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Who should invest in specific training?


We study experimentally whether employers or workers should invest in specific training. Workers have an alternative trading opportunity that takes the form of either an outside option or a threat point. Theory predicts that with outside options, employers have (weakly) better investment incentives than workers do and should therefore be the investing party. With threat points, employers and workers are predicted to invest the same. Our results are, by and large, in line with these predictions. Due to offsetting inefficiencies in the bargaining stage, however, realized inefficiencies are remarkably similar across the different situations considered.

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Fig. 1


  1. Note that training that is specific in a technological sense is necessarily specific in an economic sense.

  2. It should be noted that Becker (1962) already recognized this distinction between specificity in a technological and an economic sense (cf. Leuven 2005).

  3. See also Malcomson 1999 who notes that: “ may be too complex or too multidimensional for a court to verify whether they have been carried out as specified in a contract. Although it may, for example, be feasible to specify the number of hours of specific training unambiguously, specifying the quality of training during those hours is more problematic.”

  4. We formally prove these predictions for the setting that we consider in our experiment in Appendix B, which is available at the first author's web site: scholar/oosterbeek/main.htm. The model analyzed in that appendix is almost identical to the one analyzed in Acemoglu and Pischke (1999b, Section II.D). While the title of their paper refers to general training, they in fact analyze training that is specific in an economic sense.

  5. The theoretical literature proposes several contractual solutions to the holdup problem. But as Malcomson (1999, p. 2333) notes: “None of the contracts discussed here for inducing efficient specific investments by both parties thus seems unproblematic when applied to labor markets. This suggests a powerful case for, wherever possible, all the specific investments to be carried out by either the firm or the employee....” This provides an additional justification for our focus on settings in which only one of the parties invests.

  6. Alternative trading possibilities are thus less powerful when they are more rigid. The intuition is that the benefits of choosing the alternative opportunity are twofold: the worker not only receives the outside wage but also obtains the option of returning the original employer. The value of the latter option is decreasing in T.

  7. Two related papers focus on the effect of the value of alternative opportunities on the level of investment. Sloof et al. (2004) examine the situation where the noninvesting party has alternative opportunities; Sonnemans et al. (2001) consider the situation in which the investor has alternative opportunities. Some of the data used in the current paper have also been analyzed in Sonnemans et al. (2001).

  8. It may appear inconsistent to use the broad definition of specific training, which also includes training that is specific due to labor market imperfections, in a bargaining model with threat points, which reflect a frictionless labor market. It should be noted, however, that the labor market imperfections that may cause training to be specific do not necessarily imply that workers cannot obtain their outside wage while bargaining. The two labels of the operation of the labor market just refer to different dimensions.

  9. That the outside wage w is independent of the investment reflects the assumption that the investment is fully firm specific. In the formulation of Acemoglu and Pischke (1999b), the outside wage is allowed to increase with the level of the investment, i.e., w=w(I). The key feature of their model, however, is that the difference between the worker's productivity in the current firm R(I) and the outside wage w(I) is increasing in the investment [i.e., w′(I)<R′(I)]. This feature is also present in our setup. Specifying an outside wage that increases with the investment would thus only complicate the experiment for the subjects, without adding anything of substance.

  10. Although we feel that keeping the marginal gains from agreement constant across bargaining games is the appropriate ceteris paribus condition (cf. Knez and Camerer 1995, p. 84), one could also argue that making the bargaining stages comparable requires the total surplus to be the same, i.e., V OO=V TP=10,000. Erlei and Siemer (2004) exactly replicated our W-TP treatment, except that they chose V TP=10,000. (They did not consider the OO game and the employer invests case.) Their findings replicated most of our results. Most notably, investment levels were, by and large, the same (although for w=1,800, they find a slightly lower investment rate). However, in their experiments, the average length of the bargaining was longer, as one would expect given the lower joint costs of delaying agreement.

  11. The equal split follows from our assumption of equal bargaining power.

  12. Owing to our specification of R(I)=10,000+w+100·I under the TP game, we found that the employer always receives 5,000+50·I according to STD. The amount the employer receives in equilibrium is thus independent of w.

  13. The row corresponding to “all” just reflects the average over the three different values of w. It can be shown that in an alternative model with exogenous uncertainty, in which the true value of w becomes publicly known only after the investment is made (and in which the three values of w have ex ante equal probabilities), the equilibrium investment levels are as follows: 36 under E-OO, \(8\frac{1} {3}\) under W-OO, and 25 under both TP situations.

  14. This is formally derived in Appendix B, which is available at the first author's web site:

  15. A potential disadvantage of our design might be that variations in w theoretically do not affect investment levels under TP. However, by confronting the same subjects with different values of w, we may have created the impression that subjects are expected to change their behavior. It is, however, a priori far from clear in what direction investors should change their behavior, and our experimental results confirm this.

  16. Our bargaining game thus differs from a setup similar to that of Rubinstein (1982) in which there is a single pie that shrinks over time at a constant rate (due to discounting when agreement is delayed). In practice, bargaining over wages in an employer–worker relationship typically concerns the division of a stream of future payoffs, instead of the division of a single once-and-for-all payoff that is obtained immediately when agreement is reached. The multiple-pie framework nicely takes account of this aspect (cf. Manzini 1998). In Sloof (2005), it is shown that the subgame perfect equilibrium predictions of the OO game and the TP game employed here equal the equilibrium divisions spelled out in Table 2.

  17. Twelve Mann–Whitney rank sum tests were performed to compare mean individual investment levels conditional on the value of w. No significant differences between similar sessions were found at the 5% level.

  18. Recall that for each value of w, we have six observations for each individual investor, and that for each of the four situations considered, we have 20 investors.

  19. See, e.g., Berg et al. (1995), Ellingsen and Johannesson (2004a, b), Gantner et al. (2001), Hackett (1993; 1994) Königstein (2000; 2001), and Oosterbeek et al. (2003).

  20. Recently, some alternative behavioral theories focus on the importance of fairness and reciprocity (see Fehr and Schmidt 2002 for a comprehensive overview). These theories can only make precise predictions under strong additional assumptions (e.g., homogeneity and/or common knowledge of social preferences), but we can touch upon some indications. Fairness theories are outcome-based and predict that participants will only agree on outcomes in which both parties earn about the same. This means that the outside option will never be exercised. If both parties earn the same, the efficient investment of 50 will be optimal in all treatments. Reciprocity theories are intention-based; friendly (unfriendly) actions are rewarded (punished). If investments that are higher (lower) than the equilibrium prediction are considered friendly (unfriendly), investments will be a little more profitable for the investor. In that case, investments will be higher than the equilibrium prediction in all treatments, but the relative investment levels will stay about the same.

  21. Although, for the worker invests case, the means and standard deviations might suggest otherwise, the Wilcoxon signed-rank test for matched pairs does not yield a significant difference between w=1,800 and w=6,800 and 7,800, respectively. For the former, p=0.198; for the latter, p=0.139.

  22. Since these comparisons are not the main focus of this paper, we have suppressed symbols indicating results from these statistical tests in Table 4.

  23. The experiments reported in Sloof et al. (2004) provide an explanation for these findings. There, it is found that a self-serving bias induces investors to overlook the difference between a binding and a nonbinding outside option when making their investment decision.

  24. The finding that accepted offers are, on average, below first offers is not surprising. In our setup, the employer always makes the first offer and offers are expressed as the amount the employer obtains. If the worker accepts the first offer, the finally agreed offer equals the first offer. If not, it is likely that the worker does so in anticipation of either a higher total or a higher relative payoff. In both cases, the finally agreed offer must be lower than the first offer.

  25. Note that for an outside option value of £0, these two outcomes are identical.

  26. Binmore et al. (2002), Kahn and Murnighan (1993), and Knez and Camerer (1995) also obtained experimental evidence that showed that the worker's final payoff did not rise one-to-one with his outside option.

  27. Because we chose V TP=10,000+w, our setup corresponds with the low threat point payoff in Binmore et al. (1991, Figs. 3 and 4) where the threat point value is less than half of the overall surplus. Oosterbeek et al. (2003) also consider a threat point bargaining game treatment in which the pie up for division is exogenously fixed and find that, in their setup, STD predicts the actual bargaining outcomes better than the DMO or ES outcome does.

  28. For the £5 cake, the latter result may be due to round number focal point effects. Binmore et al. (1991) therefore also consider a larger cake size ($11), and there, sharper differences between the two bargaining games are obtained.

  29. Formally, the DMO and STD predictions within square brackets do not exactly apply for proposals made by the worker. Specifically, these two predictions have to be multiplied by \(\frac{{{\left( {9 - t} \right)}}} {{{\left( {10 - t} \right)}}}\) to obtain the worker's equilibrium proposal in even round t (cf. Sloof 2005). Out of the 1,346 interactions that finally ended in agreement, 400 (29.7%) were concluded upon in an even bargaining round.

  30. Instead of using the investors' finally accepted shares as independent variable, we can alternatively regress the employers' finally accepted shares on the explanatory variables of Table 6. Because the bargaining outcome is predicted to be independent of the identity of the investor, the three interaction terms are then predicted to have no effect. These regressions (not reported here) reveal that this is almost always the case for V·D W and w·D W (the single exception occurs for w·D W under OO nonbinding) but not so for I·D W. The latter interaction term is significant (5% level) in OO nonbinding and the TP game. We have chosen to report the regressions of Table 6 because they immediately reveal—through the (in)significance of the coefficient on I·D W—whether the private investment returns differ significantly between employers and workers. Clearly, the two types of regressions lead to similar conclusions.

  31. Appendix A reports the average number of bargaining rounds for the last nine and final three periods separately (cf. Table 11). Average delay is typically shorter in later periods. Apparently, subjects learn to avoid costly delay. Result 3 is, however, not affected by this. It is supported when we consider only periods 10 to 18 or when we just look at the final three periods.

  32. The opting-out rates under E-OO (11%) and W-OO \({\left( {12\frac{1} {2}\% } \right)}\) are fairly similar and thus do not affect the relative return on the investment in the two cases.

  33. Except for w=7,800 under W-OO and w=1,800 under W-TP, these time trends were never significant (at the 5% level).

  34. We again calculated robust standard errors that take account of correlated disturbance terms of multiple observations per subject.

  35. When we use the negative coefficients to calculate the unconstrained optima, the following “optimum” investment levels are obtained (both for W-TP): −11.48 when w=6,800 and −2.40 when w=7,800. The reported robust standard errors for these two treatments (Table 8) in fact refer to these unconstrained optima.

  36. The part of the bargaining inefficiencies that can be attributed to the worker opting out (included in the bargaining inefficiencies reported in Table 9) does not vary significantly with the identity of the investor. For the E-OO situation, the average “opting-out” inefficiencies equal 129, 923, 787, and 613 for w l, w m, w h, and all, respectively. For W-OO, they are equal to 267, 559, 882, and 570.

  37. Fehr et al. (2004) consider a setting in which paired subjects make sequential investment decisions. Before investments are made, subjects first bargain about the allocation of ownership (which in turn specifies how the returns to investments are shared). Under joint ownership, standard theory predicts no investments at all, whereas under single ownership, only the owner (which is the second investor in the experiment) is predicted to invest. In contrast to these predictions, Fehr et al. find that joint ownership is chosen most often and also that, under this ownership structure, typically both subjects invest. The latter can be explained by reciprocity; the second investor, on average, strongly reciprocates higher investments made by the first investor (although standard theory predicts that these investments are independent). This, in turn, makes it attractive for the first investor to invest under joint ownership. Note that, in contrast to our experiment, there is no ex post bargaining in these experiments.

  38. An explanation for why we do not get significant results (at the 5% level) in the middle and bottom panels is that the averages used there are based on fewer observations (three and one, respectively) and, thus, are more noisy. The reported standard deviations reflect this; in the middle and bottom panels, standard deviations are higher than in the top panel. Assume that each investor has a personal inclination for a certain behavior. Actual behavior is determined by this inclination and some “noise” or errors. The average behavior of the investor is an estimation of that individual inclination. More observations per individual means a better measurement of these inclinations and, hence, a better quality of the data used in the test. Although the test itself is independent of how many observations are included in the average, the power of the test increases if more data per individual are used.

  39. The p value of the rank sum test comparing E-OO with W-OO for w=1,800 equals p=0.060, which is close to significance at the 5% level.


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We gratefully acknowledge the useful remarks of three anonymous referees, which improved the presentation of the material considerably.

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Correspondence to Hessel Oosterbeek.

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Appendix A: Learning effects

Appendix A: Learning effects

In each session, subjects played 18 times the two-stage game in Section 2. During the course of the experiment, they may have changed their behavior, for instance, because over time, they learned how to play the game. To make sure that our conclusions are not biased due to ignoring such learning effects, we consider in this appendix the data from the last nine and the final three periods separately as well. The focus is on investment levels (cf. Result 1 and Table 4) and on delay of agreement (cf. Result 3 and Table 7). Recall that, in the regressions reported in the main text that led to Results 2 and 4, we already control for potential learning effects.

The design of the experiment was such that the first and last nine periods included the same frequency of low, intermediate, and high levels of the worker's outside wage. Moreover, each value of w was represented exactly once in the final three periods. Tables 10 and 11 (investment levels and bargaining length, respectively) report the same statistics as in Tables 4 and 7, but now, also for the last nine and final three periods separately. The top panels of Tables 10 and 11 correspond exactly with the tables presented in the main text. The middle panels only consider the data from the second half of the experiment, while the bottom panels only use the data from the final three periods.

Table 10 Mean investment levels by treatment
Table 11 Percentage of immediate agreement and mean number of rounds before agreement

Table 10 reports average investment levels by treatment. Statistical tests are again based on the average investment levels of individual investors. The results in the middle and bottom panels almost exactly reproduce the results of the top panel. The single difference is that no significant differences are found anymore under the TP game when w=7,800. This holds despite the fact that the mean levels over all investors are fairly far apart. Comparing for this particular case (i.e., w=7,800 under the TP game) the average investment levels across the different panels of Table 10 by means of a Wilcoxon signed-rank test, we find no significant differences when the worker invests (the lowest p value is 0.304). For the case in which the employer invests, however, the top panel differs significantly from both the middle (p=0.047) and bottom panels (p=0.032). Over time, employers thus tend to invest less in this case, while workers do not change their investment behavior. Based on these learning effects, we still conclude that, under the TP game, workers invest more than employers do when the outside wage is high.Footnote 38

As an additional test of learning effects, we regressed, for each of the 12 treatments, the investment levels on a variable that measures the time that the investor was confronted with this particular value of the outside wage (besides a constant term). Only in two treatments did this time trend have a statistically significant (negative) coefficient: the case where w=1,800 under E-OO and the case where w=6,800 under W-OO. As can be seen from Table 10, however, the differences in overall mean investment levels for both these treatments in the three panels are small (and they display a nonmonotonic pattern). Taking all the above checks together, we conclude that Result 1 on investment behavior is not contaminated by learning effects.

Table 11 presents for each treatment the percentage of cases in which agreement is reached immediately and the average number of bargaining rounds before agreement is reached. Columns labeled “n” give the number of observations on which the latter averages are based; observations in which one of the parties opted out (OO game) or no agreement was reached are left out. Comparing the middle with the top panel, it is observed that average delay is typically shorter in the second half than in the first half of the experiment. This follows because in almost all treatments, the average number of bargaining rounds before agreement is reached decreases when we take only the last nine periods into account (the two exceptions occur when w=6,800 under E-OO and W-TP). Apparently, subjects learn to avoid costly delay when they play the game. Result 3 on delay of agreement is, however, not seriously affected by this. It is fully supported when we consider periods 10 to 18 only.Footnote 39 For the final three periods, the same types of differences are found, although not all of them are significant. Moreover, there, we observed that overall agreement is reached sooner under the OO game when the worker invests. In case of the TP game, there are no significant differences, although when w=1,800, the overall observed mean bargaining length before agreement is substantially larger when the employer invests than when the worker invests, in line with Result 3(b).

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Oosterbeek, H., Sloof, R. & Sonnemans, J. Who should invest in specific training?. J Popul Econ 20, 329–357 (2007).

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  • Specific training
  • Investments
  • Experiments

JEL classification

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  • C91