WORKING PAPERS

The ratio estimator of a firm’s markup is the ratio of the output elasticity of a variable input to that input’s cost share in revenue. This note raises issues that concern identification and estimation of markups using the ratio estimator. Concerning identification: (i) if the revenue elasticity is used in place of the output elasticity, then the estimand underlying the ratio estimator does not contain any information about the markup; (ii) if any part of the input bundle is either used to influence demand, or is neither fully fixed nor fully flexible, then the estimand underlying the ratio estimator is not equal to the markup. Concerning estimation: (i) even with data on output quantities, it is challenging to obtain consistent estimates of output elasticities when firms have market power; (ii) without data on output quantities, as is typically the case, it is not possible to obtain consistent estimates of output elasticities when firms have market power and markups are heterogeneous. These issues cast doubt over whether anything useful can be learned about heterogeneity or trends in markups, from recent attempts to apply the ratio estimator in settings without output quantity data.

This paper studies competition between firms when consumers observe a pri-vate signal of their preferences over products. Within the class of signal structures which allow pure-strategy pricing equilibria, we derive signal structures which are optimal for firms and those which are optimal for consumers. The firm-optimal signal structure amplifies the underlying product differentiation, thereby relax¬ing competition, while ensuring that consumers purchase their preferred product, thereby maximizing total welfare. The consumer-optimal structure dampens dif¬ferentiation, which intensifies competition, but induces some consumers with weak preferences between products to buy their less-preferred product. The analysis sheds light on the limits to competition when the information possessed by con¬sumers can be designed flexibly.

An extended and improved theory is presented for marked and weighted empirical processes of residuals of time series regressions. The theory is motivated by 1-step Huber-skip estimators, where a set of good observations are selected using an initial estimator and an updated estimator is found by applying least squares to the selected observations. In this case, the weights and marks represent powers of the regressors and the regression errors, respectively. The inclusion of marks is a non-trivial extention to previous theory and requires refined martingale arguments.

Applying climate policy in practice means considering capital stocks: some assets will pro¬duce pollution whenever they are used, and some will not. Therefore long-term abatement plans should influence current investment. Moreover, newer technologies exhibit learning-by-doing in the deployment of associated infrastructure. We investigate these ideas from both theoretical and numerical perspectives. An increasing carbon tax will reduce investments in assets that pollute, and so reduce emissions in the short term: our “irreversibility effect”. We also show that the optimal innovation subsidy increases with the deployment rate: our “acceleration effect”. Considering second-best settings, we show that, although carbon taxes achieve stringent policy targets more efficiently, subsidies to the “renewables” sector deliver higher welfare when policy targets are more mild. Revised February 2019