On-The-Job Training and Learning: Formal Training versus Learning by Doing

Abstract

The paper looks at and compares two methods of on-the-job training: formal training and learning by doing. The former involves an intensive training period prior to the employee directly taking on the position for which he or she was hired for, while the latter, the employee begins immediately and is expected to learn on his or her own through experience over time. The former method allows less room for shirking but involves a period of investment in the form of the value of output or service that is effectively foregone as a result of the more resource-intensive training regime. Perhaps surprisingly, even if the formal training program does not significantly improve upon the probability of future success in production or service provision, formal training can provide higher net benefits to the training firm than learning by doing because the savings from the reduction in shirking can be greater than the cost of foregone output.

Appendices

Appendix 1

In the two-period moral hazard model with limited liability but without learning by doing, let $q$ be the probability of production success if the worker shirks and ${p}_{1}$ the probability of production success in the first and second period if the worker exerts high effort. As before, high effort costs the agent $c$ whereas shirking costs the agent nothing. The incentive compatibility constraints for the second period are:

$$\begin{array}{c}{p}_{1}{t}_{ss}+\big(1-{p}_{1}\big){t}_{sf}-c\ge q{t}_{ss}+\big(1-q\big){t}_{sf},\\ {p}_{1}{t}_{fs}+\big(1-{p}_{1}\big){t}_{ff}-c\ge q{t}_{fs}+(1-q){t}_{ff},\end{array}$$

where the two are designed respectively, to implement high effort in the event of production success or in the event of failure in the first period. These can rewritten as:

$$\begin{array}{ccc}({p}_{1}-q)({t}_{ss}-{t}_{sf})\ge c& \mathrm{and}& ({p}_{1}-q)({t}_{fs}-{t}_{ff})\ge c\end{array},$$

or as:

$$\begin{array}{ccc}{t}_{ss}-{t}_{sf}\ge \frac{c}{{p}_{1}-q}& \mathrm{and}& {t}_{fs}-{t}_{ff}\ge \frac{c}{{p}_{1}-q}.\end{array}$$

The first-period incentive compatibility constraint is:

$$\begin{array}{l}{p}_{1}\big[{t}_{s}+\big({p}_{1}{t}_{ss}+\big(1-{p}_{1}\big){t}_{sf}-c\big)\big]+ \big(1-{p}_{1}\big)\big[{t}_{f}+\big({p}_{1}{t}_{fs}+\big(1-{p}_{1}\big){t}_{ff}-c\big)\big]-\mathrm{c}\ge \\ \mathrm{q}[{t}_{s}+ \big({p}_{1}{t}_{ss}+\big(1-{p}_{1}\big){t}_{sf}-c\big)]+(1-q)[{t}_{f}+({p}_{1}{t}_{fs}+\big(1-{p}_{1}\big){t}_{ff}-c)],\end{array}$$

Rearranging we have:

$$\left({p}_{1}-q\right)\left[{t}_{s}-{t}_{f}+{p}_{1}\left({t}_{ss}-{t}_{fs}\right)+\left(1-{p}_{1}\right)\left({t}_{sf}-{t}_{ff}\right)\right]\ge c,$$

or:

$$\left[{t}_{s}-{t}_{f}+{p}_{1}\left({t}_{ss}-{t}_{fs}\right)+\left(1-{p}_{1}\right)\left({t}_{sf}-{t}_{ff}\right)\right]\ge \frac{c}{\left({p}_{1}-q\right)}.$$

Using similar arguments as in the text, the firm would like the transfers, to be made in the event of unsuccessful production, to be as low as possible but because of the limited liability constraints, they can only go as low as zero. Hence ${t}_{f}={t}_{sf}={t}_{ff}=0$ and from the binding second-period incentive compatibility constraints: ${t}_{ss}={t}_{fs}=c/({p}_{1}-q)$. Given these results, we can see that the first-period incentive compatibility constraint (the last equation above) is independent of any adjustments to second-period transfers (and the resulting agent’s second-period rent) to save on motivating the agent in the first period as ${t}_{ss}={t}_{fs}$, ${t}_{sf}={t}_{ff}$ and ${t}_{f}=0$. As the first period incentive constraint is binding, we have ${t}_{s}=c/({p}_{1}-q)$, which is also the same as the second-period incentive payments to the agent.

Appendix 2

For convenience, we first state our result again which is then followed by the proof.

Result

Given ${p}_{1}^{\tau }={p}_{1}^{d}={p}_{1}$ and ${p}_{2s}^{\tau }={p}_{2}^{d}={p}_{2}$, if the quality of second period production under learning by doing is such that ${\alpha }_{2}<\widehat{{\alpha }_{2}}$ with $\widehat{{\alpha }_{2}}=1-\left[\frac{({p}_{1}+1)}{{p}_{2}}\theta +{\alpha }_{1}\frac{{p}_{1}}{{p}_{2}}\right]$ and $\theta ={p}_{2}-{p}_{2f}^{\tau }$ along with the probability of first-period success being sufficiently high, ${p}_{1}>\widehat{{p}_{1}}$, then formal training results in higher expected payoffs compared to learning by doing.

Proof

Given the assumptions of the proposition, the expression for the difference in the expected value of production can be written as:

$$\left[{p}_{1}{p}_{2}+\left(1-{p}_{1}\right){p}_{2f}^{\tau }-{\alpha }_{1}{p}_{1}-{\alpha }_{2}{p}_{2}\right]V$$

or as

$$\left[{p}_{1}{p}_{2}+\left(1-{p}_{1}\right)({p}_{2}-\theta )-{\alpha }_{1}{p}_{1}-{\alpha }_{2}{p}_{2}\right]V.$$

The term in brackets will be weakly positive if

$${p}_{2}-\big(1-{p}_{1}\big)\theta -{\alpha }_{1}{p}_{1}-{\alpha }_{2}{p}_{2}\ge 0,$$

or as long as the following condition holds:

$$\widehat{{\alpha }_{2}}=1-\left[\frac{\left(1-{p}_{1}\right)}{{p}_{2}}\theta +{\alpha }_{1}\frac{{p}_{1}}{{p}_{2}}\right]\ge {\alpha }_{2}.$$

Note that it can be shown that ${p}_{2}\ge {\alpha }_{1}$ is sufficient for the sum in the bracketed term to be less than one. To show that the difference in costs can be negative, we can use the result in the proof of Proposition 2 since the expressions for the cost difference are the same. Thus there exists a range of ${p}_{1}$ such that if ${p}_{1}\ge \widehat{{p}_{1}}$, then $\Lambda \le 0$, and the costs are higher under learning by doing.