Does “psychological pricing” work in real estate? Most commonly, it means pricing a home at, say, $799K instead of $800K, under the assumption that buyers only look at the left-most digit in a price, that the “lower” price will stimulate multiple offers and that, as a result, the property will sell faster for more money. A less common approach is to offer a unique price like, “$765,814” rather than any round number. It’s more memorable and suggests a price based on detailed study of the property’s features, and therefore not negotiable, whereas any price ending in “000” looks like an opening bid.

Based on historical data on the San Francisco real estate market, we examine the following questions:

The literature emphasizes the effect of break points on budgets and on-line searches. Upper and lower bounds in searches are tound numbers, and a round-number price should, in principle, make the listing appear in more searches. In the data, we can see the round prices versus prices with 9s, but we cannot measure the effect of excluding 4s from prices on Chinese or Japanese buyer, or of the number format used to present prices.

Pricing Practices

The following chart is a histogram of the last five digits in the list prices, from $0 to $99999, for 30,378 properties sold in San Francisco between July, 2008 to January 2015.It clearly shows that psychological pricing is dominant.

Based on this chart, we categorize the sales as follows:

And the 30,378 listings break down as follows:

Category Number of Sales Percent of total Cum. percent of total
x99000 5351 18% 18%
xx9000 4773 16% 33%
xx5000 3917 13% 46%
x95000 3708 12% 59%
x49000 3273 11% 69%
xxx000 2328 8% 77%
x50000 1883 6% 83%
xxx900 1271 4% 88%
xx0000 1083 4% 91%
x00000 1067 4% 95%
x90000 217 1% 95%
Rare 1389 5% 100%

To establish whether it does any good, we need to check how the price patterns related to days on market and selling price.

Cumulative Days On Market

First, we examine the evolution of Cumulative Days on Market (CDOM) over time, and its distribution within each month.

Evolution Over Time

The following chart plots the median Cumulative Days on Market by month, without separating by Property Type because we didn’t think it should make a difference for this parameter. Based on just the monthly medians, a steady-state is elusive, but there is a striking series of January peaks, which suggest that the realtors spend January “winter-cleaning” stale listings. Cumulative days on market, in the period covered by the data, evolved as follows month by month.

In the above plot, the CDOM of each listing is assigned to the month in which the sale closed. We can also plot the same statistics about the month in which the property was listed instead:

It does not suggest that the January peaks in closings on stale properties correspond to any peak in listing activity in the preceding month.

Distribution

Of course, the medians don’t tell us the distribution, but the following boxplot does. 1102 outliers are omitted. The chart therefore summarizes 96% of the listings.

From this, it is clear that the distribution of CDOMs always has a long tail, and that it is reasonably steady from April, 2012 onwards, particularly if we omit the peaks around January. We also filter the properties that stayed on the market more than 9 months, on the grounds that delays of this magnitude are not related to the rightmost digits of the listing price, but instead to other factors, such as an unrealistic listing price, pending litigation, or uncooperative tenants.

We will focus on this data set to evaluate the effect of psychological pricing. As shown in the following histogram, it is both skewed and leptokurtic, and not even remotely gaussian.

Count Min 1st Quartile Median Mean 3rd Quartile Max Standard Deviation Skewness Kurtosis
13085 0 14 27 37.3 44 273 37.7 2.66 12

Influence of Price Categories on Days on Market

The following table shows statistics of the Cumulative Days On Market (CDOM) for various categories of prices, ordered by increasing medians, ranging from 23 to 33. Contrary to expectations, the roundest prices, ending in “00000” have the shortest median CDOM of 23 days, while the most common, “psychological prices” ending in “99000” have a median CDOM of 27 days.

The median is of greatest interest to individual sellers who will only go through one ordinary transaction. The mean, on the other hand, is more relevant to an agent going through tens of sales per year, because the few that require more time to close must be included in measuring his or her workload, and because the average number of deals in progress is calculated from the mean, not the median. An agent selling 30 properties/year with a mean CDOM of 40 days is working on an average of 40x30/365 = 3.3 listings at the same time.

Category Count Min 1st Quartile Median Mean 3rd Quartile Max
2 x00000 549 0 10 23 41 50 269
6 x95000 1961 0 13 24 33 40 272
4 x50000 873 0 13 24 36 42 253
3 x49000 1523 0 14 26 34 40 270
5 x90000 90 0 13 26 44 52 233
7 x99000 2514 0 15 27 37 43 271
1 Rare 472 0 13 28 44 55 271
10 xx9000 1809 0 17 28 37 44 273
9 xx5000 1576 0 14 28 40 49 270
11 xxx000 976 0 14 28 38 47 263
8 xx0000 460 0 14 29 43 55 270
12 xxx900 282 0 14 33 47 57 270
13 All 13085 0 14 27 37 44 273

Could these differences be accidental? Could another set of San Francisco listings produce a different ranking? We apply the Kruskal-Wallis rank sum test to find the answer:

## 
##  Kruskal-Wallis rank sum test
## 
## data:  CDOManalysisSubset$CDOM and as.factor(CDOManalysisSubset$Category)
## Kruskal-Wallis chi-squared = 82.484, df = 11, p-value = 4.873e-13

The hypothesis that the CDOM of the different categories are identically distributed is rejected.

Selling prices

For selling prices, we examine the ratio of selling price to listing price, and the difference between selling price and listing price. If psychological prices provide a percentage increase in the selling price, it will be reflected in the ratio; if they yield a fixed amount regardless of price, it will show in the difference.

Evolution Of Price Ratio Over Time

The following chart plots the median ratio of selling price to listing price by month, without separating by Property Type because we didn’t think it should make a difference for this parameter. It has been consistently above 1 since March, 2012, with pronounced valleys in December and January each year.

Distribution

Of course, the medians don’t tell us the distribution, but the following boxplot does. nnnn outliers are omitted. The chart therefore summarizes 96% of the listings.

## The following objects are masked from Sales_Year_Month_CDOM:
## 
##     MLS, Sale_Year_Month

From this, it is clear that the distribution of Price.Ratios always has a long tail, and that it is reasonably steady from June, 2012 onwards.

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Count Min 1st Quartile Median Mean 3rd Quartile Max Standard Deviation Skewness Kurtosis
13085 0.01 1 1.05 1.15 1.13 1000 8.74 114 13069

Influence of Price Categories on Ratio of Selling Price to Listing Price

Category Count Min 1st Quartile Median Mean 3rd Quartile Max
7 x99000 2514 0.1168 1.008 1.08 1.09 1.16 2.46
6 x95000 1961 0.6652 1.000 1.06 1.08 1.16 2.65
10 xx9000 1809 0.4947 1.000 1.05 1.07 1.13 2.92
9 xx5000 1576 0.6517 1.000 1.03 1.06 1.12 1.92
3 x49000 1523 0.6703 1.001 1.07 1.09 1.15 2.06
11 xxx000 976 0.0113 1.000 1.05 2.10 1.14 1000.00
4 x50000 873 0.1032 0.984 1.03 1.05 1.11 1.84
2 x00000 549 0.0100 0.960 1.00 1.03 1.09 10.71
1 Rare 472 0.6309 0.982 1.03 1.08 1.10 9.98
8 xx0000 460 0.6212 0.981 1.01 1.04 1.08 1.65
12 xxx900 282 0.6313 0.961 1.02 1.07 1.08 10.87
5 x90000 90 0.0102 0.977 1.00 1.03 1.11 1.42
13 All 13085 0.0100 1.000 1.05 1.15 1.13 1000.00

The following table summarizes the results by category for both Price Ratio and Cumulative Days On Market:

Category Count Price Ratio Cumulative Days On Market
8 x99000 2514 1.08 27
4 x49000 1523 1.07 26
7 x95000 1961 1.06 24
11 xx9000 1809 1.05 28
12 xxx000 976 1.05 28
2 Rare 472 1.03 28
5 x50000 873 1.03 24
10 xx5000 1576 1.03 28
13 xxx900 282 1.02 33
9 xx0000 460 1.01 29
3 x00000 549 1.00 23
6 x90000 90 1.00 26
1 All 13085 1.05 27

Influence of Price Categories on Selling Price/SqFt

Category Count Min 1st Quartile Median Mean 3rd Quartile Max
7 x99000 2042 100.21 546 676.22 702.75 842.61 2495.9
6 x95000 1561 163.73 658 811.38 829.36 974.18 2200.0
10 xx9000 1473 174.92 540 695.09 702.62 852.71 1526.8
9 xx5000 1338 146.35 552 711.01 720.04 877.62 2091.9
3 x49000 1212 159.09 557 702.92 707.55 839.43 1372.8
11 xxx000 864 113.54 486 612.70 656.91 802.06 2013.2
4 x50000 715 220.06 617 787.97 821.38 980.09 2523.6
1 Rare 448 132.89 418 562.49 582.05 715.40 1387.6
2 x00000 442 73.53 633 839.20 891.06 1094.24 2554.1
8 xx0000 405 129.17 453 614.63 638.93 806.18 1467.6
12 xxx900 272 31.79 344 456.87 488.25 600.29 1094.6
5 x90000 80 207.14 479 642.43 680.31 878.47 1332.3
13 All 10852 0.01 1 1.05 1.07 1.13 10.9

The following table summarizes the results by category for both Price Ratio, Cumulative Days On Market, and Price/SqFt:

Category Count Price Ratio Cumulative Days On Market Price/SqFt
8 x99000 2514 1.08 27 676.22
4 x49000 1523 1.07 26 702.92
7 x95000 1961 1.06 24 811.38
11 xx9000 1809 1.05 28 695.09
12 xxx000 976 1.05 28 612.70
2 Rare 472 1.03 28 562.49
5 x50000 873 1.03 24 787.97
10 xx5000 1576 1.03 28 711.01
13 xxx900 282 1.02 33 456.87
9 xx0000 460 1.01 29 614.63
3 x00000 549 1.00 23 839.20
6 x90000 90 1.00 26 642.43
1 All 13085 1.05 27 1.05

References

The Psychology of Pricing, Tery Karush Rogers, The New York Times, 2/18/2007