Travaglini, Guido (2010): Supervised Principal Components and Factor Instrumental Variables. An Application to Violent CrimeTrends in the US, 19822005.

PDF
MPRA_paper_22077.pdf Download (315kB)  Preview 
Abstract
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 reducedsize instrument set from a large database, possibly dominated by nonexogeneity and weakness. While the first method stresses the role of regressors by taking account of their datainduced tie with the endogenous variable, the second places absolute relevance on the datainduced 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 19822005. Demographic variables, and especially abortion, law enforcement and unchecked gun availability are found to be the most significant determinants.
Item Type:  MPRA Paper 

Original Title:  Supervised Principal Components and Factor Instrumental Variables. An Application to Violent CrimeTrends in the US, 19822005. 
Language:  English 
Keywords:  Principal Components; Instrumental Variables; Generalized Method of Moments; Crime; Law and Order. 
Subjects:  C  Mathematical and Quantitative Methods > C2  Single Equation Models; Single Variables > C22  TimeSeries Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models K  Law and Economics > K1  Basic Areas of Law > K14  Criminal Law C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics 
Item ID:  22077 
Depositing User:  Guido Travaglini 
Date Deposited:  14. Apr 2010 23:18 
Last Modified:  12. Feb 2013 14:21 
References:  Ahn S.C. and and Horenstein A.R. (2009) Eigenvalue Ratio Test for the Number of Factors, mimeo, Arizona State University and Instituto Autónomo Tecnológico de México. Altonji J. G. and Segal L.M. (1996) SmallSample Bias in GMM Estimation of Covariance Structures, Journal of Business and Economic Statistics, 4, 353366. Andrews D.W K. and Stock J. (2007) Testing with Many Weak Instruments, Journal of Econometrics, 138, 2446. Ayres I. and Donohue J.J. (2003) Shooting Down the ”More Guns, Less Crime” Hypothesis, Stanford Law Review, 55, 11931312. Bai J. and Ng S. (2002) Determining the Number of Factors in Approximate Factor Models, Econometrica, 70, 191221. Bai J. and Ng S. (2006) Instrumental Variable Estimation in a Data Rich Environment, NYU mimeo. Bai J. and Ng S. (2007) Determining the Number of Primitive Shocks in Factor Models, Journal of Business and Economic Statistics, 26, 52 60. Bai J. and Ng S. (2008) Selecting Instrumental Variable Estimation in a Data Rich Environment, Journal of Time Series Econometrics, 1, 132. Bair E., Hastie T., Paul D. and Tibshirani R. (2006) Prediction by Supervised Principal Components, Journal of the American Statistical Association, 101, 119137. Cattell, R.B. (1966) The scree test for the number of factors, Multivariate Behavioral Research, 1, 245276. Chamberlain G. and Rothschild M. (1983) Arbitrage, factor structure, and meanvariance analysis on large asset markets, Econometrica, 51, 12811304. Chen B. (2007) An Empirical Comparison of Methods for Temporal Distribution and Interpolation at the National Accounts, Office of Directors, Bureau of Economic Analysis, Washington D.C.. Chow, G. and Lin, A.L. (1971) Best Linear Unbiased Distribution and Extrapolation of Economic Time Series by Related Series, Review of Economic and Statistics, 53, 372375. Denton, F.T. (1971) Adjustment of Monthly or Quarterly Series to Annual Totals: an Approach Based on Quadratic Minimization, Journal of the American Statistical Society, 66, 99102. Dezhbakhsh H., Rubin P. and Shepherd J.P. (2003) Does Capital Punishment Have a Deterrent Effect?: New Evidence from Postmoratorium Panel Data, American Law and Economics Review, 5, 344376. Di Fonzo T. (2003) Temporal Disaggregation of Economic Time Series: Towards a Dynamic Extension, EUROSTAT. Donohue J. and Levitt S. ( 2001) The Impact of Legalized Abortion on Crime, Quarterly Journal of Economics, 116, 379420. Donohue J. and Levitt S. (2004) Further Evidence that Legalized Abortion Lowered Crime: A Reply to Joyce, Journal of Human Resources, 39, 2949. Donohue J. and Levitt S. (2006) Measurement Error, Legalized Abortion, and the Decline in Crime: A Response to Foote and Goetz (2005), National Bureau of Economic Research Working Paper 11987. Donohue J. and Wolfers J. (2005) Uses and Abuses of Empirical Evidence in the Death Penalty Debate, Stanford Law Review, 58, 791846. Ehrlich, I. (1975) The Deterrent Effect of Capital Punishment: A Question of Life and Death, American Economic Review, 65, 397417. Fernández R.B. (1981) A Methodological Note on the Estimation of Time Series, Review of Economics and Statistics, 63, 471476. Granger C.W.J. and Newbold P. (1974) Spurious Regressions in Econometrics, Journal of Econometrics, 2, 111120. Groen J. J. and Kapeitanos G. (2009) Parsimonious Estimation with Many Instruments, Federal Reserve Bank of New York Staff Report no. 136. Hansen L.P. (1982) Large Sample Properties of Generalized Method of Moments Estimator, Econometrica, 50, 10291054. Jolliffe, I. (1982) A note on the use of Principal Components in Regression, Applied Statistics, 31, 300303. Joyce T. (2004) Did Legalized Abortion Lower Crime?, Journal of Human Resources, 39, 128. Kapeitanos G. and Marcellino M. (2007) FactorGMM Estimation with Large Sets of Possibly Weak Instruments, Working Papers 577, Queen Mary University of London, Department of Economics. Koch I. and Naito K. (2008) Prediction of Multivariate Responses with a Select Number of Principal Components, Electronic Journal of Statistics, 1, 124. Levitt S.D. (2004) Understanding why Crime Fell in the 1990s: Four Factors that Explain the Decline and Six that Do not, Journal of Economic Perspectives, 18, 163190. Lott J.R. and Mustard D.B. (1997) Crime, Deterrence, and Righttocarry Concealed handguns, Journal of Legal Studies, 26, 168. Lott J.R. and Whitley J. (2004) Abortion and Crime: Unwanted Children and OutofWedlock Births, , Economic Inquiry, 45, 304324. Newey W. K. and West K. D. (1987) A Simple Positive SemiDefinite Heteroskedasticity and Autocorrelation Consistent Covariance Matrix, Econometrica, 55, p.703708. Newey W. and Smith R.J. (2004) Higher Order Properties of GMM and Generalized Empirical Likelihood Estimators, Econometrica, 72, 219255. Newey W. and Windmeijer F. (2008) GMM with Many Weak Moment Conditions, MIT Department of Economics, manuscript. Onatski A. (2009) Determining the Number of Factors from Empirical Distribution of Eigenvalues, manuscript, Economics Department, Columbia University. Owen A. B. (1988) Empirical Likelihood Ratio Confidence Intervals for a Single Functional, Biometrika, 75, 237249. Owen A. B. (2001) Empirical Likelihood, Chapman and Hall, New York. Proietti T. (2004) Temporal Disaggregation by State Space Methods: Dynamic Regression Methods Revisited, Working Papers, EUROSTAT. Quilis E.M. (2005) Benchmarking Techniques in the Spanish Quarterly National Accounts, EurostatOECD Workshop on Frontiers in Benchmarking Techniques and Their Application to Official Statistics, Luxembourg. Quilis E.M. (2006) A MATLAB Library of Temporal Disaggregation and Interpolation Methods: Summary, D.G. del Tesoro y Política Financiera, Madrid, Spain. Santos Silva, J.M. and Cardoso, F.N. (2001) The ChowLin Method Using Dynamic Models, Economic Modeling, 18, 269280. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/22077 