Supervised Principal Components and Factor Instrumental Variables. An Application to Violent CrimeTrends in the US, 1982-2005.

Supervised Principal Component Analysis (SPCA) and Factor Instrumental Variables (FIV) are competing methods addressed at estimating models affected by regressor collinearity and at detecting a reduced-size instrument set from a large database, possibly dominated by non-exogeneity and weakness. While the first method stresses the role of regressors by taking account of their data-induced tie with the endogenous variable, the second places absolute relevance on the data-induced structure of the covariance matrix and selects the true common factors as instruments by means of formal statistical procedures. Theoretical analysis and Montecarlo simulations demonstrate that FIV is more efficient than SPCA and standard Generalized Method of Moments (GMM) even when the instruments are few and possibly weak. The prefered FIV estimation is then applied to a large dataset to test the more recent theories on the determinants of total violent crime and homicide trends in the United States for the period 1982-2005. Demographic variables, and especially abortion, law enforcement and unchecked gun availability are found to be the most significant determinants.