Our empirical strategy exploits the availability of two years (January 2020 through January 2022) of daily data on the number of confirmed deaths and cases of COVID-19 in the 3,000 U.S. counties of the 48 contiguous states and the District of Columbia.

In the first stage of the analysis, we use daily time-series data on COVID-19 cases and deaths to fit mixed models of deaths against lagged confirmed cases for each county. Because the resulting coefficients are county specific, they relax the homogeneity assumption that is implicit when the analysis is performed using geographically aggregated cross-section units.

In the second stage of the analysis, we assume that these county estimates are functions of economic and sociodemographic factors that are taken as fixed over the course of the pandemic. Here we employ the novel one-covariate-at-a-time variable-selection algorithm proposed by Chudik et al. (2018) to guide the choice of regressors.

MSLTs can be cast in continuous time or discrete time. While the choice between the two approaches depends on the concrete research question and available data, discrete-time models have several appealing features: they are easy to apply; the computational cost is typically low; and today's empirical studies are frequently based on regularly spaced longitudinal data, which naturally suggests modeling in discrete time.

Despite these appealing features, Stata community-contributed packages have so far been developed only for continuous-time models (Crowther and Lambert 2017; Metzger and Jones 2018) or for traditional demographic life-table calculations that do not allow for covariate adjustment (Muniz 2020). This presentation introduces the recently published Stata package dtms, which seeks to fill the gap in software availability for discrete-time multistate model estimation. The dtms package provides a well-documented and easy-to-apply set of commands that cover a large set of discrete-time MSLT techniques that currently exist in the literature. It also features inference based on newly derived asymptotic covariance matrices as well as inference on group contrasts.

References:

Crowther, M. J., and P. C. Lambert. 2017. Parametric multistate survival models: Flexible modelling allowing transition-specific distributions with application to estimating clinically useful measures of effect differences. Statistics in Medicine 36: 4719–4742. https://doi.org/10.1002/sim.7448

Metzger, S. K., B. T. Jones. 2018. mstatecox: A package for simulating transition probabilities from semiparametric multistate survival models. The Stata Journal 18: 533–563.

Muniz, J. O. 2020. Multistate life tables using Stata. The Stata Journal 20: 721–45. doi: 10.1177/1536867X20953577.

They typically occur in conjoint, choice, and factorial survey experiments but have recently gained increasing popularity in field experiments, too. Technically, they allow researchers to investigate moderation as an instance of treatment heterogeneity by crossing multiple treatments.

Naturally, multifactorial designs quickly spawn a spiraling number of distinct treatment combinations: even a moderately complex design of two factors with three levels each yields 32 unique combinations. For more elaborate setups, full factorials can easily produce dozens of distinct combinations, rendering the visualization of results difficult.

This presentation introduces the new Stata command mfcurve as a potential remedy. Mimicking the appearance of a specification curve, mfcurve produces a two-part chart: the graph’s upper panel displays average effects for all distinct treatment combinations; its lower panel indicates the presence or absence of any level given the respective treatment condition. Unlike existing visualization techniques, this enables researchers to plot and inspect results from multifactorial designs much more comprehensively. Highlighting potential applications, the presentation will demonstrate mfcurve’s most important features and options, which currently include replacing point estimates by box plots and testing results for statistical significance.

We use variation across clusters to estimate coefficients with homogeneous slopes (such as time effects) and within-cluster variation to estimate the cluster-specific heterogeneity directly. We then aggregate them to population averages. We demonstrate consistency, showing robustness over standard estimators, and provide analytic standard errors for robust inference. Basic implementation is straightforward using standard software such as Stata.

In Monte Carlo simulation, PCIV performs relatively well against pooled 2SLS and fixed-effects IV (FEIV) with a finite number of clusters or finite observations per cluster. We apply PCIV in estimating the price elasticity of gasoline demand using state fuel taxes as instrumental variables. PCIV estimation allows for greater transparency of the underlying data. In our setting, we provide evidence of correlation between heterogeneity in the first and second stages, violating a key assumption underpinning consistency of standard estimators. We see significant divergence in the implicit weighting when applying FEIV from the natural weights applied in PCIV. Overlooking effect heterogeneity with standard estimators is consequential. Our estimated distribution of elasticities reveals significant heterogeneity and meaningful differences in estimated averages.

Cook (1979)’s distance is usually used to detect such anomalies in cross-sectional data. This metric may fail to flag multiple atypical cases (Atkinson 1985; Chatterjee and Hadi 1988; Rousseeuw and Van Zomeren 1990), while a local approach overcomes this limit (Lawrance 1995).

I formalize statistical measures to quantify the degree of leverage and outlyingness of units in a panel-data framework. I hence develop a unitwise method to visually detect the type of anomaly, quantify its joint and conditional influence, and quantify the direction of the enhancing and masking effects. I conduct the proposed influence analysis using two community-contributed commands.

First, xtinfluence calculates the joint and conditional influence of unit i on unit j and the relative enhancing and masking effects. A two-way scatter plot or the SSC heatplot can be used to visualize the influence exerted by each unit in the sample. Second, xtlvr2plot (a panel-data version for lvr2plot) produces unitwise plots displaying the average individual influence and the average normalized squared residual of unit i.

References:

Atkinson, A. C. 1985. Plots, transformations and regression; an introduction to graphical methods of diagnostic regression analysis. Technical report.

Chatterjee, S., and A. S. Hadi. 1988. Impact of simultaneous omission of a variable and an observation on a linear regression equation. Computational Statistics & Data Analysis, 6: 129–144.

Cook, R. D. 1979. Influential observations in linear regression. Journal of the American Statistical Association, 74: 169–174.

Lawrance, A. 1995. Deletion influence and masking in regression. Journal of the Royal Statistical Society: Series B (Methodological), 57: 181–189.

Rousseeuw, P. J., and B. C. Van Zomeren. 1990. Unmasking multivariate outliers and leverage points. Journal of the American Statistical association, 85: 633–639.

Among the matched sample, the explained component is the part of the gap attributed to compositional differences between groups in predictors of the outcome, and the unexplained component is the part of the gap that would remain if these compositional differences were eliminated. Two additional components capture how unmatched individuals in group A and group B contribute to the gap in the outcome. Ñopo’s technique directly addresses the issue of lacking common support between groups that can bias linear-regression-based decompositions, exhibits a general robustness against functional-form misspecification, and allows the evaluation of gaps over the full distribution of the outcome.

However, high dimensionality means that there is always a tradeoff between the detail of the matching set (to achieve balance between groups) and common support (the share of matches), particularly in small samples. Extending the community-contributed Stata command nopomatch (Atal et al, 2010.), our command nopo provides a comprehensive implementation of Ñopo’s matching, including different matching procedures. Postestimation commands investigate the balance after matching, explore the lack of common support, and visualize the unexplained component over the outcome distribution. We highlight the merit of this approach and our command by comparing matching with regression-based techniques using a simulation and observational data.

References:

Ñopo, H. 2008. Matching as a tool to decompose wage gaps. The Review of Economics and Statistics 90: 290–299.

Atal, J. P., A. Hoyos, and H. Ñopo. 2010. NOPOMATCH: Stata module to implement Nopo's decomposition. Statistical Software Components S457157, Boston College Department of Economics.

While the Stata commands test and lrtest implement the former two, real Stata does not have a general command for implementing the latter. This presentation introduces the new community-contributed Stata postestimation command lgrgtest that allows for straightforwardly using Lagrange multiplier test after constrained maximum-likelihood estimation.

lgrgtest is intended to be compatible with all Stata estimation commands that use maximum likelihood and allow for the options constraints(), iterate(), and from() and obey Stata's standards for the syntax of estimation commands. lgrgtest can also be used after cnsreg. lgrgtest draws on Stata’s constraint command and the accompanying option constraints(), which only allows for imposing linear restrictions on a model. This results in the limitation of lgrgtest being confined to testing linear constraints only. A (partial) replication of Egger et al. (2011) illustrates the use of lgrgtest in applied empirical work.

References:

Aitchison, J., and S. D. Silvey. 1958. Maximum-likelihood estimation of parameters subject to restraints. The Annals of Mathematical Statistics 29: 813–828.

Egger, P., M. Larch, K. E. Staub, and R. Winkelmann. 2011. The trade effects of endogenous preferential trade agreements. American Economic Journal: Economic Policy 3: 113–43.

Rao, C. R. 1948. Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation. Mathematical Proceedings of the Cambridge Philosophical Society 44: 50–57.

Silvey, S. D. 1959: The Lagrangian multiplier test. The Annals of Mathematical Statistics 30: 389–407.

While proponents highlight possible efficiency gains, opponents point to possible finite-sample bias, a loss of precision in the case of many and weak covariates, and as the increasing danger of false-positive results due to repeated model specification. This theoretical reasoning suggests that machine learning (variable selection) methods may be promising tools to keep the advantages of covariate adjustment, while simultaneously protecting against its downsides.

In this presentation, I rely on recent developments of machine learning methods for causal effects and their implementation in Stata to assess the performance of ML methods in randomized trials. I rely on real-world data and simulate treatment effects on a wide range of different data structures, including different outcomes and sample sizes. (Preliminary) results suggests that ML adjusted estimates are unbiased and show considerable efficiency gains compared with unadjusted analysis.

The results are fairly similar between different data structures used and robust to the choice of tuning parameters of the ML estimators. These results tend to support the more optimistic view on covariate adjustment and highlight the potential of ML methods in this field.