Daily gravity in the carrot trade in Japan

Kazutaka Takechi

05 February 2017



Agricultural products such as vegetables are traded inter-regionally on a daily basis. Trade patterns of such goods are quite volatile; in particular, trade often does not occur. Varying demand/supply shocks and substantial trade costs are the possible primary factors causing such a prominent lack of trade. Thus, a framework that accounts for zero trade and heteroskedasticity caused by daily shocks and trade costs is required.

Santos Silva and Tenreyro (2006) demonstrate how the Poisson pseudo-maximum likelihood (PPML) estimator handles data with zero trade and heteroskedasticity in a gravity model. As mentioned, because zero trade and heteroskedasticity are prominent in daily trade data, my research uses PPML to study the local daily transaction data of individual products, in this case, carrots (Takechi 2016).

There are two reasons why it is important to use daily data to investigate trade patterns. One is that there is a variety of large shocks in daily data. Normally, trade data are collected yearly or, at best, monthly. The effects of highly frequent shocks have not been examined extensively in the literature to my knowledge. Hence, a gravity model with the usual determinants may not work. For example, the distance between two regions typically captures the effect of trade costs. Whether or how the distance is related to changing daily trading patterns is unclear. From the daily delivery choice point of view, distance is a predictable element compared with supply and demand shocks, and it may not affect the changing states between zero trade and active trade.

Another important aspect of using daily data is related to the nature of trade costs. If fixed costs of trade are incurred at greater than a daily basis, the daily delivery decision is subject not only to variable trade costs but also fixed costs to a large extent. It is difficult to distinguish the amount of variable and fixed trade costs empirically. Hence, we consider the nonlinearity of trade costs regarding the distance to markets. If there is significant nonlinearity, we can interpret it as a presence of fixed costs.

Table 1 shows an example of a regional trade pattern, looking at carrot trade data between prefectures in Japan. The largest supplier prefecture is Hokkaido, and the shows how carrots produced in Hokkaido are traded domestically for three days from 11 October 2007 to 13 October 2007. On 11 October, carrots were delivered to two markets: Morioka and Maebashi. However, on the following day, no delivery was made to these markets, but deliveries were made to two other prefectures: Yamagata and Kumamoto. On 13 October, the markets which received a delivery on 11 October (Morioka and Maebashi) received a delivery again, but of the markets which received a delivery on 12 October, only Kumamoto received another. We consider that supply and demand shocks and trade costs cause such frequent changes in the supply pattern.

Table 1 Example of a regional trade pattern

Note: Price refers to yen per kilogram

We confirm our argument by estimating a simple gravity model with various estimation procedures: ordinary least squares (OLS), different Tobit models, and PPML. The estimation results are consistent with findings in the previous literature. There is a negative, significant distance effect on trade. As noted in Head and Mayer (2014), if there is a substantial difference in the estimation results between OLS and PPML, the presence of heteroskedasticity is implied. From our empirical analysis, there is a large difference (the distance coefficient is -0.622 in OLS and -1.225 in PPML), which suggests that the volatile supply pattern is a result of various demand and supply shocks changing daily.

We also estimate the gravity model with several different specifications in trade cost function. We use a simple iceberg-type trade cost that is a log-linear function of distance, and also use a trade cost function with an additional quadratic distance term. The coefficient of the quadratic term captures the nonlinearity of trade costs, and we find a significant effect of the quadratic term. Because fixed trade costs are incurred on a longer time horizon than daily, the impact of fixed trade costs on the daily delivery decision is large. Both variable and fixed trade costs are the central ingredients of modern trade theory, and their presence is found to be significant in our empirical analysis. In general, it is hard to identify whether the cost of a particular type of activity belongs to variable or fixed trade costs. Here, because we attempt to identify distance-elastic trade costs, it is relatively easier to distinguish between distance-related activities and those conducted at one geographical point. This distinction may help us to understand precisely the structure of trade cost function in this dimension.

Concerning the shocks to trade, the effects of large shocks (such as the one after the collapse of Lehman Brothers) on trade have been examined in the trade literature. However, the effects of frequently changing shocks on trade have not been an issue because of data limitations. After controlling for heteroskedasticity and zero trade, trade costs are found to be significant and large. The usual gravity model determinant plays a vital role even in such situation. The success of the gravity model in international trade has been recognised in this field. It is often viewed as showing a long-term relationship between trade and its determinants; our results also report the success of describing volatile trade patterns.

Because agricultural products harvested on different days are considered as different products, we treat our daily data as large pooled data, not panel data (if we find that these products are the same and the source prefecture is the same, we can construct a panel data). Hence, we have not identified the transmission and persistence of shocks and how they affect prices (e.g. Cruchini, et al. 2015). Due to these limitations, we cannot tell whether shocks are the main factors and how information gathering or risk sharing is necessary for efficient allocation mechanism. Similarly, we cannot argue whether an efficient market mechanism requires shocks to be transmitted smoothly. However, our study suggests that the gravity model works even if volatile shocks exist.

As shown in my research, the effect of trade costs is still significant, and therefore the reduction of trade costs may have a large impact on the efficiency of the national economy. In particular, the nonlinearity of the trade cost function implies the presence of fixed trade costs. Transport infrastructure is a major factor for trade costs, and the costs of associated activities with no relation to distance, such as inventory, loading, and discharge costs, can be substantial. Policies to reduce fixed costs, such as better management of inventory and improvement of traffic control, are required even in a country with sufficient transport infrastructure such as Japan.

Editors' note: The main research on which this column is based appeared in a Discussion Paper of the Research Institute of Economy, Trade and Industry (RIETI) of Japan.


Crucini, M J, M Shintani and T Tsuruga (2015) “Noisy information, distance and law of one price dynamics across US cities,” Journal of Monetary Economics 74, 52-66.

Head, K and T Mayer (2014) “Gravity Equations: workhorse, toolkit, and cookbook,” in G Gopinath, E Helpman and K Rogoff (eds), Handbook of International Economics, North Holland, pp. 131-195.

Santos Silva, J and S Tenreyro (2006) “The log of gravity,” Review of Economics and Statistics 88: 641-658.

Takechi, K (2016) “Daily Gravity,” RIETI Discussion Paper 16-E-095.



Topics:  International trade

Tags:  trade patterns, daily trade, Agriculture, trade costs, supply and demand shocks, Japan

Professor in the Faculty of Economics, Hosei University; Research Fellow, RIETI