Essays in macroeconomics and labor economics

This doctoral thesis is made up of three chapters at the intersection between macroeconomics and labor economics, all dealing with topics related to search frictions in the labor market. In the first chapter, I develop a tractable model of firm and worker reallocation over the business cycle that emphasizes the interplay between firms with heterogeneous productivities and on-the-job search. I use this framework to study the role of search frictions in determining aggregate labor productivity following a large economic contraction. In the model, search frictions slow down worker reallocation after a recession, as employed workers face increased competition from a larger pool of unemployed workers. This crowding-out effect holds back the transition of employed workers from less to more productive firms, thus lowering aggregate productivity. Quantitatively, the model implies that worker reallocation has sizable and persistent negative effects on aggregate labor productivity. I provide evidence for this channel from data on the universe of British firms which show that the allocation of workers to firms has downgraded in the aftermath of the Great Recession. In the second chapter, I study the unemployment risks faced by self-employed workers. Though public unemployment insurance (UI) schemes represent an important feature of the social safety net in most advanced economies, the self-employed are generally excluded from these programs. This chapter shows that, similarly to employees on a wage contract, the self-employed do go through unemployment spells in US data. It then calibrates a job search model to evaluate the potential welfare gains from extending UI benefits to this group of workers. The model features workers moving between paid- and self-employment who face the risk of becoming unemployed. Agents can also privately save and borrow to self-insure. My results suggest that extending UI benefits to the self-employed yields modest welfare gains. In the third chapter, I use longitudinal data on patents to quantify sorting in knowledge production. The dimension of sorting I study is that arising between inventors and their ``firm'' (private corporations, universities, public research institutes). My analysis points to the existence of clear, positive inventor-firm sorting. This mechanism accounts on average for five percent of the total variance of inventor output in the US between 1975 and 2010. This framework further suggests that the geographical sorting of inventors and firms is a key channel to explain regional disparities in inventor output

Capillary buckling of a thin film adhering to a sphere

We present a combined theoretical and experimental study of the buckling of a thin film wrapped around a sphere under the action of capillary forces. A rigid sphere is coated with a wetting liquid, and then wrapped by a thin film into an initially cylindrical shape. The equilibrium of this cylindrical shape is governed by the antagonistic effects of elasticity and capillarity: elasticity tends to keep the film developable while capillarity tends to curve it in both directions so as to maximize the area of contact with the sphere. In the experiments, the contact area between the film and the sphere has cylindrical symmetry when the sphere radius is small, but destabilises to a non-symmetric, wrinkled configuration when the radius is larger than a critical value. We combine the Donnell equations for near-cylindrical shells to include a unilateral constraint with the impenetrable sphere, and the capillary forces acting along a moving edge. A non-linear solution describing the axisymmetric configuration of the film is derived. A linear stability analysis is then presented, which successfully captures the wrinkling instability, the symmetry of the unstable mode, the instability threshold and the critical wavelength. The motion of the free boundary at the edge of the region of contact, which has an effect on the instability, is treated without any approximation

Thin front propagation in steady and unsteady cellular flows

Front propagation in two dimensional steady and unsteady cellular flows is investigated in the limit of very fast reaction and sharp front, i.e., in the geometrical optics limit. In the steady case, by means of a simplified model, we provide an analytical approximation for the front speed, $v_{{\scriptsize{f}}}$, as a function of the stirring intensity, $U$, in good agreement with the numerical results and, for large $U$, the behavior $v_{{\scriptsize{f}}}\sim U/\log(U)$ is predicted. The large scale of the velocity field mainly rules the front speed behavior even in the presence of smaller scales. In the unsteady (time-periodic) case, the front speed displays a phase-locking on the flow frequency and, albeit the Lagrangian dynamics is chaotic, chaos in front dynamics only survives for a transient. Asymptotically the front evolves periodically and chaos manifests only in the spatially wrinkled structure of the front.Comment: 12 pages, 13 figure

Parameter estimation in kinetic reaction models using nonlinear observers facilitated by model extensions

An essential part of mathematical modelling is the accurate and reliable estimation of model parameters. In biology, the required parameters are particularly difficult to measure due to either shortcomings of the measurement technology or a lack of direct measurements. In both cases, parameters must be estimated from indirect measurements, usually in the form of time-series data. Here, we present a novel approach for parameter estimation that is particularly tailored to biological models consisting of nonlinear ordinary differential equations. By assuming specific types of nonlinearities common in biology, resulting from generalised mass action, Hill kinetics and products thereof, we can take a three step approach: (1) transform the identification into an observer problem using a suitable model extension that decouples the estimation of non-measured states from the parameters; (2) reconstruct all extended states using suitable nonlinear observers; (3) estimate the parameters using the reconstructed states. The actual estimation of the parameters is based on the intrinsic dependencies of the extended states arising from the definitions of the extended variables. An important advantage of the proposed method is that it allows to identify suitable measurements and/or model structures for which the parameters can be estimated. Furthermore, the proposed identification approach is generally applicable to models of metabolic networks, signal transduction and gene regulation

One-dimensional modeling of necking in rate-dependent materials

This paper presents an asymptotically rigorous one-dimensional analytical formulation capable of accurately capturing the stress and strain distributions that develop within the evolving neck of bars and sheets of rate-dependent materials stretched in tension. The work is an extension of an earlier study by the authors on necking instabilities in rate-independent materials. The one-dimensional model accounts for the gradients of the stress and strain that develop as the necking instability grows. Material strain-rate dependence has a significant influence on the strain that can be imposed on a bar or sheet before necking becomes pronounced. The formulation in this paper enables a quantitative assessment of the interplay in necking retardation due to rate-dependence and that due to the development of hydrostatic tension in the neck. The connection with a much simpler long-wavelength approximation which does not account for curvature induced hydrostatic tension in the neck is also emphasized and extended