Instructors’ Manual for
Regression Modeling with Actuarial and Financial Applications
Edward W. Frees
iii
Data Sets
Anscombe’s Data, 1
Automobile Bodily Injury Claims, 2
Automobile UK Collision Claims, 3
Automobile Insurance Claims, 4
Capital Asset Pricing Model, 5
Insurance Redlining, 6
CEO Compensation, 7
Galton Heights, 8
MEPS Health Expenditures, 9
Hong Kong Horse Racing, 12
Hospital Costs, 13
Initial Public Offering (IPO), 14
Stock Market Liquidity, 15
Massachusetts Bodily Injury, 16
Insurance Company Expenses, 17
Outlier Example, 18
Refrigerator Prices, 19
Risk Managers Cost Effectiveness, 20
Singapore Automobile Claims, 21
Swedish Motor Insurance, 22
Term Life Insurance, 23
National Life Expectancies, 25
Nursing Home Utilization, 26
Wisconsin Hospital Costs, 27
Wisconsin Lottery Sales, 28
Workers Compensation, 29
Euro Exchange Rates, 30
Hong Kong Exchange Rates, 31
Inflation Bond Prices, 32
Labor Force Participation Rate, 33
Medical Component of the CPI, 34
Medicare Hospital Costs, 35
Prescription Drug Prices, 36
Standard and Poor’s 500 Daily, 37
Standard and Poor’s 500 Quarterly, 38
Auto Industry, 39
Medical Care, 40
Reinsurance General Liability, 41
Reinsurance General Liability 2004, 42
Singapore Auto Injury, 43
Singapore Auto Property Damage, 44
1
Table 1. Anscombe’s Data
The data is due to Anscombe (1973). The purpose of dealing with this data set is to
demonstrate how plotting data can reveal important information that is not evident in
numerical summary statistics.
File Name: Number of Number of
AnscombeData obs: 11 variables: 7
Number of
Variable Obs Missing Description
ObsNum The number of the observation
x1 Generic explanatory variable
y1 Generic dependent variable
y2 Version 2 of the dependent variable
y3 Version 3 of the dependent variable
x2 Version 2 of the explanatory variable
y4 Version 4 of the dependent variable
Source: Anscombe (1973).
Table 1
Example of the first five observations:
ObsNum x1 y1 y2 y3 x2 y4
1 1 10 8.04 9.14 7.46 8 6.58
2 2 8 6.95 8.14 6.77 8 5.76
3 3 13 7.58 8.74 12.74 8 7.71
4 4 9 8.81 8.77 7.11 8 8.84
5 5 11 8.33 9.26 7.81 8 8.47
2
Table 2. Automobile Bodily Injury Claims
We consider automobile injury claims data using data from the Insurance Research Council
(IRC), a division of the American Institute for Chartered Property Casualty Underwriters
and the Insurance Institute of America. The data, collected in 2002, contains information
on demographic information about the claimant, attorney involvement and the economic
loss (LOSS, in thousands), among other variables. We consider here a sample of n = 1,340
losses from a single state. The full 2002 study contains over 70,000 closed claims based on
data from thirty-two insurers. The IRC conducted similar studies in 1977, 1987, 1992 and
1997.
File Name: Number of Number of
AutoBI obs: 1340 variables: 8
Number of
Variable Obs Missing Description
CASENUM Case number to identify the claim
ATTORNEY Whether the claimant is represented by an attorney
(=1 if yes and =2 if no)
CLMSEX 12 Claimant’s gender (=1 if male and =2 if female)
MARITAL 16 claimant’s marital status (=1 if married, =2 if single,
=3 if widowed, and =4 if divorced/separated)
CLMINSUR 41 Whether or not the driver of the claimant’s vehicle was
uninsured (=1 if yes, =2 if no, and =3 if not applicable)
SEATBELT 48 Whether or not the claimant was wearing a seatbelt/child
restraint (=1 if yes, =2 if no, and =3 if not applicable)
CLMAGE 189 Claimant’s age
LOSS The claimant’s total economic loss (in thousands)
Source: Insurance Research Council (IRC).
Table 2
Example of the first five observations:
CASENUM ATTORNEY CLMSEX MARITAL CLMINSUR SEATBELT CLMAGE LOSS
1 5 1 1 NA 2 1 50 34.940
2 13 2 2 2 1 1 28 10.892
3 66 2 1 2 2 1 5 0.330
4 71 1 1 1 2 2 32 11.037
5 96 2 1 4 2 1 30 0.138
3
Table 3. Automobile UK Collision Claims
This data is due to Mildenhall (1999). Mildenhall (1999) considered 8,942 collision losses
fromprivatepassengerUnitedKingdom(UK)automobileinsurancepolicies. Thedatawere
derived from Nelder and McCullagh (1989, Section 8.4.1) but originated from Baxter et al.
(1980). We consider here a sample of n = 32 of Mildenhall data for eight driver types (age
groups) and four vehicle classes (vehicle use). The average severity is in pounds sterling
adjusted for inflation.
File Name: Number of Number of
AutoCollision obs: 32 variables: 4
Number of
Variable Obs Missing Description
Age Age of driver
Vehicle Use Purpose of the vehicle use:
“DriveShort” means drive to work but less than 10 miles
“DriveLong” means drive to work but more than 10 miles
Severity Average amount of claims (in pounds sterling)
Claim Count Number of claims
Source: Mildenhall (1999).
Table 3
Example of the first five observations:
Age Vehicle_Use Severity Claim_Count
1 17-20 Pleasure 250.48 21
2 17-20 DriveShort 274.78 40
3 17-20 DriveLong 244.52 23
4 17-20 Business 797.8 5
5 21-24 Pleasure 213.71 63
4
Table 4. Automobile Insurance Claims
We examine claims experience from a large midwestern (US) property and casualty insurer
for private passenger automobile insurance. The dependent variable is the amount paid
on a closed claim, in (US) dollars (claims that were not closed by year end are handled
separately). Insurers categorize policyholders according to a risk classification system. This
insurer’s risk classification system is based on automobile operator characteristics and ve-
hicle characteristics, and these factors are summarized by the risk class categorical variable
CLASS.
File Name: Number of Number of
Autoclaims obs: 6773 variables: 5
Number of
Variable Obs Missing Description
STATE Codes 01 to 17 used, with each code randomly assigned to an actual
individual state
CLASS Rating class of operator, based on age, gender, marital status, use of
vehicle, as coded in a separate PDF file
GENDER Gender of operator
AGE Age of operator
PAID Amount paid to settle and close a claim
Source: Insurance company data provided as a personal communication to the author.
Table 4
Example of the first five observations:
State_Code Class Gender Age Paid
1 STATE 14 C6 M 97 1134.44
2 STATE 15 C6 M 96 3761.24
3 STATE 15 C11 M 95 7842.31
4 STATE 15 F6 F 95 2384.67
5 STATE 15 F6 M 95 650.00
5
Table 5. Capital Asset Pricing Model
We study a financial application, the Capital Asset Pricing Model, often referred to by the
acronym CAPM. The name is something of a misnomer in that the model is really about
returns based on capital assets, not the prices themselves. The types of assets that we
examine are equity securities that are traded on an active market, such as the New York
Stock Exchange (NYSE).
An intuitively appealing idea, and one of the basic characteristics of the CAPM, is that
there should be a relationship between the performance of a security and the market. One
rationale is simply that if economic forces are such that the market improves, then those
same forces should act upon an individual stock, suggesting that it also improve. Another
rationale for a relationship between security and market returns comes from financial eco-
nomics theory. Other things equal, investors would like to select a return with a high
expected value and low standard deviation, the latter being a measure of riskiness.
Testing economic theory, or models arising from any discipline, involves collecting data.
The CAPM theory is about ex-ante (before the fact) returns even though we can only test
with ex-post (after the fact) returns. Before the fact, the returns are unknown and there
is an entire distribution of returns. After the fact, there is only a single realization of the
security and market return. Because at least two observations are required to determine a
line, CAPM models are estimated using security and market data gathered over time. In
this way, several observations can be made. For the purposes of our discussions, we follow
standard practice in the securities industry and examine monthly prices. Specifically, these
data consist of monthly returns over the five year period from January, 1986 to December,
1990, inclusive.
File Name: Number of Number of
CAPM obs: 60 variables: 3
Number of
Variable Obs Missing Description
AMERICAN Monthly returns of American Family Company
LINCOLN Monthly security returns from the Lincoln National Insurance Corporation
MARKET Monthly market returns from index of the Standard & Poor’s 500 Index
Source: Center for Research on Security Prices, University of Chicago.
Table 5
Example of the first five observations:
AMERICAN LINCOLN MARKET
1 0.303167 0.164588 0.004702
2 0.080092 0.030238 0.067982
3 -0.015054 -0.006289 0.052660
4 0.043668 -0.065401 -0.014899
5 0.107950 0.041002 0.045552
6
Table 6. Insurance Redlining
Do insurance companies use race as a determining factor when making insurance available?
Fienberg (1985) gathered data from a report issued by the U.S. Commission on Civil Rights
about the number of homeowners and residential fire insurance policies issued in Chicago
over the months of December 1977 through February 1978. Policies issued were categorized
as either part of the standard voluntary market or the substandard, involuntary market.
The involuntary market consists of “fair access to insurance requirements” (FAIR) plans;
thesearestateinsuranceprogramssometimessubsidizedbyprivatecompanies. Theseplans
provide insurance to people who would otherwise be denied insurance on their property
due to high-risk problems. The main purpose is to understand the relationship between
insurance activity and the variable “race”, the percentage minority. Data are available for
n = 47 zip codes in the Chicago area. These data have also been analyzed by Faraway
(2005).
To help control for the size of the expected loss, Fienberg also gathered theft and fire data
from Chicago’s police and fire departments. Another variable that gives some information
about loss size is the age of the house. The median income, from the Census Bureau, gives
indirect information on the size of the expected loss as well as whether the applicant can
afford insurance.
File Name: Number of Number of
Chicago obs: 47 variables: 8
Number of
Variable Obs Missing Description
zipcode Zip (postal) code
race Racial composition in percent minority
fire Fires per 1,000 housing units
theft Thefts per 1,000 population
age Percent of housing units built in or before 1939
volact New homeowner policies plus renewals, minus cancellations
and non-renewals per 100 housing units
involact New FAIR plan policies and renewals per 100 housing units
income Median family income
Source: Fienberg (1985).
Table 6
Example of the first five observations:
zipcode race fire theft age volact involact income
1 60626 10.0 6.2 29 60.4 5.3 0.0 11744
2 60640 22.2 9.5 44 76.5 3.1 0.1 9323
3 60613 19.6 10.5 36 73.5 4.8 1.2 9948
4 60657 17.3 7.7 37 66.9 5.7 0.5 10656
5 60614 24.5 8.6 53 81.4 5.9 0.7 9730
7
Table 7. CEO Compensation
The data were drawn from the May 25, 1992 issue of Forbes Magazine entitled “What
800 Companies Paid for their Bosses.” This article provides several measures of CEO
compensation, aswellascharacteristicsoftheCEOandmeasuresofhisfirm’sperformance.
We say “his” because of the 800 CEOs studied in this article, only one was a woman. The
data is used to study CEO and firm characteristics to determine the important factors
influencing CEO compensation.
To understand the determinants of CEO compensation, one hundred observations were
randomly selected from the 800 listed in the Forbes article. Although the Forbes article
did not cite the basis for a firm to be included in its survey, the 800 companies seem
to represent the largest publicly traded companies in the United States. Our sample of
one hundred CEOs and their firms represent a cross-sectional sample of America’s largest
corporations. In our cross-section, the CEO and firm characteristics were based on 1991
measures.
File Name: Number of Number of
CeoCompensation obs: 100 variables: 12
Number of
Variable Obs Missing Description
COMP Sum of salary, bonus and other 1991 compensation, in thousands of
dollars. Other compensation does not include stock gains.
AGE The CEOs age, in years
EDUCATN The CEOs education level, 1 for no college degree, 2 for a college
undergraduate degree and 3 for a graduate degree
BACKGRD Background type, 0 for unknown, 1 for technical, 2 for insurance, 3
for operations, 4 for banking, 5 for legal, 6 for marketing, 7 for
administration, 8 for sales, 9 for financial and 10 for journalism
TENURE Number of years employed by the firm
EXPER Number of years as the firm CEO
SALES 1991 sales revenues, in millions of dollars
VAL Market value of the CEO’s stock, in natural logarithmic units
PCNTOWN Percentage of firm’s market value owned by the CEO
PROF 1991 profits of the firm, before taxes, in millions of dollars
COMPANY Company name
BIRTH The CEOs birthplace
Source: Forbes Magazine.
Table 7
Example of the first five observations:
COMP AGE EDUCATN BACKGRD TENURE EXPER SALES VAL PCNTOWN PROF COMPANY BIRTH
1 1948 55 1 1 23 23.0 1227 7.6 0.55 145 AdvM chi
2 809 59 1 2 38 0.5 19196 0.4 0.01 505 aetna chi
3 721 53 2 1 26 0.5 839 1.5 0.10 -60 aller sanf
4 2027 62 2 2 25 5.0 8379 3.4 0.04 806 amer vertx
5 2094 63 1 3 41 8.0 10818 5.9 0.04 1166 ameri bigrun
8
Table 8. Galton Heights
These data are from Galton’s 1885 paper, including the heights of 928 adult children,
classified by an index of their parents’ height. Here, all female heights were multiplied by
1.08, and the index was created by taking the average of the father’s height and rescaled
mother’s height. Galton was aware that each column could be adequately approximated by
a normal curve. In developing regression analysis, he provided a single model for the entire
data set.
Galton’s 1885 regression data shows that much of the information concerning the height of
an adult child can be attributed to, or “explained,” in terms of the parents’ height.
File Name: Number of Number of
Galton obs: 102 variables: 5
Number of
Variable Obs Missing Description
NUMBER Number of families in a cell category
MIDPARNT Category for the height of the midparent that defines the column of the
cell
CHILD Category for the height of the child that defines the row of the cell
PARENTC Average of father’s height and rescaled (multiplied by 1.08) mother’s
height, that defines the column of the cell
CHILDC Height of adult child in inches, that defines the row of the cell
Source: Stigler (1986).
Table 8
Example of the first five observations:
NUMBER MIDPARNT CHILD PARENTC CHILDC
1 1 1 12 74.5 72.2
2 3 1 13 74.5 73.2
3 1 2 8 73.5 68.2
4 2 2 9 73.5 69.2
5 1 2 10 73.5 70.2
9
Table 9. MEPS Health Expenditures
The data were from the Medical Expenditure Panel Survey (MEPS), conducted by the
U.S. Agency of Health Research and Quality. MEPS is a probability survey that provides
nationally representative estimates of health care use, expenditures, sources of payment,
and insurance coverage for the U.S. civilian population. This survey collects detailed
information on individuals of each medical care episode by type of services including
physician office visits, hospital emergency room visits, hospital outpatient visits, hospital
inpatient stays, all other medical provider visits, and use of prescribed medicines. This
detailedinformationallowsonetodevelopmodelsofhealthcareutilizationtopredictfuture
expenditures. You can learn more about MEPS at http://www.meps.ahrq.gov/mepsweb/.
We consider MEPS data from the panels 7 and 8 of 2003 that consists of 18,735 individuals
between ages 18 and 65. From this sample, we took a random sample of 2,000 individuals.
From this sample, there are 157 individuals that had positive inpatient expenditures.
There are also 1,352 that had positive outpatient expenditures. We will analyze these
two samples separately. Our dependent variables consist of amounts of expenditures for
inpatient(EXPENDIP)andoutpatient(EXPENDOP)visits. ForMEPS,outpatientevents
include hospital outpatient department visits, office-based provider visits and emergency
room visits excluding dental services. (Dental services, compared to other types of health
care services, are more predictable and occur in a more regular basis.) Hospital stays with
the same date of admission and discharge, known as “zero-night stays”, were included in
outpatient counts and expenditures. (Payments associated with emergency room visits
that immediately preceded an inpatient stay were included in the inpatient expenditures.
Prescribed medicines that can be linked to hospital admissions were included in inpatient
expenditures, not in outpatient utilization.)
10
File Name: Number of Number of
HealthExpend obs: 2000 variables: 28
Number of
Variable Obs Missing Description
AGE Age in years between 18 and 65
ANYLIMIT Any activity limitation (=1 if any functional/activity limitation, =0
if otherwise)
COLLEGE 1 if college or higher degree
HIGHSCH 1 if high school degree
GENDER Indicate gender of patient (=1 if female, =0 if male)
MNHPOOR Self-rated mental health (=1 if poor or fair, =0 if good to excellent
mental health)
insure Insurance coverage (=1 if covered by public/private health insurance
in any month of 1996, =0 if have no health insurance in 1996)
USC 1 if dissatisfied with one’s usual source of care
UNEMPLOY Employment status of patients
MANAGEDCARE 1 if enrolled in an HMO or gatekeeper plan
famsize Family size of patients
COUNTIP Number of inpatient visits
EXPENDIP Amounts of expenditures for inpatient visits
COUNTOP Number of outpatient visits
EXPENDOP Amounts of expenditures for outpatient visits
RACE Race of patient described by words (Asian, Black, Native, White and
other)
RACE1 Race of patient described by numbers (=1 if Asian, =2 if Black, =3
if Native, =4 if White and =0 if others)
REGION Region of patient described by words (WEST, NORTHEAST,
MIDWEST and SOUTH)
REGION1 Region of patient described by numbers (=0 if WEST, =1
if NORTHEAST, =2 if MIDWEST and =3 if SOUTH)
EDUC Level of education received described by words (LHIGHSC,
HIGHSCH and COLLEGE)
EDUC1 Level of education received described by numbers (=0 if lower than
high school, =1 if high school and =2 if college)
MARISTAT Married status of patients described by words (NEVMAR,
MARRIED, WIDOWED and DIVSEP)
MARISTAT1 Married status of patients described by words (=0 if never married,
=1 if married, =2 if widowed and =3 if divorced or seperated)
INCOME Income compared to poverty line described by words (POOR,
NPOOR, LINCOME, MINCOME and HINCOME)
INCOME1 Income compared to poverty line described by numbers (=0 if poor,
=1 if near poor, =2 if low income, =3 if middle income and =4 if
high income)
PHSTAT Self-rated physical health status described by words (EXCE, VGOO,
GOOD, FAIR and POOR)
PHSTAT1 Self-rated physical health status described by numbers (=0 if
excellent, =1 if very good, =2 if good, =3 if fair and =4 if poor)
INDUSCLASS Industry each patient belongs to
Source: Medical Expenditure Panel Survey (MEPS).
11
Table 9
Example of the first five observations:
AGE ANYLIMIT COLLEGE HIGHSCH GENDER MNHPOOR insure USC UNEMPLOY MANAGEDCARE famsize
1 30 0 0 0 0 0 0 0 0 0 3
2 56 1 0 1 0 0 1 1 1 1 3
3 55 1 1 0 0 0 1 1 0 0 2
4 47 0 1 0 1 0 1 1 0 0 2
5 50 0 1 0 1 0 1 1 1 1 1
COUNTIP EXPENDIP COUNTOP EXPENDOP RACE RACE1 REGION REGION1 EDUC EDUC1
1 0 0.00 0 0.00 WHITE 4 MIDWEST 2 LHIGHSC 0
2 0 0.00 5 2384.56 BLACK 2 SOUTH 3 HIGHSCH 1
3 2 16121.45 42 29729.56 WHITE 4 MIDWEST 2 COLLEGE 2
4 0 0.00 4 110.00 BLACK 2 NORTHEAST 1 COLLEGE 2
5 0 0.00 43 3298.95 WHITE 4 WEST 0 COLLEGE 2
MARISTAT MARISTAT1 INCOME INCOME1 PHSTAT PHSTAT1 INDUSCLASS
1 MARRIED 1 MINCOME 3 EXCE 0 TRANSINFO
2 MARRIED 1 MINCOME 3 GOOD 2
3 MARRIED 1 HINCOME 4 EXCE 0 NATRESOURCE
4 MARRIED 1 HINCOME 4 FAIR 3
5 DIVSEP 3 LINCOME 2 GOOD 2
12
Table 10. Hong Kong Horse Racing
The race track is a fascinating example of financial market dynamics at work. From racing
forms, newspapers and so on, there are many explanatory variables that are publicly
available that might help us predict whether a horse wins. Some candidate variables may
include the age of the horse, recent track performance of the horse and jockey, pedigree
of the horse, and so on. These variables are assessed by the investors present at the
race, the betting crowd. Like many financial markets, it turns out that one of the most
useful explanatory variable is the crowd’s overall assessment of the horse’s abilities. These
assessments are not made based on a survey of the crowd, but rather based on the wagers
placed. Information about the crowd’s wagers is available on a large sign at the race called
the tote board. The tote board provides the odds of each horse winning a race and the odds
can be readily converted to the crowd’s assessment of the probabilities of winning.
Here we consider data from 925 races run in Hong Kong from September, 1981 through
September, 1989. In each race, there were ten horses, one of whom was randomly selected
to be in the sample. In the data, the response variable FINISH is the indicator of a
horse winning a race and the explanatory variable WIN is the crowd’s a priori probability
assessment of a horse winning a race.
File Name: Number of Number of
HKHorse obs: 925 variables: 2
Number of
Variable Obs Missing Description
FINISH Indicator of a horse winning a race
WIN Crowd’s a priori probability assessment of a horse winning a race
Source: Frees (1996).
Table 10
Example of the first five observations:
FINISH WIN
1 0 0.04387264
2 0 0.10525265
3 0 0.17812790
4 0 0.13731299
5 0 0.02147788
13
Table 11. Hospital Costs
ThedatawerefromtheNationwideInpatientSampleoftheHealthcareCostandUtilization
Project(NIS-HCUP),anationwidesurveyofhospitalcostsconductedbytheUSAgencyfor
HealthcareResearchandQuality(AHRQ).WerestrictconsiderationtoWisconsinhospitals
and analyze a random sample of n = 500 claims from 2003 data. Although the data comes
from hospital records, it is organized by individual discharge and so we have information
about the age and gender of the patient discharged. Specifically, we consider patients aged
0-17 years. We will use these data to consider the frequency of hospitalization. The data
will also be used to model the severity of hospital charges, by age and gender.
File Name: Number of Number of
HospitalCosts obs: 500 variables: 6
Number of
Variable Obs Missing Description
AGE Age of the patient discharged
FEMALE Binary variable that indicates if the patient is female
LOS Length of stay, in days
RACE 1 Race
TOTCHG Hospital discharge costs
APRDRG All patients refined diagnosis related group
Source: Nationwide Inpatient Sample of the Healthcare Cost and Utilization Project (NIS-HCUP),
conducted by the US Agency for Healthcare Research and Quality (AHRQ).
Table 11
Example of the first five observations:
AGE FEMALE LOS RACE TOTCHG APRDRG
1 17 1 2 1 2660 560
2 17 0 2 1 1689 753
3 17 1 7 1 20060 930
4 17 1 1 1 736 758
5 17 1 1 1 1194 754
14
Table 12. Initial Public Offering (IPO)
As a financial analyst, one wishes to convince a client of the merits of investing in firms
thathavejustenteredastockexchange, asanIPO(initialpublicoffering). Thus, wegather
data on 116 firms that priced during the six-month time frame of January 1, 1998 through
June 1, 1998. By looking at this recent historical data, we are able to compute RETURN,
the firm’s one-year return (in percent).
We are also interested in looking at financial characteristics of the firm that may help us
understand (and predict) the return. We initially examine REVENUE, the firm’s 1997
revenues in millions of dollars. Unfortunately, this variable was not available for six firms.
Thus, only 110 firms that have both REVENUES and RETURNS.
File Name: Number of Number of
IPO obs: 116 variables: 6
Number of
Variable Obs Missing Description
COMPANY Name of the company
TICKER Ticker symbol
RETURN The firm’s one-year return (in percent)
REV 6 The firm’s revenues in millions of dollars
LnREV 6 Logarithm of revenues
PRICEIPO Initial price of the stock
Source: .
Table 12
Example of the first five observations:
COMPANY TICKER RETURN REV LnREV PRICEIPO
1 Inktomi Corp. INKT 4.333333333 5.785000 1.755268 18
2 IBS Interactive IBSX 2.458333333 2.741000 1.008323 6
3 Frontline Communications Corp. FCCN 2.09375 0.098699 -2.315680 4
4 MIPS Technologies MIPS 2.080357143 40.307000 3.696525 14
5 Broadcom Corp. BRCM 1.921875 36.955000 3.609701 24
15
Table 13. Stock Market Liquidity
An investor’s decision to purchase a stock is generally made with a number of criteria in
mind. First, investors usually look for a high expected return. A second criterion is the
riskiness of a stock which can be measured through the variability of the returns. Third,
manyinvestorsareconcernedwiththelengthoftimethattheyarecommittingtheircapital
with the purchase of a security. Many income stocks, such as utilities, regularly return
portions of capital investments in the form of dividends. Other stocks, particularly growth
stocks, return nothing until the sale of the security. Thus, the average length of investment
in a security is another criterion. Fourth, investors are concerned with the ability to sell the
stockatanytimeconvenienttotheinvestor. Werefertothisfourthcriterionastheliquidity
of the stock. The more liquid is the stock, the easier it is to sell. To measure the liquidity,
in this study we use the number of shares traded on an exchange over a specified period
of time (called the VOLUME). We are interested in studying the relationship between the
volume and other financial characteristics of a stock.
We begin this study with 123 companies whose options were traded on December 3, 1984.
ThestockdatawereobtainedfromFrancisEmoryFitch, Inc. fortheperiodfromDecember
3, 1984 to February 28, 1985.
File Name: Number of Number of
Liquidity obs: 123 variables: 9
Number of
Variable Obs Missing Description
AVGT Average time between transactions, in minutes
VOLUME Three months total trading volume, in millions of shares
NTRAN Three months total number of transactions
PRICE Opening stock price on January 2, 1985, in U.S. dollars
SHARE Number of outstanding shares on December 31, 1984, in millions of shares
VALUE Market equity value obtained by taking the product of PRICE and SHARE
DEBEQ Debt-to-equity ratio, financial leverage
TIC Company ticker symbol
COMPANY Company name
Source: Francis Emory Fitch, Inc., Standard & Poor’s Compustat, and
University of Chicago’s Center for Research on Security Prices.
Table 13
Example of the first five observations:
AVGT VOLUME NTRAN PRICE SHARE VALUE DEBEQ TIC COMPANY
1 3.452 16.221 6273 37.250 81.141 3.002 0.897 AA ALUMINUM CO AMER
2 13.561 5.693 1548 22.500 27.088 0.609 6.394 AAL ALEXANDER & ALEX SVCS
3 2.884 11.965 7582 21.000 189.680 4.007 1.792 AEP AMERICAN ELEC PWR INC
4 5.674 3.834 3771 24.375 13.492 0.325 3.089 AGE EDWARDS AG INC
5 2.909 13.235 7434 28.750 72.600 2.087 0.644 AHS AMERICAN HOSP SUPPLY
16
Table 14. Massachusetts Bodily Injury
Rempala and Derrig (2005) considered claims arising from automobile bodily injury insur-
ance coverages. These are amounts incurred for outpatient medical treatments that arise
from automobile accidents, typically sprains, broken collarbones and the like. The data
consists of a sample of claims from Massachusetts that were closed in 2001 (by “closed”,
we mean that the claim is settled and no additional liabilities can arise from the same acci-
dent). Rempala and Derrig were interested in developing procedures for handling mixtures
of “typical” claims, and those from providers who reported claims fraudulently. For this
sample, we consider only those “typical” claims, ignoring the potentially fraudulent ones.
Potentially fraudulent claims are from provider=A, our analysis consists of claims from
“Other” providers.
File Name: Number of Number of
MassBodilyInjury obs: 348 variables: 5
Number of
Variable Obs Missing Description
Rownum Identification of the claim
claims Claims arising from automobile bodily injury insurance coverages
provider Health care provider is either “A” or “Other”
providerA Binary variable indicating the presence of “Other” provider
logclaims Logarithm of claims
Source: Rempala and Derrig (2005).
Table 14
Example of the first five observations:
ID claims provider providerA logclaims
1 1 0.045 Other 1 -3.101
2 2 0.047 Other 1 -3.058
3 3 0.070 Other 1 -2.659
4 4 0.075 Other 1 -2.590
5 5 0.077 Other 1 -2.564
17
Table 15. Insurance Company Expenses
Like every other business, insurance companies seek to minimize expenses associated with
doing business in order to enhance profitability. To study expenses, we examine a random
sample of 500 insurance companies from the National Association of Insurance Commis-
sioners (NAIC) database of over 3,000 companies. The NAIC maintains one of the world’s
largest insurance regulatory databases; we consider here data that is based on 2005 annual
reports for all the property and casualty insurance companies in United States. The annual
reports are financial statements that use statutory accounting principles.
File Name: Number of Number of
NAICExpense obs: 384 variables: 15
Number of
Variable Obs Missing Description
COMPANY NAME Name of the company
GROUP Indicates if the company is affiliated
MUTUAL Indicates if the company is a mutual company
STOCK Indicates if the company is a stock company
RBC Risk-Based Capital
EXPENSES Total expenses incurred, in millions of dollars
STAFFWAGE Annual average wage of the insurer’s administrative staff,
in thousands of dollars
AGENTWAGE 19 Annual average wage of the insurance agent, in thousands of dollars
LONGLOSS Losses incurred for long tail lines, in millions of dollars
SHORTLOSS Losses incurred for short tail lines, in millions of dollars
GPWPERSONAL Gross premium written for personal lines, in millions of dollars
GPWCOMM Gross premium written for commercial lines, in millions of dollars
ASSETS Net admitted assets, in millions of dollars
CASH Cash and invested assets, in millions of dollars
LIQUIDRATIO The ratio of the liquid assets to the current liabilities level
Source: National Association of Insurance Commissioners (NAIC).
Table 15
Example of the first five observations:
COMPANY_NAME GROUP MUTUAL STOCK RBC EXPENSES
1 Tift Area Captive Ins Co 0 0 1 228184000 0.0008019802
2 Alliance Of Nonprofits For Ins RRG 0 0 0 1627708000 0.0044878635
3 GA Timber Harvesters Mut Captive 0 1 0 422907000 0.0019045075
4 American Natl Lloyds Ins Co 1 0 0 652906000 0.0022909382
5 Chubb Natl Ins Co 1 0 1 8124624000 0.0182956574
STAFFWAGE AGENTWAGE LONGLOSS SHORTLOSS GPWPERSONAL GPWCOMM ASSETS
1 84.40508 77.46100 0.0001873308 0.000000000 0.00000000 0.001375438 0.002949942
2 81.56754 84.87802 0.0027822909 0.000000000 0.00000000 0.012272512 0.022170349
3 84.40508 77.46100 0.0010121463 0.001329539 0.00000000 0.005028351 0.004617343
4 82.49788 75.71071 0.0000000000 0.002979557 0.02954504 0.001986159 0.043719914
5 79.26495 78.24790 0.0107939577 0.011777314 0.04061412 0.058094479 0.144773034
CASH LIQUIDRATIO
1 0.003258406 110.45661
2 0.019760347 89.12961
3 0.003499702 75.79472
4 0.040934885 93.62984
5 0.138424153 95.61460
18
Table 16. Outlier Example
This data set we considered here is a fictitious data set of 19 points plus three points,
labeledA,B,andC.Thinkofthefirst19pointsas“good”observationsthatrepresentsome
type of phenomena. We want to investigate the effect of adding a single aberrant point.
File Name: Number of Number of
OutlierExample obs: 22 variables: 3
Number of
Variable Obs Missing Description
X Explanatory variable
Y Response variable
CODES Codes for type of point: 0 if basic, 1 if an outlier, 2 if an influential
point that is not an outlier and 3 if an outlier that is influential
Source: Author calculations.
Table 16
Example of the first five observations:
X Y CODES
1 1.5 3.0 0
2 1.7 2.5 0
3 2.0 3.5 0
4 2.2 3.0 0
5 2.5 3.1 0
19
Table 17. Refrigerator Prices
What characteristics of a refrigerator are important in determining its price (PRICE)? We
consider here several characteristics of a refrigerator, including the size of the refrigerator in
cubic feet (RSIZE), the size of the freezer compartment in cubic feet (FSIZE), the average
amount of money spent per year to operate the refrigerator (ECOST, for “energy cost”),
the number of shelves in the refrigerator and freezer doors (SHELVES), and the number of
features(FEATURES).Thefeaturesvariableincludesshelvesforcans,see-throughcrispers,
ice makers, egg racks and so on.
Both consumers and manufacturers are interested in models of refrigerator prices. Other
things equal, consumers generally prefer larger refrigerators with lower energy costs
that have more features. Due to forces of supply and demand, we would expect con-
sumers to pay more for these refrigerators. A larger refrigerator with lower energy costs
that has more features at the similar price is considered a bargain to the consumer.
How much extra would the consumer be willing to pay for this additional space? A
model of prices for refrigerators on the market provides some insight to this question.
File Name: Number of Number of
Refrigerator obs: 37 variables: 8
Number of
Variable Obs Missing Description
PRICE Price of a refrigerator
ECOST Average amount of money spent per year to operate the refrigerator
RSIZE Size of the refrigerator in cubic feet
FSIZE Size of the freezer compartment in cubic feet
SHELVES Number of shelves in refrigerator and freezer doors
S SQ FT Amount of shelf space, measured in square feet
FEATURES Number of features
BRANDNAM Brand name of the refrigerator
Source: Consumer Reports, 1992, July. “Refrigerators: A Comprehensive Guide to the Big White Box”.
Table 17
Example of the first five observations:
PRICE ECOST RSIZE FSIZE SHELVES S.SQ.FT FEATURES BRANDNAM
1 595 75 12.8 5.7 3 25.4 2 Admiral
2 685 75 12.9 5.7 3 26.7 1 Admiral
3 535 67 13.3 4.5 1 24.0 6 Amana
4 600 67 13.2 4.5 3 23.5 5 Amana
5 605 67 13.3 4.5 3 24.0 3 Amana
20
Table 18. Risk Managers Cost Effectiveness
The data for this study were provided by Professor Joan Schmit and are discussed in
more detail in the paper, “Cost effectiveness of risk management practices,” Schmit and
Roth (1990). The data are from a questionnaire that was sent to 374 risk managers of
large U.S.-based organizations. The purpose of the study was to relate cost effectiveness
to management’s philosophy of controlling the company’s exposure to various property
and casualty losses, after adjusting for company effects such as size and industry type.
File Name: Number of Number of
RiskSurvey obs: 73 variables: 7
Number of
Variable Obs Missing Description
FIRMCOST The measure of the firm’s risk management cost effectiveness, defined as
total property and casualty premiums and uninsured losses as a percentage
of total assets
ASSUME Per occurrence retention amount as a percentage of total assets
CAP Indicates that the firm owns a captive insurance company
SIZELOG Logarithm of total assets
INDCOST A measure of the firm’s industry risk
CENTRAL A measure of the importance of the local managers in choosing the amount
of risk to be retained
SOPH A measure of the degree of importance in using analytical tools
Source: Schmit and Roth (1990).
Table 18
Example of the first five observations:
FIRMCOST ASSUME CAP SIZELOG INDCOST CENTRAL SOPH
1 3.29 0.29 1 9.55 0.32 1 25
2 9.31 0.89 0 8.04 0.33 2 24
3 4.07 1.67 0 7.90 0.34 2 15
4 6.94 1.21 0 8.10 0.34 1 16
5 5.35 0.28 0 7.74 0.09 3 18
21
Table 19. Singapore Automobile Claims
Frees and Valdez (2008) investigated hierarchical models of Singapore driving experience.
Here we examine in detail a subset of their data, focusing on 1993 counts of automobile
accidents. The purpose of the analysis is to understand the impact of vehicle and driver
characteristics on accident experience. These relationships provide a foundation for an ac-
tuary working in ratemaking, that is, setting the price of insurance coverages.
The data are from the General Insurance Association of Singapore, an organization consist-
ing of general (property and casualty) insurers in Singapore (see the organization’s website:
www.gia.org.sg). From this database, several characteristics are available to explain auto-
mobile accident frequency. These characteristics include vehicle variables, such as type and
age, as well as person level variables, such as age, gender and prior driving experience.
File Name: Number of Number of
SingaporeAuto obs: 7483 variables: 15
Number of
Variable Obs Missing Description
SexInsured Gender of insured, including male (M), female(F) and unspecified (U)
Female =1 if female, =0 otherwise
VehicleType The type of vehicle being insured, such as automobile (A),
truck (T), and motorcycle (M)
PC =1 if private vehicle, =0 otherwise
Clm Count Number of claims during the year
Exp weights Exposure weight or the fraction of the year that the policy is in effect
LNWEIGHT Logarithm of exposure weight
NCD No Claims Discount. This is based ont he previous accident
record of the policyholder.
The higher the discount, the better is the prior accident record.
AgeCat The age of the policyholder, in years grouped into seven categories.
0-6 indicate age groups 21 and younger, 22-25, 26-35, 36-45, 46-55,
56-65, 66 and over, respectively
VAgeCat The age of the vehicle, in years, grouped into seven categories.
0-6 indicate groups 0, 1, 2, 3-5, 6-10, 11-15, 16 and older, respectively
AutoAge0 =1 if private vehicle and VAgeCat = 0, =0 otherwise
AutoAge1 =1 if private vehicle and VAgeCat = 1, =0 otherwise
AutoAge2 =1 if private vehicle and VAgeCat = 2, =0 otherwise
AutoAge =1 if Private vehicle and VAgeCat = 0, 1 or 2, =0 otherwise
VAgecat1 VAgeCat with categories 0, 1, and 2 combined
Source: Frees and Valdez (2008).
Table 19
Example of the first five observations:
SexInsured Female VehicleType PC Clm_Count Exp_weights LNWEIGHT NCD AgeCat
1 U 0 T 0 0 0.6680356 -0.40341383 30 0
2 U 0 T 0 0 0.5667351 -0.56786326 30 0
3 U 0 T 0 0 0.5037645 -0.68564629 30 0
4 U 0 T 0 0 0.9144422 -0.08944106 20 0
5 U 0 T 0 0 0.5366188 -0.62246739 20 0
AutoAge0 AutoAge1 AutoAge2 AutoAge VAgeCat VAgecat1
1 0 0 0 0 0 2
2 0 0 0 0 0 2
3 0 0 0 0 0 2
4 0 0 0 0 0 2
5 0 0 0 0 0 2
22
Table 20. Swedish Motor Insurance
These data were compiled by the Swedish Committee on the Analysis of Risk Premium in
Motor Insurance, summarized in Hallin and Ingenbleek (1983) and Andrews and Herzberg
(1985). The data are cross-sectional, describing third party automobile insurance claims
for the year 1977.
The outcomes of interest are the number of claims (the frequency) and sum of payments
(theseverity), inSwedishkroners. Outcomesarebasedon5categoriesofdistancedrivenby
avehicle, brokendownby7geographiczones, 7categoriesofrecentdriverclaimsexperience
and9typesofautomobile. Eventhoughthereare2,205potentialdistance, zone, experience
and type combinations (5 × 7 × 7 × 9 = 2,205), only n = 2,182 were realized in the 1977
data set.
File Name: Number of Number of
SwedishMotorInsurance obs: 2182 variables: 7
Number of
Variable Obs Missing Description
Kilometres Distance driven by a vehicle, grouped into five categories
Zone Graphic zone of a vehicle, grouped into 7 categories
Bonus Driver claim experience, grouped into 7 categories
Make The type of a vehicle
Insured The number of policyholder years.
A “policyholder year” is the fraction of the year that the
policyholder has a contract with the issuing company.
Claims Number of claims
Payment Sum of payments
Source: Hallin and Ingenbleek (1983) and Andrews and Herzberg (1985).
Table 20
Example of the first five observations:
Kilometres Zone Bonus Make Insured Claims Payment
1 1 1 1 1 455.13 108 392491
2 1 1 1 2 69.17 19 46221
3 1 1 1 3 72.88 13 15694
4 1 1 1 4 1292.39 124 422201
5 1 1 1 5 191.01 40 119373
23
Table 21. Term Life Insurance
Like all firms, life insurance companies continually seek new ways to deliver products to
the market. Those involved in product development wish to know “who buys insurance
and how much do they buy?” Analysts can readily get information on characteristics of
current customers through company databases. Potential customers, those that do not
have insurance with the company, are often the main focus for expanding market share.
we examine the Survey of Consumer Finances (SCF), a nationally representative sample
that contains extensive information on assets, liabilities, in- come, and demographic
characteristics of those sampled (potential U.S. customers). We study a random sample of
500 households with positive incomes that were in- terviewed in the 2004 survey.
For term life insurance, the quantity of insurance is measured by the policy FACE, the
amount that the company will pay in the event of the death of the named insured. Charac-
teristics that will turn out to be important include annual INCOME, the number of years
ofEDUCATIONofthesurveyrespondentandthenumberofhouseholdmembers,NUMHH.
File Name: Number of Number of
TermLife obs: 500 variables: 18
Number of
Variable Obs Missing Description
GENDER Gender of the survey respondent
AGE Age of the survey respondent
MARSTAT Marital status of the survey respondent (=1 if married,
=2 if living with partner, and =0 otherwise)
EDUCATION Number of years of education of the survey respondent
ETHNICITY Ethnicity
SMARSTAT Marital status of the respondent’s spouse
SGENDER Gender of the respondent’s spouse
SAGE Age of the respondent’s spouse
SEDUCATION Education of the respondent’s spouse
NUMHH Number of household members
INCOME Annual income of the family
TOTINCOME Total income
CHARITY Charitable contributions
FACE Amount that the company will pay in the event of the death
of the named insured
FACECVLIFEPOLICIES Face amount of life insurance policy with a cash value
CASHCVLIFEPOLICIES Cash value of life insurance policy with a cash value
BORROWCVLIFEPOL Amount borrowed on life insurance policy with a cash value
NETVALUE Net amount at risk on life insurance policy with a cash value
Source: Survey of Consumer Finances (SCF).
24
Table 21
Example of the first five observations:
GENDER AGE MARSTAT EDUCATION ETHNICITY SMARSTAT SGENDER SAGE SEDUCATION NUMHH INCOME
1 1 30 1 16 3 2 2 27 16 3 43000
2 1 50 1 9 3 1 2 47 8 3 12000
3 1 39 1 16 1 2 2 38 16 5 120000
4 1 43 1 17 1 1 2 35 14 4 40000
5 1 61 1 15 1 2 2 59 12 2 25000
TOTINCOME CHARITY FACE FACECVLIFEPOLICIES CASHCVLIFEPOLICIES BORROWCVLIFEPOL
1 43000 0 20000 0 0 0
2 0 0 130000 0 0 0
3 90000 500 1500000 0 0 0
4 40000 0 50000 75000 0 5
5 1020000 500 0 7000000 300000 5
NETVALUE
1 0
2 0
3 0
4 0
5 0
25
Table 22. National Life Expectancies
Who is doing health care right? Health care decisions are made at the individual, corporate
and government levels. Virtually every person, corporation and government have their own
perspective on health care; these different perspectives result in a wide variety of systems
for managing health care. Comparing different health care systems help us learn about
approaches other than our own, which in turn help us make better decisions in designing
improved systems.
Here, we consider health care systems from n = 185 countries throughout the world. As a
measureofthequalityofcare, weuseLIFEEXP,thelifeexpectancyatbirth. Thereare185
countries consider in this study, not all countries provided information for each variable.
Data not available are noted under the column “Number Missing”.
File Name: Number of Number of
UNLifeExpectancy obs: 185 variables: 15
Number of
Variable Obs Missing Description
REGION Categorical variable for region of the world
COUNTRY The name of the country
LIFEEXP Life expectancy at birth, in years
ILLITERATE 14 Adult illiteracy rate, % aged 15 and older
POP 1 2005 population, in millions
FERTILITY 4 Total fertility rate, births per woman
PRIVATEHEALTH 1 2004 Private expenditure on health, % of GDP
PUBLICEDUCATION 28 Public expenditure on education, % of GDP
HEALTHEXPEND 5 2004 Health expenditure per capita, PPP in USD
BIRTHATTEND 7 Births attended by skilled health personnel (%)
PHYSICIAN 3 Physicians per 100,000 people
SMOKING 88 Prevalence of smoking, (male) % of adults
RESEARCHERS 95 Researchers in R & D, per million people
GDP 7 Gross domestic product, in billions of USD
FEMALEBOSS 87 Legislators, senior officials and managers, % female
Source: United Nations Human Development Report, available at http://hdr.undp.org/en/.
Table 22
Example of the first five observations:
REGION COUNTRY LIFEEXP ILLITERATE POP FERTILITY PRIVATEHEALTH
1 4 Afghanistan 42.9 72.0 25.1 7.5 3.7
2 7 Albania 76.2 1.3 3.2 2.2 3.7
3 1 Algeria 71.7 30.1 32.9 2.5 1.0
4 6 Angola 41.7 32.6 16.1 6.8 0.4
5 3 Antigua and Barbuda 73.9 14.2 0.1 NA 1.4
PUBLICEDUCATION HEALTHEXPEND BIRTHATTEND PHYSICIAN SMOKING RESEARCHERS GDP
1 NA 19 14 19 NA NA 7.3
2 2.9 339 98 131 60 NA 8.4
3 NA 167 96 113 32 NA 102.3
4 2.6 38 45 8 NA NA 32.8
5 3.8 516 100 17 NA NA 0.9
FEMALEBOSS
1 NA
2 NA
3 NA
4 NA
5 45
26
Table 23. Nursing Home Utilization
The nursing home data are provided by the Wisconsin Department of Health and Fam-
ily Services (DHFS). The State of Wisconsin Medicaid program funds nursing home care
for individuals qualifying on the basis of need and financial status. As part of the condi-
tions for participation, Medicaid-certified nursing homes must file an annual cost report to
DHFS, summarizing the volume and cost of care provided to all of its residents, Medicaid-
funded and otherwise. These cost reports are audited by DHFS staff and form the basis for
facility-specific Medicaid daily payment rates for subsequent periods. The data are publicly
available; see http://dhfs.wisconsin.gov/provider/prev-yrs-reports-nh.htm for more infor-
mation.
The DHFS is interested in predictive techniques that provide reliable utilization forecasts
to update their Medicaid funding rate schedule of nursing facilities. The data here is in
cost report years 2000 and 2001. There are 362 facilities in 2000 and 355 facilities in 2001.
Typically, utilization of nursing home care is measured in patient days (“patient days” is
the number of days each patient was in the facility, summed over all patients).
File Name: Number of Number of
WiscNursingHome obs: 717 variables: 12
Number of
Variable Obs Missing Description
hospID Hospital identification number
CRYEAR Cost report year
TPY Total patient years
NUMBED Number of beds
SQRFOOT 10 Square footage of the nursing home
MSA Metropolitan Statistical Area code, 1-13, 0 for rural
URBAN 1 if urban, 0 if rural
PRO 1 if for profit, 0 for non-profit
TAXEXEMPT 1 if tax-exempt
SELFFUNDINS 1 if self-funded for insurance
MCERT 1 if Medicare certified
ORGSTR 1 for profit, 2 for tax-exempt, 3 for governmental unit
Source: Rosenberg et al. (2008).
Table 23
Example of the first five observations:
ID CRYEAR TPY NUMBED SQRFOOT MSA URBAN PRO TAXEXEMPT SELFFUNDINS MCERT ORGSTR
1 101 2000 16.48087 18 10.861 0 0 0 1 0 0 2
2 103 2000 59.24590 63 19.782 0 0 0 0 1 1 3
3 105 2000 49.63661 54 26.868 1 1 1 0 1 1 1
4 107 2000 51.87432 60 26.319 0 0 0 1 1 1 2
5 108 2000 94.56011 104 30.700 10 1 1 0 0 1 1
27
Table 24. Wisconsin Hospital Costs
Identifying predictors of hospital charges can provide direction for hospitals, government,
insurers and consumers in controlling these factors that in turn leads to better control of
hospital costs. We study the impact of various predictors on hospital charges in the state
of Wisconsin. The data for the year 1989 were obtained from the Office of Health Care
Information, Wisconsin’s Department of Health and Human Services. Cross sectional data
are used, which details the 20 diagnosis related group (DRG) discharge costs for hospitals
in the state of Wisconsin, broken down into nine major health service areas and three types
of payer (Fee for service, HMO, and other). Even though there are 540 potential DRG, area
and payer combinations (20×9×3 = 540), only 526 combinations were actually realized
in the 1989 data set. Other predictor variables included the logarithm of the total number
of discharges (NO DSCHG) and total number of hospital beds (NUM BEDS) for each
combination. The response variable is the logarithm of total hospital charges per number
of discharges (CHGNUM).
File Name: Number of Number of
WiscHospCosts obs: 526 variables: 9
Number of
Variable Obs Missing Description
TOT CHG Hospital discharged costs
HSA Health service area
A variable that categorizes Wisconsin into nine areas
DRG Diagnostic related group, a classification code to label the reason
for hospital care
PAYER The type of payer, 1 if fee-for-service, 2 if health maintenance
organization, and 3 otherwise
NO DSCHG Number of patients discharged from the hospital
POPLN Size of the area population
NUM EDS Number of hospital beds, a measure of capacity
INCOME Average income within the area, a measure of the ability to pay
for hospital utilization
CHG NUM Hospital discharged costs per patient
Source: Office of Health Care Information, Wisconsin Department of Health and Human Services.
Table 24
Example of the first five observations:
TOT_CHG HSA DRG PAYER NO_DSCHG POPLN NUM_BEDS INCOME CHG_NUM
1 5810558 1 14 1 1164 869000 3256 10355 4991.888
2 463455 1 14 2 65 869000 3256 10355 7130.077
3 585057 1 14 3 91 869000 3256 10355 6429.198
4 5004093 1 89 1 1084 869000 3256 10355 4616.322
5 254151 1 89 2 60 869000 3256 10355 4235.850
28
Table 25. Wisconsin Lottery Sales
State of Wisconsin lottery administrators are interested in assessing factors that affect
lottery sales. This data set described a sample of 50 geographic areas (zip codes) containing
sales data on the Wisconsin state lottery (SALES). Sales consists of online lottery tickets
that are sold by selected retail establishments in Wisconsin. These tickets are generally
pricedat$1.00,sothenumberofticketssoldequalsthelotteryrevenue. Weanalyzeaverage
lottery sales (SALES) over a forty-week period, April, 1998 through January, 1999, from
fifty randomly selected areas identified by postal (ZIP) code within the state of Wisconsin.
File Name: Number of Number of
WiscLottery obs: 50 variables: 10
Number of
Variable Obs Missing Description
ZIP Zip code within the state of Wisconsin
PERPERHH Persons per household
MEDSCHYR Median years of schooling
MEDHVL Median home value in $1000s for owner-occupied homes
PRCRENT Percent of housing that is renter-occupied
PRC55P Percent of population that is 55 or older
HHMEDAGE Household median age
MEDINC Estimated median household income, in $1000s
SALE Online lottery sales to individual consumers
POP Population, in thousands
Source: Frees and Miller (2003).
Table 25
Example of the first five observations:
ZIP PERPERHH MEDSCHYR MEDHVL PRCRENT PRC55P HHMEDAGE MEDINC SALES POP
1 53003 3.0 12.6 71.3 21 38 48 54.2 1285.400 435
2 53033 3.2 12.9 98.0 6 28 46 70.7 3571.450 4823
3 53038 2.8 12.4 58.7 25 35 45 43.6 2407.037 2469
4 53059 3.1 12.5 65.7 24 29 45 51.9 1223.825 2051
5 53072 2.6 13.1 96.7 32 27 42 63.1 15046.400 13337
29
Table 26. Workers Compensation
We consider a standard example in worker’s compensation insurance, examining losses
due to permanent, partial disability claims. The data are from Klugman (1992), who
considers Bayesian model representations, and are originally from the National Council on
Compensation Insurance. We consider n=121 occupation, or risk, classes, over T=7 years.
To protect the data source, further information on the occupation classes and years is not
available. Source: Frees, E. W., Young, V. and Y. Luo (2001). Case studies using panel
data models. North American Actuarial Journal, 4, No. 4, 24-42.
File Name: Number of Number of
WiscLottery obs: 847 variables: 4
Number of
Variable Obs Missing Description
CL Occupation class identifier, 1-124
YR Year identifier, 1-4
PR Payroll, a measure of exposure to loss, in tens of millions of dollars
LOSS Losses related to permanent partial disability, in tens of millions of dollars
Source: Klugman (1992).
Table 26
Example of the first five observations:
CL YR PR LOSS
1 1 21798086 538707
1 2 22640528 439184
1 3 22572010 1059775
1 4 24789710 560013
1 5 25876764 1004997
30
Table 27. Euro Exchange Rates
The exchange rate that we consider is the amount of Euros that one can purchase for one
U.S. dollar. We have T = 699 daily observations from the period April 1, 2005 through
January 8, 2008. These data were obtained from the Federal Reserve (H10 report).
Note: The data are based on noon buying rates in New York from a sample of market
participants and they represent rates set for cable transfers payable in the listed currencies.
These are also the exchange rates required by the Securities and Exchange Commission for
the integrated disclosure system for foreign private issuers.
File Name: Number of Number of
EuroExchange obs: 699 variables: 3
Number of
Variable Obs Missing Description
date Calendar date
exhkus The number of Hong Kong dollars that one can purchase for one U.S.
dollar
exeuus The number of Euro dollars that one can purchase for one U.S. dollar
Source: Federal Reserve Bank of New York.
Table 27
Example of the first five observations:
date exhkus exeuus
1 04/01/05 7.7989 0.7754
2 04/04/05 7.7991 0.7789
3 04/05/05 7.7995 0.7787
4 04/06/05 7.7993 0.7771
5 04/07/05 7.7990 0.7748
31
Table 28. Hong Kong Exchange Rates
For travelers and firms, exchange rates are an important part of the monetary economy.
The exchange rate that we consider here is the number of Hong Kong dollars that one can
purchase for one U.S. dollar. We have T = 502 daily observations for the period April 1,
2005 through May 31, 2007 that were obtained from the Federal Reserve (H10 report).
File Name: Number of Number of
HKExchange obs: 502 variables: 3
Number of
Variable Obs Missing Description
DATE Calendar date
EXHKUS The number of Hong Kong dollars that one can purchase for one U.S.
dollar
EXEUROUS The number of Euro dollars that one can purchase for one U.S. dollar
Source: Foreign Exchange Rates (Federal Reserve, H10 report).
Table 28
Example of the first five observations:
DATE EXHKUS EXEUROUS
1 1-Apr-05 7.7989 0.7754
2 4-Apr-05 7.7991 0.7789
3 5-Apr-05 7.7995 0.7787
4 6-Apr-05 7.7993 0.7771
5 7-Apr-05 7.7990 0.7748
32
Table 29. Inflation Bond Prices
Beginning in January of 2003, the US Treasury Department established an inflation bond
index that summarizes the returns on long-term bonds offered by the Treasury Department
that are inflation-indexed. For a treasury inflation protected security (TIPS), the principal
of the bond is indexed by the (three month lagged) value of the (non-seasonally adjusted)
consumer price index. The bond then pays a semi-annual coupon at a rate determined at
auction when the bond is issued. The index that we examine is the unweighted average of
bid yields for all TIPS with remaining terms to maturity of 10 or more years (Source:US
Treasury). Monthly values of the index from January 2003 through March 2007 are consid-
ered, for a total of T = 51 returns.
File Name: Number of Number of
InflationBond obs: 51 variables: 2
Number of
Variable Obs Missing Description
date Calendar date
INFBOND Inflation Bond Index that summarizes the returns on long-term bonds
offered by the Treasury Department that are inflation-indexed
Source: US Treasury.
Table 29
Example of the first five observations:
date INFBOND
1 31-Jan-03 2.72
2 28-Feb-03 2.50
3 31-Mar-03 2.52
4 30-Apr-03 2.72
5 31-May-03 2.40
33
Table 30. Labor Force Participation Rate
Labor force participation rate (LFPR) forecasts, coupled with forecasts of the population,
provide us with a picture of a nation’s future workforce. This picture provides insights to
the future workings of the overall economy, and thus LFPR projections are of interest to a
number of government agencies. In the United States, LFPRs are projected by the Social
Security Administration, the Bureau of Labor Statistics, the Congressional Budget Office
and the Office of Management and Budget. In the context of Social Security, policy-makers
use labor force projections to evaluate proposals for reforming the Social Security system
and to assess its future financial solvency.
The labor force participation rates are the civilian labor force divided by the civilian non-
institutional population. These data are compiled by the Bureau of Labor Statistics. For
illustration purposes, we examine a specific demographic cell and show how to forecast it -
forecasts of other cells may be found in Fullerton (1999) and Frees (2006). Specifically, we
examine 1968-1998 for females, aged 20-44, living in a household with a spouse present and
at least one child under six years of age.
File Name: Number of Number of
LaborForcePR obs: 31 variables: 3
Number of
Variable Obs Missing Description
TIME Time, 1, ..., 31
YEAR Calendar year
MSC6U Labor Force Participation Rates for females aged 20-24, living in a
household with a spouse present and at least one child under six years
of age
Source: Census Bureau.
Table 30
Example of the first five observations:
TIME YEAR MSC6U
1 1 1968 0.2778812
2 2 1969 0.2868593
3 3 1970 0.3065709
4 4 1971 0.2981785
5 5 1972 0.3053743
34
Table 31. Medical Component of the CPI
The CPI is a breadbasket of goods and services whose price is measured by the Bureau of
Labor Statistics. By measuring this breadbasket periodically, consumers get an idea of the
steadyincreaseinpricesovertimewhich,amongotherthings,servesasaproxyforinflation.
The CPI itself is composed of many components, reflecting the relative importance of each
component to the overall economy. Here, we study the medical component of the CPI,
the fastest growing part of the overall breadbasket since 1967. The data we consider are
quarterly values of the medical component of the CPI (MCPI) over a sixty year period from
1947 to the first quarter of 2007, inclusive. Over this period, the index rose from 13.3 to
346.0. This represents a twenty-six fold increase over the sixty year period which translates
roughly into a 1.36% quarterly increase.
File Name: Number of Number of
MedCPISmooth obs: 241 variables: 10
Number of
Variable Obs Missing Description
yearInt Calendar year
Month The last month of the quarter
Quarter Number of quarter
value Quarterly values of the medical component of the CPI (MCPI)
PerMEDCPI 1 Quarterly increase of the medical component of the CPI, in percent
YEAR Year plus a fraction for the quarter
MCPISM4 1 Medical component of consumer’s price index, smoothed with k=4
MCPISM8 1 Medical component of consumer’s price index, smoothed with k=8
MCPISMw 2 1 Medical component of consumer’s price index, smoothed with w=.2
MCPISMw 8 1 Medical component of consumer’s price index, smoothed with w=.8
Source: Bureau of Labor Statistics.
Table 31
Example of the first five observations:
yearInt Month Quarter value PerMEDCPI YEAR MCPISM4 MCPISM8 MCPISMw_2 MCPISMw_8
1 1947 3 1 13.3 NA 1947.167 NA NA NA NA
2 1947 6 1 13.5 1.504 1947.417 1.504 1.504 1.504 1.504
3 1947 9 1 13.7 1.481 1947.667 1.493 1.493 1.486 1.499
4 1947 12 1 13.9 1.460 1947.917 1.482 1.482 1.465 1.491
5 1948 3 1 14.1 1.439 1948.167 1.471 1.471 1.444 1.481
35
Table 32. Medicare Hospital Costs
We consider T=6 years, 1990-1995, of data for inpatient hospital charges that are covered
by the Medicare program. The data were obtained from the Health Care Financing Admin-
istration,BureauofDataManagementandStrategy. Toillustrate, in1995thetotalcovered
charges were 157.8 billions for twelve million discharges. For this analysis, we use state as
the subject, or risk class. Thus, we consider n=54 states that include the 50 states in the
Union, the District of Columbia, Virgin Islands, Puerto Rico and an unspecified ”other”
category.
File Name: Number of Number of
Medicare obs: 324 variables: 9
Number of
Variable Obs Missing Description
STATE State identifier, 1-54
YEAR Year identifier, 1-6
TOT CHG Total hospital charges, in millions of dollars.
COV CHG Total hospital charges covered by Medicare, in millions of dollars.
MED REIM Total hospital charges reimbursed by the Medicare program, in millions
of dollars.
TOT D Total number of hospitals stays, in days.
NUM DSHG Number discharged, in thousands.
AVE T D Average hospital stay per discharge in days.
NMSTATE Name of the state.
Source: Frees, Young, and Luo (2001)
Table 32
Example of the first five observations:
STATE YEAR TOT_CHG COV_CHG MED_REIB TOT_D NUM_DCHG AVE_T_D NMSTATE
1 1 1 2211617271 2170240349 972752944 1932673 230015 8 AL
2 1 2 2523987347 2468263759 1046016144 1936939 234739 8 AL
3 1 3 2975969979 2922611694 1205791592 2016354 245027 8 AL
4 1 4 3194595003 3149745611 1307982985 1948427 243947 8 AL
5 1 5 3417704863 3384305357 1376211788 1926335 258384 7 AL
36
Table 33. Prescription Drug Prices
WeconsideraseriesfromtheStateofNewJersey’sPrescriptionDrugProgram,thecostper
prescription claim. This monthly series is available over the period August, 1986 through
March, 1992, inclusive. It shows that the series is clearly nonstationary, in that cost per
prescription claims are increasing over time. There are a variety of ways of handling this
trend. One may begin with a linear trend in time and include lag claims to handle auto-
correlations. For this series, a good approach to the modeling turns out to be to consider
the percentage changes in the cost per claim series.
File Name: Number of Number of
PrescriptionDrug obs: 68 variables: 10
Number of
Variable Obs Missing Description
PAID CLM Monthly paid prescription claims paid by the New Jersey Prescription
Drug Program
NPRESCRP Number of prescription claims
TIME Sequence number, time
MONTH Month
COST CLM Cost per claim, defined to be (PAID CLM)/NPRESCRP
RATEC C 1 Rate of change of the cost per claim as a percentage, defined by
100*[(current COST CLM/previous COST CLM)-1]
SINET The sine function evaluated at TIME
COST The cosine function evaluated at TIME
SINE2T The sine function evaluated at 2*TIME
COS2T The cosine function evaluated at 2*TIME
Source: Frees (1995).
Table 33
Example of the first five observations:
PAID_CLM NPRESCRP TIME MONTH COST_CLM RATEC_C SINET COST
1 992300 68213 1 8 14.54708 NA 0.5000000 8.660254e-01
2 1143249 77920 2 9 14.67209 0.8593202 0.8660254 5.000000e-01
3 935150 63179 3 10 14.80160 0.8826852 1.0000000 -4.371140e-08
4 962309 65855 4 11 14.61254 -1.2772441 0.8660254 -5.000001e-01
5 1106053 77364 5 12 14.29674 -2.1611750 0.5000001 -8.660254e-01
SINE2T COS2T
1 8.660254e-01 0.5000000
2 8.660254e-01 -0.5000001
3 -8.742280e-08 -1.0000000
4 -8.660254e-01 -0.4999999
5 -8.660254e-01 0.4999999
37
Table 34. Standard and Poor’s 500 Daily
Thesedataconsistsofthe1759dailyreturnsforthecalendaryears2000through2006ofthe
Standard and Poor’s (S&P) value weighted index. Each year, there are about 250 days on
which the exchange is open and stocks were traded - on weekends and holidays it is closed.
For each trading day an average of the closing, or last, price of various stocks were taken to
form the S&P equally weighted index for that day. There are several indices to measure the
market’s overall performance. The value weighted index is created by assuming that the
amount invested in each stock is proportional to its market capitalization. Here, the mar-
ket capitalization is simply the beginning price per share times the number of outstanding
shares.
Financial economic theory states that if the market were predictable, many investors would
attempt to take advantage of these predictions, thus forcing unpredictability. For example,
suppose a statistical model reliably predicted mutual fund A to increase two-fold over the
next 18 months. Then, the no arbitrage principle in financial economics states that several
alertinvestors, armed withinformation fromthe statisticalmodel, wouldbidto buymutual
fund A, thus causing the price to increase because demand is increasing. These alert in-
vestors would continue to purchase until the price of mutual fund A rose to the point where
the return was equivalent to other investment opportunities in the same risk class. Any
advantagesproducedbythe statisticalmodelwoulddisappearrapidly, thuseliminatingthis
advantage.
Thus, financial economic theory states that for liquid markets such as stocks represented
through the S&P index there should be no detectable patterns, resulting in a white noise
process. In practice, it has been found that cost of buying and selling equities (called trans-
actions costs) are large enough so as to prevent us from taking advantage of these slight
tendencies in the swings of the market. This illustrates a point known as statistically sig-
nificant but not practically important. This is not to suggest that statistics is not practical
(heavens forbid!). Instead, statistics in and of itself does not explicitly recognize factors,
such as economic, psychological and so on, that may be extremely important in any given
situation. It is up to the analyst to interpret the statistical analysis in light of these factors.
File Name: Number of Number of
SP500Daily obs: 1759 variables: 2
Number of
Variable Obs Missing Description
caldt Calendar date
vwretd The Standard and Poor’s 500 daily value weighted return
Source: Center for Research on Security Prices, University of Chicago.
Table 34
Example of the first five observations:
caldt vwretd
1 20000103 -0.0093845450
2 20000104 -0.0384355500
3 20000105 0.0008613558
4 20000106 -0.0028339380
5 20000107 0.0321512800
38
Table 35. Standard and Poor’s 500 Quarterly
Animportanttaskofafinancialanalystistoquantifycostsassociatedwithfuturecashflows.
We consider here funds invested in a standard measure of overall market performance, the
Standard and Poor’s (S&P) 500 Composite Index. The goal is to forecast the performance
of the portfolio for discounting of cash flows. In particular, we examine the S&P Composite
Quarterly Index for the years 1936 to 2007, inclusive.
File Name: Number of Number of
SP500Quarterly obs: 284 variables: 5
Number of
Variable Obs Missing Description
YEAR Year
SPINDEX The Standard and Poor’s (S&P) 500 Composite Index
DIFFINDEX The difference of the SPINDEX between this year and last year
LNSPINDEX The natural logarithm of SPINDEX
DIFFLNSP The difference of LNSPINDEX between this year and last year
Source: Center for Research on Security Prices, University of Chicago.
Table 35
Example of the first five observations:
YEAR SPINDEX DIFFINDEX LNSPINDEX DIFFLNSP
1 1936.166667 14.92000008 0 2.7027026 0
2 1936.416667 14.84000015 -0.079999923 2.697326248 -0.005376352
3 1936.666667 16.01000023 1.170000076 2.773213541 0.075887293
4 1936.916667 17.18000031 1.170000076 2.843745934 0.070532393
5 1937.166667 17.92000008 0.739999771 2.885917412 0.042171477
39
Table 36. Auto Industry
The data represent industry aggregates for private passenger auto liability/medical cover-
ages from year 2004, in millions of dollars. They are based on insurance company annual
statements, specifically, Schedule P, Part 3B. The elements of the triangle represent cumu-
lative net payments, including defense and cost containment expenses.
File Name: Number of Number of
IndustryAuto obs: 55 variables: 3
Number of
Variable Obs Missing Description
Incurral Year The year in which a claim has been incurred
Development Year The number of years from incurral to the time when the payment is
made
Claim Cumulative net payments, including defense and cost containment
expenses
Source: Wacek (2007).
Table 36
Example of the first five observations:
Incurral Year Development Year Claim
1 1995 1 17674
2 1996 1 18315
3 1997 1 18606
4 1998 1 18816
5 1999 1 20649
40
Table 37. Medical Care
These data for 36 months of medical care payments, from January 2001 through December
2003, inclusive. These are payments for medical care coverage with no deductible nor
coinsurance. There were relatively low co-payments, such as $10 per visit. The payments
exclude prescription drugs that typically have a shorter payment pattern compared with
other medical claims.
File Name: Number of Number of
MedicalCare obs: 390 variables: 4
Number of
Variable Obs Missing Description
Members Total number of members
Month The month in which a claim has been incurred
Delay The number of months from incurral to the time when the payment is made
Payments The payments excluding prescription drugs that typically have a shorter
payment pattern compared with other medical claims
Source: Gamage et al. (2007).
Table 37
Example of the first five observations:
Members Month Delay Payments
1 11154 1 1 180
2 11118 2 1 5162
3 11070 3 1 42263
4 1106 4 1 20781
5 11130 5 1 20346
41
Table 38. Reinsurance General Liability
The data originate from the 1991 edition of the ”Historical Loss Development Study” pub-
lished by the Reinsurance Association of American (page 91). These data have been widely
used to illustrate triangle methods, beginning with Mack (1994) and later by England and
Verrall (2002). These data are from automatic facultative reinsurance business in general
liability (excluding asbestos and environmental) coverages. (Under a facultative basis, each
risk is underwritten by the reinsurer on its own merits.) The data contains data for years
1981-1990, inclusive.
File Name: Number of Number of
ReinsGenLiab obs: 55 variables: 3
Number of
Variable Obs Missing Description
Incurral Year The year in which a claim has been incurred
Development Year The number of years from incurral to the time when the payment is made
Claim Incremental incurred losses in thousands of US dollars
Source: The Reinsurance Association of American.
Table 38
Example of the first five observations:
Incurral Year Development Year Claim
1 1 1 5012
2 2 1 106
3 3 1 3410
4 4 1 5655
5 5 1 1092
42
Table 39. Reinsurance General Liability 2004
The data is an excerpt from Braun (2004) that is based on the 2001 edition ”Historical Loss
Development Study” published by the Reinsurance Association of American. The data
contains data for years 1987-2000, inclusive.
File Name: Number of Number of
ReinsGL2004 obs: 105 variables: 3
Number of
Variable Obs Missing Description
Incurral Year The year in which a claim has been incurred
Development Year The number of years from incurral to the time when the payment is made
Claim Incremental incurred losses from 1995-2000, in thousands of US dollars
Source: The Reinsurance Association of American.
Table 39
Example of the first five observations:
Incurral Year DevelopmentYear Claim
1 1987 1 59966
2 1988 1 49685
3 1989 1 51914
4 1990 1 84937
5 1991 1 98921
43
Table 40. Singapore Auto Injury
The data contain payments from a portfolio of automobile policies for a Singapore property
and casualty (general) insurer. Payments, deflated for inflation, are for third party injury
from comprehensive insurance policies. The data are for policies with coverages from 1993-
2001, inclusive.
File Name: Number of Number of
SingaporeInjury obs: 45 variables: 3
Number of
Variable Obs Missing Description
Month The month in which a claim has been incurred
Delay The number of months from incurral to the time when the payment is
made
Payments Incremental payments, deflated for inflation, for third party injury from
comprehensive insurance policies.
Source: Frees and Valdez (2008).
Table 40
Example of the first five observations:
Year Delay Payment
1 1993 1 14695
2 1994 1 153615.21
3 1995 1 24741.26
4 1996 1 68630.4
5 1997 1 29177.17
44
Table 41. Singapore Auto Property Damage
The data report incremental payments from a portfolio of automobile policies for a Singa-
pore property and casualty (general) insurer. Here, payments are for third party property
damage from comprehensive insurance policies. All payments have been deflated using a
Singaporean consumer price index, so they are in constant dollars. The data are for policies
with coverages from 1997-2001, inclusive.
File Name: Number of Number of
SingaporeProperty obs: 15 variables: 3
Number of
Variable Obs Missing Description
Year The year in which a claim has been incurred
Delay The number of years from incurral to the time when the payment is
made
Payments Incremental payments, deflated for inflation, for third party property
damage from comprehensive insurance policies.
Source: Frees and Valdez (2008).
Table 41
Example of the first five observations:
Year Delay Payments
1 1997 1 1188675
2 1998 1 1235401.82
3 1999 1 2209849.65
4 2000 1 2662545.97
5 2001 1 2457265.33
