# Why won’t firms provide worker training if there is a “skills gap” ?

Posted on Tue 07 January 2014 in Random Thoughts

Manufacturing sector in India is projected to have a very large short-fall of skilled workers (90 million by the year 2022, according to National Skills Development Corporation). Executives consistently stress that “skill development is the most pressing challenge to the manufacturing sector in India” (report from World Economic Forum). Recommendation have often times focused on implementing effective government programs to tackle this “skill gap.” This same issue repeatedly came up in an Industry panel discussion in Hyderabad that was organized by ISB and POMS.

Obviously, there is some sort of “market failure” if there is such large shortage of skilled workers coexists along with large number of unskilled workers. Specifically, why is it that the firms themselves do not train the workers? I guess there are labor economic models (of job search and training) that answer this question. But since I am not a labor economist, and these two-sided matching models (of workers and firms) seem to be too much heavy-weight machinery for just thinking through and developing some intuition, I’ll try to develop a heuristic model of worker training and see what the model can teach me.

Suppose that when a worker is given training $$\alpha$$, his productivity increases by $$\alpha$$, and suppose that the fraction of this productivity that can be appropriated by the firm is $$\lambda$$. This fraction possibly represents the bargaining power of the firm with respect to the worker. Let $$\theta$$ be the fraction of skilled workers in the labor pool. Then, $$\lambda$$ is probably increasing in $$\theta$$ (since we would expect that given the better outside option, the firm can negotiate and get more of the value); i.e., $$\lambda\left( \theta \right)$$is increasing in $$\theta$$. Suppose that the training cost corresponding to $$\alpha$$ training is $$\frac{1}{2}\alpha^{2}$$, and suppose that government picks up $$\rho$$ fraction of the training cost. Then, the firms optimization problem is $$\lambda\alpha - \left( {1 - \rho} \right)\frac{1}{2}\alpha^{2}$$; hence, the optimal training is $$\alpha^{*} = \frac{\lambda}{1 - \rho}$$; and the optimal net value is $$\frac{\lambda^{2}}{2\left( {1 - \rho} \right)}$$.

Note that these are increasing in $$\theta$$ and in $$\rho$$. Moreover, these are complementary. Hence, subsidizing the training and setting up vocational training (thus improving the pool) are complementary, and both have a positive effect on net value from the manufacturing sector.

What does this toy model say about collective bargaining? Interestingly, the collective bargaining reduces the fraction $$\lambda$$ that can be appropriated by the firm and can thus reduce the training and resulting total value. Of course, this is rather simplistic since it is also possible that with the possibility of interesting contracts the value $$\lambda$$ can increase. For instance, suppose it is possible to have labor contracts where workers give a bond (or sign away the right to work in a competing firm or a similar job). Then, $$\lambda$$ “increases” (or equivalently, the initial pay can be lowered and the entire future value can be appropriated by the worker, specifically, an apprenticeship type of model).

Alternatively, what about switching costs for the worker? Lower switching cost reduces the $$\lambda$$ (since the workers outside option now looks better), and consequently reduces the training and the total value. One of the policy recommendations in manufacturing policy is that we should try to have special economic zones to have manufacturing clusters. This does help in some respects by allowing economies of scale etc for infrastructure, but this would also reduce the switching cost. Specifically, a newly trained worker will be able to move to a different firm much more easily compared to the case where the move would need to be to a different geographical location. Thus, it seems possible that density of the clusters might be inversely related to the actual training that a firm is willing to provide.