Working Papers

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 Asymmetry and Capital Structure: Theory and Evidence
(with Amy Hongfei Sun)

Abstract: We propose a new theory of capital structure based on two layers of asymmetric information over investment opportunities. In our model, firms operate projects of privately-known quality to generate random outputs, the realization of which is also private information. To obtain external funding, firms choose either a transparent contract or an opaque contract to offer to investors: respectively with and without having quality revealed ex-ante. We prove the following: First, the optimal transparent contract is an equity contract as it offers investors a proportion of the firm’s actual output. The optimal opaque contract is a debt contract in that investors are paid a rate of return that is independent of the project quality. Debt and equity arise endogenously in equilibrium as alternative methods of external financing. Secondly, the project quality, such as its productivity and success rate, matters for the optimal financing method. All else equal, the higher the expected productivity, the more likely for a firm to choose equity instead of debt financing. Otherwise, firms optimally choose debt. Thirdly, internal funds also matter. Conditional on the expected productivity being sufficiently high, a firm will only choose to use equity given an intermediate level of internal funds. Firms with rather low or high internal funds choose debt. Finally, the cost of quality verification matters, too. Ceteris paribus, the higher this cost, the fewer firms end up with equity financing and thus the more with debt. Our theory can reconcile a variety of well-documented evidence on firm financing. We also find new evidence, in support of our theory, that suggests a U-shaped relationship between firms’ internal funds and debt ratios.

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)