Large Dimensional Latent Factor Modeling with Missing Observations and Applications to Causal Inference

Abstract

This paper develops the inferential theory for latent factor models estimated from large dimensional panel data with missing observations. We estimate a latent factor model by applying principal component analysis to an adjusted covariance matrix estimated from partially observed panel data. We derive the asymptotic distribution for the estimated factors, loadings and the imputed values under a general approximate factor model. The key application is to estimate counterfactual outcomes in causal inference from panel data. The unobserved control group is modeled as missing values, which are inferred from the latent factor model. The inferential theory for the imputed values allows us to test for individual treatment effects at any time. We apply our method to portfolio investment strategies and find that around 14% of their average returns are significantly reduced by the academic publication of these strategies.

Matrix Completion, Counterfactuals, and Factor Analysis of Missing Data

“…Our analysis is similar in objective to that of Su et al (2019) and Xiong and Pelger (2019) but differs in two ways. First, our results hold for arbitrary type of missing data and does not require assumptions about the missing data mechanism.…”

“…A finding that emerges from Su et al (2019) is that imputation noise from the initial estimation will affect all subsequent factor estimates, a consequence of the fact that principal components are weighted averages of all data, including the imputed ones. Xiong and Pelger (2019) also initializes the missing values to zero but re-weights the data to remove bias while allowing the probability of missing data to depend on observables. However, the inferential theory assumes that the probabilities are known.…”

“…Both Su et al (2019) and Xiong and Pelger (2019) assume that the number of missing data points as a fraction of T • N is bounded away from zero. If the balanced block is of dimension T o × N o , they implicitly require that T o and T are of the comparable order, and likewise for N o and N .…”

Time-Series Imputation with Wasserstein Interpolation for Optimal Look-Ahead-Bias and Variance Tradeoff

“…Single imputation refers to the use of a specific number (i.e., a best guess) in place of each missing value, which includes for example, k-nearest neighbor, mean/median imputation, smoothing, interpolation [21] and spline. Matrix completion and matrix factorization [5,6,7,24,20] are often used to impute panel data, as well as latent factor modelling [10,2,33]. Recently, there is a surge in the application of the recurrent neural network for imputation [9,11,22,8], as well as the generative adversarial network [34].…”

Low-Rank Approximations of Nonseparable Panel Models

“…Versions of this model have been considered by Hsiao, Steve Ching and Ki Wan (2012), Gobillon and Magnac (2016), Athey, Bayati, Doudchenko, Imbens and Khosravi (2017), Li and Bell (2017), Xu (2017), Li (2018), Bai and Ng (2019a), Xiong and Pelger (2019), and Chan and Kwok (2020). Example 1 is a special case with…”