Examining the tradeoff between fixed pay and performance-related pay: A choice experiment approach

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2 Examining the tradeoff between fixed pay and performance-related pay: A choice experiment approach JUNYI SHEN * Reearch Intitute for Economic and Buine Adminitration, Kobe Univerity KAZUHITO OGAWA Faculty of Sociology, Kanai Univerity HIROMASA TAKAHASHI Faculty of International Studie, Hirohima City Univerity Abtract Previou invetigation on performance-related pay have mainly analyzed it relationhip with earning, productivity, and job atifaction. Le attention ha been devoted to the invetigation of individual preference for the performance-related payment ytem per e and conequently the tradeoff between fixed pay and performance-related pay. In thi paper, we firt ue a choice experiment approach to invetigate the tradeoff between fixed pay and performance-related pay, and then link the tradeoff for each individual with their rik preference. Our main reult indicate that individual preference for the payment ytem per e and the magnitude of tradeoff between fixed pay and performance pay are different according to their rik preference. Keyword: fixed pay; performance-related pay; choice experiment; rik preference JEL code: C35, J33 * Correponding author. Junyi Shen. Reearch Intitute for Economic and Buine Adminitration, Kobe Univerity, 2-1 Rokkodai, Nada, Kobe , Japan. Tel/Fax: ; hen@rieb.kobe-u.ac.jp

3 1. Introduction Individual are normally employed by firm under a variety of type of payment ytem: fixed pay, performance-related pay, and payment combining fixed pay and performance-related pay. The iue of effective performance and reward management ha been a topic of continuou reearch and dicuion within the dicipline of peronnel economic and human reource management (Baruch et al., 2004). In recent year, performance-related pay, either eparated from or combined with fixed pay, ha been much more widely ued a part of the human reource policie of organization, where the aim of thi increaed ue ha been to increae the output (e.g., number of product, quality of ervice, and revenue) from the input (both quantitative and qualitative) of employee. Support for performance-related pay i theoretically grounded in expectancy theory (Pearce and Perry, 1983) and reinforcement theory (Perry et al., 2006). Expectancy theory (Vroom, 1964) i predicated on a belief that individual will exert effort if they expect it to reult in an outcome that they value. In the cae of performance-related pay, employee will work harder if they value monetary reward and believe that uch reward will reult from their increaed effort. Reinforcement theory poit a direct relationhip between a deired target behavior (e.g., performance) and it conequence (e.g., pay). It ugget that pay can be ued to create conequence for deired behavior uch a high performance that will reinforce the behavior (Perry et al., 2009). Previou empirical invetigation on performance-related pay have mainly analyzed it relationhip with earning (Booth and Frank, 1999; McNabb and Whitfield, 2007), with productivity (Lazear, 2000), and with job atifaction (Green and Heywood, 2008; Heywood and Wei, 2006). Le attention ha been devoted to the invetigation of individual preference for the performance-related payment ytem per e and conequently the tradeoff between fixed pay and performance-related pay. We think thi may be due to it being quite difficult to find a uitable and appropriate method to elicit individual preference for the tradeoff between fixed pay and performance-related pay. Therefore, the firt motivation of thi paper i to try to olve thi preference elicitation problem by uing a choice experiment approach, which i frequently applied in environmental economic, tranportation economic, and marketing cience. Our econd purpoe i to manifet the link of the magnitude of individual tradeoff between fixed pay and performance-related pay to their rik preference, becaue thi i a natural extenion of the tudy of performance-related pay but i eldom invetigated in the related literature. Our analyi i baed on data from a quetionnaire urvey conducted at Kanai Univerity, Japan. In the urvey, we ued a choice experiment in order to elicit the tradeoff between fixed pay and performance-related pay. In the choice experiment, we do not directly oberve the tradeoff, but only the repondent choice in certain ituation. In the econometric analye, we therefore apply a latent cla logit model, which aume that the population conit of a number of latent clae and

4 the unoberved heterogeneity among individual can be captured by thee clae through etimating a different parameter vector in the correponding utility function. Although we do not oberve the tradeoff directly, we can etimate the tradeoff value for each repondent from the parameter etimated by thi model. After the tradeoff for each repondent ha been etimated, we then examine it relationhip with the rik preference of each repondent. Note that the rik preference of each repondent were alo elicited from the quetionnaire urvey. The ret of the paper i organized a follow. Section 2 contain a decription of the urvey and the econometric approach applied. In Section 3 we preent the reult from the empirical analye, and finally in Section 4 we conclude the paper. 2. Methodological iue 2.1 Survey In a choice experiment, individual are uually aked to make repeated election of their preferred alternative in the choice et preented to them. In our urvey, before the choice et were preented, a hypothetical cenario relating to a job decription wa firt provided to the repondent. The cenario include the following: (i) each repondent i aumed to undertake a 5-hour part-time job of elling nack at a local fetival; (ii) the price of each nack would be 150 JP yen; (iii) the number of participant in the fetival would be about 500; (iv) there would be no other hop elling nack in the fetival; and (v) each repondent can elect their preferred payment ytem from the alternative we provided. In each choice et, we provided three alternative, named Payment A, Payment B, and Payment C. Each payment ha two common attribute hourly pay and pay per nack old. Note that in our experimental deign, the former correpond to fixed pay and the latter refer to performance-related pay. The attribute level conidered for each payment type are provided in Table 1. A hown in the table, ince the level of the performance-related pay in Payment A and the fixed pay in Payment B are et to be alway zero, Payment A and Payment B repreent a pure fixed payment ytem and a pure performance-related payment ytem, repectively. In contrat, Payment C i correpond to a combined payment ytem with both fixed pay and performance-related pay. 1 Concerning the iue of creating the choice et in our choice experiment, a full factorial deign wa adopted and 27 (i.e., 3 3 ) choice et were finally created. Thee choice et were then randomly divided into 3 different block of choice et, which were randomly allocated to the repondent. Each block conit of 9 choice et. An example of a choice et i preented in Table 2. The urvey wa conducted between July and November 2013 at Kanai Univerity, Japan. All 1 Although it i clear from the choice et that Payment A, B, and C repreent a pure fixed payment, a pure performance-related payment, and a mixed payment, we till applied thee unlabeled name in order to avoid poible anchoring effect from the label.

5 the repondent were undergraduate at Kanai Univerity. They were originally recruited to attend an economic experiment. After the experiment, they were aked to anwer a pot-experiment quetionnaire, the data of which are ued for the preent tudy. The quetionnaire conit of the choice experiment quetion mentioned above and everal other quetion related to their experimental behavior and rik attitude. 2 The average time for anwering thi quetionnaire wa approximately 15 minute. In total, 238 valid ample were collected, correponding to 98 male and 140 female repondent. 2.2 Econometric model Choice model are baed on random utility theory. The baic aumption embodied in the random utility approach to choice modeling i that deciion maker tend to act a utility maximizer, i.e., given a et of alternative the deciion maker will chooe the alternative that maximize utility. The utility of an alternative for an individual (U) i modeled a the um of a determinitic component (V ) and a random error term ( ). Formally, individual q utility of alternative i can be expreed a U. (1) V Hence the probability that individual q chooe alternative i from a particular et J that comprie j alternative can be written a P PU ( U ; j( i) J) P( V V ; j( i) J). (2) jq jq jq Converting the random utility model into a choice model require certain aumption about the joint ditribution of the vector of random error term. If the random error term are aumed to follow the type I extreme value (EV1) ditribution and be independently and identically ditributed (IID) acro alternative and cae (or obervation), the multinomial (or ometime called conditional) logit (MNL) model (McFadden, 1974) i obtained. In the MNL model, the choice probability in Equation (2) i expreed a P J exp( V ) / exp( V ). (3) j1 jq Then, making the further aumption that the determinitic component of utility i linear and 2 The experimental reult are to be reported in another paper.

6 additive in parameter, V X, the probability in Equation (3) can be given a P J exp( X ) / exp( X ) (4) j1 jq where repreent a cale parameter that determine the cale of the utilitie, which i typically normalized to 1.0 in the MNL model; X are explanatory variable of V, which normally include alternative-pecific contant (ASC), the attribute of the alternative i, and the ocial-economic characteritic of the individual q ; and i the parameter vector aociated with the matrix X. It i well known that heterogeneity among individual i extremely difficult to examine in the MNL model. Thi limitation could be relaxed, to ome extent, by interaction term between individual-pecific characteritic and variou choice. However, thi method i limited in that it require a priori election of key individual characteritic and attribute and involve merely a limited election of individual pecific variable (Boxall and Adamowicz, 2002). One way of circumventing thi difficulty i uing etimation obtained from the latent cla logit (LCL) model. The LCL model aume that the population conit of a number of latent clae S and the unoberved heterogeneity among individual can be captured by thee clae through etimating a different parameter vector in the correponding utility function. Formally, the choice probability of individual q of cla i expreed a P J exp( X ) / exp( X jq ) j1 1,..., S (5) where and are cla-pecific cale and utility parameter, repectively. Then, in accordance with Boxall and Adamowicz (2002), Louviere et al. (2000), and Swait (1994, 2007), the probability of individual q in cla (H q ) can be expreed a H exp( Z )/ exp( Z ) (6) q q q 1 S where i a cale factor typically normalized to 1.0, i the parameter vector in cla, and Z denote a et of characteritic (e.g., individual-pecific characteritic) determining the q claification probability. Combining conditional choice equation (5) and memberhip claification equation (6), the unconditional probability of chooing alternative i i given a

7 S S J S P P H q exp( X )/ exp( X ) jq exp( Z q)/ exp( Z. (7) q ) 1 1 j1 1 In equation (7), when we et and equal to one 3, the parameter vector and imultaneouly etimated by the maximum likelihood method to explain choice behavior. 4 can be However, the LCL model cannot be etimated unle S (the number of clae) in equation (7) i given, becaue S i dicrete but maximum likelihood etimation theory require that the parameter pace be continuou and etimate be in the interior of the pace (Swait, 2007). Therefore, the central iue in the LCL model i how to determine S. The literature ha recommended a number of information criteria for thi purpoe (e.g., Boxall and Adamowicz, 2002; Greene and Henher, 2003; Louviere et al., 2000; Morey el al., 2006; Shen, 2006; Swait, 2007). Among thee, four meaure baed on the log likelihood at convergence with clae, ample ize, and number of parameter are popular for determining S. Thee are defined a follow Akaike Information Criterion, AIC 2(log L* K ) (8) Akaike 2, 2 1 [ AIC / ( 2 log L )] (9) 0 Bozdogan Akaike Information Criterion, AIC3 2log L* 3K (10) Bayeian Information Criterion, BIC log L* ( K log N)/ 2 (11) where logl* i the log likelihood at convergence with clae, K i the number of parameter in the model with clae, L0 i the log likelihood of the ample with equal choice probabilitie, and N i the ample ize. An alternative approach that can account for individual heterogeneity i called the random parameter logit (RPL) or mixed logit (ML) model; thi model allow model parameter to vary randomly according to aumed ditribution (e.g., normal, log-normal, or triangular) over individual (e.g., Bhat and Goen, 2004; Bjørner et al., 2004; Greene and Henher, 2003; He et al., 2005; McFadden and Train, 2000; Revelt and Train, 1998; Train, 1998). In thi approach, each individual ha their own et of cale and utility parameter. From thi viewpoint, one could regard the RPL/ML model a the cae where each individual in the ample can be conidered a an individual cla, which i indeed the LCL model with N (ample ize) clae. In other word, the LCL model control individual heterogeneity with clae, where i between 1 and N. Compared 3 Boxall and Adamowicz (2002) note that utilizing the LCL model in empirical etimation require all cale factor in equation (7) to be et equal to one. 4 The parameter vector in one of the latent clae mut be normalized to zero (e.g., 1 0 ) to run the etimation. Therefore, the remaining are identified relative to thi normalization.

8 to the RPL model, there are two major advantage of the LCL model. Firt, the LCL approach i emi-parametric, o it doe not require any pecific aumption about the ditribution of parameter acro individual (Greene and Henher, 2003). Second, the LCL model yield the probabilitie in each cla. Thi mean that although each repondent i aumed to belong to one cla, it i taken into account that there i uncertainty about a repondent cla memberhip. 3. Reult Table 3 and 4 preent the reult aociated with the MNL/LCL pecification. All the reult preented were analyzed by uing NLOGIT 5.0, a pecialit dicrete modeling package in LIMDEP (Econometric Software, Inc.). With regard to the overall impreion of the MNL and LCL etimate hown in Table 4, we find that compared to the MNL model, the goodne-of-fit meaure (e.g., log-likelihood, Peudo R 2, and predictive power) are ignificantly improved by applying the LCL approach. 3.1 Determining the number of latent clae A dicued in Section 2, the meaure of AIC, 2, AIC3, and BIC were applied to help determine the number of latent clae. We attempted variou number of clae (1, 2, 3, 4, 5, and 6 clae) and ummarize the tatitic in Table 3. The log-likelihood value at convergence reveal that the greater the number of clae, the better the model fit i. Thi i not urpriing, becaue log-likelihood value normally increae in magnitude when there are more parameter to be etimated (Shen and Saijo, 2009). From the meaure of AIC3 and BIC, we find that the minimum value are in the 4-cla model, uggeting that the 4-cla model i optimal. Furthermore, although the minimum of AIC and the maximum of 2 eem to upport the 6-cla model a the bet olution, the improvement from 4 clae to 6 clae i o mall a to be negligible. Therefore, we determined to elect 4 clae for etimating the LCL model in thi tudy. 3.2 Reult of the 4-cla LCL model The etimated reult of the 4-cla LCL model are lited in Table 4. For comparion purpoe, the MNL etimate are alo provided. Two alternative pecific contant (i.e., Payment A and Payment B) and two attribute (i.e., Hourly pay and Pay for each nack old) were etimated a explanatory variable. Note again that Payment A and Payment B repreent the pure fixed payment and pure performance-related payment ytem, repectively. Firt, look at the parameter of Payment A and Payment B. Compared to the MNL etimate, the LCL etimate help u achieve freh inight into repondent preference over different type of payment ytem. Baed on the etimated ign and ignificance, about 37% of the repondent (i.e., repondent in cla 3) prefer the pure performance-related payment ytem and do not prefer the

9 pure fixed payment ytem, relative to the payment ytem that mixe both fixed pay and performance-related pay. In contrat, about 13% of the repondent (i.e., repondent in cla 1) and 19% of the repondent (i.e., repondent in cla 4) favor the pure fixed payment and the pure performance-related payment ytem, repectively, over the mixed payment ytem. Furthermore, the remaining 30% of the repondent (i.e., repondent in cla 2) have no difference with repect to type of payment ytem. Concerning the etimated poitive parameter of Hourly pay and Pay for each nack old, we find that both are highly ignificant in all clae. Thi reult indicate that the higher the pay, either fixed or performance-related, the happier the repondent are. Furthermore, baed on thee etimated parameter, we can calculate the value of the marginal tradeoff between fixed pay and performance-related pay for each cla by dividing the latter parameter by the former. The value are calculated a in cla 1, 7.67 in cla 2, 5.89 in cla 3, and 8.29 in cla 4. It hould be noted that the larger the value of the tradeoff, the more likely repondent are to prefer the marginal increae in the fixed pay. Therefore, from thee cla-baed value, it i clear that repondent in cla 1 prefer the marginal increae in the fixed pay the mot, and repondent in cla 3 prefer the marginal increae in the fixed pay the leat. It i worth noting that thi evidence i conitent with that obtained from the pecific alternative. That i to ay, on the one hand the repondent in cla 1 prefer the pure fixed payment ytem to the other two, and thu they have the highet value of the marginal tradeoff; on the other hand the repondent in cla 3 prefer the pure performance-related payment ytem to the other two, and thu they have the lowet value of the marginal tradeoff. 3.3 Rik preference and individual tradeoff between fixed pay and performance-related pay We aked the repondent to anwer three quetion relating to rik attitude in the urvey, aiming at eliciting their rik preference. The detailed quetion are provided in the Appendix. We categorized repondent rik preference into rik-avere, rik-neutral, and rik-loving by the criterion that rik-avere i aigned by Q1 if the anwer of Q1 i greater than 0.5, by Q2 if the anwer of Q2 i greater than 0.25, and by Q3 if the anwer of Q3 i maller than 0.5; rik-neutral i aigned by Q1 if the anwer of Q1 i equal to 0.5, by Q2 if the anwer of Q2 i equal to 0.25, and by Q3 if the anwer of Q3 i equal to 0.5; and rik-loving i aigned by Q1 if the anwer of Q1 i maller than 0.5, by Q2 if the anwer of Q2 i maller than 0.25, and by Q3 if the anwer of Q3 i larger than 0.5. By uing the reult of the 4-cla LCL model and conditioning thee on the individual choice, it i poible to obtain the value of the marginal tradeoff between fixed pay and performance-related pay for each individual. The mean individual tradeoff categorized into the above-decribed three rik categorie are preented in Figure 1. A hown in the figure, the mean individual tradeoff between fixed pay and performance-related pay decreae a the degree of rik-eeking goe up for

10 all three quetion. Thi i plauible becaue rik lover are uually willing to acrifice aured pay in order to purue a greater poible reward; a a reult, they are willing to accept a maller marginal increae in the performance-related pay. We alo conducted a two-tailed t-tet for the null hypothei that there i no difference in the mean tradeoff between rik averter and rik lover. A a reult, the null hypothei i ignificantly rejected at the 5% level in Q1 (t = 2.225, p = 0.027, degree of freedom = 222) and 10% level in Q2 (t = 1.783, p = 0.076, degree of freedom = 186) and Q3 (t = 1.764, p = 0.079, degree of freedom = 180), which provide upportive evidence that rik lover are willing to accept a maller ratio of performance-related pay to fixed pay. 4. Concluion The latent cla logit approach allow u to etimate both the value of the cla-baed and individual-baed marginal tradeoff between fixed pay and performance-related pay. Our empirical reult imply that repondent belonging to different clae have not only different preference with repect to the fixed payment and/or performance-related payment ytem per e but alo different value of the marginal tradeoff between fixed pay and performance-related pay. In other word, individual preference for the payment ytem and the magnitude of tradeoff between different kind of pay are different. Thi raie an important implication that firm or employer hould deign more-flexible payment ytem to meet with their employee preference for payment. However, thi i very difficult to put into operation in the real world becaue firm or employer do not normally know their employee true preference in advance. Our analyi on linking the value of the tradeoff between fixed pay and performance-related pay with rik preference may be, to ome extent, a hortcut to olve thi problem. Our reult ugget that rik lover are more willing to chooe a performance-related payment ytem and rik averter are more willing to chooe a fixed payment ytem. Baed on thi, individual preference for payment ytem can be elicited from their rik preference, while eliciting rik preference i conidered to be relatively eay. Acknowledgement Financial upport from the Japanee Minitry of Education, Culture, Sport, Science and Technology through Grand-in-aid for Scientific Reearch (C) i gratefully acknowledged. All of the view expreed in thi paper and any error are the ole reponibility of the author. Appendix. Quetion related to rik preference Q1. There are two alternative. Alternative 1 i that you will obtain 100 thouand JP yen with a probability of 100%. Alternative 2 i that you will obtain 200 thouand JP yen with a probability of ( ) %. Pleae fill in the parenthei with a numeral o that thee two alternative have the ame value to you.

11 Q2. There are two alternative. Alternative 1 i that you will obtain 100 thouand JP yen with a probability of 50%. Alternative 2 i that you will obtain 200 thouand JP yen with a probability of ( ) %. Pleae fill in the parenthei with a numeral o that thee two alternative have the ame value to you. Q3. When you go out, you will bring the umbrella if a ( ) % chance of rain i announced a the weather forecat. Pleae fill in the parenthei with a numeral. Reference Baruch, Y., K. Wheeler, and X. Zhao Performance-related pay in Chinee profeional port. International Journal of Human Reource Management 15(1): Bhat, C. R. and R. Goen A mixed multinomial logit model analyi of weekend recreational epiode type choice. Tranportation Reearch Part B 38: Bjørner, T. B., L. G. Hanen, and C. R. Ruell Environmental labeling and conumer choice: An empirical analyi of the effect of the Nordic Swan. Journal of Environmental Economic and Management 47: Booth, A. L. and J. Frank Earning, productivity and performance related pay. Journal of Labor Economic 17(3): Boxall, P. C. and W. L. Adamowicz Undertanding heterogeneou preference in random utility model: A latent cla approach. Environmental and Reource Economic 23: Green, C. and J. S. Heywood Doe performance pay increae job atifaction?. Economica 75: Greene, W. H. and D. A. Henher A latent cla model for dicrete choice analyi: contrat with mixed logit. Tranportation Reearch Part B 37: He, S., M. Bierlaire, and J. W. Polak Etimation of value of travel-time aving uing mixed logit model. Tranportation Reearch Part A 39: Heywood, J. S. and X. Wei Performance pay and job atifaction. Journal of Indutrial Relation 48: Lazear, E. P Performance pay and productivity. American Economic Review 90(5): Louviere, J. J., D. A. Henher, and J. D. Swait Stated Choice Method: Analyi and Application. Cambridge Univerity Pre. McFadden, D. and K. Train Mixed MNL model for dicrete repone. Journal of Applied Econometric 15: McNabb, R. and K. Whitfield The impact of varying type of performance-related pay and

12 employee participation on earning. International Journal of Human Reource Management 18(6): Morey, E., J. Thacher, and W. Breffle Uing angler characteritic and attitudinal data to identify environmental preference clae: A latent-cla model. Environmental and Reource Economic 34: Pearce, J. L. and J. L. Perry Federal merit pay: A longitudinal analyi. Public Adminitration Review 43(4): Perry, J. L., T. A. Engber, and Y. J. So Back to the future? Performance-related pay, empirical reearch, and the peril of peritence. Public Adminitration Review 69(1): Perry, J. L., D. Mech, and L. Paarlberg Motivating employee in a new governance era: The performance paradigm reviited. Public Adminitration Review 66(4): Revelt, D. and K. Train Incentive for appliance efficiency in a competitive energy environment: Random parameter logit model of houehold choice. Review of Economic and Statitic 80: Swait, J A tructural equation model of latent egmentation and product choice for cro-ectional revealed preference choice data. Journal of Retailing and Conumer Service 1: Shen, J A review of tated choice method. International Public Policy Reearch 10(2): Shen, J. and T. Saijo Doe energy efficiency label alter conumer purchaing deciion? A latent cla approach on Shanghai data. Journal of Environmental Management 90: Swait, J Advanced choice model. In B. J. Kanninen (Ed), Valuing Environmental Amenitie Uing Stated Choice Studie. Springer. Train, K Recreation demand model with tate difference over people. Land Economic 74: Vroom, V. H Work and Motivation. New York: Wiley.

13 Table 1. Attribute and their level for each payment ytem Attribute Level of attribute Payment A Payment B Payment C Hourly pay (JP yen) 800/900/ Pay for each nack old (JP yen) 0 80/90/100 30/40/50 Table 2. An example of a choice et Payment A Payment B Payment C Hourly pay (JP yen) Pay for per nack old (JP yen) Pleae chooe one mot-deirable payment plan by placing a in a Table 3. Information criteria for different number of latent clae Clae Log-likelihood AIC 2 AIC3 BIC Table 4. Etimation reult of the MNL and LCL model MNL LCL Cla 1 Cla 2 Cla 3 Cla 4 Payment A ** ** *** Payment B * ** * Hourly pay *** *** *** *** *** Pay for each nack old *** *** *** *** *** Cla probability Log likelihood Peudo R Predictive power 50.27% 77.68% Obervation Note: Predictive power refer to the proportion of choice correctly predicted by the model. *, **, and *** denote that the etimated parameter i ignificantly different from zero at the 10%, 5%, and 1% level, repectively. Standard error and z value are omitted to ave pace.

14 Rik-avere, Q1, Rik-avere, Q2, Rik-neutral, Q1, Rik-loving, Q1, Rik-neutral, Q2, Rik-loving, Q2, Rik-avere, Q3, Rik-neutral, Q3, Rik-avere Rik-loving, Q3, Rik-neutral Rik-loving Figure 1. Etimated individual tradeoff between fixed pay and performance-related pay