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UNEMPLOYMENT, GDP, AND CRIME RATE:
THE SHORT- AND LONG-RUN RELATIONSHIP
FOR THE AUSTRALIAN CASE
Alicia N. Rambaldi, Tony Auld and Jonathan Baldry
No. 82 - November 1995
ISSN
0 157 0188
ISBN
1 86389 292 3
Unemployment, GDP, and Crime Rate: The Short- and Long- run relationship for the
Australian Case.
Alicia N. Rambaldi*, Tony Auld**, and Jonathan Baldry***
Abstract:
Some categories of crime are found to have a long-ran relationship with GDP and unemployment.
The impulse response analysis of the cointegrated system between crime categories, GDP, and
unemployment reveals the response from a shock in the unemployment rate is non-significant for
any crime category, while a shock in GDP produces a small positive response in the number of
charges and convictions for some criminal offenses.
The authors would ll):e to acknowledge valuable comments from D.S.Prasada Rao and
M.A.Taslim.
Departmem of Econometrics. UNE. Armidale, NSW.
National Centre for Development Studies, ANU. ACT.
Department of Economics. UNE. Armidale, NSW.
Unemployment, GDP, and Crime. The Short- and Long- run relationship for the Australian
Case.
1. Introduction
The link between economic conditions and crime has been the subject of considerable research. In
a micro-economic context, the research has concentrated on modelling criminal behaviour from an
expected utility perspective. The seminal work of Becket (1968) introduced an economic model which
analysed the criminal choice decision in terms of the expected utility derived from participation in legal and
illegal activities. Extensions of this model were introduced by several authors including Ehrlich (1973),
Block and Lind (1975), Block and Heineke (1975). In a macro-economic context, the interest has
focused more on the rehtionship between the business cycle and crime, see for instance Cook and Zarkin
(1985). A sociological viewpoint is offered by Devine, Sheley, and Smith (1988).
This paper concentrates on the relationship between several categories of crime and the business
cycle represented by GDP and the unemployment rate. The analysis combines both the short- and longrun dynamics of the rehtionship in a single dynamic model. For those categories of crime that show a
long-run relationship to GDP and unemployment, an error correction model (ECM) is estimated and the
corresponding impulse response analysis is presented. Our results indicate that for the period analysed,
oft~nces against persons, property and good order (defined shortly) hold a long-run relationship with GDP
and the unemployment rate.
This paper is organised as follows: The categories of crime used in the study and the macroeconomic model are introduced in Section 2. Section 3 explains the methodology employed in the
analysis. Section 4 presents the results and Section 5 the conclusions.
2. Crime and the Macroeconomy
2.1. Criminal Statistics
Australia has somewhat of a chequered history regarding criminal statistics. The need for uniform
crime statistics that are comparable by offence category between states and overtime has long been
acknowledged. The main problems, common to federal systems in which the criminal law and law
enforcement are state responsibilities, are differences in the definitions of offences and differences in the
procedures used for collecting and classifying offences. In addition, changes in definitions and
classifications over time within any given jurisdiction - a problem with all criminal statistics - makes timedseries comparisons extremeley difficult. In Australia a review of offence categories and classifications,
implemented in the early 1970s (and revised in 1977), led to irreconcilable discontinuation in the country’s
criminal statistics, which restricted the potential sample for this study to the years before 1971 (71 years).
This is undoubtedly a major shortcoming of this study since it is possible that the relationship between
crime and economic cycles (recessions and prosperity) has changed after 1971. However, the considerable
amount of statistical compilation carried out by the Australian Institute of Criminology has provided a
reasonably comprehensive range of data including police, judicial, demographic and death statistics. The
data were collected in the Source Book of Criminal and Social Statistics (Mukherjee, Jacobsen and
Walker, 1981) - hereafter, Source Book.
Given the difficulties of utilising large data sets for, in particular, fairly disaggregated offence
categories, four broad classes are u "ttlised in this analysis. These are: Total offences, Offences Against the
Person, Offences Against Property and Offences Against Good Order. These series are defined by The
Source Book of Criminal and Social Statistics, Australian Institute of Criminology pp. 228-229, as:
Total Offences (TO) - The sum of Offences Against the Person, Offences Against Property, Offences
Against Good Order and Petty Offences.
Offences Against the Person (PER) - includes murder and attempt; manslaughter by driving; infanticide;
abortion; kidnapping and abduction; rape and attempt; carnal knowledge; incest; bigamy; bestiality; sexual
assault; indecent assault; aggravated major assault; inflicting grievous bodily harm; stabbing; shooting or
wounding; common/minor assault; dangerous driving causing injury;, administering poison.
Offences Against Property (PRO) - includes break, enter and steal; larceny or illegal use of vehicle or
boat; stealing from the person; horse cattle and sheep stealing; malicious/wilful damage; embezzlement
(including larceny by a clerk or servant); false pretences; fraudulent misappropriation; receiving; unlawful
possession of property; arson; robbery.
Offences Against Good Order (GO) - drunkenness; drunk and disorderly; incident, riotous or offensive
behaviour; vagrancy; offensive, threatening or abusive language; evading fare on a public vehicle; public
mischief escape from custody; conduct scandalous or lewd; hindering/resisting arrest.
These offences are recorded at Magistrates’ Courts. The crimes for each offence category are
reported as "charges, convictions, discharges (includes acquittals, dismissals, withdrawals, and remands)
and committals to higher court for triaL" Any empirical analysis of the detemainants of crime desirably
u’~ a measure of true offence rates. These are generally not available, and the researcher is forced to
rely at best on recorded offence rates (or "crimes known to the police"), perhaps incorporating into the
model certain assumptions about the relationship between true and recorded rates. See, for example,
Carr-Hill and Stem (1973). Otherwise research must focus explicitly on the determinants of the recorded
offence rate, estimating what are in effect reduced-form equations which incorporate the direct effects of
exogenous influences on the ratio of offences recorded, and the indirect effects operating via the true
offence rate.
Unfortunately, the limitations on data availability and the need for a long time series means that the
recorded offences data are not available. The best that can be done is to use "charges". This measure,
along with "convictions", is used in the following analysis. Figure 1 presents a diagram of the criminal
data available.
Figure 1. Criminal Data Availability
Offences Committed
(Unknown)
Crimes known to Police
(Recorded from the mid 1960s)
Charges
(Series available from 1901 to 1971)
Convictions
Dismissals
(1901 - 1971)
stop
Conviction Dismissal
Penalty
,_1
stop
stop
Initially, almost all charges must be heard in Magistrates’ Courts, about 3% of those "Charges" are
committed to a higher court for trial Given that both series Charges and Convictions were available since
the beg-inning of the cemury (1901) to 1971, we compare the findings for each one of the offence
categories.
2.2 The Economic Model
The simple model under study states that in a macroeconomic context, the number of criminal
offences (O) is related to the overall rate of unemployment (U) and GDP.
(1)
O =f( U, GDP)
In a theoretical context, the influence of economic activity variables on crime has beeen examined
by, amongst others, Ehrlich (1973) and Sjoquist (1973). Invariably, measures of unemployment rates, and
one or more income measure are also utilised as independent variables in all econometric studies of crime,
for example Avio and Clark (1976), Withers (1984). The theoretical arguments for inclusion are that the
relative returns to legal work fall during economic downturns (high unemployment, low GDP), hence
providing an increased incentive to generate income via illegal work, or to pursue illegal methods of
generating utility. However, there are other factors which might complicate this simple relationship. First,
high unemployment may be associated with closer and more effective supervision of (crime-prone) young
people by their parents. Secondly, low GDP also reduces the expected gains from theft (there is less to
steal), so some studies have focused on increased income disparities as causal influences (Sjoquist, 1973,
Withers, 1984). The empirical evidence reflects this ambiguity. While the weight of evidence supports
the incentives story, there remains some doubt about the direction of influence of the "economic"
variables.
As explained in section 2.1, data problems mean that variable O is not observable. Using charges
(C) and convictions (K) as alternative dependent variables means that the relationships being investigated
are of the forms
C = g(O; U, GDP) = ~(U, GDP)
K = h(O; U, GDP) = ~U, GDP)
(2)
(3)
In other words, we are estimating reduced-form relationships whose interpretation is fairly
complex. A positive measured coefficient on U, for example, could reflect a positive effect on O and a
positive effect of O on C, which is not outweighed by any direct negative impact of U on C. (Some of
these matters are further considered in section 5.)
3. The methodology
5
The variables in the economic system under study are Offence Category (measured by charges or
convictions) GDP and the unemployment rate (U). They can be represented in vector autoregressive
(VAR) form as:
I
An(L) A~2(L)A~3(L)][ Ot
+
A~I(L)A~(L)
A~3~)[/GDP~
A(L) Z~ = [i~
g3
A~,(L) A3~(L) A33(L)J[ U,
t= 1 .....T
This is the basic VAR model for three variables and p lags, where el ......
eT are ££d. N - (0,E), L is the lag
operator, and the maximum lag in A(L) is p. The error-correction form (or error correction model ECM)
of this model has become its most common representation. The ECM expresses the short-run changes of
the variables in the system as a function of their short-run dynamics (lagged changes) and the long-run
dynamics (the error correction term):
AZt = 8 + FIAZt-t + ... + Fp.lAZt_p+l - FIzt_p + e~
(5)
where
Fi= -O3-A1-...-A0, i= 1 ......p-l,
and
17= I3 - A1- ... - Ar~
where 13 is an identity matrix of order 3, and 17 is known as the impact matrix. In compact notation (2)
reduces to:
Zo = FZ~ + 17Zp + E
(6)
where Zo is a k x T matrix of observations on first differences of Zt, Z1 contains the lagged differences, and
Z~ is the pth lag of Zt. The ECM representation allows for the variables in the system to be cointegrated.
There is cointegration when the rank of 17 equals r (0 < r < 3). The ECM reduces to a VAR in differences
(only short-run dynamics) if rank(H) = 0. The variables in the system are stationary if rank(H) = 3 (in
which case estimating (5) does not offer any advantages over estimating (4)). When co-integration is
present, I7 can be written in its restricted form as the product of two matrices
17 =
(7)
where ~ and I~ are k x r matrices, 13 is the cointegrating vector, o~ is the loading matrix, and r is the number
of cointegrating relations in 13’Zt 1
Representing the system of economic variables through an ECM allows testing for cointegration
by testing the hypothesis H(r): rank(I’l) = r. Two tests for this hypothesis were proposed by Johansen
(1988) and Johansen and Juselius (1990), and they are known as the Trace and the Maximal Eigenvalue
statistics. If 0< r < k, the system can be estimated by a maximum likelihood procedure (known as the
Johansen estimator of cointegrated systems)2.
The impulse response (or dynamic multiplier) analysis of vector autoregressive systems has been a
common tool of applied macroeconomic research. However, when systems are cointegrated, the
estimation involves a few extra steps. Impulse response analysis of cointegated systems is extensively
discussed by Ltitkepohl and Reimers (1992), and Lt~tkepohl (1993), thus our explanation is very brief.
Following Ltitkepohl and Reimers (1992) we denote the impulse response of variable za to a unit
shock in variable z~, n periods ago,
¯ n = ((P~,,n) = ~ ~n-J Aj n = 1, 2 ......
(8)
j=l
Where ¢o = Ik, and A~ = 0 for j > p, (k = 3 in our case). The orthogonalised impulses are defined as
®n = (0~,,.)= ¢,P, where P is the lower triangular Cholesky decomposition of Z (i.e. the variancecovariance matrix of E in equation (6)), that is, PP’ = Z. These impulses can be thought of as transformed
residuals of the form wt = P-1 et which have identity covariance matrix. Thus, a unit impulse response has
size one standard deviation in this case. One of the important differences between impulse responses in
cointegrated systems and their stationary counterparts is that for the former the effect of a shock in one of
the variables will in general not die out in the long-run. That is, a one-time shock may shift the system to a
new equilibrium (permanent effect). Standard errors for 6, can be obtained following Ltitkepohl and
Reimers (1992) and Ltitkepohl (1990).
This restriction also provides some insight into the causality implications of cointegration whereby
causality can come about through the cointegrating relations 13"Zt or by conditioning on c~ such
that a row of o~ equating zero essentially excludes "long- run causality" in the corresponding
equation.
The estimator has been shown to outperform other estimators of cointegrated systems (See
Gonzalo, 1994).
7
4. Empirical Results
The per capita number of charges and convictions for the four offences defined in Section 2.1 (i.e.,
TO, PER, PRO, and GO), GDP per capita, and the unemployment rate between 1901 and 1971 for
Australia were individually tested for non-stationarity. All series were found to be integrated of order one,
I(1). An error correction model as in equation (5) was fitted with each offence category for lags p=2 and
p=3. Some residual correlations were detected for the two lags model (p=2), therefore the final
estimation was a VAR(3), with error correction representation:
A Zt = [i + F1 A Zt-1 + F2 A Zt-2
rI z~.3 + e~
(9)
Table 1 shows the results of the cointegration tests (Trace and Maximal Eigenvalue Statistics,
with critical values from Osterwald-Lenum (1992), Table 1).
The results indicate evidence for one cointegrating relationship between offences,
unemployment rate and GDP at the 5% for the following offences: Charges and convictions for
offences against property, and charges for offences against good order. At the 10% significance
level we found evidence for cointegration in the cases of: Charges for offences against the person
and convictions for offences against good order. The existence of a long-run relationship between
these economic variables imply that changes in GDP and/or unemployment may have a permanent
effect on charges and convictions for the particular offence. In all other cases, the results indicate
that changes in GDP and/or unemployment only have a temporary effect on those categories of
offences. The estimates of the cointegrating vectors (normalised by the offence category) are
presented in Table 2.
Table 1. Results of Cointegration Tests - Johansen Maximum Likelihood Procedure
( 68 observations from 1904 to 1971. Maximum lag in VAR = 3).
Series
Charges
TO, GDP,
U
Convictions
TO, GDP,
U
Charges
PER, GDP,
U
Convictions
PER, GDP,
U
Charges
PRO, GDP,
U
Convictions
PRO, GDP,
U
Eigenvalues
in descending
order
Trace
Null Alternative Critical
r=0
r=l Value
r = 2 95%
r<= 1
r=3
r<= 2
.1924
.0900
.0217
.1837
.0889
.0168
22.4432
7.9123
1.4942
21.2941
7.4923
1.1573
26.2082
7.0651
2.5848
22.3390
7.2921
2.2309
34.4582
10.7090
4.4351
31.9244
10.0225
4.0447
Max. Eigenvalue
Null Alternati~?e
r=l
r=0
r<= 1
r= 2
r<= 2
r= 3
14.5309
6.4181
1.4942
13.8018
6.3350
1.1573
19.1431"
4.4803
2.5848
Critical
Value
95%
20.9670
14.0690
3.7620
20.9670
14.0690
3.7620
20.9670
14.0690
3.7620
20.9670
14.0690
3.7620
20.9670
14.0690
3.7620
29.6800
15.4100
3.7620
29.6800
15.4100
3.7620
29.6800
.3434
15.4100
.0989
3.7620
.0283
29.6800
15.0469
.1985
15.4100
5.0612
.0717
3.7620
2.2309
.0322
23.7492
.2947
29.6800
15.4100
6.2739
.0881
4.4351
.0631
3.7620
29.6800
21.9018
.2753
15.4100
5.9779
.0841
3.7620
4.0447
.0577
29.6800
21~254
Charges
.2713
29.2218"
15.4100
4.9399
0.700
7.6965
GO, GDP,
3.7620
2.7566
.0397
2.7566
U
29.6800
19.6251"
Convictions
.2506
28.4586*
15.4100
6.8371
GO, GDP,
.0956
8.8335
3.7620
1.9964
U
.0289
1.9964
* Significant at 10% (Critical values, Trace= 26.7850, Max Eig= 18.5980).
20.9670
14.0690
3.7620
20.9670
14.0690
3.7620
20.9670
14.0690
3.7620
Table 2. Estimates of cointegrating relationship between offences, unemployment rate and
GDP
~’ = (GDP, U, O)
OFFENCE
Charges for Offences Against the Person
-0.406112
0.505894
1.00
Charges for Offences Against property
-2.101577
-0.515873
1.00
Convictions for Offences Against property
-2.396482
-0.458876
1.00
Charges for Offences Against good order
1.039292
0.496926
1.00
Convictions for Offences Against good order
1.163214
0.372337
1.00
The estimates show that in the long-run, charges for offences against the person increase with
increases in the unemployment rate and decrease with increases in GDP. This is not however the
case for property and good order offences. Charges and convictions for offences against property
would decrease with increases in both the unemployment rate or per capita GDP; while charges and
convictions against good order will both increase with increases in the unemployment rate or per
capita GDP. Ltitkepohl and Reimers (1992) argue that the interpretation of cointegration relations
may be difficult or misleading in applied cases, and thus the virtue of impulse response analysis since
impuse responses may give interesting insights into the short- and long-run relations among the
variables.
Figures 2, 3 and 4 present the orthogonal impulse responses of "charges" and "convictions"
for different offences to a one-time shock in the unemployment rate or GDP per capita. The system
is assumed to start at equilibrium (the equilibrium is placed at the origin of the coordinate system).
The confidence bounds are of size two standard errors (2*se)3 and they are depicted by the broken
lines. Since the responses have been orthogonalised, a one-time shock in unemployment (GDP) has
size one standard deviation, and it is considered permanent ff the variable does not return to its
previous equilibrium state. When impulse responses are orthogonalised, the order of the variables in
the system is important since contemporaneous feedback is restricted to occur only from the left to
right in the ordering. In our case the order was GDP, U, O. This ordering allows for GDP and U to
have an instantaneous effect on crime, and assumes there is a lag between occurrence of crime and
its effect on unemployment and GDP. In four cases the effect of a one-time shock appears
permanent and significant, that is, the new equilibrium settles at a significantly different value from
the initial state4. These cases are GDP --> charges for PER, GDP --> charges for GO, GDP -->
convictions for GO, and GDP --> convictions for PRO. For charges and convictions for good order
(Figure 4), the responses to a GDP shock are slightly positive. A one-time shock in GDP has a
significant positive permanent effect on the number of charges and convictions for offences against
good order, and charges for offences against the person (Figure 2). However, the new equilibrium is
only scarcely different from zero. Finally, for the case of convictions for offences against property, a
The standard errors were computed from Proposition 1 Ltitkepohl (1990).
Significantly different is taken to be when the confidence bound does not include zero (the initial
equilibrium value).
GDP shock shows an initial negative response and a convergence to a level slightly positive. The
shock does not have a permanent effect in the case of GDP --> charges for PRO. The initial
response is negative, with the value returning to the zero origin. In all other cases (i.e, shocks in
unemployment), the responses are insignificant with the confidence bound containing zero. These
results indicate that the impact of changes in the unemployment rate on the number of charges or
convictions is not permanent for the offences studied.
5. Conclusions
This paper has presented the results of a study into the dynamics of GDP, unemployment,
and four offence categories. We found evidence of cointegration in five models: (1) Charges for
offences against the person, GDP and the unemployment rate; (2) Charges for offences against
property, GDP and the unemployment rate; (3) Convictions for offences against property, GDP and
the unemployment rate; (4) Charges for offences against good order, GDP and the unemployment
rate; and, (5) Convictions for offences against good order, GDP and the unemployment rate. The
dynamics of these relationships were further analysed through an impulse response analysis. In
general, charges and convictions’ responses to increases in GDP or unemployment did not have a
substantial effect on crime (charges and convictions) for the sample period under study, 1901-1971.
Changes in GDP have a small positive effect on the number of convictions for offences against good
order, offenses against the person, and the number of charges for offences against good order, the
person, and the property. This positive value may signal the problem of measuring "crime" by
"charges" and "convictions" instead of "number of crimes committed." During booming economic
times, it is likely that more resources are available to the enforcement agencies, as well as a higher
pressure from the community for a "crime free society." It is still unclear what type of relationship
"crimes committed" have with "charges." Changes in the unemployment rate did not have a
significant long-run effect on charges or convictions for any of the crime categories studied.
Structural changes in the relationship between crime, GDP, and the unemployment rate may
have occurred after 1971, and thus our conclusions may not be entirely transferable to the situation
of the 1980s and 1990s. However, the results seem to point at two important conclusions. The ftrst
is that some of the determinants of the business cycle (GDP) may have a long-run relationship with
some categories of crime. The second (and perhaps more important message) is that the effect is
relatively small. In other words, a large increase (decrease) in GDP is not likely to trigger a large
11
increase (decrease) in crime. And, a large increase (decrease) in unemployment is not likely to have
a significant effect on crime.
Figure 2. Offences Against the Person
~
9L’O
~0"0 00"0 ~’0"0-
~L’O-
0~’0-
9FO gO’O 00"0 1,0’0- Z[’O- 0~’0-
Figure 3. Offences Against the Property
9vO gO’O 00"0 ~’0"0- ~t’O- OZ’O-
Figure 4. Offences Against Good Order
9FO
80"0 00’0 iO’O-
suods~;~
8L’O
~i’O-
~
80"0 00"0 )’0"0- ~I’0-
Og’O-
6. References
Becker, G.S. (1968). "Crime and Punishment by Imprisonment: An Economic Approach" Journal
ofPolitical Economy, 76(2), 169-217.
Block, M.K. and Heineke, J.M (1975). "A Labor Theoretic Analysis of Criminal Choice," American
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Block, M.K. and Lind, R.C. (1975). " An Economic Analysis of Crimes Punishable by
Imprisonment," Journal of Legal Studies, 4, 479-492.
Carr-Hill, R.A. and N.H. Stern (1973). "An econometric model of the supply and control of
recorded offences in England and Wales," Journal of Public Economics 2, 289-318.
Cook, P.J. and Zarkin, GA (1985). "Crime and the Business Cycle," Journal of Legal Studies, 14,
115-128.
Ehrlich, I. (1973). "Participation in ILlegitimate Activities: A theoretical and Empirical Investigation,"
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Devine, J.A., Sheley, J.F., and Smith, M.D. (1988), "Macro-economic and Social Control Policy
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Gonzalo, J. (1994). "Five alternative methods of estimating long-run equilibrium relationships,"
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Johansen, S. (1988). "Statistical Analysis of Cointegration Vectors", Journal of Economic
Dynamics and Control, Vol 12, pp. 231-254.
Johansen, S. and Juselius, K. (1990). "Maximum Likelihood Estimation and Inference on
Cointegration- with applications to the demand for money", Oxford Bulletin of Economics and
Statistics, Vol. 52, pp. 169-210.
Johansen, S. and Juselius K. (1992). "Testing Structural Hypotheses in a Multivariate Cointegration
Analysis of the PPP and the UIP for UK", Journal of Econometrics, Vol 53, pp. 211-244.
Ltitkepohl, H. (1990). Asymptotic Distributions of Impulse Response Functions and Forecast Error
Variance Decompositions of Vector Autoregressive Models," Review of Economics and
Statistics 72 pp. 116-125.
Ltitkepohl, H. (1993). Introduction to Multiple Time Series, Berlin: Springer-Verlag.
Ltitkepohl, H. and H. Reimers (1992a). "Granger-Causality in Cointegrated VAR processes",
Economic Letters Vol. 40 pp. 263-268. Ltitkepohl, H. and H. Reimers (1992b). " Impulse
Response Analysis of Cointegrated Systems", Journal of Economic Dynamics and Control
Vol. 16 pp. 53 - 78.
Mukherjee, S.K., Jacobsen, E.N. and J.R. Walker (1981). Source Book of Australian Criminal and
Social Statistics, 1900-1980, Australian Institute of Criminology, Canberra.
Osterwald-Lenum, M (1992). "A Note with Quantiles of the Asymptotic Distribution of the
Maximum Likelihood Cointegration Rank Test Statistics," Oxford Bulletin of Economics and
Statistics, 54 3 pp. 462-471.
Sjoquist, D. (1973). "Property Crime and Economic Behavior: Some Empirical Results," American
Economic Review, 63,439-46.
Withers, G. (1984). "Crime, Punishment and Deterrence in Australia: an Empirical Investigation,"
Economic Record, 60, 176-85.
WORKING PAPERS IN ECONOMETRICS AND APPLIED STATISTICS
~~ :6iaeo~z ~o~. Lung-Fei Lee and William E. Griffiths,
No. I - March 1979.
Howard E. Doran and Rozany R. Deen, No. 2 - March 1979.
Noi~eag Za~ ~~~aaa~_do~ @anna Made!.
William Griffiths and Dan Dao, No. 3 - April 1979.
~o2nia:. G.E. Battese and W.E. Griffiths, No. 4 - April 1979.
D.S. Prasada Rao, No. 5 - April 1979.
~eZe~ ~eq~ ~ed~. George E. Battese and
Bruce P. Bonyhady, No. 7 - September 1979.
Howard E. Doran and David F. Williams, No. 8 - September 1979.
D.S. Prasada Rao, No. 9 - October 1980.
~ Do//x~z - 1979. W.F. Shepherd and D.S. Prasada Rao,
No. 10 - October 1980.
v~ ~o~o~eq~~ano, in~ ~L0ka. W.E. Griffiths and
J.R. Anderson, No. 11 - December 1980.
2z~_k-O~-~ Year in tAe ~aaaanceo~ R~. Howard E. Doran
and Jan Kmenta, No. 12 - April 1981.
~iru~ Oade~~~i~. H.E. Doran and W.E. Griffiths,
No. 13 - June 1981.
Pauline Beesley, No. 14 - July 1981.
$o/~ Dola. George E. Battese and Wayne A. Fuller, No. 15 - February
1982.
~)ec~. H.I. Tort and P.A. Cassidy, No. 16 - February 1985.
H.E. Doran, No. 17 - February 1985.
J.W.B. Guise and P.A.A. Beesley, No. 18 - February 1985.
W.E. Griffiths and K. Surekha, No. 19- August 1985.
Sn~ ~. D.S. Prasada Rao, No. 20 - October 1985.
H.E. Doran, No. 21- November 1985.
~e-~ex~ g~rna~~t~qxg/Wi ~ede!. William E. Griffiths,
R. Carter Hill and Peter J. Pope, No. 22 - November 1985.
~n~ ~u~. William E. Griffiths, No. 23 - February 1986.
~ Dain~ ~~. T.J. Coelli and G.E. Battese. No. 24 February 1986.
~a~~ua~~ing~DaZzz. George E. Battese and
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George E. Battese, No. 28 - June 1986.
Nan--. D.S. Prasada Rao and J. Salazar-Carrillo, No. 29 - August
1986.
H.E. Doran,
W.E. Griffiths and P.A. Beesley, No. 30 - August 1987.
William E. Griffiths, No. 31 - November 1987.
~eaLD~ ~ Ri~ ~t~. Chris M. Alaouze, No. 32 - September, 1988.
G.E. Battese, T.J. Coelli and T.C. Colby, No. 33- January, 1989.
~ao~ ~aa~ ~~: ~ guide t~ the ~o~ ~aegaam,
Tim J. Coelli, No. 34- February, 1989.
#~I~~ ~ ~c~-~ide ~~. Colin P. Hargreaves,
No. 35 - February, 1989.
William Griffiths and George Judge, No. 36 - February, 1989.
~{zp~Za ~olea ~ ~ru~. Chris M. Alaouze, No. 38 July, 1989.
Chris M. Alaouze and Campbell R. Fitzpatrick, No. 39 - August, 1989.
Da~a. Guang H. Wan, William E. Griffiths and Jock R. Anderson, No. 40 September 1989.
o~$hz22_dR~ Op~. Chris M. Alaouze, No. 41 - November,
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~ ~Aean9 and ~Dn~ ~. William Griffiths and
Helmut Lfitkepohl, No. 42 - March 1990.
Howard E. Doran, No. 43 - March 1990.
~ainq ~heXa~ Yi/ieata $atZmate~u/~-gap~. Howard E. Doran,
No. 44 - March 1990.
Howard Doran, No. 45 - May, 1990.
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2O
~u%d ~n~ ~ai~2_~. D.S. Prasada Rao and E.A. Selvanathan,
No. 47 - September, 1990.
gc~~t~a~the~ni~ o~Neu~ gag&mud. D.M. Dancer and
H.E. Doran, No. 48 - September, 1990.
D.S. Prasada Rao and E.A. Selvanathan, No. 49 - November, 1990.
~~n ~ ~~. George E. Battese,
No. 50 - May 1991.
Fea~Non-N~~eda6~. Howard E. Doran, No. 52 - May 1991.
g~wnti~no~ ~ ~oa~and ~amA 9aadur~n ~~:
~on~ ~. C.J. O’Donnell and A.D. Woodland,
No. 53 - October 1991.
~~$ecio~. C. Hargreaves, J. Harrington and A.M.
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Colin Hargreaves, No. 55 - October 1991.
~aanti2n ~aaduatian ~unc2inn~, Fe2Jmirxi g~ic~ and ~an2/ Dais: ~LtA
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No. 56 - November 1991.
2.0. T.J. Coelli, No. 57- October 1991.
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Colin Hargreaves, No. 62 - November 1991.
21
O~ ~oneaz~ ~a~e. Duangkamon Chotikapanich, No. 63 - May 1992.
Viggo~. G.E. Battese and G.A. Tessema, No. 64- May 1992.
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~naame$~ ~a ~, 1960-1985: ~ ~~~.
Ma. Rebecca J. Valenzuela, No. 67 - April, 1993.
Mo~ L% ZAe ~.$. Alicia N. Rambaldi, R. Carter Hill and
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~ulo~e L% Vea~ ~ ~/q~. Tim J. Coelli, No. 71 December, 1993.
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Zo~ ~r~ ~ an ~(i) gazum’t ~ede~. William E. Griffiths,
No. 77 - September, 1994.
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~as2~. Ma. Rebecca J. Valenzuela, No. 79- August, 1995.
Ho~ g~4~$an~. William E. Griffiths and
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~0~ On ~0~/~.
No. 81 - November, 1995.
Alan T.K. Wan and William E. Griffiths,