This paper develops a model for the freight transport market where transport time is endogenously determined in the market. We estimate the freight charge function, highway choice model, and transit time function using freight flow microdata in Japan. Reducing transport time has great benefits for the economy: transport companies (carriers) save labor and capital costs; manufacturing companies (shippers) increase the value of their products;.

It considers the equilibrium in the freight market and derives the value of the transit time which is equal to the derivative of the freight rate with respect to the transit time. We extend the model in Konishi, Mun, Nishiyama, and Sung (2014) by including uncertainty in transit times. For ease of explanation, we first present the model assuming no uncertainty in the transport time in subsection 2.1.

This implies that the attempt to reduce the transport time affects the expected transport time, only µij. So, the time spent on delivering the cargo is equal to taj −tid, regardless of the realized transportation time. In other words, in equilibrium, the derivative of the function of the cost of goods with respect to the expected time of transportation is equal to the value of time for the sender, in both cases with and without the determination of time.

We investigate the effect of uncertainty on the expected transport time by differentiating (2.18) with respect to σij.

## Econometric Model

### Case of no time designation .1 Model specification

*Model estimation*

Thus, the first term of (2.28) is likely to be smaller than the second term, in this case, ij 0. Even if it does not hold, the cost of transportation may increase by increasing the uncertainty. Next we will consider the effect of determining the arrival time on the cost of transportation.

As we have shown, carriers spend more time delivering within the designated delivery time and also incur costs for scheduling delays. One might therefore suspect that freight costs should be higher in the case of time stamping. Let CijD and CijN be the equilibrium freight costs for the suitcases with and without time stamps, respectively.

However, the second term is ambiguous since µijN < µijD could theoretically be the case. We assume that the truck rental g q( ) depends linearly on the shipment size, q, since the truck is sized to accommodate the load of size q, g q ( ) = + α α1 2ln q. Note that the sign of β1 is unknown, because it is the sum of the parameters rL >0, rKα1>0, α3<0 which have different signs.

In our model, highway use is assumed to be an endogenous variable in trucking firms' decision-making as described in Section 2. We further consider the effects of shipment size, transportation distance, and type of cargo transported on transportation time. The transport time function must be continuous at tiN =tS, where the following relation is satisfied.

After estimating the choice of highway function from (3.4), we can obtain the predictor of Hˆ and calculate tˆijN using (3.5). Since H is endogenous, we use the predictor Hˆ from regression (3.2) as the regressor, then transport time function is estimated as,. Applying OLS estimation to (3.7), we obtain 2SLS estimates of β,γ that are consistent under the endogeneity.

Case of time designated delivery

## Empirical Results

### Estimation Results

*Expressway choice model**Transportation time function**Freight charge function*

The coefficients of the difference between the driving time for the use of highway and ordinary road (𝑡𝑡𝑖𝑖𝑖𝑖𝑁𝑁0− 𝑡𝑡𝑖𝑖𝑖𝑖𝑁𝑁1) are significantly positive as expected = 1.𝑁1,𝜂., 0 = 1. 0. 187, for the designated delivery time and no time. designated delivery, respectively. The driving time can be saved by using highway. 𝜂𝜂2 is the coefficient of the difference between monetary costs for using highway and ordinary road. 11 Appendix 4-1 shows estimation results for designated date delivery and designated morning or afternoon delivery. the positive coefficients for two cases. 𝜂𝜂3 is the coefficient of the dummy variable.

In the case of timed delivery, we add the difference in transport time variation between regular road and highway as an explanatory variable. The coefficients 𝜂𝜂0 for the constant term are only significantly negative for no time designation result. The value of 𝜅𝜅1 for the specified delivery time (1.060) is less than the value for no time specification (1.132).

This indicates that, in the case of time designated delivery, trucks spend additional time (e.g. waiting near the destination) to deliver the cargo on time under the variability of transit time (due to traffic congestion, weather conditions or other unexpected events). The estimates of 𝜅𝜅3 are 2.277 for the time designated delivery and 3.936 for no time designated delivery. The coefficient is positive and the greater the variance of the transit time in a certain distance band, the longer the transit time.

We also add 𝐶𝐶𝐵𝐵𝑘𝑘𝑘𝑘𝑂𝑂𝑖𝑖𝑑𝑑𝐵𝐵 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 to the estimate to observe the differences in transportation time within Hokka ido, the coefficient for timestamp is negative and significant. We obtained the estimate of -1076.9 for time-sensitive delivery and -4587.5 for non-time-sensitive delivery, and so we know that the negative effect is dominant. The coefficient is positive and the greater the variance of the transportation time in a given distance band, the more expensive the freight costs.

In the case of delivery without a fixed time, the coefficient of the variable Border-dummy is positive but insignificant. Coefficient 𝑛𝑛𝑑𝑑𝑑𝑑 𝑡𝑡𝑟𝑟𝑑𝑑𝑡𝑡𝑘𝑘 𝑓𝑓𝑖𝑖𝑟𝑟𝑑𝑑𝑠𝑠 for timed delivery we consider the coefficient fficient is positive and significant. We only considered the coefficient 𝑇𝑇𝐵𝐵𝑘𝑘𝑑𝑑𝐵𝐵_𝑂𝑂𝑠𝑠𝑂𝑂𝑘𝑘𝑂𝑂 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑 For time marking, the result is statistically significant and its positive value.

### Time designation, transportation time and freight cost

𝐵𝐵𝐵𝐵𝑟𝑟𝑑𝑑𝑒𝑒𝑟𝑟 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 has value one if the destination is in the region next to the origin (the region that shares the border). This result may reflect the fact that freights to very close locations do not waste the carrier's time for the return trip and thus the opportunity cost is lower. We expected it to have a negative effect on P, but this turns out not to be significant in either case.

To examine the commodity-specific effects on the freight charge, we use eight dummy variables for classification of transported goods as Table 4. In the case of no time indication result, the coefficients of all commodities are not significant. On the other hand, we found the negative values and significant of all commodity coefficients on time-denomination estimation results.

It can be seen that the transportation time for timed delivery is longer than that without timed delivery. This result is consistent with the theoretical prediction: carriers choose too early a departure time to reduce the possibility of a late arrival. On the other hand, the results regarding the freight rate, as the theory suggests, are ambiguous.

The freight costs with time stamp are smaller than those without time stamp for short distance transport, while for short distances the ratio is reversed. For long distances, the uncertainty in transportation time is greater and therefore the carrier must arrange the schedule in such a way that the possibility of late arrival is minimized. This response would incur the additional cost and the carrier would offer the higher price for the freight charges.

As we observe the stated delivery time in reality, there are shippers who accept the higher shipping fee for timed delivery. The difference in shipping costs between cases with and without a time indication can thus be a measure of willingness to pay for timely arrival. For example, from Table 6, the difference is 11403 Yen for transporting 2 tons of cargo over a distance of 360 km, which is greater than 20% of the freight cost.

Conclusion

Descriptive Statistics (No time designation)

### Descriptive Statistics (Time designation)

Estimated results of Expressway Choice (𝐶𝐶) on specified date delivery and designated morning or afternoon delivery. Estimated transit time results (𝑡𝑡𝑖𝑖𝑖𝑖) on specified date of delivery and specified morning or afternoon delivery. We choose ( 𝑇𝑇𝑡𝑡= 10,𝑞𝑞̄= 8) and ( 𝑇𝑇𝑡𝑡 = 11,̄ 𝑞𝑞̄= ) for the estimated result in the case of no timed delivery and fixed delivery time, respectively.