This article proposes a panel data generalization for a recently suggested instrumental variable‐free estimation method that builds on joint estimation. The author shows how the method can be extended to linear panel models by combining fixed-effects transformations with the common generalized least squares transformation to allow for heterogeneous intercepts. To account for between-regressor dependence, the author proposes determining the joint distribution of the error term and all explanatory variables using a Gaussian copula function, with the distinction that some variables are endogenous and the others are exogenous. The identification does not require any instrumental variables if the regressor–error relation is nonlinear. With a normally distributed error, nonnormally distributed endogenous regressors are therefore required. Monte Carlo simulations assess the finite sample performance of the proposed estimator and demonstrate its superiority to conventional instrumental variable estimation. A specific advantage of the proposed method is that the estimator is unbiased in dynamic panel models with small time dimensions and serially correlated errors; therefore, it is a useful alternative to generalized-method-of-moments-style instrumentation. The practical applicability of the proposed method is demonstrated via an empirical example.
AcemogluDaronMosconaJacobRobinsonJames A. (2016), “State Capacity and American Technology: Evidence from the Nineteenth Century,” American Economic Review, 106 (5), 61–67.
2.
ArellanoManuel (1993), “On the Testing of Correlated Effects with Panel Data,” Journal of Econometrics, 59 (1/2), 87–97.
3.
ArellanoManuelBondStephen (1991), “Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations,” Review of Economic Studies, 58 (2), 277–97.
4.
ArellanoManuelBoverOlympia (1995), “Another Look at the Instrumental Variable Estimation of Error-Components Models,” Journal of Econometrics, 68 (1), 29–51.
5.
BaltagiBadi H.LiQi (1991), “A Transformation that Will Circumvent the Problem of Autocorrelation in an Error-Component Model,” Journal of Econometrics, 48 (3), 385–93.
6.
BeckerJan-MichaelProkschDorianRingleChristian M. (2022), “Revisiting Gaussian Copulas to Handle Endogenous Regressors,” Journal of the Academy of Marketing Science, 50, 46–66.
7.
BeckerMarenWiegandNicoReinartzWerner J. (2019), “Does It Pay to Be Real? Understanding Authenticity in TV Advertising,” Journal of Marketing, 83 (1), 24–50.
BlundellRichardBondStephen (1998), “Initial Conditions and Moment Restrictions in Dynamic Panel Data Models,” Journal of Econometrics, 87 (1), 115–43.
10.
BlundellRichardBondStephenWindmeijerFrank (2001), “Estimation in Dynamic Panel Data Models: Improving on the Performance of the Standard GMM Estimator,” in Nonstationary Panels, Panel Cointegration, and Dynamic Panels, Vol. 15 of Advances in Econometrics, BaltagiB.H.FombyT.B.HillR.C., eds. Bingley, UK: Emerald, 53–91.
11.
BonfrerAndréChintaguntaPradeep K.RobertsJohn H.CorkindaleDavid (2020), “Assessing the Sales Impact of Plain Packaging Regulation for Cigarettes: Evidence from Australia,” Marketing Science, 39 (1), 234–52.
12.
BronnenbergBart J.KrugerMichael W.MelaCarl F. (2008), “Database Paper—The IRI Marketing Data Set,” Marketing Science, 27 (4), 745–48.
13.
BruceNorris I.BeckerMarenReinartzWerner J. (2020), “Communicating Brands in Television Advertising,” Journal of Marketing Research, 57 (2), 236–56.
14.
ChamberlainGary (1982), “Multivariate Regression Models for Panel Data,” Journal of Econometrics, 18 (1), 5–46.
15.
ChamberlainGary (1984), “Panel Data,” in Handbook of Econometrics, GrilichesZ.IntriligatorM.D., eds. Amsterdam: North Holland, 1247–1318.
16.
ChaoJohn C.PhillipsPeter C.B. (1998), “Posterior Distributions in Limited Information Analysis of the Simultaneous Equations Model Using the Jeffreys Prior,” Journal of Econometrics, 87 (1), 49–86.
17.
ChenYung-ShunWangShiu-Tung (2004), “The Empirical Evidence of the Leverage Effect on Volatility in International Bulk Shipping Market,” Maritime Policy & Management, 31 (2), 109–24.
18.
ChintaguntaPradeepDubéJean-PierreGohKhim Yong (2005), “Beyond the Endogeneity Bias: The Effect of Unmeasured Brand Characteristics on Household-Level Brand Choice Models,” Management Science, 51 (5), 832–49.
19.
DanaherPeter J.SmithMichael S. (2011), “Modeling Multivariate Distributions Using Copulas: Applications in Marketing,” Marketing Science, 30 (1), 4–21.
20.
DattaHannesAilawadiKusum L.Van HeerdeHarald J. (2017), “How Well Does Consumer-Based Brand Equity Align with Sales-Based Brand Equity and Marketing-Mix Response?” Journal of Marketing, 81 (3), 1–20.
21.
DostFlorianPhielerUlrikeHaenleinMichaelLibaiBarak (2019), “Seeding as Part of the Marketing Mix: Word-of-Mouth Program Interactions for Fast-Moving Consumer Goods,” Journal of Marketing, 83 (2), 62–81.
22.
ElhorstJ. Paul (2010), “Dynamic Panels with Endogenous Interaction Effects When T is Small,” Regional Science and Urban Economics, 40 (5), 272–82.
23.
GalbraithJohn W.Zinde-WalshVictoria (1992), “The GLS Transformation Matrix and a Semi-Recursive Estimator for the Linear Regression Model with ARMA Errors,” Econometric Theory, 8 (1), 95–111.
24.
GielensKatrijnGeyskensIngeDeleersnyderBarbaraNoheMax (2018), “The New Regulator in Town: The Effect of Walmart’s Sustainability Mandate on Supplier Shareholder Value,” Journal of Marketing, 82 (2), 124–41.
25.
GijsenbergMaarten J. (2014), “Going for Gold: Investigating the (Non)Sense of Increased Advertising Around Major Sports Events,” International Journal of Research in Marketing, 31 (1), 2–15.
26.
GladyNicolasLemmensAurélieCrouxChristophe (2015), “Unveiling the Relationship Between the Transaction Timing, Spending and Dropout Behavior of Customers,” International Journal of Research in Marketing, 32 (1), 78–93.
27.
GonçalvesSílviaKaffoMaximilien (2015), “Bootstrap Inference for Linear Dynamic Panel Data Models with Individual Fixed Effects,” Journal of Econometrics, 186 (2), 407–26.
28.
GonçalvesSílviaKilianLutz (2004), “Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form,” Journal of Econometrics, 123 (1), 89–120.
29.
GretzRichard T.MalsheAshwinBauerCarlosBasuroySuman (2019), “The Impact of Superstar and Non-Superstar Software on Hardware Sales: The Moderating Role of Hardware Lifecycle,” Journal of the Academy of Marketing Science, 47 (3), 394–416.
30.
HorskyDanNelsonPaul (2006), “Testing the Statistical Significance of Linear Programming Estimators,” Management Science, 52 (1), 128–35.
31.
JeffersonPhilip N. (2005), “Deriving the GLS Transformation Parameter in Elementary Panel Data Models,” The American Economist, 49 (1), 45–48.
32.
JudgeGeorge G.GriffithsWilliam E.HillRufus CarterLütkepohlHelmutLeeTsoung-Chao (1985), The Theory and Practice of Econometrics, 2nd ed, Hoboken, NJ: John Wiley & Sons.
33.
JudgeGeorge G.HillRufus CarterGriffithsWilliam E.LütkepohlHelmutLeeTsoung-Chao (1988), Introduction to the Theory and Practice of Econometrics, 2nd ed., Hoboken, NJ: John Wiley & Sons.
34.
KapetaniosGeorge (2008), “A Bootstrap Procedure for Panel Data Sets with Many Cross-Sectional Units,” Econometrics Journal, 11 (2), 377–95.
35.
KellerWiebke I.Y.DeleersnyderBarbaraGedenkKaren (2019), “Price Promotions and Popular Events,” Journal of Marketing, 83 (1), 73–88.
36.
KimJun B.AlbuquerquePauloBronnenbergBart J. (2010), “Online Demand Under Limited Consumer Search,” Marketing Science, 29 (6), 1001–23.
37.
KivietJan F. (1995), “On Bias, Inconsistency, and Efficiency of Various Estimators in Dynamic Panel Data Models,” Journal of Econometrics, 68 (1), 53–78.
38.
KleibergenFrankZivotEric (2003), “Bayesian and Classical Approaches to Instrumental Variable Regression,” Journal of Econometrics, 114 (1), 29–72.
39.
KumarViswanathanZhangXiLuoAnita (2014), “Modeling Customer Opt-In and Opt-Out in a Permission-Based Marketing Context,” Journal of Marketing Research, 51 (4), 403–19.
40.
LeeJu-YeonSridharShrihariPalmatierRobert W. (2017), “The Effect of Firms’ Structural Designs on Advertising and Personal Selling Returns,” International Journal of Research in Marketing, 34 (1), 173–93.
41.
LiuYupingYangRong (2009), “Competing Loyalty Programs: Impact of Market Saturation, Market Share, and Category Expandability,” Journal of Marketing, 73 (1), 93–108.
42.
LovettMitchell J.PeresRenanaXuLinli (2019), “Can Your Advertising Really Buy Earned Impressions? The Effect of Brand Advertising on Word of Mouth,” Quantitative Marketing and Economics, 17 (3), 215–55.
43.
LvXiao-GuangHuangTing-Zhu (2007), “A Note On Inversion of Toeplitz Matrices,” Applied Mathematics Letters, 20 (12), 1189–93.
MooneyChristopher Z.DuvalRobert D. (1993), Bootstrapping: A Nonparametric Approach to Statistical Inference, Vol. 95 of Quantitative Applications in the Social Sciences, 1st ed. Newbury Park, CA: SAGE Publications.
46.
MorenoAntonioTerwieschChristian (2017), “The Effects of Product Line Breadth: Evidence from the Automotive Industry,” Marketing Science, 36 (2), 254–71.
47.
NarayanVishalKadiyaliVrinda (2016), “Repeated Interactions and Improved Outcomes: An Empirical Analysis of Movie Production in the United States,” Management Science, 62 (2), 591–607.
48.
NelsenRoger B. (2006), An Introduction to Copulas, Springer Series in Statistics, 2nd ed. New York: Springer.
49.
NgomPapaMoussaFreedath Djibrilde Dieu NkurunzizaJean (2018), “Strongly Consistent of Kullback-Leibler Divergence Estimator and Tests for Model Selection Based on a Bias Reduced Kernel Density Estimator,” https://arxiv.org/abs/1805.07088.
50.
NickellStephen (1981), “Biases in Dynamic Models with Fixed Effects,” Econometrica, 49 (6), 1417–26.
51.
PapadopoulosAlecos (2021), “Accounting for Endogeneity in Regression Models Using Copulas: A Step-By-Step Guide for Empirical Studies,” Journal of Econometric Methods (published online April 12), https://doi.org/10.1515/jem-2020-0007.
52.
PapiesDominikEbbesPeterVan HeerdeHarald J. (2017), “Addressing Endogeneity in Marketing Models,” in Advanced Methods for Modeling Markets, Vol. 1 of International Series in Quantitative Marketing, LeeflangP.WieringaJ.BijmoltT.PauwelsK., eds. Basel, Switzerland: Springer, 581–627.
53.
ParkSunghoGuptaSachin (2012), “Handling Endogenous Regressors by Joint Estimation Using Copulas,” Marketing Science, 31 (4), 567–86.
54.
PrasadK. ManjunathaBapatR.B. (1992), “The Generalized Moore-Penrose Inverse,” Linear Algebra and its Applications, 165, 59–69.
55.
RandolphWilliam C. (1988), “A Transformation for Heteroscedastic Error Components Regression Models,” Economics Letters, 27 (4), 349–54.
56.
RossiPeter E. (2014), “Even the Rich Can Make Themselves Poor: A Critical Examination of IV Methods in Marketing Applications,” Marketing Science, 33 (5), 655–72.
57.
SchweidelDavid A.ParkYoung-HoonJamalZainab (2014), “A Multiactivity Latent Attrition Model for Customer Base Analysis,” Marketing Science, 33 (2), 273–86.
58.
SethuramanRajTellisGerard J.BrieschRichard A. (2011), “How Well Does Advertising Work? Generalizations from Meta-Analysis of Brand Advertising Elasticities,” Journal of Marketing Research, 48 (3), 457–71.
59.
ShiYuyingLimJeremy M.WeitzBarton A.FranceStephen L. (2018), “The Impact of Retail Format Diversification on Retailers’ Financial Performance,” Journal of the Academy of Marketing Science, 46 (1), 147–67.
60.
SklarM. (1959), “Fonctions de Repartition An Dimensions et Leurs Marges,” Publications de l’institut de Statistique de L’Universit de Paris, 8, 229–31.
61.
StockJames H.WrightJonathan H.YogoMotohiro (2002), “A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments,” Journal of Business & Economic Statistics, 20 (4), 518–29.
62.
TranKien C.TsionasEfthymios G. (2015), “Endogeneity in Stochastic Frontier Models: Copula Approach Without External Instruments,” Economics Letters, 133, 85–8.
63.
TranKien C.TsionasMike G. (2021), “Efficient Semiparametric Copula Estimation of Regression Models with Endogeneity,” Econometric Reviews (published online August 14), https://doi.org/10.1080/07474938.2021.1957284.
64.
Van HeerdeHarald J.DinnerIsaac M.NeslinScott A. (2019), “Engaging the Unengaged Customer: The Value of a Retailer Mobile App,” International Journal of Research in Marketing, 36 (3), 420–38.
65.
Villas-BoasJ. MiguelWinerRussell S. (1999), “Endogeneity in Brand Choice Models,” Management Science, 45 (10), 1324–38.
66.
VombergArndHomburgChristianGwinnerOlivia (2020), “Tolerating and Managing Failure: An Organizational Perspective on Customer Reacquisition Management,” Journal of Marketing, 84 (5), 117–36.
67.
WangHung-JenHoChia-Wen (2010), “Estimating Fixed-Effect Panel Stochastic Frontier Models by Model Transformation,” Journal of Econometrics, 157 (2), 286–96.
68.
Xue-Kun SongPeter (2000), “Multivariate Dispersion Models Generated from Gaussian Copula,” Scandinavian Journal of Statistics, 27 (2), 305–20.
69.
YangShaChenYuxinAllenbyGreg M. (2003), “Bayesian Analysis of Simultaneous Demand and Supply,” Quantitative Marketing and Economics, 1 (3), 251–75.
70.
ZhangXiKumarV.CosgunerKoray (2017), “Dynamically Managing a Profitable Email Marketing Program,” Journal of Marketing Research, 54 (6), 851–66.
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