Indirect simultaneity

• Author: Thomas B. Marvell
• Published date: 01 February 2019
• DOI: http://doi.org/10.1111/1745-9133.12432
• Date: 01 February 2019

DOI: 10.1111/1745-9133.12432

POLICY ESSAY

MORE COPS, FEWER PRISONERS?

Indirect simultaneity

Thomas B. Marvell

Justec Research

Correspondence

ThomasB. Mar vell,Justec Research, 155 Ridings Cove, Williamsburg, VA23185.

Email:mar vell@cox.net

The problem of simultaneity in criminology regression analysis has been a hot topic for more than 50

years. An important paper on this topic is by Fisher and Nagin (1978), who described simultaneity

problems in the crime equation, questioned prior attempts to address it, and were pessimistic about

future attempts. Simultaneity occurs when the dependent variable causes the independent variable of

interest (the “key variable”). This backwardcausation results in a “biased” or “inconsistent” coefficient

on the key variable, meaning that the regression results are wrong. The key variable is endogenous

because it is correlated with the regression error term, which in turn is cor related with the dependent

variable.

For example, when studying whether prison populations affect crime rates, one has to worry about

reverse causation: More crime can lead to more prisoners through several mechanisms. The coefficient

on the prison variable in the crime equation reflects an unknown combination of prison's impact on

crime and crime's impact on prison. The researcher cannot tell from the regression output whether this

bias occurs. The major procedure for testing its presence is a Hausman test, for which aninstr umental

variable is required (Wooldridge, 2016).1

Simultaneity occurs indirectly in two ways (Antonakis, Bendahan, Jacquart, & Lalivev, 2010). The

first is intuitively obvious: The dependent variable causes a third variable that in turn causes the key

variable. There may be several intervening variables in the chainof causation. The second occurs when

a third variable, not in the regression, causes both the dependent variable and the key variable. Here

the dependent variable and the key variable are both correlated with the error term through the missing

variable. (This should be distinguished from the common notion of missing variable bias, whereby the

missing variable accounts for some of the impact that the key variable has on the dependent variable.) I

refer to these as “outside causes” (other common labels are “endogenous omitted variables” or “latent

confounding effects”). Indirect simultaneity is usually less obvious than direct simultaneity. In the

prison example, if a state's economy improvesand tax revenues increase, local governments can expand

efforts to reduce crime and the state can enlarge prisons. The economy and tax revenues are indirect

causes absent from the regression.

There are likely to be many candidates forindirect causes, known and unknown, and ruling them out

is a daunting task given the complexity of human and organizational behavior. Researchers have the

difficult task of proving a negative, and as a practical matter, all they can do is reverse the burden of

proof, albeit implicitly.Typically, they address and discard severalpossible simultaneity issues, leaving

Criminology & Public Policy. 2019;18:201–206. wileyonlinelibrary.com/journal/capp © 2019 American Society of Criminology 201