Mark W. Watson’s research while affiliated with Princeton University and other places

Standard extreme value theory implies that the distribution of the largest observations of a large cross section is well approximated by a parametric model, governed by a location, scale and shape parameter. The extremes of a panel of independent cross sections are all governed by the same parameters as long as the underlying distribution as well as the size of the cross sections are time invariant. We derive inference about these parameters, and tests of the null hypothesis of time invariance, under asymptotics that do not require the number of extremes or the number of time periods to increase. We further apply Hamiltonian Monte Carlo techniques to estimate the path of time-varying parameters. We illustrate the approach in four examples of U.S. data: damages from weather-related disasters, financial returns, city sizes and firm sizes.

This paper proposes a model for, and investigates the consequences of, strong spatial dependence in economic variables. Our findings echo those of the corresponding “unit root” time series literature: Spatial unit root processes induce spuriously significant regression results, even with clustered standard errors or spatial HAC corrections. We develop large‐sample valid unit root and stationarity tests that can detect such strong spatial dependence. Finally, we use simulations to study strategies for valid inference in regressions with persistent spatial data, such as spatial analogues of first‐differencing transformations. Regressions from Chetty, Hendren, Kline, and Saez (2014) are used to illustrate the issues and methods.

We consider inference about a scalar coefficient in a linear regression with spatially correlated errors. Recent suggestions for more robust inference require stationarity of both regressors and dependent variables for their large sample validity. This rules out many empirically relevant applications, such as difference-in-difference designs. We develop a robustified version of the SCPC method of Müller and Watson (2022a) that addresses this challenge. We find that the method has good size properties in a wide range of Monte Carlo designs that are calibrated to real world applications, both in a pure cross sectional setting, but also for spatially correlated panel data. We provide numerically efficient methods for computing the associated spatial-correlation robust test statistics, critical values and confidence intervals.

The social cost of carbon dioxide (SC-CO2) measures the monetized value of the damages to society caused by an incremental metric tonne of CO2 emissions and is a key metric informing climate policy. Used by governments and other decision-makers in benefit-cost analysis for over a decade, SC-CO2 estimates draw on climate science, economics, demography, and other disciplines. However, a 2017 report by the US National Academies of Sciences, Engineering, and Medicine1 (NASEM) highlighted that current SC-CO2 estimates no longer reflect the latest research. The report provided a series of recommendations for improving the scientific basis, transparency, and uncertainty characterization of SC-CO2 estimates. Here we show that improved probabilistic socioeconomic projections, climate models, damage functions, and discounting methods that collectively reflect theoretically consistent valuation of risk, substantially increase estimates of the SC-CO2. Our preferred mean SC-CO2 estimate is $185 per tonne of CO2 ($44-413/t-CO2: 5-95% range, 2020 US dollars) at a near-term risk-free discount rate of 2 percent, a value 3.6-times higher than the US government’s current value of $51/t-CO2. Our estimates incorporate updated scientific understanding throughout all components of SC-CO2 estimation in the new open-source GIVE model, in a manner fully responsive to the near-term NASEM recommendations. Our higher SC-CO2 values, compared to estimates currently used in policy evaluation, substantially increase the estimated benefits of greenhouse gas mitigation and thereby increase the expected net benefits of more stringent climate policies.

We propose a method for constructing confidence intervals that account for many forms of spatial correlation. The interval has the familiar “estimator plus and minus a standard error times a critical value” form, but we propose new methods for constructing the standard error and the critical value. The standard error is constructed using population principal components from a given “worst‐case” spatial correlation model. The critical value is chosen to ensure coverage in a benchmark parametric model for the spatial correlations. The method is shown to control coverage in finite sample Gaussian settings in a restricted but nonparametric class of models and in large samples whenever the spatial correlation is weak, that is, with average pairwise correlations that vanish as the sample size gets large. We also provide results on the efficiency of the method.

We propose a method for constructing confidence intervals that account for many forms of spatial correlation. The interval has the familiar `estimator plus and minus a standard error times a critical value' form, but we propose new methods for constructing the standard error and the critical value. The standard error is constructed using population principal components from a given `worst-case' spatial covariance model. The critical value is chosen to ensure coverage in a benchmark parametric model for the spatial correlations. The method is shown to control coverage in large samples whenever the spatial correlation is weak, i.e., with average pairwise correlations that vanish as the sample size gets large. We also provide results on correct coverage in a restricted but nonparametric class of strong spatial correlations, as well as on the efficiency of the method. In a design calibrated to match economic activity in U.S. states the method outperforms previous suggestions for spatially robust inference about the population mean.

We investigate the flattening Phillips relation by making two departures from standard specifications. First, we measure slack using real activity variables that are bandpass filtered or year‐over‐year changes in activity (these are similar), instead of gaps. Second, we study the components of inflation instead of the standard aggregates. We find that some inflation components have strong and stable correlations with the cyclical component of real activity; these components tend to be relatively well‐measured and domestically determined. Other components, typically prices that are poorly measured or internationally determined, have weak and/or unstable correlations with cyclical activity. We construct a new inflation index, cyclically sensitive inflation, that weights the components by their joint cyclical covariation with real activity. The index has strong and stable correlations with cyclical activity and provides a real‐time measure of cyclical movements in inflation.

We develop a Bayesian latent factor model of the joint long-run evolution of GDP per capita for 113 countries over the 118 years from 1900 to 2017. We find considerable heterogeneity in rates of convergence, including rates for some countries that are so slow that they might not converge (or diverge) in century-long samples, and a sparse correlation pattern (“convergence clubs”) between countries. The joint Bayesian structure allows us to compute a joint predictive distribution for the output paths of these countries over the next 100 years. This predictive distribution can be used for simulations requiring projections into the deep future, such as estimating the costs of climate change. The model's pooling of information across countries results in tighter prediction intervals than are achieved using univariate information sets. Still, even using more than a century of data on many countries, the 100-year growth paths exhibit very wide uncertainty.

This paper studies Structural Vector Autoregressions in which a structural shock of interest (e.g., an oil supply shock) is identified using an external instrument. The external instrument is taken to be correlated with the target shock (the instrument is relevant) and to be uncorrelated with other shocks of the model (the instrument is exogenous). The potential weak correlation between the external instrument and the target structural shock compromises the large-sample validity of standard inference. We suggest a confidence set for impulse response coefficients that is not affected by the instrument strength (i.e., is weak-instrument robust) and asymptotically coincides with the standard confidence set when the instrument is strong.