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Posts tagged pricing

By Jabus Tyerman (email: jabus@delvbio.com)

A post by Mark Perry about U-Haul truck rental prices suggested that so many people were moving away from San Jose, CA that it was causing shortages of U-Haul rental trucks in San Jose. In response to high demand for rental trucks, U-Haul was adjusting one-way truck rental prices for leaving San Jose to be many multiples of the prices to move from the same cities to San Jose. For example, Perry reported that the price to rent a truck to move from San Jose to Las Vegas, NV was 16x more than the price to move from Las Vegas to San Jose.

Perry suggested that U-Haul would use dynamic pricing to optimize one-way truck rental prices in response to local supply and demand, and that we could use the ratio of Outbound moving prices compared to Inbound moving prices to infer net movement of people between pairs of cities. I wondered if we could use this idea to get a real-time measurement of movement patterns (“migration”) among other US cities?

Because Perry only reported on price imbalances between San Jose and six other cities, I wanted to start by looking more broadly at pricing imbalances across the US. I collected U-Haul pricing data for the 100 largest US cities (by population), with the intention of ranking cities for Outflow (and Inflow), based on average imbalance in truck rental prices.

I paired each focal city (“A”) with every other city (“B”), and used the U-Haul website to collect one-way pricing quotes to rent a 10′ truck to move from A to B (Outbound), and from B to A (Inbound). I calculated the log(Outbound/Inbound) for each city pair, and then used the average result of all city pairs (for each focal city) to generate an index of migration for that city. I called this index the U-Haul Moving Index, or UMI.

For example, using San Jose, CA as the focal city (A):  The Outbound and Inbound one-way truck rental prices between San Jose and Tucson, AZ (B) were $1271 and $161 respectively. The Outbound/Inbound is $1271/$161 = 7.9 (and taking the log of 7.9 yields 2.06). This value was calculated using San Jose as A, and all cities as B, and the median value (“UMI”) for San Jose was 0.69.

[I converted the ratio of Outbound/Inbound to a log scale because taking the natural log of a ratio transforms the asymmetric linear scale into a symmetrical log scale. In this way, an Outbound price that is 2x the Inbound price will have the same scaling as an Outbound price that is 0.5x the Inbound price, i.e. a factor of 2 in both cases.]

Findings

The main results are illustrated in Figures 1 and 2 below.

Figure 1 ranks cities according to the U-Haul Moving Index (UMI). Cities having positive UMI (purple) are cities where Outbound prices are greater than Inbound prices, suggesting that trucks are in short supply, due to a net outflow of people. Cities having negative UMI (orange) are cities where Outbound prices are less than Inbound prices, due to a net inflow of people.

umi_plot

Figure 1. Cities ranked by Outflow (and Inflow) using the U-Haul Moving Index (UMI). Positive UMI (purple) cities are cities where Outbound prices are greater than Inbound prices (on average), suggesting trucks are in short supply relative to demand, due to a net outflow of people. Negative UMI (orange) cities are cities where Outbound prices are less than Inbound prices (on average), suggesting trucks are in surplus relative to demand, due to a net inflow of people.

(Click here for a high resolution .pdf of Figure 1)

Figure 2 is a map of 100 cities, colored by U-Haul Moving Index (UMI), and highlights strong regional patterns in these data.

Regions having positive UMIs — dominated by people leaving the regions — include California,  Chicago (and surrounding Lake Michigan states), New York City (and north eastern seaboard states), and Miami, FL.

Regions having negative UMIs — dominated by people arriving in the regions — include the south eastern states, Texas & Oklahoma, Arizona, and Boise, ID.

usa_map_of_umis

FIGURE 2. Map of US cities colored by U-Haul Moving Index (size reflects population).

How do these data compare to other studies?

Previously, U-Haul has analyzed its own data to report on migration trends. U-Haul used  total number of one way arrivals in 2017 to rank cities as US destinations, and found that Houston, TX and Chicago, IL were the top two destination cities. In contrast, UMI (this analysis) ranked Houston #42 (of 100) inflow cities, and Chicago as the top outflow city after California cities (Chicago was ranked 15/100). Additionally, U-Haul’s total one way arrival method ranked San Jose, CA as #42 in its list of top 50 destination cities, and this study using UMI ranks San Jose, CA as tied for top outflow city (#1 of 100). These differences in ranking may reflect differences in methodology.  However, because data in these studies came from different time periods (2017 for one way arrival data, and June 2018 for UMI data) it is conceivable that differences in city rankings are due to underlying differences in migration patterns rather than methodology. Whether one method is more accurate at describing patterns of migration has not been determined. In my opinion, however, the total one way arrivals method used by U-Haul appears to ignore the numbers of one-way departures, and may therefore not present a full accounting of inflows and outflows required to calculate the net flow of people to/from the city. Rental pricing — if dynamically optimized in response to local supply and demand — could better integrate information about in- and outflows of people.

The company Redfin has used house search data to estimate the movement of people and ranked San Francisco, New York and LA as top outflow cities (with Chicago as #5) — a result more in line with the UMI rankings in this study. However, Redfin also identified Sacramento, Phoenix and Las Vegas as top Destination cities, while the UMI in this study strongly ranked Sacramento as an outflow city and Las Vegas as having more balanced in- and outflow of people. (Phoenix had a moderately negative UMI suggesting it was a moderate inflow city). As with the U-Haul total one-way arrival method, it is unknown whether differences in city rankings between Redfin and this study stem from differences in methodology or differences in moving patterns due to the data being captured during different time periods.

One practical advantage of using the UMI method described in this study over the U-Haul total one-way arrival method and the Redfin home search method, is that U-Haul prices required for UMI calculations are readily available from the U-Haul website, while one way arrivals are available only to U-Haul, and home search data is available only to Redfin.

Conclusions

I used imbalances in U-Haul pricing data to generate U-Haul Moving Indices (UMI) for 100 US cities. This work builds on the ideas of Mark Perry in order to generate (near) real-time estimates of net people flows (Out- and Inflow) for each city.

While these data may reflect near real-time patterns of migration, they do not provide explanations why people are moving to- and from cities. Others have argued that taxes, cost of living, etc. spur people to leave cities and move on where conditions are better.

One of the assumptions I made (as did Perry) is that price is dynamically determined by U-Haul based on local supply and demand of rental trucks. U-Haul may  use other factors to set truck rental prices.

Follow up

This is a work in progress and I may update this post over time. If you have feedback or questions, I’d love to hear from you.

Methods

Cities are top U.S. cities (in lower 48 states) by population, based on 2013 census estimates using data available here.

U-Haul prices were obtained for one-way truck rentals (10′ trucks) collected over ~2 days from the U-Haul web site (https://www.uhaul.com) in June 2018.

Acknowledgements

Thanks to Andy Idsinga for fruitful discussions and insights that motivated this work.

Notes

  1. The blog post and study that motivated this work: Mark Perry (Feb 2018) SF Bay Area experiences mass exodus of residents, leading to a shortage of U-Haul trucks and sky-high prices for scarce outbound trucks. AEIdeas Blog. Last accessed 2018-06-18 from URL: http://www.aei.org/publication/san-francisco-bay-area-experiences-mass-exodus-of-residents-reflected-in-one-way-u-haul-truck-rental-rates/
  2. The U-Haul report on migration that used total one-way arrivals data: U-Haul (May 2018) U-Haul Migration Trends: Houston Ranks as No. 1 U.S. Destination. U-Haul Blog. Last accessed 2018-06-18 from URL: https://www.uhaul.com/Articles/About/14384/U-Haul-Migration-Trends-Houston-Ranks-As-No-1-Us-Destination/
  3. The Redfin study using home searches: Greg McCarriston (Feb 2018) Affordable Inland Metros Drew People from San Francisco, New York and Los Angeles. Redfin Blog. Last accessed 2018-06-14 from URL https://www.redfin.com/blog/2018/02/q4-migration-report.html.
  4. Blog post discussing explanations for people moving among cities (and states): Mark Perry (Feb 2018) . AEIdeas Blog. Last accessed 2018-06-18 from URL: https://www.aei.org/publication/americas-top-10-inbound-vs-top-10-outbound-states-how-do-they-compare-on-a-variety-of-tax-burden-business-climate-fiscal-health-and-economic-measures/

 

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