Identifying and Distinguishing Among Teachers’ Supplementary Curriculum Use Patterns Using the Lasso

Research has shown that officially-adopted textbooks comprise only a small part of teachers’ enacted curriculum. Teachers often supplement their core textbooks with unofficial materials, but empirical study of teacher curriculum supplementation is relatively new and underdeveloped. Grounding our work in the Teacher Curriculum Supplementation Framework, we use data from two state-representative teacher surveys to describe different supplement use patterns and explore their correlates. (We use RAND’s American Teacher Panel survey of K-12 ELA teachers, representative of Louisiana, Massachusetts, and Rhode Island, and Harvard’s National Evaluation of Curriculum Effectiveness survey of fourth and fifth grade math teachers, representative of California, Louisiana, Maryland, New Jersey, New Mexico, and Washington.) We find evidence of four distinct supplement use patterns. We then predict each pattern, producing sparse models using the lasso estimator. We find that teacher-, school-, and textbook-level characteristics are predictive of teachers’ supplement use, suggesting that it may be affected by structures and policies beyond the individual teacher. We recommend researchers use consistent measures to explore the causes and consequences of supplementation.

Forecasting the Volatility of Crude Oil: The Role of Uncertainty and Spillovers

We use a dataset for the group of G7 countries and China to study the out-of-sample predictive value of uncertainty and its international spillovers for the realized variance of crude oil (West Texas Intermediate and Brent) over the sample period from 1996Q1 to 2020Q4. Using the Lasso estimator, we found evidence that uncertainty and international spillovers had predictive value for the realized variance at intermediate (two quarters) and long (one year) forecasting horizons in several of the forecasting models that we studied. This result holds also for upside (good) and downside (bad) variance, and irrespective of whether we used a recursive or a rolling estimation window. Our results have important implications for investors and policymakers.

Uncertainty, Spillovers, and Forecasts of the Realized Variance of Gold Returns

Using data for the group of G7 countries and China for the sample period 1996Q1 to 2020Q4, we study the role of uncertainty and spillovers for the out-of-sample forecasting of the realized variance of gold returns and its upside (good) and downside (bad) counterparts. We go beyond earlier research in that we do not focus exclusively on U.S.-based measures of uncertainty, and in that we account for international spillovers of uncertainty. Our results, based on the Lasso estimator, show that, across the various model configurations that we study, uncertainty has a more systematic effect on out-of-sample forecast accuracy than spillovers. Our results have important implications for investors in terms of, for example, pricing of related derivative securities and the development of portfolio-allocation strategies.

Multiple structural breaks in cointegrating regressions: a model selection approach

In this paper, we propose a new approach to model structural change in cointegrating regressions using penalized regression techniques. First, we consider a setting with known breakpoint candidates and show that a modified adaptive lasso estimator can consistently estimate structural breaks in the intercept and slope coefficient of a cointegrating regression. Second, we extend our approach to a diverging number of breakpoint candidates and provide simulation evidence that timing and magnitude of structural breaks are consistently estimated. Third, we use the adaptive lasso estimation to design new tests for cointegration in the presence of multiple structural breaks, derive the asymptotic distribution of our test statistics and show that the proposed tests have power against the null of no cointegration. Finally, we use our new methodology to study the effects of structural breaks on the long-run PPP relationship.

UNIFORM ASYMPTOTICS AND CONFIDENCE REGIONS BASED ON THE ADAPTIVE LASSO WITH PARTIALLY CONSISTENT TUNING

We consider the adaptive Lasso estimator with componentwise tuning in the framework of a low-dimensional linear regression model. In our setting, at least one of the components is penalized at the rate of consistent model selection and certain components may not be penalized at all. We perform a detailed study of the consistency properties and the asymptotic distribution which includes the effects of componentwise tuning within a so-called moving-parameter framework. These results enable us to explicitly provide a set $\mathcal {M}$ such that every open superset acts as a confidence set with uniform asymptotic coverage equal to 1, whereas removing an arbitrarily small open set along the boundary yields a confidence set with uniform asymptotic coverage equal to 0. The shape of the set $\mathcal {M}$ depends on the regressor matrix as well as the deviations within the componentwise tuning parameters. Our findings can be viewed as a broad generalization of Pötscher and Schneider (2009, Journal of Statistical Planning and Inference 139, 2775–2790; 2010, Electronic Journal of Statistics 4, 334–360), who considered distributional properties and confidence intervals based on components of the adaptive Lasso estimator for the case of orthogonal regressors.

Aggregating Knockoffs for False Discovery Rate Control with an Application to Gut Microbiome Data

Recent discoveries suggest that our gut microbiome plays an important role in our health and wellbeing. However, the gut microbiome data are intricate; for example, the microbial diversity in the gut makes the data high-dimensional. While there are dedicated high-dimensional methods, such as the lasso estimator, they always come with the risk of false discoveries. Knockoffs are a recent approach to control the number of false discoveries. In this paper, we show that knockoffs can be aggregated to increase power while retaining sharp control over the false discoveries. We support our method both in theory and simulations, and we show that it can lead to new discoveries on microbiome data from the American Gut Project. In particular, our results indicate that several phyla that have been overlooked so far are associated with obesity.