Together with their associated statistical routines, this paper describes the control and sensitivity methods that can be employed by accounting researchers to address the important issue of unobserved (omitted) variable bias in regression and matching models according to the types of variables employed. As with other social science disciplines, an important and pervasive issue in observational (non-experimental) accounting research is omitted variable bias (endogeneity). Causal inferences for endogenous explanatory variables are biased. This occurs in regression models where an unobserved (confounding) variable is correlated with both the dependent (outcome) variable in a regression model and the causal explanatory (often a selection) variable of interest. The Heckman treatment effect model has been widely employed to control for hidden bias for continuous outcomes and endogenous binary selection variables. However, in accounting studies, limited (categorical) dependent variables are a common feature and endogenous explanatory variables may be other than binary in nature. The purpose of this paper is to provide an overview of contemporary control methods, together with the statistical routines to implement them, which extend the Heckman approach to binary, multinominal, ordinal, count and percentile outcomes and to where endogenous variables take various forms. These contemporary methods aim to improves causal estimates by controlling for hidden bias, though the price of increased complexity. A simpler approach is to conduct sensitivity analysis. This paper also presents a synopsis of a number of sensitivity techniques and their associated statistical routines which accounting researchers can employ routinely to appraise the vulnerability of causal effects to potential (simulated) unobserved bias when estimated with conventional regression and propensity score matching estimators.