The relationship between monetary policy and firm dynamics

The product market has undergone great transformation over the past thirty years. This has implications in various fields of economics, from discussions about the labour share of income to the slump in productivity. It has implications for policy, too. Product markets have been associated with rising mark-ups and product market concentration - both measures of market power - with consequences for monetary policy transmission.
The discussion of the effect of developments on the Phillips Curve - the relationship between inflation and unemployment - illustrates how these developments can be important for monetary policy. The Phillips Curve is important for monetary policy because it provides a relationship between economic slack and inflation and gaining control over inflation is the main target for central banks. In the textbook New Keynesian model, where firms are monopolistically competitive and subject to nominal rigidities, rising mark-ups are associated with a steepening of the Phillips Curve. This would suggest that inflation rises more sharply as the economy reaches its full potential. On the other hand, recent research has argued that market structure and not just mark-ups are important in this discussion. Modelling firms competing under oligopoly leads to a significant flattening of the Phillips Curve when compared to monopolistic competition. Understanding how recent trends in the product market impact such relationships in reality is therefore important for understanding monetary policy transmission.
Building on this discussion, there are two main avenues I wish to explore in my research.
Firstly, as alluded to, in order to understand the effect of recent developments on the monetary policy transmission mechanism, it is first crucial to consider the effects of product market developments on certain macroeconomic relationships in isolation. I intend to investigate these relationships in models that capture the recent trends.
Secondly, in the context of recent developments in the product market, firm heterogeneity has become a more important feature of markets. The question of whether monetary policy favours certain types of firms over others then naturally arises. This is an important one for at least two reasons. Firstly, policy could have implications for market structure. Secondly, it could matter in a distributional sense, given the distribution of firm ownership and the labour share of income across the productivity distribution. Recent work evidencing that lower interest rates disproportionately benefit markets leaders over followers - at least in terms of their equity prices - provides motivation for further research into this area.