Research

We develop a general framework of identification and estimation for automatic debiased machine learning (DML) where the parameter of interest θ₀ is identified by a moment condition involving a nuisance γ₀ that may be high dimensional. We establish conditions under which the Riesz representer α₀, which is at the core of DML, is identified, and show that the identification occurs precisely when α₀ uniquely optimizes a quadratic functional. This characterization enables us to develop a general estimation procedure for α₀ that allows for generic γ₀ including those defined by models with endogeneity and encompasses both classical sieves and modern architectures such as deep neural networks. To improve estimation precision and mitigate the curse of dimensionality, we incorporate shape constraints on γ₀ by embedding them into a possibly nonlinear parameter space. We illustrate our estimation procedure through simulations and empirical applications.

Forecasting inflation rate is of tremendous importance for firms, consumers, as well as monetary policy makers. Besides macroeconomic indicators, professional surveys deliver experts’ expectation and perception of the future movements of the price level. This research studies survey-based inflation forecast in an extended recent sample covering the Great Recession and its aftermath. Traditional methods extract the central tendency in mean or median and use it as a predictor in a simple linear model. Among the three widely cited surveys, we confirm the superior forecasting capability of the Survey of Professional Forecasters (SPF). While each survey consists of many individual experts, we utilize machine learning methods to aggregate the individual information. In addition to the off-the-shelf machine leaning algorithms such as the Lasso, the random forest and the gradient boosting machine (GBM), we tailor the standard Lasso by differentiating the penalty level according to an expert’s experience, in order to handle for participants’ frequent entries and exits in surveys. The tailored Lasso delivers strong empirical results in the SPF and beats all other methods except for the overall best performer, GBM. Combining forecasts of the tailored Lasso model and GBM further achieves the most accurate inflation forecast in both the SPF and the Livingston Survey, which beyonds the reach of a single machine learning algorithm. We conclude that combination of machine learning forecasts is a useful technique to predict inflation, and averaging should be exercised in a new generation of algorithms capable of digesting disaggregated information.