To infinity and beyond: Efficient computation of ARCH(∞) Models
(with Morten Ørregaard Nielsen)
- Latest version is June 29, 2020
- Reference: Nielsen and Noel (2020, QED working paper 1425).
- The associated computer codes can be downloaded here.
- R&R at Journal of Time Series Analysis
Abstract: This paper provides an exact algorithm for efficient computation of the time series of conditional variances, and hence the likelihood function, of models that have an ARCH(∞) representation. This class of models includes, e.g., the fractionally integrated generalized autoregressive conditional heteroskedasticity (FIGARCH) model. Our algorithm is a variation of the fast fractional difference algorithm of Jensen and Nielsen (2014). It takes advantage of the fast Fourier transform (FFT) to achieve an order of magnitude improvement in computational speed. The efficiency of the algorithm allows estimation (and simulation/bootstrapping) of ARCH(∞) models, even with very large data sets and without the truncation of the filter commonly applied in the literature. We also show that the elimination of the truncation of the filter substantially reduces the bias of the quasi-maximum-likelihood estimators. Our results are illustrated in two empirical examples.
Information Asymmetries, Capital Structure and the U-Shaped Distribution of Debt Ratios
(with Amy Hongfei Sun)
Abstract: We propose a microfounded theory of capital structure that explains the coexistence of debt and publicly held shares. We also document new evidence of firm financing behavior that is consistent with our theory. Our model nests adverse selection and agency cost in an environment with ex ante heterogeneous firms. With our model, we prove the following: First, there exists a unique perfect Bayesian equilibrium, in which debt and equity contracts arise endogenously and coexist in equilibrium as optimal methods of external financing. Second, the unique equilibrium can be one of two types, either pooling with debt only or mixing. Third, individual firm characteristics drive the optimal financing choice. With a lower level of expected productivity, a firm will always use debt financing regardless of its internal funds available. With a sufficiently high level of expected productivity, a firm will choose equity only for an intermediate level of internal funds, and debt otherwise. Consistent with this particular theoretical finding, we have uncovered novel evidence that suggests a U-shaped distribution of debt ratios across deciles of firm cash flows.
Measurement Error and Consumption Inequality in Canada
(work in progress with Brant Abbott and Samuel Brien)
WTO, tariffs negotiations and bargaining power
(work in progress)