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It is common to assume that worker productivity is normally distributed, but this assumption is rarely, if ever, tested. We estimate the distribution of worker productivity, where individual productivity is measured with error, using the productivity of teachers as an example. We employ a nonparametric density estimator that explicitly accounts for measurement error using data from the Tennessee STAR experiment, and longitudinal data from North Carolina and Washington. Statistical tests show that the productivity distribution of teachers is not Gaussian, but the differences from the normal distribution tend to be small. Our findings confirm the existing empirical evidence that the differences in the effects of individual teachers on student achievement are large and the assumption that the differences in the upper and lower tails of the teacher performance distribution are far larger than in the middle of the distribution. Specifically, a 10 percentile point movement for teachers at the top (90th) or bottom (10th) deciles of the distribution is estimated to move student achievement by 8-17 student percentile ranks, as compared to a change of 2-7 student percentile ranks for a 10 percentile change in teacher productivity in the middle of the distribution.

The recently published Intergovernmental Panel on Climate Change (IPCC) projections to 2100 give likely ranges of global temperature increase in four scenarios for population, economic growth and carbon use1. However these projections are not based on a fully statistical approach. Here we use a country-specific version of Kaya's identity to develop a statistically-based probabilistic forecast of CO2 emissions and temperature change to 2100. Using data for 1960-2010, including the UN's probabilistic population projections for all countries2-4, we develop a joint Bayesian hierarchical model for GDP per capita and carbon intensity. We find that the 90% interval for cumulative CO2 emissions includes the IPCC's two middle scenarios but not the extreme ones. The likely range of global temperature increase is 2.0-4.9°C, with median 3.2°C and a 5% (1%) chance that it will be less than 2°C (1.5°C). Population growth is not a major contributing factor. Our model is not a "business as usual" scenario, but rather is based on data which already show the effect of emission mitigation policies. Achieving the goal of less than 1.5°C warming will require carbon intensity to decline much faster than in the recent past.

Temperature variation within a year can impact biological processes driving population abundances. The implications for the ecosystem services these populations provide, including food production from marine fisheries, are poorly understood. Whether and how temperature variability impacts fishery yields may depend on the number of harvested species and differences in their responses to varying temperatures. Drawing from previous theoretical and empirical studies, we predict that greater temperature variability within years will reduce yields, but harvesting a larger number of species, especially a more functionally diverse set, will decrease this impact. Using a global marine fisheries dataset, we find that within-year temperature variability reduces yields, but current levels of functional diversity (FD) of targeted species, measured using traits related to species' responses to temperature, largely offset this effect. Globally, high FD of catch could avoid annual losses in yield of 6.8% relative to projections if FD were degraded to the lowest level observed in the data. By contrast, species richness in the catch and in the ecosystem did not provide a similar mitigating effect. This work provides novel empirical evidence that short-term temperature variability can negatively impact the provisioning of ecosystem services, but that FD can buffer these negative impacts.

We set out a Gibbs sampler for the linear instrumental-variable model withnormal errors and normal priors, and we show how to compute the marginallikelihood.

Use of heteroskedasticity-robust standard errors has become common in frequentist regressions. I offer here a Bayesian analog. The Bayesian version is derived by first focusing on the likelihood function for the sample values of the identifying moment conditions of least squares and then formulating a convenient prior for the variances of the error terms. The first step introduces a sandwich estimator into the posterior calculations, while the second step allows the investigator to set the sandwich for either heteroskedastic or homoskedastic error variances. If desired, the Bayesian estimator can be made to look very similar to the usual heteroskedasticity-robust frequentist estimator. Bayesian estimation is easily accomplished by a standard MCMC procedure.

Standard models of intertemporal utility maximization assume that agents discount future utility flows at a constant rate—exponential discounting. Euler equations estimated over different time horizons should have equal discount rates but they do not. Rising term yield premia imply discount rates that rise with longer horizons since uncertainty is much too small to account for the difference in interest rates. Such deviations from exponential discounting are large enough to make a significant difference in consumption choices over long horizons. Our results can be viewed as providing estimates of horizon-specific discounts, or as a further puzzle concerning intertemporal substitution and uncertainty.

Standard estimation of ARMA models in which the AR and MA roots nearly cancel, so that individual coefficients are only weakly identified, often produces inferential ranges for individual coefficients that give a spurious appearance of accuracy. We remedy this problem with a model that mixes inferential ranges from the estimated model with those of a more parsimonious model. The mixing probability is derived using Bayesian methods, but we show that the method works well in both Bayesian and frequentist setups. In particular, we show that our mixture procedure weights standard results heavily when given data from a well-identified ARMA model (which does not exhibit near root cancellation) and weights heavily an uninformative inferential region when given data from a weakly-identified ARMA model (with near root cancellation). When our procedure is applied to a well-identified process the investigator gets the “usual results,” so there is no important statistical cost to using our procedure. On the other hand, when our procedure is applied to a weakly-identified process, the investigator learns that the data tell us little about the parameters—and is thus protected against making spurious inferences. We recommend that mixture models be computed routinely when inference about ARMA coefficients is of interest.

Education reform advocates who base policy decisions on empirical research often face the argument that because background variables explain so much of student outcomes, it follows that policy interventions cannot be effective. This policy brief explains the logical fallacy in the argument, illustrating with two examples, one taken from the teacher quality literature and one taken from the class size literature.

At the start of the 2020 school year, some colleges chose to reopen in person while others offered primarily online classes. We find that colleges responded to financial and other incentives largely as one might expect. Larger shares of revenue attributed to in-person activities, such as dorms and dining halls, led schools to reopen in person. In general, the share of revenue due to tuition and fees had little association with reopening in-person, which is consistent with the idea that the effect of the mode of reopening on enrolment was ambiguous. However, private schools experiencing financial distress due to tuition and fees were more likely to reopen in-person while public schools were less likely. Public colleges were influenced by political pressures and the fraction of students from out of state, while private schools responded to the severity of COVID in their local community. [ABSTRACT FROM AUTHOR]

In many econometric models the asymptotic variance of a parameter estimate depends on the value of another structural parameter in such a way that the data contain little information about the former when the latter is close to a critical value. This paper introduces the zero-information-limit-condition (ZILC) to identify such models where 'weak identification' leads to spurious inference. We find that standard errors tend to be underestimated in these cases, but the size of the asymptotic t-test may either be too great (the intuitive case emphasized in the 'weak instrument' literature) or too small as in two cases illustrated here. JEL classifications: C120; C220; C300 Keywords: Weak identification; Spurious inference; Weak instruments