Callaway, Brantly Mercer, IV; Rytchkov, Oleg; Swanson, Charles E.; Bean, Austin B.; Murtazashvili, Irina (Temple University. Libraries, 2020)
      Firms’ research and development (R&D) efforts are known to generate spillover effects on other firms’ outcomes, e.g., innovation and productivity. Policy recommendations that ignore spillover effects may not be optimal from a social perspective whence the importance of accounting for spillover effects. Quantifying R&D spillover effects typically requires a spatial matrix that characterises the structure of interaction between firms. In practice, the spatial matrix is often unknown due to factors that include multiplicity of forms of connectivity and unclear guidance from economic theory. Estimates can be biased if the spatial matrix is misspecified, and they can also be sensitive to the choice of spatial matrix. This dissertation develops robust techniques that estimate the spatial matrix alongside other parameters from data using a two-pronged approach: (1) model elements of the spatial matrix using spatial covariates (e.g., geographic and product market proximity) and a parameter vector of finite length and (2) estimate the spatial matrix as a set of parameters from panel data. Approaches (1) and (2) address two identification challenges - uncertainty over relevant forms of connectivity and high-dimensionality of the design matrix - in single-index models. In this three-chapter dissertation, the first approach is applied in the first and third chapters, while the second approach is applied in the third chapter. Chapter 1 proposes a parsimonious approach to estimating the spatial matrix and parameters from panel data when the spatial matrix is partly or fully unknown. By controlling for several forms of connectivity between firms, the approach is made robust to misspecification of the spatial matrix. Also, the flexibility of the approach allows data to determine the degrees of sparsity and asymmetry of the spatial matrix. The chapter establishes consistency and asymptotic normality of the MLE under conditional independence and conditional strong-mixing assumptions on the outcome variable. The empirical results confirm positive spillover and private effects of R&D on firm innovation. There is evidence of time-variation and asymmetry in the interaction structure between firms. Geographic proximity and product market proximity are confirmed as relevant forms of connectivity between firms. Moreover, connectivity between firms is not limited to often-assumed notions of proximity; it is also linked to past R&D and patenting behaviour of firms. Single-index models suffer non-identification due to rank deficiency when the design matrix is high-dimensional. Chapter 2 proposes an estimator that projects a high-dimensional parameter vector into a reduced consistently estimable one. This estimator generalises the assumption of sparsity which is required for shrinkage methods such as the Lasso, and it applies even if the high-dimensional parameter vector’s support is bounded away from zero. Monte Carlo simulations demonstrate high approximating ability, improved precision, and reduced bias of the estimator. The estimator is used to estimate the network structure between firms in order to quantify the spillover effects of R&D on productivity using panel data. The empirical results show that firms on average generate positive R&D spillovers on firm productivity. The spatial autoregressive (SAR) model has wide applicability in economics and social networks. It is used to estimate, for example, equilibrium and peer effects models. The SAR model, like other spatial econometric models, is not immune to challenges associated with misspecification or uncertainty over the spatial matrix. Chapter 3 applies the approach developed in Chapter 1 to estimate the spatial matrix in the SAR model with autoregressive disturbances in a parsimonious yet flexible way using GMM. The asymptotic properties of the GMM estimator are established, and Monte Carlo simulations show good small sample performance.