DOCUMENT DE TREBALL
XREAP2013-09

Testing extreme value copulas
to estimate the quantile
Zuhair Bahraoui (RFA-IREA, XREAP)
Catalina Bolancé (RFA-IREA, XREAP)
Ana M. Pérez-Marín (RFA-IREA, XREAP)

Testing extreme value copulas to estimate the quantile
Zuhair Bahraoui, Catalina Bolanc´ and Ana M. P´rez-Mar´
e
e
ın
Department of Econometrics, Riskcenter-IREA, University of Barcelona,
Av. Diagonal, 690, 08034 Barcelona, Spain
November 28, 2013

Abstract
Testing weather or not data belongs could been generated by a family of extreme value
copulas is difficult. We generalize a test and we prove that it can be applied whatever the
alternative hypothesis. We also study the effect of using different extreme value copulas
in the context of risk estimation. To measure the risk we use a quantile. Our results have
motivated by a bivariate sample of losses from a real database of auto insurance claims.
Methods are implemented in R.
Keywords: Extreme value copula, Extreme value distributions, Quantile

1

Introduction

Let S be the sum of k dependent random variables (X1 , ..., Xk ) , i.e. S = X1 + ... + Xk . The
distribution of S depends on the multivariate distribution, i.e. the relationship between random
variables Xj , j = 1, ...k (see [33] for a review of the construction methods of multivariate distributions). Analyzing the distribution of S is essential in finance and insurance for quantifying
1

the risk of loss. In this regard, there are studies that have analyzed the stochastic behavior of
the sum of dependent risks and the way in which the dependency between these marginal risks
may affect the total risk of loss (see [12], [25], [11], [9] and [21]). The aim of this paper is to
analyze the test proposed by Kojadinovic et al. in [26] that allows to test whether or not our
data have been generated by an extreme value copula. We conclude that weak convergence of
the test statistic is true for any of the alternative hypothesis. Using a real data base, we have
analyzed how the error in the selection of the copula can affect the risk estimate. Throughout
this paper we simplify the notation for the bivariate case.
As noted by Fisher in [14], copulas are interesting for statisticians due to two basic reasons:
firstly, because of their application in the study of nonparametric measures of dependence and,
secondly, as a starting point for constructing multivariate distributions representing dependency
structures, even when the marginals follow extreme value distributions (EVD). Also, we know
that the choice of the marginals may be crucial to model the dependency behavior of variables.
According to Nelsen (see [27]), in the coupling of the joint distribution with marginals, the
copula captures the link between the two behaviors. The relationship between the joint distribution and the marginals is established in the fundamental theorem proposed by Sklar in [32].
This theorem shows that a bivariate cumulative distribution function (CDF) H of a random
vector of variables (X1 , X2 ) with marginal cumulative distribution functions (CDFs) F1 and F2
includes a copula C according to the following expression:
H(x1 , x2 ) = C(F1 (x1 ), F2 (x2 ))∀x1 , x2 ∈ R.

(1)

Due to the fact that the joint distribution (and therefore the dependency structure) is unknown,
specific tests for choosing the best copula are necessary. This has been the motivation for
developing tests for the adequacy of copulas. It is worth mentioning the paper by Genest and
Rivest (see [15]) on inference for bivariate Archimedean copulas, the test proposed in [31] on
the positive quadrant dependence hypothesis and, finally, the test of symmetry in bivariate
2

copulas introduced in [29].
Regarding the inference for extreme value copulas, we can mention the test proposed in [18]
based on a Cram´r-von Mises statistic and the test analyzed in [19] based on an U-statistic.
e
However, Kojadinovic et al. in [26] uses the max − stable property to test the adequacy of an
extreme value copula that is also based on the Cram´r-von Mises statistic. In our study we
e
find a similar result for the bivariate case and we obtain the weak convergence of the statistic
proposed in the general case.
In section 2, first, we present our main result and, second, we describe three examples of
copulas which are extreme value copulas: Gumbel, Galambos and Hustler-Reiss. In section 3
we describe a real database of auto insurance claims which we use in the empirical application.
In section 4 we report the results of our empirical study, firstly we apply the test described
in section 2 and, secondly, calculating the quantile using different extreme value copulas and
comparing these results with those obtained when using a widely known non extreme value
copula, such as a Gaussian copula. We use two alternative marginal distributions and we
compare them: the log-normal, that is a EVD Type I (Gumbel), and the Champernowne
distribution, which converges to a Pareto in the tail and therefore is an EVD Type II (Frechet).
We also remark that the Champernowe distribution looks more like a log-normal near 0. We
conclude in section 5.

2

Test for extreme value copulas

A copula is max − stable if for every positive real number r and all u1 , u2 in [0, 1], C(u1 , u2) =
1/r

1/r

C r (u1 , u2 ). Then we formulate the null hypothesis and its alternative as:
⎧
⎨ H r : C(u , u ) = C r (u1/r , u1/r ), ∀u , u ∈ [0, 1], ∀r > 0
1
2
1
2
1
2
0
.
1/r
1/r
⎩ H r : C(u , u ) = C r (u , u ), ∃u , u ∈ [0, 1], ∃r > 0
1
2
1
2
1
1
2
3

Specifically we need to test the max − stable hypothesis,
⎧
⎨ H :
r
0
r>0 H0
⎩ H :
H r,
1

r>0

1

r
in practice we only can test H0 for some values of r.

Let (Xi1 , Xi2 ), ∀i = 1, ...n be a bivariate sample of n independent and identically distributed
observations. We consider the functions:
Dr (u1 , u2) =
n
Dr (u1 , u2) =

√
√

1/r

1/r

r
n Cn (u1 , u2 ) − Cn (u1 , u2 )
1/r

1/r

n C(u1 , u2 ) − C r (u1 , u2 ) ,

where Cn (u1, u2 ) is the empirical copula defined as:
1
Cn (u1 , u2) =
n

n

I(F1n (Xi1 ) ≤ u1 , F2n (Xi2 ) ≤ u2 ),

u1 , u2 ∈ [0, 1]2 ,

(2)

i=1

where F1n and F2n are empirical marginal distributions. To test the max − stable property
we need to analyze if we can use Dr (u1 , u2) as an estimator of Dr (u1, u2 ). Then we find the
n
convergence to a Gaussian process of the difference Dr (u1 , u2) − Dr (u1 , u2 ).
n
We use the result by Fermanian et al. in [13] for the weak convergence of the empirical
copula Cn to a Gaussian process G in the space of all bounded real-valued functions on [0, 1]2 ,
i.e. l∞ ([0, 1]2 ), which is expressed as follows:
√

G(u1 , u2 )

(3)

= B(u1 , u2) − ∂1 C(u1 , u2)B(u1 , 1) − ∂2 C(u1 , u2)B(1, u2 ),
where

n (Cn (u1 , u2 ) − C(u1 , u2))

(4)

indicates weak convergence and B is a Brownian bridge on [0, 1]2 with covariance

functions:
E[B(u1 , u2 )B(u1 , u2 )] = C(u1 ∧ u1 , u2 ∧ u2 ) − C(u1 , u2 )C(u1 , u2),
where ∧ is the minimum.
4

Proposition 1 If the partial derivatives of a copula C(u1 , u2) are continuous then for any
r > 0 we have:
Dr (u1 , u2 ) − Dr (u1 , u2 )
n

1/r

1/r

1/r

1/r

Cr (u1, u2 ) = G(u1 , u2) − rC r−1 (u1 , u2 )G(u1 , u2 ),

(5)

r
r
in l∞ ([0, 1]2). Result in (5) is true under H0 and H1 .
r
Kojadinovic et al. (see [26]) proved the weak convergence under H0 of Dr (u1 , u2 ) towards the
n

same process defined in Proposition 1 but with opposite sign. We have proved weak convergence
r
r
of the difference Dr (u1 , u2 ) − Dr (u1 , u2 ) that is true under H0 and H1 .
n

Proof 1 In order to prove the result in Proposition 1 we consider the function:
1/r

1/r

Γ : C(u1 , u2 ) −→ C r (u1 , u2 ), r > 0.
Γ is a differentiable function as proposed by Hadamard (see [30]). We use the Delta functional
1/r

1/r

method to analyze the weak convergence of Γ (C(u1 , u2 )) = C r (u1 , u2 ). To find the derivative
1/r

1/r

of C r (u1 , u2 ) we consider the function:

1/r

1/r

1/r

1/r

h(t) = Γ (C + tΔ)(u1 , u2 ) − Γ C(u1 , u2 )
1/r

1/r

1/r

1/r

= (C + tΔ)r (u1 , u2 ) − C r (u1 , u2 ),
where tΔ is a function representing a difference. Then we calculate Γ as the derivative of
function h at t = 0. Using the expression of the Pascal triangle:
n

n

(a + b) =

(
k=0

5

n
k

)an−k bk ,

we obtain that:
r

h(t) =

(

k

k=0

= (

r

1/r

1/r

1/r

r

(

+

r
k

k=2

1/r

1/r

1/r

1/r

1/r

1/r

1/r

1/r

)C r−k (u1 , u2 )tk Δk (u1 , u2 ) − C r (u1 , u2 )
r

1/r

)C r (u1 , u2 ) + (

0

.

r

1/r

1

1/r

1/r

)C r (u1 , u2 )tΔ(u1 , u2 )

1/r

1/r

1/r

)C r−k (u1 , u2 )tk Δk (u1 , u2 ) − C r (u1 , u2 )

If we differentiate at t = 0, we obtain:
∂h(t)
1/r
1/r
1/r
1/r
|t=0 = Γ (Δ) = rC r−1 (u1 , u2 )Δ(u1 , u2 ),
∂t
1/r

1/r

where Γ (Δ) if the first derivative of function Γ(C(u1 , u2)) = C r (u1 , u2 ) with respect to
function t evaluated at t = 0. The result in Proposition 1 is archived observing that:
Dr (u, v) − Dr (u, v) =
n

√

1/r

1/r

1/r

1/r

r
n (Cn (u1 , u2 ) − C(u1 , u2 )) − (Cn (u1 , u2 ) − C r (u1 , u2 )) ,

using the convergence of the empirical copula given by Fermanian et al. (see [13]) we obtain:
√

n (Cn (u1 , u2) − C(u1 , u2 ))

G(u1 , u2),

and, finally, applying the Delta functional method, we obtain:
√

1/r

1/r

1/r

1/r

r
n Cn (u1 , u2 ) − C r (u1 , u2 )

Γ (G(u1 , u2 ))

Under the hypothesis H0 we have that Dr (u1 , u2) = 0 and in this case Dr (u1 , u2 ) weakly
n
converges to process (5).
For hypothesis testing given a fixed r, we use a Cram´r-von Mises statistic:
e
r
Sn =

1
0

1
0

(Dr (u1 , u2 ))2 du1du2 ,
n
6

(6)

As propose by Kojadinovic et al. in [26] for a range of values of r, r1 , ..., rp , the following
statistic can be considered:

p
r
Sn1 ,...,rp

r
Sni .

=

(7)

i=1

To calculate the critical values we use the method proposed by Van der Vaart in [34], consisting
r
on generating independent copies of Sn . The procedure is as follows:
r,(1)

1. Generating N independent copies of Dr , Dn
n
(Dr , Dr,(1) , . . . Dr,(N ) )
n
n
n

r,(N )

, . . . , Dn

, such that

(Dr , Dr,(1) , . . . Dr,(N ) ),

where Dr,(1) , . . . , Dr,(N ) are independent copies of Dr .
r,(1)

2. Calculating (Sn

r,(2)

, Sn

r,(N )

. . . , Sn

) such that:

r
r,(1)
r,(2)
r,(N
(Sn , Sn , Sn . . . , Sn ) )

(S r , S r,(1) , S r,(2) . . . , S r,(N ) ),

where (S r,(1) , S r,(2) . . . , S r,(N ) ) are independent copies of S r .
3. Obtaining the p-value as:
1
N

N

r,(k)
r
I(Sn ≥ Sn ).

k=1

The Van der Vaart method is implemented in the software R with the function evTestC().

2.1

Three examples of extreme value copulas

In the application presented in the next section, we compare thee examples of extreme value
copulas: Gumbel, Galambos and Hustler-Reiss, which are described in this section.
The functional form of Gumbel copula (see [23]) is given by:
Cθ (u1 , u2 ) = exp − (− ln(u1 ))θ + (− ln(u2 ))θ
7

1/θ

,

where θ ∈ [1, +∞) is the parameter controlling the dependency structure. Note that, the
dependence is perfect when θ → ∞, while independence corresponds to the case when θ = 1.
For the Gumbel copula, it is well known that lower tail dependence is λL = 0 and upper tail
1

dependence is λU = 2 − 2 θ , i.e. the Gumbel copula has upper tail dependence.
The Galambos copula was proposed by Galambos [16] and has the following form:
C(u1 , u2) = u1 u2 exp

(− ln(u1 ))−θ + (− ln(u2 ))−θ

−1/θ

,
1

where the range of θ is [0, ∞) and the upper tail dependence is λU = 2 − 2 θ .
Another example of extreme value copulas is the H¨ stler-Reiss copula that was developed
u
by H¨ stler and Reiss in [24]. Its functional form is given by:
u
ˆ
C(u1 , u2 ) = exp −u1 Φ

1 1
+ θ ln
θ 2

u1
ˆ
u2
ˆ

− u2 Φ
ˆ

1 1
+ θ ln
θ 2

u2
ˆ
u1
ˆ

,

where the range of θ is [0, ∞) and Φ is cdf of the standard Gaussian, u1 = − ln(u1 ) and
ˆ
u2 = − ln(u2).
ˆ

3

The data

Our example is motivated by a problem in the context or insurance. When there is an accident,
the total cost to be paid to a policyholder is the sum of two components: (1) the material damage
and (2) the bodily injury compensation. The insurance company is interested in evaluating the
risk of a given claim exceeding a certain amount. So the right-tail quantiles are important to
understand the risk that an accident claim is very costly.
We work with a random sample of 518 observations containing two types of costs: Cost1,
representing property damages and compensation of the loss, and Cost2, which corresponds to
the expenses related to medical care and hospitalization. In general, cost of bodily injuries is
covered by the National Institute of Health, however the insured has to bear the cost of some
8

medical expenses and rehabilitation, technical assistance, drugs, etc . . . , including compensation for pain, suffering and loss of income.
Bodily injury claims typically take years to be settled. Nevertheless, all the claims in our
sample were already settled in 2002, according to the company, (see [9]). Finally, we should
mention that the compensation may include payments to third parties that have been damaged
in one way or another.
In Table 1 we summarize the descriptive statistics of the sample for Cost1, Cost2 and the
Total Cost. The variables Cost1 and Cost2 are always positive, and there is a big difference
between the corresponding maximum and minimum values. Furthermore, we observe that
variables described in Table 1 have right skewness. In Figure 1 we show the histograms where
we represent the shape of the distribution associated with the variables Cost1 and Cost2.
Cost

Average

Std.Dev.

Skewness

Min

Max

Cost1

182.80

686.80

15.65

13.00 137900.00 677.00

Cost2

283.92

863.17

8.04

1.00

Total Cost

211.20

752.00

15.27

32.00 149800.00 789.00

11855.00

Median

88.00

Table 1: Descriptive statistics.
The K-Plot (related to Kendall Plot, see [17]) is a visual method that allows us to analyze
in a descriptive way if our bivariate data have been generated by an extreme value copula. In
Figure 2 we show the K-Plot, that compare the order in real data (H, pseudo-observations
generated by the bivariate empirical distribution) with the order supposing that the data have
been generated by the independence copula (W , expected pseudo-observations). We note that
costs have a positive association (as shown in the values of the K-plot above the diagonal, which
indicates independence). Almost all points are between the straight line and the boundary curve
indicating perfect positive dependence. It seems that according to the increasing values of W ,
9

Medical care

Frequency

200
100

200

0

0

100

Frequency

300

300

400

400

500

Property damages

0

20000

40000

60000

80000

100000

120000

140000

0

2000

Cost1

4000

6000

8000

10000

12000

Cost2

Figure 1: Histograms.
the data is closed to the case of a perfect positive dependence. This means that the higher the
severity of the claim, the higher is the correlation between the medical costs and compensation.

4

Results

In this section we report the results that we have obtained in an empirical application of the
methodology that we have presented. For estimating the total risk of loss, our goal is to
determine the dependency structure between the data corresponding to a sample of claims
provided by a major insurance company which operates in Spain. For testing if our data are
generated by an extreme value copula we calculate the value of the Cram´r-Von Mises statistic
e
in (7), with r = 3, 4, 5. We have estimated the significance level of the test statistic using the
method proposed by Van der Vaart in [34]. In total, we generated 1000 independent copies of
3,4,5
Sn . The results are shown in Table 2 and allow us to conclude that the analyzed bivariate

data are generated by an extreme value copula.
We estimate the parameters of the tree extreme value copulas described in section 2.1:

10

1.0

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x
xx x x

0.0

0.2

0.4

H

0.6

0.8

x

0.0

0.2

0.4

0.6

0.8

1.0

W1:n

Figure 2: K-Plot associated to copula of (Cost1, Cost2).
Statistic
3,4,5
Sn

Estimation

p-value

0.2680

0.1773

Table 2: Cram´r-Von Mises statistics.
e
Gumbel, Galambos and H¨ sler-Reiss. In Table 3 we show the estimated parameters for these
u
three copulas together with those obtained for the Gaussian and the t-Student copulas. To
estimate the dependence parameter of Gaussian, Gumbel, Galambos and H¨ sler-Reiss copulas
u
we have used the inversion of Kendall’s tau method (Itau). To estimate dependence parameter
and degree of freedom of t-Student copula we have used maximum likelihood estimation (MLE).
For selecting the copula we have used two known statistical information criteria, the Akaike
Information Criteria AIC = −2 log L(θ, u1 , u2) + 2k and the Bayesian Information Criteria
BIC = −2 log L(θ, u, v) + log(n)k, where k is the number of parameters to be estimated and
L the value of the likelihood function. Also, we have also used the copula information criteria

11

CIC propose by Gronneberg and Hjort [20]. The corresponding results are presented in Table
3, in practice we observe that AIC and CIC values are very similar. We observe that the
Gumbel copula is the one that best reflects the dependence structure of our data.
Gaussian

t-Student

Gumbel

0.6193

0.5981

1.7397

1.0208

1.4946

AIC -212.3695

-217.0000 -246.3839

-243.3305

-237.8542

BIC -208.1195

-208.5000 -242.1339

-239.0805

-233.6042

CIC -208.1195

-208.5000 -242.1339

-239.0805

-233.6042

Parameters

Galambos Hustler-Reiss

d.f.= 9.6442

Kendall Tau=0.4252
Table 3: Copula estimation results.
Once the dependency structure is estimated, the next step is to estimate the marginal
distribution functions. Considering the histograms in Figure 1, we proposed to use two EVD.
Namely, we compare the log-normal distribution, that is a EVD Type I (Gumbel), with the
modified Champernowne distribution1 , which converges to a Pareto in the tail and therefore it is
an EVD Type II (Frechet), besides the Champernowe distribution looks more like a log-normal
near 0. The Champernowne distribution have been analyzed en the context of semiparametric
estimation of EVD (see, for example, [3], [6], [4] and [1]). Furthermore, this distribution has
1

The cdf of the modified Champernowne distribution is:
F (x) =

(x + c)δ − cδ
, x ≥ 0,
(x + c)δ + (H + c)δ − 2cδ

with parameters δ > 0, H > 0 and c ≥ 0. The estimation of transformation parameters is performed using the
maximum likelihood method described in [10].

12

been used to model the operational risk, where the loss distribution is similar to those analyzed
in this work (see [7], [28], [8] and [22]).
In Table 4 we show the results for the maximum likelihood estimation of the marginal
distributions. We can see that for Cost1 Log-normal and Champernowne have similar AIC and
BIC, however for Cost2 Champernowne provides lower values of AIC and BIC.
Log-normal
CDFs
X1 =Cost1

Champernowne
2
− (t−μ)
2σ 2

log x
√ 1
e
−∞
2πσ2

(x+c)δ −cδ
,
(x+c)δ +(H+c)δ −2cδ

dt, x ≥ 0

μ = 6.4437, σ = 1.3349,

x≥0

δ = 1.3271, H = 677, c = 0

AIC = 8448.8950 and BIC = 8452.7190 AIC = 8448.163 and BIC = 8453.899
X2 =Cost2

μ = 4.3755, σ = 1.5189,

δ = 1.1622, H = 88, c = 0

AIC = 9425.1340 and BIC = 9428.9590 AIC = 6443.7150 and BIC = 6449.4510
Table 4: Maximum likelihood estimation of marginal distributions.
For evaluating the risk of total loss we estimate the quantile at confidence level α (qα ). We
use Monte Carlo simulation method, the procedure is as follows:
ˆ ˆ
1. We generate the pseudo-random sample U1i , U2i , ∀i = 1, ..., r, from the bivariate copulas whose estimate parameters are shown in Table 3.
−1 ˆ
−1 ˆ
ˆ
ˆ
2. Using the inverse of marginal CDFs we calculate X1i = F1 (U1i ), X2i = F2 (U2i ) , ∀i =

1, ..., l, where the sample volume l is large.
ˆ
ˆ
ˆ
3. We calculate Si = X1i + X2i , ∀i = 1, ..., l and we estimate qα (S) empirically from the
generated pseudo-sample. We generate l = 10, 000 samples.
In Table 5 we show the results of the estimations of qα for α = 0.95, 0.99, 0.995, 0.999. On
the first row of Table 5 we provide the empirical values of the qα (S) calculated with the 518
13

observations in the sample of the aggregate loss S = X1 + X2 for different confidence levels
α, below we show the same qα (S) that have been estimated by the Monte Carlo simulation
method for the five copulas considered here. We remark the importance of using an extreme
value copula and extreme value marginal distributions when the data indicate this behavior.
α
Empirical

0.95

0.99

0.995

0.999

7905.6000 24821.1400 28420.8700 92112.9300
Log-normal

Normal

6635.427

15628.804

20762.765

39733.894

t-Student

6547.524

16638.175

22521.175

39547.101

Gumbel

6432.017

15464.969

22011.382

40001.210

6429.16

15471.40

22066.00

39925.67

6421.028

15465.126

22122.110

39841.559

Galambos
Hustler-Reiss

Champernowne
Normal

7237.591

25504.175

38682.444 110082.261

t-Student

7302.165

25740.933

42223.504 117447.015

Gumbel

7264.831

23944.798

41461.743 119401.409

Galambos

7253.166

24056.946

41409.717 118982.012

Hustler-Reiss

7241.504

24103.038

41107.537 118539.744

Table 5: Quantiles of total loss.
In Table 5 we show that by using log-normal marginal distributions, the estimated quantile
is below the empirical quantile for the five copulas considered here. Therefore, risk is underestimated. We also remark that the selected copula does not have much influence on the risk
estimation. However, if we use Champernowne marginal distributions, which has a heavier
right tail than log-normal distribution, the influence of the selected copula is not significant at
14

lower confidence levels (0.95 and 0.99) but it is significant for extreme confidence levels (0.995
and 0.999). As indicated by the goodness of fit measures for our data, the best selection is the
Gumbel copula with Champernowne marginal distributions.

5

Conclusions

The test we have introduced for the adequacy of extreme value copulas lets us to determine
the suitable copula, especially when the data have extreme values.
In our empirical application, the K-Plot identified a positive and increasing dependence
between variables related to automobile insurance claims, and the new test we presented for
extreme value copulas confirms that, in our case, we should use an extreme value copula. The
results show the inportance
In the selection of the marginal distribution we have considered a modified Champernowne
distribution. It provides interesting results, due to its similarity to the log-normal distribution
for low values of the variable and, additionally, due to its convergence to a Pareto distribution
in the right tail.
When the marginal distributions have heavy right tail, as is the Champernowne distribution
and if the aim is to estimate extreme quantiles, the results show the importance of testing the
adequacy of the data to an extreme value copula.

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19

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Miguélez, E. (AQR-IREA); Gómez-Miguélez, I.
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XREAP2011-18
García-Pérez, J. I.; Hidalgo-Hidalgo, M.; Robles-Zurita, J. A.
“Does grade retention affect achievement? Some evidence from PISA”
(Novembre 2011)
XREAP2011-19
Arespa, M. (CREB)
“Macroeconomics of extensive margins: a simple model”
(Novembre 2011)
XREAP2011-20
García-Quevedo, J. (IEB), Pellegrino, G. (IEB), Vivarelli, M.
“The determinants of YICs’ R&D activity”
(Desembre 2011)
XREAP2011-21
González-Val, R. (IEB), Olmo, J.
“Growth in a Cross-Section of Cities: Location, Increasing Returns or Random Growth?”
(Desembre 2011)
XREAP2011-22
Gombau, V. (GRIT), Segarra, A. (GRIT)
“The Innovation and Imitation Dichotomy in Spanish firms: do absorptive capacity and the technological frontier matter?”
(Desembre 2011)
2012
XREAP2012-01
Borrell, J. R. (GiM-IREA), Jiménez, J. L., García, C.
“Evaluating Antitrust Leniency Programs”
(Gener 2012)
XREAP2012-02
Ferri, A. (RFA-IREA), Guillén, M. (RFA-IREA), Bermúdez, Ll. (RFA-IREA)
“Solvency capital estimation and risk measures”
(Gener 2012)
XREAP2012-03
Ferri, A. (RFA-IREA), Bermúdez, Ll. (RFA-IREA), Guillén, M. (RFA-IREA)
“How to use the standard model with own data”
(Febrer 2012)
XREAP2012-04
Perdiguero, J. (GiM-IREA), Borrell, J.R. (GiM-IREA)
“Driving competition in local gasoline markets”
(Març 2012)
XREAP2012-05
D’Amico, G., Guillen, M. (RFA-IREA), Manca, R.
“Discrete time Non-homogeneous Semi-Markov Processes applied to Models for Disability Insurance”
(Març 2012)
XREAP2012-06
Bové-Sans, M. A. (GRIT), Laguado-Ramírez, R.
“Quantitative analysis of image factors in a cultural heritage tourist destination”
(Abril 2012)

SÈRIE DE DOCUMENTS DE TREBALL DE LA XREAP
XREAP2012-07
Tello, C. (AQR-IREA), Ramos, R. (AQR-IREA), Artís, M. (AQR-IREA)
“Changes in wage structure in Mexico going beyond the mean: An analysis of differences in distribution, 1987-2008”
(Maig 2012)
XREAP2012-08
Jofre-Monseny, J. (IEB), Marín-López, R. (IEB), Viladecans-Marsal, E. (IEB)
“What underlies localization and urbanization economies? Evidence from the location of new firms”
(Maig 2012)
XREAP2012-09
Muñiz, I. (GEAP), Calatayud, D., Dobaño, R.
“Los límites de la compacidad urbana como instrumento a favor de la sostenibilidad. La hipótesis de la compensación en Barcelona medida a través
de la huella ecológica de la movilidad y la vivienda”
(Maig 2012)
XREAP2012-10
Arqué-Castells, P. (GEAP), Mohnen, P.
“Sunk costs, extensive R&D subsidies and permanent inducement effects”
(Maig 2012)
XREAP2012-11
Boj, E. (CREB), Delicado, P., Fortiana, J., Esteve, A., Caballé, A.
“Local Distance-Based Generalized Linear Models using the dbstats package for R”
(Maig 2012)
XREAP2012-12
Royuela, V. (AQR-IREA)
“What about people in European Regional Science?”
(Maig 2012)
XREAP2012-13
Osorio A. M. (RFA-IREA), Bolancé, C. (RFA-IREA), Madise, N.
“Intermediary and structural determinants of early childhood health in Colombia: exploring the role of communities”
(Juny 2012)
XREAP2012-14
Miguelez. E. (AQR-IREA), Moreno, R. (AQR-IREA)
“Do labour mobility and networks foster geographical knowledge diffusion? The case of European regions”
(Juliol 2012)
XREAP2012-15
Teixidó-Figueras, J. (GRIT), Duró, J. A. (GRIT)
“Ecological Footprint Inequality: A methodological review and some results”
(Setembre 2012)
XREAP2012-16
Varela-Irimia, X-L. (GRIT)
“Profitability, uncertainty and multi-product firm product proliferation: The Spanish car industry”
(Setembre 2012)
XREAP2012-17
Duró, J. A. (GRIT), Teixidó-Figueras, J. (GRIT)
“Ecological Footprint Inequality across countries: the role of environment intensity, income and interaction effects”
(Octubre 2012)
XREAP2012-18
Manresa, A. (CREB), Sancho, F.
“Leontief versus Ghosh: two faces of the same coin”
(Octubre 2012)
XREAP2012-19
Alemany, R. (RFA-IREA), Bolancé, C. (RFA-IREA), Guillén, M. (RFA-IREA)
“Nonparametric estimation of Value-at-Risk”
(Octubre 2012)

SÈRIE DE DOCUMENTS DE TREBALL DE LA XREAP
XREAP2012-20
Herrera-Idárraga, P. (AQR-IREA), López-Bazo, E. (AQR-IREA), Motellón, E. (AQR-IREA)
“Informality and overeducation in the labor market of a developing country”
(Novembre 2012)
XREAP2012-21
Di Paolo, A. (AQR-IREA)
“(Endogenous) occupational choices and job satisfaction among recent PhD recipients: evidence from Catalonia”
(Desembre 2012)
2013
XREAP2013-01
Segarra, A. (GRIT), García-Quevedo, J. (IEB), Teruel, M. (GRIT)
“Financial constraints and the failure of innovation projects”
(Març 2013)
XREAP2013-02
Osorio, A. M. (RFA-IREA), Bolancé, C. (RFA-IREA), Madise, N., Rathmann, K.
“Social Determinants of Child Health in Colombia: Can Community Education Moderate the Effect of Family Characteristics?”
(Març 2013)
XREAP2013-03
Teixidó-Figueras, J. (GRIT), Duró, J. A. (GRIT)
“The building blocks of international ecological footprint inequality: a regression-based decomposition”
(Abril 2013)
XREAP2013-04
Salcedo-Sanz, S., Carro-Calvo, L., Claramunt, M. (CREB), Castañer, A. (CREB), Marmol, M. (CREB)
“An Analysis of Black-box Optimization Problems in Reinsurance: Evolutionary-based Approaches”
(Maig 2013)
XREAP2013-05
Alcañiz, M. (RFA), Guillén, M. (RFA), Sánchez-Moscona, D. (RFA), Santolino, M. (RFA), Llatje, O., Ramon, Ll.
“Prevalence of alcohol-impaired drivers based on random breath tests in a roadside survey”
(Juliol 2013)
XREAP2013-06
Matas, A. (GEAP & IEB), Raymond, J. Ll. (GEAP & IEB), Roig, J. L. (GEAP)
“How market access shapes human capital investment in a peripheral country”
(Octubre 2013)
XREAP2013-07
Di Paolo, A. (AQR-IREA), Tansel, A.
“Returns to Foreign Language Skills in a Developing Country: The Case of Turkey”
(Novembre 2013)
XREAP2013-08
Fernández Gual, V. (GRIT), Segarra, A. (GRIT)
“The Impact of Cooperation on R&D, Innovation andProductivity: an Analysis of Spanish Manufacturing and Services Firms”
(Novembre 2013)
XREAP2013-09
Bahraoui, Z. (RFA); Bolancé, C. (RFA); Pérez-Marín. A. M. (RFA)
“Testing extreme value copulas to estimate the quantile”
(Novembre 2013)

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