Stochastics and Statistics Tackling the omitted variables problem without the strong assumptions of proxies Jonathan E. Leightner a, * , Tomoo Inoue b,1 a College of Business Administration, Augusta State University, 2500 Walton Way, Augusta, GA 30904-2200, USA b Seikei University, 3-3-1 Kichijoji-kitamachi, Musashino-shi, Tokyo 180-8633, Japan Received 3 March 2005; accepted 27 February 2006 Available online 18 April 2006 Abstract Omitted variables that interact with included independent variables change the vertical placement of observations. Thus, by projecting the data to an output oriented VRS DEA frontier, the influence of omitted variables can be eliminated. After this is done once, the efficient observations can be eliminated and the process repeated. Each subsequent iteration shows the relationship between the dependant and known independent variable for progressively less favorable omitted variables. Building on these ideas, we introduce a new analytical technique named ‘‘Reiterative Truncated Projected Least Squares’’ (RTPLS). We provide both a theoretical argument and simulation evidence that RTPLS produces less bias than ordinary least squares (OLS) when there are omitted variables that interact with the included variables. By way of example, we show how omitted variables have affected the relationship between the monetary base (MB) and the money supply (M2 + CDs) for Japan using monthly data from January 1970 to April 2003. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Data envelopment analysis; Omitted variables; Monetary policy 1. Introduction Most regressions conducted by economists can be critiqued for omitting some important independent vari- ables – variables that may cause the estimated relationships to change. Variables are often omitted when they cannot be measured, when it is impossible to sufficiently cull down the list of potential additional variables, when it is impossible to model how the omitted variables interact with the included variables, and when the influence of the omitted variables are not known. Traditional techniques for dealing with omitted variables use proxy variables or instrumental variables. However the correct use of proxy variables and instrumental 0377-2217/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2006.02.022 * Corresponding author. Tel.: +1 706 667 4545; fax: +1 706 667 4064. E-mail addresses: jleightn@aug.edu (J.E. Leightner), tinoue@cc.seikei.ac.jp (T. Inoue). 1 Tel.: +81 422 37 3570; fax: +81 422 37 3865. European Journal of Operational Research 178 (2007) 819–840 www.elsevier.com/locate/ejor