Matching Estimation, Casino Gambling and the Quality of Life. Michael Wenz

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1 Matching Estimation, Casino Gambling and the Quality of Life Michael Wenz Department of Economics and Finance Winona State University 310 Somsen Hall Winona, MN 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.

2 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 gambling 1. 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).

3 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

4 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 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 nonbanking 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

5 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 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 , 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).

6 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: P i = P(s 1, s 2,, s n ) (1) and δp/δs j 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 Rosen 3. 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).

7 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 and P i = P(s 1, s 2, s j (C), s k (C), ) (2) δp i /δc = Σ j (δp i /δs j )(δs j /δc) (3) For illustrative purposes, let s j 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.

8 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 δp i /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

9 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 Y t,1 Y t,0, where Y t,1 is the outcome which would exist at time t in the presence of a casino, and Y t,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.

10 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

11 10 propensity score gives some confidence that the values have not been influenced by the treatment 4. 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-indifferences matching estimator assumes: E(Y t,0 Y t-1,0 P(X), C=1) = E(Y t,0 Y t-1,0 P(X), C=0) (5) and 0 < Pr (C=1 X) <1 (6) where Y t,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.

12 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.

13 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 ). 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

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

15 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 distanceweighted match for all of the observations within a bandwidth of 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

16 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

17 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 noncasino 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 , and the average distance is just 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 and the average distance between matches at just 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

18 17 exception of Starr County, TX, mentioned above, whose nearest match is a probability distance of away. Otherwise, the largest distance in propensity scores is 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 (d i /b) 2 ) 2 (7) where d i 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

19 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 Nearly all casino counties had a bandwidth of less than 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.

20 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

21 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 = Y i Y j (8) Y i is the observed outcome in casino county i, and Y j is the observed outcome in matched county j. Note that Y j is an amalgamation of outcomes from each county matched with county i by the propensity score matching process. Assume Y i and and Y j are given by the following functions: Y i = f(x i ) + g(c i ) + ε i (9) and Y j = f(x j ) + ε j (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(X i ) f(x j )] = 0, and g(c j ) = 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 Y i = f(x i ) + g(c i ) + µ i + ε i (9) and Y j = f(x j ) + g(c j ) + µ j + ε j (10) where the µ s are region-specific error terms. Then the estimated effect becomes

22 21 i = g(c i ) + (µ i - µ j ) + (ε i - ε j ). (11) The term (µ i - µ j ) 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 µ i = µ j, 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 (d j /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 (d j /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

23 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.

24 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.

25 24 References American Gaming Association. State of the States: The AGA Survey of Casino Entertainment. Washington, D.C., Blomquist, G. C., Berger, M. C., and Hoehn, J. P.: New estimates of quality of life in urban areas. American Economic Review. 78(1): , Eadington, W. R.: The economics of casino gambling. Journal of Economic Perspectives. 13(3): , Evans, W. N. and Topoleski, J. H.: The social and economic impact of Native American casinos. NBER Working Paper No. 9198, Grinols, E. L. and Mustard, D. B.: Casinos, Crime, and Community Costs. Review of Economics and Statistics, 88(1): 28-45, 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: , Gyuorko, J. and Tracy, J.: The structure of local public finance and the quality of life. Journal of Political Economy 99(4): , Heckman, J.J., Ichimura, H. and Todd, P.: Matching as an econometric evaluation estimator. Review of Economic Studies. 65(2): , 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 , New York, Palgrave Macmillan, Roback, J.: Wages, rents, and the quality of life. Journal of Political Economy, vol. 90(6): , Rosen, S.: Hedonic prices and implicit markets: Product differentiation in pure competition. Journal of Political Economy. 82(1): 34-55, 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, Todd, Petra. A Practical Guide to Implementing Matching Estimators. Unpublilshed Manuscript, Walker, D. M.: Methodological issues in the social cost of gambling. Journal of Gambling Studies. 19(2): , 2003.

26 25 Walker, D. M. and Barnett, A. H.: The social costs of gambling: An economic perspective. Journal of Gambling Studies, 15(3): , Wenz, M. Casino Gambling and Economic Development. Ph.D. Dissertation, University of Illinois at Chicago

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

28 27 Table 1. Binomial logit coefficient estimates full model Dependent Variable: Parameter (Std. Error) Any Casino Marginal Effect Intercept (2.165) *** MANUF (0.015) UNEMP (3.092) VACANCY (0.009) lnpop (0.147) lnlandarea (0.156) URBANPCT (0.006) lnpop50in (0.121) lnpop50out (0.019) NEARESTOUT (0.002) FISCAL (0.008) FISCALCHG (0.003) VOTEDEM (0.014) VOTEPEROT (0.026) CATHRELIG (0.007) FUNDRELIG (0.011) NATIVEPOP (0.009) COASTAL (0.257) ** *** *** *** ** * *** *** ***

29 28 Parameter (Std. Error) RIVER (0.319) REASTNORTHCENTRAL (0.548) RWESTNORTHCENTRAL (0.575) RSOUTHATLANTIC (0.803) REASTSOUTHCENTRAL (0.752) RWESTSOUTHCENTRAL (0.669) RMOUNTAIN (0.636) RPACIFIC (0.590) Marginal Effect *** *** *** *** ** *** *** Likelihood Ratio (R) Upper Bound of R (U) McFadden's LRI *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.

30 29 Table 2. Data sources for casino location model. Variable Description Source CASINO Dummy variable identifying whether there are any casinos in the county. UNEMP MANUF VACANCY DENSITY POP50IN POP50IN NEARESTIN NEARESTOUT FISCAL County Unemployment Rate 1990 % Employees in county employed in manufacturing industry, 1990 % Vacant Housing Units, 1990 Population per square mile, 1990 Population for census block groups within 50 miles of the county, inside the same state, Population for census block groups within 50 miles of the county, outside the same state, Distance from county centroid to nearest casino outside the county and in the same state. Distance from county centroid to nearest casino outside the county and outside the same state. Ratio of county government revenuesexpenses/expenses accessed October U.S. Census of Population and Housing, 1990, Summary Tape File 3 U.S. Census of Population and Housing, 1990, Summary Tape File 3 U.S. Census of Population and Housing, 1990, Summary Tape File 3 U.S. Census of Population and Housing, 1990, Summary Tape File 3 U.S. Census of Population and Housing, 1990, Summary Tape File 1 and Summary Tape File 3 U.S. Census of Population and Housing, 1990, Summary Tape File 1 and Summary Tape File 3 Casino locations from County Centroids computed using Maptitude computer software and TIGER/Line files from the U.S. Census. Casino locations from County Centroids computed using Maptitude computer software and TIGER/Line files from the U.S. Census. County and City Data Books. Retrieved February 2006 from the University of Virginia, Geospatial and Statistical Data Center: Variable Description Source