Matching Estimation, Casino Gambling and the …rate of growth of consumer spending on casino...

Matching Estimation, Casino Gambling and the Quality of Life

Michael Wenz

Department of Economics and Finance Winona State University

310 Somsen Hall Winona, MN 55987 [email protected]

507-452-5698 Abstract: Little consensus exists in the literature as to the impact of casino gambling on regional economic development. This paper uses a propensity score matching estimator to assess the bottom line impact of casino gambling on the welfare of local residents. It extends the literature in two important ways. First, the traditional matching estimation model is extended to consider a kernel weighting formula that corrects for correlation between the outcome error term and characteristics of the regressors used in generating the propensity scores. Second, by using the matching procedure to control for selection bias in the casino location decision, this paper generates improved estimates for the impact of casino gambling on key economic variables and on local quality of life. Casinos are found to have no statistically significant net impact on the quality of life in their host counties, though Native American casinos do generate some additional economic activity in the form of increased population, employment, and housing starts. JEL Codes: O12, R1, R13, R58 I gratefully acknowledge support from the U.S. Department of Housing and Urban Development Doctoral Dissertation Research Grant Program. This paper was prepared during my time as a graduate student at University of Illinois at Chicago. I am thankful also for helpful comments from Dan McMillen, Barry Chiswick, Joe Persky, Gib Bassett, John Tauras and Josh Linn. Any errors are my own.

1

Introduction

A primary challenge in assessing the economic impact of an event or a policy is the

construction of a counterfactual for identifying whether the outcome would have occurred but for

the event. The construction of an appropriate counterfactual is essential if one hopes to attribute

causation to the event. One method of developing a counterfactual is by using propensity score

matching. This method will be applied here to the case of casino gambling.

Little consensus exists in the literature as to the bottom line social welfare impact

associated with casino gambling1. The nonrandom nature of site selection by governments and

casino operators suggests that simply comparing outcomes across the treated (casino) group and

the nontreated (non-casino) control group of regions will suffer from selection bias. Propensity

score matching involves pairing each observation in the treatment group with a matched

observation constructed from the control group in a way that eliminates selection bias, and

comparing the difference in outcomes between the two groups. The traditional matching

estimator will be extended to consider bias introduced by correlations between observed

characteristics used in the propensity score model and measured outcomes. It will be used to

assess the impact of casinos on key economic variables, and to relate these measures to welfare

and quality of life.

Casinos may have a positive impact on the quality of life by increasing economic profits,

tax revenues, or consumer surplus, and may negatively impact quality of life by creating

externalities through increased incidence of problem or pathological gambling. Prior research

suggests that casinos are associated with increases in economic activity (Evans and Topoleski

2002) and increases in crime (Grinols and Mustard, 2006), but previous work has struggled to 1 See, for example, Grinols and Mustard (2001), Walker and Barnett (1999), Walker (2003).

2

assess the bottom line impact of casinos on communities. This study applies a hedonic pricing

model using data from the 1990 and 2000 census to calculate the implicit willingness to pay to

live near a casino. The key results indicate that on net, casinos neither raise nor lower the quality

of life in their host county, though Native American casinos do generate increased economic

activity as measured by employment, housing starts, and population. These results are robust to

a number of different specifications of the matching estimator.

This paper begins with a brief history of casino gambling in the United States. The

second section extends the quality of life model developed by Roback (1982) to consider casino

gambling. The third section discusses matching estimation. The fourth section discusses the

data used in constructing the propensity score and the matched outcomes. The fifth section

presents the results of the model under a number of different specifications and extends the

matching estimator to correct for a specific form of potential bias. The final section concludes.

A brief history of casino gambling

In 1988, Congress passed the Indian Gaming Regulatory Act (IGRA), which explicitly

outlined the terms of legalized gambling on reservations. This act followed a series of

contentious legal battles between states and Indian reservations surrounding tribal attempts to

open casinos and high-stakes bingo parlors. The IGRA removed much of the uncertainty

surrounding the legality of casino gambling, and marked the beginning of a widespread

expansion of gambling on both Native American and on non-Native American lands. By 2000,

29 states were home to casino-style gambling.

Though gambling has long been legal in 48 states, mostly in the form of state-sponsored

lotteries, casino-style gambling has largely been prohibited. In 1976, Atlantic City, NJ joined the

3

state of Nevada as the second jurisdiction in the United States with legalized casino-style

gambling. Around this time, a handful of Native American tribes operated high-stakes bingo

parlors, notably the Penobscot Tribe of Maine, which opened a high-stakes bingo parlor in 1973,

and the Seminoles of Florida, which opened a high-stakes bingo parlor in 1978. These

establishments met with resistance from state governments, who filed several lawsuits attempting

to put an end to gambling on reservations. Most importantly, the case of California v. Cabazon

and Morongo Bands of Mission Indians went to the U. S. Supreme Court, which ruled in 1987

that if states allow a particular form of gambling within the state, they have no ability to regulate

that form of gambling on tribal lands.

It was in response to this decision that congress passed the IGRA (Evans and Topoleski

2002). The IGRA identifies three classes of gaming:

Class I: Social games for prizes of minimal value and traditional forms of Indian gaming

engaged in as part of tribal ceremonies or celebrations.

Class II: Bingo and games similar to it such as pull-tabs, tip jars, and certain non-

banking card games.

Class III: All other forms of gaming including banking card games, slot machines, craps,

parimutuel horse racing, dog racing, and lotteries. Casinos fall into this category.

Class I games are subject only to tribal regulation; Class II games are subject to tribal regulation

and oversight from the National Indian Gaming Commission (NIGC), and Class III games are

legal only if approved by the NIGC and agreed upon by a tribal-state compact. A tribal-state

compact can only permit Class III gaming of forms which are legal in some form in the state,

though the courts have given this a very loose interpretation. For instance, Connecticut allowed

non-profit organizations to host “Casino Nights” as fund raisers, and the Mashantucket Pequots

4

successfully used this as legal support for their efforts to open the largest casino in the world

(Evans and Topoleski 2002). Compacts generally restrict the size and scope of gaming

operations, as well as the types of gaming devices and games available. In some cases, they

include a payment to the state, often in exchange for the right to be the exclusive provider of

casino gambling.

Passage of the IGRA triggered rapid expansion of casino gambling, not just on Native

American lands, but all across the United States. Iowa legalized riverboat gambling in 1989, and

opened their first riverboat casino in 1991. In November of 1989, the mining town of

Deadwood, SD became the first place outside of Atlantic City and Nevada to open a non-Native

American casino. Gambling in Deadwood and in three mining towns in Colorado was limited to

historic buildings and placed strict limits on the size of a wager. In Deadwood, for instance, the

maximum wager is $100. Riverboat casinos were legalized in Illinois, Mississippi, Louisiana,

Missouri, and Indiana between 1990 and 19932, and New Orleans (1992) and Detroit (1996)

authorized land-based casinos as well. Outside Nevada, by 2000, there were 358 Class III style

casinos operating in 28 states. Of these, 176 were Native American and 182 were non-Native

American. A map of casino locations as of 2000 is displayed in Figure 1. By 2000, 189

counties had at least one operating casino, either Native American or non-Native American.

The rate of growth in casino locations has slowed, but expansion continues to be an

important political topic in many states, including Illinois, Minnesota, and Kentucky. Even as

the growth in the number of casinos has slowed, the number of gaming stations at each location

continues to increase, and casino-style gambling is expanding into race tracks. Additionally, the

2 Riverboats and cruising requirements appear to have been used in an attempt to protect customers from excessive gambling by using time constraints to limit their maximum loss on a particular excursion. Over time, cruising requirements have been relaxed or eliminated, and riverboats bear little practical distinction from land-based casinos. See Eadington (1999).

5

rate of growth of consumer spending on casino gambling remains high, growing from $16 billion

in 1995 to $24.5 billion in 2000, to $30.3 billion in 2005 (American Gaming Association 2006).

Understanding the economic impact of casino gambling remains an important issue.

Quality of life modeling and casinos

The primary goal of this paper is to obtain an estimate of the net benefit (or cost) of a

casino to its home region. As an alternative to the cost-benefit analysis used in previous

research, a hedonic quality of life model is used to infer the valuation of living in an area with a

casino. (1974) shows that a differentiated good can be expressed as a vector of its

characteristics. The price of good i depends on the marginal valuation of the good’s

characteristics:

Pi = P(s1, s2, …, sn) (1)

and δP/δsj represents the marginal implicit price of characteristic j. In the case of a house, the

characteristics may include, for instance, the physical features of the house, the level of local

public services and taxes, the risk of crime, and the weather. In particular, the social costs and

benefits associated with living near a casino will be characteristics that influence house prices,

and will have a corresponding implicit price.

Housing represents a differentiated good, and the implicit prices of its characteristics can

be determined in the method outlined by Rosen3. House prices differ across space, based on the

different quantities of characteristics available at each location. However, utility levels are

3 The use of hedonic models to value environmental amenities has a long history in the literature. See, for example, Palmquist (1984) and Greenstone and Chay (2005).

6

assumed to be constant across space. The implicit price of the social costs and benefits of a

casino is given by the equilibrium differential that allocates individuals among locations so that

utility levels across space are equal. If casinos provide a net benefit to nearby individuals, they

should be willing to pay higher house prices; otherwise, people could increase their utility by

moving to the region, placing upward pressure on land values and house prices in the region.

This differential represents the marginal willingness to pay for the bundle of amenities associated

with a casino.

Suppose that the amount of some characteristics (j, k,…) which enter into the hedonic

price function depend on the presence of a casino. Then the price of house i is

Pi = P(s1, s2, … sj(C), sk(C),…) (2)

and

δPi/δC = Σj (δPi/δsj)(δsj/δC) (3)

For illustrative purposes, let sj represent the amount of crime. Then term j represents the

increase in the level of crime associated with the casino times the implicit price of an incremental

increase in crime. In other words, it is the marginal willingness to pay to avoid the increase in

crime caused by the casino. To the extent that casinos impact other characteristics that influence

utility, their marginal impact is expressed in other terms in equation (3). Roback (1982) extends

the model to include the labor market, noting that both housing prices and wages work to

allocate people across space. The full implicit price of the amenity bundle, then, includes a term

for the impact of casinos on house prices and a term for the impact of casinos on wages.

7

Blomquist et. al. (1988) explicitly account for the fact that housing is produced using both land

and housing materials, so the full implicit price of the amenity bundle becomes

δPi/δC = H(dr/ds) – (dw/ds) (4)

where H represents the quantity of housing consumed, r represents land rent, w represents the

wage rate, and s is the vector of amenities influenced by the casino.

The advantage of the hedonic approach compared to traditional cost-benefit studies is that

it does not require the identification and measurement of an itemized list of costs and benefits.

Traditional cost-benefit analysis requires a measure of each term in equation (3) to compute an

estimate of costs and benefits, but the hedonic approach only requires the calculation of the

change in house prices and the change in wages, both of which are observable.

One difficulty with using a hedonic price function to estimate the implicit price of an

amenity such as casino gambling is the potential presence of unobserved characteristics that are

correlated with both the level of the amenity and housing prices. In particular, the casino

location decision is likely to be endogenous, and to the extent that the decision by communities

to supply casino gambling is influenced by unobservables which also affect house prices, the

hedonic estimates may be biased. The matching estimator employed here is designed to control

for this source of bias.

Matching as an empirical estimation strategy

The estimation strategy employed here will use a difference-in-differences approach in

the construction of a propensity score matching estimator. The goal is to identify the change in

8

quality of life due to the presence of a casino, which requires an estimate of the change in wages

and house prices in two states of the world, one with a casino (state 1) and one without (state 0).

The impact of the casino on a particular outcome is given by Yt,1 – Yt,0, where Yt,1 is the outcome

which would exist at time t in the presence of a casino, and Yt,0 is the outcome which would

prevail at time t without a casino. This second term is inherently unknowable, since at time t,

only one of the states is possible. One possible solution would be to compare the difference in

mean outcomes of each group, the casino group and the non-casino group, but this is problematic

for reasons outlined below.

The propensity score matching method was developed to address the problem of

measuring the true effect of a treatment on the treated when selection into the treatment group is

not random, but depends on the characteristics of the subject. For example, suppose two students

ask for extra assistance in preparation for an exam, but the teacher has time to help only one.

Suppose further that both students received a B on the exam. We might conclude that the extra

assistance did not help. If, however, we knew that the student who received help was selected to

receive help because their prior performance was C-level, compared to the B-level performance

of the student who was not selected, then we might conclude that in fact the extra assistance did

help. Propensity score matching provides a way to compare the outcomes of subjects with

similar probabilities of being selected into the treatment group—that is, to compare the

differences in outcomes of previously C-level students who received assistance with the

outcomes of other C-students who did not receive assistance. In the case of casino gambling, the

concern is that casinos endogenously locate in places which are good candidates for growth

otherwise, and that comparing them to a random sample of other places will yield a biased

estimate of the impact of casinos on local quality of life.

9

Construction of a difference-in-differences matching estimator is a two-step process

requiring repeated cross-sectional data on both casino locations and non-casino locations. The

first step in applying the estimator involves the construction of a propensity score based on the

determinants of selection into the treatment group. A parametric procedure such as logit

estimation is used to construct a propensity score for each observation, where the propensity

score represents the probability that an observation is selected into the treatment group.

Rosenbaum and Rubin (1983) show that under certain assumptions discussed below,

observations in the non-treatment group can be selected to provide an unbiased counterfactual to

use for comparisions. In the second step, observations in the treatment group are matched with

observations in the non-treatment group, and the difference in mean outcomes is computed.

Several methods have been proposed for matching observations, including the simple average

nearest neighbor estimator and the kernel regression matching estimator (Todd 1999). The

nearest neighbor method simply chooses one or a small number of observations that are closest

in propensity score to each member of the treatment group. These observations form the

comparison group, and the difference between the outcome of treated observation and the

average outcome of the comparison observations is the observed effect of the treatment. A

kernel regression estimator assigns different weights to each nearby non-treated observation

based on their distance from the treatment observation. This requires choosing a bandwidth from

which to choose the observations. In either case, the sensitivity of results to the choice of the

number of nearby observations or the appropriate bandwidth to use should be examined.

In choosing the model parameters to be used in constructing the propensity score, it is

important to be sure that these values are not influenced by the treatment (Heckman et. al., 1998,

Todd 1999). Using only the pre-treatment values for the variables in the construction of the

10

propensity score gives some confidence that the values have not been influenced by the

treatment4.

The outcome measures of interest are the mean change in house prices and the mean

change in earnings in matched pairs of casino and non-casino counties. A difference-in-

differences matching estimator assumes:

E(Yt,0 – Yt-1,0 | P(X), C=1) = E(Yt,0 – Yt-1,0 | P(X), C=0) (5)

and

0 < Pr (C=1| X) <1 (6)

where Yt,0 represents the outcome of an observation at time t who did not receive the treatment,

X is a vector of characteristics which influence selection, P(X) is the propensity score, and C is a

dummy variable indicating whether the observation received the treatment (a casino) or not

(Rosenbaum and Rubin 1983, Todd 1999). In other words, equation (8) says the expectation for

the outcome of a non-treated observation, conditional on P(X), is the same as the expectation for

a treated outcome conditional on P(X), had the treated subject not received the treatment. The

left-hand side of equation (8) is unobservable, though this is the desired comparison group. The

right-hand side of equation (8) is observable and provides the necessary counterfactual to

measure the effect of the treatment. This underscores the importance of the propensity score,

which is being relied upon to identify the suitability of comparisons. Heckman et. al.(1998)

demonstrate that with selection based on observed characteristics, estimation of the effect of

treatment on the treated does not depend on the choice of functional form or the distribution of

unobservables. The second step in the estimating process is thus reduced to a one-dimensional,

non-parametric estimation problem. The key assumption required comes in the first step in the

4 It is possible that house prices and wages move in anticipation of the opening of the casino, and that announcement dates would be more appropriate than opening dates. This would affect only a few observations in this study.

11

process, the assumption that the creation of the propensity score sufficiently captures the factors

which influence selection into the treatment group or the non-treatment group.

Equation (9) indicates that matching will not work for values of X that guarantee

selection with certainty into either the treatment group or the control group. This requires

investigation for regions of common support, where a value for X includes both observations

selected for treatment and observations which are not. It is unlikely that each observation in the

treatment group will share an identical set of X characteristics with an observation in the control

group, so this issue in practice reduces down to finding observations in one group that are nearby

in terms of propensity score distance to observations in the other group. Matching can lead to

some unintuitive pairs of observations. Suppose for instance that one county is very likely to

have a casino because it has a high concentration of Native Americans, while another is likely to

have a casino mostly because it has a low concentration of fundamentalist Christians. This can

lead to the matching of counties that are not necessarily similar to each other. It should be noted

that the matching estimator does not directly seek to match similar counties, but to create a

control distribution that closely resembles the treatment distribution. In essence, matching takes

a nonrandom experiment and randomizes it. The matching method is more appropriate when, for

each observation in the treatment group, there are many similar observations that did not receive

the treatment. Aside from the issue of overlapping support, a lack of potential comparison

observations in a propensity score range can lead to some observations being selected as

comparisons multiple times. This can lead to giving very large weight to a few observations.

These issues will be discussed below as they relate to the data used in this study.

12

Data

The construction of a matching estimator takes place in two steps. First, a propensity

score model assigns predicted probabilities of receiving the treatment to each observation, and

second, the treatment observations are matched with control observations to assess the impact of

the treatment. The difference-in-differences matching estimator can be employed with repeated

cross-sectional data. The data used here is from the 1990 and 2000 U.S. Census of Population.

The unit of observation is the county

The propensity score model used here is drawn directly from Wenz (2006, Table X, p.

58-59). The likelihood that a county will open a casino is linked to a number of factors,

including population, local attitudes toward gambling, characteristics of neighboring

communities, and the region of the country. A logit model constructed predicted probabilities

for the presence of a casino in each county. The model parameters are shown in Table 1, and

data definitions and sources are provided in Table 2.

Some interesting results from the propensity score model are presented in Table 3. Note

that Cook County, IL is the second-most likely county to open a casino among those that have

not. For at least the past six years, efforts to bring a casino to Cook County have been in the

works and are currently tied up in the courts. Aside from Starr County, TX, the rest are in states

with a heavy gaming presence. Starr County is generally an anomaly. Much of their propensity

score owes to a 40.8% unemployment rate, the highest recorded in the dataset. Of the counties

that have casinos despite low propensity scores, the general tendency is for them to be located in

states without much gaming, and far away from the population center of the state. Oneida, NY is

far away from New York City, for instance, and Swain County, NC is in a remote area at the

foothills of Smoky Mountain National Park in far western North Carolina. Table 4 outlines the

13

distribution of propensity scores across casino and non-casino counties. There is overlapping

support in all areas of the data, though it is much thinner when predicted probabilities are above

60%.

The variables needed for the quality of life analysis are the change in the county median

house price and the change in the county median income between the 1990 and 2000 Censuses.

The house price measure in the census is the respondent’s estimated house value, and the median

level is reported for each county. The income measure is the median income in 1989 and 1999

for households in the county. Other economic outcomes include the change in median rents, the

change in population, employment and housing units, and the number of new housing units

constructed.

As noted above, the possibility of feedback between the explanatory variables and the

treatment needs to be considered. One advantage of using a difference-in-differences approach

is the ability to use observed explanatory variables before the treatment. That is, the measures

that go into the construction of the propensity score can be viewed at pre-treatment levels. In the

propensity score model applied here, a few difficulties arise. First, it is difficult to pinpoint the

opening dates of Native American casinos. Some existed prior to passage of the IGRA, and

some existed as Class II gaming facilities before becoming casinos, and there is no readily

apparent way to verify the opening dates of casinos with certainty. What is known is that no

gaming compacts were signed prior to 1990, that there were only a small number of Native

casinos prior to 1990, and that the first non-Native casinos outside of Nevada and Atlantic City

opened in November of 1989 in Deadwood, SD. The estimation method used here treats all of

the counties in the dataset as if there were no casino in the county as of 1990. This approach

assumes that for the small number of casinos open prior to the taking of the 1990 census, the

14

casino did not impact the levels of the explanatory variables. It also assumes that variables do

not move in anticipation of a casino opening. This is not a problem for things like whether the

county is on a river, but casinos may possibly affect things like the unemployment rate and may

even affect things like the proportion of fundamentalist Christians in a region, though changes in

the religious makeup or voter attitudes in a region are likely to be very slow and not change

much in a year or two. With respect to the quality of life estimates, another concern is that house

prices move in anticipation of the opening of a casino, though it is difficult to imagine that in

early 1990 when the census was taken that residents had much information about how casinos

would affect house prices. In any case, it is likely that less than 10 of the 188 casino counties

would see any influence of the casino in either their explanatory variables or their outcome

variables.

Econometric Specification

A number of different ways of applying the matching estimator will be presented based

on this specification of the propensity score model from Wenz (2006) described above. The first

approach is to estimate this model on the full sample of counties and on three other subsamples,

and to create a one-to-one nearest neighbor match for each of the subsamples. The second

approach is to estimate the full model on the full sample of counties and to construct a distance-

weighted match for all of the observations within a bandwidth of 0.05. The third approach uses a

distance-weighted nearest neighbor method that fixes the number of observations to be used in

the comparison group, rather than the bandwidth. Finally, the model is estimated on the full

15

sample of counties with using a bandwidth of 0.10, but constraining the comparison observations

to come from the same census region and from similarly sized counties.

Single Nearest Neighbor Matching

The logit model developed in the preceeding chapter was used to construct propensity

scores for the full sample of counties. A simple one-to-one nearest neighbor match selected one

county from the treatment (casino) group and one from the control (non-casino) group. In most

instances, the control group match was simply the non-casino county with the propensity score

nearest to the propensity score of the casino county. One problem that arises from this approach

is that some control counties are the nearest neighbor to multiple treatment counties and would

thus receive disproportionately large weight in the analysis. In this study, there are many

observations to choose from that are very close neighbors even if not the closest

neighbor. Rather than limit the matches to the absolutely closest match, then, the following

method was used. All counties were sorted according to their propensity score. If two casino

counties shared the same control county as their nearest neighbor, the one with the closest

unused casino county was matched to the unused county, provided that the unused casino county

was closer than any other casino county. Otherwise, the closest county was simply used multiple

times. By using this method, 165 counties were chosen as comparisons for the 188 casino

counties, with one county used four times and 20 counties used twice as a control.

Once the comparison group was formed, mean differences in outcomes were computed

for the matched pairs. Of some concern in applying a matching estimator is the existence of

overlapping support. One paradoxical issue in applying matching estimators arises when noting

that a model which estimates treatment probabilities extremely well will sort the data into two

16

distinct groups that have little overlap in propensity scores. This issue comes into play

somewhat here. About 87% of non-casino counties have a predicted probability under 10%,

while only about 31% of casino counties fall in this region. Fortunately, there are 2876 non-

casino counties in the dataset, but only 188 casino counties so there are generally plenty of

counties for the control group. The longest distance between a treatment county and its match is

a propensity score distance of 0.0386, and the average distance is just 0.000051.

Results are provided in the first column of Table 5. The outcome measures are the

percentage changes in median home prices (MEDIANVALUE), median income

(MEDIANINCOME), median rent (MEDIANRENT), county population (POPULATION),

county employment (EMPLOYMENT), county housing units (UNITS), and housing units in the

county constructed since 2000 (NEWUNITS). This specification indicates that casinos are

associated with about a 3% increase in population, employment, and new housing units, while

impacts on incomes, house prices, and rents are not statistically significant. An examination of

the signs shows that house prices in casino counties fell relative to their control group, and that

incomes rose, suggesting that casinos are associated with a reduction in quality of life, but the

large variances suggest that this result should be interpreted with caution.

The logit model was estimated and propensity scores were generated for three

subsamples, with results presented in Table 5, Columns 2-4. The first subsample excluded

counties with only a non-Native American casino. There was still generally strong overlapping

support, with the largest matched distance increasing only to 0.0529 and the average distance

between matches at just 0.0010. The second subsample excluded counties with only a Native

American casino, and overlapping support was still generally good. The third subsample

includes counties with less than 100,000 people, and support is generally good with the

17

exception of Starr County, TX, mentioned above, whose nearest match is a probability distance

of 0.1262 away. Otherwise, the largest distance in propensity scores is 0.028. The results of

these three specifications generally find no statistically significant impact on the outcome

measures, except for a 5.7% increase in employment in non-Native counties.

Fixed bandwidth distance-weighted matching

One shortcoming of the one-to-one nearest neighbor matching method described above is

that it unnecessarily removes a great deal of information from the analysis by limiting the control

group to a small subset of observations. An alternative method is to choose a bandwidth for each

casino observation and use all control observations within that propensity score distance to form

the control group. A bandwidth of 0.05 was chosen, and for each observation in the control

group, a weight was placed on it so that observations closer to the casino county were given

heavier weight. A number of weighting methods have appeared in the literature (for example,

Heckman, Ichimura and Todd 1997, Todd 1999, McMillen 2004). This literature suggests that

weighting function should be chosen to ensure consistency in estimation and identifies a number

of appropriate weighting functions. The estimator chosen here is the biweight kernel. Weights

are given to each observation by the following kernel formula:

K=15/16(1 – (di/b)2)2 (7)

where di is the distance from the control observation to the treatment observation, and b is the

bandwidth. The weights are then normalized to sum to one for each observation. The

normalized weights are used to create a comparison observation for each treatment observation,

and estimation proceeds as above. In the dataset analyzed here, using this method assigns

18

positive weight to each non-casino county.5 At least two observations were used to create each

comparison observation, and in some cases, over 2000 observations fell within the bandwidth.

The results from this method are presented in Table 6. The mean differences in outcomes

are presented for the full sample, non-Native casino counties, and Native casino counties. In the

full sample, casinos significantly increase population, employment, and new construction, but it

is apparent from inspecting the last two columns of Table 6 that these increases are driven almost

entirely by the Native casino counties. The estimated impact of Native American casinos on

population, employment, housing units, and new housing units is positive and on the order of

magnitude of approximately 3-5%, while the impact of non-Native counties is negatively signed

and statistically insignificant. Non-Native counties see a statistically significant fall in house

prices on the order of about 8% and an insignificant, negative effect on wages. This is

inconsistent with an improvement in the quality of life.

Nearest neighbor distance-weighted matching

An alternative to a fixed bandwidth is to choose a fixed number of nearest neighbors and

allow the bandwidth to vary. Either a simple average or weighting method can be used to create

the comparison observations. In this case, the five nearest neighbors were used and a biweight

kernel placed heavier weight on the nearest observations. The largest bandwidth needed to find

five nearest neighbors was 0.21, and five counties required a bandwidth greater than 0.10.

Nearly all casino counties had a bandwidth of less than 0.01. Results from this approach are

presented in Table 7. This specification yields very similar results to the fixed bandwidth

approach. Population, employment, housing units, and new housing units all grow by a

5 This is not generally true, but is for this sample.

19

statistically significant amount of 3-5% in areas with Native American casinos, and house prices

fall in areas with non-Native casinos.

Split-kernel distance weighted matching

The assumption implicit in this approach so far is that errors are not correlated across

observations. A byproduct of this assumption is that comparison counties are sometimes not

intuitively appealing. For instance, in the one nearest neighbor matching method, the

comparison county for Orleans Parish, LA (New Orleans, population 484,000) is Apache

County, AZ, a geographically large, rural county with about 63,000 residents. If there are

differences in the impact of casinos on outcomes that are correlated across different groups of

counties, then placing additional restrictions on the matches can improve the estimator. Two

such groupings are examined here, region and county population. If there are regional

characteristics influencing outcomes that are not captured by the propensity score, forcing the

matches to come from the same region will eliminate the bias in the error term caused by

unobservables which are correlated with region. Additionally, if the size of the county

influences the outcome variables in some unobservable way, constraining the matches to come

from similarly sized counties will reduce the unobserved variables bias to the extent that the

unobservables are correlated with county size. The split kernel approach applied here loosely

follows McMillen (2004) and constrains the mean outcome to be constant across regions and

county sizes. This differs from the locally weighted regression model in McMillen (2004),

which allows effects to vary across different values of the explanatory variables and the locally

weighted regression model in Todd (1999), which allows the treatment effect to vary across

different values of the propensity score. The assumption here is that errors are correlated across

20

regions and county sizes, but the effect of casinos on outcomes does not vary across regions or

county sizes. An alternative weighting function is considered here.

The matching estimator works by calculating the mean impact of treatment on the treated,

where the observed treatment effect in each county is given by the following equation:

∆i = Yi – Yj (8)

Yi is the observed outcome in casino county i, and Yj is the observed outcome in matched

county j. Note that Yj is an amalgamation of outcomes from each county matched with county i

by the propensity score matching process. Assume Yi and and Yj are given by the following

functions:

Yi = f(Xi) + g(Ci) + εi (9)

and

Yj = f(Xj) + εj (10)

where f(X) represents non-casino impacts on the outcome, g(C) represents the casino impacts on

the outcome, and ε is an assumed independent random error. By using propensity score

matching, as shown by Rosenbaum and Rubin (1983), E[f(Xi) – f(Xj)] = 0, and g(Cj) = 0, since

the treatment counties do not have casinos. Then ∆i reduces down to the casino impact plus a

random error term.

Suppose however that the errors are not random, but systematic. In particular, suppose

that the errors are correlated by the geographic regions of the country. Then (9) and (10) become

Yi = f(Xi) + g(Ci) + µi + εi (9)’

and

Yj = f(Xj) + g(Cj) + µj + εj (10)’

where the µ’s are region-specific error terms. Then the estimated effect becomes

21

∆i = g(Ci) + (µi - µj) + (εi - εj). (11)

The term (µi - µj) represents bias that occurs from ignoring this correlation between outcomes

and regions.

One solution to this problem is to constrain the matched control counties to come from

the same region. Then µi = µj, and this bias is eliminated. To do that, the weighting function

needs to be modified to give zero weight to matched counties from other regions. This is fairly

straightforward. Define a function M(i,j) where M=1 if i and j are in the same region, and M=0

otherwise. Combining this with the biweight kernel function to place higher weights on

observations that are closer in propensity score yields the following weighting function.

W(i,j) = [15/16(1 – (dj/b)2)2] M(i,j). (12)

These weights are then normalized to sum to one for each match. This weighting function will

eliminate the bias present in equation (14). Any other correlations in the error term can be

corrected in identical fashion. In this case, define a function N(i,j) where N=1 if i and j are of

similar size, and N=0 otherwise. Then

W(i,j) = [15/16(1 – (dj/b)2)2] M(i,j) N(i,j) (13)

constrains matched counties to be of similar size and from the same region.

The cost of improving the estimator in this fashion is that the more constraints placed on

the matched counties, the more difficult it becomes to find regions of overlapping support.

In the first split-kernel specification, a bandwidth of 0.10 was used, with observations

weighted by a biweight kernel if they fell within the same region and given zero weight if they

did not. There were four counties which had no counties suitable for a match, so they were

dropped from the analysis. Each of the eliminated counties had a predicted probability of

between 67% and 90% of having a casino, which made the data for predicted probabilities above

22

67% somewhat sparse, but there were still 13 counties with casinos in this range. The results are

presented in Table 8. Again, Native American casinos generate economic activity in the form of

employment growth, population growth, and new housing units in their counties. In this

specification, housing prices fall across the board, but the impact on rents in non-Native casino

counties is positive, significant, and rather large at 5.6%.

An additional restriction was added to the model to force comparisons to come from

counties of similar size. This is particularly important because of the heterogeneity of casino

impacts in areas of different population density identified in Wenz (2006). Note that non-Native

casinos choose counties with much larger populations than the average non-casino county.

Constraining the matches to come from similarly sized counties ensures that the measured effects

are not a product of the differences in effects due to city size. Comparisons were restricted to

counties within 50% to 150% of the casino county population. Results are presented in Table 9.

In this specification, as in the others, the Native casinos have statistically significant and positive

impacts on employment, population, housing units and new housing units on the order of

magnitude of between 3% and 4%. Here, however, the impact on housing prices is insignificant

and positively signed. Non-Native casino counties tended to be much larger on average than

non-casino counties, so the comparisons tended to come from smaller counties. If smaller

counties saw house prices rise at a different rate than large counties, independent of the casino

location decision, then the fall in relative house prices would be a function of county size rather

than the casino. By constraining the matches to come from similarly sized counties, this

correlation between unmeasured characteristics and city size is removed. Additionally, and more

importantly, the negative relationship between non-Native casinos and house prices disappears in

this specification.

23

Conclusions and implications

Assessing the impact of casino gambling on economic outcomes requires some

understanding of what outcomes might have occurred had the casino not been present. The

method applied here to construct a counterfactual is that of propensity score matching.

Based on the probability of each county opening a casino, treatment (casino) counties were

paired with control group counties. The propensity scores play an important role in weighting

the control group in a way that makes it as if the treatment and control observations came from

the same underlying density function.

Propensity score matching can be implemented in a number of different ways, and it is

helpful to investigate whether the results are sensitive to the exact implementation method.

Here, the results are very consistent across the nearest neighbor method, the fixed bandwidth

method, and a split-kernel method developed in this paper that places additional restrictions on

the match. Native American casinos are positively and statistically significantly associated with

an increase in population, employment, and housing units in their counties. These measures

grow 3%-5% faster in non-Native counties than in native counties. In some specifications, non-

Native casinos were associated with falling housing prices, but when restricting the match group

to counties with similar population sizes, this effect disappeared. This restriction is important

and appropriate due to the heterogeneity of casino impacts by population.

Casinos do not have a discernable impact on quality of life. In the final model

specification, they do not significantly impact house prices, wages, or rents, though Native

American casinos do generate some additional economic activity.

24

References American Gaming Association. State of the States: The AGA Survey of Casino

Entertainment. Washington, D.C., 2006. Blomquist, G. C., Berger, M. C., and Hoehn, J. P.: New estimates of quality of life in

urban areas. American Economic Review. 78(1): 89-107, 1988. Eadington, W. R.: The economics of casino gambling. Journal of Economic

Perspectives. 13(3): 173-192, 1999. Evans, W. N. and Topoleski, J. H.: The social and economic impact of Native American

casinos. NBER Working Paper No. 9198, 2002. Grinols, E. L. and Mustard, D. B.: Casinos, Crime, and Community Costs. Review of

Economics and Statistics, 88(1): 28-45, 2006.

Grinols, E. L. and Mustard, D. B.: Business profitability versus social profitability: Evaluating industries with externalities, the case of casinos. Managerial and Decision Economics, 22: 143-162, 2001.

Gyuorko, J. and Tracy, J.: The structure of local public finance and the quality of life.

Journal of Political Economy 99(4): 774-806, 1991. Heckman, J.J., Ichimura, H. and Todd, P.: Matching as an econometric evaluation

estimator. Review of Economic Studies. 65(2): 261-294, 1998. McMillen, D.P.: Locally weighted regression and time-varying distance gradients. In:

Spatial Econometrics and Spatial Statistics. Getis, A., Mur, J., and Zoller, H. (eds.), pp. 232-249, New York, Palgrave Macmillan, 2004.

Roback, J.: Wages, rents, and the quality of life. Journal of Political Economy, vol.

90(6): 1257-1278, 1982. Rosen, S.: Hedonic prices and implicit markets: Product differentiation in pure competition. Journal of Political Economy. 82(1): 34-55, 1974. Rosenbaum, P.R. and Rubin, D.B.: The central role of the propensity score in

observational studies for causal effects. Biometrika. 70(1): 41-55, 1983. Todd, Petra. A Practical Guide to Implementing Matching Estimators. Unpublilshed

Manuscript, 1999. Walker, D. M.: Methodological issues in the social cost of gambling. Journal of

Gambling Studies. 19(2): 149-183, 2003.

25

Walker, D. M. and Barnett, A. H.: The social costs of gambling: An economic perspective.” Journal of Gambling Studies, 15(3):181-212, 1999.

Wenz, M. Casino Gambling and Economic Development. Ph.D. Dissertation, University of

Illinois at Chicago. 2006.

26

Figure 1. Map of casino locations in the United States as of the year 2000.

27

Table 1. Binomial logit coefficient estimates—full model

Parameter

(Std. Error) Marginal

Effect Dependent Variable: Any Casino

Intercept

-11.0957 (2.165)

***

MANUF

-0.0109 (0.015)

-0.0005

UNEMP

6.5704 (3.092)

**

0.2828

VACANCY

0.0276 (0.009)

***

0.0012

lnPOP

0.7496 (0.147)

***

0.0323

lnLANDAREA

0.2097 (0.156)

0.0090

URBANPCT

0.0025 (0.006)

0.0001

lnPOP50IN

-0.3880 (0.121)

***

-0.0167

lnPOP50OUT

0.0130 (0.019)

0.0006

NEARESTOUT

-0.0051 (0.002)

**

-0.0002

FISCAL

0.0022 (0.008)

0.0001

FISCALCHG

0.0014 (0.003)

0.0001

VOTEDEM

0.0259 (0.014)

*

0.0011

VOTEPEROT

0.0326 (0.026)

0.0014

CATHRELIG

0.0055 (0.007)

0.0002

FUNDRELIG

-0.0362 (0.011)

***

-0.0016

NATIVEPOP

0.0469 (0.009)

***

0.0020

COASTAL

1.0417 (0.257)

***

0.0448

28

Parameter

(Std. Error)

Marginal

Effect

RIVER

1.5386 (0.319)

***

0.0662

REASTNORTHCENTRAL

1.9018 (0.548)

***

0.0818

RWESTNORTHCENTRAL

2.3837 (0.575)

***

0.1026

RSOUTHATLANTIC

0.0591 (0.803)

0.0025

REASTSOUTHCENTRAL

2.3931 (0.752)

***

0.1030

RWESTSOUTHCENTRAL

1.3990 (0.669)

**

0.0602

RMOUNTAIN

2.1895 (0.636)

***

0.0942

RPACIFIC

3.4726 (0.590)

***

0.1494

Likelihood Ratio (R) 462.08

Upper Bound of R (U) 1413.5

McFadden's LRI 0.3269

*significant at the 90% confidence level; **significant at the 95% confidence level; ***significant at the 99% confidence level.

Source: Wenz, M. Casino Gambling and Economic Development. Ph.D. Dissertation, University of Illinois at Chicago, 2006.

29

Table 2. Data sources for casino location model. Variable Description Source CASINO Dummy variable

identifying whether there are any casinos in the county.

www.gamblinganswers.com, accessed October 2003.

UNEMP County Unemployment Rate 1990

U.S. Census of Population and Housing, 1990, Summary Tape File 3

MANUF % Employees in county employed in manufacturing industry, 1990


VACANCY % Vacant Housing Units, 1990


DENSITY Population per square mile, 1990


POP50IN Population for census block groups within 50 miles of the county, inside the same state, 1990.

U.S. Census of Population and Housing, 1990, Summary Tape File 1 and Summary Tape File 3

POP50IN Population for census block groups within 50 miles of the county, outside the same state, 1990.

U.S. Census of Population and Housing, 1990, Summary Tape File 1 and Summary Tape File 3

NEARESTIN Distance from county centroid to nearest casino outside the county and in the same state.

Casino locations from www.gamblinganswers.com; County Centroids computed using Maptitude computer software and TIGER/Line files from the U.S. Census.

NEARESTOUT Distance from county centroid to nearest casino outside the county and outside the same state.

Casino locations from www.gamblinganswers.com; County Centroids computed using Maptitude computer software and TIGER/Line files from the U.S. Census.

FISCAL Ratio of county government revenues-expenses/expenses

County and City Data Books. Retrieved February 2006 from the University of Virginia, Geospatial and Statistical Data Center: http://fisher.lib.virginia.edu/collections/stats/ccdb/.

Variable Description Source

30

FISCALCHG Percentage change in county expenditures, 1982-1987


VOTEPEROT Percentage of Ross Perot votes for President, 1992


VOTEDEM Percentage of Democratic votes for President, 1992


RELIG Percentage of county residents adhering to fundamentalist religions, 1990

Bradley, et.al. (1992). Churches and Church Membership in the United States, 1990. Accessed at the Association of Religious Data Archives, www.ARDA.com, accessed February 2006.

NATIVEAMER Percentage of county residents of American Indian/Alaska Native Race


Source: Wenz, M. Casino Gambling and Economic Development. Ph.D. Dissertation, University of Illinois at Chicago, 2006.

31

Table 3. Most and least likely counties to have casinos 10 Most Likely Counties Without A Casino Predicted Probability Imperial County, California 86.4%Cook County, Illinois 85.4%Lane County, Oregon 74.1%Starr County, Texas 69.3%Apache County, Arizona 68.6%Spokane County, Washington 66.6%Monterey County, California 63.5%Sonoma County, California 61.9%Rio Arriba County, New Mexico 61.6%Multnomah County, Oregon 56.1% 10 Most Likely Counties With A Casino Predicted Probability Los Angeles County, California 89.6%St. Louis County, Minnesota 89.3%King County, Washington 84.0%San Diego County, California 82.5%Humboldt County, California 81.5%St. Louis County, Missouri 73.0%San Bernardino County, California 69.9%Orleans Parish, Louisiana 67.8%Yuma County, Arizona 67.5%Riverside County, California 67.4% 10 Least Likely Counties With A Casino Predicted Probability Swain County, North Carolina 0.4%Ohio County, Indiana 0.4%Neshoba County, Mississippi 0.4%Massac County, Illinois 0.7%Gilpin County, Colorado 1.0%Allen Parish, Louisiana 1.1%Bossier Parish, Louisiana 1.3%Doniphan County, Kansas 1.9%Clarke County, Iowa 2.0%Oneida County, New York 2.1%

32

Table 4. Distribution of predicted probabilities in casino/non-casino counties.

Predicted Probability of Opening a Casino

Number of Counties With Casino

Number of Counties Without a Casino

<1% 5 1205 1-5% 18 974

5-10% 36 319 10-20% 32 212 20-40% 42 123 40-60% 35 34 60-70% 14 6 70-80% 1 1 80-90% 5 2

90-100% 0 0

33

Table 5. One nearest neighbor match

All Casino Counties

Native Casino Counties

Non-Native Casino

Counties

Small (<100,000)

Casino Counties

Mean Effect (t-statistic)




mdiffMEDIANVALUEpct -2.76% (-0.88)

-3.52% (-0.87)

1.07% (0.20)

0.09% (0.03)

mdiffMEDIANINCOMEpct 1.14% (0.86)

-0.12% (-0.07)

2.79% (1.08)

2.51% (1.40)

mdiffMEDIANRENTpct 1.25% (0.85)

0.08% (0.03)

0.14% (0.05)

0.43% (0.22)

mdiffPOPULATIONpct 3.23% (2.19)

* 1.97% (0.98)

2.22% (0.92)

1.50% (0.73)

mdiffEMPLOYMENTpct 3.14% (1.90)

* 1.48% (0.70)

5.74% (2.02)

* 2.38% (1.02)

mdiffUNITSpct 1.95% (1.44)

1.92% (1.07)

1.66% (0.87)

0.60% (0.34)

mdiffNEWUNITSpct 2.59% (2.08)

* 2.05% (1.25)

2.58% (1.33)

0.95% (0.57)

*Statistically significant at a 90% confidence level.

34

Table 6. Match with bandwidth=0.05, distance-weighted

All Casino Counties

Non-Native Casino Counties






-8.02% (-1.98)

* 1.23% (0.43)


-1.22% (-0.70)

1.79% (1.24)


2.69% (1.17)

-0.02% (-0.02)


* -1.29% (-0.59)

4.30% (3.25)

*


* -0.79% (-0.29)

4.99% (3.68)

*


-1.80% (-1.06)

2.85% (2.31)

*


* -1.20% (-0.70)

3.27% (3.00)

*


35

Table 7. Match with 5 nearest neighbors, distance-weighted

All Casino Counties






mdiffMEDIANVALUEpct

-1.51% (-0.59)

-7.50% (-1.73)

*

1.03 (0.33)

mdiffMEDIANINCOMEpct

0.99% (0.83)

-1.39% (-0.79)

2.01 (1.32)

mdiffMEDIANRENTpct

1.30% (1.05)

3.78% (1.59)

0.25 (0.17)

mdiffPOPULATIONpct

3.24% (2.65)

*

-0.11% (-0.05)

4.66 (3.32)

*

mdiffEMPLOYMENTpct

3.71% (2.76)

*

0.05% (0.02)

5.27 (3.58)

*

mdiffUNITSpct

1.95% (1.79)

*

-0.75% (-0.39)

3.09 (2.37)

*

mdiffNEWUNITSpct

2.42% (2.43)

*

-0.10% (-0.05

3.49 (3.03)

*

*statistically significant at a 90% confidence level.

36

Table 8. Match with bandwidth=0.10, distance-weighted, constrained by region

All Casino Counties







* -5.18% (-1.68)

* -5.04% (-1.82)

*

mdiffMEDIANINCOMEpct -0.09% (-0.08)

-2.70% (-1.42)

0.99% (0.69)


5.58% (2.80)

* -1.43% (-1.05)


* -0.07% (-0.04)

3.52% (2.93)

*


* -0.09% (-0.04)

3.39% (2.68)

*


-1.23% (-0.66)

2.61% (2.35)

*


* -0.88% (-0.47)

3.35% (3.33)

*


37

Table 9. Match with bandwidth=0.10, distance-weighted, constrained by region and population.

All Casino Counties

Non-Native Casino

Counties

Native Casino

Counties





0.77% (0.30)

-3.05% (-1.05)


1.24% (0.70)

0.48% (0.36)


3.28% (1.38)

-0.23% 0.17)


* -0.57% (-0.25)

3.73% (2.84)

*


* 0.68% (0.26)

3.65% (2.66)

*


* -1.72% (-0.86)

3.49% (3.09)

*


* -0.74% (-0.38)

3.62% (3.51)

*


Matching Estimation, Casino Gambling and the …rate of growth of consumer spending on casino...

Documents

Transcript of Matching Estimation, Casino Gambling and the …rate of growth of consumer spending on casino...