Acocella, Caplice, and Sheffi

Opportunities for market-based freight contracts

The end of “set it and forget it” pricing? Opportunities for market-based
freight contracts

Angela Acocella, Chris Caplice, Yossi Sheffi Center for Transportation &
Logistics, Massachusetts Institute of Technology,
<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
In the for-hire truckload market, firms often experience unexpected
transportation cost increases due to contracted transportation service
provider (carrier) load rejections. The dominant procurement strategy results
in long-term, fixed-price contracts that become obsolete as transportation
providers’ networks change and freight markets fluctuate between times of over
and under supply. We build behavioral models of the contracted carrier’s load
acceptance decision under two distinct freight market conditions based on
empirical load transaction data. With the results, we quantify carriers’
likelihood of sticking to the contract as their best known alternative priced
load options increase and become more attractive; in other words, carriers’
contract price stickiness. Finally, we explore carriers’ contract price
stickiness for different lane, freight, and carrier segments and offer
insights for shippers to identify where they can expect to see substantial
improvement in contracted carrier load acceptance as they consider
alternative, market-based pricing strategies.

Truckload transportation, freight procurement, supply contracts, indexed
pricing

##  1 Introduction

One of the unique aspects of the truckload (TL) freight industry is the non-
binding nature of the contracts. Shippers (firms with goods that must be
moved) contract with transportation service providers, or carriers (i.e.,
trucking companies) to haul their freight.

Contract prices are set at the time of the shipper’s strategic transportation
procurement event. The shipper communicates its forecasted demand for each
lane (pickup origin to drop-off destination pair) with carriers upfront.
However, volume and capacity commitments for both parties are not strict
contractual obligations. First, the shipper is not required to offer the
expected volume to the contracted carrier. In fact, the shipper may offer more
than, less than, or even none of the awarded volume, with no direct financial
penalty. This is because forecasting the precise time and lane of future
demand for trucking capacity is not realistic, especially when projections are
done often months or even a year in advance. Moreover, forecasting errors are
amplified when shippers’ end customer demand changes over the course of the
transportation contract.

Second, contracted carriers are not obligated to accept 100% of the volume
that is offered or tendered to them. Responding to many shippers’ uncertain
demand makes committing a truck to a specific future time and location almost
impossible, especially when commitments are expected to be in effect for a
year or more in most cases. As a result, a carrier can enter a contract with a
shipper for an expected amount of freight on a lane but uncertainties
introduced from other customers, general market dynamics, or changes in the
carrier’s own business require the flexibility to reject loads in real-time
capacity allocation decisions.

It is useful to think about the interactions between shippers and their for-
hire motor carriers as two stages of TL transportation: 1) the strategic
procurement process with its long-term carrier-lane matching decisions and 2)
the shipper’s operational, real-time load-carrier matching decisions with the
corresponding carrier acceptance or rejection decisions. We describe these
processes further in the following subsections.

###  1.1 Strategic Transportation Procurement

During the strategic procurement process (see Caplice (2007) for a detailed
description), shippers conduct a reverse auction in which they send a request
for proposals (RFPs) to a group of carriers. The RFP documents the lanes
(origin-destination pairs) on which the shipper requires priced transportation
services. It also includes the expected volumes on those lanes and other
service level expectations. Carriers respond to the RFPs by bidding the price
they are willing to accept to serve the expected demand on each lane in which
they are interested. The prices a carrier bids depend on the general
attractiveness of serving the origin and destination regions, attributes of
the freight itself, the carrier’s previous experience working with that
shipper, how well that lane fits within the carrier’s existing networks, and
the general market environment at the time.

The shipper awards the business to one or more carriers on each lane, which
are referred to as the contracted, awarded, or primary carriers. Typically a
carrier is selected because it is one of the lowest bidding carriers on the
lane and has high expected level of service (e.g., load acceptance rates, on-
time pickup and delivery, technological sophistication for communication,
information and data exchange, and payments, etc.).

Due to the possibility that primary carriers may reject loads, shippers
construct a routing guide for each lane. The routing guide is a sequential
list beginning with the primary carriers followed by a set of backup carriers.
These backup carriers typically have unsuccessfully bid on the lane, thus
expressing ability and willingness to serve at least some of the demand on
that lane. Most often, these carriers had bid higher prices than the winning
carrier(s). The backup carriers are entered into the routing guide at their
bid price, however, there is no contract in place between the shipper and
backup carriers. This means the backup carriers’ routing guide price is not
binding. Further, there is a much lower implicit assumption that backup
carriers will produce capacity.

###  1.2 Operational Load Tendering, Acceptance & Rejection

At the time a load needs to be moved, the shipper’s transportation management
system (TMS) tenders the load to the first carrier in the routing guide (the
primary, awarded carrier) at the contracted price. If the carrier accepts the
load, it agrees to move it at the contracted price. If the primary carrier
rejects the load, the load is offered to the first backup carrier at the price
denoted in the routing guide. Not only is this price between shipper and
backup carrier non-binding, it is likely higher than the primary carrier’s
price. Depending on prevailing market conditions, shippers price escalations
with backup carriers reach more than 18% above the primary carrier’s
contracted price (Acocella et al. 2020).

Like primary carriers, backup carriers may accept or reject load offers. The
shipper proceeds down the routing guide until a backup carrier accepts the
load or some price or time threshold is hit. At that point, the shipper may
turn to the spot market. In this case, the shipper consults a load board where
it can post information regarding the load’s pickup, drop-off, timing, and
other requirements and view carriers who have posted currently available
capacity and associated prices on the lane.

Shippers find a carrier on the spot market for independent transactions, but
there is no single spot market price at any given time, even for spot loads on
the same lane. Instead, when we refer to the “spot market price” it is the
average of a range of prices. Figure 1 illustrates this point.

Figure 1: Daily Spot Prices for Single Lane

It depicts actual loads fulfilled on the spot market from 6 shippers on a
single lane in October 2017. Each day, there may be one, many, or no loads
that require spot capacity. Each load is fulfilled at a different price set by
the individual carrier and depends on the carrier’s network structure at that
moment. In the remainder of this study, we discuss the dynamic average lane-
specific spot price, depicted in the figure, which represents an underlying
distribution of individual realized spot load prices.

####  1.2.1 Contractual relationships and the best known alternative

Spot market prices are highly volatile and represent the dynamic nature of
immediate balance between trucking supply and demand. For shippers and
carriers alike, the spot market represents alternative price options to a
contracted load. When trending spot prices are high relative to contract
prices, carriers may be tempted away from adhering to their contractual
agreements. A primary carrier can either uphold its contractual commitments
with the shipper by accepting loads and maintaining the relationship, or it
can act opportunistically by rejecting loads and offering its capacity on the
spot market with higher expected profit. However, by reneging on its contract
and rejecting loads, the carrier risks potential future business from that
shipper.

About 72% of for-hire TL freight is accepted by the primary carrier, while
about 5% is fulfilled by spot capacity (Caplice 2007). The remaining 23% is
moved by backup carriers within the shipper’s routing guide. When spot market
prices are higher than average contract prices - a condition referred to as a
tight market - shippers typically pay a price premium of 35% above the
contract price if they end up using spot carriers (Aemireddy and Yuan 2019).

Even when backup carrier prices or spot market prices are below a shipper’s
contracted carrier’s price, there are substantial benefits to working with
primary carriers rather than backup or spot carriers. The shipper’s RFP is a
vetting process. Over the course of weeks, sometimes months, the shipper and
its bidding carriers not only communicate expected demand, service
expectations, and pricing, but the carriers have also have demonstrated fast
and simple communication processes, and technological sophistication to
integrate with the shipper’s electronic data interchange (EDI) and payment
systems.

An account manager is assigned by each of the contracting parties. This person
continuously evaluates performance over the course of the contract and is the
point of contact when performance issues arise. As a result, the value for the
shipper of working with a primary carrier includes the ease of business
processes and relationship developed. Due to its transactional nature, none of
these process or communication channels are established for spot loads.
Furthermore, the spot market price is not known to the shipper in advance.
Thus, both service level and actual price to be paid to spot market carriers
are largely uncertain. Therefore, it is typically in shippers’ best interest
to encourage primary carriers to accept loads, even if the spot market price
is expected to be better (i.e., lower) than contract prices.

As freight markets fluctuate between periods of over and under supply - soft
and tight markets, respectively - shippers’ fixed contract prices can become
stale. As a result, the amount of freight that is accepted and moved at the
original contracted price declines over the course of the contract. To
mitigate this issue and ensure contract prices remain market competitive,
there has been growing interest from both shippers and carriers to explore
market-based pricing into their portfolio of TL freight contracts.
Understanding carriers’ willingness to stick to (or defect from) their
contracted load price helps practitioners identify the most promising network,
lane, freight, and carrier segments for this market-driven approach.

The remainder of this paper is structured as follows. Section 2 discusses
practitioners’ considerations regarding index-based contracts, Section 3
offers a review of the relevant literature, Section 4 summarizes our research
question and the hypotheses tested, and Section 5 describes our empirical
dataset and model specifications. We present the results of the models in
Section 6 and their implications, particularly for market-based pricing
consideration, in Section 7. We conclude in Section 8 with a discussion of
limitations of this research and areas for further exploration.

##  2 Market-based Freight Contracts

For every load a contracted carrier is tendered on a contracted lane, it can
either accept the load or reject it and fill available capacity with a load on
the spot market. Carriers may also have other contracted shippers on the same
or similar lanes and thus other contracted business available as an
alternative option. However, because the shipper has no knowledge of its
contracted carriers’ other customers and because spot prices and contract
prices move up and down together, albeit with some lag (see Pickett (2018)),
we use the average lane-specific spot market price to represent carriers’
alternative options.

As the average price of spot market loads available to the carrier increases
relative to the contracted price, an opportunistic carrier with low contract
price stickiness will be incentivized away from accepting the contracted
shippers’ loads. For each load offered to a contracted carrier, we calculate
its Spot Rate Differential (SRD), or how much the current lane-specific spot
price is above or below the load’s contract price, as a percentage:

$SRD_{k,i,j,t}=\dfrac{(SpotPrice_{i,j,t}-ContractPrice_{k,i,j,t})}{ContractPrice_{k,i,j,t}}\times
100$ (1)

where $k$ is the load tendered to the carrier on lane with origin $i$ and
destination $j$ at time $t$.

This Spot Rate Differential is the percent difference between the contract
price and spot market price at a given time and the key metric for carrier
contract price stickiness. Building off of the literature described in
Subsection 3.3 we define contract price stickiness as the rate at which the
contract price must change (relative to the current lane-specific spot price)
as factors exogenous to the contract change.

A market-based pricing strategy aims to appeal to carriers with low contract
price stickiness. Market- or index-based pricing is commonly used in
industrial, agricultural, and energy commodities markets. Similar to the
truckload market, these products see cyclical supply and demand fluctuations.
Market-based pricing helps simplify price negotiations and increase
transparency for long-term contracts between sellers and buyers, particularly
when price volatility over time is a concern (Singh et al. 2016). Interest in
indexed pricing has grown in the truckload freight market as both shippers and
carriers seek ways to mitigate the risks incurred by freight market cycles.

Figure 2 demonstrates the dynamic nature of the truckload freight market. We
present the Truckload Linehaul Index reported by Cass Information Systems,
Inc. - a leading industry provider of information and payment solutions - and
national average contract and spot market prices from our empirical dataset
from September 2015 to January 2020.111The Cass Truckload Linehaul Index is
comprised of 95% contract load transaction data and 5% spot load data.
Discussion of how our empirical dataset appropriately represents dynamics in
the truckload freight market is found in Section 5.

Figure 2: Industry Index, Spot, and Contract prices

The variations in market index and spot and contract prices over this time
period reflect both soft and tight market periods. Until July of 2017, the
industry experienced a soft market, where we see low prices and index values.
Following this time, the industry experienced a very tight market, with high
prices and severely deteriorated primary carrier acceptance rates. In fact, in
the first soft market period, average primary carrier acceptance rates were
81.9%. This number dropped to 68.5% in the subsequent tight market period.
Acocella et al. (2020) provide quantitative justification of these market
periods and, along with Aemireddy and Yuan (2019) and Sokoloff and Zhang
(2020), analyze market-driven primary carrier acceptance rates.

As the freight market cycles between soft and tight periods, index-based
pricing strategies aim to allow contract prices to adjust automatically with
changes in the broad market. Otherwise, shippers manually adjust prices
through full RFPs or “mini-bids” (targeted carrier or lane price adjustments
specifically focused on under-performing segments, typically resulting in
short-term fixed-price agreements). With index-based strategies, the
contracted price between a shipper and primary carrier increases or decreases
with a market-based indicator such as those reported by Cass Information
Systems Inc. or DAT Freight & Analytics.

A handful of large shippers that operate in the consumer packaged goods, food
and beverage, and manufacturing industries, and their carriers (both asset and
non-asset) have explored index-based pricing strategies in practice. Those
that have to date, however, have only done so on a small set of trial or pilot
lanes (Sinha and Thykandi 2019). In addition, some carriers, particularly 3PLs
and brokerages (i.e., non-asset providers), have dedicated resources to offer
dynamic pricing options for their shipper customers (see Convoy (2020),
Schneider Transportation (2019), Uber Freight (2021), and BR Williams (2020)).

Despite the potential benefits of market-based pricing strategies, the
advantages of traditional fixed-price contracts remain. Shippers and carriers
alike seek consistency and predictability - both in terms of demand or
capacity availability and prices. Shippers run annual RFPs to establish fixed
contract prices around which they can budget. Carriers intend to provide high-
quality service to their customers but need to know they will be able to cover
their costs in the process. Keeping this in mind, we aim to help shippers and
carriers understand where this traditional fixed-price approach is effective
and where an alternative market-driven approach may be beneficial.

##  3 Literature Review

In this research, we quantify carrier’s willingness to stick to contracts by
constructing empirical behavioral models that include industry dynamics not
captured in previous literature.

###  3.1 Supply chain contracts

Much of the extant literature on supply chain contracting explores the ways
contracts help coordinate or share risks between buyer and supplier (Lariviere
1999). Agents seek risk-sharing contracts to encourage both sides to remain
committed to the contract terms through buy-back (Pasternack 1985, Deneckere
et al. 1997), revenue sharing (Cachon and Lariviere 2005), and options
(Barnes-Schuster et al. 2002) contracts. (See Cachon (2003) and Simchi-Levi et
al. (2014) for surveys of these contracting mechanisms.)

The non-binding TL freight contract is similar to the self-enforcing
agreements studied in the context of repeated games literature, which explores
agreements that result in both parties maintaining the terms of the agreement
over time without the interference of an external party (Telser 1980).
Instead, informal mechanisms are used for contract enforcement. As the
transportation provider considers each load, if it sticks to the contract by
accepting the load, it maintains that relationship with its shipper. On the
other hand, the transportation provider can defect from the contract, reject
the load, and damage the relationship with each rejection (see Scott et al.
(2020)). This self-interested, opportunistic behavior that violates the
existing contract may be influenced to higher priced alternative options on an
external spot market (Williamson 1975, 1985, Wathne and Heide 2000). However,
the value of future potential business - i.e., the shadow of the future -
encourages carrier contract compliance (Heide and Miner 1992, Oxley 2012).

For shippers, the incentive to stick to their contracts stems from the initial
investment and vetting involved with securing the contracted carriers in the
first place. The procurement process discussed in Section 1.1 takes months of
preparation, communication, and analysis to establish contracted carriers on
each lane. Transaction Cost Theory considers the costs incurred as a result of
the information search, negotiation, and monitoring involved in the exchange
of a good or service between agents – effectively, the frictions of a
transaction (Williamson 1985, 1979). The theory justifies the use of contracts
as a means of defining the terms of inter-firm agreements (Williamson 2002),
made particularly important with uncertainty and high frequency of
interactions (Williamson 1979). Masten (2010) underscores the benefit of
contract use, noting that the contract collects many repeated heterogeneous
transactions under one common pricing policy, reducing the transaction costs
needed to repeatedly negotiate prices for each transaction.

###  3.2 Shipper-carrier relationships

We further motivate the research by expanding the extant body of literature on
shipper-carrier relationships, specifically that on primary carrier load
acceptance decisions. Rather than direct measures of the shipper-carrier
interactions, however, much of the literature considers attributes of the
lanes and freight to determine primary carrier acceptance rate (PAR). PAR is
measured as the percentage of loads a primary carrier accepts relative to the
number of loads it is tendered on its contracted lanes. High lane volume
(Harding 2005), low lane volume volatility (Kim 2013), high prices (Amiryan
and Bhattacharjee 2015), and high lane consistency, or cadence, (Aemireddy and
Yuan 2019) have been found to be positively correlated with higher PAR, all
else equal.

The shipper-carrier relationship itself, however, has been found to contribute
to carrier PAR in a few studies. Scott et al. (2016) analyze contract and spot
market transactions and the impact of the history of the shipper-carrier
relationship on freight acceptance. The authors find that less frequent load
offers increase the likelihood of a primary carrier rejecting a load, while
higher offered volume, lower load offer volatility, and higher revenue
transacted between the shipper and carrier increase the likelihood of
carrier’s load acceptance. Zsidisin et al. (2007) define a “good” shipper-
carrier relationship as one in which a contract is in place and find that
contracted carriers outperform non-contracted carriers in terms of freight
acceptance, on-time delivery, and pre-positioned capacity. These two studies
each obtain data from a single shipper, which limits their ability to
generalize across types of shippers or segment their datasets to offer
insights specific for types of shippers’ business.

The impact of market dynamics on carriers’ freight acceptance decision is
studied in Acocella et al. (2020). The authors consider two distinct market
conditions: soft, where shippers have low demand relative to available
capacity and thus corresponding low contract and spot prices, and tight, where
demand for TL capacity outstrips supply and prices are high (spot prices
typically exceed contract prices). The authors find one of the main
contributor to primary carriers’ tight market acceptance decision to be how
competitive the shippers’ contracted load offer price is with prevailing
market prices. Scott et al. (2016) also consider a measure of market condition
- Spot Premium - in determining carrier load acceptance decisions and find
that carriers consider overall market conditions and alternative priced loads
when making contracted load acceptance decisions.

The nature of existing TL contracts, external market conditions, and their
impact on carriers’ load acceptance decisions are studied in Scott et al.
(2020). The authors find that explicit contracts (those that have more
formally defined service level expectations) as compared to implicit contracts
illicit higher primary carrier acceptance rates from carriers. In addition,
and similar to the findings by Acocella et al. (2020), as the market tightens
and becomes more attractive to carriers, the benefit seen by these explicit
contracts diminishes.

Finally, Lindsey and Mahmassani (2015) consider TL carriers’ reservation
prices and willingness to accept loads. Using spot market prices and a
discrete choice survey experiment, the authors find that carriers’ contracted
load acceptance decisions are impacted by higher-priced hypothetical
alternative load options. We expand this research by using empirical data to
study actual carrier decisions and explore how these decisions differ across
shippers’ freight networks, carriers’ service types, and overall freight
market conditions.

###  3.3 Supplier price stickiness

While our research builds on the transportation literature, we also draw from
that which models price stickiness - in other words, the rate at which prices
change in response to internal firm or external market dynamics. Much of this
literature focuses on how suppliers’ prices change as a collective at the
industry level, rather than the micro, firm level.

The most relevant stream of literature to our research consists of a set of
studies focused on producer pricing stickiness to customer demand patterns or
to external market prices. Manufacturers adjust prices due to underlying costs
and customer demand changes (Loupias and Sevestre 2013) and beliefs that
competitors are also changing prices (known as coordination failure) (Blinder
(1991) and Blinder et al. (1998)).

This coordination failure comes into play in the TL context during the
strategic RFP stage. Carriers do not coordinate with one another on pricing of
lanes. However, while carriers submit lane bid prices according to their own
network fit, if they want to be competitive, they must also factor in their
beliefs about how other carriers may be pricing the lanes they want.
Submitting bids that are too high may mean another carrier is awarded the
business; too low and they may be chosen for the contract, but at a price that
cuts into critical profit margins. This coordination failure may result in a
race to the bottom and cause the shipper to award poor-fitting carriers to
lanes.

Studies by Fabiani et al. (2006) and Fabiani et al. (2007) use a survey of
over 11,000 firms across Europe and find that most firms consider both
historical market information and expectations of the market when making
pricing decisions. The authors conclude that not only is price stickiness
influenced by market conditions, it is also related to customer relationships
as defined by explicit and implicit contracts. These findings underscore
truckload practitioner sentiments and findings by Scott et al. (2020) that a
combination of market conditions and standing shipper-carrier relationships
are key determinants for carrier pricing and load acceptance decisions.

The above studies also find that individual firms’ rate of price change tends
to be slower than that of the general market. This time- and market state-
dependent supplier price stickiness is further explored by Loupias and Ricart
(2006), Hall et al. (2000), and Apel et al. (2005). Similar results are
observed in the TL freight context as carriers’ contract price changes tend to
lag those of spot prices (see Pickett (2018)). In addition, contract freight
rates rise more quickly than they fall.

The extant literature shines light on how producers make (predominantly
strategic) pricing decisions. However, there are few studies of if or how
suppliers choose to offer their product or service at an operational level to
contracted customers or to non-contracted customers on a spot-like market. We
aim to add to the literature in this way.

##  4 Research Question and Hypotheses

As discussed above, the long-term, fixed-price contracts between shippers and
their TL carriers are non-binding in volume and capacity commitments. They
often result in degraded performance and unexpected price escalations as
exogenous market conditions change. Alternative contract forms, in particular
those based on indexed pricing, have drawn recent attention. With this
research, we aim to help shippers and carriers determine the most promising
areas within their networks for index-based pricing in their portfolio of
freight contracts. Thus, we address the following research question:
For which segments of shippers’ networks - lanes, volume, demand patterns, and
carriers - should they consider index-based contracts?

To answer this question, we model primary carrier load acceptance decisions
based on the load’s offered price relative to the carrier’s best-known
alternative option: the current lane-specific spot market price. In this way,
we can demonstrate carriers’ contract price stickiness. We formulate our first
hypothesis as:

H1: A load is more likely to be accepted by a primary carrier the higher the
contracted price is relative to the current, lane-specific spot market price.

This claim is the basis for our behavioral assumptions that carriers prefer
higher priced loads (Williamson 1975, Wathne and Heide 2000).

Next, we consider carriers’ willingness to stick with contract prices for
different lane and freight types. We measure how primary carriers’ likelihood
of accepting a load is impacted as the offered price of the load changes
relative to the spot market price for these lane and freight segments of
interest. First, we consider a lane’s distance. While carriers each have
individual preferences and strategies relating lane distances, we aim to
isolate segments to determine general patterns. We define the following
hypothesis:

H2: The likelihood a primary carrier accepts a load increases with lane
distance and further increases as the load’s contracted price increases
relative to the current, lane-specific spot price.

Next, we consider how price adjustments impact primary carrier load acceptance
for different lane demand patterns. Shippers’ infrequent and inconsistent
tendering behaviors lead to lower primary carrier acceptance (see Section
3.2). For lanes on which a shipper tenders loads inconsistently, it may be
more difficult or require longer distances driven empty for a carrier to re-
position capacity when a load is tendered. A higher price incentive may
improve the probability the carrier accepts the load.

We expect that index-based pricing for lanes with inconsistent demand will
result in higher primary carrier acceptance and less reliance on backup or
spot alternatives. Moreover, carriers would benefit by being able to better
cover additional internal costs for serving unanticipated demand. This leads
us to the following two hypotheses:

H3: The likelihood a primary carrier accepts a load increases with higher
shipper tendering frequency on the awarded lane and further increases as the
load’s contracted price increases relative to the current, lane-specific spot
price.

H4: The likelihood a primary carrier accepts a load increases with lower
shipper tendered volume volatility on the awarded lane and further increases
as the load’s contracted price increases relative to the current, lane-
specific spot price.

In the above hypotheses, we capture lane-level demand patterns that make
carrier acceptance difficult. Next, we measure a load characteristic: surge
volume. Recall, the contract agreement between a shipper and a primary carrier
includes a (non-binding) awarded or expected volume However, due to poor
forecasts, network changes, or other unanticipated end customer demand,
shippers may tender more loads to a contracted carrier than the awarded volume
in a given week.222A similar issue for primary carriers may arise if the
shipper tenders much less than the awarded volume. While this is an important
issue to address, it is out of the scope of the present research. This
additional surge volume above the carrier’s allocated capacity to that lane
may be more difficult or costly to cover and may require an additional price
incentive for the carrier to accept the surge loads. Thus, we identify each
load that is tendered above the awarded weekly volume as surge loads and test
the following hypothesis:

H5: The likelihood a primary carrier accepts a surge load increases as the
load’s contracted price increases relative to the current lane-specific spot
price.

Finally, we aim to determine which carrier types are best suited for indexed
pricing. Carriers fall into one of two categories based on the services
provided: asset-based carriers that own the trucks and trailers used to move
freight, and non-asset providers, often referred to as brokers or third party
logistics (3PL) providers. This latter group of providers remove the shippers’
burden of securing capacity and act as the middle man between shippers and
asset-based carriers. Brokers access a vast pool of typically smaller, asset-
based carriers, aggregate their capacity, and match it to shippers’ demand.
These brokers, or non-asset providers, typically buy and sell transportation
based on their expectations of the general market; their profit margins are
tied to how well they are able to manage the cycles. We test the following
hypothesis:

H6: Non-asset primary carriers are less likely than asset-based primary
carriers to stick to fixed-price contracts as spot market prices rise.

We test this hypothesis by calculating the rate of primary carrier load
acceptance (PAR) as Spot Rate Differential changes. A higher rate of change
(i.e., decrease in PAR as spot price increases relative to contract price)
suggests lower contract price stickiness. A similar approach is taken by
Lindsey and Mahmassani (2015) to measure carriers’ load price elasticity.

We further characterize asset carriers based on their fleet size. We expect
that larger carriers may be better insulated from fluctuations in the market
and may be more willing to forego opportunistic spot market loads than smaller
carriers. We formulate our final hypothesis as follows:

H7: Larger asset carriers are more likely than smaller carriers to stick to
fixed-price contracts as spot market prices rise.

By exploring each of these hypotheses individually, we can measure carriers’
contract price stickiness for different freight segments of interest and
identify which areas of a shipper’s network each carrier type may be most
amenable to index-based pricing. In this way, we address our central research
question.

##  5 Carrier load acceptance model specification

In this section, we summarize our empirical data, describe our carrier
acceptance model, and define the variables we use to build the model. Our
partner company - a major US freight transportation management firm - provides
us with transaction data over four years (2015-2019) of all of the TL loads
for 68 shippers of various sizes and industry verticals and their 412 (primary
and backup) carriers, both asset and non-asset. The data represent each load’s
tender sequence. This includes the date, time, and price at which each load is
tendered to the primary carrier with its accept or reject decision, and, if
needed, backup carriers’ accept or reject decisions. The reported tender
sequence continues down the routing guide waterfall until a carrier - primary
or otherwise - accepts the load and the price the load is accepted at,
including an indication if it ultimately is moved on the spot market.

The set contains 1.7 million long-haul loads (i.e., loads that move a distance
greater than 250 miles)333We use this long-haul distinction because pricing
structures for the alternative, short-haul moves, differ from those we
consider and discuss in this research. all of which originate and terminate in
the continental US. From the subset of tenders to primary carriers, we model
the probability a load is either accepted or rejected (a binary outcome) by
the primary carrier based on associated load, lane, shipper, and carrier
characteristics described in the following subsections.

Logistic regression models are widely used in econometric literature to
isolate the relationships between a binary dependent variable and independent
input variables. Moreover, these models are the predominant modeling choices
for authors studying producer and consumer price stickiness (Loupias and
Sevestre 2013, Cecchetti 1986, Cao et al. 2012). We adopt a logistic model
choice as well and, to allow for non-linearity between independent and
dependent variables (Morris and Joyce 1988), we discretize continuous input
variables and include them as categorical variables.

Our dataset is comprised of multiple load accept/reject decisions by each
carrier. As such, we must account for repeated measures of the same individual
carrier. With repeated measures data, typical (logistic) regression modeling
neglects to account for the correlations between the set of decisions made by
the same individual. This within-subject correlation results in inefficient
estimators. In other words, the calculated estimators have a greater spread
around the true population values. Instead, General Estimating Equations
(GEEs) model the average response of an individual in the population (Liang
and Zeger 1986, Ballinger 2004). The regression coefficient estimates in GEE
models consider the covariance matrix between the outcomes in the sample
associated with the same individual. GEE estimators reduce to those obtained
through OLS if the dependent variable is normally distributed and no within-
individual response correlations exists (Hardin and Hilbe 2012, Greene 2003).

We use a GEE model with a logistic link function where the coefficient
estimates represent the marginal increase or decrease in the (log) odds a
carrier accepts a load:

$logit(y_{c,k})=log\Big{(}\dfrac{y_{c,k}}{1-y_{c,k}}\Big{)}=x_{c,k}^{T}\boldsymbol{\beta}$
(2)

where each individual primary carrier, $c$, makes a binary accept/reject
decision for each load it is tendered, $k$ (the positive outcome, $y_{c,k}=1$,
is a load acceptance), and the matrix of explanatory variables, $x_{c,k}$, are
the lane, freight, shipper, and carrier variables described in the following
subsections.

###  5.1 Load Spot Rate Differential

We define the Spot Rate Differential (SRD) in Section 2 and Eq. 1 as the
percent difference between the current lane-specific spot market price and the
contracted price of a load. The SRD calculation requires knowledge of each
lane’s spot price at the time a load is offered. While we do not have such
data consistently across all lanes and time, given the breadth of our dataset,
we can calculate benchmark spot market prices.

Our dataset approximately represents the general freight market trends as it
is comprised of many shippers’ load tenders across the continental US. We
corroborate this claim by comparing two statistics from our dataset to
external industry data. First, we measure the correlation between the time
series of average primary carrier acceptance rate (PAR) in our dataset, a
real-time primary carrier behavior, and the Morgan Stanley Freight Index,
which represents overall practitioner sentiment of the market’s supply and
demand. The correlation between the two time series is 85.2% (see Scott et al.
(2016) for a similar justification process). Second, the correlation between
our national average contract linehaul price and that of the Cass Truckload
Linehaul Index is 91.8%. We conclude that our dataset is sufficiently
representative of the overall freight market.

Next, we reconstruct spot prices for each origin region to destination region
combination. Regions of the US differ in attractiveness to carriers based on
the business opportunities that are expected in those areas. For example,
regions with high outbound demand are typically more attractive for carriers
to accept loads going into because they are more likely to easily find a
follow-on load. To account for the dynamic nature of spot prices, we include
the year and month indicator in the spot price model.

Daganzo (2005) shows that point-to-point transportation costs (e.g., linehual
costs) result from a combination of fixed and variable costs. Based on this,
we model spot prices using multiple linear regression with heteroskedastic
robust standard errors. We regress the point-to-point linehaul price of loads
that are accepted on the spot market in our dataset on origin and destination
region binary variables and a month and a year binary variable. These
represent fixed costs. We include a continuous distance variable, which
represents the carriers’ variable costs (Ballou 1991, Scott 2015). Acocella et
al. (2020) further detail the price benchmarking methodology used here.

Our base case lane (i.e., the binary variables omitted to avoid
multicollinearity) originates in the Lower Atlantic region of the US and
terminates in the South Central region in January of 2016. These ommitted
variable choices correspond to the most volume (i.e., greatest number of
observations) within each categorical variable. The lane-specific spot price
for a given time, $Spot_{i,j,t}$ is defined as:

$\begin{split}Spot_{i,j,t}&=\hat{\beta}_{base}+\hat{\beta}_{dist}\overline{X}^{(i,j)}_{dist}+\sum_{i\in
I,i\neq i_{base}}\hat{\beta}_{i}X_{i}+\sum_{j\in J,j\neq
j_{base}}\hat{\beta}_{j}X_{j}\\\ &+\sum_{m\in M,m\neq
m_{base}}\hat{\beta}_{m}X_{m}+\sum_{y\in Y,y\neq
y_{base}}\hat{\beta}_{y}X_{y}\end{split}$ (3)

The intercept term, $\hat{\beta}_{base}$, is the fixed cost of the base case,
and $\hat{\beta}_{dist}$, is a distance (i.e. variable cost) coefficient
associated with the average distance of loads between $i$ and $j$,
$\overline{X}^{(i,j)}_{dist}$. The fixed cost of the origin and destination
regions that are different from the base case are represented by the $I$-1
origin coefficients, $\hat{\beta}_{i}$ (where $I$ is the set of origin regions
and $X_{i}$ the corresponding $I$ binary variables indicating in which region
the load originates), and $J$-1 destination coefficients, $\hat{\beta}_{j}$
(where $J$ is the set of destination regions and $X_{j}$ the corresponding
destination binary variables). The 15 mutually exclusive and collectively
exhaustive regions are key market areas defined by our industry partner
representing geographic clusters of transportation demand patterns. The origin
and destination coefficients of our linear regression model, $\hat{\beta}_{i}$
and $\hat{\beta}_{j}$, can be interpreted as spot price premiums associated
with an origin or destination different from the base case lane.

Finally, $\hat{\beta}_{m}$ and $\hat{\beta}_{y}$ measure the dynamic, time-
based changes in spot prices for each month and year, respectively, and
capture both seasonal and underlying market structural trends.444We choose to
include month and year variables (as opposed to a single variable that treats
each month in the time frame separately - that is, $m\in\\{1,60\\}$ and no
$X_{y}$ variable) to ensure enough observations are in each time-based outcome
variable for robust coefficient estimates. As a notational simplification, for
the remainder of this paper, we combine $m$ and $y$ for a time-dependent
variable by denoting it with a subscript $t$.

With the results of this model, we calculate a single average spot price for
every origin-destination-month-year combination in the dataset. As discussed
in Section 1.2, this spot price represents the average of a distribution of
underlying spot load prices. We use this average spot market price to
calculate the Spot Rate Differential (SRD) for each load, $k$, using Equation
1 as the key metric to test carriers’ contract price stickiness.

###  5.2 Lane distance

Carriers’ preferences regarding lane distance may vary depending on individual
operations. Each carrier tries to maximize asset utilization - in other words,
miles driven carrying a paid load. We measure a lane’s distance by the number
of days it takes to drive that distance, assuming a driver can drive 400 miles
per day based on federally mandated hours of service regulations and actual
driving patterns (J.B. Hunt 2015). For a more detailed discussion of carrier
economics, see Belzer and Sedo (2018), Masten (2010), and Burks and Monaco
(2019).

Our lane distance measure is broken into five binary “travel-days” variables
based on whether the lane is expected to take up to 1 day to drive, 1-2 days,
2-3 days, 3-4 days, or more than 4 days. Rather than using a continuous
variable for distance (or travel-days), we decompose the variable into these
categories to avoid a linear assumption on the relationship between carrier
acceptance and distance.

###  5.3 Lane demand cadence

In the supplier-buyer relationship, frequency of interactions points to more
positive relationship; infrequent demand patterns are problematic for
suppliers (Rinehart et al. 2004). This aspect of the relationship is
particularly true in the TL industry. Inconsistent or infrequent tendered
volume from one shipper (the customer) makes it difficult for the
transportation suppliers (carriers) to plan where and when they need to
position capacity to balance their networks and serve each of their other
customers.

One metric carriers use to measure shipper performance is tender cadence, or
the frequency at which loads are tendered (J.B. Hunt 2015, C.H. Robinson
2015). Scott et al. (2016) incorporate this frequency of interactions as a
contributor to load acceptance by measuring the number of days since the
previous load was offered to a carrier by a shipper. The authors find that
carriers are less willing to accept loads that are tendered at unpredictable
frequencies. Moreover, Acocella et al. (2020) demonstrate that primary carrier
acceptance increases with the percentage of weeks in which loads are tendered
to that carrier on that lane.

We use this latter measure to characterize a lane’s frequency. For each load,
we calculate the percent of the preceding four weeks in which that shipper
tendered at least one load to that carrier on that lane. The resulting cadence
metric is a discrete measure, taking on values of 0%, 25%, 50%, 75%, or 100%.
Our input variables to the carrier acceptance decision models are binary
variables indicating which of these discrete values the cadence measure takes.

###  5.4 Lane demand volatility

In addition to the frequency of interactions, consistency of demand is an
important factor for carriers to anticipate capacity needs (J.B. Hunt 2015,
C.H. Robinson 2015). Both practitioners and the literature note the importance
of reducing tendered volume variability to improve carrier freight acceptance,
reduce the cost of loads, and help carriers better utilize their capacity
(Harding 2005, Scott et al. 2016, Aemireddy and Yuan 2019, Acocella et al.
2020).

We incorporate a measure of lane-level tendering volatility between a shipper
and primary carrier acceptance. Each load is assigned the corresponding lane-
level tendering volatility, which we calculate as the shifted 4-week rolling
average week-over-week change (measured as the square difference) in tendered
volume from the shipper to the carrier on that lane:

$Vol_{i,j,t}=\sqrt{\dfrac{\sum^{t-4}_{\tau=t-1}(d_{i,j,\tau}-d_{i,j,\tau-1})^{2}}{4}}$
(4)

where load $k$ is tendered on lane $(i,j)$ in time period $t$ and
$d_{i,j,\tau}$ is the number of loads tendered on the lane in week $\tau$. We
consider only weeks in which loads materialize and are tendered to the carrier
- in other words, weeks in which $d_{i,j,\tau}>0$. This is because we want a
measure of the volatility of the materialized volume. We already capture how
frequently there are no-volume weeks with the Cadence measure.

###  5.5 Surge volume

Next, we consider surge volume, a load characteristic defined as tendered
loads that are above the awarded, or expected, weekly volume. Carriers report
that they can typically manage to make capacity available when the number of
loads tendered from a shipper in a week is within about 10% of the lane award
volume. However, as volume reaches and surpasses 20% of the award volume,
carriers often are unable to serve the excess demand. Moreover, shippers
commonly call for contracted carriers to flex up with increased demand, often
up to 20% above the awarded volume, as a stipulation of the service level
expectations in the contract (Singh 2021). Such service level expectations
highlight the non-binding nature of the contract: while agreed upon and
defined in the contract, they are not legally or contractually enforceable by
the shipper. The main incentive for the carrier to uphold them is the promise
of continued business from the shipper (i.e., the shadow of the future).

While the expected volume is part of the information communicated to carriers
during the RFP, many shippers do not keep careful record of the awarded volume
to each carrier on each lane after the bid is complete. As such, our dataset
does not include the primary carriers’ awarded volume for each lane. Instead,
we use a proxy for this awarded volume: the preceding shifted 4-week rolling
average of the tendered volume to the primary carrier on the lane. Scott et
al. (2016) use a similar proxy to rank loads. The authors measure the average
daily volume on a given lane over the 30 days preceding the load of interest
and denote how the load’s rank within the day measures relative to that 4-week
rolling average daily volume. We similarly rank each load within the week and
categorize it based on how its rank compares to the awarded weekly volume
proxy.

Each load is assigned to its corresponding surge category. If the load’s rank
within the week is less than or equal to the awarded volume proxy, it is given
a Surge category of Within Mean. If the load’s rank is more than the average
but less than or equal to 10% above the mean, it is in the Up to 10% Surge
category, if it is more than 10% but less than or equal to 20% of the average
volume, it is in the Up to 20% Surge category, and if the load’s rank is more
than 20% above the awarded volume proxy, it is in the Over 20% Surge category.
We expect the higher the surge volume category a load is in, the less likely
it is to be accepted by a primary carrier.

###  5.6 Carrier service type

Asset and non-asset carriers offer different services which drive their
relationships with shippers and how they interact with the overall market. On
one hand, asset carriers own the trucks (tractors) they operate. They have
fixed available capacity to manage across their networks and serve customers.

On the other hand, non-asset carriers - otherwise known as brokers or freight
forwarders - do not own the tractors or trailers that move their customers’
loads. Instead, non-asset providers match shippers with asset-based carriers.
The advantage to shippers of working with a non-asset carrier is that they are
able to aggregate smaller (asset) carriers’ capacity to serve the shipper’s
needs. Often, shippers aims to maintain a manageable carrier base size (i.e.,
number of contracted carriers) across their networks. Rather than contracting
with many, small carriers, they prefer to allow brokerages to manage these
carriers. The benefit for smaller asset carriers of working with a broker or
3PL is that often they might not otherwise have access to some shippers’
business. For larger asset carriers, the broker may provide opportunities to
fill backhauls or moves to re-position a truck that does not have contracted
volume and would otherwise be an empty, unpaid trip.

A shipper may set up a contract with a non-asset provider on a lane to lower
the risk that loads go to the less predictable, volatile spot market. Brokers
set prices with shippers for a contract term length and then typically pay
(close to) spot market prices for their asset carriers over the course of the
contract. They aim to hedge the market and, over time, still make a reasonably
sustainable margin. When spot market prices are high, they may be paying
carriers more than they are receiving from their contracted shippers. However
when spot market prices are lower in a soft market, they receive higher
payments from their fixed-price contracts than the price at which they are
buying capacity on the market.

Because of the difference between how asset and non-asset providers utilize
markets, we predict non-asset carriers are more likely than asset carriers to
be pulled from their contracted loads when spot prices are high and more
attractive than contract prices. Thus they would be more responsive to index-
based pricing.

Using an auction theory lens, this distinction in behaviors between how asset
and non-asset carriers approach bid pricing is addressed in Scott (2018). We
aim to expand on this by modeling the behaviors of asset and non-asset
carriers separately.555Some carriers also offer both services. For example,
large asset carriers J.B. Hunt, Schneider, and Knight-Swift all run a
brokerage division of their business. In our dataset, we can distinguish
between whether a company’s asset or non-asset arm was awarded or tendered
loads because they fall under different SCAC codes. SCACs, or Standard Carrier
Alpha Codes, are unique 2- or 4-letter codes assigned by The National Motor
Freight Traffic Association, Inc., (NMFTA) to identify transportation
companies and are used throughout the freight industry for consistent carrier
identification. In this way, we extract each type of carriers’ contract price
stickiness for different freight and lane segments independently.

###  5.7 Asset carrier fleet size

Within the asset provider segment, carriers’ cost structures vary by fleet
size. For example, large carriers may be more able to absorb variations in
market prices than would a smaller, owner-operator that owns a single truck
and trailer. The distribution of asset carrier fleet size - both across the
industry in the US and in our dataset - is highly skewed; about 60% of total
for-hire carriers in the US are independent owner-operators, and 96% of fleets
have fewer than 20 trucks. To account for this, we include the log of the
carrier’s fleet size (tractor count) as our measure of asset carrier size.

Figure 3: Distribution of Asset Carrier Fleet Size

Figure 3 depicts the skewed distribution of carriers’ number of tractors in
the fleet and the normalized distribution of the log of carrier fleet size
from our dataset.

###  5.8 Other fixed effects

While we do not make formal hypotheses regarding the following variables, we
do control for their fixed effects in our model and report their effects on
carrier acceptance decisions. These include the shipper’s size, measured by
the log of its total monthly tendered volume across all lanes, and the
shipper’s industry vertical.

Indicators for the lane’s origin and destination regions are also included to
account for their relative attractiveness. As discussed in Section 5.1 and
Acocella et al. (2020), carrier acceptance is expected to vary across
different inbound or outbound regions due to the business opportunities
present at the origin and destination. We include in our carrier acceptance
model a binary variable for each of the 15 regions of the US defined by
general market demand patterns of our transportation management partner
company, at both an origin and destination.

The results of our model indicate which load, lane, and carrier
characteristics are statistically significant indicators for predicting
primary carrier acceptance rate (PAR) at a load transaction level. Further, we
address our carrier price stickiness research question by quantifying the
changes in PAR as the contracted load price relative to the spot market price
(i.e. SRD) changes for the resulting statistically significant freight and
carrier segments.

###  5.9 Market Condition

Building off the research outlined in Section 3, we expect carriers’ contract
price stickiness to differ depending on the general market condition. Our
dataset spans two distinct market conditions: a soft market observed from the
first week of February 2016 to the first week of July 2017 and again after the
second week of January 2019 until the end of the time frame covered by the
dataset; and a tight market observed before the first week of February 2016
and from the first week of July 2017 to the second week of January 2019.
Acocella et al. (2020) justify these market periods by identifying the weeks
in which a statistically significant change is observed in the underlying
structure of the TL freight market. We develop four distinct acceptance
models: (1) asset carriers in soft markets, (2) non-asset carriers in soft
markets, (3) asset carriers in tight markets, and (4) non-asset carriers in
tight markets.

##  6 Results

In this section, we summarize our results by discussing the full GEE logistic
regression models and use them to predict the (log) likelihood a load is
accepted for each hypothesis. The regression results are tabulated in the
electronic companion. The separate reported tables comprise a single model
with the input variables described in Sections 5.1-5.8.

As validation of each of our four models, we report the Brier Score, which is
the appropriate scoring metric when probability outcomes are the desired
result (Wallace and Dahabreh 2014, Niculescu-Mizil and Caruana 2005, Zadrozny
and Elkan 2002, Brier 1950). The Brier Score, $BS$, is the mean square error
between the predicted probability an observation is in the the positive class,
$p_{n}$ (here, an accepted load, $y_{c,k}=1$), and the actual outcome,
$o_{n}\in\\{0,1\\}$:

$BS=\dfrac{1}{N}\sum^{N}_{n=1}(p_{n}-o_{n})^{2}$ (5)

where $N$ is the total number of observations in the dataset. The Brier Score
takes on values between 0 and 1. Better models have lower Brier Scores.

To build our models, we segment each of the datasets for the four models into
a training set on which we fit the model and a test set to measure model
performance with a 70%:30% split. In each of the four pre-split datasets, the
relative frequency of accepted loads is much higher than that of rejected
loads. To develop unbiased models that do not naively favor accepted load
predictions, we use a stratified sampling technique to define each of the
training and test sets such that the ratio of the number of accepted loads to
number of rejected loads in each split set is the same as that of the original
pre-split dataset. In this way, the validated models can better predict
carriers’ load acceptance or rejection probabilities on new data.

Table 1: Test set Brier Scores Model | Brier Score
---|---
Asset carriers Soft market | 0.049
Asset carriers Tight market | 0.032
Non-asset carriers Soft market | 0.075
Non-asset carriers Tight market | 0.064

The Brier Scores for each of our four models on their respective test datasets
are reported in Table 1. Recall that the closer a score is to 0, the better. A
“good” Brier Score largely depends on the dataset itself. However, we draw
from the literature for reasonable comparison. Zadrozny and Elkan (2002)
report test set Brier Scores for the best calibrated probability prediction
models of five datasets ranging from 0.012 to 0.204. Similarly, Wallace and
Dahabreh (2014) report calibrated model Brier Scores for 34 datasets between
0.042 to 0.319. All four of our models’ Brier Scores sit below the average
Brier Score value of the best fitting models in these previous studies. Thus,
we conclude that our models perform well in predicting loads acceptance
probability.

###  6.1 Carrier price stickiness by service type and market condition

The results of the GEE logistic regression models are reported in Table 2.
Hypothesis H1, which addresses carriers’ overall contract price stickiness is
supported: in general, primary carriers are more likely to accept a load with
a contract price that is higher relative to the current, lane-specific spot
market price. The statistically significant coefficients in Table 2 show that
as SRD increases and the spot price rises above contract prices, the
probability a carrier accepts the load decreases for both carrier types in
both market conditions. This suggests that in general, carriers can be
incentivized away from their contracted loads as the external spot market
increases relative to those contract prices.

Figure 4 illustrates this behavior for each carrier type and market condition.
To construct the figure, we plot the probability a load is accepted at each of
the statistically significant SRD values for a base case lane and fit a linear
model to these plotted results./footnoteWe show only the segments of these
linear models over the SRD ranges that apply to the associated market
condition. In other words, soft market models apply when SRD negative (spot
market prices are below contract prices) and tight market models apply when
SRD is positive. The slope term of each linear model represents the carrier’s
contract price stickiness, or willingness to stick to contracted loads as spot
market prices change relative to contract prices in the corresponding market
condition.

Both carrier types are about twice as likely to be pulled from contract load
prices in a tight market as they are in a soft market: asset carriers have a
slope of -0.29 in tight markets as compared to -0.12 in a soft market and non-
asset carriers have a slope of -0.65 in soft markets and -1.32 in tight
markets. Moreover, H7 is supported: non-asset carriers are about five times
more likely to be pulled from contracted loads than their asset-based
counterparts in each market condition.

For shippers considering indexed contract pricing strategies, these results
suggest that all else equal, non-asset carriers are more likely to respond to
market-based pricing than asset carriers and that both carrier types may be
more responsive to such pricing strategies in tight markets than soft.

Figure 4: Carrier Contract Price Stickiness Models

Next, we discuss the results for specific freight and lane segments
highlighted in our hypotheses. We demonstrate carriers’ contract price
stickiness by holding spot price constant at $1000 for both soft and tight
markets and plotting the contract price needed to maintain a 90% likelihood
the primary carrier accepts the contracted load over the range of values each
freight or lane segment of interest takes. We choose 90% PAR because most
shippers expect at least this level of service from their contracted carriers.
Many may expect higher acceptance rates, however this threshold represents
basic service level expectations in the shipper-carrier relationship. Our
method of presenting contract price stickiness follows those discussed in
Section 3 on general supplier price stickiness and responses to factors
exogenous to the supply contract.666The figures identify segments where
primary carriers require higher price incentive to stick to their contracts as
the spot price approaches or surpasses the contract price. Contract prices of
categorical variable values for which the GEE regression model coefficients
are not statistically significant (see 2) are presented as the contract price
associated with the baseline value.

###  6.2 Contract price stickiness: lane demand consistency

Results for both lane tendering frequency and volatility are summarized in 4.
They show that hypotheses H3 and H4 are supported particularly for asset
carriers in both market conditions. Carriers prefer lanes with more frequently
and consistently tendered volume; that is, carriers are more willing to stick
to their contract prices on lanes with high frequency load tendering and lower
week-to-week volume volatility.

Importantly, the shipper often cannot control its load tendering consistency;
it is subject to external factors such as its own customers’ demand patterns,
inbound suppliers’ schedules, and congestion on roadways or at ports. While
the shipper does not control when its demand for trucks materializes, it does
control what carriers are offered the loads when they do appear. Moreover, the
shipper has historical knowledge of its lane demand patterns. Thus, the
shipper’s decision here is what bid prices to accept and how to tender loads
that do appear for lanes with historically irregular cadence or inconsistent
volumes.

####  6.2.1 Tendering cadence

The results weakly support Hypothesis H3: lanes on which loads are tendered
less frequently see lower primary carrier acceptance. Moreover, both asset and
non-asset carriers in both market conditions are less willing to stick to
their contract prices for these low cadence lanes. (See 4.)

Figure 5 shows that as lane tendering cadence decreases, asset carriers’
contract price needed to maintain 90% PAR increases about 7% in soft markets
(to $682 per load from $617) and 2.5% in tight markets (to $857 from $830).

Similarly, non-asset carriers require a 6% contract price increase in soft
markets to maintain 90% PAR on low cadence lanes. While they do not appear to
make load acceptance decisions based on lane tendering cadence in tight
markets, these non-asset carriers set the highest contract prices for all
cadence levels in tight markets. This may be because shippers often use non-
asset brokerage services specifically for infrequently tendered lanes. These
providers may be familiar with the undesirable, infrequently tendered lanes
and knowingly set higher contract prices during the RFP.

Figure 5: Contract Price Stickiness, Tender Cadence

The results suggest that both carrier types are willing to stick with contract
prices on moderate and high cadence lanes under both market conditions.
However, lanes with very infrequent load tenders require higher contract
prices relative to going spot market prices. Shippers may see better primary
carrier acceptance on these low frequency lanes with market-based pricing
strategies. Important to note, transportation practitioners and the literature
both highlight that there must be enough business between the buyer and
supplier (on a lane) to offset the additional effort involved in introducing
either non-traditional, or more explicit contracts (Scott et al. 2020, Sinha
and Thykandi 2019).

####  6.2.2 Tendered volume volatility

Next, we consider the tendered volume volatility on a lane from a shipper to
its primary carrier. Consistent with Hypothesis H4, higher tendered volatility
leads to lower load acceptance probabilities, particularly for asset carriers.
The GEE logistic regression model results are presented in Table 4 and Figure
6 below demonstrates carrier contract price stickiness. In soft markets, asset
carriers stick to their contract prices for lanes with week-to-week tendered
volume volatility up to 50%.

Figure 6: Contract Price Stickiness, Lane Volatility

However, as tendering volatility increase, they are more likely to be pulled
from the contract priced loads unless contract prices are much closer to the
current spot market price. Specifically, contract prices needed to maintain
90% acceptance are 17% higher on these high volatility lanes than low
volatility lanes in soft markets.

In tight markets, as compared to soft markets, even higher contract prices are
needed for asset carriers to maintain high acceptance rates. Moreover, these
price escalations begin at lower volatility lanes (i.e., 11-25%). Contract
prices needed on high volatility lanes are 26% higher than those on low
volatility lanes in tight markets. This suggests that in tight markets, asset
carriers are more easily pulled from their contracts on lanes with lower
tendering volatility than in soft markets.

Non-asset carriers are more willing to stick to their contract prices at high
lane volatility in both market conditions as compared to their asset-based
counterparts. Contract prices needed for non-asset providers to maintain 90%
load acceptance rates remain steady for lanes with more than 10% week-over-
week change in tendered volume, with an increase of only 5% in soft markets
for moderate and high volatility lanes.

Shippers should pay close attention to moderate and high volatility lanes in
their networks. These lanes are particularly difficult for asset carriers to
accommodate due to fixed capacities and a network of many customers’ demand
they continuously balance while non-asset providers do not. For the lanes on
which a shipper’s demand volatility is difficult to control or smooth out (by
splitting the volume and tendering to multiple carriers, for example), it may
be beneficial to introduce a market-based pricing strategy that adjusts
contract load prices as spot market prices change to better incentivize
primary asset carriers to accept loads.

###  6.3 Contract price stickiness: surge volume

Table 5 summarizes the GEE logistic regression models’ results demonstrating
carriers’ likelihood of accepting loads considered surge volume. Hypothesis H5
is strongly supported for asset carriers: asset primary carriers are less
likely to accept loads that are above the lane awarded volume - particularly
those over 20% above awarded volume - than loads within their expected weekly
tendered volume. Put another way, asset carriers are less willing to stick to
their contract prices for excessive surge volume, especially in tight markets.

Figure 7: Contract Price Stickiness, Surge Volume

Figure 7 shows that the contract price required to maintain 90% acceptance for
asset carriers in soft markets increases by 9% for loads that are over 20%
above the awarded volume. These asset carrier contract prices further increase
in tight markets. For surge volume over 20% above the award in tight markets,
shippers pay $940 per load - almost at the $1000 spot market price level -
which equates to a 13% increase in contract price from the awarded volume
loads.

The contract price required to maintain high acceptance rates for loads up to
10% and 10-20% above awarded volumes with asset carriers stays relatively
steady. This moderate surge volume requires contract price increases of 4-6%
in both soft and tight markets. Asset carriers are willing to stick to their
contract prices for these mid-level surge loads. This may be because shippers
often communicate an expectation of primary carriers to accept anywhere from
10-20% above the awarded volume without reducing acceptance or other carrier
performance metrics in their (non-binding) contract service level agreements.
Although asset carriers may have more difficulty providing this additional
capacity than non-asset carriers, they may have factored some additional
capacity into their strategic capacity allocation decisions during the
original RFP. Surge loads over this 20% threshold require higher contract
prices, especially in tight markets, and asset carriers are more willing to be
pulled from contracts for better priced alternatives on the spot market.

Non-asset carriers, on the other hand, do not appear to be incentivized away
from contracts with higher priced alternatives on surge volume, even for loads
that are more than 20% above the awarded volume. This difference between asset
and non-asset carriers is expected. Non-asset carriers are not limited in
capacity in the way asset carriers are. While non-asset carriers must also
balance supply and demand of capacity, they are better equipped to serve
excess demand because they can access a large pool of asset carriers and
aggregate capacity accordingly. Moreover, non-asset carriers already require
higher contract prices to maintain 90% acceptance for all volume - in fact,
very close to the spot market price - regardless of surge classification.
Thus, they may already be adequately incentivized to offer that capacity.

Shippers may see the most benefit from implementing indexed pricing applied to
specific surge volume loads with asset carriers. This type of volume-based
pricing strategy has been seen in practice. It is referred to as tier pricing,
where levels of surge volume are set at a higher fixed price - determined
during the strategic RFP - than that of the base awarded volume.

###  6.4 Contract price stickiness: lane distance

Table 3 summarizes the lane distance portion of the GEE logistic regression
model results. It shows weak support of Hypothesis H2: non-asset carriers
prefer longer lanes. In soft markets, loads on shorter lanes - specifically
those with only a one-day travel time - are less likely to be accepted than
all other lane distances. In tight markets, loads on longer lanes (three- and
four-day lanes) are more likely to be accepted than loads on shorter lanes.
However, there is no statistically significant difference in probability of
load acceptance for asset carriers on different lane distances, suggesting
that asset carriers do not consider lane distance in their load acceptance
decision.

###  6.5 Asset carrier contract price stickiness by fleet size

The preceding sections consider carriers based on their service type: asset
and non-asset. However, asset carriers range widely in their fleet sizes
(Figure 3), which directly impact their internal cost structures, tolerance to
price fluctuations, access to network model optimization software to plan
strategically, and as a result, willingness and ability to accept loads. Table
6 summarizes the GEE logistic regression models’ results for an asset
carriers’ fleet size. Hypothesis H8 is not supported: all else equal, we do no
find statistically significant evidence that the size of the asset carrier
(measured here as log of Tractor Count) indicates its primary acceptance rate
in soft or tight markets.

##  7 Discussion and Implications for Index-based Pricing

In this study we explore supplier price stickiness in response to customer
demand patterns and exogenous market conditions. We take the case of firms
that outsource their TL transportation service needs and aim to help them
determine when, where, and with which transportation suppliers they should
consider alternative pricing strategies from the standard, fixed-price
contracts. In particular, we consider dynamic market-based pricing by
measuring primary carriers’ contract price stickiness, or the change in
contract price relative to the going spot price needed so carriers maintain a
reasonable load acceptance service level.

1\. Shippers should not delay or skip RFPs or mini-bids as markets tighten.
Both carrier types (asset and non-asset) are twice as likely to stick to their
contract priced loads in a soft market than a tight market. Shippers can use
this to inform the timing of their strategic procurement event as market
conditions may be changing. For example, say a shipper runs its annual
strategic RFP in January. In the preparation months leading up to the event,
the shipper may observe that spot market prices or other leading indicators of
general market conditions are rising. Some shippers in this situation may
consider delaying the RFP and keeping the current contracted prices that had
been set during a softer, lower-priced market rather than opening itself up
for carriers to lock in higher prices. Alternatively, the shipper may choose
to run the RFP anyway, perhaps allowing for slightly increased contract
prices, and assume it can expect good primary carrier acceptance rates for the
next year even as markets further tighten. Finally, the shipper may take a
middle-ground approach and proactively increase rates for certain core
carriers on specific important lanes to keep them out of an RFP.

However, the results of our study suggest that no matter the decision, if spot
prices continue to rise as the market tightens further, the contract prices
will become less competitive (i.e., their spot rate differential will
increase) and primary carriers with low contract price stickiness will begin
opportunistically rejecting loads at higher rates, defecting to either fresher
contract prices with other shippers or to the spot market. Therefore, when
markets are tightening, shippers need to continuously ensure their contract
prices stay competitive with the going spot market prices, regardless of their
RFP timing. One approach shippers can take as market conditions become more
constrained is to execute smaller, focused, more frequent “mini-bids” with
core primary carriers on the most important, susceptible lanes. These mini-
bids result in shorter term (e.g., 30-, 60-, or 90-day) contracts. Another
approach is to implement a market-based pricing strategy, as we propose in
this study, which effectively ensures contract prices are up-to-date.

2\. Non-asset carriers are best suited for market-based contracts. All else
equal, asset primary carriers are five times more likely to stick to their
contract priced loads than non-asset primary carriers, or brokers, in both
soft and tight markets. In fact, across most network and freight segments,
shippers must pay these non-asset primary carriers just about spot market
prices to maintain high load acceptance rates. This suggests that brokers may
respond to index-based contracts better than asset-based providers.

3\. Market-based pricing shows promise for volatile demand, low frequency
lanes, and surge volume. Asset primary carriers are less likely to stick to
their contract priced loads on lanes with infrequently tendered loads and high
week-to-week volatility of tendered volume. Shippers often have little control
over when loads actually materialize and carriers’ capacity is needed.
However, they do know historical demand patterns on their lanes. They can
control which carriers they tender the loads that do materialize and the
pricing strategies they are willing to implement. Our results suggest a
market-based pricing strategy for these low cadence or high volatility lanes
would better incentivize asset carriers to stick to their contracts.

In addition to these lanes types, shippers can expect asset carriers to
respond to market-based pricing for surge volume - in other words, loads that
are in excess of the expected weekly volume communicated during the RFP. This
finding relates to the two stages of TL transportation. During the first
stage, the strategic RFP, the shipper communicates the expected weekly volume
on each lane that the carriers bid on. Once the carrier wins the lane, it
plans to allocate capacity for that expected volume, perhaps with an
additional 10-20% buffer. It also uses this knowledge of expected demand to
balance the demand for trucks across its existing network and to inform its
bid strategy in other shippers’ RFPs. However, during the second stage, the
operational stage when loads materialize and are tendered to that carrier, the
actual demand may well exceed the capacity for which the carrier has planned.
Asset carriers in particular are constrained in their total capacity available
at any one time. To maintain high acceptance rates of loads that exceed 20%
over the awarded volume on a lane, carriers require a price incentive. This is
an important segment of shippers’ freight: consistently across our time
horizon, 10-15% of total tendered volume is in this surge category.

In fact, a tier pricing strategy where surge volume is priced higher than the
baseline awarded volume is used by some shippers and their larger or core
carriers, precisely for the reasons described. However, these tier-based rates
are still fixed at the time the contract is established. A dynamic market-
based price, on the other hand, would ensure the tiered price incentive
remains competitive with the current market.

4\. Indexed pricing may result in lower load acceptance if applied in soft
markets. Important to note that we discuss market-based pricing with the
implication that contracted load prices increase as market prices increase in
a tight market, but also decrease as prices decrease in soft markets - in
other words, “symmetric” indexing. Shippers may want to consider using dynamic
market pricing as an incentive for primary carriers whereby indexed contract
prices only increase as the market tightens, but settles to the competitive,
fixed contract price when the market prices are decreasing. Otherwise, for
segments that require a contract price premium (i.e., higher contract price
than spot market price) for high primary carrier acceptance, the shipper would
expect to see decreased primary carrier acceptance when the indexed price
symmetrically decreases.

Our study suggests that there is still a place for the widely used fixed-price
contracts. On lanes where tendered volume is consistent and frequent, both
shippers and carriers prefer a set price to plan and budget around. While
these prices may also become outdated as spot market prices increase, carriers
are more willing to stick to their contracts for attractive freight.777While
low tight market period primary carrier acceptance rates are undesirable, the
majority of freight still moves under fixed contract rates even in tight
markets. However, we find evidence that a market-based approach would improve
primary carrier acceptance rates. Moreover, competitive fixed price contracts
may still be best suited for soft market conditions.

##  8 Limitations and Future Research

Our empirical modeling results offer both academic and practical
contributions. First, we add to the econometric literature on supplier price
stickiness in response to demand and exogenous market dynamics. We do so by
quantifying TL transportation suppliers’ price stickiness as market prices
change and for different customer demand patterns, freight segments,
characteristics of shippers’ networks, and supplier service types. Our work
explores real-time decision that previous literature overlooks; transportation
suppliers have the spot market as a dynamic alternative option to their
contracted business for every transaction.

In addition, we add to the literature specific to shipper and carrier
relationships, particularly with a focus on how changing market conditions
impact behaviors. We do so by utilizing a uniquely extensive and detailed
dataset. Previous empirical studies in the space have been limited in that
their data represent only a single shipper’s business, and often contain
limited or no tendering or carrier acceptance service level information.

This study is not without its limitations. Precisely due to the observational
nature of our dataset, we cannot control for outside influences on carriers’
acceptance decisions. We attempt to account for these factors by segmenting
the contract price stickiness analysis by lane, load, and carrier types and
other fixed effects that have been previously identified as contributing
factors. In doing so, we build models with good performance (i.e., very low
Brier Scores). However, there may still be alternative explanations for
carriers’ acceptance decisions.

Notwithstanding these limitations, our study further adds to the existing
shipper-carrier relationship literature by isolating the impact of market
prices on the way carriers make freight acceptance decision for their
contracted shippers. As discussed in the motivation of this research, there
has been growing interest in index-based pricing in the TL industry. This
research serves as a starting point. We demonstrate where shippers can expect
to see carrier acceptance behaviors most influenced by dynamic, market-based
pricing methods. An interesting future stream of literature could develop
strategies for shippers and carriers to design and implement these freight
contracts.

The authors would like to thank the anonymous reviewers for greatly improving
the quality of this manuscript.

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E-Companion for “The end of ‘set it and forget it’ pricing? Opportunities for
market-based freight contracts”

This e-companion reports the detailed results of the logistic regression
model, which is used to quantify carriers’ contract price stickiness for
segments indicated by model variables.

Table 2: GEE model results: Spot Rate Differential, asset and non-asset
carriers, soft and tight markets

Spot Rate Differential |  Asset carriers Soft market |  Asset carriers Tight market |  Non-asset carriers Soft market |  Non-asset carriers Tight market
---|---|---|---|---
Constant | 2.0032 | 1.2945 | 0.634 | 1.0894
| (0.882) | (1.121) | (0.837) | (1.451)
SRD: | 0.4862** | 0.6254* | 0.3237 | 0.2436
$(<-50\%)$ | (0.236) | (0.382) | (0.431) | (0.466)
SRD: | 0.6307*** | 0.7545** | 0.5789** | 0.4886
$[-50\%,-45\%)$ | (0.233) | (0.332) | (0.292) | (0.846)
SRD: | 0.3642* | 0.1127 | 0.2974 | 0.0262
$[-45\%,-40\%)$ | (0.202) | (0.272) | (0.425) | (0.415)
SRD: | 0.3445 | 0.242 | 0.6138** | 0.0223
$[-40\%,-35\%)$ | (0.233) | (0.290) | (0.279) | (0.432)
SRD: | 0.467*** | -0.0195 | 0.5006* | -0.1933
$[-35\%,-30\%)$ | (0.183) | (0.245) | (0.267) | (0.436)
SRD: | 0.3231* | -0.1767 | 0.4178* | 0.4921
$[-30\%,-25\%)$ | (0.195) | (0.233) | (0.239) | (0.444)
SRD: | 0.1934 | 0.028 | 0.0378 | 0.7571***
$[-25\%,-20\%)$ | (0.196) | (0.209) | (0.211) | (0.253)
SRD: | 0.2504 | -0.1155 | 0.0674 | 0.2454
$[-20\%,-15\%)$ | (0.200) | (0.198) | (0.218) | (0.269)
SRD: | 0.2193 | -0.1083 | 0.0619 | -0.2322
$[-15\%,-10\%)$ | (0.171) | (0.177) | (0.204) | (0.406)
SRD: | 0.0146 | 0.1091 | 0.1712 | -0.1569
$[-10\%,-05\%)$ | (0.151) | (0.179) | (0.238) | (0.266)
SRD: | -0.0314 | 0.2073* | -0.1154 | 0.3754*
$[-05\%,0\%)$ | (0.150) | (0.124) | (0.256) | (0.202)
SRD: | omitted | omitted | omitted | omitted
$[0\%,05\%)$ |  |  |  |
SRD: | 0.0264 | -0.2026 | -0.0804 | -0.0055
$[05\%,10\%)$ | (0.1360) | (0.149) | (0.395) | (0.250)
SRD: | -0.0054 | -0.1423 | -0.0226 | -0.0968
$[10\%,15\%)$ | (0.165) | (0.148) | (0.246) | (0.247)
SRD: | 0.026 | -0.1789 | 0.1061 | -0.2498
$[15\%,20\%)$ | (0.149) | (0.158) | (0.309) | (0.361)
SRD: | -0.152 | -0.1171 | 0.5717** | -0.8346***
$[20\%,25\%)$ | (0.297) | (0.182) | (0.267) | (0.340)
SRD: | 0.0913 | -0.2481 | -0.2945 | -0.5186
$[25\%,30\%)$ | (0.208) | (0.191) | (0.436) | (0.385)
SRD: | -0.3266 | -0.1904 | 0.7472*** | -0.5058
$[30\%,35\%)$ | (0.287) | (0.189) | (0.308) | (0.371)
SRD: | -0.1179 | 0.266 | -0.0413 | -0.5918**
$[35\%,40\%)$ | (0.300) | (0.201) | (0.638) | (0.286)
SRD: | -0.2114 | -0.1257 | 1.8206*** | -0.7198**
$[40\%,45\%)$ | (0.325) | (0.225) | (0.695) | (0.314)
SRD: | -0.286 | 0.0457 | 1.1126 | -0.6647**
$[45\%,50\%)$ | (0.299) | (0.217) | (0.800) | (0.332)
SRD: | 0.0406 | -0.1655 | 0.9579*** | -0.8166***
$[>50\%)$ | (0.275) | (0.207) | (0.320) | (0.284)

Note: robust standard errors reported in parentheses
significance level: *0.1; **0.05; ***0.01

Table 3: GEE model results: Lane Distance (measured in Travel Days), asset and
non-asset carriers, soft and tight markets

Travel days |  Asset carriers Soft market |  Asset carriers Tight market |  Non-asset carriers Soft market |  Non-asset carriers Tight market
---|---|---|---|---
1 day | -0.0152 | 0.0594 | -0.3804** | 0.3756*
| (0.167) | (0.168) | (0.192) | (0.212)
2 days | omitted | omitted | omitted | omitted
3 days | 0.2134 | -0.0518 | 0.0866 | 0.6837***
| (0.220) | (0.162) | (0.268) | (0.206)
4 days | 0.3755 | -0.3351 | -0.2664 | 0.8952**
| (0.260) | (0.244) | (0.363) | (0.409)
$>$4 days | 0.5188 | -0.0202 | 0.3404 | 0.2598
| (0.402) | (0.373) | (0.309) | (0.268)

Note: robust standard errors reported in parentheses
significance level: *0.1; **0.05; ***0.01

Table 4: GEE model results: Lane Tendering Consistency, asset and non-asset
carriers, soft and tight markets

Consistency variable |  Asset carriers Soft market |  Asset carriers Tight market |  Non-asset carriers Soft market |  Non-asset carriers Tight market
---|---|---|---|---
Cadence: | -0.3690*** | -0.2296** | -0.4965*** | -0.3933
25% | (0.105) | (0.119) | (0.195) | (0.249)
Cadence: | -0.1291** | -0.1145 | -0.1757 | -0.0943
50% | (0.063) | (0.088) | (0.141) | (0.152)
Cadence: | omitted | omitted | omitted | omitted
75% |  |  |  |
Cadence: | -0.1195 | -0.0611 | 0.243 | 0.199
100% | (0.093) | (0.077) | (0.198) | (0.200)
Volatility: | 0.9023*** | 0.9203*** | 0.6908*** | 0.6318*
Up to 10% | (0.243) | (0.219) | (0.169) | (0.373)
Volatility: | 0.4429*** | 0.3591*** | 0.2136 | 0.5434***
(10-25%] | (0.139) | (0.106) | (0.219) | (0.161)
Volatility: | omitted | omitted | omitted | omitted
(25-50%] |  |  |  |
Volatility: | -0.3142*** | -0.3789*** | 0.0508 | 0.2485**
(50-75%] | (0.065) | (0.098) | (0.132) | (0.110)
Volatility: | -0.5076*** | -0.6222*** | -0.050 | 0.1623
(75-100%] | (0.086) | (0.133) | (0.177) | (0.232)
Volatility: | -0.8049*** | -0.8206*** | -0.1754 | 0.1213
(100-125%] | (0.119) | (0.133) | (0.254) | (0.210)
Volatility: | -0.7579*** | -0.8419*** | 0.0278 | 0.1355
(125-150%] | (0.116) | (0.140) | (0.285) | (0.220)
Volatility: | -0.6011*** | -0.8065*** | -0.0155 | 0.1349
(150-200%] | (0.127) | (0.182) | (0.304) | (0.238)
Volatility: | -0.4359*** | -0.746*** | 0.1467 | 0.2419
Over 200% | (0.143) | (0.175) | (0.313) | (0.266)

Note: robust standard errors reported in parentheses
significance level: *0.1; **0.05; ***0.01

Table 5: GEE model results: Surge Volume, asset and non-asset carriers, soft
and tight markets

Surge Category |  Asset carriers Soft market |  Asset carriers Tight market |  Non-asset carriers Soft market |  Non-asset carriers Tight market
---|---|---|---|---
Within | 0.1757** | 0.1009 | 0.0181 | 0.2668*
Mean | (0.089) | (0.084) | (0.251) | (0.146)
Mean to | omitted | omitted | omitted | omitted
10% Surge |  |  |  |
10-20% | -0.0203 | -0.1837** | 0.1271 | 0.124
Surge | (0.108) | (0.094) | (0.294) | (0.150)
Over 20% | -0.1559** | -0.2334*** | -0.1387 | -0.0099
Surge | (0.079) | (0.083) | (0.265) | (0.120)

Note: robust standard errors reported in parentheses
significance level: *0.1; **0.05; ***0.01

Table 6: GEE model results: Carrier Fleet Size, asset carriers, soft and tight
markets

Fleet size No. tractors |  Asset carriers Soft market |  Asset carriers Tight market
---|---|---
Log Tractor Count | -0.0109 | -0.0088
| (0.079) | (0.103)

Note: robust standard errors reported in parentheses
significance level: *0.1; **0.05; ***0.01

Table 7: GEE model results: Shipper Fixed Effects, asset and non-asset
carriers, soft and tight markets

Shipper fixed effects variable |  Asset carriers Soft market |  Asset carriers Tight market |  Non-asset carriers Soft market |  Non-asset carriers Tight market
---|---|---|---|---
Shipper size | 0.4033** | 0.284 | 0.5908** | 0.3054
(log monthly volume) | (0.177) | (0.271) | (0.27) | (0.406)
Vertical: | 0.655*** | 0.8121*** | -0.3843 | 0.2414
Automotive | (0.216) | (0.261) | (0.279) | (0.451)
Vertical: | 0.9596*** | 0.9327*** | -0.4351 | 0.1938
F&B/CPG | (0.194) | (0.280) | (0.266) | (0.439)
Vertical: | omitted | omitted | omitted | omitted
Paper & Packaging |  |  |  |
Vertical: | 0.5557 | 0.5942* | -0.8417* | 0.5001
Manufacturing | (0.381) | (0.336) | (0.468) | (0.531)
Vertical: | -0.2443 | 0.9402 | 1.3812*** | -0.2445
Other | (0.602) | (0.636) | (0.467) | (0.684)

Note: robust standard errors reported in parentheses
significance level: *0.1; **0.05; ***0.01