Essays on Firm Heterogeneity with Empirical Applications in Economic History and Agricultural Economics

This thesis uses models of firm-heterogeneity to complete empirical analyses in economic history and agricultural economics. In Chapter 2, a theoretical model of firm heterogeneity is used to derive a statistic that summarizes the welfare gains from the introduction of a new technology. The empirical application considers the use of mechanical steam power in the Canadian manufacturing sector during the late nineteenth century. I exploit exogenous variation in geography to estimate several parameters of the model. My results indicate that the use of steam power resulted in a 15.1 percent increase in firm-level productivity and a 3.0-5.2 percent increase in aggregate welfare. Chapter 3 considers various policy alternatives to price ceiling legislation in the market for production quotas in the dairy farming sector in Quebec. I develop a dynamic model of the demand for quotas with farmers that are heterogeneous in their marginal cost of milk production. The econometric analysis uses farm-level data and estimates a parameter of the theoretical model that is required for the counterfactual experiments. The results indicate that the price of quotas could be reduced to the ceiling price through a 4.16 percent expansion of the aggregate supply of quotas, or through moderate trade liberalization of Canadian dairy products. In Chapter 4, I study the relationship between farm-level productivity and participation in the Commercial Export Milk (CEM) program. I use a difference-in-difference research design with inverse propensity weights to test for causality between participation in the CEM program and total factor productivity (TFP). I find a positive correlation between participation in the CEM program and TFP, however I find no statistically significant evidence that the CEM program affected TFP.

Tight-Binding Approximations in 1D and 2D Coupled-Cavity Photonic Crystal Structures

Light confinement and controlling an optical field has numerous applications in the field of telecommunications for optical signals processing. When the wavelength of the electromagnetic field is on the order of the period of a photonic microstructure, the field undergoes reflection, refraction, and coherent scattering. This produces photonic bandgaps, forbidden frequency regions or spectral stop bands where light cannot exist. Dielectric perturbations that break the perfect periodicity of these structures produce what is analogous to an impurity state in the bandgap of a semiconductor. The defect modes that exist at discrete frequencies within the photonic bandgap are spatially localized about the cavity-defects in the photonic crystal. In this thesis the properties of two tight-binding approximations (TBAs) are investigated in one-dimensional and two-dimensional coupled-cavity photonic crystal structures We require an efficient and simple approach that ensures the continuity of the electromagnetic field across dielectric interfaces in complex structures. In this thesis we develop \textrm{E} -- and \textrm{D} --TBAs to calculate the modes in finite 1D and 2D two-defect coupled-cavity photonic crystal structures. In the \textrm{E} -- and \textrm{D} --TBAs we expand the coupled-cavity \overrightarrow{E} --modes in terms of the individual \overrightarrow{E} -- and \overrightarrow{D} --modes, respectively. We investigate the dependence of the defect modes, their frequencies and quality factors on the relative placement of the defects in the photonic crystal structures. We then elucidate the differences between the two TBA formulations, and describe the conditions under which these formulations may be more robust when encountering a dielectric perturbation. Our 1D analysis showed that the 1D modes were sensitive to the structure geometry. The antisymmetric \textrm{D} mode amplitudes show that the \textrm{D} --TBA did not capture the correct (tangential \overrightarrow{E} --field) boundary conditions. However, the \textrm{D} --TBA did not yield significantly poorer results compared to the \textrm{E} --TBA. Our 2D analysis reveals that the \textrm{E} -- and \textrm{D} --TBAs produced nearly identical mode profiles for every structure. Plots of the relative difference between the \textrm{E} and \textrm{D} mode amplitudes show that the \textrm{D} --TBA did capture the correct (normal \overrightarrow{E} --field) boundary conditions. We found that the 2D TBA CC mode calculations were 125-150 times faster than an FDTD calculation for the same two-defect PCS. Notwithstanding this efficiency, the appropriateness of either TBA was found to depend on the geometry of the structure and the mode(s), i.e. whether or not the mode has a large normal or tangential component.