A Bayesian Instrumental Variable Model of the Coverage of Corruption... Piero Stanig

A Bayesian Instrumental Variable Model of the Coverage of Corruption in the Mexican Press
Piero Stanig
Ph.D. Candidate, Department of Political Science, and Graduate Fellow, ISERP. Columbia University.
[email protected]
5
Qroo
4
3
Gro
2
Tlax
Sin
Mor
DF
Dgo
Yuc Camp
Coah
Hgo
Camp
Oax
Qroo
Coah
Sin
Mex
Gto
Slp
Jal
Chih
Dgo
Bcn
Pue
Bcs
ChihMor Ags
HgoChih
Ags
Nay
Qro
Son
0.5
Zac
Mich
Mich
Col
Tamps
Tab
Ver
Chis
Table 1:
1.0
1.5
2.0
2.5
Incidence of Defamation Indictments
Col
Bcs
Ags
Ags
Coah
Coah
Chih
Chih
Chih
Son
Bcn
Bcn
Slp
Gto
Gto
Qroo
Qroo
Zac
Tamps
Tamps
Nay
Tlax
Tlax
Hgo
Hgo
Chis
Yuc
Yuc
NL
Camp
Camp
Oax
Mor
Mor
Sin
Sin
Ver
Ver
Qro
Tab
Dgo
Dgo
Mich
Mich
Jal
Jal
Pue
Pue
Gro
Gro
Mex
DF
DF
DF
0
1
2
3
4
5
Average Number of Articles, by Newspaper
Figure 1: Average number of articles, by newspaper. Newspapers sorted
according to increasing level of corruption in the state, as measured by surveybased Transparencia Mexicana index. Dark grey and black bars identify chain
newspapers. Light grey bars are independent dailies. The horizontal line is
the mean number of articles in the whole sample.
Definition of corruption
Illegal act of a bureaucrat, politician, judge or law enforcement officer related to the public position held or
sought by the culprit described in the newspaper article.
2.5
3.0
2.5
2.0
2.0
density
1.5
density
1.5
1.0
1.0
0.5
0.5
gamma2
gamma3
beta
beta
0.0
Figure 4:
0.0
Joint posterior distribution of the structural parameter β and
the coefficients γ on the two instrumental variables. Local non-identification is
µj = ξXj + βγZj + j
terval is the central interval B such that p(β ∈ B) = 0.8. The p value is the
posterior probability p(β > 0) (Gill 1999).
average per capita indictments for defamation, with least squares fit. The label
P RIORS
• Uninformative prior on η and weakly informative
prior on the magnitude of :
5
4
3
Θ ∼ Wishart(S, 3)
S=
2
daily counts
are nested within newspapers that are in turn
nested within states and newspaper chains.
Counts can be modeled as draws from a Poisson distribution, accounting for overdispersion. The model is
D
ATA HAS MULTILEVEL STRUCTURE :
1
3. Hierarchical Poisson model
0
yijk ∼ Poisson(λijk )
log λijk = µj + νk + υijk
where k indexes the newspapers, j the states, i the
days.
The state-specific parameter is
µj = βDj + ξXj + j
D measures severity of defamation law with per capita
defamation indictments (1998-2000 average). An important component of the cost imposed on journalists are legal expenses and pre-trial detention. More
indictments mean that requirements to prosecute for
defamation are looser, hence the law is more severe.
• Confounders in X:
– Index of corruption in the state (survey-based measure collected by
Transparencia Mexicana)
– GDP per capita
– Extra-legal risk for investigative journalists (5-point ranking by the Inter
American Press Association)
– Partisanship of the state (percent of votes for the former dominant party,
the PRI, in the 2000 presidential election)
• Regression models also for
– the newspaper-specific parameter: predictors are ownership indicators
interacted with partisanship of the state
– the newspaper-day specific parameter: predictors are indicators for upcoming gubernatiorial and state legislature elections.
P RIORS
• Weakly informative half-Cauchy prior (Gelman
2006) with scale 2 for the variance of j , the state
random intercept.
• Independent normal priors for β and ξ, flat priors on
the variance: ξ` ∼ N (0, σξ2 ) and σξ` ∼ U (0, 1000)
`
−1.0
−0.5
0.0
0.5
1.0
Defamation Indictments, 1998−2000 Average
Figure 3:
Fifty and eighty percent posterior intervals of the expected
0.1 0
0 0.001
• Normal prior with common precision for β and ξ, and
uninformative hyperprior on the precision: predictors are on the same scale, their coefficients are of
the same order of magnitude
• The parameters of the assignment equation are
drawn from a multivariate normal distribution, with
a Wishart prior on the precision:
[γ, δ] ∼ MultivariateNormal(0, Ω)
number of articles —for a median newspaper— conditional on the measure of
severity of defamation law .
Ω ∼ Wishart(C, 10)
5. Potential problems with the
Poisson regression results
of the regression presented above
might be driven by a strong confounder. Moreover, the result might underestimate the chilling effect
of defamation law if :
a. legislators stiffen the law to protect themselves from
“watchdog” journalists
T
HE RESULT
The scale C is equal to an identity matrix of dimension 7, multiplied by 0.1.
—————————————
Three chains of 100.000 simulations in WinBUGS, the
second half of each chain saved (with thinning). R̂ = 1
for all parameters.
7. IV Results: the “chilling
effect”
T
c. as a consequence the severity of the law is endogenous to the coverage that politicians expect.
ATIVE ACCORDING TO THE INSTRUMENTAL VARIABLE
model (e.g, Dréze
1976, Chamberlain and Imbens 1996, Lancaster
2004) can help overcome these potential problems.
A
N INSTRUMENTAL VARIABLE
−1.0
−0.5
0.0
0.5
1.0
Defamation Indictments (Instrumented)
Figure 5:
Fifty and eighty percent posterior intervals of the expected
number of articles, from the instrumental variable estimation.
8. Conclusion: defamation law
chills the press
between
severity of defamation law and articles on corruption and police misconduct detected in Mexican newspapers after accounting for potential confounders:
A
SYSTEMATIC NEGATIVE ASSOCIATION
• COVERAGE
OF CORRUPTION IS SUBSTANTIALLY AF -
FECTED BY MORE RESTRICTIVE REGULATION OF
SPEECH .
b. the law becomes more punitive when the unobserved style of the newspapers is aggressive
6. Bayesian IV regression model
3
j , ηj ∼ MultivariateNormal(0, Θ)
2
Average number of articles, by newspaper, against 1998-2000
4
5
Dj = δXj + γZj + ηj
1
Figure 2:
Expected number of articles per day
• Data on 54 randomly selected state-level dailies, at
least one from each of Mexico’s 32 federal units
(324 newspaper-day observations)
• Exploiting variation in regulation of speech across
federal units in Mexico to provide an estimate of the
numer of articles not published due to legal restrictions to media freedom
• Data collected on six-day random reconstructed
weeks: the scheme
– accounts for day-to-day variation
– does not generate correlation among individual
(newspaper-day) observations
• Attention restricted to local events to control for
prevalence of corruption, an important confounder.
3.5
not an issue.
The posterior distribution of the parameter β. The credible in-
is the state of publication of the newspaper.
2. An original dataset on the
coverage of corruption
In the assignment equation, the coefficients γ for
the two instruments have posterior mean respectively
0.17 and 0.54, with 80% central posterior intervals
[0.08, 0.28] and [0.37, 0.72].
0
REAUCRATIC CORRUPTION .
Posterior Mean
80% c. i. p-value
(Standard Deviation)
-0.55
[-0.9 , -0.2 ] 0.02
(0.27)
The severity of criminal law for other offenses in
the Penal Codes provides instruments for severity of
defamation law.
The law for other crimes:
• cannot directly affect corruption coverage
• is related to the overall severity of the Penal Code in
a state and therefore to severity of defamation law.
Two instruments in the matrix Z:
1) the minimum mandatory sentence for homicide
2) the maximum sentence for aiding and abetting the
escape of a prisoner.
—————————————
A SIMULTANEOUS EQUATIONS MODEL FOR µj ( STATE LEVEL COMPONENT OF THE P OISSON PARAMETER )
AND FOR D ( SEVERITY OF DEFAMATION LAW ):
Expected number of articles per day
COVERING SENSITIVE TOPICS LIKE POLITICAL AND BU -
AND CORRUPTION COVERAGE IS RELIABLY NEG -
Ver
F JOURNALISTS FEAR BEING SUED OR TRIED FOR
WRITING AN ARTICLE , THEY MIGHT REFRAIN FROM
HE RELATIONSHIP BETWEEN SEVERITY OF LAW
ATIVE .
Tamps
DF
Pue
Gro Bcn
NL
0.0
I
T
Tlax
DF
0
1. Background
Continuous predictors centered and divided by two
standard deviations to standardize. Model fit in WinBUGS: 3 chains of 15000 simulations. Gelman and
Rubin(1992) R̂ statistic equal to 1 for all parameters,
compatible with convergence.
4. Results: stricter defamation
law related to less coverage
Yuc
1
Legal regulation of speech affects how newspapers
cover corruption. In Mexico, defamation is a criminal
offense regulated by each state’s Penal Code. I exploit
the variation in the severity of the law to estimate the
reduction in coverage that follows from punitive regulation of speech, using an original dataset of counts of
articles on corruption in 54 local newspapers for 2001.
Many articles on corruption are “missing” each week
in newspapers from states with the most punitive laws.
A Bayesian instrumental variable model bypasses the
problems of confounding and endogeneity and confirms that the relation between punitive law and corruption coverage is negative.
Number of articles on corruption, mentioning an identifiable culprit, published on a particular day by a newspaper
Average Number of Articles per Day
Abstract
Outcome variable
• RESULT
SURVIVES IN THE
PRETATION OF
“ CHILLING
β
IV
MODEL : THE INTER -
AS AN ESTIMATE OF A CAUSAL
EFFECT ” IS NOT UNWARRANTED.
HE RELATIONSHIP BETWEEN SEVERITY OF LAW
AND CORRUPTION COVERAGE IS RELIABLY NEG -
References
MODEL .
Posterior Mean
80% c. i. p-value
(Standard Deviation)
-1.3
[-1.9 , -0.8 ]
0
(0.4)
Table 2:
The posterior distribution of the parameter β in the instrumental
variable model.
[1] Chamberlain, Gary, and Guido W. Imbens. 1996. “Hierarchical Bayes Models with Many Instrumental
Variables.” NBER Technical Working Paper 204.
[2] Dréze, Jacques H.. 1976. “Bayesian Limited Information Analysis of the Simultaneous Equations Model.”
Econometrica 44(5):1045-1075.
[3] Gelman, Andrew. 2006. “Prior Distributions for Variance Parameters in Hierarchical Models.” Bayesian
Analysis 1(3):515-533.
[4] Gelman, Andrew, and Donald B. Rubin.1992. “Inference from Iterative Simulation Using Multiple Sequences.” Statistical Science 7(4):457-472.
[5] Gill, Jeff. 1999. “The Insignificance of Null Hypothesis Significance Testing.” Political Research Quarterly
52: 647-674.
[6] Lancaster, Tony. 2004. An Introduction to Modern Bayesian Econometrics. Malden, MA: Blackwell.