My research spans econometric and statistical theory of time series and network processes. I apply these techniques to climate and health econometrics and develop asymptotically valid procedures for empirical researchers.

Papers (under review and published)

Cointegration without unit roots with James Duffy. (Revise and resubmit at Quantitative Economics)

Abstract In response to the criticism voiced in Elliott (1998), we propose a new concept of cointegration, termed quasi-cointegration, that treats unit and near unit roots of the characteristic polynomial of a vector autoregressive model in the same manner. We identify the quasi-cointegrating matrix as an extension of its classical counterpart defined in Johansen (1995) as the object that produces linear combinations of the series that exhibit rapid mean-reversion. We proceed via restricted maximum likelihood where the invariant subspace of the characteristic polynomial associated with near and actual unit roots appear as restrictions on the VAR parameters. We then offer an estimation and inference procedure that is asymptotically valid and avoids the bias which gave rise to this problem. The ‘nearness to unity’ parameter appears as a nuisance coefficient which we eliminate via a Bonferroni-based procedure to form valid confidence sets. To attain statistical power, we use the method of Elliott, Mueller, Watson (2015). Our results indicate that in the presence of near unit roots, our method remains size-controlled with good power properties while conventional methods become severely size-distorted. Indeed, 5% tests showed rejection probabilities of up to 80% for a small departure from a unit root. In the classical unit root case, our method retains power and quasi-cointegrating vectors are identical to their classical counterparts. An application demonstrates the usability of this approach.

Forecasting dementia incidence with Eric French, Yuntao Chen, and Eric Brunner

under review at JASA

Slides

Abstract We proceed in two stages. Using UK ELSA data, we first estimate dementia incidence rates from 2002 to 2016 and derive a data array comparable to a life table. Second, we employ a rank 1 factor model according to Lee and Carter (1992) to decompose the incidence rates into a period and age effect. We feed the period effect time series into a specially designed Kalman filter with restricted time-dependent observational variance to estimate filtered states. On this basis, we found that a random walk model fits best and construct forecasts for all age groups and both sexes. We find that despite a recently observed uptick in dementia trends, the overall trend is flat.

Effectiveness of medical treatment for bipolar disorder with Fitzgerald et al. British Journal of Psychiatry vol. 221(5) (2022) pp. 692-700

Abstract Mood stabilisers are the main treatment for bipolar disorder. However, it is uncertain which drugs have the best outcomes.

We investigate whether rates of suicide, self-harm and psychiatric hospital admission in individuals with bipolar disorder differ between mood stabilisers.

A cohort design was applied to people aged 15+ years who were diagnosed with bipolar disorder and living in Denmark during 1995–2016. Treatment with lithium, valproate, other mood stabilisers and antipsychotics were compared in between- and within-individual analyses, and adjusted for sociodemographic characteristics and previous self-harm.

Lithium was associated with lower rates of suicide, self-harm and psychiatric hospital readmission in all analyses. With respect to suicide, lithium was superior to no treatment. Although confounding by indication cannot be excluded, lithium seems to have better outcomes in the treatment of bipolar disorder than other mood stabilisers.

Working papers

Hypothesis testing on invariant subspaces of non-symmetric matrices with applications to network statistics

preparation for submission to Biometrika

Replication files

Slides

Abstract This paper extends the inference procedure of Tyler (1981) to generic invariant subspaces of non-symmetric and non-diagonalisable matrices. We establish distribution theory for a Wald and t-test for full-vector and individual coefficient hypotheses, respectively. Our test statistics originate from eigenprojections of non-symmetric matrices. Representing projections as a mapping from the underlying matrix to its spectral data, we find derivatives through analytic perturbation theory. These results demonstrate how the analytic perturbation theory of Sun (1991) is a useful tool in multivariate statistics and are of independent interest. We offer an application via confidence sets for eigenvector centralities estimated from digraph adjacency matrices.

Hidden Threshold Models with applications to asymmetric cycles with Andrew Harvey

Abstract Threshold models are set up so that there is a switch between regimes for the parameters of an unobserved components model. When Gaussianity is assumed, the model is handled by the Kalman filter. The switching depends on a component crossing a boundary, and, because the component is not observed directly, the error in its estimation leads naturally to a smooth transition mechanism. A prominent example motivating thresholds is that of a cyclical time series characterized by a downturn that is more, or less, rapid than the upturn. The situation is illustrated by fitting a model with three potentially asymmetric cycles, each with its own threshold, to observations on ice volume in Antarctica since 799,000 BCE. The model is able to produce multi-step forecasts with associated prediction intervals. A second example shows how a hidden threshold model is able to deal with the asymmetric cycle in monthly US unemployment.

Determining climate sensitivity using the quasi-cointegrated VAR

Abstract Climate sensitivity is temperature deviation from its long-run mean in response to a doubling of carbon dioxide stocks. To find confidence intervals for the climate sensitivity parameter, we write the popular Hasselmann (1976) model as a quasi-cointegrated vector autoregression. Sherwood et al. (2020) find this interval to be [2.6, 4.1]. Using quasi-cointegration methods, the maximum likelihood interval is [1.37,2.17]. The class of model we consider places the global climate on a persistent process that becomes a random walk in the limit with implied equilibria around those disturbances. Necessarily, we obtain a nuisance parameter that regulates persistence. We use the method of Elliott, Mueller, Watson (2015) to eliminate the nuisance parameter and find a confidence interval based on a most powerful test.

Selected Work in Progress

Dynamic panel data models for centrality measures (JMP)

Abstract We derive asymptotically normal GMM estimators for semi-parametric, dynamic models of network centrality measures. We define a data-generating process based on a panel VAR of a low-rank approximation of the underlying network adjacency matrices which we observe over time.

Fixed bandwidth asymptotic theory for network HAC estimators with Michael Leung

Abstract We employ an alternative asymptotic approach developed by Kiefer and Vogelsang (2002) to study the limiting distribution of the heteroskedasticity and autocorrelation-robust covariance matrix estimator. To obtain critical values, we establish a functional central limit theorem for network processes.

Uniform asymptotics for weak and strong factors with Alexei Onatskiy

Abstract Factor models are a popular tool in many econometric applications, especially in settings where data reduction is important. However, in those circumstances, the signal contained in the data may be weak, which may lead to asymptotic approximations breaking down. We propose an asymptotic theory of estimators of factors that is independent of factor strength.