Density Forecasts in Panel Data Models: A Semiparametric Bayesian Perspective

This article constructs individual-specific density forecasts for a panel of firms or households using a dynamic linear model with common and heterogeneous coefficients as well as cross-sectional heteroscedasticity. The panel considered in this article features a large cross-sectional dimension N but short time series T. Due to the short T, traditional methods have difficulty in disentangling the heterogeneous parameters from the shocks, which contaminates the estimates of the heterogeneous parameters. To tackle this problem, I assume that there is an underlying distribution of heterogeneous parameters, model this distribution nonparametrically allowing for correlation between heterogeneous parameters and initial conditions as well as individual-specific regressors, and then estimate this distribution by combining information from the whole panel. Theoretically, I prove that in cross-sectional homoscedastic cases, both the estimated common parameters and the estimated distribution of the heterogeneous parameters achieve posterior consistency, and that the density forecasts asymptotically converge to the oracle forecast. Methodologically, I develop a simulation-based posterior sampling algorithm specifically addressing the nonparametric density estimation of unobserved heterogeneous parameters. Monte Carlo simulations and an empirical application to young firm dynamics demonstrate improvements in density forecasts relative to alternative approaches.</p

Additional file 2 of Diagnostic accuracy of eHealth literacy measurement tools in older adults: a systematic review

Additional file 2: Supplementary file 2. Grey literature databases searched

Additional file 1 of Diagnostic accuracy of eHealth literacy measurement tools in older adults: a systematic review

Additional file 1: Supplementary file 1. Search strategy

Self-rated glaucoma risk and physician-rated glaucoma risk, unweighted.

Self-rated glaucoma risk and physician-rated glaucoma risk, unweighted.</p

Patient questionnaire (original language).

Questionnaire used in the current study. (PDF)</p

Logistic regression for factors associated with high risk, weighted.

Logistic regression for factors associated with high risk, weighted.</p

Weighted sample characteristic (n = 1203).

Weighted sample characteristic (n = 1203).</p

Patient questionnaire (English).

Questionnaire used in the current study. (DOCX)</p

Marginal effects of glaucoma knowledge.

a. Shows the average marginal effect of glaucoma knowledge score by education at various age intervals. b. Shows the average marginal effect of glaucoma knowledge score by sex at various age intervals. c. Shows the effect of glaucoma knowledge by each education/sex stratum. The marginal effects for Fig 1A–1C should be interpreted as the effect on the predicted probability of being in the “High concern group” in percentage points (point estimate × 100).</p

Characteristics of the spinal cord injury group versus the comparison cohort.

<p>Pre-school age: 0–5 years; School age: 6–12 years; Teenagers: 13–18 years.</p