measurement errors and capital punishment

11
This article was downloaded by: [The University of Manchester Library] On: 10 October 2014, At: 12:58 Publisher: Routledge Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Applied Economics Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/raec20 Measurement errors and capital punishment Kenneth L. Avio a a Department of Economics , University of Victoria , Victoria, B.C., CanadaV8W 2Y2 Published online: 24 May 2006. To cite this article: Kenneth L. Avio (1988) Measurement errors and capital punishment, Applied Economics, 20:9, 1253-1262, DOI: 10.1080/00036848800000128 To link to this article: http://dx.doi.org/10.1080/00036848800000128 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions

Upload: kenneth-l

Post on 09-Feb-2017

215 views

Category:

Documents


4 download

TRANSCRIPT

This article was downloaded by: [The University of Manchester Library]On: 10 October 2014, At: 12:58Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK

Applied EconomicsPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/raec20

Measurement errors and capital punishmentKenneth L. Avio aa Department of Economics , University of Victoria , Victoria, B.C., CanadaV8W 2Y2Published online: 24 May 2006.

To cite this article: Kenneth L. Avio (1988) Measurement errors and capital punishment, Applied Economics, 20:9, 1253-1262,DOI: 10.1080/00036848800000128

To link to this article: http://dx.doi.org/10.1080/00036848800000128

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) containedin the publications on our platform. However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of theContent. Any opinions and views expressed in this publication are the opinions and views of the authors, andare not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon andshould be independently verified with primary sources of information. Taylor and Francis shall not be liable forany losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoeveror howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of theContent.

This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Applied Economics, 1988, 20, 1253-1262

Measurement errors and capital punishment

K E N N E T H L. A V 1 0

Department of Economics, University of Victoria, Victoria, B.C., Canada, V8 W 2Y2

I . I N T R O D U C T I O N

The positive economic model of crime specifies a simultaneous system which describes the interrelations between the various agents' affected by, and affecting, criminal activity. Component parts of the system include equations which model the supply response of offenders, the demand for protection services by society, and the provision of protection services by the criminal justice system (Ehrlich, 1974, 1981). Equilibrium levels of crime are generated as solutions to the simultaneous system.

The normative economic model of crime posits the choice of values for certain control variables in an attempt to minimize the overall social costs of crime, or alternatively, to' maximize net social wealth (Becker, 1968). The costs of crime include the net direct harm of offences as well as the expenditures necessary for the apprehension, conviction and punishment of offenders. The variables that society has available to influence crime rates are typically taken to be1 the certainty and severity of punishment as well as the specific form of punishment (fines, incarceration, corporal punishment).

Economists have tended to view the risks of apprehension as well as the threatened punishments as implicit prices which are hypothesized to elicit a supply response. Not surprisingly, the majority of the empirical work to date has attempted to verify this contentious hypothesis, often referred to loosely as the 'deterrence' hypothesis. This verification has proceeded through the estimation of supply of crime equations. Time-series, cross-section and pooled data sets have been used to analyse individual categories of crime as well as 'total' crime rates. Research has been conducted at various levels of spatial aggregation (municipalities, regions, nations), and at both the level of the individual offender (using micro data) as well as in the more standard approach using published aggregate crime data. Among other things, attempts have been made: to distinguish the incapacitation effects of imprisonment from the deterrent effects of longer sentences; to determine the degree of substitution between crimes; and to estimate the importance of crime spillovers from neighbouring jurisdictions. The majority of the reported research appears to confirm that the supply of crime is responsive to changes in the certainty and severity of punishment as perceived by offender^.^

lSocio-economic variables such as the unemployment rate and income distribution are included in empirical formulations of the economic model of crime. However, these are not normally treated as policy instruments which society has available to induce changes in crime rates. 'Econometric research on the estimation of supply of offence functions is surveyed in Pyle (1983), Ehrlich (1979), Nagin (1978), Taylor (1978) and Palmer (1977).

0003-6846/88 $03.00+ . l 2 0 1988 Chapman and Hall Ltd. 1253

Dow

nloa

ded

by [

The

Uni

vers

ity o

f M

anch

este

r L

ibra

ry]

at 1

2:58

10

Oct

ober

201

4

K . L. Avio

Despite the apparent conformity of the empirical findings with the economic theory, a number of questions have been raised in various contexts about the empirical implement- ation of the model.3 One of these questions concerns the construction of variables used as proxies for the subjective punishment risks and severities. The empirical models generally represent these theoretical constructs as measured frequency ratios. For example, the unconditional risk of apprehension is typically represented as the ratio of recorded police clearances to recorded offences. These ratio representations may cause special difficulties if independent and dependent variables in an equation (or two or more independent variables in the-same equation) share a common term which suffers from errors in measurement. A standard example (Cook, 1977; Pyle, 1983) involves regressing the risk of capture (and other variables) upon the crime rate. The recorded number of offences forms the numerator of the crime rate (offences/population) and the denominator of the ratio variable representing the risk of capture (clearances/offences). Now consider a cross-section composed of identical populations and with the exact same true number of crimes. If there are recording errors in the crime rate which are not uniform over the observations, then an inverse relation between the recorded crime rate and the variable measuring the risk of capture will appear even though the true data could not possibly generate such a relationship. More sophisticated analysis suggests that the direction of the bias depends upon the actual supply elasticity response (Ehrlich, 1974; Taylor, 1978).

Researchers who have acknowledged the measurement error problem in this context have been content to obtain consistent estimates by employing standard instrumental variable techniques. Other researchers employ the same techniques, but with reference to the simultaneity problem inherent in estimating the economic model of crime. Finally, some researchers simply ignore both the simultaneity and measurement error problems and proceed with OLS estimation, apparently trusting that any biases are sufficiently small not to invalidate the results (Wolpin, 1978; Sjoquist, 1973).

11. T H E K L E I N , F O R S T A N D FILATOV C O N J E C T U R E

The measurement error problem noted above is considered here in the context of the estimation of one particular supply of offence equation. The starting point is a conjecture by Klein, Forst and Filatov (1978) in their review of Ehrlich's (1975a) research on capital punishment. Klein et al. (1978) consider bias arising from measurement errors in 'linked' variables constructed as ratios, i.e. those variables which are constructed so that the numerator of one variable serves as the denominator of a n ~ t h e r . ~ The authors posit that measurement errors in these circumstances create an artificial correlation which biases estimated coefficients in the direction of the finding of a deterrent effect, when in fact, none may exist. Moreover, this bias is alleged to occur whether the link is direct (i.e. measurement errors in data used to form the denominator of an independent variable and the numerator of the dependent variable) or indirect (measurement errors in data used to form the denominator of one independent variable and the numerator of a different independent variable, which in turn has a denominator formed from data used in the numerator of the dependent variable).

'See the references in note 2, above. 4For ease of exposition the 'linked' rubric is used to describe all such circumstances, whether or not instrumental variable techniques are used.

Dow

nloa

ded

by [

The

Uni

vers

ity o

f M

anch

este

r L

ibra

ry]

at 1

2:58

10

Oct

ober

201

4

Measurement errors and capital punishment 1255 -

In an attempt to test the hypothesis in its direct form, Klein, et al. (1978) report an exercise in which the value of the conditional risk of execution is first artificially constrained to be constant for all observations. This constancy is achieved by adjusting the number of executions (numerator of the ratio representing the conditional risk of execution) for each observation to yield a value for the ratio variable equal to its mean value for the sample. Random measurement error is then induced in the number of offences (used to form an estimate of the denominator of the frequency ratio), and regression coefficients of the murder supply equation are generated using the resulting error-ridden data. In effect, the authors conduct an experiment based upon the premise of no possible relationship between the variables, but with measurement errors. The authors interpret their empirical results as supporting the hypothesis that small measurement errors impart a marked bias in favour of the deterrence hypothesis. Moreover, they report similar findings for the hypothesis in its indirect form, and whether or not instrumental variable techniques are employed.

Ehrlich and Mark (1977) respond that the Klein, et al. (1978) exercise is irrelevant for the determination of bias in Ehrlich's (1975a) study. They argue that a speculative experiment which artificially imposes upon the data no true relationship between variables cannot illuminate the impact of measurement errors when indeed the variables are causally related. The authors note that whereas Klein, et al. impose measurement errors upon the data, Ehrlich (1975a) used instrumental variable techniques in an attempt to cleanse the data of whatever measurement errors existed in order to reveal the true relationship between variables.

An attractive and obvious alternative to the Klein, et al. Monte Carlo exercise is to compare regression equations using linked and unlinked constructions of the variables. If a relatively error-free data series can be identified, then the purpose of the Klein, et al. exercise can be accomplished free of the Ehrlich and Mark objection. If the regression results differ markedly and in a predictable manner, then support for the Klein, et al. conjecture may be affirmed. Data exigencies, however, typically preclude this approach.

111. CANADIAN E V I D E N C E

In American and British deterrence studies of capital punishment, the crucial execution risk variable is generally adapted from the ratio of executions to (an estimate of) convictions, and the (unconditional) conviction rate is adapted from the ratio of convictions to offences. In neither regime apparently is it possible to construct a credible execution risk variable which is formed using a denominator which is not also found in the numerator of the variable used to measure conviction risk. Hence the Klein et al. conjecture may apply to these studies.

The Canadian time-series does permit construction of 'unlinked' measures of the risks of conviction and execution. In Canada, the death sentence was mandatory for the crime of murder. Moreover, the Canadian Federal Cabinet considered every capital case just shortly prior to the scheduled execution date.5 Hence two alternative measures of the number of convicted offenders at risk in receiving the death sentence are available: the number of convictions for murder (court data) and' the number of summed executions and commut- ations (Cabinet data). Figure 1 displays these two series for the years 1926-60.

There are several reasons why the series are not identical even though the mandatory nature of the penalty suggests otherwise. Some convictions were quashed on appeal; retrials

5See Avio (1987a, 1987b) for a discussion of the procedures followed by Cabinet in capital cases.

Dow

nloa

ded

by [

The

Uni

vers

ity o

f M

anch

este

r L

ibra

ry]

at 1

2:58

10

Oct

ober

201

4

Dow

nloa

ded

by [

The

Uni

vers

ity o

f M

anch

este

r L

ibra

ry]

at 1

2:58

10

Oct

ober

201

4

Measurement errors and capital punishment 1257

were called; multiple convictions were applied to the same murderer; a murder conviction and subsequent consideration by Cabinet for clemency did not necessarily occur in the same calendar year;6 and some convicted murderers died prior to consideration by the commut- ation authorities. Moreover, the pattern of discrepancies might not be uniform across the sample due to the timing of institutional changes. For example, the lag between conviction and final adjudication by the Crown probably increased over time as a result of increased appeal activity.

To test the Klein et al. conjecture, homicide supply equations using Canadian data over the period 1926-60 are employed.' A wide variety of equations were estimated using different formulations of the risk variables as well as different estimation techniques (OLS and instrumental variables, both with and without correction for first-order autocorrelation8). Table 1 presents a representative variety of homicide supply equations, with the only difference between data used to estimate an odd-numbered equation and the following even-numbered equation is that the former equation utilizes summed executions plus commutations to construct the denominator of the variable representing the condi- tional risk of execution whereas the latter equation employs the number of murder convictions for the same purpose. Thus the odd-numbered equations in principle employ 'linked' explanatory variables; the execution risk variable is not similarly linked in the even- numbered equations.

Equations 1 and 2 assume that prospective offenders forecast risks from current period data. In Equations 3-6 the execution risk variables are computed as 5 year moving averages. In Equations 7-10 the current period number of executions is replaced by a moving average (4 years in Equations 7 and 8; 5 years in Equations 9 and 10) to form the numerator of execution risk. In Equations 11 and 12, 5 year moving averages are used to form the conditional risk of execution, and a 5 year moving average of the number of murder convictions is used in the numerator of the ratio used to construct the risk of conviction. This mix of empirical interpretations of the conditional risk of execution is motivated in part by Ehrlich (1977b).

61n 1953 for example there were more executions than convictions, which taken at face value would imply a meaningless objective risk of execution greater than unity. 'Two Canadian econometric studies on capital punishment have been published. Avio (1979) finds no evidence of a deterrent effect over the period of 1926-60 whereas Layson (1983) comes to a different conclusion upon extending Avio's sample to 1977 and verifying, via a Chow test, that the extension is appropriate. Avio (1984) responds that Layson's stability tests are unreliable. He notes a strong correlation ( p = -0.97) between each of Layson's reduced form measures of execution risk and a dichotomous variable changing value in 1961. Thus Avio argues that the crucial execution risk variable is acting essentially as a dichotomous variable over the full period, which is hypothesized to explain why the data pass the Chow test. Avio (1984) demonstrates that the data fail a test for the stability of the coefficient of execution risk given the constancy of all other coefficients. Moreover, following the Wilson (1983) hypothesis that the ethos of self-expression and personal liberty increased the demand for violence in the murder-prone age group in the 1960s and 1970s, the coefficient of the variable representing the proportion of the population that is in this age group is allowed to vary. Not only does the test confirm the Wilson hypothesis, but the apparent deterrent effectiveness of the conditional risk of execution disappears. (For a related discussion of the US time-series studies, see Passe1 and Taylor (1977) and Ehrlich's response (1977a). In any event, as with the US and UK samples, the Canadian series beyond the early 1960s does not permit construction of measures of execution risk which are analogous to the linked and unlinked constructions for the pre-1960 period.

Table 1 equations were estimated with and without correction for first-order serially correlated error terms. The qualitative results concerning the significance of the criminal justice variables in linked and unlinked formulations appear invariant to whether or not such a correction is made.

Dow

nloa

ded

by [

The

Uni

vers

ity o

f M

anch

este

r L

ibra

ry]

at 1

2:58

10

Oct

ober

201

4

Table la. The impact of measurement errors in the conditional risk of execution

Dependent variable

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (1 1) (12) lnHR lnHR lnHR lnHR lnHR lnHR lnHR lnHR lnHR lnHR lnHR lnHR

lnPCON

lnPE

InY

InU

DWAR

TT

Constant

SSR l3w Z,

Estimation method

- 0.079 (-0.986)

0.071 (0.896) 1.389

(2.601) 0.241 (2.800) - 0.088

(- 1.464) - 0.043

( - 3.963) - 12.965 (- 3.91 l )

0.468 1.796

OLS

- 0.085 (- 1.014) -0.01 1

(-0.191) 1.080

(2.199) 0.190 (2.433)

-0.088 (- 1.435) -0.038

(-3.717) - 11.058 (-3.651)

0.480 1.659

OLS

-0.076 (-0.901) -0.032

(-0.189) 1.056

(1.898) 0.187 (2.172) - 0.088

(- 1.437) - 0.038

(- 3.206) - 10.895 (-3.135)

0.480 1.691

OLS

-0.122 ( - 1.527) -0.337

(- 1.844) 0.682 (1.408) 0.146 (2.03 1)

-0.116 (- 1.933) - 0.032

(-3.216) -8.718

( - 2.936) 0.429 1.558

OLS

Notes: Odd-numbered equations form the conditional risk of execution utilizing summed executions and commutations as a measure of the number at risk; the immediately following even-numbered equation substitutes the number of murder convictions. The two-stage least squares equations are estimated over 1927-60 and the OLS equations over 1926-60. Endogenous variables in the two-stage equations are noted by '^' over the'estimated coefficient. The risk of conviction (PCON) is formed from the ratio CONJHOM, with CON the current period number of murder convictions in all Equations except 11 and 12, where CON is constructed as a 5 year moving average. The conditional risk ofexecution (PE) is formed from: the ratio EXEC/(EXEC+ COMM) in Equation 1 and EXECICON in Equation 2; a 5 year moving average of EXEC/(EXEC cCOMM) in Equations 3, 5 and 11, and a 5 year moving average of EXECJCON in Equations 4,6 and 12; the ratio AEXEC/(EXCE + COMM) in Equations 7 and 9 and AEXECJCON in Equations 8 and 10, with AEXEC a 4 year moving average of the number ofexecutions in Equations 7 and 8, and a 5 year moving average of the number of executions in Equations 9 and 10. Instrumental variables for Equations 5-12 include InMVR, InPOP, 1nCJEXP- ,, InXGOV, lnA1524, InY, InU, DWAR, TT, and a constant. The conditional risk of execution is added as an instrument in Equations 9 and 10. In Equations 11 and 12, lagged values of all endogenous and exogenous variables appearing in the equation (except DWAR, TT and the constant) are additional instruments. D

ownl

oade

d by

[T

he U

nive

rsity

of

Man

ches

ter

Lib

rary

] at

12:

58 1

0 O

ctob

er 2

014

Measurement errors and capital punishment

Table l b. Regression variables.

HR PCON PE Y U DWAR TT MVR POP CJEXP(- 1)

A1524 XGOV

Number of homicides per 1000 Canadian population Probability of murder conviction Conditional probability of execution Real disposable income per capita Unemployment rate War dummy (equals unity, 194W5) Time trend Motor vehicle registrations per 1000 population Population (in 1000's; excludes Yukon and Northwest Territories) Real per capital expenditures on the criminal justice system lagged one year Proportion of the male population between 15 and 24 years of age Real per capita non-defence expenditures of government

Variable sources are listed in Avio (1979) and Layson (1983).

The results indicate that the even-numbered equations are considerably more favourable to the deterrence hypothesis, consistent with the Klein et al. conjecture. In every case the estimated coefficients for the conditional risk of execution become 'stronger' when the linked and error-ridden execution risk data are used. Significantly, this result occurs whether or not estimation techniques to ameliorate measurement errors are employed. Moreover, the conviction rate coefficients also exhibit increased support for the deterrence hypothesis when the linked formulations are used, with the sole exception found in the Equation pair 11 and 12.' Qualitatively similar results are obtained when the unconditional risk of conviction is replaced by the risk pair consisting of the conditional risk of conviction and the unconditional risk of apprehension (not reported in Table 1). In this instance all three risk variables appear to be substantially influenced by the seemingly innocuous substitution of convictions for summed executions plus commutations in the construction of the condi- tional execution risk variable.''

It could, of course, be argued that an alternative explanation of the Table 1 equations is that offenders form their subjective conditional probabilities of execution from the frequency ratio of executions to convictions, and not from the frequency ratio of executions to summed

9 0 f the six equation pairs in Table 1 and with reference to the risk of conviction variable, 5 yield larger (negative) t-statistics, and 5 have larger (negative) coefficients in the linked formulations. 1°The counterpart of Table 1 equations using 3 risk variables and with and without correction for first order serial correlation were estimated. The results are qualitatively similar to those reported in Table 1. For example, coefficients and t-statistics for the risk of apprehension, the conditional risk of conviction and the conditional risk of execution in estimated equations corresponding to Equation pairs 7-8 and 9-10 (and with correction for serially correlated errors) are:

(7') (8') (9') (10') risk of apprehension 0.644 - 0.643 0.665 - 0.607

(0.249) (- 5.618) (0.403) (- 6.958)

conditional risk of conviction 0.109 -0.353 0.649 -0.212 (0.591) (- 4.408) (0.297) ( - 5.337)

conditional risk of execution -0.144 -0.286 -0.055 - 0.474 (- 1.000) (-4.314) (-0.723) (- 5.670)

Dow

nloa

ded

by [

The

Uni

vers

ity o

f M

anch

este

r L

ibra

ry]

at 1

2:58

10

Oct

ober

201

4

K. L. Avio

executions plus commutations. Under these circumstances the odd-numbered equations would hold, lending stronger support to the deterrence hypothesis. However, offenders have no rational basis for forming their forecasts in this way. The ratio of executions to summed executions plus commutations is the objective conditional risk of execution for any given year; in Canada it was the social control variable produced by the Governor-General-in- Council, which was required to render a decision on the exercise of the Royal Prerogative of Mercy for each convicted murderer after all appeals (if any) had been exhausted. Moreover, information on commutations and execution came from a single authority and was widely available, and hence must have been relatively inexpensive to obtain. There is no readily apparent reason why offenders would utilize a less reliable forecast of their prospects. Indeed, such activity would seem to be inconsistent with the economic model, which assumes that offenders are rational.

IV. C O N C L U D I N G C O M M E N T

The vast majority of econometric studies of criminal deterrence rely upon linked risk variables and/or linked independent and dependent variables to estimate equation coeffic- ients. Included are the major studies of capital punishment for the US and the UK without exception. Ehrlich's well known time-series study (1975a) relies upon estimates for the number of offences, the arrest rate and the conditional conviction rate to construct an estimate of conditional execution risk. Ehrlich and Mark (1977), sensitive to the concerns discussed here, argue that Ehrlich's cross-section results (1977b) provide 'perhaps the strongest evidence bearing on the errors problem in connection with the estimation df the execution-risk effect. . . ' (p. 300). This is because the execution risk data are constructed independently of the number of offences, as was the case in Ehrlich's 1975 time-series study. However, all five of Ehrlich's empirical interpretations of the conditional risk of execution in (1977b) rely upon (an estimate of) the number of murder convictions,'' and hence one must suspect a bias similar to that noted here. Wolpin's UK study (1978) also relies entirely on estimates of the conditional execution risk formed using a variable linked to the risk of conviction. Both variables are constructed using summed murder convictions and man- slaughter convictions that have been accorded life imprisonment. Wolpin's results are additionally suspect because no attempt is made to adopt estimation techniques to correct for measurement errors.12

It should be emphasized that the estimated equations of Table 1 probably do not utilize error-free series on the number of offences,which is used to construct various formulations of

"Ehrlich estimates the number of convictions by the number of prisoners admitted to state prisons (1977b). In any case, the 'link' remains. ''Layson (1985) also relies on OLS estimation techniques after employing Hausman specification tests (Hausman, 1978). Layson's concern is whether a single equation or simultaneous equation specification is to be preferred, but the same test may apply for measurement errors. Mixed (ungeneralizable) results were obtained when Hausman tests were undertaken here using both linked and unlinked formulations. The relevant point is that regardless whether a particular specification is supported or otherwise by a Hausman test, and regardless of the estimation method employed, estimates relying on unlinked data invariably display weaker support for the deterrence hypothesis than those using linked formulations. For this reason Layson's (1985) results, which rely entirely on linked constructions, must be viewed with some suspicion.

Dow

nloa

ded

by [

The

Uni

vers

ity o

f M

anch

este

r L

ibra

ry]

at 1

2:58

10

Oct

ober

201

4

Measurement errors and capital punishment 1261

risk variables as well as to construct the dependent variable in supply of crime equations. Even though one would not expect large errors in the crime rate for murder, as noted here in examining errors in the number at risk in the commutation-execution decision, relatively small errors can have a large impact on the regression results when frequency ratios are used.13 With respect to crimes other than murder, errors in the crime rate itself are notorious, and one must wonder about the impact of these errors in the published studies, even when standard techniques are used to ameliorate bias. In any case, progress on the deterrence issue will require further experimentation and theorizing on the impact of measurement errors.

REFERENCES

Avio, K. L. (1979) Capital punishment in Canada: a time-series analysis of the deterrent hypothesis, Canadian Journal of Economics, 12, 647-76.

Avio, K. L. (1984) Capital punishment again, Discussion Paper No. 84-1, Department of Economics, University of Victoria.

Avio, K. L. (1987a) Clemency in economic and retributive models of punishment, International Review of Law and Economics, 7, 79-88.

Avio, K. L. (1987b) The quality of mercy: exercise of the royal prerogative in Canada, Canadian Public Policy, 13, 366-79. '

~ecker,-G. S: (1968) Crime and punishment: an economic approach, Journal of Political Economy, 78, 169-217.

Bowers, W. J. and Pierce, G. L. (1975) The illusion of deterrence in Isaac Ehrlich's research on capital punishment, Yale Law Journal, 85, 187-207.

Cook, P. J. (1977) Punishment and crime: a critique of current findings concerning the preventive effects of punishment, Law and Contemporary Problems, 41, 164-204.

Ehrlich, I. (1974) Participation in illegitimate activities: an economic analysis, in G. S. Becker and W. M. Landes (eds.), Essays in the Economics of Crime and Punishment, National Bureau of Economic Research, New York.

Ehrlich, I. (1975a) The deterrent effect of capital punishment: A Question of Life and Death, American Economic Review, 65, 397417.

Ehrlich, I. (1975b) Deterrence: evidence and inference, Yale Law Journal, 85, 1209-27. Ehrlich, I. (1977a), The deterrent effect of capital punishment: reply, American Economic Review, 67,

452-8. Ehrlich, I. (1977b) Capital punishment and deterrence: some further thoughts and additional evidence,

Journal of Political Economy, 85. 741-88. Ehrlich, I. (1979) The economics of crime: a preliminary estimate, in S. L. Messinger and E. Bittner

(eds.), Criminology Review Yearbook, Sage Publications, London.

131n an attempt to isolate the impact of measurement errors in the number of offences alone (of all the crime data), equations were constructed and estimated as follows. The counterpart of Table 1 equations were estimated forming the unconditional risk of punishment from the ratio of summed executions plus commutations to homicides, and forming the conditional risk of execution from the ratio of executions to summed executions plus commutations. Thus these equations comprise a third comparison set, which are constructed identical to the odd-numbered equations of Table 1 except for the numerator of the unconditional risk of punishment. Like the even-numbered equations of Table 1 a 'link' is maintained between the two risk variables, but like the odd-numbered equations the objective measure of conditional execution risk is relatively error-free. Mean values for the crime-related coefficients for comparison sets consisting respectively of the odd-numbered equations of Table 1, the even-numbered equations of Table 1, and the equations just specified are- - 0.129, -0.154 and - 0.266 (risk of punishment); and -0.139, -0.400 and -0.073 (risk of execution).

Dow

nloa

ded

by [

The

Uni

vers

ity o

f M

anch

este

r L

ibra

ry]

at 1

2:58

10

Oct

ober

201

4

K. L. Avio

Ehrlich, I. (1981) On the usefulness of controlling individuals: an economic analysis of rehabilitation, incapacitation, and deterrence, American Economic Review, 71, 307-22.

Ehrlich, I. and Mark, R. (1977) Fear of deterrence: a critical evaluation of the 'Report of the Panel on Research on Deterrent and Incapacitative Effects', Journal of Legal Studies, 6, 293-316.

Hausman, J. A. (1978) Specification tests in econometrics, Econometrica, 46, 1251-71. Klein, L. R., Forst, B. and Filatov, V. (1978) The deterrent effect of capital punishment: an assessment

of the estimates, in A. Blumstein, J. Cohen and D. Nagin (eds.), Deterrence and Incapacitation: Estimating the Eflects of Criminal Sanctions on Crime Rates, Panel on Research on Deterrent and Incapacitative Effects, National Academy of Sciences, Washington, DC.

Layson, S. (1983) Homicide and Deterrence: Another View of the Canadian Time-Series 'Evidence, Canadian Journal of Economics, 16, 52-73.

Layson, S. (1985) Homicide and deterrence: a reexamination of the United States time-series evidence, Southern Economics Journal, 52, No 1, 68-89.

Nagin, D. (1978) General deterrence: a review of the empirical evidence, in A. Blumstein, J. Cohen and D. Nagin (eds.), Deterrence and Incapacitbtion: Estimating the Eflects of Criminal Sanctions on Crime Rates, Panel on Research on Deterrent and Incapacitative Effects, National Academy of Sciences, Washington, DC.

Palmer, J. (1977) Economic analyses of the deterrent effect of punishment: a review, Journal of Research in Crime and Delinquency, 14, 4-21.

Passell, P. and Taylor, J. B. (1977) The deterrent effect of capital punishment: another view, American Economic Review, 67, 445-51.

Pyle, D. J. (1983) The Economics of Crime and Law Enforcement, Macmillan Press, London. Sjoquist, D. (1973) Property crime and economic behaviour: some empirical results, American

Economic Review, 63,439-46. Taylor, J. B. (1978) Econometric models of criminal behavior: a review, in Econometric models of

Criminal Behavior, by J . M. Heineke (ed.), North-Holland, The Netherlands. Wilson, J. Q. (1983) Crime and American Culture, The Public Interest, 70, 22-48. Wolpin, K. I. (1978), An economic analysis of crime and punishment in England and Wales,

1894-1967, Journal of Political Economy, 86b, 815-40.

Dow

nloa

ded

by [

The

Uni

vers

ity o

f M

anch

este

r L

ibra

ry]

at 1

2:58

10

Oct

ober

201

4