A standard way to measure productivity is to take output growth and subtract input growth. Typically input growth is growth in capital and growth in labor weighted by their share in production. Whatever remains after subtracting is known as total factor productivity (TFP).
Under specific circumstances, this productivity measure also reflects underlying technology growth. This is important for economists because they struggle to measure underlying technology at an aggregate level, but it is a key variable to understand the behaviour of the economy.
However when we diverge from some basic assumptions, such as perfect competition, the TFP measure no longer reflects underlying technology. Therefore using our TFP measure to represent technology could lead to incorrect conclusions.
In this paper I show that when we recognize the slow adjustment of firms to arbitrage profits and the effect that slowly entering firms have on competition, the relationship between our measure of TFP and technology becomes much more complex. In fact, when we observe changing TFP, it will compose changing technology, changing profits and changing markups. This decomposition allows us to understand how we can get a true measure of underlying technology from our calculated TFP measure. It emphasizes that the composition of profits and markups vary in importance as firm entry takes place.
You can download the complete paper here.