Building a hedonic pricing model for booth location on your own floorplan

The commercial director asks what the entrance is worth. Not the entrance zone. The entrance itself, in dollars per square foot per hundred feet of distance from it, because she is deciding whether to move registration to the west end and wants to know what that does to the rate card.

Nobody in the room can answer. The zone multipliers were set in 2017 by someone who has since left, nobody has ever fitted a hedonic pricing model to the booth locations, the map has been redrawn twice, and the only evidence anyone can offer is that the aisle by the theatre feels busy.

You have three years of contracts. That is enough to answer her properly.

What is a hedonic pricing model actually doing?

Rosen set out the framework in the Journal of Political Economy in 1974, in an article on hedonic prices and implicit markets running from page 34 to page 55 of volume 82. The argument is that a differentiated good is a bundle of attributes, that the market clears on the whole bundle rather than the parts, and that the implicit price of each attribute can be recovered by regressing observed transaction prices on the attributes.

Housing economists have used it for fifty years to price a bedroom, a garden and a school catchment. A floorplan is a much cleaner application than a housing market, because you drew the product yourself and you know every attribute of every unit exactly.

The claim you get out of it is specific: holding size, hall and everything else fixed, an additional open side is worth this many dollars per square foot. That is a sentence a rate card can be built from. It is also what zone lines should be cut from, once the fitted values exist.

Building the row

One row per contracted booth, per edition. Three editions of a mid-sized show gives somewhere between 900 and 1,500 rows, which is enough.

The outcome is paid rate per net square foot. This matters more than anything else on the list. If you fit list rate, the model will return your own rate card with an R-squared close to 1, because list rate is a deterministic function of the attributes you are about to use as predictors. You will have proved that your card is your card. Paid rate is what the account actually contracted at, and the gap between the two is the entire point of the exercise.

The predictors that are worth carrying, all readable off the plan:

• Open sides, one to four.
• Aisle frontage in feet, the total length of booth boundary touching an aisle.
• Distance to the nearest main entrance in feet, measured along the walkable route rather than straight line.
• Distance to the nearest feature area, whether that is catering, the theatre or the charging lounge.
• Hall or building, as a set of dummies.
• Booth area, to absorb the size ladder so it does not contaminate the location coefficients.
• Neighbour category, the product category of the adjacent booths, which on category-clustered floors is a real price driver.

Edition should go in as a dummy too, otherwise a general rate increase across the three years loads onto whichever attribute happened to move.

Fitting it and reading the coefficients

Ordinary least squares is the right first model and probably the right last one. Something like this comes back:

rate = 26.40 + 1.85 times open sides + 0.021 times frontage feet minus 0.0062 times entrance distance plus 2.10 for hall A minus 0.0011 times area

Read them one at a time.

An additional open side is worth 1.85 dollars per square foot. Going from one open side to four is 5.55 dollars, which on a 400 square foot booth is 2,220 dollars. Compare that against what your card charges for an island premium and you have your first genuine cross-check.

Entrance distance costs 0.0062 dollars per square foot per foot, so 100 feet of distance is 0.62 per square foot. A 400 square foot booth 120 feet from the entrance and the same booth 420 feet from it differ by 1.86 per square foot, or 744 dollars. That is the answer to the commercial director's question, in the units she asked for.

Hall A carries 2.10 per square foot over hall B. On 400 square feet that is 840 dollars, and multiplied across the annex it is the number to set against the annex's fixed cost.

The negative area coefficient is your existing size ladder showing up in the data, which is a useful validity check. If it comes back positive, either your ladder is inverted or something is wrong with the file.

Reading the residuals

Fit the model, predict every booth, subtract. The residual is what the account paid above or below what its position was worth, and it is the most interesting column in the output.

Take an island in hall A, 120 feet from the entrance, four open sides, 80 feet of frontage, 400 square feet. The model predicts 26.40 plus 7.40 plus 1.68 minus 0.74 plus 2.10 minus 0.44, or 36.40. The account contracted at 31.90. The residual is minus 4.50 per square foot, which on 400 square feet is 1,800 dollars below the position's value.

One residual is a story. The distribution of them is a finding. Sort the file by residual and the tail is your discounting policy, made visible without anyone having to admit to it.

Say 26 accounts come back with residuals below minus 2.00, averaging minus 3.20 across a mean booth size of 640 square feet. That is 3.20 times 640 times 26, or 53,248 dollars of implicit discount concentrated in 26 contracts. Nothing in your reporting layer produces that number today, and it is computed entirely from data you already hold. It is the kind of figure exhibitor analytics should be producing and mostly does not.

Positive residuals matter too, and they are the ones to check first. An account paying well above its position's value is either a renewal that never repriced or a sponsorship bundle where space was booked at a blended figure, and the second kind should come out of the file before you trust anything.

What trap breaks a floorplan regression?

Booths near each other share attributes you did not measure. A dead corner behind a structural column, a run of aisle that everyone walks past on the way to the toilets, a block of stands that all backed onto the same construction hoarding. Those unobserved effects make the residuals of neighbouring booths correlate, which is spatial autocorrelation, and it does specific damage: the coefficients stay roughly right while the standard errors come back far too small, so you will believe an estimate is precise when it is not.

Carter and Haloupek addressed exactly this case in the International Real Estate Review in 2000, in volume 3, applying weighted least squares to correct for spatial autocorrelation in the residuals of hedonic regressions on stores inside shopping centres. A mall and a hall have the same structure: distinguishable units at fixed positions, with rents driven by location, and neighbours who share unobservables.

The cheap fix for an organiser is to cluster the standard errors by row or by block, which takes one argument in most statistical packages. The next fix up is block level fixed effects, which removes the problem and also removes your ability to estimate anything that varies only across blocks, including the entrance distance coefficient you wanted. Deciding between those is a real trade and it should be made deliberately.

Before either, plot the residuals on the floorplan and colour them. Clustering that is obvious to the eye is worth more than a test statistic in a meeting.

Refitting, and what moves

Refit annually, on a rolling three editions, and keep the old coefficient tables.

The coefficients move for reasons you can usually name. The entrance distance term weakens when you add a second entrance. Hall A's premium collapses the year you move the keynote theatre into hall B. Open sides gets stronger in a tight year, because the accounts still buying islands are the ones who can afford to.

A coefficient that moves without an explanation is a prompt to check the data rather than a finding. The most common cause is a change in what got recorded as space revenue, which is the same failure that breaks any rate per square foot series.

Where this stops

The deepest limit is that you set the prices. A hedonic model fitted to your own paid rates recovers a mixture of your rate card and whatever negotiation moved it, and both of those were produced by your own beliefs about location. If your 2017 card overpriced the entrance, sellers discounted near the entrance, paid rates fell, and the model will report a smaller entrance premium than the market would bear. The estimate is anchored to the card that generated it, and no amount of data fixes that from inside the file. Estimating what buyers would have paid needs evidence from outside it.

You also only observe positions that sold. Booths that sat unsold at list have no paid rate and drop out of the regression, which biases the sample towards positions that cleared. On a floor with a soft back corner, the model will be quietly optimistic about back corners because the worst of them never made it into the data.

Open sides and area are correlated by construction, since almost all your islands are large and almost all your small units are inline. The two coefficients trade against each other, and if you want to trust either one, refit within a single size band and see whether the open sides estimate survives.

None of that argues against fitting the model. It argues for treating the coefficients as a description of your own floor at your own prices, which is a much better basis for next year's card than a multiplier somebody chose in 2017.

Export last edition's contracts with paid rate per square foot, open sides, booth area and straight line distance to the main entrance, and fit those four predictors alone. It takes an afternoon, and the entrance coefficient by itself will settle an argument your team has been having since the plan was redrawn.