Optimal Selection of Matched Pairs From Large Data Bases

Abstract

This paper considers the problem of selecting matched pairs of observations for the reduction of bias in statistical hypothesis testing. A Euclidean distance function is suggested for measuring the similarity between paired observations. The matching process is then formulated initially as an assignment problem. Alternative formulations of the problem that would reduce computational difficulty are considered. INTRODUCTONMany observational studies are designed to investigate the relationship between a continuous variable (often some measure of performance) and a dichotomous variable used to define group membership. The dichotomous variable (independent variable) is often thought to influence the continuous (dependent) variable. The frequent purpose of such studies is to investigate the consequences of alternative courses of action in order to make better decisions.Consider a commercial bank attempting to decide whether to seek membership in the Federal Reserve System. A prime consideration in the decision might be the effect of membership (the dichotomous variable) upon bank profitability (the continuous variable). A possible decision rule would be to select the alternative (membership or non-membership) that is expected to result in higher profitability. A prerequisite to an informed decision would be to investigate the relationship between membership and profitability, perhaps by contrasting the average profitability of member banks with non-member banks.'Other studies of this type include the following examples: a study to determine whether the viewing of a television broadcast affects viewer attitudes [2], a comparison of certain characteristics between financially sound and problem firms [I41 (151, and a study to determine the effect of a specific personnel program on worker turnover.A complicating factor often encountered in this type of study is the presence of additional variables, called covariables or concomitant variables (e.g., bank size and age in our first example), that are not of direct interest in the study but 'Studies of the relationship between membership in the Federal Reserve System and bank profitability have been undertaken by Gilbert and Peterson [7] and Sinkey and Walker [lS]. 62

Neural network detection of management fraud using published financial data

“…Using a matched pair design has many benefits (Hunt and Ord, 1988;Sibley and Burch, 1979). An important benefit of matched pairs is that it controls for external factors.…”

“…An important benefit of matched pairs is that it controls for external factors. Since our study matches on more than one variable this eliminates most standard randomizing methods (Sibley and Burch, 1979). Therefore we used a manual matching process that reduced the differences for the matched variables for the fraudulent and the control companies.…”

Underwriters and the Broken Chinese Wall: Institutional Holdings and Post-IPO Securities Litigation

“…our sample period, must belong to the same industry, 14 and must be similar to the sued firm with respect to size and return momentum, as measured by total return over a period from four quarters to one quarter before the lawsuit (from TÀ4 to TÀ1). Specifically, we follow the approach by Sibley and Burch (1979) and Antunovich and Sarkar (2006) and select a control firm for every event firm in our sample by minimizing the global distance between the two firms as follows:…”

Underwriters and the Broken Chinese Wall: Institutional Holdings and Post‐ipo Securities Litigation

“…To be included as a nonsued match, the matched firm must have had its IPO within +/− six months of the sued firm, must not have been involved in any securities litigation during our sample period, must belong to the same industry, and must be similar to the sued firm with respect to size and return momentum, as measured by total return over a period from four quarters to one quarter before the lawsuit (from T −4 to T −1). Specifically, we follow the approach by Sibley and Burch () and Antunovich and Sarkar () and select a control firm for every event firm in our sample by minimizing the global distance between the two firms as follows: where d i is the Euclidean distance between the event firm i and control firm c , Size T −4 ,i and Size T −4 ,c are the market capitalizations of firm i and control firm c at time T −4, and Ret T −4, T −1 ,i and Ret T −4 ,T −1, c are the returns for the two firms, calculated over the three‐quarter period between time T −4 and time T −1. Finally, and are the cross‐sectional variances of the average market values and returns, respectively.…”