Instrumenting Police Levels with Federal Law Enforcement Spending: An Assessment of Recent Efforts John L. Worrall Tomislav V. Kovandzic

Police Levels and Crime Police levels may be endogenous Reverse causality Methods of dealing with (or skirting) endogeneity Time series w/ lagged police Time series w/ creative interventions (e.g., terror alert levels—Klick and Tabarrok, 2005) Granger causality test IV Regression Need instrument(s) for police levels

Review of Non-spending Instruments Levitt (1997) Electoral cycles Levitt (2002) Firefighters Cornwell and Trumbull (2004) Offense ratios and tax revenues Other studies Various combinations of demographic variables

Federal Spending (Grants) Instruments GAO (2005) 7 instruments (Hiring, MORE, Innovative COPS grants, Misc. COPS grants, Byrne, LLEBG, Non- cops grants) Overidentified Evans and Owens (2007) “paid officers granted” instrument =.75*UHP + CIS Just identified

Instrument Requirements Two requirements for “good” instruments Relevance (correlated with endogenous variable) Significant in first stage regressions & joint F-stat. > 10 (Staiger & Stock, 1997) Validity (independent of error process in main equation) Hansen’s J (Hansen, 1982)

Our Contribution Research questions Do federal law enforcement grants make “good” (i.e., relevant & valid) instruments? Are police levels associated with crime? Answer to question 2 Yes and no Hiring instruments are better (generally relevant & valid) Other federal grants make weak instruments Answer to question 2 Yes, but not as much as previously estimated

Data Panel of 5,199 cities, Dependent—7 index crimes (cleaned) Independent Police levels, UHP, CIS, DNP, Hiring, MORE, Innovative COPS grants, Misc. COPS grants, Byrne, LLEBG, Non-cops grants (grant draw-downs) Income, Nonwhite, Under 24, Unemployment (county) Unit and year dummies

Estimation Procedure Analysis GMM Models w/ -xtivreg2- in Stata Analysis in levels & rates per 10,000 or percentages Instruments lagged one period for delayed effect Robust std. errors w/ corrections for state-level clustering Models Hiring grants (roughly in line with Evans and Owens) UHP, DNP, CIS All federal law enforcement grants (GAO’s focus) Hiring, MORE, Innovative COPS grants, Misc. COPS grants, Byrne, LLEBG, Non-cops grants

First Stage, Hiring Instruments

Endogenous Police (Hiring Instruments)

First Stage, Federal Grant Instruments

Endogenous Police (Federal Grant Instruments)

First Stage, UHP & Lagged Police Instruments

Endogenous Police (UHP and Lagged Police Instruments)

Conclusion Be cautious with grants as instruments Grants may be correlated w/ unobservables (heterogeneity in grant-getting); lagged police may temper that effect