A Simple Feasible Alternative Procedure to Estimate Models with High-Dimensional Fixed Effects

In this paper we describe an alternative iterative approach for the estimation of linear regression models with high-dimensional fixed-effects such as large employer-employee data sets. This approach is computationally intensive but imposes minimum memory requirements. We also show that the approach can be extended to non-linear models and potentially to more than two high dimensional fixed effects.high dimensional fixed effects, linked employer-employee data

Real Wages and the Business Cycle: Accounting for Worker and Firm Heterogeneity

Using a longitudinal matched employer-employee data set for Portugal over the 1986-2005 period, this study analyzes the heterogeneity in wages responses to aggregate labor market conditions for newly hired workers and existing workers. Accounting for both worker and firm heterogeneity, the data support the hypothesis that entry wages are much more procyclical than current wages. A one-point increase in the unemployment rate decreases wages of newly hired male workers by around 2.8% and by just 1.4% for workers in continuing jobs. Since we estimate the fixed effects, we were able to show that unobserved heterogeneity plays a non-trivial role in the cyclicality of wages. In particular, worker fixed effects of new hires and separating workers behave countercyclically, whereas firm fixed effects exhibit a procyclical pattern. Finally, the results reveal, for all workers, a wage-productivity elasticity of 1.2, slightly above the one-for-one response predicted by the Mortensen-Pissarides model.wage cyclicality, hires, firm-specific effects, compositional effects, labor productivity

Real Wages and the Business Cycle: Accounting for Worker and Firm Heterogeneity

Using a longitudinal matched employer-employee data set for Portugal over the 1986-2005 period, this study analyzes the heterogeneity in wages responses to aggregate labor market conditions for newly hired workers and existing workers. Accounting for both worker and firm heterogeneity, the data support the hypothesis that entry wages are much more procyclical than current wages. A one-point increase in the unemployment rate decreases wages of newly hired male workers by around 2.8% and by just 1.4% for workers in continuing jobs. Since we estimate the fixed effects, we were able to show that unobserved heterogeneity plays a non-trivial role in the cyclicality of wages. In particular, worker fixed effects of new hires and separating workers behave countercyclically, whereas firm fixed effects exhibit a procyclical pattern. Finally, the results reveal, for all workers, a wage-productivity elasticity of 1.2, slightly above the one-for-one response predicted by the Mortensen-Pissarides model.wage cyclicality; hires; firm-specific effects; compositional effects; labor productivity

Application of adaptive methods based on finite difference discretizations to systems of PDAEs

In this paper two adaptive algorithms are presented for the solution of systems of evolutive one-dimensional Partial Differential/ AIgebraic Equations (PDAEs). A spatial discretization based on finite difference approximations on arbitrarily spaced grids: transforms the original problem in a set of Ordinary Differential Equations (ODEs), solved via an implicit integrator package (DASSL). The temporal integration is coupled with a spatial adapting strategy. The identification of the spatial subdomains: where the introduction of grid adaptivity is needed, is done through the comparison of the solutions computed with two fixed grids of different sizes. The subproblems generated are solved by two adaptive strategies: the Grid Refinement Method (GRM), that refines the subgrids detected in the previous step, and the Moving Mesh Method (MMM), that includes an additional differential equation for the nodal mobility in each original subproblem. In this paper, these algorithms were successfully applied to the solution of two problems: an isothermal tubular reactor model and a fiame propagation system described by two PDEs referring to fuel mass density and temperature dynamics. The performance of each algorithm is compared to the results obtained by Duarte [1], based on the application of a formulation of the Moving Finite Elements Method, with cubic Hermite polynomials approximations. The MMM algorithm revealed its robustness in dealing with the chosen models. The GRM algorithm originated poorer results, mainly due to errors associated with the boundary conditions procedure

Adaptive collocation methods for the numerical solution of differential models

A PDE integration algorithm that associates a Method of Lines (MOL) strategy based on finite differences or high resolution space discretizations, with a collocation strategy based on increasing level one or two-dimensional dyadic grids is presented. It reveals potential either as a grid generation procedure for predefined steep localised functions, and as an integration scheme for moving steep gradient PDE problems, namely 1D and 2D Burgers equations. Therefore, it copes satisfactorily with an example characterized by a steep 2D travelling wave and an example characterised by a forming steep travelling shock, which confirms its flexibility in dealing with diverse types of problems, with reasonable demands of computational effort

Application of adaptive methods based on finite difference discretizations in the simulation of a tubular reactor system

In this paper two adaptive algorithms are presented for the solution of systems of evolutive one-dimensional Partial Differential/ Algebraic Equations (PDAEs). The temporal integration is coupled with a spatial adapting strategy. The identification of the spatial subdomains. where a regridding technique is introduced, is done through the comparison of the solutions computed with two fixed grids of different sizes. The subproblems generated are solved by two adaptive strategies: the Grid Refinement Method (GRM), that promotes the refinement of the subgrids detected in the previous step, and the Moving Mesh Method (MMM) includes an additional differential equation for the nodal mobility. The two algorithms proposed were successfully applied to the solution of an nonisothermal tubular reactor pseudo-homogeneous model described by two PDEs referring to reagent concentration and system temperature dynamics. The performance of each algorithm is compared to the results obtained by [3], based on the application of a formulation of the Moving Finite Elements Method, with cubic Hermite polynomials approximations

Adaptive collocation methods for the solution of partial differential equations

An integration algorithm that conjugates a Method of Lines (MOL) strategy based on finite differences space discretizations, with a collocation strategy based on increasing level dyadic grids is presented. It reveals potential either as a grid generation procedure and a Partial Differential Equation(PDE) integration scheme. It copes satisfactorily with a example characterized by a steep travelling wave and a example that presented a forming steep shock, which demonstrates its versatility in dealing with different types of steep moving front problems, exhibiting features like advection-diffusion, widely common in the standard Chemical Processes simulation models

A Simple Feasible Alternative Procedure to Estimate Models with High-Dimensional Fixed Effects

In this paper we describe an alternative iterative approach for the estimation of linear regression models with high-dimensional fixed-effects such as large employer-employee data sets. This approach is computationally intensive but imposes minimum memory requirements. We also show that the approach can be extended to non-linear models and potentially to more than two high dimensional fixed effects.