It is well known from management studies dating back before WW2 that people learn by doing – a worker gets more productive the longer he is on the job making goods. This has well-known implications for IO. For instance, gaining a small initial advantage in a new industry is very valuable because by earning those initial sales, you learn by doing, becoming the cost leader in the industry forever. Importantly, though, firms also *forget* when they don’t make things, whether because employees are fired or workers are just sitting idle. It turns out that adding forgetting to a model does not just negate the effects of learning, but can amplify such effects.

Besanko et al compute numerical Markov perfect equilibria for price setting and firm knowledge (similar to many papers by Ariel Pakes), necessitating some new numerical analysis algorithms in order to spot many of the multiple equilibria. Two firms with heterogeneous goods compete by choosing price in each period, with de facto stochastic demand from consumers over the two goods given the price vector. The firm who makes the sale in each period stochastically learns (lowers its future marginal cost), while the firm which does not stochastically forgets (raises its future marginal cost). More knowledgeable firms are made to forget more knowledge when idle than less knowledgeable firms. Naively, if learning by doing leads to monopoly because of the initial price advantage for the first firm to start learning, then one might imagine that forgetting lessens such monopolistic pressure; the gains of learning from doing under forgetting are transitory, not permanent, and forgetting “naturally” equalizes knowledge between the knowledge leader and the follower.

The opposite result turns out to be true. Price behavior is more aggressive under forgetting. Without forgetting, I am willing to price aggressively both to move down my marginal cost curve, and to keep my opponent from doing the same if he were to make the sale. With forgetting, I am even more aggressive, since if I make the sale, I also ensure I won’t forget this period, and I create a chance for my opponent to forget, which would be advantageous for me in future periods. That is, forgetting and learning by doing both encourage aggressive pricing and market dominance.

The equilibria in this game are particularly crazy to compute, even though firms are restricted to Markov perfect strategies. The state variable is the “level of learning” that each firms possesses. Note that if I have a very low marginal cost, and you have a high marginal cost, then I can infer (to some degree) what our history of play has looked like in order to reach such an equilibrium. In that way, history reenters equilibria even when pricing strategies are, in theory, Markov. An interesting implication is that, if the strength of learning by doing (called the progress ratio) is similar to the speed of forgetting, there can be multiple equilibria. For instance, one equilibria has firms believing that in the long run, only one firm will have low marginal cost and the other high marginal cost, with a “trench” separating the two in which a credible price war will keep the high marginal cost firm from pricing such that they will “learn too much”. In this case, firms will initially price very aggressively in an attempt to become the low marginal cost firm. Alternatively, firms may believe that both can coexist in the long run with low marginal cost. If both firms will eventually learn and reach low marginal cost, then there is no incentive to price very aggressively at the beginning.

One caveat here: nearly all of the results in this paper are numerical. I understand the empirical guys need results where pure analytical solutions may not exist. But it strikes me that the main results of this paper could be explained with examples (and a note showing why such and such an example is not trivial) in 10 pages, rather than with borderline incomprehensible pictures representing numerical solutions across a giant grid for 40 pages. Who cares if delta=.45, rho=.9 gives a certain multiplicity of equilibria, since that numerical result is generated using totally arbitrary assumptions on demand and production? All I care about is why there might be multiplicity of equilibria. To give a related example, I wrote the (quite complicated) code for a paper on optimal taxation that ended up in a very good macro journal recently. The model gave results along the lines of “the optimal tax of type Y is 17% given our parameterization”. But surely everyone understands that the model itself is so abstract that such statements are meaningless. Statements like “in general, tax type Y should be lower than tax type Z for reason X”, shown via simple examples, seem much more useful to me, at least.

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.153.1744&rep=rep1&type=pdf (Working paper – final version in Econometrica March 2010)

But if anything can happen, what do we learn?

I suppose we learn that different industrial structures can be sustained even with a very simple model…