Economic and financial time series data can exhibit nonstationary and nonlinear patterns si- multaneously. This paper studies copula-based time series models that capture both patterns. We introduce a procedure where nonstationarity is removed via a filtration, and then the nonlinear temporal dependence in the filtered data is captured via a flexible Markov copula. We propose two estimators of the copula dependence parameters: the parametric (two-step) copula estimator where the marginal distribution of the filtered series is estimated parametrically; and the semiparametric (two-step) copula estimator where the marginal distribution is estimated via a rescaled empirical distribution of the filtered series. We show that the limiting distribution of the parametric copula estimator depends on the nonstationary filtration and the parametric marginal distribution estimation, and may be non-normal. Surprisingly, the limiting distribution of the semiparametric copula estimator using the filtered data is shown to be the same as that without nonstationary filtration, which is normal and free of marginal distribution specification. The simple and robust properties of the semiparametric copula estimators extend to models with misspecified copulas, and facilitate statistical inferences, such as hypothesis testing and model selection tests, on semiparametric copula-based dynamic models in the presence of nonstationarity. Monte Carlo studies and real data applications are presented.
We show how incorporating Gilboa, Maccheroni, Marinacci, and Schmeidler’s (2010) notion of objective rationality into the alpha-MEU model of choice under ambiguity (Hurwicz, 1951) can overcome several challenges faced by the baseline model without objective rationality. The decision-maker (DM) has a subjectively rational preference $\succsim^\wedge$, which captures the complete ranking over acts the DM expresses when forced to make a choice; in addition, we endow the DM with a (possibly incomplete) objectively rational preference $\succsim^*$, which captures the rankings the DM deems uncontroversial. Under the objectively founded alpha-MEU model, $\succsim^\wedge$ has an alpha-MEU representation and $\succsim^*$ has a unanimity representation à la Bewley (2002), where both representations feature the same utility index and set of beliefs. While the axiomatic foundations of the baseline alpha-MEU model are still not fully understood, we provide a simple characterization of its objectively founded counterpart. Moreover, in contrast with the baseline model, the model parameters are uniquely identified. Finally, we provide axiomatic foundations for prior-by-prior Bayesian updating of the objectively founded alpha-MEU model, while we show that, for the baseline model, standard updating rules can be ill-defined.
This study presents the design and results of a rapid-fire survey that collects labor market data for households in the United States. The Yale Labor Survey, or YLS, uses an online panel from YouGov to replicate the Current Population Survey (CPS), which is the source of the government’s monthly household statistics. Questions in the YLS concern current and retrospective employment, hours, and income. Because the YLS draws upon an existing pool of potential respondents, it can generate responses inexpensively and quickly (within 24 hours). Moreover, the YLS can develop new questions in real time to study unusual patterns of work and unemployment during the pandemic. Results from the YLS track those from the CPS over the period of April through June of 2020, with relatively accurate estimates of employment but greater difficulty capturing unemployment. The major issue statistical issue dealt with in this paper is the sample weighting required to overcome the bias in using an online panel.
Economic and financial time series data can exhibit nonstationary and nonlinear patterns simultaneously. This paper studies copula-based time series models that capture both patterns. We propose a procedure where nonstationarity is removed via a filtration, and then the nonlinear temporal dependence in the filtered data is captured via a flexible Markov copula. We study the asymptotic properties of two estimators of the parametric copula dependence parameters: the parametric (two-step) copula estimator where the marginal distribution of the filtered series is estimated parametrically; and the semiparametric (two-step) copula estimator where the marginal distribution is estimated via a rescaled empirical distribution of the filtered series. We show that the limiting distribution of the parametric copula estimator depends on the nonstationary filtration and the parametric marginal distribution estimation, and may be non-normal. Surprisingly, the limiting distribution of the semiparametric copula estimator using the filtered data is shown to be the same as that without nonstationary filtration, which is normal and free of marginal distribution specification. The simple and robust properties of the semiparametric copula estimators extend to models with misspecified copulas, and facilitate statistical inferences, such as hypothesis testing and model selection tests, on semiparametric copula-based dynamic models in the presence of nonstationarity. Monte Carlo studies and real data applications are presented.
Tracking human activity in real time and at fine spatial scale is particularly valuable during episodes such as the COVID-19 pandemic. In this paper, we discuss the suitability of smartphone data for quantifying movement and social contact. We show that these data cover broad sections of the US population and exhibit movement patterns similar to conventional survey data. We develop and make publicly available a location exposure index that summarizes county-to-county movements and a device exposure index that quantifies social contact within venues. We use these indices to document how pandemic-induced reductions in activity vary across people and places.
We show how incorporating Gilboa, Maccheroni, Marinacci, and Schmeidler’s (2010) notion of objective rationality into the α-MEU model of choice under ambiguity can overcome several challenges faced by the baseline model without objective rationality. The decision-maker (DM) has a subjectively rational preference ≿^, which captures the complete ranking overacts the DM expresses when forced to make a choice; in addition, we endow the DM with a (possibly incomplete) objectively rational preference ≿*, which captures the rankings the DM deems uncontroversial. Under the objectively founded α-MEU model, ≿^ has an α-MEU representation and ≿*has a unanimity representation à la Bewley (2002), where both representations feature the same utility index and set of beliefs. While the axiomatic foundations of the baseline α-MEU model are still not fully understood, we provide a simple characterization of its objectively founded counterpart. Moreover, in contrast with the baseline model, the model parameters are uniquely identified. Finally, we provide axiomatic foundations for prior-by-prior Bayesian updating of the objectively founded α-MEU model, while we show that, for the baseline model, standard updating rules can be ill-defined.
We construct a model of rm dynamics with heterogenous productivity and distortions. The productivity distribution evolves endogenously as the result of the decisions of firms seeking to upgrade their productivity over time. Firms can adopt two strategies toward that end: imitation and innovation. The theory bears predictions about the evolution of the productivity distribution. We structurally estimate the stationary state of the dynamic model targeting moments of the empirical distribution of R&D and TFP growth in China during the period 2007-2012. The estimated model ts the Chinese data well. We compare the estimates with those obtained using data for Taiwan and find the results to be robust. We perform counterfactuals to study the effect of alternative policies. We find large effects of R&D misallocation on long-run growth.