Optimal Universal and Categorical Benefit Provision with Classification Errors and Imperfect Enforcement

• Published date: 01 April 2017
• Author: SEAN SLACK,DAVID ULPH
• DOI: http://doi.org/10.1111/jpet.12218
• Date: 01 April 2017

OPTIMAL UNIVERSAL AND CATEGORICAL BENEFIT PROVISION

WITH CLASSIFICATION ERRORS AND IMPERFECT ENFORCEMENT

SEAN SLACK

University of St. Andrews

DAVID ULPH

University of St. Andrews

Abstract

We determine the optimal combination of a universal benefit and cat-

egorical benefit when individuals differ in their ability to work and, if

able to work, their productivity. The categorical benefit is conditioned

ex ante on applicants being unable to work and ex post on recipients not

working. The awards test makes Type I/II errors. If the ex post condition

is (i) not enforced, the optimal categorical benefit is positive only if the

awards test has discriminatory power, while maximum welfare falls with

both error propensities; but if (ii) fully enforced, the optimal categorical

benefit is positive always and maximum welfare can increase with the

Type II error propensity.

1. Introduction

Partial universal welfare systems can be defined as those which (i) provide an uncondi-

tional universal benefit to all individuals in society; but also (ii) allow for additional tar-

geted assistance to those judged by the policymaker to be most in need.1While targeted

transfers play the prominent role in modern welfare systems, much debate surrounds

the extent to which they reach those in need, for example due to misclassifications or

non-take-up (Moffitt 1983; Currie 2006). This has led numerous authors to discuss pro-

posals for partial universal programs (Callan et al. 1999; Van Parijs 2004). In particular,

Atkinson (1995) analyzes universal benefit provision within a linear income tax model,

where a fraction of the population may be involuntarily unemployed and may also re-

ceive a categorical benefit.

1The universal benefit may also be referred to as a basic income or demogrant (Van Parijs 2004).

Sean Slack, School of Economics and Finance, University of St. Andrews, Castlecliffe, The Scores,

St. Andrews, Fife, KY16 9AR, Scotland, U.K. (sean.ses34@gmail.com). David Ulph, School of Eco-

nomics and Finance, University of St. Andrews, Castlecliffe, The Scores, St. Andrews, Fife, KY16 9AR,

Scotland, U.K. (du1@st-andrews.ac.uk).

Financial support from the AXA Research Fund is gratefully acknowledged. We also acknowledge

SIRE for a conference presenter grant to present an earlier version of this paper at PET 14 Seatle, July

11–13, 2014. Finally, we wish to thank an anonymous referee for their highly detailed and constructive

feedback.

Received May 30, 2016; Accepted June 21, 2016.

C2016 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 19 (2), 2017, pp. 289–311.

289

290 Journal of Public Economic Theory

Categorical benefits are an important form of targeting and have two salient

features2:

(1) Double Conditionality. Categorical benefits are typically conditioned in two di-

mensions: ex ante an applicant must belong to some categorical group and sat-

isfy other initial conditions to be awarded the benefit; while ex post a recipient

must comply with certain behavioral criteria. For example, disability benefits

are often conditioned ex ante on applicants having a disability that significantly

affects their ability to work; and ex post on some form of work restriction.

(2) Imperfect Enforcement. Both dimensions of conditionality may be imperfectly

enforced. First, ex ante conditionality may be violated by classification errors

of Type I (false rejection) and Type II (false award) in the screening process.

Again, disability benefits provide a good example because certain medical con-

ditions (e.g., musculoskeletal disease, mental illness) can be difficult to verify,

as can be their impact on functional criteria.3Second, ex post conditionality may

be violated because the authorities fail to detect all recipients who break the re-

quirements; while the sanctions imposed if successfully detected are insufficient

to deter such behavior (Fuller, Ravikumar, and Zhang 2015).

Note that in many cases an individual who is ex ante eligible will automatically satisfy

ex post requirements. For example, an individual who is truly unable to work due to

disability and awarded benefits on this basis will automatically satisfy any ex post no-work

requirement. To this extent, Type II errors will be the source of ex post enforcement

issues.

In the context of partial universal programs, three central questions therefore

arise:

(1) How does the propensity of the awards technology to make Type I and Type

II errors affect the optimal levels of a universal benefit and categorical benefit,

respectively? In particular, are there conditions under which it is optimal to

choose either a purely universal or purely categorical system, as opposed to a

partial system?

(2) How do these error propensities affect the resulting level of social welfare?

(3) How do the answers to both of the above questions depend on how well the

ex post conditionality is enforced?

The contribution of this paper is to address the three questions raised above within

a framework that allows for a systematic comparison of how the answer to the first two

questions depends on how well the ex post conditionality is enforced. We first discuss the

key literature related to this paper and then proceed to outline our framework and key

results.

2Many types of benefit may condition on categorical status: these may fall under social assistance (e.g.,

Supplementary Security Income in the United States); social insurance (e.g., Social Security Disability

Insurance in the United States); or instead be strictly categorical (i.e., the amount awarded to legitimate

recipients is independent of means or insurance contributions). The model presented in this paper is

most related to the latter case.

3A number of studies estimate error propensities for real-world programs (Nagi 1969; Duclos 1995;

Benitez-Silva, Buchinsky, and Rust 2004).