On the Demand and Supply of Golf

Transcription

1 On the Demand and Supply of Golf Peter C. Melvin and Robert E. McCormick 1 Assistant Professor Department of Economics and Finance Anderson College February 6, 2001 Professor and BB&T Scholar Department of Economics Clemson University Abstract The analysis here uses an exhaustive golf course database that contains over 100 variables on more than 17,000 courses in the United States and Canada for the years 1995 through 1997 to estimate quality adjusted structural demand and supply curves for golf. For instance, our hedonic estimates show that golfers pay $3.28 more in greens fees for courses serving beer and wine and $7.30 more for courses with a full bar relative to courses that serve no alcohol. Golfers pay over $23 more for courses with caddy services, excluding the cost of the caddie. Similarly we estimate that requiring soft spikes adds approximately $2.00 to the greens fee as compared to courses that allow metal spikes. Above and beyond the hedonic/characteristic value analysis, we simultaneously estimate hedonic demand and supply equations for golf. We believe that these are the first quality adjusted structural equation estimates using the Rosen technique. Our models show that there is strong statistical evidence that the First Law of Demand holds for golf and that the demand for golf is actually quite elastic. INTRODUCTION This paper is a contemporary, detailed look at golf courses in the United States. At present there are more than 17,000 golf courses in the United States with approximately 1,400 new golf courses opening in the past five years. A recent National Golf Foundation report estimates there are approximately 27 million golfers in the United States accounting for approximately 10 percent of the total population. In 1997 the average weekend eighteen hole price to golf with a cart was approximately $51, and less than 8 percent of all golf courses provide caddie services. The primary work in the paper focuses on the quality-adjusted empirical demand and supply estimates for golf. The first step in this process estimates a golf course hedonic pricing model. This allows us to assign a dollar value to each observable golf course characteristic. We then use the quality-adjusted prices from the hedonic model to simultaneously estimate demand and supply equations for golf. Thus, we report, what are to our knowledge, the first hedonic models of supply and demand for any market in the economics literature. SOME CURRENT DATA ON GOLF COURSES IN THE UNITED STATES AS OF 1997 In this section we briefly summarize the extensive GOLF MAGAZINE Golf Course Guide database used in this paper. For the present research the GOLF MAGAZINE Golf Course Guide contains three years of data from 1995 to No data are available for New course variables recently available in the 2000 version include maintenance costs, the number of members, membership pricing and requirements, and ownership of the club, among others. The new variables will provide opportunities for further golf course research. 2 1 We can be contacted at pmelvin@anderson-college.edu or sixmile@clemson.edu. We owe a significant intellectual debt to Scott Wilbur, Matt Lindsay, Mike Maloney, Sherwin Rosen, R. Skip Sauer, Laura Speake, and John Warner. 2 We have obtained access to these data for academic research without charge. Other uses of the data require a license fee paid to Golf Magazine. The update contains all the variables in the 1995 database plus the new variables added in 1996 and For example, ANNUAL ROUNDS PLAYED was not available in 1995 but was added to the 1996 and 1997 databases. Also, due to recent golf course policies requiring soft spikes, a SPIKES variable is added to the 1997 database. In 1997 there are 104 possible variables on each course. The number of relevant variables used in our analysis is 78 in 1995, 85 in 1996, and 92 in Through collaboration with the United States Golf Association, the Page 1 of 25

2 A full list and brief description of the 1997 variables are provided in the appendix, and a few are described here to give a feel for the types of quality characteristics that are measured. For instance, PAR measures are available for every set of tees on a course. 3 COURSE SLOPE and RATING measures are also available for each set of tees. Both Slope and Course Rating are measures created by the United States Golf Association to calibrate course difficulty. According to the USGA Course Rating is the USGA's mark that indicates the evaluation of the playing difficulty of a course for scratch golfers under normal course and weather conditions. It is expressed as strokes taken to one decimal place, and is based on yardage and other obstacles to the extent that they affect the scoring ability of a scratch golfer. The USGA defines a male scratch golfer as an amateur player who plays to the standard of the field of the stroke-play qualifiers competing in the U.S. Amateur Championship. He can hit tee shots an average of 250 yards and can reach a 470-yard hole in two shots. Slope Rating is the USGA's service mark which is used to measure a player's potential scoring ability on a course relative to the scoring ability of a scratch golfer on that course. It is a measure of how much above or below the Course Rating a player with a given Handicap Index will score. A golf course of standard relative playing difficulty has a Slope Rating of 113. The lowest USGA Slope Rating is 55 and the highest is GRASS TYPE identifies the strains of grass on the course s putting surfaces. Eleven different types of green grasses are listed. The two most common grasses are Bermuda and Bent. In percent of greens were Bent grass and 19.7 percent were Bermuda grass. 5 WATERHAZARD indicates whether water comes into play on the course. YARDAGE MARKERS lists various types of yardage markers used by courses. Some of these include: the Kirby Marking System; yardage marked on sprinkler heads; yard bird house markers; 250, 200, 150, & 100 yard markers; and electronic range systems. Table 1 lists relevant summary statistics for eighteen-hole courses for the 1997 database. From 1995 to 1997 the average weekend greens fee for eighteen holes increased from $34.62 in 1995 to $38.14 in 1997, for an increase of 10.2 percent. The previous figures include new courses added to the database. The cart fee for eighteen holes increased from $14.71 in 1995 to $16.13 in 1997 for an increase of 9.7 percent. The combination cart and green fee increased from $46.48 in 1995 to $50.94 in 1997 for an increase of 9.6 percent. 6 Table Numeric Variable Summary Statistics for 18 Hole Courses Variable Number of Observations Average Std. Dev. Minimum Maximum Weekend 18 Hole Greens Fee 11,247 $ $27.44 $3.00 $ Weekday 18 Hole Greens Fee 11,248 $ $27.00 $3.00 $ Weekend 18 Hole Cart and Greens Fee 11,110 $ $26.06 $3.00 $ Weekday 18 Hole Cart and Greens Fee 11,111 $ $25.73 $3.00 $ Weekend 9 Hole Greens Fee 11,247 $ $26.23 $2.50 $ Professional Golfers Association, and other prominent golfing institutions, GOLF MAGAZINE estimates the 1997 database contains 98 percent of the courses in the United States. The number of courses and clubs in the database is also increasing over the years. For example, the number of courses in the 1995 database was 14,954 and the number of clubs was 14,573. In 1997 there are 17,584 courses and 17,105 clubs. The distinction between a course and a club is necessary because many clubs have more than one course. For example, in 1995 there were 381 clubs with more than one course. GOLF MAGAZINE collects the data by telephone survey of each golf course in the database. This process takes them about 8 months to complete. Hence, the data we are reporting here, for 1997, were collected throughout the calendar year As stated by the USGA Par is the score that an expert golfer would be expected to make for a given hole. Par means errorless play without flukes and under ordinary playing conditions, allowing two strokes on the putting green.. The USGA Handicap System, 4 Cite to USGA goes here. 5 The 2000 version of the database includes information on the type of grass on the fairways. 6 The GDP Implicit price deflator increased 3.9 percent from the end of the third quarter of 1995 to the end of the third quarter of Page 2 of 25

3 Table Numeric Variable Summary Statistics for 18 Hole Courses Variable Number of Observations Average Std. Dev. Minimum Maximum Weekday 9 Hole Greens Fee 11,248 $ $25.36 $2.50 $ Cart Fee for 18 Holes 8,660 $ $5.71 $3.00 $50.00 Cart Fee for 9 Holes 8,660 $ 9.51 $4.27 $2.50 $50.00 Rounds Played per day 4, ,222 Championship Yardage 9,626 6, ,877 7,705 Men's Yardage 11,293 6, ,611 Women's Yardage 11,271 5, ,822 Championship Slope Rating 9, Men's Slope Rating 10, Women's Slope Rating 9, Championship Course Rating 9, Men's Course Rating 10, Women's Course Rating 10, Championship Par 9, Men's Par 11, Women's Par 11, In rank order Resort courses have the highest weekend eighteen hole greens fees (including cart) at $67.08, next are Private courses at $45.02, Semi-private courses at $28.05, Public courses at $21.57, and the Military courses at $ The oldest courses on average are Private and the newest are Resorts. The toughest courses as measured using Course Ratings are Resort courses with a 71.8 rating and the least difficult are Public courses with a 70.3 rating. On average, the greatest number of annual eighteen-hole equivalent rounds played occur on Public courses with 38,896 and the least on Resort courses with 22,558. The same high low ordering is true when looking at monthly eighteen-hole equivalent rounds played. Regarding ownership, 39.3 percent of courses are independently owned, 26.2 percent are equity owned, and 17.1 percent are corporate owned. Only 7.8 percent of clubs provide caddie services. A full bar is available at 62.5 percent of clubs, and only 17.6 percent of clubs do not offer any form of alcohol to golfers. Metal spikes can still be worn at 75 percent of all courses. Bent and Bermuda grass are the most common grass types on course greens with 75.1 and 19.7 percent respectively. Private clubs make up 6 percent of the 7.8 percent of total clubs who offer caddies. The greens fee data as received from the GOLF MAGAZINE Golf Course Guide are the highest seasonal weekend and weekday prices for nine and eighteen holes. A number of the clubs include their cart fee in their greens fee and do not list a separate cart fee. For example, 2,816 courses in 1997 included their cart fee in their greens fee price. For purposes of comparison across all courses we created a new, full price variable, which is the 18-hole fee plus cart fee (where not already included). See Figure 1 for a plot of these data averaged by state. This provides a combined greens and cart fee for eighteen hole clubs. The other major adjustment required is for the variable ROUNDS PLAYED. Since this variable is the total for the year across all courses at the club, we made a number of adjustments to account for number of holes and the length of season the course is open. For example, Augusta National is closed for the summer and northern courses are often closed in the winter. First we adjusted the raw ROUNDS PLAYED numbers by the TOTAL HOLES at the club to put all the rounds played in eighteen-hole terms. For example, if the course is a nine-hole facility we multiplied the rounds played by 2 and if the club is a 45-hole facility we divided the reported rounds played number by 2.5. Second we calculated the number of months per year that each course was open, and from this computed the rounds played per month. For example, if a course opens on March 15th and closes at the end of October then our months open number for the course is 7.5. These adjustments allow us an accurate measure of rounds played for the variety of club seasons and number of holes. After making the above adjustments, we create three different rounds figures. These are the (18-hole equivalent) rounds played per day, the rounds played per month, and annual rounds played. In 1997, Florida had the greatest number of courses with 1269, California was second with 968, and Alaska was at the bottom with 16. Nevada and Kentucky saw the largest increase while a number of states did not Page 3 of 25

4 Figure 1 Mean Cart and Greens Fees 1997 Mean Cart & Greens Fee $84.3 to $96.5 (1) $72 to $84.3 (1) $59.7 to $72 (6) $47.4 to $59.7 (18) $35.1 to $47.4 (25) experience any growth over the period The greatest numbers of Resort courses appear in warm southern coastal states. Florida takes the top spot and California is second. The greatest numbers of public courses are in Michigan with New York, Ohio, and Texas coming in a close second. Semi-private courses dominate the southeast, Texas, and New York. Florida has the most private courses with California and Texas not far behind. The remaining concentration of private courses is east of the Mississippi River. When adjusting for the portion of the year that clubs are open, the northern states experience the greatest number of rounds played per month. These results indicate that golfers in northern climates take full advantage of their golfing opportunities. In effect, demand is compressed during winter and vented during summer. In annual rounds by state the West Coast states lead the pack especially California, Hawaii, Oregon, and Utah. This can in part be attributed to the lower rainfall amounts in these states. The northern central states have the greatest number of courses per capita along with South Carolina and New Hampshire. Alaska, California, Louisiana, Maryland and New Jersey have the lowest. The western states dominate in terms of greens fees with Hawaii and Nevada coming in one and two. More western states, Arizona, California, Colorado and Oregon along with New Hampshire and New Jersey in the east fall into the third highest green fee category. The top seven states with the longest courses are Alaska, Colorado, Hawaii, New Mexico, Nevada, South Carolina, and Wyoming. The shortest courses on average are in Delaware. The toughest states as measured by course rating are Alaska, Hawaii, Illinois, Kansas, Nebraska, Nevada, Rhode Island, South Carolina, and Texas. The easiest courses are found in Arizona, West Virginia and a majority of the northwestern states. Figure 2 plots total courses and chained gross domestic product from 1929 to Visually the two series trend together with greater variance in chained gross domestic product than aggregate courses. The Pearson correlation coefficient is Page 4 of 25

5 Courses Chained GDP Aggregate Courses Figure 2 Growth of Golf Courses and Chained GDP Chained Gross Domestic Product Figure 3 demonstrates the cycle of new golf courses constructed during the 20 th century. During the decade From 1988 to 1997 the average is well over 250 a year. The first noticeable upswing in golf courses occurs in 1920, the Bobby Jones era, with growth leveling during the economic downturn of the Great Depression. 500 Number of Courses Built Figure 3 The Golf Construction Cycle The next and more pronounced upturn occurs in the early 1950s and continues into the 1990s with only a slight slowdown in the middle 1970s. This early 1950s upswing could be due to the emergence of Arnold "The King" Palmer. Figure 4 plots championship course rating averaged by state across the country. States with average course ratings of or higher are Alaska, Hawaii, Illinois, Kansas, Nebraska, Nevada, Texas, South Carolina and Rhode Island. lead the way. On average upper west states have the lowest course ratings along with Arizona, Maine and West Virginia. Page 5 of 25

6 Course Ratings to (9) to (10) to (10) to (11) 68.5 to (11) Figure 4 Where is Golf the Hardest? Figure 5 plots the cumulative number of courses by organizational structure over the past century. For the club to be in the database it still must in operation. Public courses have shown the most growth since the late 1950s and currently have the largest market share with 46 percent of the golf market. Semi-private and private courses have also experienced growth since the late 1950s. Private courses have the second highest market share with 27%, Semiprivate courses are third with 20%, and Resort courses have 6% Figure 5 Types of Golf Courses Built Over Time Private Public Semiprivate Resort Military 7 Numerous other golf course statistics are available upon request including maps, tables and time series. Page 6 of 25

7 HEDONIC LITERATURE This section reviews the literature on hedonic pricing. At least since Working (1928), hedonic pricing models have been employed in myriad ways. Waugh, in Brendt (1991), attempted to determine the implicit prices of asparagus based on characteristic bundles, that is, width, number of stalks, and color. Since Working, numerous other prominent scholars have contributed to the theory and understanding of hedonic pricing. As computational costs have decreased, economists have increasingly used hedonic methods to analyze the pricing of both durable and non-durable goods. The automotive industry is by far the most widely analyzed. Cowling and Cubbin (1972) worked on the United Kingdom motor industry, De Pelsmacker (1988) on the Belgian car market and further studies of the United States automotive industry have been done by Griliches (1961), Hogarty (1975), and Triplett (1969), among others. More recently, hedonic pricing models have been used to analyze the computer industry, housing, clean air, real estate, Bordeaux wine, milk components, and, interestingly, the genetic merit of dairy bulls in Alberta. Rosen's (1974) seminal paper most aptly applies to the analysis of golf courses. Rosen's model brings together producers and consumers in a spatial context. The producers themselves develop goods that contain final consumer characteristics and receive returns from economies of specialized production through the standard division of labor and specialization. Consumers then match their preferences to the products available in the market. In relating this to golfers, course owners attempt to develop a course in an area that suits the characteristics of the golfers in the area and those willing to travel. 8 Deviating from Lancaster (1966), this model assumes products are not divisible. Indivisibility means that a golfer cannot purchase the right to play on one course's fairways and putt on another courses greens while eating in another's restaurant. When a golfer pays her greens fee she is purchasing a bundled, pure consumption good. Another theoretical finding in the hedonic model is that there is a natural tendency toward market segmentation. This applies where golfers can decide on whether or not to become a member of a private club with its corresponding privileges or play at daily fee clubs. Private club privileges include less course congestion, a venue to entertain clients, networking opportunities, and reputation effects. A private membership also signals the individual is committed or bonded to the area. Section four of Rosen's paper provides a test methodology for estimating the theoretical model on both the demand and supply side. As required on the demand side, data are available on characteristics purchased by, in this case, golfers and also their exogenous demand shift variables. On the supply side, data are required on product characteristics, factor prices, and technological differences among sellers. The following represents the demand and supply equations ignoring error terms p i ( a ) G ( a 1,..., a n, X 1 ) i = (demand), i p i ( a ) = H ( a 1,..., a n, X 2 ) (supply), where i=1,..., n and where p i and a i are all joint dependent price variables and X 1 and X 2 are exogenous demand and supply shifters. Again following Rosen, this procedure requires a three-stage process. The first step is to regress observed differentiated product prices on all relevant characteristics without regard to the exogenous shifters. Obviously, the best fitting functional form is to be used in this standard hedonic approach. According to Rosen "This econometrically duplicates the information acquired by agents in the market, on the basis of which they make their decisions." (p. 50) Next, we compute a set of marginal implicit prices by differentiating observed differentiated product prices by each product characteristic. Simply, observing the coefficients by taking the partial derivative with respect to each characteristic in the standard hedonic method generates the predicted quality adjusted prices. Finally, we use the estimated 8 Rosen assumes there are a sufficiently large number of differentiated products in the market so the available product characteristic combinations are continuous for all practical purposes. He remarks that this assumption is more realistic in some markets than others. He points out that this assumption was originally made by Court (1941) and allows the use of marginal analysis rather than programming methods as required by Lancaster (1966). Here, given the amount of data available, a continuous spectrum of course characteristics is not unreasonable. The only possible draw back is that not all regions or markets will have golf courses that suit area golfers' consumption preferences. Another related assumption is that there are no second hand markets, or alternatively, that goods represent pure consumption. Both cases apply to golfers. Page 7 of 25

8 marginal implicit prices as endogenous variables in simultaneously estimating the original demand and supply equations above by simply replacing the direct prices with the marginal implicit prices. The implicit price results here generate the same identification problem that exists when using direct price observations. 9 Combris, Lecocq, and Visser (1997) estimate a hedonic price equation for Bordeaux wine and attempt to determine if quality matters. Others writing in the hedonic tradition include Do and Grudnitski (1995) who analyze how the selling price of single family residential property is affected when it abuts a golf course. Witte, Sumka, and Erekson (1979), following the empirical model developed by Rosen (1974), estimate a simultaneous equations model for rental housing attributes in order to account for the heterogeneity of the housing good. Gilley and Pace (1995) address the problem of the lack of independent variation or multicollinearity seen in the non-traded characteristics of hedonic pricing models. Hartman (1989) evaluates product design and pricing strategies using hedonic methods in the luxury hotel industry. Triplett (1986) discusses how to interpret hedonic results. This survey piece discusses creating price indexes for the computer industry and in particular the hedonic work done by the economics department of the IBM Corporation. The high rates of quality change for computers have rendered conventional price comparisons obsolete. The use of hedonic methods can reflect a more accurate view of quality-adjusted prices. Triplett (1968) also considers the findings by Griliches (1961, 1964) that the increases in the automobile component of the CPI between 1954 and 1960 could be attributed to the substantial quality improvement in automobiles and therefore support the charge of upward bias in price indexes. 10 A dissertation by Krock (1999) in the economics department at the University of Chicago models the supply and demand of public golf in Chicago. Krock employs techniques from the urban economics, hedonic pricing, and spatial competition fields. The data are restricted to 251 public courses in the Chicago area. His empirical results find "that golf prices are increasing in the course difficulty, the number of hotels, being ranked, and local household value." (p. 64) He also finds that prices are decreasing the greater the course's distance from Downtown Chicago, the age of the course, and the proportion of married people in the area. Krock's marriage result corroborates a theory proposed by some golf insiders who theorize that married men golf more after work during the week than on weekends. THE MODEL AND ITS ESTIMATION In this section we estimate quality-adjusted demand and supply equations for golf in the United States. The empirical analysis includes all 1997 public, resort and semi-private eighteen-hole courses in the GOLF MAGAZINE Golf Course Guide. Each course is a minimum three thousand sixty-four yards with a par of at least 36 from the men's tees. This demarcation eliminated the bottom 25 percent of the observations for yardage and par. Military and private courses are not included because the reported greens fees are not 9 Rosen goes on to discuss four possible identification problems. The first occurs when all buyers are different but cost conditions are identical across firms. This would cause the supply shift variables to drop out of the supply equation and therefore the sample observations on implicit prices and characteristics identify compensated supply functions. The second happens when buyers do not differ but sellers do. This is a mirror image to the situation above so demand shifters would fall out of the demand equation and the sample estimates compensated demand functions. The third possibility occurs when both buyers and sellers are identical. In this situation the consumption and production choices, represented by offer curves in the Rosen model, are tangent at a single point and no product differentiation is present in the market. The final and most realistic possibility is that both buyers and sellers fall within their own distinct distribution. In this case both demand and supply shifters have nonzero variance. 10 Epple (1987) questions the parameter estimates when quality-adjusted prices derived from hedonic models are used as endogenous variables to simultaneously estimate demand and supply using ordinary least squares. He states that the applications of Rosen s econometric modeling strategy that use ordinary least squares in estimating the hedonic equation (step one) and the simultaneous estimation of demand and supply (step two) will generate coefficients in the second stage of estimation that are inconsistent. An intuitive explanation is that since the quality-adjusted prices derived from the hedonic model are used as dependent variables in simultaneously estimating demand and supply, and are all functions the hedonic characteristics, the error terms from the demand and supply equations will be correlated. The absence of orthogonal errors terms will thus generate inconsistent parameter estimates when using ordinary least squares. However, Epple does mention that by correctly specifying error sources and orthogonal conditions, stochastic structures can be compatible with equilibrium conditions thereby permitting identification and estimation of model parameters. For these conditions to be met the model must contain extensive characteristics on the product, demanders, and suppliers. It is also mentioned that for some specifications estimating the entire model using maximum likelihood can alleviate this problem but the absence of unobservable variables and their effects should still be weighed. Page 8 of 25

9 market-determined. Military courses are obviously government subsidized and private course greens fees are essentially guest fees that are often intended to limit nonmember play. There are 7,519 courses remaining after eliminating the bottom 25 percent of courses by distance and par. We are missing data for some variables for some courses and in the analysis that follows, 3,638 observations are used. This differs somewhat from the sample summary statistics reported in Table 1 where we used the entire database. For instance the average weekend greens fee with cart in the regression sample is $48.69 which is about $2 lower than the mean in the full sample. The primary reason a course drops out of the sample is absence of data on rounds played. Many courses prefer to keep this information private. 11 Hedonic Equation Our empirical model follows Rosen (1974). The first step is to estimate a standard hedonic model for golf by regressing full price (including cart and for the weekend greens fees for eighteen holes) on numerous golf course characteristics. Estimates are obtained in levels and logs and tested to determine proper functional form. The predicted quality-adjusted prices from step one are then used to estimate structural demand and supply equations in step two. Formally: (levels) p i = $ x +, i, and (logs) log(p i ) = "x (. where p i is the combination cart and weekend greens fee for eighteen holes and x is a vector of golf course characteristics. The x vector variables are: 12 Championship Yardage Championship Yardage Squared Championship Slope Championship Slope Squared Championship Rating Championship Rating Squared Yardage Markers Homes on the Golf Course Driving Range Available Alcohol Served Grass Type on the Greens Caddies Available Carts Available Metal Spikes Allowed Dress Code Requirements Over Seeding Training Facilities Water Hazards on the Course Course in a Golf Community The next step is to search for the best fitting functional form. Here the proper functional form is determined by finding a levels equivalent estimate of the coefficient of determination from the logged model. It turns out the coefficients of determination are virtually identical for the level and log equations. 11 We do not think this creates a sample selection bias. For instance, the average rounds per day in the full and truncated samples is almost identical, (full) and (truncated). Sample means on other important variables. For instance year built, slope, and yardage, are also quite similar. 12 We also included the variables, Pro Shop Products, Are Tee Times Accepted, Year Course was Built, and Is there a Professional on Site in the original estimates. However data are missing for some of these characteristics and none of them are statistically significant. Therefore, the model estimates below exclude these course characteristics. Page 9 of 25

10 Therefore, only the hedonic pricing regression in levels is reported and its predicted prices used to estimate the demand and supply equations in step two. Table 2 reports the results of the standard linear hedonic regression model. The hedonic model reveals that golfers pay more for courses that serve alcohol, provide caddie services, do not allow metal spikes, and have various training facilities that include a golf school. Golfers pay $3.28 more in greens fees for courses serving beer and wine and $7.30 more for courses with a full bar relative to courses that serve no alcohol. Golfers pay over $23 more for courses with caddies and $1.80 more for courses not allowing metal spikes in golf shoes. Courses with a putting green, teaching pro, and golf school charge almost $27 per round played more than a course without any training facilities. Table 2 Estimation of Hedonic Equation Dependent Variable: Weekend 18 Hole Cart & Greens Fee Dependent Number of Observations R 2 F Value Prob. > F Mean Analysis of Variance Mean Square Source Degrees of Freedom Error F- Value Prob. > F Championship Yardage Championship Yardage Squared Championship Slope Championship Slope Squared Championship Rating Championship Rating Squared Yardage Markers Homes on the Golf Course Driving Range Available Alcohol Served Restaurant Grass Type on the Greens Caddies Available Carts Available Metal Spikes Allowed Dress Code Requirements Over-Seeding Policy Training Facilities Water Hazards on the Course Course in a Golf Community Parameter Estimates Dummy Variable Classification Parameter Estimate t ratio prob t >0 Intercept Championship Yardage Championship Yardage Squared Championship Slope Championship Slope Squared Championship Rating Championship Rating Squared Yardage Markers 200,150,100 Yrd, Sprinker Heads & Kirby Markers Page 10 of 25

11 200,150,100 Yrd & Sprinkler Heads Marked Electronic Range System Yrd Bird Hourse Markers Kirby Marking System No Yardage Markers Yrd Markers Only Sprinkler Heads Marked ,150,100 Yrd Markers ,200,150,100 Yrd Markers Course Marked Every 25 Omitted Level, Incl. in Intercept Yrds. Homes on Golf Course No Driving Range Available Grass & Mats Grass Only Mats Only No Omitted Level, Incl. in Intercept Alcohol Served Beer & Wine Beer Only Full Bar No Omitted Level, Incl. in Intercept Restaurant Beverage Cart, Restaurant, &Snack Bar Restaurant & Snack Bar Convenience Food Restaurant Only Snack Bar Only Beverage Cart Only No Food Facilities Beverage Cart & Snack Bar Restaurant & Beverage Cart Omitted Level, Incl. in Intercept Grass Type on Greens Alaska Bluegrass Bermuda Buffalo Bluegrass Bent Poa Annua Sand Tifdward Winter Rye Zoysia Omitted Level, Incl. in Intercept Caddies Available No Carts Available Included in Greens Fee Metal Spikes Allowed No Dress Code Requirements Collared Shirt Required Shirt & Shoes Required No Denim & Collared Shirt Required No Dress Code Collared Shirt Required, No cutoffs, Denim OK No Denim Page 11 of 25

12 No Tank Tops or Cutoffs Omitted Level, Incl. in Intercept Over-Seeding Policy April/Closed April/Open August/Closed August/Open December/Closed December/Open February/Open January/Closed January/Open July/Open June/Open March/Closed March/Open May/Open No Overseeding November/Closed November/Open October/Closed October/Open September/Closed September/Open Omitted Level, Incl. in Intercept Training Facilities Putting Green Only Putting Green, Sand Bunker & Chipping Area Teaching Pro & Putting Green Only Teaching Pro, Putting, Sand & Chipping Area Teaching Pro, Golf School, Putting, Sand & Chipping Putting Green, Teaching Pro & Golf School Putting and Chipping Green Putting Green, Chipping Area & Teaching Pro No Training Facilities Omitted Level, Incl. in Intercept Water Hazards No Course in Golf Community No Note: Coefficients for each class variable are relevant to the omitted level that is included in the intercept. A contradictory result is found in the Driving Range variable. The estimates predict that golfers are willing to pay more for courses with mats on the driving range than grass. This result contradicts widely held opinion among most golfers. This result is likely capturing some other components of the course, for example location and volume of play. Courses in high demand have difficulty maintaining grass driving areas and therefore opt for mats. Many of the course characteristic variables have more than two classifications. For example, the class variable Grass Type on the Greens lists 10 different varieties of grass. Individually none of the grass types are significant yet as a group they have an F-value of This is true for many of the course characteristics used in the standard hedonic model. The only course characteristics without significant F- values are the Homes on the Golf Course, Championship Rating and Championship Rating Squared, and Water Hazards on the Course. Simultaneous Estimation of Demand and Supply Using Quality Adjusted Prices Next, the quality-adjusted predicted prices from the first step are used to simultaneously estimate structural Page 12 of 25

13 demand and supply equations using two-stage least squares and three-stage least squares. Each model is regressed in linear and log forms. Formally: Demand: pˆ = x φ + Ω and Supply: pˆ = y ψ + Ω where p^ is the quality-adjusted predicted prices from the standard hedonic pricing model, N and R are vectors of variables that affect demand and supply including golf rounds played per day and S and SN are the error variance and covariance structures. The independent numeric and character variables in the structural demand equation are: Championship Yardage Championship Yardage Squared 1990 County Per Capita Income Competitive Price Variable (average quality adjusted price of all other courses in the county) 1990 County Population Average Rain Totals by State (this is an average of multiple sites per state) Hotel Employment per State (proxy for tourism) Rounds Played per Day and zero or one dummy variables for Yardage Markers Driving Range Available If the course is a Resort Bar Caddies Training Facilities Dress Code Over Seeding Metal Spikes Allowed Pro on Site It is predicted golfers value courses with yardage markers, a driving range, alcohol, caddies, training facilities, a dress code, and a professional on site. Over-seeding, resort courses, and longer courses are also expected to garner higher greens fees. Courses are projected to charge higher prices the greater the per capita income, population, and tourism in the surrounding area. It is projected the more rainfall in an area the lower the demand for golf due to limited opportunities. Also the quantity variable Rounds Played per Day is expected to be negative supporting the First Law of Demand. For the structural supply equation the independent numeric and character variables are: Yearbuilt Yearbuilt Squared Championship Slope Championship Slope Squared Average Rain Totals by State Average Cooling Days Average Hourly Manufacturing Wage by State Average Building Permit Value by State Number of Courses per County Rounds Played per Day Page 13 of 25

14 Page 14 of 25 zero or one dummy variables for Bent Grass Greens Homes on Course Caddies Driving Range Available Bar Pro on Site Resort Course Over Seeding Training Facilities and Golf Community. The following variables are expected to increase the cost of supplying golf: Yearbuilt, Course Slope, Bent Grass Greens, Homes on Course, Caddies, Driving Range Available, Bar, Pro on Site, Over-seeding, Training Facilities, Average Cooling Days, Building Permit Value by State, Average Hourly Manufacturing Wage by State, Number of Courses per County, Resort Course, and Golf Community. For example new courses cost more to maintain and providing caddies services, a driving range, a bar, and other course features are costly. Building permit values attempt to capture area real estate costs. Also the higher rainfall amounts are expected to decrease maintenance costs while a slope rating is expected to increase these costs. Slope measures the difficulty of a course, i.e. water hazards, bunkers, mounding, etc., and these course features are costly to maintain. The squared variables are dropped in the log models and obviously only the numeric variables are converted to logs. Therefore the specific classification of each character variable is not available as in the hedonic model. Two-Stage Least Squares Table 3 reports the results for the two-stage least squares model in levels. The model generates an R 2 of 0.45 and an adjusted R 2 of Rounds Played per Day is negative and significant with a t statistic of The First Law of Demand is not rejected. Table 3 Two-Stage Least Squares Estimation in Levels Panel A Model: DEMAND Dependent variable: Predicted Greens Fees from Hedonic Equation Number of Observations R2 F- Value Prob.>F Dep. Mean Parameter Estimates Variable Parameter Estimate t ratio Prob.> t Intercept Yardage Markers Driving Range Available Alcohol Served Caddies Available Pro on Site Resort Course Championship Yardage Championship Yardage Squared Per Capita Income- County Level Population- County Level Average County Predicted Greens Fees Over-Seeding Policy Metal Spikes Allowed Training Facilities

15 Dress Code Requirements Average State Rainfall Hotel Employees by State Rounds Played per Day Table 2 Panel B Model: SUPPLY Dependent variable: Predicted Greens Fees from Hedonic Equation Number of Observations R 2 F- Value Prob.>F Dep. Mean Variable Parameter Estimate t ratio Prob.> t Intercept Bent Grass Greens Homes on Course Caddies Available Year Course Built Year Course Built Squared Alcohol Served Driving Range Available Pro on Site Championship Slope Rating Championship Slope Rating Resort Course Average State Rain Over-Seeding Policy Training Facilities Golf Community Average Value of State Building Number of Courses per County Average Cooling Days Average State Manufacturing Rounds Played per Day The only variables that are not statistically significant at the 5 percent level are Yardage Markers, Driving Range Available, Over-seeding Policy, and Training Facilities. According to the estimates courses charge higher greens fees if they provide caddies services, serve alcohol, have a professional on site, are a resort course, and do not allow metal spikes or have a dress code. All of these follow intuition except Dress Code Requirements, which has a negative effect on price. Other exogenous variables that positively influence demand are county level per capita income and population, state hotel employees as a proxy for tourism, and the average predicted greens fee price by county. Again all the significant variables follow intuition except for Dress Code.\ Talk about relations in more detail here The relation between yardage and price is negative over virtually all ranges of our data. The parabola has a minimum at 7,761 yards. The longest course in our database is 7,705. Hence, the relation between length and price is negative over all observed ranges. Page 15 of 25

16 On the supply side the R 2 and adjusted R 2 are both The supply curve is positively sloped with Rounds Per Day having a coefficient of and a t statistic of Here the variables not significant at the 5 percent level are Driving Range, Over-seeding Policy, Training Facilities, Golf Community, Average Value of State Building Permit, and Average Cooling Days. The course specific variables that positively influence supply price are Homes on Course, Caddies Available, Alcohol Served, Pro on Site, Resort Course, Number of Courses per County and Average State Manufacturing Wage used as a proxy for labor costs. As is expected, it is also more costly these items at a golf club. The variables with a negative supply influence are Average State Rain, Bent Grass Greens, and Year Course Built. Table 4 reports the two-stage least squares estimates in logs. The log results are very similar to those in the levels model. The model estimates the price elasticity of demand to be elastic at The log demand equation's R 2 and adjusted R 2 are and Also, on the demand side, Driving Range Available is now significant and Dress Code loses its significance. These changes are positive given the sign on Dress Code is negative in levels and experience suggests that golfers prefer a course with a driving range. Table 4 Two-Stage Least Squares Estimation in Natural Logs Model: DEMAND Dependent variable: *Predicted Greens Fees from Hedonic Equation Number of Observations R 2 F- Value Prob.>F Parameter Estimates Variable Parameter Estimate t ratio Prob.> t Intercept Yardage Markers, (0,1) Dummy Driving Range Available, (0,1) Dummy Alcohol Served, (0,1) Dummy Caddies Available, (0,1) Dummy Pro on Site, (0,1) Dummy Resort Course, (0,1) Dummy * Championship Yardage * Per Capita Income- County Level * Population- County Level * Average Predicted Greens Fee by County Over-Seeding Policy, (0,1) Dummy Metal Spikes Allowed, (0,1) Dummy Training Facilities, (O,1) Dummy Dress Code Requirements, (o,1) Dummy * Average State Rainfall * Hotel Employees by State * Rounds Played per Day *- natural log Panel B Model: SUPPLY Dependent variable: * Predicted Greens Fees from Hedonic R 2 F- Value Prob.>F Page 16 of 25

17 Variable Parameter Estimate t ratio Prob.> t Intercept Bent Grass Greens, (0,1) Dummy Homes on Course, (0,1) Dummy Caddies Available, (0,1) Dummy * Year Course Built Alcohol Served, (0,1) Dummy Driving Range Available, (0,1) Dummy Pro on Site, (0,1) Dummy * Championship Slope Rating Resort Course, (0,1) Dummy * Average State Rain Over-Seeding Policy, (0,1) Dummy Training Facilities, (0,1) Dummy Golf Community, (0,1) Dummy * Average Cooling Days * Average State Manufacturing * Average Value of State Building Permits * Rounds Played per Day *- natural log On the supply side R 2 and adjusted R 2 also increase to and The supply results are also similar to those found in levels. The price elasticity of supply estimate is 2.86 revealing an elastic supply of golf. Driving ranges lose their significance and courses in a golf community now increase costs. The golf community result is now consistent with courses having homes lining the fairways. Otherwise, the variables maintain their signs and significance as compared to the supply equation in levels. 14 On the Price Elasticity of Demand We estimate, using the logs or levels model, that the demand for golf is actually quite elastic. The values are (logs) and (levels). 15 This means that golfers are quite price sensitive. We estimate that a 5 percent increase in average greens fees would lead to a 9 percent reduction in rounds played. Of course this is a national, average estimate and holds only for the country taken as a whole. (Should we estimate for each region, state???) Summary Table 5 compares the results for each demand and supply variable using the different estimation techniques. The two-stage and three-stage least squares models in levels and logs generate demand and supply results in line with the economic theory of golf courses except for a few variables. The variable coefficient estimates of the two techniques are nearly identical. The three-stage least squares model does generate higher system weighted R 2 than the individual demand and supply R 2 in two-stage least squares. 14 We also used iterative three-stage least squares estimation to correct for the potential correlation of error terms in the demand and supply equations. The results follow those in the two-stage least squares models implying that error term correlation is not a problem. In levels three-stage least squares generates a low correlation between demand and supply of The system weighted R 2 and mean squared error are 0.71 and On the demand and supply sides the estimates each have the same sign as in the two-stage least squares model and maintain their significance. In logs the correlation between demand and supply is the same at 0.032, the mean squared error is 0.59 and the R 2 falls slightly to The price elasticity estimates of demand and supply remain the same at -1.8 and The three-stage log demand and supply estimates also follow those found in the two-stage least squares model. Also, xxx (vvv) has discussed problems associated with 3sls estimation and recommended maximum likelihood estimation. This alternative approach yields results comparable to the ones reported here. 15 With price the dependent variable as we have estimated it, the elasticity is the reciprocal of the coefficient on rounds played, that is from the logs estimation, 1/(-0.56) = Page 17 of 25