies, we demonstrate the method in an empirical application of air travel demand.<\/jats:p>","DOI":"10.3982\/qe2147","type":"journal-article","created":{"date-parts":[[2023,11,9]],"date-time":"2023-11-09T08:28:45Z","timestamp":1699518525000},"page":"1251-1294","source":"Crossref","is-referenced-by-count":7,"title":["Demand estimation with infrequent purchases and small market sizes"],"prefix":"10.3982","volume":"14","author":[{"given":"Ali","family":"Horta\u00e7su","sequence":"first","affiliation":[{"name":"Department of Economics, University of Chicago"},{"name":"NBER"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Olivia R.","family":"Natan","sequence":"additional","affiliation":[{"name":"Haas School of Business, University of California"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hayden","family":"Parsley","sequence":"additional","affiliation":[{"name":"Department of Economics, University of Texas"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Timothy","family":"Schwieg","sequence":"additional","affiliation":[{"name":"Booth School of Business, University of Chicago"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kevin R.","family":"Williams","sequence":"additional","affiliation":[{"name":"School of Management, Yale University"},{"name":"NBER"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2359","published-online":{"date-parts":[[2023]]},"reference":[{"key":"quan200301-bib-0001","unstructured":"Abaluck, Jason, Giovanni Compiani, and Fan Zhang (2022), \u201cA method to estimate discrete choice models that is robust to consumer search.\u201d Working Paper."},{"issue":"5","key":"quan200301-bib-0002","doi-asserted-by":"crossref","first-page":"1196","DOI":"10.1287\/msom.2020.0878","volume":"23","author":"Abdallah","year":"2021","journal-title":"Manufacturing & Service Operations Management"},{"key":"quan200301-bib-0003","doi-asserted-by":"crossref","unstructured":"Adam, Hammaad, Pu He, and Fanyin Zheng (2020), \u201cMachine learning for demand estimation in long tail markets.\u201d Working Paper.","DOI":"10.2139\/ssrn.3702093"},{"key":"quan200301-bib-0004","unstructured":"Amano, Tomomichi, Andrew Rhodes, and Stephan Seiler (2022), \u201cFlexible demand estimation with search data.\u201d Working Paper."},{"key":"quan200301-bib-0005","doi-asserted-by":"crossref","unstructured":"Armona, Luis, Greg Lewis, and Georgios Zervas (2021), \u201cLearning product characteristics and consumer preferences from search data.\u201d Working Paper.","DOI":"10.2139\/ssrn.3858377"},{"key":"quan200301-bib-0006","first-page":"183","volume":"1","author":"Berry","year":"2006","journal-title":"Advances in Airline Economics"},{"issue":"5","key":"quan200301-bib-0007","doi-asserted-by":"crossref","first-page":"1749","DOI":"10.3982\/ECTA9027","volume":"82","author":"Berry","year":"2014","journal-title":"Econometrica"},{"key":"quan200301-bib-0008","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1146\/annurev-economics-080315-015050","volume":"8","author":"Berry","year":"2016","journal-title":"Annual Review of Economics"},{"issue":"4","key":"quan200301-bib-0009","doi-asserted-by":"crossref","first-page":"841","DOI":"10.2307\/2171802","volume":"63","author":"Berry","year":"1995","journal-title":"Econometrica"},{"issue":"2","key":"quan200301-bib-0010","doi-asserted-by":"crossref","first-page":"242","DOI":"10.2307\/2555829","volume":"25","author":"Berry","year":"1994","journal-title":"The RAND Journal of Economics"},{"issue":"3","key":"quan200301-bib-0011","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1111\/j.1467-937X.2004.00298.x","volume":"71","author":"Berry","year":"2004","journal-title":"The Review of Economic Studies"},{"issue":"2","key":"quan200301-bib-0012","first-page":"353","volume":"1","author":"Blackwell","year":"1973","journal-title":"The Annals of Statistics"},{"key":"quan200301-bib-0013","author":"Buchholz","year":"2021","journal-title":"The Review of Economic Studies"},{"issue":"2","key":"quan200301-bib-0014","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1016\/j.jeconom.2011.09.001","volume":"166","author":"Burda","year":"2012","journal-title":"Journal of Econometrics"},{"issue":"2","key":"quan200301-bib-0015","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1198\/000313001750358545","volume":"55","author":"Chen","year":"2001","journal-title":"The American Statistician"},{"issue":"1","key":"quan200301-bib-0016","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1257\/000282803321455142","volume":"93","author":"Chevalier","year":"2003","journal-title":"American Economic Review"},{"issue":"4","key":"quan200301-bib-0017","doi-asserted-by":"crossref","first-page":"1108","DOI":"10.1111\/1756-2171.12352","volume":"51","author":"Conlon","year":"2020","journal-title":"The RAND Journal of Economics"},{"issue":"4","key":"quan200301-bib-0018","first-page":"1","volume":"5","author":"Conlon","year":"2013","journal-title":"American Economic Journal: Microeconomics"},{"key":"quan200301-bib-0019","author":"Dub\u00e9","year":"2021","journal-title":"Marketing Science"},{"issue":"1","key":"quan200301-bib-0020","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1111\/j.1756-2171.2007.tb00048.x","volume":"38","author":"Einav","year":"2007","journal-title":"The Rand Journal of Economics"},{"key":"quan200301-bib-0021","volume-title":"Poisson Processes","author":"Gallager","year":"1996"},{"issue":"2","key":"quan200301-bib-0022","doi-asserted-by":"crossref","first-page":"381","DOI":"10.3982\/QE1593","volume":"14","author":"Gandhi","year":"2023","journal-title":"Quantitative Economics"},{"key":"quan200301-bib-0023","unstructured":"Grieco, Paul L. E., Charles Murry, Joris Pinkse, and Stephan Sagl (2023), \u201cConformant and efficient estimation of discrete choice demand models.\u201d Working Paper."},{"issue":"4","key":"quan200301-bib-0024","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1111\/1756-2171.12073","volume":"45","author":"Honka","year":"2014","journal-title":"The RAND Journal of Economics"},{"key":"quan200301-bib-0025","author":"Horta\u00e7su","journal-title":"The Quarterly Journal of Economics"},{"key":"quan200301-bib-0026","doi-asserted-by":"crossref","unstructured":"Horta\u00e7su, Ali, Olivia R. Natan, Hayden Parsley, Timothy Schwieg, and Kevin R. Williams (2023), \u201cSupplement to \u2018Demand estimation with infrequent purchases and small market sizes\u2019.\u201d Quantitative Economics Supplemental Material, 14, https:\/\/doi.org\/10.3982\/QE2147.","DOI":"10.3982\/QE2147"},{"issue":"1","key":"quan200301-bib-0027","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1287\/opre.2014.1326","volume":"63","author":"Jain","year":"2015","journal-title":"Operations Research"},{"issue":"2","key":"quan200301-bib-0028","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/j.jeconom.2008.12.010","volume":"149","author":"Jiang","year":"2009","journal-title":"Journal of Econometrics"},{"issue":"4","key":"quan200301-bib-0029","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1177\/002224378902600401","volume":"26","author":"Kamakura","year":"1989","journal-title":"Journal of Marketing Research"},{"issue":"6","key":"quan200301-bib-0030","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.1287\/mksc.1100.0574","volume":"29","author":"Kim","year":"2010","journal-title":"Marketing Science"},{"key":"quan200301-bib-0031","unstructured":"Lee, Jarod Y. L., Peter J. Green, and Louise M. Ryan (2017), \u201cOn the \u2018Poisson trick\u2019 and its extensions for fitting multinomial regression models.\u201d"},{"key":"quan200301-bib-0032","unstructured":"Li, Jing (2019), \u201cCompatibility and investment in the us electric vehicle market.\u201d Working Paper."},{"key":"quan200301-bib-0033","unstructured":"Lima, Lucas (2021), \u201cDemand estimation with zeros: Moving costs in the us.\u201d Working Paper."},{"key":"quan200301-bib-0034","unstructured":"Murphy, Kevin P. (2007), \u201cConjugate Bayesian analysis of the Gaussian distribution.\u201d Working Paper."},{"issue":"2","key":"quan200301-bib-0035","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1287\/msom.2014.0475","volume":"16","author":"Newman","year":"2014","journal-title":"Manufacturing & Service Operations Management"},{"issue":"1","key":"quan200301-bib-0036","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1509\/jmkr.47.1.3","volume":"47","author":"Petrin","year":"2010","journal-title":"Journal of Marketing Research"},{"issue":"4","key":"quan200301-bib-0037","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1111\/1756-2171.12255","volume":"49","author":"Quan","year":"2018","journal-title":"The RAND Journal of Economics"},{"key":"quan200301-bib-0038","doi-asserted-by":"crossref","DOI":"10.1515\/9781400850303","volume-title":"Bayesian Non- and Semi-Parametric Methods and Applications","author":"Rossi","year":"2014"},{"issue":"2","key":"quan200301-bib-0039","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1177\/002224379303000204","volume":"30","author":"Rossi","year":"1993","journal-title":"Journal of Marketing Research"},{"key":"quan200301-bib-0040","volume-title":"Bayesian Statistics and Marketing","author":"Rossi","year":"2012"},{"issue":"2","key":"quan200301-bib-0041","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1287\/opre.1110.1012","volume":"60","author":"Vulcano","year":"2012","journal-title":"Operations Research"},{"issue":"4","key":"quan200301-bib-0042","doi-asserted-by":"crossref","first-page":"1044","DOI":"10.1287\/opre.2020.2059","volume":"69","author":"Wang","year":"2021","journal-title":"Operations Research"},{"issue":"2","key":"quan200301-bib-0043","doi-asserted-by":"crossref","first-page":"831","DOI":"10.3982\/ECTA16180","volume":"90","author":"Williams","year":"2022","journal-title":"Econometrica"},{"issue":"3","key":"quan200301-bib-0044","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1023\/B:QMEC.0000003327.55605.26","volume":"1","author":"Yang","year":"2003","journal-title":"Quantitative Marketing and Economics"}],"container-title":["Quantitative Economics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.3982\/QE2147","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,9]],"date-time":"2023-11-09T08:30:48Z","timestamp":1699518648000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.econometricsociety.org\/doi\/10.3982\/QE2147"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"references-count":44,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023]]}},"alternative-id":["10.3982\/QE2147"],"URL":"https:\/\/doi.org\/10.3982\/qe2147","relation":{},"ISSN":["1759-7323"],"issn-type":[{"value":"1759-7323","type":"print"}],"subject":[],"published":{"date-parts":[[2023]]}}}