#  Financing Costs, Per-Shipment Costs and Shipping Frequency:
Firm-Level Evidence from Bangladesh 111 I am grateful to Dr. Georg Schaur for
all his feedback on this study.

Md Deluair Hossen University of Tennessee, Knoxville<EMAIL_ADDRESS>
( March, 2023
)

###### Abstract

In international trade, firms face lengthy ordering-producing-delivery times
and make shipping frequency decisions based on the per-shipment costs and
financing costs. In this paper, I develop a model of importer-exporter
procurement where the importer procures international inputs from exporting
firms in developing countries. The exporters are credit constrained for
working capital, incur the per-shipment fixed costs, and get paid after goods
are delivered to the importer. The model shows that the shipping frequency
increases for high financing costs in origin and destination. Furthermore,
longer delivery times increase shipping frequency as well as procurement
costs. The model also shows that the higher per-shipment fixed costs reduce
the shipping frequency, in line with previous literature. Reduced transaction
costs lower the exporter’s demand for financial services through shipping
frequency adjustment, mitigating the financial frictions of the firm. Then, I
empirically investigate whether the conclusions regarding the effect of per-
shipment fixed costs on shipping frequency from the theoretical model and in
the existing literature extend to developing countries. My estimation method
addresses several biases. First, I deal with aggregation bias with the firm,
product, and country-level analysis. Second, I consider the Poisson Pseudo
Maximum Likelihood (PPML) estimation method to deal with heteroscedasticity
bias from the OLS estimation of log-linear models. Third, I fix the distance
non-linearity of Bangladeshi exports. Finally, I consider the effect of
financing cost on shipping frequency to address omitted variable bias. Using
transaction-level export data from Bangladesh, I find that 10% higher per-
shipment costs reduce the shipping frequency by 3.45%. This shipping frequency
response is considerably higher than that of developed countries. The findings
are robust to different specifications and subsamples.

##  1 Introduction

Ordering, producing, and shipping products in international trade take
considerable time (Anderson and Van Wincoop,, 2004; Hummels and Schaur,,
2013). This creates some challenges. Firms engaged in international trade must
determine the optimal order and shipping frequency to minimize procurement
costs. Long-time lags are costly for suppliers in developing countries because
standard trade financing contracts require them to borrow working capital for
longer. Furthermore, ICC Global Survey on Trade Finance, 2018, reports a $1.5
trillion trade finance gap between demand and supply. This shortage of capital
creates credit constraints for firms located in a country with weak financial
conditions (ICC,, 2018). These problems are discussed in two disconnected
works of literature. The shipping frequency literature focuses on the trade-
off between the per-shipment fixed costs, and inventory storage costs
(Alessandria et al., 2010a, ; Alessandria et al., 2010b, ; Alessandria et
al.,, 2011; Kropf and Sauré,, 2014; Hornok and Koren, 2015a, ). The financial
constraints literature focuses on interest costs, types of financial
contracts, and firm heterogeneity (Amiti and Weinstein,, 2011; Manova,, 2012;
Antras and Foley,, 2015).

In the theoretical part of the paper, I develop a model that combines these
two kinds of literature. In the model, the importer procures a product from a
financially constrained exporter in a developing country. The exporter gets
paid after delivery and requires working capital financing for production. A
long delivery time creates a trade-off between the variable financing costs
and the per-shipment fixed costs for determining optimal shipping size. An
increase in delivery time raises the marginal procurement cost of order size
relative to the marginal cost of placing an additional shipment. In my model,
this has implications for the effects of financing costs and delivery times on
order frequency and size. Moreover, the effects of per-shipment costs on the
financing demand are stronger in financially constrained countries.

This paper contributes to the buyer-seller procurement contract literature
(Taylor and Wiggins,, 1997; Bajari and Tadelis,, 1999, 2001; Liker and Choi,,
2004; Antras and Helpman,, 2004; Nunn,, 2007; Heise et al.,, 2015). In
particular, this paper is closely related with Taylor and Wiggins, (1997),
which solves the shipping frequency optimization problem when the buyer is
sourcing their procurement from the sellers with a per-shipment fixed
inspection cost. The authors optimize order size for two distinct types of
buyer-suppliers relations, what they term Japanese and American procurement
systems. On the one hand, I am simplifying their model by ignoring
inspections. On the other hand, I am focusing on the problem of delivery times
and asymmetric interest rates in an international trade setting. My extension
makes several contributions to the literature.

My model shows how asymmetric financing costs affect shipping frequencies in
the importer and exporter countries. Higher exporters’ borrowing rates
increase financing costs as well as shipping frequency. Greater discounting in
the importer country leads to more frequent shipments as delaying immediate
costs over small shipments is cheaper. This contributes to the financial
constraint literature (Amiti and Weinstein,, 2011; Chor and Manova,, 2012;
Manova,, 2012; Wagner,, 2014; Feenstra et al.,, 2014). In this context,
Manova, (2012) focuses on the financial development of countries and the
financial vulnerability of different sectors. In their model, the exogenous
financial constraints on the fixed costs determine trade volume, whereas, in
my model, exogenous financing costs on the variable costs determine shipping
size. Illustrating how shipping size adapts to financial constraints, as I do
in this study, is an important addition to this literature.

With the gradual decline of tariff barriers, recent studies focus on the per-
shipment fixed costs, which include order processing, monitoring, customs
clearance, and sanitary checking costs (Alessandria et al., 2010b, ; Hornok
and Koren, 2015b, ; Békés et al.,, 2017; Zhao and Chen,, 2019). The trade-off
between the variable inventory costs and the per-shipment fixed costs
determines optimal shipping frequency and explains lumpy, infrequent trade.
However, these studies do not consider the financing costs for determining
shipping frequency. For example, Hornok and Koren, 2015a  shows that the
demand-side time preference of consumers and the per-shipment fixed costs
determine the frequency and size of the shipment. Kropf and Sauré, (2014)
considers the firm’s trade-off between the per-shipment fixed costs and the
variable storage costs at the destination for shipping frequency optimization.
By considering the financing cost’s effect on shipping frequency, I show how
financing the per-shipment fixed costs later in the supply chain can
significantly affect the exporter’s financing demand.

My model shows that the effect of longer delivery times on trade costs depends
on financing and per-shipment costs. The intuition is that longer delivery
times increase procurement costs, which increase even more for higher per-
shipment costs. A long literature examines the effects of delivery times on
trade costs (Djankov et al.,, 2010; Berman et al.,, 2012; Hummels and Schaur,,
2013; Martincus et al.,, 2015; Bourgeon et al.,, 2016; Li,, 2019). This
literature identifies time as a trade cost and investigates the sources of
these costs. My model contributes to identifying the nexus between delivery
time, financing costs, and per-shipment costs as a potential source of the
time cost. Furthermore, the time costs literature speculates on how financing
costs may be a driving factor for times costs. My model shows that shipping
frequencies are important to understand this mechanism, and that has been
ignored.

Recent trade finance literature considers payment contract tools and financing
methods to understand trade patterns (Schmidt-Eisenlohr,, 2013; Glady and
Potin,, 2011; Ahn,, 2014; Antras and Foley,, 2015; Niepmann and Schmidt-
Eisenlohr, 2017b, ). This literature does not consider the effect of the
shipping frequency on the trade flow. The shipping frequency decisions can
mitigate the demand for trade finance and should be endogenized to get the
full effect of trade finance on trade patterns. Regarding trade finance, my
model is similar to the model developed by Schmidt-Eisenlohr, (2013), which
considers the financing cost of the origin and destination, contract
enforceability, and delivery time to predict the flow of trade. Using the
variables above and abstracting away from trade flow, my model endogenizes the
shipping frequency decision. Furthermore, the lag of international trade and
trade finance mode are intertwined with the shipping frequency decisions.

My model also shows that higher per-shipment costs lead to greater financing
demand. The intuition is that higher per-shipment costs increase total fixed
costs, which reduce shipping frequency but increase shipping size. The working
capital for a large shipment increases the financing demand. Conversely, low
per-shipment costs smooth out demands for financial services through multiple
shipments. This proposition is policy-relevant. Recent trade policy focuses on
trade facilitation which has large effects on per-shipment costs (Hoekman and
Nicita,, 2010; Moïsé et al.,, 2013; Carballo et al., 2016b, ; Carballo et
al.,, 2018).

In the empirical part of the paper, I consider the fact that, in international
trade, shipping frequency is important to understand procurement costs (Taylor
and Wiggins,, 1997), inventory adjustment (Alessandria et al., 2010b, ;
Alessandria et al.,, 2011), pricing to market and exchange rate pass-through
(Aizenman,, 2004), the transmission of shocks across markets (Békés et al.,,
2017), and effects of trade facilitation policies (Carballo et al., 2016b, ).
Furthermore, I test the effect of per-shipment fixed costs on shipping
frequency, a theoretical outcome from the model. Recent evidence examines the
determinants of shipping frequency. In particular, for developed countries
using product and country-level data, Hornok and Koren, 2015a ; Hornok and
Koren, 2015b  provide evidence that per-shipment fixed costs are an important
determinant to understanding shipping frequencies. To date, evidence for
developing countries using firm-level data does not exist.

There are several reasons why the existing evidence might not immediately
extend to developing countries, such as Bangladesh, which is my focus. First,
at the product and country level, estimates might be subject to aggregation
bias (Lewbel,, 1992; Van Garderen et al.,, 2000; Albuquerque,, 2003). Second,
the OLS estimation of log-linear models in the existing literature might be
biased due to heteroscedasticity (Silva and Tenreyro,, 2006). Third, existing
specifications do not consider financing costs and might therefore be subject
to omitted variable bias (Taylor and Wiggins,, 1997). Fourth, Bangladesh’s
unique position in the supply chain and focus on apparel products with main
target markets in Europe and the US suggest that existing specifications are
inappropriate for understanding shipping frequency determinants. For example,
given the geographic location of Bangladesh, it is not clear that shipping
frequencies are linearly decreasing in distance, as a common assumption of
existing specifications. In this paper, my research question is if the
conclusions regarding per-shipment fixed costs in the existing literature
extend to developing countries.

To answer this research question, I employ transaction-level export data from
Bangladesh from 2006 to 2013. Consistent with the existing literature, I
measure shipping frequency as the number of export shipments a firm in
Bangladesh engages in with foreign buyers for a given product within a year. I
apply robust estimators appropriate for count models concerning the
heteroscedasticity bias in log-linear models. I account for non-linear
distance effects in my empirical model and provide evidence for aggregation
bias considering product, country, and mode of transportation levels of
aggregation. To examine omitted variable bias, I extend the model for various
measures of financing costs and take advantage of my firm-level data to
specific unobserved heterogeneity with fixed effects.

My main findings are that OLS estimation of the log-linear model of Hornok and
Koren, 2015a ; Hornok and Koren, 2015b  underestimates the per-shipment cost
effects on the shipping frequency at both the country and product levels. The
Poisson Pseudo Maximum Likelihood (PPML) estimation method can overcome this
underestimation. I find that the per-shipment cost estimates are overestimated
at the higher levels of aggregation. I also find evidence of omitted variable
bias as adding financing cost increases the elasticity of the per-shipment
costs. Finally, I find that for Bangladeshi trade, fixing distance non-
linearity is crucial to understand the effect of per-shipment costs on the
shipping frequency. By fixing all of these biases, I find that for a 10%
increase in the per-shipment costs, the shipping frequency decreases by
$3.24$% for Bangladesh. By comparing the findings of Hornok and Koren, 2015b ,
this shipping frequency reduction is 1.28 times larger than the US and 3.22
times larger than Spain.

My empirical results provide four contributions to the existing literature.

First, by solving various identification problems in the existing literature,
my evidence shows that per-shipment fixed costs are more important in
developing countries relative to developed countries. At the exporter level,
the per-shipment elasticity is -0.227 by accounting for a product-mode-year
effect. This elasticity is higher than the findings of Hornok and Koren, 2015b
for the product-level Spanish exports.

Second, my evidence shows that applications in the existing literature are
subject to biases. One such relevant bias is omitted variable bias. When I
introduce financing costs and narrow the fixed effects to account for
unobserved heterogeneity, the per-shipment cost elasticity increased by 1.48
times. Moreover, the effect of financing costs on shipping frequency remains
robust to additional measures of financing costs. Furthermore, addressing
omitted variable problems also increases the effects of country size (GDP),
income (GDP per capita), and distance on the shipping frequency.

Third, financial constraints are an important determinant of trade flows and a
firm’s selection into export markets (Muûls,, 2008; Bellone et al.,, 2010;
Amiti and Weinstein,, 2011; Chor and Manova,, 2012; Manova,, 2012; Buono and
Formai,, 2013; Besedeš et al.,, 2014; Paravisini et al.,, 2014; Fauceglia,,
2015; Bergin et al.,, 2017). Existing procurement models show that if there is
heterogeneity in financing costs across exporter and importer locations, then
financing costs are also an important determinant of shipping frequencies
(Taylor and Wiggins,, 1997; Schmidt-Eisenlohr,, 2013). Understanding if
financing costs are a determinant of shipping frequencies is important because
if they are, then shipping frequencies affect the demand for financial
services, and policies that reduce per-shipment fixed costs have the potential
to relax financial constraints. Consistent with the predictions from these
models, I provide evidence that greater exporter interest rates increase
shipping frequency more for higher importer discount rates. However, higher
importer discount rates decrease shipping frequency, contradicting the
theoretical predictions. Overall, fixed cost-reducing policies can decrease
the severity of financial constraints more in high-interest rate countries
than low-interest rate countries by increasing shipping frequency.

Finally, the WTO agreement on trade facilitation strives to reduce transaction
barriers in international trade. Reducing trade costs in a developing country
is a key goal of the Aid for Trade (WTO,, 2013) and trade facilitation
programs (OECD/WTO,, 2014). Evidence shows that these policies reduce fixed-
per-shipment costs (Moïsé et al.,, 2013; Goldberg and Pavcnik,, 2016; Carballo
et al., 2016a, ; Carballo et al., 2016b, ; Carballo et al.,, 2018). For
example, Bangladesh, a developing country, continues to reduce trade costs as
a beneficiary country of the Trade Facilitation Support Program by the World
Bank. This study shows that these policies reduce trade costs and relax the
demand for financial services in financially constrained countries. This
provides a mechanism for evaluating the influence of trade policies. Based on
my estimates, these policies might be more effective for developing countries
like Bangladesh than developed countries. Furthermore, these policies are
especially important compared to developed countries in determining exchange
rate pass-through, inventory adjustment, and the transmission of shocks across
markets due to increased shipping frequencies.

Having discussed the background and related literature, the remainder of this
paper is organized as follows. Section 2 builds up the model and explains the
theoretical outcomes with propositions. Section 3 describes the data and
estimation strategies. Section 4 presents the results, and section 5 checks
robustness with several subsamples and alternative specifications. Section 6
concludes.

##  2 The Model Setup

I develop a simple model of the exporter-importer procurement system with
financial constraints and delivery times. An importer procures quantity $q$
and minimizes cost by choosing an order size $x$, which implies that the
shipping frequency is $n=\frac{q}{x}$. I treat the choice of order size and
shipping frequency as exogenous while focusing on the exporter’s problem. The
importer pays after receiving the order. This assumption is consistent with
standard trade financing contracts literature (Schmidt-Eisenlohr,, 2013;
Niepmann and Schmidt-Eisenlohr, 2017a, ). These payments after delivery create
a financing problem for the exporter.222The exporter financing due to payment
after delivery is more common in developing countries. For example, export
financing is used for 44.36 % of Bangladeshi exports by volume (Habib and
Shah,, 2017).

###  2.1 The Exporter’s Problem

The exporter receives an order of size $x.$ The exporter’s constant marginal
cost of production is $c.$ Therefore, the production cost is $cx.$ Located in
a developing country, the exporter, is financially constrained and borrows
working capital from domestic financial intermediaries to cover production and
other costs (Chan,, 2014). Let $\Delta$ be the time between the importer’s
order and the goods delivered, defined here as delivery time. This includes
time for production, domestic transportation to the port, customs clearance,
and port-to-port transportation. Assume $\Delta$ is independent of order size
$x$ as most of the delivery time’s components are fixed except production
time. For example, a garment shipment from a firm in Bangladesh to JC Penny in
the USA may take 116 days from getting the order to the product delivered,
whereas production time is only 23 days (Haque,, 2009). Let $r$ be the
interest at which the exporter borrows the entire working capital for
$\Delta.$ With the continuous compounded interest rate, a $1 borrowing
requires $\big{(}\mathrm{e}^{\Delta r}\big{)}$ payment at the end of $\Delta$
period. The total production cost, including financing cost, is then
$\big{(}cx\mathrm{e}^{\Delta r}\big{)}.$

After production, the firm ships the goods to the importer. Here, I am
modeling the per-shipment fixed costs as if they appear later in the supply
chain, which does not require upfront borrowing (Barry,, 2016; Schutte et
al.,, 2019). I am considering this because it is a more interesting case to
understand the trade-off between the financing cost and the per-shipment costs
for determining the shipping frequency.333Regarding the per-shipment fixed
costs for shipping $f$, there are two possible assumptions. The per-shipment
costs are borrowed immediately or paid later in the supply chain and do not
require borrowing. I show the first case in Appendix-A. With the per-shipment
cost, the total cost of producing and delivering an individual shipment is
$(cx\mathrm{e}^{\Delta r}+f)$.

The exporter is willing to produce and deliver if the payment from the
importer $w(x)$ at least covers the total cost to produce and ship the order.
Therefore, the exporter’s participation constraint is

$w(x)\geq cx\mathrm{e}^{\Delta r}+f$

###  2.2 The Importer’s Problem

I derive an importer’s cost for a single order in this section. I then
aggregate all the orders to get the total procurement cost and optimize the
order size. Finally, I derive propositions.

With all the bargaining power, the importer covers costs only (i.e., pays no
rent to the exporter). Moreover, with the constant marginal cost and
competitive environment, the exporter’s participation is ensured even if the
payment only covers the costs. The exporter participation gives

$w(x)=cx\mathrm{e}^{\Delta r}+f$ (1)

Equation 1 shows that if exporters are financially constrained and delivery
times are long, importers need to make a greater payment for procurement to
cover higher financing costs.

As the importer pays for the order after receiving the shipment, the
importer’s present value of cost for this single shipment is

$\mathrm{e}^{-\Delta r_{1}}w(x)$

Here, $r_{1}$ is the importer’s domestic annual interest rate, which is
assumed to be independent of $\Delta$. Furthermore, the importer discounts the
procurement costs of a single order by $(\mathrm{e}^{-\Delta r_{1}})$.

The importer buys in batches of the same size $x,$ similarly spaced throughout
the entire period. Figure 1 shows a case where the delivery time is larger
than the time between two consecutive orders. It takes $\Delta$ time from the
first order to the first delivery. Although goods arrive after $\Delta$ time
after the order is placed, the buyer still gets products $\frac{x}{q}$ time
apart in his warehouse. The importer discounts each order cost for the time
duration of $\frac{x}{q}.$ Infinite numbers of such discounted single-order
costs are added to get the importer’s aggregated present procurement costs of
the indefinite supply stream. Thus, the total procurement cost of $C$ is

$C=w(x)\mathrm{e}^{-\Delta
r_{1}}(1+\mathrm{e}^{-\frac{r_{1}x}{q}}+\mathrm{e}^{-\frac{2r_{1}x}{q}}+....)=\frac{w(x)\mathrm{e}^{-\Delta
r_{1}}}{1-\mathrm{e}^{-\frac{r_{1}x}{q}}}$

The importer chooses the optimal shipment size to minimize costs.

$\min_{x}\frac{w(x)\mathrm{e}^{-\Delta
r_{1}}}{1-\mathrm{e}^{-\frac{r_{1}x}{q}}}$ (2)

Substituting $w(x)$ from equation 1 into equation 2 yields following
optimization problem with asymmetric interest rates444 Interest rates
segmentation (Mishkin,, 1984) and the capital market-deepening (Rajan and
Zingales,, 1998) ensure asymmetric interest rates for any particular exporter-
importer country pair $(r\neq r_{1}).$

$\min_{x}\dfrac{(cx\mathrm{e}^{\Delta r}+f)\mathrm{e}^{-\Delta
r_{1}}}{1-\mathrm{e}^{-\frac{r_{1}x}{q}}}$

Taking derivatives of the above equation concerning $x$ and setting equal to
zero yield

$\dfrac{c\mathrm{e}^{\Delta r}(\mathrm{e}^{-\Delta
r_{1}})}{1-\mathrm{e}^{-\frac{r_{1}x}{q}}}-\dfrac{r_{1}(\mathrm{e}^{-\Delta
r_{1}})(c\mathrm{e}^{\Delta
r}x+f)\mathrm{e}^{-\frac{r_{1}x}{q}}}{q(1-\mathrm{e}^{-\frac{r_{1}x}{q}})^{2}}=0$

Rearranging,

$\bigg{[}\dfrac{c\mathrm{e}^{\Delta r}(\mathrm{e}^{-\Delta
r_{1}})}{1-\mathrm{e}^{-\frac{r_{1}x}{q}}}-\dfrac{r_{1}(\mathrm{e}^{-\Delta
r_{1}})(c\mathrm{e}^{\Delta
r}x)\mathrm{e}^{-\frac{r_{1}x}{q}}}{q(1-\mathrm{e}^{-\frac{r_{1}x}{q}})^{2}}\bigg{]}-\dfrac{r_{1}(\mathrm{e}^{-\Delta
r_{1}})f\mathrm{e}^{-\frac{r_{1}x}{q}}}{q(1-\mathrm{e}^{-\frac{r_{1}x}{q}})^{2}}=0$

An increase of $x$ makes the marginal transaction cost in the second term of
the above equation smaller but makes the immediate marginal purchasing costs
in the square-bracketed term larger. Thus, for choosing $x$, the firm faces a
trade-off between the more per-shipment fixed cost of an additional order and
more immediate procurement costs of a larger shipment due to one less order.

After manipulation, the optimized order size is the root of the following
equation:

$qc\mathrm{e}^{\Delta
r}(\mathrm{e}^{\frac{r_{1}x^{*}}{q}}-1)-c\mathrm{e}^{\Delta
r}r_{1}x^{*}=fr_{1}$ (3)

The equation 3 shows that the optimized order size is a function of financing
costs, delivery times, marginal cost, and quantity. Thus,
$x^{*}=x(r,r_{1},\Delta,f,c,q).$555Considering the dependency of order size on
interest rates, procurement amount, and per-shipment costs, this closely
follows Baumol’s model of the transactions demand for money (Baumol,, 1952).

Proposition 1. For $x>0$, there exists a unique shipping size, $x^{*}$ that
minimized the firm’s procurement costs.

Proof: See Appendix-A

For positive shipping size, solving equation 3 yields a unique shipping size.
This shipping size depends on additional variables than the optimal shipping
size derived in Taylor and Wiggins, (1997). The origin and destination
financing costs and delivery times are now crucial for the procurement’s
shipping size decision. The effect of delivery time on the shipping size in my
model results from taking the buyer-seller domestic setup of Taylor and
Wiggins, (1997) to international trade.

####  2.2.1 Shipping Frequency

The optimized order size yields the shipping frequency. As the shipping
frequency is an important decision factor for trade, I investigate how other
relevant model variables can affect the shipping frequency in the following
proposition.

Proposition 2. All else unchanged, shipping frequency (i) increases if the
interest rate in the exporter’s country increases: $\frac{\partial n}{\partial
r}\geq 0$, (ii) increases if the interest rate in the importer’s country
increases: $\frac{\partial n}{\partial r_{1}}\geq 0$, (iii) increases if the
delivery time is longer: $\frac{\partial n}{\ \partial\Delta}\geq 0$, and (iv)
decreases if the per-shipment fixed costs increase: $\frac{\partial
n}{\partial f}\leq 0$.

Proof: See Appendix-A

The intuition for the first result is as follows. First, if exporters’
financing costs increase, they require a higher payment, and importers respond
by increasing shipping frequency to push added costs into the future. Thus,
facing the higher-interest rate in the exporter country, the importer
increases the shipping frequency. Next, if financing costs increase in the
importer country, importers choose small-size orders to benefit from higher
discount rates. As the fixed costs are spanned throughout the entire period
over smaller shipment sizes, greater discounting reduces the total costs.
Finally, the financing need arises for the exporter from the delayed payment
after delivery to the importer. The longer delivery times increase the
exporter’s financing need for an extended period, increasing financing costs.
To avoid these high financing costs, the firm chooses more frequent shipments.
Considering a fixed amount of procurement, anything that makes the exporter’s
production costly forces the importers to choose a small lot size, reducing
some of the financing costs through a small time window between shipments.

The simple intuition for the last result is that high transaction costs make
frequent shipments costly to the importer. The importer chooses less frequent
shipments to mitigate these fixed costs by placing larger orders. This finding
is in line with Kropf and Sauré, (2014).

After finding the shipping frequency responses to the financing costs,
delivery time, and per-shipment fixed costs, I now investigate how the
shipping frequency mechanism affects the financing demand to emphasize the
relationship between financing demand and trade facilitation.

####  2.2.2 Financing Demand

The financing demand is an important factor for the exporting decision
(Humphrey,, 2009; Nagaraj,, 2014). Due to financial constraints in a
developing country, the exporter can only borrow working capital for the order
in process. Thus, the firm’s demand for financial services is a simple measure
of the amount of loan the firm holds at any given point in time in the entire
inventory period. The financing demand of the exporter is $D=cx^{*}(.)$.

Proposition 3. a) All else unchanged, the financing demand of the exporter (i)
decreases for higher financing costs of the exporter: $\frac{\partial
D}{\partial r}\leq 0$, (ii) decreases for higher financing costs of the
importer: $\frac{\partial D}{\partial r_{1}}\leq 0$, (iii) decreases for
longer delivery times: $\frac{\partial D}{\partial\Delta}\leq 0$, and (iv)
increases for higher per-shipment fixed costs: $\frac{\partial D}{\partial
f}\geq 0$.

b) All else unchanged, if per-shipment costs are high, then an increase in
financing costs or delivery times results in a greater financing demand
decrease than when per-shipment costs are low: $\frac{\partial^{2}D}{\partial
r\partial f}\leq 0$, $\frac{\partial^{2}D}{\partial r_{1}\partial f}\leq 0$,
and $\frac{\partial^{2}D}{\partial\Delta\partial f}\leq 0$.

Proof: See Appendix-A

The higher financing costs at both origin and destination reduce the order
size, which reduces the exporter’s financing demand. Similarly, the higher
delivery times make order sizes smaller, which lowers the financing demand.
From Proposition 2, I can see that the higher per-shipment fixed costs
increase order size. This requires a higher financing demand for the exporter.
As less frequent shipments due to high per-shipment costs increase demand for
working capital financing and bolster the severity of financial constraints,
financial demand adjustment through shipping decisions is essential.

The exporter’s financing demand is affected by the per-shipment costs because
of the shipping frequency adjustment. At a lower per-shipment cost, the
increase in shipping frequency reduces the exporter’s financing demand, which
is now less responsive to the higher financing costs and longer delivery
times. This important finding indicates that the effect of an increase in the
financing costs and delivery times on the financing demand is mitigated by the
firm’s ability to increase shipping frequency. Thus, if the developing
countries can lower the fixed costs, they benefit more from lessened financing
demand.

####  2.2.3 Procurement Cost

In my model, an increase in the delivery time raise procurement costs adding
to the literature that shows that delivery time is costly (Djankov et al.,,
2010; Berman et al.,, 2012; Hummels and Schaur,, 2013). As the increase in
procurement cost depends on the severity of the fixed trade barriers (e.g.,
the per-shipment costs), I now investigate how procurement costs are affected
by the model variables, and, consequently, by the fixed costs.

Proposition 4. a) All else unchanged, the procurement costs (i) increase for
higher interest rates in the exporter country: $\frac{\partial C}{\partial
r}\geq 0$, (ii) increase for longer delivery times: $\frac{\partial
C}{\partial\Delta}\geq 0$, (iii) increase for higher per-shipment costs:
$\frac{\partial C}{\partial f}>0$, and (iv) decrease for higher interest rates
in the importer country: $\frac{\partial C}{\partial r_{1}}\leq 0$.

b) All else unchanged, if per-shipment costs are high, then an increase in (i)
exporter’s interest rates or delivery time results in a greater cost increase
than when per-shipment costs are low: $\frac{\partial^{2}C}{\partial r\partial
f}\geq 0$ and $\frac{\partial^{2}C}{\partial\Delta\partial f}\geq 0$, (ii)
importer’s interest rates result in a lower cost increase than when per-
shipment costs are low: $\frac{\partial^{2}C}{\partial r_{1}\partial f}<0$.

Proof: See Appendix-A

The procurement cost is a non-linear function of the optimized order size and
relevant parameters,
$C=f(x^{*}(.),\Delta,f,...).$ Using this function, I find that the exporter
financing costs, the delivery times or the per-shipment costs increase
procurement costs. The simple intuition is that higher financing costs, longer
delivery time, and high per-shipment costs require more working capital
financing for a longer period at a higher per-shipment cost, raising the total
financing costs and fixed costs. This, in turn, raises the procurement costs
of an order. Thus, these variables increase the procurement cost of an extra
order relative to the per-shipment costs of placing an additional shipment.
The costs increase due to delivery time lag is in line with the time as fixed
cost literature. However, the intuition is not simple for explaining why the
importer’s interest rate is reducing procurement costs. In this case, a higher
interest rate increases the discounting of an order’s immediate purchasing
cost for the importer. Although the shipping frequency increases for a higher
interest rate, the immediate purchases’ accumulated present value is lower.

The increase in procurement costs due to longer delivery time or the financing
costs depends on the per-shipment costs. For the higher per-shipment cost, the
exporter financing costs and delivery time increase procurement costs at a
higher rate than lower per-shipment costs. The intuition for this result is
that the importer of a country with lower per-shipment fixed costs can
increase shipping frequency. This mitigates the effect of the financing costs
and delivery times on procurement costs. If firms can adjust shipping
frequencies, greater financing costs and longer delivery times can be easily
accommodated. However, for the importer financing costs, higher per-shipment
costs, and delivery time decrease procurement costs at a higher rate due to
the negative effect of importer interest rates on the procurement cost.

###  2.3 Discussion

The theoretical analysis gives some empirically testable predictions. From
Proposition 2, I find that the financing costs and the delivery time
positively affect the shipping frequency, and the per-shipment costs
negatively affect the shipping frequency. These predictions can be tested
empirically with transaction-level trade data and financing data. Depending on
the extent of financial development, the degree of capital market deepening,
the severity of financial frictions, and the existence of capital control, the
magnitude of the financing cost’s effect on the shipping frequency may vary.
Therefore, in the next section, I take testable predictions to a developing
country’s trade data to determine the effects on the shipping frequency.

Depending on the data availability, Proposition 3 is testable if bank-firm
matched data is available, and Proposition 4 is testable if exporter-importer
paired data is available. The theoretical analysis changes if the per-shipment
fixed costs are paid upfront. Here, the exporting firms are taking external
funds immediately after receiving the importer’s order to finance the per-
shipment costs (see Appendix-A for this alternative setup). In this case, the
origin financing and the delivery times do not affect shipping decisions.
Therefore, higher financing costs in the exporter country and longer delivery
times do not affect the financing demand. Except for monitoring cost, this
alternative finding is equivalent to the shipping size of the model of Taylor
and Wiggins, (1997). Only empirical analysis can shed light on which modeling
setup is appropriate for a country for its relevance with the data.

Using a partial equilibrium model to understand the financial demand
adjustment through shipping frequency has limitations. I abstract away from
other factors, such as price, demand effect, credit market, and the business
cycle, important factors of shipping frequency decisions. I argue that in
developing countries, the per-shipment fixed costs and the working capital
financing costs are considerably higher than in developed economies.
Furthermore, the exporter lacks bargaining power for pricing and shipping
frequency decisions. Against this backdrop, the financing costs and the
delivery times for emerging economies are essential to trade barrier issues
for understanding the shipping frequency. However, the model’s outcome will be
undermined if the exporters use destination financing.

##  3 Data and Estimation Strategy

This section discusses the data and estimation strategies I will use in the
estimation.

###  3.1 Firm-Level Trade Data

Shipping frequency data is calculated from transaction-level export data from
the Bangladesh Customs Authority, National Board of Revenue (NBR). The NBR
collects customs data using ASYCUDA++, a computerized system designed by the
United Nations Conference on Trade and Development (UNCTAD). I get this
transaction-level data on export from the International Growth Center
(IGC).666IGC facilitates research and provides policy advice in Africa and
South Asia. They posted the Bangladeshi trade data on their website. The data
can be downloaded from the following link:
https://www.theigc.org/country/bangladesh/data/. For details about the
accuracy of this data, see Ahsan and Iqbal, (2017). The data includes the date
of export, the exporter’s unique identification number, the freight on board
export value, the export volume, Harmonized System eight-digit codes (HS8) of
the product, the export destination, and the port of export. In the dataset, I
have data from July 1, 2004, to December 31, 2013. In this study, I use annual
data for all control variables. Thus, I eliminate data from July 1, 2004, to
December 31, 2004. I lose 163,393 observations. Furthermore, observations with
the missing firm identification number are eliminated. I also drop data from
2005 as the per-shipment fixed costs are missing for many countries. I lose
0.35 million observations. Finally, I trim the data at the extreme tail of the
per-shipment export value to eliminate any potential outliers by eliminating
the observations smaller than one percentile and larger than 99 percentiles. I
lose 96,162 observations.777In the robustness checks, I show that including
these observations does not affect the results.

After data refinement, the final sample has 4.97 million transactions spanning
eight years, where 18,327 firms export 4,234 HS8 products to 179 destinations.
In the data, all monetary values are in constant 2010 Bangladeshi Currency,
Taka (BDT). I convert these export values to match other macro variables using
the average annual exchange rates against US dollars (USD). Table 1 summarizes
the Bangladeshi export data. The total export volume is $156.7 billion (in
constant 2010 USD). The average shipping size is $31,472, and the median
shipment size is $14,245. Most of the exports go to only a few developed trade
partners, as reported in table 2. About 59.51 % of exports shared by volume
are going to the top 5 export destinations. The US covers 23.37 % of export
share by volume and 17.08% share of shipments with 13.69 average shipments by
the firm-product-year. The UK’s export share by volume is 9.95 %, but the
shipment share is comparatively higher, 14.13%. Thus, there is variation in
shipping frequency relative to shipping volume across destinations, which I am
interested in examining in the estimation sections.

I use the firm identifier to get the shipping frequency. A shipment is a
single transaction at the port with a distinct Customs form. I aggregate all
the shipments for a firm exporting an eight-digit HS code product to an
exporting destination in a year. Thus, the shipping frequency variable
captures all observations of firm-product-destination-year data combinations
for 2006-2013. I find that there are 544,486 firm-good-year-destination
observations. The largest firms make about two thousand shipments. However,
the average shipping frequency for a firm is 8.92. Table 3 provides the year-
wise shipping frequency, the number of exporting firms, the number of new
firms, and the number of firms with a single shipment. Column 2 of table 3
reports considerable shipping frequency growth over the year. Therefore, in
some specifications, I examine the effect of this growth by accounting for a
year effect. The number of single shipment firms in column 4 shows that only
2,943 firms out of 18,327 have only single shipments throughout the study
period. Thus, more than 80% firms make multiple shipments of an HS8 product to
a specific destination. I report high-frequency firms (more than 100
shipments) in column 5 of table 3, which shows the significant presence of
high-frequency exporters. Finally, I calculate the per-shipment value by
dividing the aggregated export value by shipping frequency.

Figure 2 shows the shipping frequency for the exporter for 2006-2013. The
figure confirms the stylized facts of international trade that shipments are
infrequent and lumpy. Many single shipment firms contribute about 45% of the
shipments at the exporter-product-mode-destination-year observation level. The
distribution of the size of the shipments is presented in figure 3. Excluding
a few small and very few large-sized shipments, most shipping sizes are close
to the median value of $14,245. Figure 3 shows that the distribution of
shipping frequency is similar to a negative binomial distribution.

###  3.2 Country-Level Data

For the importer’s financing cost, I get interest rates (lending rates) from
the International Financial Statistics (IFS) of the International Monetary
Fund (IMF). For the exporter’s financing cost, I use scheduled bank average
interest rates taken from the central bank of Bangladesh (Bangladesh Bank).

I need additional data about the financial constraints of the destinations to
deal with omitted variable bias. The debt to GDP ratio data comes from Beck
and Demirguc-Kunt, (2009). The debt-to-GDP ratio measures the level of
financial development of an economy. I use a credit and bank confidence scores
to consider the economy’s financial frictions. A credit score measures
accessibility to finance by considering the strength of credit reporting
systems and the effectiveness of collateral and bankruptcy laws in
facilitating interest. I get a credit score from the Doing Business Survey
database of the World Bank for credit accessibility. For the cultural
perception of the financial sector, I use confidence in bank measures from the
World Values Survey (WVS) database (Inglehart and Welzel,, 2010). For
alternative measures of interest rates, I use net interest rate margins taken
from Beck and Demirguc-Kunt, (2009). The net interest margin considers loss
due to non-performing loans and captures the average ex-post markup on
interest. It comes from the accounting value ratio of financial
intermediaries’ net interest revenues and their total earning assets.
Therefore, the net interest margin captures the financial intermediaries’
opportunity cost while the interest rates capture the importer’s real
financing cost if they borrow from the banking system.

I take the per-shipment fixed costs from the Doing Business Survey (DBS)
database of the World Bank. For per-shipment costs, DBS measures the costs of
documentary compliance, border compliance, and domestic transport, excluding
tariffs.

The bilateral distance (in kilometers, between most populated cities of a
country-pair) data comes from the Center for International Prospective Studies
(CEPII) Geodist dataset (Mayer and Zignago,, 2011). I use sea-distance data
from the CERDI sea-distance database (Bertoli et al.,, 2016) for alternative
distance measurements. This database contains bilateral maritime distances
between 227 countries and territories. The relevant port(s) for countries with
the most shipping lines are considered for computing sea distance (landlocked
countries are linked to the foreign port with the shortest road distance to
its capital city). I calculate transport time from this database using an
average speed of 13 knots.888The average container vessel speed comes from
searates.com. I add the import port delay with the transport time for the
total time. Import port delay data is taken from the DBS database. I also use
an alternative measure of the trade barrier, the Logistics Performance Index
(LPI), which comes from the World Bank.

Control variables such as GDP (in constant US dollars), GDP per capita (in
constant US dollars), common religion (an index), island (a dummy), landlocked
(a dummy), common legal origin (a dummy), and common colony (a dummy) are
taken from the Center for International Prospective Studies (CEPII) Gravity
dataset (Head et al.,, 2010).

The table 4 includes all regression variables’ summary statistics and data
sources.

###  3.3 Estimation Strategy

Lewbel, (1992) discusses the presence of aggregation bias for log-linear panel
data where mean-scaling is not ensured. This is likely true for shipping
frequency data as the number of exporter shipping to a destination are
correlated over the panel period. Furthermore, the more important source of
bias is that in aggregate-level data, the number of shipments depends on the
number of exporters and the number of times they ship. Thus, it is not clear
if estimates capture the effect on the number of exporters or the number of
shipments. To investigate this, I start with the country-level analysis,
followed by product and firm-level analysis.

For the country level, I estimate the following model of Hornok and Koren,
2015a :

$\begin{multlined}ln\ N_{jt}=\alpha+\beta_{1}ln\ f_{jt}+\beta_{2}ln\
distance_{j}+\theta X_{jt}+\lambda_{j}+\xi_{t}+\epsilon_{jt}\end{multlined}ln\
N_{jt}=\alpha+\beta_{1}ln\ f_{jt}+\beta_{2}ln\ distance_{j}+\theta
X_{jt}+\lambda_{j}+\xi_{t}+\epsilon_{jt}$ (4)

The dependent variable is $ln\ N_{jt}$, the log of the number of shipments
from Bangladesh to the country $j$ in year $t$. $ln\ f_{jt}$ is the log of the
per-shipment fixed costs from Bangladesh to the importer country $j$ in year
$t$. $ln\ distance_{j}$ is the log of the distance from Bangladesh to the
export destination $j$. $X_{jt}$ contains control variables. For control
variables, I use GDP and GDP per capita to control quantity and demand effects
(Anderson,, 2011). The dummies capture the demand and fixed costs for the
island, landlocked, common legal origin, and common colony, and index for
common religion (Head and Mayer,, 2014). Thus, $X_{jt}$ contains the log of
$GDP_{jt}$, log of the per capita $GDP_{jt}$, island dummy, landlocked dummy,
common colony dummy, common legal origin dummy, and common religion index.
Although the common language is considered in Hornok and Koren, 2015b  as a
control variable, there is no trade partner except India, which speaks
Bengali. Instead, I consider a common religion dummy for Bangladeshi trade.
Bangladesh, an 89% Muslim majority country, exports more religion-specific
goods (e.g., Halal products) to Islamic countries. I include country fixed
effect $\lambda_{j}$ to account for destination-specific unobservables.
$\xi_{t}$ is year fixed effect. Finally, the error term is $\epsilon_{jt}$.
The coefficients of interest $\beta_{1}$ capture the effects of the per-
shipment fixed costs on the shipping frequency. Previous studies, as well as
my theory, predict that $\beta_{1}<0$. A negative value of $\beta_{1}$ refers
to reduced shipping frequency for higher per-shipment costs. According to
previous studies, distance has a negative effect on the shipping frequency,
which means $\beta_{3}<0$.

The estimates from OLS estimation of log-linear models are biased (Silva and
Tenreyro,, 2006). Furthermore, the shipping frequency is a count variable.
Thus, the PPML estimation method is better suited to this empirical analysis.
I use the following model999I use reghdfe and ppmlhdfe packages in Stata for
OLS and PPML estimation. This can deal with high-dimensional fixed effects
(Correia,, 2017; Correia et al., 2019a, ; Correia et al., 2019b, ).

$\begin{multlined}N_{jt}=exp\big{[}\alpha+\beta_{1}ln\ f_{jt}+\beta_{2}ln\
distance_{j}+\theta
X_{jt}+\lambda_{j}+\xi_{t}\big{]}\times\epsilon_{jt}\end{multlined}N_{jt}=exp\big{[}\alpha+\beta_{1}ln\
f_{jt}+\beta_{2}ln\ distance_{j}+\theta
X_{jt}+\lambda_{j}+\xi_{t}\big{]}\times\epsilon_{jt}$ (5)

Being a developing country located in a specific geographic location, distance
is non-linearly related to trade flow and shipping frequency. Especially, the
high export share with the EU (biggest export destination) and the US (second
biggest export destination) create the non-linearity between shipping
frequency and distance. Investigating shipping data, I find three splines
provide the most reasonable fix for distance non-linearity. The first spline
(spline1) includes only neighbor countries inside 3970 kilometers radius, the
second spline (spline2) includes European countries and other destinations
beyond neighbor countries inside 9283 kilometers radius, and the third spline
(spline3) includes the US and the rest of the destinations. Thus, I modify
model 5 for distance fix by introducing two dummies for three distance
splines. The modified model is as follows:

$\begin{multlined}N_{jt}=exp\big{[}\alpha+spline1+spline2+\beta_{1}ln\
f_{jt}+\beta_{2}ln\ distance_{j}+\beta_{3}spline1\\\ \times ln\
distance_{j}+\beta_{4}spline2\times ln\ distance_{j}+\theta
X_{jt}+\lambda_{j}+\xi_{t}\big{]}\times\epsilon_{jt}\end{multlined}N_{jt}=exp\big{[}\alpha+spline1+spline2+\beta_{1}ln\
f_{jt}+\beta_{2}ln\ distance_{j}+\beta_{3}spline1\\\ \times ln\
distance_{j}+\beta_{4}spline2\times ln\ distance_{j}+\theta
X_{jt}+\lambda_{j}+\xi_{t}\big{]}\times\epsilon_{jt}$ (6)

Next, I focus on the product-level analysis and estimate the model of Hornok
and Koren, 2015b :

$\begin{multlined}lnN_{gmjt}=\alpha+\beta_{1}ln\ f_{jt}+\beta_{2}ln\
distance_{j}+\theta
X_{jt}+\eta_{g}+\phi_{m}+\xi_{t}+\epsilon_{gmjt}\end{multlined}lnN_{gmjt}=\alpha+\beta_{1}ln\
f_{jt}+\beta_{2}ln\ distance_{j}+\theta
X_{jt}+\eta_{g}+\phi_{m}+\xi_{t}+\epsilon_{gmjt}$ (7)

Where $N_{gmjt}$ is the number of the shipments from a firm in Bangladesh
exporting product $g$ by transport mode $m$ to country $j$ in year $t$. I
include products fixed effect $\eta_{g}$ to account for product-specific
unobservables. Transport mode-specific shocks are absorbed by $\phi_{m}$.
$\epsilon_{gmjt}$ is the error term. Other notations are similar to the
previous model.

My preferred specification comes from 6 with product-level modification

$\begin{multlined}N_{gmjt}=exp\big{[}\alpha+spline1+spline2+\beta_{1}ln\
f_{jt}+\beta_{2}ln\ distance_{j}+\beta_{3}spline1\\\ \times ln\
distance_{j}+\beta_{4}spline2\times ln\ distance_{j}+\theta
X_{jt}+\eta_{g}+\phi_{m}+\xi_{t}\big{]}\times\epsilon_{gmjt}\end{multlined}N_{gmjt}=exp\big{[}\alpha+spline1+spline2+\beta_{1}ln\
f_{jt}+\beta_{2}ln\ distance_{j}+\beta_{3}spline1\\\ \times ln\
distance_{j}+\beta_{4}spline2\times ln\ distance_{j}+\theta
X_{jt}+\eta_{g}+\phi_{m}+\xi_{t}\big{]}\times\epsilon_{gmjt}$ (8)

To overcome the aggregation bias, now, I consider firm-level analysis by
modifying model 8

$\begin{multlined}N_{igmjt}=exp\big{[}\alpha+spline1+spline2+\beta_{1}ln\
f_{jt}+\beta_{2}ln\ distance_{j}+\beta_{3}spline1\\\ \times ln\
distance_{j}+\beta_{4}spline2\times ln\ distance_{j}+\theta
X_{jt}+\lambda_{i}+\eta_{g}+\phi_{m}+\xi_{t}\big{]}\times\epsilon_{igmjt}\end{multlined}N_{igmjt}=exp\big{[}\alpha+spline1+spline2+\beta_{1}ln\
f_{jt}+\beta_{2}ln\ distance_{j}+\beta_{3}spline1\\\ \times ln\
distance_{j}+\beta_{4}spline2\times ln\ distance_{j}+\theta
X_{jt}+\lambda_{i}+\eta_{g}+\phi_{m}+\xi_{t}\big{]}\times\epsilon_{igmjt}$ (9)

Where $N_{igmjt}$ is the number of the shipments from a firm $i$ in Bangladesh
exporting product $g$ by transport mode $m$ to country $j$ in year $t$.
$\lambda_{i}$ is the firm fixed effect, which absorbs firm heterogeneity.
$\epsilon_{igmjt}$ is the error term.

The model of procurement of the previous section shows that higher interest
rates and longer delivery times increase financing costs, reduce shipping size
and increase shipping frequency. The intuition for these predictions is that
higher interest rates in the exporter country increase the exporter’s costs
for borrowing working capital. This increases the importer’s immediate
procurement cost. To mitigate this cost increase, the importer chooses more
frequent small-sized shipments. Furthermore, higher discounting due to higher
interest rates in the importing country increases the shipping frequency by
moving more small shipments into the future. By adding financing costs to the
model 9, I estimate the following model

$\centering\begin{multlined}N_{igmjt}=exp\big{[}\alpha+spline1+spline2+\beta_{1}ln\
f_{jt}+\beta_{2}ln\ distance_{j}+\beta_{3}spline1\\\ \times ln\
distance_{j}+\beta_{4}spline2\times ln\
distance_{j}+\beta_{5}r^{exp}_{t}+\beta_{6}r^{imp}_{jt}+\beta_{7}r^{exp}_{t}\times
r^{imp}_{jt}\\\ +\theta
X_{jt}+\lambda_{i}+\eta_{g}+\phi_{m}+\xi_{t}\big{]}\times\epsilon_{igmjt}\end{multlined}N_{igmjt}=exp\big{[}\alpha+spline1+spline2+\beta_{1}ln\
f_{jt}+\beta_{2}ln\ distance_{j}+\beta_{3}spline1\\\ \times ln\
distance_{j}+\beta_{4}spline2\times ln\
distance_{j}+\beta_{5}r^{exp}_{t}+\beta_{6}r^{imp}_{jt}+\beta_{7}r^{exp}_{t}\times
r^{imp}_{jt}\\\ +\theta
X_{jt}+\lambda_{i}+\eta_{g}+\phi_{m}+\xi_{t}\big{]}\times\epsilon_{igmjt}\@add@centering$
(10)

Where the exporter’s interest rates are $r^{exp}_{t}$ in year $t$, in
percentage, the importer’s interest rate is $r^{imp}_{jt}$ of the importer
country $j$ in year $t$, expressed in percentage. The interaction effect of
the exporter’s and importers interest rates is captured by $\beta_{7}$. Higher
financing costs in origin and destination should increase shipping frequency;
I expect positive coefficients for $\beta_{5}-\beta_{7}$. For the PPML
estimation method, the dependent variable is in level, whereas the dependent
variable is in logs for the OLS estimator. $\beta_{5}-\beta_{7}$ in the model
capture semi-elasticity as the interest rates of the exporters and the
importers (independent variables) are in levels.

It is assumed that the exporting firms face their domestic interest rates as
the funding costs for trade finance of working capital. Similarly, the
importing firms consider discounting based on their domestic interest rates.
Thus, firm-specific characteristics do not affect the financing cost. In most
specifications, exporter-product-mode-year specific unobservables (e.g.,
common shocks to the firm-product-mode-year observation) are absorbed through
the firm by product by mode by year fixed effects to capture only interest
rate variations across the destinations. The standard errors are robust and
clustered with the exporter group clusters. As the disturbances are correlated
within exporters, robust clustered standard errors can account for the
correlation of the exporters’ observations.

Based on the empirical models above, I will consider several types of fixed
effects for absorbing relevant heterogeneity. I will also conduct additional
empirical exercises focusing on other measures of financing costs.
Furthermore, I will provide several robustness checks considering the
additional distance and time measures and sample restrictions.

##  4 Results

I run empirical analysis in three steps. First, I show that the findings of
the higher per-shipment costs decrease shipping frequency remains valid for a
developing country. Second, I show that financing costs affect the shipping
frequency. Finally, I check whether the main specification’s findings remain
consistent with alternative measures of financing costs.

###  4.1 Per-Shipment Costs and Shipping Frequency

For the country-level aggregation, the estimation results for regressions of
model 4 are presented in table 5. In column 1, I present the OLS regression
results with destination-fixed effects. Standard errors are robust and
clustered with destination group clusters. The coefficient for the per-
shipment cost (including fixed import costs) is insignificant. Considering the
total per-shipment cost (includes fixed export and fixed import costs), Hornok
and Koren, 2015a  finds -0.451, with a $p$-value of 0.24. Considering only
year fixed effects, I get a negative effect of per-shipment fixed cost on
shipping frequency with an elasticity of -0.678, significant at a 1% level. To
deal with heteroscedasticity biases of OLS estimation of the log-linear model,
I consider the PPML estimation method for model 5 in column 3. The per-
shipment cost coefficient becomes non-significant. When I include distance
splines to fix distance non-linearity and estimate model 6, the elasticity is
smaller and significant at a 5% level, as reported in column 4.

Now, I consider the product-level aggregation model 8 and report the results
in columns 5-7 of table 5. In column 5, I present the OLS regression results
with eight-digit HS product by transport mode by year fixed effects. Standard
errors are robust and clustered with exporter group clusters. The per-shipment
cost coefficient is very small and non-significant. I find a much stronger
response for per-shipment cost in the PPML estimation method than in the OLS
method, as reported in column 6. By including distance splines, the
coefficient for per-shipment costs is even stronger. I find that for a 10%
increase in the per-shipment costs; the shipping frequency reduces by
$(1.1^{-0.406}-1)\times 100=3.95$%. This is a larger shipping frequency
response for the per-shipment cost for a developing country (e.g., Bangladesh)
than Hornok and Koren, 2015b  findings of developed countries (2.53% for the
US and 0.99% for Spain). Considering PPML and OLS estimation approaches, the
advantage of PPML is that it is robust concerning heteroscedasticity but
suffers from inconsistency with many fixed effects due to the incidental
parameters problem.

To check whether there is aggregation bias, I now regress model 9 for
exporter-level data. In column 8 of table 5, I present the PPML regression
results with same-year fixed effects considered in the country-level analysis.
The shipping frequency response of per-shipment costs is less than half that
in column 4. The elasticity is -0.156. Thus, a 10% increase in the per-
shipment costs reduces the shipping frequency by $(1.1^{-0.156}-1)\times
100=1.49$%. Column 9 shows exporter-level analysis with the same fixed effects
of product-level. The export level’s per-shipment elasticity is -0.227, much
lower than the product-level elasticity of -0.406. Comparing columns 4 and 7
with columns 8 and 9, I find that the per-shipment cost estimates are twice as
large with similar fixed effects in the country and exporter levels. This
shows evidence of aggregation bias. At a more aggregated level, the per-
shipment cost elasticity is higher because of both the number of shipments and
the number of exporter effects. In the exporter-level data, the per-shipment
cost elasticity comes from only the number of shipment effects.

Now, I focus on the effects of distance on shipping frequency. The distance
coefficient is negative and significant at the country level, as reported in
column 2 of table 5. However, the elasticity is much smaller than that
reported in Hornok and Koren, 2015a . At the product level, the coefficient
for distance is not significant unless the distance fix is considered. Column
7 shows that the distance coefficient is negative for spline1 (elasticity,
-2.268+1.018=-1.25) and spline3 (elasticity, -2.268) but positive for spline2
(elasticity, -2.268+3.713=1.445). Thus, for Bangladeshi trade, the effect of
the distance on shipping frequency depends on the region, mostly negative and
in line with Hornok and Koren, 2015a ; Hornok and Koren, 2015b  for non-EU
regions. Overall, distance has a non-linear effect, and accounting for that is
important to determine the effect of per-shipment costs on shipping
frequencies.

The size and income level of the export destinations capture the demand effect
and determine the shipping frequency. Here, I investigate GDP and GDP per
capita. At the country level, considering the destination fixed effects, the
effect of GDP is 3.7 times higher than that found in Hornok and Koren, 2015a .
GDP and GDP per capita positively affect shipping frequency across all other
specifications, as shown in columns 2-9 of table 5. At the product level,
these elasticities are much larger in Bangladesh than in developed countries.
Overall, the effects of GDP and GDP per capita increase with a higher level of
aggregation.

I also estimate and compare other regressors. In column 9 (exporter-level
specification), the island dummy’s coefficients are flipped from the previous
columns. A very small and non-significant island coefficient is different from
the finding of Hornok and Koren, 2015b , due to very concentrated export to
the non-island destinations. The landlocked dummy coefficients are significant
and negative, capturing a high trade barrier effect on the shipping frequency.
The coefficients for common religion, common legal origins, and common colony
are positive, capturing a low trade barrier effect on the shipping frequency.
Except for the island dummy, these control variable coefficients are similar
in sign and significance, larger in magnitude than the findings of Hornok and
Koren, 2015b . Except for the island and landlocked dummy, these control
variables’ magnitudes are higher at higher-level of aggregation.

###  4.2 Omitted Variable Bias and Financing Costs

Now I deal with omitted variable bias by adding narrower fixed effects. As the
shipping decisions are made at the firm level, absorbing the variations at a
broader level might weaken the findings. Therefore, I verify whether the
results remain robust for a stricter specification. I start with extensive
fixed effects and narrow the fixed effects to check if the estimates remain
consistent. The results are presented in table 6. The per-shipment cost’s
effect on shipping frequency gets stronger from the broader to stricter fixed
effects. The elasticity ranges from -0.179 for exporter fixed effects in
column 1 to -0.331 for exporter-HS4-mode-year fixed effects in column
6.101010For firm by-product by year fixed effects, lots of singleton
observations are dropped. For reducing these lost observations and from a
shipment perspective, goods classification is best captured by HS4 instead of
HS8. For example, consider the HS8 code for cotton T-shirts, 61099000, a
textile and apparel industry good. The chapter heading on apparel and clothing
knitted is 61. The next two digits, 09, are for the sub-heading T-shirt. The
next two digits, 90, are for materials sub-divisions. Finally, the last two
digits, 00, are for cotton. The coefficients for GDP and GDP per capita hold
for both broader and stricter fixed effects. Other control variables have
robust responses too. For example, Island and colony coefficients are more
significant for narrower fixed effects. Overall, absorbing more omitted
variables with stricter fixed effects increases the elasticity of per-shipment
fixed costs. Column 6 is my preferred specification as it absorbs variations
for any exporter shipping HS four-digit product by a particular shipping mode
in a specific year. In the preferred specification, a 10% increase in the per-
shipment costs reduces the shipping frequency by $(1.1^{-0.331}-1)\times
100=3.21$%.

Next, I check the theoretical prediction regarding the effects of financing
costs on shipping frequency to deal with omitted variable bias. Table 7
reports regressions results for model 10. Introducing the importer financing
costs (interest rates) lowers the per-shipment cost effect on the shipping
frequency; the coefficient changes from -0.227 to -0.196. This confirms that
per-shipment cost effects are overestimated, and financing costs can capture
some per-shipment effects. Column 1 also shows that the importer’s interest
rate has a negative effect on the shipping frequency. As the coefficient
captures semi-elasticity, for a 1% higher interest rates in the importer
country, the shipping frequency goes down by $(\mathrm{e}^{0.004}-1)\times
100=0.40$%, which contradicts the prediction. One explanation for these
contradictory findings may come from the deviation from the theoretical
assumptions that the importer has most of the bargaining power and that the
exporter is financially constraint. Although these conditions are more likely
met for exporters in Bangladesh, I do not have any way to verify this in the
data. Another potential reason could be the theoretical model’s omission of
some trade costs. For example, the Generalized Scheme of Preferences (GSP) for
the Bangladeshi exporter in the US (continued until the study period, 2013)
and the EU reduces trade costs (Ahmed,, 2009). Allowing year variation, column
2 shows that the exporter’s interest rate positively affects the shipping
frequency, supporting the theoretical prediction.

Next, I check the interaction between the exporter’s and the importer’s
interest rate in column 3 of table 7. The coefficient is positive and
significant at a 1% level, which implies that shipping frequency increases
more for higher interest rates both in origin and destination. However, the
interaction effects are very small in magnitude. In column 4, I use a narrower
exporter by eight-digit HS product by mode by year fixed effects. The per-
shipment cost elasticity is much higher than the elasticity of product and
country-level analysis. The interaction term is also stronger. From now on, I
will consider this specification as the main specification and the findings of
column 4 as the main findings. Thus, by addressing all the biases, I find that
for a 10% increase in the per-shipment costs, the shipping frequency decreases
by $(1.1^{-0.335}-1)\times 100=3.24$%.

In summary, columns 1-4 of table 7 show that omitting financing costs may lead
to minimal overestimation of per-shipment cost for allowing exporter
heterogeneity to a severe underestimation of per-shipment cost for absorbing
exporter heterogeneity. The effect of per-shipment costs increases when I add
the financing costs of the exporter and importer and their interaction, as
reported in column 4. Thus, my preferred specification shows that models
underestimate the effects of per-shipment cost on shipping frequency by
ignoring financing costs and other unobserved variables.

The shipping frequency response also depends on how fast transport is done.
Longer delivery time in ocean transport requires more financing resulting in
more frequent shipments. Furthermore, time-sensitive goods are prevalent in
air shipments, which mute the financing costs effect on shipping frequency
because of the urgency in the supply chain (Hummels,, 2007; Hummels and
Schaur,, 2013). Thus, considering transport mode can reveal whether the
interest rates have a stronger shipping frequency response for lengthy ocean
transport. I consider transport mode effects in columns 5-7 of table 7. Column
5 shows that the financing costs effects are negligible for air freight goods.
The shipping frequency response for the per-shipment cost is stronger in ocean
shipment than in the air shipment mode, as reported in column 6. Moreover, the
importer interest rates have a higher negative effect on ocean mode. The
coefficients for other control variables remain similar to the main results.
With only 4643 observations, the land freight mode shows that the per-shipment
cost elasticity is stronger than the main results. The land transport mode
also shows the positive effects of exporter financing costs, matching the
theoretical predictions. As there are only three destinations for land
transports of Bangladesh (Kathuria,, 2018), time-invariant variables drop out
of the regression. Overall, ocean freight goods’ shipping frequency responds
more to the per-shipment and financing costs than other transport modes.

###  4.3 Additional Measures of Financing Costs

Facing a few data points for the exporter’s annual interest rates, I now focus
on the destination’s financing costs. To determine the full impact of the
financing costs on the shipping frequency, I consider other influencing
variables of financing costs such as credit accessibility, bank confidence
indicator, and the export destinations’ credit-GDP ratio in the main
specification as only interest rates might not capture the financial
constraints of the firm. Columns 1-3 of table 8 report this result. Higher
credit accessibility facilitates trade by increasing trade volume (Bremus and
Neugebauer,, 2018). This explains a positive effect on shipping frequency for
greater accessibility to credit, as reported in column 1. Bank confidence
indicators capture the cultural dimension of financing costs. Financial
literacy and cultural perceptions are key factors in the financial environment
(Dutta and Mukherjee,, 2012).111111I use bank confidence indicators from the
WVS database, which encodes lower confidence in the banking system as a higher
indicator value. The indicator is calculated by aggregating the country-level
average of the values chosen by all survey respondents of a country. Low
confidence shows perceptional mistrust about financial services and weak
financial development, increasing the financial costs of any credit contract.
Consequently, this increases the shipping frequency. As expected, weaker
confidence in the banking system has a strong positive significant effect on
the shipping frequency, as reported in column 2. The literature uses the
credit-GDP ratio to measure the credit constraints (Manova,, 2012; Fauceglia,,
2015). Column 3 shows a minimal negative effect of the credit deepening on the
shipping frequency. The finding aligns with the prediction that low financing
costs lead to less frequent shipments. Across these three specifications, the
interest rate coefficients are negative and significant. Furthermore, per-
shipment cost effects remain the same by controlling for the credit-GDP ratio,
increasing bank confidence, and decreasing by controlling for access to
credit.

Now, I use the alternative measure of financing costs. The net interest margin
is a common metric in finance studies (Beck and Demirguc-Kunt,, 2009; Yuksel
and Zengin,, 2017). I find a significant negative coefficient of interest rate
interaction in column 4 of table 8. One reason for this anomalous result could
be that the net interest rate may not capture the importing firm’s actual
financing cost of borrowing from the banking channel; instead, it captures the
financial intermediary’s opportunity cost for assets. Across columns, other
coefficients are roughly similar in sign and magnitude to the main results. In
summary, controlling for additional financing measures does not change the
main financing cost’s effect on shipping frequency but changes the magnitude
of per-shipment cost’s effect on shipping frequency.

##  5 Robustness Check

I run several robustness checks. First, I investigate whether the findings
remain consistent if I control for additional distance and time measures. Sea
distance, transport time based on sea distance, total transport time with port
delay, and logistics performance index are used for additional control. Table
9 reports these results. As sea distance is relevant for only ocean-
transported goods, columns 1-3 only consider sea transport observations. In
columns 1 and 2, I consider sea distance and transport time based on sea
distance, respectively. The shipping frequency response for per-shipment costs
is less than half of the main results. However, the per-shipment cost
elasticity is closer to the main findings for the total transport time, as
reported in column 3. LPI captures the supply chain and logistical barriers
for exports (Martí et al.,, 2014). In column 4, I find a positive effect of
LPI on shipping frequency, which means lower logistical costs for importing
increase shipping frequency.

Second, I use different group clusters for calculating standard errors to see
if the regression statistics are affected by different clusters. Table 10
reports the results for the preferred specification with the exporter by
eight-digit HS product by mode fixed effects. I narrow down to exporter by
industry (HS2) by destination by year clusters, starting with bigger clusters
of export destinations. The columns show that the coefficient’s standard
errors get smaller with the larger numbers of clusters. For example, for the
coefficient of per-shipment cost, the standard error is 0.085 for exporter
clustering and 0.019 for exporter by industry (HS2) by destination-by-year
clustering. However, different clustering does not change the basic
statistical conclusion of the analysis.

Third, I consider various subsamples based on data characteristics. I check
whether the main findings remain consistent for the subsamples based on
relevant data restrictions. Table 11 reports this result. All columns show
regression for estimation model 10. In column 1, I consider the observations
with an export value of more than 2500 USD to compare with the previous
studies (Kropf and Sauré,, 2014; Hornok and Koren, 2015b, ). To exclude data
anomaly from 2007 (the total shipment number and export volume decreased in
Bangladesh due to political instability) and global recession effects, I only
consider data from 2010 to 2013 in column 2. Column 3 drops all single
shipment firms. In column 4, I exclude all high-frequency firms with more than
100 shipments to a product-destination-year triplet. Column 5 reports result
for the full sample, including smaller than 1% and larger than 99% per-
shipment value. Excluding high-frequency exporters reduces the elasticity by
half, as reported in column 4. Across all other columns, the results are
robust to these sample restrictions.

Finally, to investigate whether the per-shipment and financing costs effect
are robust on the shipping size and export volume (by value or by weight), I
regress these variables on the explanatory variables and report the result in
the Appendix-B. Except for the effect of the per-shipment cost on sipping
size, the results align with Hornok and Koren, 2015b .

##  6 Conclusion

Financial constraints and shipping frequency are interrelated in international
trade. I develop a simple export-import procurement model to capture this,
incorporating delivery time, financing costs, and per-shipment fixed costs.
The model shows that longer delivery times and higher financing costs increase
shipping frequency because of financial constraints. The existing shipping
frequency or financial constraints literature does not discuss this shipping
frequency adjustment.

The shipping frequency and trade finance aspects capture the significance of
the time costs of trade. The procurement cost is increased for longer delivery
time and higher financing costs, more so at higher per-shipment costs than
lower per-shipment costs. The conjunction of the financing cost, the per-
shipment cost, and the delivery times provide key insights about the
procurement costs, which are not explored in the delivery time literature or
time trade barrier literature.

The model also predicts that higher per-shipment fixed costs decrease the
shipping frequency in line with previous studies. This, in turn, shows that
the exporter’s financing demand decreases with the lower per-shipment fixed
costs. From a policy perspective, this shows that if trade facilitation policy
lowers per-shipment fixed costs, then that not only lowers transaction costs
but also relaxes financial constraints.

As understanding the shipping frequency margin is emphasized due to the nature
of lumpy trade and transmission of various macro shocks to the exporter, in
this empirical exercise, I find that more aggregated data provides over-
estimated elasticity for per-shipment costs. I also find that the OLS
estimation of per-shipment costs of log-linear models is underestimated due to
heteroscedasticity bias. Moreover, ignoring financing costs yields
underestimated per-shipment costs effects on shipping frequency because of
omitted variable bias. By addressing these biases, I find that statistically,
for 10% higher per-shipment costs, the shipping frequency decreases by 3.24%.
I also find that higher financing costs in origin and destination lead to more
frequent shipments. These findings remain consistent for various alternative
financial constraints, distance, or time measures.

The higher elasticity of shipping frequency for per-shipment costs in the
developing country indicates that the per-shipment fixed costs reduction
policies will benefit from lower financing demand and conventional advantages
of low trade barriers. For developing countries (e.g., Bangladesh), if trade
policies can reduce per-shipment cost and facilitate financing aid (Auboin,,
2007), it may have more substantial trade-enhancing effects through shipping
frequency adjustment. Although the magnitude of shipping frequency is useful
to determine the impact of reducing trade costs, this paper’s policy
implications are incomplete due to limited data points of the exporter’s
actual financing costs. For proper identification, firm-level financing costs
are needed. One can use the bank-firm merged financing costs data to overcome
this problem (Paravisini et al.,, 2014; Fan et al.,, 2015). As lowering trade
costs and providing financial services are vital components of trade aid,
these policy evaluations could be one avenue of future research.

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Order1Order20$\frac{x}{q}$$\frac{2x}{q}$$\frac{x}{q}$$\frac{2x}{q}$1TimeOrder1Delivery10$\Delta$Importer’s
Inventory Figure 1: Ordering Process in International Trade

Note: The bottom arrow represents order time between two consecutive orders.
The top arrow represents the delivery time between the order initiated and the
goods delivered.

Figure 2: Frequency of Shipments of Bangladeshi Exports, Data Combinations of
Exporter-Product-Mode-Destination-Year for 2006-2013. The upper limit of
shipping frequency is cut to 50 shipments.

Figure 3: Size of Shipments of Bangladeshi Exports in USD (logged), Data
Combination of Exporter-Product-Mode-Destination-Year for 2006-2013. The upper
limit of shipping size is cut at 3.27 million USD.

Table 1: Exports of Bangladesh (2006-2013) Total exports volume (billion US$) | 156.7
---|---
Number of exporters | 18,327
Number of products | 4,234
Number of destinations | 179
Number of shipments | 4,979,958
Average shipment value (US$) | 31,472
Median shipment value (US$) | 14,245
Table 2: Top Export Destinations Destination | Export share (%) | Export share (%)
---|---|---
| by volume | by shipping frequency
United States | 23.37 | 17.08
Germany | 15.45 | 10.81
United Kingdom | 9.95 | 11.72
France | 6.28 | 6.44
Spain | 4.46 | 3.43
Table 3: Descriptive Data of Shipping Frequency Year | Shipping frequency | Exporting firms | Single shipment | High frequency
---|---|---|---|---
| (million) |  | firms |  firms (shipment$\geq$100)
2006 | 0.46 | 5,789 | 752 | 602
2007 | 0.35 | 5,828 | 756 | 430
2008 | 0.49 | 6,579 | 926 | 673
2009 | 0.52 | 6,678 | 962 | 716
2010 | 0.64 | 6,947 | 1,027 | 944
2011 | 0.68 | 7,219 | 1,074 | 996
2012 | 0.85 | 7,622 | 1,142 | 1,278
2013 | 0.98 | 9,374 | 1,263 | 1,287
Total | 4.98 | 18,327 | 2,943 | 7,298

Table 4: Summary of Regression Variables Variable | Mean | Std. Dev. | Min | Max | Data Sources
---|---|---|---|---|---
Export |  |  |  |  | Bangladesh Customs
Ln shipping frequency | 1.05 | 1.23 | 0 | 7.57 |
Ln per-shipment value | 9.42 | 1.58 | -1.73 | 20.33 |
Ln export value | 10.48 | 2.13 | -1.73 | 20.33 |
Ln export weight | 8.09 | 2.29 | -4.61 | 19.79 |
Distance and time |  |  |  |  |
Ln per-shipment costs | 7.08 | 0.39 | 5.90 | 9.89 | Doing Business Survey database (WB)
Time to import (days) | 9.35 | 5.61 | 4 | 117 | Doing Business Survey database (WB)
Port to port transport time (days) | 22.67 | 6.69 | 0 | 37 | searates.com
Ln distance | 8.88 | 0.51 | 6.06 | 9.81 | CEPII distance dataset
Ln Sea-distance | 9.45 | 0.38 | 7.81 | 9.98 | CERDI sea-distance database
Logistics performance index | 2.87 | 0.57 | 1.34 | 4.11 | LPI database (WB)
Financing costs (%) |  |  |  |  |
Exporter’s interest rates | 12.69 | 0.93 | 11.30 | 13.77 | Bangladesh Bank
Importer’s interest rates | 5.15 | 3.52 | 0.5 | 58.98 | International Financial Statistics (IMF)
Exporter’s net interest margin | 4.29 | 0.99 | 2.77 | 5.57 | Beck and Demirguc-Kunt, (2009)
Importer’s net interest margin | 2.30 | 1.45 | 0.12 | 20.48 | Beck and Demirguc-Kunt, (2009)
Debt-GDP ratio | 123.04 | 50.21 | 2.17 | 906.38 | Beck and Demirguc-Kunt, (2009)
Control variables |  |  |  |  | CEPII gravity dataset
Ln GDP | 27.87 | 1.49 | 18.46 | 30.45 |
Ln GDP per capita | 10.23 | 0.96 | 5.09 | 11.63 |
Island | 0.13 | 0.34 | 0 | 1 |
Landlocked | 0.03 | 0.17 | 0 | 1 |
Common religion | 0.09 | 0.23 | 0 | 0.86 |
Common colony | 0.07 | 0.26 | 0 | 1 |
N = |  |  |  | 544,486 |
Table 5: Per-Shipment Cost and Shipping Frequency | Country | Product | Exporter
---|---|---|---
| (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9)
Ln per-shipment cost | -0.062 | -0.678*** | -0.174 | -0.359* | -0.054 | -0.307* | -0.406** | -0.156*** | -0.227***
| [0.183] | [0.185] | [0.217] | [0.187] | [0.078] | [0.179] | [0.202] | [0.030] | [0.030]
Ln distance |  | -0.411*** | -0.456** | -1.991* | -0.098 | -0.048 | -2.268*** | 0.463*** | 0.084
|  | [0.140] | [0.225] | [1.159] | [0.076] | [0.156] | [0.715] | [0.157] | [0.161]
Spline1 |  |  |  | -1.241 |  |  | -11.733* | 6.860*** | 3.467***
|  |  |  | [10.555] |  |  | [6.834] | [1.217] | [1.262]
Spline2 |  |  |  | -31.388*** |  |  | -34.290*** | 1.165 | -3.909**
|  |  |  | [11.421] |  |  | [8.385] | [1.691] | [1.644]
Spline1$\times$Ln distance |  |  |  | -0.186 |  |  | 1.018 | -0.762*** | -0.423***
|  |  |  | [1.121] |  |  | [0.751] | [0.127] | [0.131]
Spline2$\times$Ln distance |  |  |  | 3.429*** |  |  | 3.713*** | -0.075 | 0.463***
|  |  |  | [1.200] |  |  | [0.890] | [0.178] | [0.172]
Ln GDP | 2.122*** | 0.986*** | 0.756*** | 0.806*** | 0.342*** | 0.643*** | 0.677*** | 0.204*** | 0.231***
| [0.615] | [0.060] | [0.058] | [0.062] | [0.033] | [0.071] | [0.069] | [0.008] | [0.008]
Ln GDP per capita | -0.677 | 0.135 | 0.682*** | 0.694*** | 0.205*** | 0.630*** | 0.600*** | 0.082*** | 0.130***
| [0.703] | [0.095] | [0.096] | [0.109] | [0.035] | [0.076] | [0.095] | [0.019] | [0.019]
Island |  | -0.342 | -1.047*** | -0.545** | -0.178** | -0.960*** | -0.579*** | -0.007 | 0.003
|  | [0.343] | [0.305] | [0.241] | [0.080] | [0.212] | [0.175] | [0.041] | [0.041]
Landlocked |  | -0.399 | -0.855*** | -0.824*** | -0.199 | -0.712*** | -0.682*** | 0.143*** | 0.102**
|  | [0.316] | [0.265] | [0.272] | [0.128] | [0.221] | [0.214] | [0.050] | [0.050]
Common religion |  | 0.191 | -0.118 | 0.881* | -0.006 | 0.179 | 0.900*** | 0.335*** | 0.411***
|  | [0.349] | [0.460] | [0.481] | [0.129] | [0.305] | [0.342] | [0.068] | [0.067]
Common legal origin |  | 0.527* | 0.209 | -0.015 | 0.246** | 0.108 | -0.059 | 0.271*** | 0.184***
|  | [0.302] | [0.210] | [0.287] | [0.102] | [0.195] | [0.216] | [0.059] | [0.062]
Colony |  | 0.971 | 1.736*** | 1.191*** | 0.521*** | 1.670*** | 1.253*** | 0.140* | 0.174**
|  | [0.691] | [0.303] | [0.328] | [0.185] | [0.235] | [0.222] | [0.073] | [0.078]
Constant | -41.120*** | -11.972*** | -13.242*** | 1.126 | -8.602*** | -16.079*** | 5.020 | -8.121*** | -4.970***
| [9.962] | [2.385] | [1.989] | [11.274] | [1.149] | [2.305] | [6.811] | [1.458] | [1.508]
Fixed Effects | Country | Year |  HS8 $\times$ Mode | Year |  HS8 $\times$ Mode
|  |  |  $\times$ Year |  |  $\times$ Year
SE Clusters | Country | Exporter
Observations | 1,180 | 1,189 | 1,189 | 1,189 | 90,502 | 90,502 | 90,502 | 595,651 | 587,171
R-squared | 0.966 | 0.768 |  |  | 0.481 |  |  |  |
Pseudo R-squared | . | . | 0.918 | 0.934 | . | 0.813 | 0.820 | 0.0371 | 0.183

Note: OLS regressions of the estimation equation 4 in columns 1-2, and 7 in
column 5, where the dependent variable is the log number of shipments. PPML
regressions of the estimation equation 5 in column 3, 6 in column 4, 8 in
columns 6-7, and 9 in columns 8-9, where the dependent variable is the number
of shipments. ***$p<0.01$; **$p<0.05$; *$p<0.1$.

0

Table 6: Shipping Frequency Response for More Strict Fixed Effects | (1) | (2) | (3) | (4) | (5) | (6)
---|---|---|---|---|---|---
Ln per-shipment cost | -0.179*** | -0.192*** | -0.221*** | -0.227*** | -0.266*** | -0.331***
| [0.025] | [0.028] | [0.028] | [0.030] | [0.028] | [0.031]
Ln distance | -0.479*** | 0.342** | 0.228 | 0.084 | -0.965*** | -1.074***
| [0.143] | [0.165] | [0.167] | [0.161] | [0.150] | [0.158]
Spline1 | -0.207 | 7.244*** | 5.068*** | 3.467*** | -5.934*** | -6.450***
| [1.185] | [1.284] | [1.314] | [1.262] | [1.227] | [1.309]
Spline2 | -12.312*** | -0.899 | -2.319 | -3.909** | -17.644*** | -19.400***
| [1.397] | [1.692] | [1.695] | [1.644] | [1.498] | [1.621]
Spline1$\times$Ln distance | -0.094 | -0.836*** | -0.591*** | -0.423*** | 0.517*** | 0.552***
| [0.125] | [0.133] | [0.136] | [0.131] | [0.129] | [0.138]
Spline2$\times$Ln distance | 1.377*** | 0.143 | 0.295* | 0.463*** | 1.939*** | 2.129***
| [0.146] | [0.178] | [0.178] | [0.172] | [0.157] | [0.170]
Ln GDP | 0.215*** | 0.223*** | 0.228*** | 0.231*** | 0.247*** | 0.276***
| [0.007] | [0.008] | [0.008] | [0.008] | [0.008] | [0.009]
Ln GDP per capita | 0.118*** | 0.116*** | 0.126*** | 0.130*** | 0.162*** | 0.185***
| [0.017] | [0.018] | [0.019] | [0.019] | [0.018] | [0.020]
Island | -0.072** | 0.044 | 0.034 | 0.003 | -0.162*** | -0.221***
| [0.037] | [0.040] | [0.040] | [0.041] | [0.039] | [0.042]
Landlocked | -0.021 | 0.136*** | 0.116** | 0.102** | -0.087* | -0.116**
| [0.047] | [0.050] | [0.050] | [0.050] | [0.050] | [0.053]
Common religion | 0.443*** | 0.389*** | 0.413*** | 0.411*** | 0.490*** | 0.508***
| [0.055] | [0.067] | [0.067] | [0.067] | [0.060] | [0.065]
Common legal origin | 0.213*** | 0.214*** | 0.189*** | 0.184*** | 0.126** | 0.105*
| [0.050] | [0.061] | [0.062] | [0.062] | [0.053] | [0.056]
Colony | 0.055 | 0.091 | 0.138* | 0.174** | 0.252*** | 0.322***
| [0.068] | [0.076] | [0.078] | [0.078] | [0.072] | [0.075]
Constant | 0.690 | -7.407*** | -6.291*** | -4.970*** | 4.863*** | 5.543***
| [1.308] | [1.535] | [1.560] | [1.508] | [1.368] | [1.446]
Fixed Effects | Exporter | HS8 |  HS8 $\times$ Mode |  HS8 $\times$ Mode |  HS8 $\times$ Mode |  HS4 $\times$ Mode
|  |  |  |  $\times$ Year |  $\times$ Year + Exporter |  $\times$ Year $\times$ Exporter
Observations | 591,808 | 594,533 | 593,352 | 587,171 | 583,315 | 480,657
Pseudo R-squared | 0.254 | 0.143 | 0.169 | 0.183 | 0.384 | 0.492

Note: PPML regressions of the estimation equation 9. The dependent variable is
the number of shipments. Standard errors are robust and clustered with
exporter clusters. ***$p<0.01$; **$p<0.05$; *$p<0.1$.

Table 7: Financing Costs and Shipping Frequency |  |  |  |  | Air | Ocean | Land
---|---|---|---|---|---|---|---
| (1) | (2) | (3) | (4) | (5) | (6) | (7)
Ln per-shipment cost | -0.196*** | -0.159*** | -0.198*** | -0.335*** | -0.310*** | -0.352*** | -0.888***
| [0.034] | [0.032] | [0.034] | [0.038] | [0.072] | [0.038] | [0.285]
Ln distance | 0.569*** | 0.992*** | 0.551*** | -0.904*** | -0.319 | -0.973*** | -73.982***
| [0.179] | [0.194] | [0.178] | [0.179] | [0.340] | [0.191] | [20.103]
Spline1 | 5.652*** | 9.487*** | 5.488*** | -5.023*** | 1.781 | -105.202*** |
| [1.386] | [1.493] | [1.381] | [1.423] | [3.383] | [31.736] |
Spline2 | 1.509 | 5.275** | 1.322 | -19.402*** | -13.294*** | -19.924*** |
| [1.977] | [2.108] | [1.964] | [1.977] | [3.940] | [2.087] |
Spline1$\times$Ln distance | -0.584*** | -0.980*** | -0.568*** | 0.410*** | -0.298 | 0.510*** |
| [0.145] | [0.154] | [0.144] | [0.149] | [0.368] | [0.151] |
Spline2$\times$Ln distance | -0.107 | -0.500** | -0.087 | 2.135*** | 1.484*** | 2.190*** |
| [0.208] | [0.221] | [0.206] | [0.208] | [0.421] | [0.219] |
Importer interest rate | -0.004** | -0.016*** | -0.043*** | -0.083*** | 0.006 | -0.104*** | 1.877***
| [0.002] | [0.002] | [0.014] | [0.018] | [0.027] | [0.019] | [0.348]
Exporter interest rate |  | 0.036*** |  |  |  |  | 2.094***
|  | [0.007] |  |  |  |  | [0.322]
Importer interest rate $\times$Exporter interest rate |  |  | 0.003*** | 0.006*** | -0.001 | 0.007*** | -0.165***
|  |  | [0.001] | [0.001] | [0.002] | [0.001] | [0.029]
Ln GDP | 0.230*** | 0.222*** | 0.230*** | 0.300*** | 0.294*** | 0.301*** | -14.041***
| [0.008] | [0.008] | [0.008] | [0.010] | [0.024] | [0.010] | [3.283]
Ln GDP per capita | 0.157*** | 0.130*** | 0.157*** | 0.248*** | 0.282*** | 0.232*** | 14.426***
| [0.020] | [0.020] | [0.020] | [0.025] | [0.048] | [0.025] | [3.424]
Island | -0.050 | -0.032 | -0.051 | -0.234*** | -0.201** | -0.240*** |
| [0.041] | [0.041] | [0.041] | [0.046] | [0.078] | [0.051] |
Landlocked | 0.081 | 0.087* | 0.082 | -0.162*** | -0.234 | -0.147*** |
| [0.050] | [0.050] | [0.050] | [0.057] | [0.184] | [0.055] |
Common religion | 0.488*** | 0.514*** | 0.490*** | 0.789*** | 1.025*** | 0.663*** |
| [0.103] | [0.102] | [0.103] | [0.117] | [0.239] | [0.115] |
Common legal origin | 0.269*** | 0.288*** | 0.268*** | 0.081 | -0.053 | 0.117 |
| [0.071] | [0.072] | [0.071] | [0.069] | [0.092] | [0.075] |
Colony | 0.167** | 0.082 | 0.169** | 0.359*** | 0.500*** | 0.326*** |
| [0.077] | [0.078] | [0.077] | [0.082] | [0.107] | [0.090] |
Constant | -10.105*** | -14.318*** | -9.914*** | 2.859* | -3.450 | 3.830** | 918.859***
| [1.716] | [1.885] | [1.710] | [1.666] | [3.032] | [1.765] | [244.615]
Fixed Effects |  HS8 $\times$ Mode |  HS8 $\times$ |  HS8 $\times$ Mode |  Exporter $\times$ HS8 |  Exporter $\times$ |  Exporter $\times$ | Exporter
|  $\times$ Year | Mode | Year |  Mode$\times$ Year |  HS8 $\times$ Year |  HS8 $\times$ Year |  $\times$ Year
Observations | 539,257 | 545,159 | 539,257 | 371,871 | 92,077 | 279,790 | 4,643
Pseudo R-squared | 0.184 | 0.172 | 0.184 | 0.564 | 0.523 | 0.567 | 0.681

Note: PPML regressions of the estimation equation 10. The dependent variable
is the number of shipments. Standard errors are robust and clustered with
exporter clusters. ***$p<0.01$; **$p<0.05$; *$p<0.1$.

0

Table 8: Alternative Financing Costs | (1) | (2) | (3) | (4)
---|---|---|---|---
Ln per-shipment cost | -0.250*** | -0.430*** | -0.347*** | -0.389***
| [0.035] | [0.050] | [0.042] | [0.035]
Ln distance | -1.017*** | -1.635*** | -2.257*** | -1.636***
| [0.186] | [0.255] | [0.291] | [0.244]
Spline1 | -5.804*** | -9.817*** | -12.037*** | -9.541***
| [1.429] | [1.775] | [1.946] | [1.702]
Spline2 | -21.049*** | -17.129*** | -30.206*** | -21.007***
| [2.073] | [2.294] | [3.118] | [2.496]
Spline1$\times$Ln distance | 0.494*** | 0.896*** | 1.037*** | 0.828***
| [0.149] | [0.182] | [0.196] | [0.175]
Spline2$\times$Ln distance | 2.311*** | 1.812*** | 3.227*** | 2.244***
| [0.218] | [0.240] | [0.325] | [0.261]
Importer interest rate | -0.078*** | -0.142*** | -0.130*** |
| [0.018] | [0.021] | [0.020] |
Importer interest rate $\times$Exporter interest rate | 0.006*** | 0.010*** | 0.009*** |
| [0.001] | [0.002] | [0.002] |
Access to credit | 0.026*** |  |  |
| [0.007] |  |  |
Bank confidence |  | 0.444*** |  |
|  | [0.092] |  |
Debt-GDP ratio |  |  | -0.003*** |
|  |  | [0.000] |
Importer net interest margin |  |  |  | 0.069***
|  |  |  | [0.025]
Importer net interest margin$\times$Exporter net interest margin |  |  |  | -0.021***
|  |  |  | [0.006]
Ln GDP | 0.290*** | 0.283*** | 0.311*** | 0.281***
| [0.010] | [0.012] | [0.013] | [0.011]
Ln GDP per capita | 0.248*** | 0.319*** | 0.529*** | 0.399***
| [0.025] | [0.035] | [0.036] | [0.030]
Island | -0.226*** | -0.536*** | -0.527*** | -0.664***
| [0.046] | [0.044] | [0.044] | [0.048]
Landlocked | -0.231*** | 1.295*** | 1.462*** | 0.571***
| [0.062] | [0.368] | [0.363] | [0.214]
Common religion | 0.873*** | 0.486*** | 0.669*** | 0.842***
| [0.119] | [0.125] | [0.140] | [0.086]
Common legal origin | -0.038 | 0.024 | -0.133 | -0.085
| [0.080] | [0.089] | [0.105] | [0.088]
Colony | 0.322*** | 0.581*** | 0.670*** | 0.556***
| [0.082] | [0.170] | [0.166] | [0.161]
Constant | 3.326** | 9.430*** | 13.439*** | 9.579***
| [1.688] | [2.351] | [2.701] | [2.237]
Observations | 371,871 | 175,814 | 173,652 | 196,751
Pseudo R-squared | 0.564 | 0.635 | 0.634 | 0.619

Note: PPML regressions of the estimation equation 10. The dependent variable
is the number of shipments. Exporter by product by mode by year fixed effects
is used in all regressions. Standard errors are robust and clustered with
exporter clusters. ***$p<0.01$; **$p<0.05$; *$p<0.1$.

Table 9: Robustness Check: Alternative Distance and Time | (1) | (2) | (3) | (4)
---|---|---|---|---
Ln per-shipment cost | -0.233*** | -0.163*** | -0.352*** | -0.273***
| [0.039] | [0.040] | [0.039] | [0.045]
Ln distance | -1.195*** | -1.642*** | -0.976*** | -0.655***
| [0.203] | [0.225] | [0.193] | [0.209]
Spline1 | -6.147*** | -11.686*** | -5.878*** | -4.311***
| [1.573] | [1.748] | [1.477] | [1.539]
Spline2 | -21.370*** | -24.908*** | -20.008*** | -15.835***
| [2.224] | [2.394] | [2.144] | [2.360]
Spline1$\times$Ln distance | 0.574*** | 1.204*** | 0.497*** | 0.362**
| [0.164] | [0.185] | [0.153] | [0.158]
Spline2$\times$Ln distance | 2.369*** | 2.752*** | 2.199*** | 1.754***
| [0.234] | [0.253] | [0.226] | [0.248]
Ln sea-distance | 0.553*** |  |  |
| [0.078] |  |  |
Transport time (days) |  | 0.035*** |  |
|  | [0.004] |  |
Total transport time (days) |  |  | 0.000 |
|  |  | [0.003] |
Logistic Performance Index |  |  |  | 0.259***
|  |  |  | [0.072]
Importer interest rate | -0.092*** | -0.085*** | -0.103*** | -0.097***
| [0.019] | [0.019] | [0.019] | [0.018]
Importer interest rate $\times$Exporter interest rate | 0.007*** | 0.006*** | 0.007*** | 0.007***
| [0.001] | [0.001] | [0.001] | [0.001]
Ln GDP | 0.312*** | 0.319*** | 0.302*** | 0.290***
| [0.010] | [0.011] | [0.010] | [0.011]
Ln GDP per capita | 0.219*** | 0.201*** | 0.237*** | 0.149***
| [0.025] | [0.025] | [0.027] | [0.036]
Island | -0.034 | -0.050 | -0.237*** | -0.270***
| [0.062] | [0.056] | [0.060] | [0.052]
Landlocked | -0.038 | -0.007 | -0.150*** | -0.145***
| [0.056] | [0.057] | [0.057] | [0.056]
Common religion | 1.220*** | 0.994*** | 0.680*** | 0.749***
| [0.133] | [0.119] | [0.121] | [0.119]
Common legal origin | 0.225*** | 0.244*** | 0.112 | 0.168**
| [0.075] | [0.074] | [0.077] | [0.075]
Colony | -0.039 | -0.062 | 0.327*** | 0.296***
| [0.106] | [0.098] | [0.099] | [0.091]
Constant | -0.617 | 7.445*** | 3.771** | 0.429
| [1.909] | [1.982] | [1.785] | [1.957]
Fixed Effects |  Exporter$\times$ HS8 |  Exporter$\times$ HS8 |  Exporter$\times$ HS8 |  Exporter $\times$ HS8
|  $\times$ Year |  $\times$ Year |  $\times$ Year |  Mode $\times$ Year
Observations | 278,922 | 278,928 | 278,928 | 278,928
Pseudo R-squared | 0.569 | 0.569 | 0.567 | 0.567

Note: PPML regressions of the estimation equation 10. The dependent variable
is the number of shipments. Standard errors are robust and clustered with
exporter clusters. ***$p<0.01$; **$p<0.05$; *$p<0.1$.

Table 10: Robustness Check: Standard Errors Clustering | (1) | (2) | (3) | (4) | (5) | (6)
---|---|---|---|---|---|---
Ln per-shipment cost | -0.335*** | -0.335*** | -0.335*** | -0.335*** | -0.335*** | -0.335***
| [0.119] | [0.058] | [0.058] | [0.052] | [0.036] | [0.020]
Ln distance | -0.904** | -0.904*** | -0.904*** | -0.904*** | -0.904*** | -0.904***
| [0.415] | [0.152] | [0.313] | [0.244] | [0.173] | [0.107]
Spline1 | -5.023 | -5.023*** | -5.023* | -5.023** | -5.023*** | -5.023***
| [3.929] | [1.949] | [2.935] | [2.318] | [1.400] | [0.895]
Spline2 | -19.402*** | -19.402*** | -19.402*** | -19.402*** | -19.402*** | -19.402***
| [6.117] | [2.375] | [3.560] | [2.764] | [1.907] | [1.170]
Spline1$\times$Ln distance | 0.410 | 0.410* | 0.410 | 0.410 | 0.410*** | 0.410***
| [0.433] | [0.218] | [0.319] | [0.252] | [0.147] | [0.094]
Spline2$\times$Ln distance | 2.135*** | 2.135*** | 2.135*** | 2.135*** | 2.135*** | 2.135***
| [0.658] | [0.265] | [0.380] | [0.295] | [0.201] | [0.123]
Importer interest rate | -0.083* | -0.083*** | -0.083* | -0.083** | -0.083*** | -0.083***
| [0.044] | [0.024] | [0.044] | [0.039] | [0.015] | [0.018]
Importer interest rate $\times$Exporter interest rate | 0.006* | 0.006*** | 0.006* | 0.006** | 0.006*** | 0.006***
| [0.003] | [0.002] | [0.003] | [0.003] | [0.001] | [0.001]
Ln GDP | 0.300*** | 0.300*** | 0.300*** | 0.300*** | 0.300*** | 0.300***
| [0.032] | [0.029] | [0.014] | [0.018] | [0.009] | [0.005]
Ln GDP per capita | 0.248*** | 0.248*** | 0.248*** | 0.248*** | 0.248*** | 0.248***
| [0.073] | [0.031] | [0.033] | [0.026] | [0.020] | [0.011]
Island | -0.234* | -0.234*** | -0.234*** | -0.234*** | -0.234*** | -0.234***
| [0.123] | [0.046] | [0.055] | [0.045] | [0.045] | [0.024]
Landlocked | -0.162 | -0.162** | -0.162 | -0.162** | -0.162*** | -0.162***
| [0.245] | [0.077] | [0.102] | [0.077] | [0.053] | [0.029]
Common religion | 0.789** | 0.789*** | 0.789*** | 0.789*** | 0.789*** | 0.789***
| [0.314] | [0.183] | [0.152] | [0.129] | [0.092] | [0.054]
Common legal origin | 0.081 | 0.081 | 0.081 | 0.081 | 0.081 | 0.081**
| [0.157] | [0.056] | [0.078] | [0.060] | [0.058] | [0.033]
Colony | 0.359** | 0.359*** | 0.359*** | 0.359*** | 0.359*** | 0.359***
| [0.168] | [0.083] | [0.077] | [0.060] | [0.075] | [0.040]
Constant | 2.859 | 2.859 | 2.859 | 2.859 | 2.859* | 2.859***
| [4.017] | [2.075] | [2.902] | [2.279] | [1.680] | [1.045]
SE Clusters | Country | Exporter | Country |  Country $\times$ |  Country $\times$ |  Exporter $\times$ HS2
|  |  |  $\times$ Year |  HS2 $\times$ Year |  HS2 $\times$ Exporter |  $\times$ Country $\times$ Year
Observations | 371,871 | 371,871 | 371,871 | 371,871 | 371,871 | 371,871
Pseudo R-squared | 0.564 | 0.564 | 0.564 | 0.564 | 0.564 | 0.564

Note: PPML regressions of the estimation equation 10. The dependent variable
is the number of shipments. Exporter by product by mode by year fixed effects
is used in all regressions. ***$p<0.01$; **$p<0.05$; *$p<0.1$.

0

Table 11: Robustness Check: Subsamples | (1) | (2) | (3) | (4) | (5)
---|---|---|---|---|---
Ln per-shipment cost | -0.344*** | -0.399*** | -0.343*** | -0.159*** | -0.336***
| [0.038] | [0.039] | [0.039] | [0.021] | [0.038]
Ln distance | -0.792*** | -0.982*** | -0.733*** | -0.971*** | -0.856***
| [0.190] | [0.189] | [0.189] | [0.096] | [0.178]
Spline1 | -4.376*** | -6.618*** | -4.644*** | -4.990*** | -4.365***
| [1.523] | [1.445] | [1.512] | [0.920] | [1.438]
Spline2 | -17.968*** | -19.697*** | -17.014*** | -16.062*** | -18.926***
| [2.090] | [2.075] | [2.091] | [1.153] | [1.972]
Spline1$\times$Ln distance | 0.355** | 0.589*** | 0.395** | 0.424*** | 0.340**
| [0.160] | [0.150] | [0.159] | [0.099] | [0.152]
Spline2$\times$Ln distance | 1.984*** | 2.165*** | 1.883*** | 1.742*** | 2.083***
| [0.220] | [0.218] | [0.220] | [0.123] | [0.207]
Importer interest rate | -0.079*** | -0.126*** | -0.076*** | -0.054*** | -0.083***
| [0.018] | [0.024] | [0.019] | [0.011] | [0.018]
Importer interest rate $\times$Exporter interest rate | 0.006*** | 0.010*** | 0.006*** | 0.004*** | 0.006***
| [0.001] | [0.002] | [0.001] | [0.001] | [0.001]
Ln GDP | 0.294*** | 0.300*** | 0.278*** | 0.197*** | 0.304***
| [0.010] | [0.010] | [0.011] | [0.005] | [0.010]
Ln GDP per capita | 0.231*** | 0.239*** | 0.220*** | 0.208*** | 0.244***
| [0.025] | [0.025] | [0.026] | [0.014] | [0.025]
Island | -0.225*** | -0.240*** | -0.252*** | -0.113*** | -0.218***
| [0.047] | [0.043] | [0.047] | [0.024] | [0.045]
Landlocked | -0.142** | -0.127*** | -0.122** | -0.174*** | -0.173***
| [0.057] | [0.048] | [0.059] | [0.034] | [0.057]
Common religion | 0.728*** | 0.685*** | 0.778*** | 0.607*** | 0.807***
| [0.119] | [0.127] | [0.124] | [0.073] | [0.114]
Common legal origin | 0.107 | 0.128* | 0.135* | -0.108*** | 0.077
| [0.071] | [0.076] | [0.072] | [0.028] | [0.069]
Colony | 0.325*** | 0.345*** | 0.303*** | 0.318*** | 0.338***
| [0.083] | [0.086] | [0.084] | [0.037] | [0.082]
Constant | 2.215 | 4.194** | 2.399 | 5.068*** | 2.364
| [1.760] | [1.771] | [1.770] | [0.934] | [1.661]
Observations | 333,132 | 228,524 | 218,642 | 366,099 | 375,216
Pseudo R-squared | 0.565 | 0.581 | 0.552 | 0.447 | 0.565

Note: PPML regressions of the estimation equation 10. The dependent variable
is the number of shipments. Exporter by product by mode fixed effects is used
in all regressions. Standard errors are robust and clustered with exporter
clusters. ***$p<0.01$; **$p<0.05$; *$p<0.1$.

##  7 Appendix

###  7.1 Appendix-A

### Propositions

Proof of Proposition 1:

Rewriting the objective function

$\min_{x}\dfrac{(cx\mathrm{e}^{\Delta r}+f)\mathrm{e}^{-\Delta
r}}{1-\mathrm{e}^{-\frac{r_{1}x}{q}}}$

Taking the derivative of the objective function for $x$, the first-order
condition (FOC) is

$\dfrac{c\mathrm{e}^{{\Delta}r-{\Delta}r_{1}}}{1-\mathrm{e}^{-\frac{r_{1}x}{q}}}-\dfrac{r_{1}\left(c\mathrm{e}^{{\Delta}r}x+f\right)\mathrm{e}^{-\frac{r_{1}x}{q}-{\Delta}r_{1}}}{q\left(1-\mathrm{e}^{-\frac{r_{1}x}{q}}\right)^{2}}$

For cost minimization, I look at the second-order condition (SOC)

$\begin{multlined}-\dfrac{cr_{1}\mathrm{e}^{-\frac{r_{1}x}{q}-{\Delta}r_{1}+{\Delta}r}}{q\left(1-\mathrm{e}^{-\frac{r_{1}x}{q}}\right)^{2}}+\dfrac{r_{1}^{2}\left(c\mathrm{e}^{{\Delta}r}x+f\right)\mathrm{e}^{-\frac{r_{1}x}{q}-{\Delta}r_{1}}}{q^{2}\left(1-\mathrm{e}^{-\frac{r_{1}x}{q}}\right)^{2}}+\dfrac{2r_{1}^{2}\left(c\mathrm{e}^{{\Delta}r}x+f\right)\mathrm{e}^{-\frac{2r_{1}x}{q}-{\Delta}r_{1}}}{q^{2}\left(1-\mathrm{e}^{-\frac{r_{1}x}{q}}\right)^{3}}-\dfrac{cr_{1}\mathrm{e}^{{\Delta}r-{\Delta}r_{1}}\mathrm{e}^{-\frac{r_{1}x}{q}}}{q\left(1-\mathrm{e}^{-\frac{r_{1}x}{q}}\right)^{2}}\end{multlined}-\dfrac{cr_{1}\mathrm{e}^{-\frac{r_{1}x}{q}-{\Delta}r_{1}+{\Delta}r}}{q\left(1-\mathrm{e}^{-\frac{r_{1}x}{q}}\right)^{2}}+\dfrac{r_{1}^{2}\left(c\mathrm{e}^{{\Delta}r}x+f\right)\mathrm{e}^{-\frac{r_{1}x}{q}-{\Delta}r_{1}}}{q^{2}\left(1-\mathrm{e}^{-\frac{r_{1}x}{q}}\right)^{2}}+\dfrac{2r_{1}^{2}\left(c\mathrm{e}^{{\Delta}r}x+f\right)\mathrm{e}^{-\frac{2r_{1}x}{q}-{\Delta}r_{1}}}{q^{2}\left(1-\mathrm{e}^{-\frac{r_{1}x}{q}}\right)^{3}}-\dfrac{cr_{1}\mathrm{e}^{{\Delta}r-{\Delta}r_{1}}\mathrm{e}^{-\frac{r_{1}x}{q}}}{q\left(1-\mathrm{e}^{-\frac{r_{1}x}{q}}\right)^{2}}$

I simplify SOC by rearranging the above condition

$SOC=\dfrac{r_{1}e^{\frac{r_{1}x}{q}-\Delta
r_{1}}}{q^{2}(e^{\frac{r_{1}x}{q}}-1)^{3}}\bigg{(}(ce^{\Delta
r}r_{1}x+fr_{1})(e^{\frac{r_{1}x}{q}}+1)-2cqe^{\Delta
r}(e^{\frac{r_{1}x}{q}}-1)\bigg{)}$

By using equation 3, I get

$SOC=\frac{r_{1}e^{\frac{r_{1}x}{q}-\Delta
r_{1}}}{q^{2}(e^{\frac{r_{1}x}{q}}-1)^{3}}\bigg{(}(ce^{\Delta
r}r_{1}x+fr_{1})(e^{\frac{r_{1}x}{q}}-1)\bigg{)}$

By using equation 3 again,

$SOC=\frac{cr_{1}e^{\frac{r_{1}x}{q}-\Delta r_{1}+\Delta
r}}{q(e^{\frac{r_{1}x}{q}}-1)}$

For $x>0$,

$SOC>0$

The SOC is strictly positive, so I have a unique minimizer $x^{*}$. To
strengthen this case, let’s consider the FOC again,

$\big{[}qc\mathrm{e}^{\Delta
r}(\mathrm{e}^{\frac{r_{1}x}{q}}-1)-c\mathrm{e}^{\Delta
r}r_{1}x\big{]}-fr_{1}$

At the limit, if $x=0$, the square bracketed term is zero, and the above
statement is negative. Taking the derivative of the square bracketed term
concerning $x$ gives

$cr_{1}\mathrm{e}^{\Delta
r}(\mathrm{e}^{\frac{r_{1}x}{q}})-c\mathrm{e}^{\Delta r}r_{1}$

Rearranging,

$cr_{1}\mathrm{e}^{\Delta r}(\mathrm{e}^{\frac{r_{1}x}{q}}-1)\geq 0$

This shows that the square bracketed term is increasing in $x$. When $x$
approaches $q$, the statement is positive. Thus, there must be a unique
$x^{*}$ where FOC is zero.

Proof of Proposition 2:

(i) Taking the derivative with respect to $r$

$\frac{\partial FOC}{\partial
r}=\dfrac{c{\Delta}\left(q\mathrm{e}^{\frac{r_{1}x}{q}}-r_{1}x-q\right)\mathrm{e}^{{\Delta}r+\frac{r_{1}x}{q}-{\Delta}r_{1}}}{q\left(\mathrm{e}^{\frac{r_{1}x}{q}}-1\right)^{2}}$

Here, I use inequality of $\mathrm{e}^{x}\geq 1+x$. In this case, I have
$\mathrm{e}^{\frac{r_{1}x}{q}}-1\geq\frac{r_{1}x}{q}$. Rearranging,
$q(\mathrm{e}^{\frac{r_{1}x}{q}}-1)-r_{1}x\geq 0$. Using the above statement,
I get $\frac{\partial FOC}{\partial r}\geq 0$.

Implicit function theorem for r gives, $\frac{\partial x}{\partial
r}=\frac{-\frac{\partial FOC}{\partial r}}{SOC}\leq 0$. The exporter chooses a
small shipment size for high financing costs in the exporter country.

For the relationship between n and r, I use $n=\dfrac{q}{x}$. Taking
derivative with respect to $r$ and using $\frac{\partial x}{\partial r}\leq 0$
give

$\dfrac{\partial n}{\partial r}=-\dfrac{q}{x(.)^{2}}\dfrac{\partial
x(.)}{\partial r}\geq 0$

(ii) Taking derivative of FOC with respect to $r_{1}$

$\displaystyle\dfrac{\partial FOC}{\partial
r_{1}}=-\dfrac{cx\mathrm{e}^{-\frac{xr_{1}}{q}-{\Delta}r_{1}+{\Delta}r}}{q\left(1-\mathrm{e}^{-\frac{xr_{1}}{q}}\right)^{2}}-\dfrac{\left(-\frac{x}{q}-{\Delta}\right)\left(c\mathrm{e}^{{\Delta}r}x+f\right)r_{1}\mathrm{e}^{-\frac{xr_{1}}{q}-{\Delta}r_{1}}}{q\left(1-\mathrm{e}^{-\frac{xr_{1}}{q}}\right)^{2}}-\dfrac{\left(c\mathrm{e}^{{\Delta}r}x+f\right)\mathrm{e}^{-\frac{xr_{1}}{q}-{\Delta}r_{1}}}{q\left(1-\mathrm{e}^{-\frac{xr_{1}}{q}}\right)^{2}}$
$\displaystyle+\dfrac{2x\left(c\mathrm{e}^{{\Delta}r}x+f\right)r_{1}\mathrm{e}^{-\frac{2xr_{1}}{q}-{\Delta}r_{1}}}{q^{2}\left(1-\mathrm{e}^{-\frac{xr_{1}}{q}}\right)^{3}}-\dfrac{c{\Delta}\mathrm{e}^{{\Delta}r-{\Delta}r_{1}}}{1-\mathrm{e}^{-\frac{xr_{1}}{q}}}$

By using equation 3,

$\dfrac{\partial FOC}{\partial r_{1}}=\dfrac{c\mathrm{e}^{\Delta r-\Delta
r_{1}}}{1-\mathrm{e}^{\frac{-r_{1}x}{q}}}\bigg{[}\frac{-x\mathrm{e}^{\frac{-r_{1}x}{q}}}{q(1-\mathrm{e}^{\frac{-r_{1}x}{q}})}+\dfrac{x}{q}+\Delta-\dfrac{1}{r_{1}}-\Delta+\dfrac{2x}{q(1-\mathrm{e}^{\frac{-r_{1}x}{q}})}\bigg{]}$

After manipulation

$\dfrac{\partial FOC}{\partial r_{1}}=\dfrac{c\mathrm{e}^{\Delta r-\Delta
r_{1}}}{1-\mathrm{e}^{\frac{-r_{1}x}{q}}}\bigg{[}\frac{x(3-2\mathrm{e}^{\frac{-r_{1}x}{q}})}{q(1-\mathrm{e}^{\frac{-r_{1}x}{q}})}-\dfrac{1}{r_{1}}\bigg{]}$

By using inequality property of $1-e^{\frac{-r_{1}x}{q}}\leq\frac{r_{1}x}{q}$,
I get $\frac{x}{q(1-\mathrm{e}^{\frac{-r_{1}x}{q}})}\geq\frac{1}{r_{1}}$.
Using $(3-2\mathrm{e}^{\frac{-r_{1}x}{q}})>1$, the square bracketed term is
positive. From the equation above, I get $\frac{\partial FOC}{\partial
r_{1}}\geq 0$.

Implicit function theorem for $r_{1}$ gives $\frac{\partial x}{\partial
r_{1}}=\frac{-\frac{\partial FOC}{\partial r_{1}}}{SOC}$. By using $SOC>0$ and
$\frac{\partial FOC}{\partial r_{1}}\geq 0$, I get $\frac{\partial x}{\partial
r_{1}}\leq 0.$ The importer chooses a small shipment size for high financing
costs in the importer country.

Using the relationship between n and r, and using $\frac{\partial x}{\partial
r}\leq 0$ give

$\dfrac{\partial n}{\partial r_{1}}=-\dfrac{q}{x(.)^{2}}\dfrac{\partial
x(.)}{\partial r_{1}}\geq 0$

(iii) Taking the derivative of FOC with respect to $\Delta$

$\dfrac{\partial
FOC}{\partial\Delta}=-\dfrac{\left(\left(\left(cqr_{1}-cqr\right)\mathrm{e}^{\frac{r_{1}x}{q}}+\left(crr_{1}-cr_{1}^{2}\right)x-cqr_{1}+cqr\right)\mathrm{e}^{r{\Delta}}-fr_{1}^{2}\right)\mathrm{e}^{\frac{r_{1}x}{q}-{\Delta}r_{1}}}{q\left(\mathrm{e}^{\frac{r_{1}x}{q}}-1\right)^{2}}$

Rearranging and by using equation 3,

$\dfrac{\partial
FOC}{\partial\Delta}=\dfrac{frr_{1}\mathrm{e}^{\frac{r_{1}x}{q}-{\Delta}r_{1}}}{q\left(\mathrm{e}^{\frac{r_{1}x}{q}}-1\right)^{2}}\geq
0$

Implicit function theorem for $\Delta$ gives $\frac{\partial
x}{\partial\Delta}=\frac{-\frac{\partial FOC}{\partial\Delta}}{SOC}\leq 0$.

Using the relationship between n and $\Delta$ and using $\frac{\partial
x}{\partial\Delta}\leq 0$, I have

$\frac{\partial n}{\partial\Delta}=-\frac{q}{x(.)^{2}}\frac{\partial
x(.)}{\partial\Delta}\geq 0$

(iv) Taking derivative of FOC with respect to $f$

$\dfrac{\partial FOC}{\partial
f}=-\dfrac{r_{1}\mathrm{e}^{\frac{r_{1}x}{q}-{\Delta}r_{1}}}{q\left(\mathrm{e}^{\frac{r_{1}x}{q}}-1\right)^{2}}\leq
0$

Implicit function theorem for $f$ gives, $\frac{\partial x}{\partial
f}=\frac{-\frac{\partial FOC}{\partial f}}{SOC}$. By using $\dfrac{\partial
FOC}{\partial f}\leq 0$, I get

$\frac{\partial x}{\partial f}\geq 0$ (11)

For the relationship between n and $f$, I have

$\dfrac{\partial n}{\partial f}=-\dfrac{q}{x(.)^{2}}\dfrac{\partial
x(.)}{\partial f}$

By using $\frac{\partial x}{\partial f}\geq 0$ from equation 11 gives

$\dfrac{\partial n}{\partial f}\leq 0$

Proof of Proposition 3:

a)

(i-iii) The exporter’s financing demand is $D=cx^{*}(.)$. I take derivative of
$D$ with respect to $r$, $r_{1}$, and $\Delta$

$\dfrac{\partial D}{\partial r}=c\frac{\partial x}{\partial r}$
$\dfrac{\partial D}{\partial r_{1}}=c\frac{\partial x}{\partial r_{1}}$
$\dfrac{\partial D}{\partial\Delta}=c\frac{\partial x}{\partial\Delta}$

By using $\frac{\partial x}{\partial r}\leq 0$, $\frac{\partial x}{\partial
r_{1}}\leq 0$, and $\frac{\partial x}{\partial\Delta}\leq 0$, I find

$\dfrac{\partial D}{\partial r}\leq 0$ $\dfrac{\partial D}{\partial r_{1}}\leq
0$ $\dfrac{\partial D}{\partial\Delta}\leq 0$

(iv) I take derivative of $D$ with respect to $f$

$\dfrac{\partial D}{\partial f}=c\frac{\partial x}{\partial f}$

By using $\frac{\partial x}{\partial f}\geq 0$ from equation 11, I find

$\dfrac{\partial D}{\partial f}\geq 0$

b)

For $r$,

$\dfrac{\partial^{2}D}{\partial r\partial f}=c\frac{\partial^{2}x}{\partial
r\partial f}$

We need to sign $\frac{\partial^{2}x}{\partial r\partial f}$. By using
$\frac{\partial x}{\partial f}=\frac{-\frac{\partial FOC}{\partial f}}{SOC}$,
$\frac{\partial FOC}{\partial
f}=-\frac{r_{1}\mathrm{e}^{\frac{r_{1}x}{q}-{\Delta}r_{1}}}{q\left(\mathrm{e}^{\frac{r_{1}x}{q}}-1\right)^{2}}$
and $SOC=\frac{cr_{1}e^{\frac{r_{1}x}{q}-\Delta r_{1}+\Delta
r}}{q(e^{\frac{r_{1}x}{q}}-1)}$, I get

$\frac{\partial x}{\partial
f}=\dfrac{\mathrm{e}^{-{\Delta}r}}{c\left(\mathrm{e}^{\frac{r_{1}x}{q}}-1\right)}$

Which gives,

$\frac{\partial^{2}x}{\partial r\partial
f}=-\dfrac{\Delta\mathrm{e}^{-{\Delta}r}}{c\left(\mathrm{e}^{\frac{r_{1}x}{q}}-1\right)}\leq
0$

Thus,

$\dfrac{\partial^{2}D}{\partial r\partial f}\leq 0$

For $r_{1}$,

$\frac{\partial^{2}x}{\partial r_{1}\partial
f}=-\dfrac{x\mathrm{e}^{\frac{r_{1}x}{q}-\Delta
r}}{qc\left(\mathrm{e}^{\frac{r_{1}x}{q}}-1\right)^{2}}\leq 0$

Thus,

$\dfrac{\partial^{2}D}{\partial r_{1}\partial f}\leq 0$

For $\Delta$,

$\frac{\partial^{2}x}{\partial\Delta\partial
f}=-\dfrac{r\mathrm{e}^{-{\Delta}r}}{c\left(\mathrm{e}^{\frac{r_{1}x}{q}}-1\right)}\leq
0$

Thus,

$\dfrac{\partial^{2}D}{\partial\Delta\partial f}\leq 0$

Proof of Proposition 4:

a)

(i) By plugging in optimized order size in the objective function to get the
total procurement cost

$C(\Delta,f,..)=\dfrac{\left(c\mathrm{e}^{{\Delta}r}x(.)+f\right)\mathrm{e}^{{-\Delta}r_{1}}}{1-\mathrm{e}^{-\frac{r_{1}x(.)}{q}}}$

By using envelop theorem, I can get how the change in $r$ affects procurement
costs121212There is a closed form solution of the FOC. I can write equation 3
as  $\mathrm{e}^{ax}-ax-b=0$ Where, $a\equiv\frac{r_{1}}{q}$ and
$b\equiv(\frac{fr_{1}}{cq\mathrm{e}^{\Delta r}}+1)$. The closed form solution
of above equation is $x=-\dfrac{W(-\frac{1}{\mathrm{e}^{b}})+b}{a}$. Where,
$W$ is a Lambert W function, which can solve equations with $x$ both in the
base and the exponent. The Lambert W function shows that for positive $x$
values and the real number $a$ and $b$, there exists a unique $x^{*}$.

$\dfrac{\partial C(\Delta,f,..)}{\partial
r}=\dfrac{cx(.)\Delta\mathrm{e}^{\Delta
r{-\Delta}r_{1}}}{1-\mathrm{e}^{-\frac{r_{1}x(.)}{q}}}$

For $x>0$,

$\dfrac{\partial C(\Delta,f,..)}{\partial r}>0$

(ii) Using the envelope theorem, I can understand how the change in $\Delta$
affects procurement costs.

$\dfrac{\partial
C(\Delta,f,..)}{\partial\Delta}=\dfrac{cx(.)(r-r_{1})\mathrm{e}^{{\Delta}(r-r_{1})}-fr_{1}\mathrm{e}^{-{\Delta}r_{1}}}{1-\mathrm{e}^{-\frac{r_{1}x(.)}{q}}}$

The sign of the above derivative is ambiguous. For a clear effect, I need to
consider the more realistic scenario behind the model. According to the model
setup, for a firm of a developing country exporting to a developed country,
$r>r_{1}$. I also know that production and financing costs are much higher
than the per-shipment fixed costs, $cx\mathrm{e}^{\Delta r}>>f$. Thus, I get

$\dfrac{\partial C(\Delta,f,..)}{\partial\Delta}\geq 0$

(iii) By using envelop theorem, I can get how the change in $f$ affects
procurement costs

$\dfrac{\partial C(\Delta,f,..)}{\partial
f}=\dfrac{\mathrm{e}^{{-\Delta}r_{1}}}{1-\mathrm{e}^{-\frac{r_{1}x(.)}{q}}}$

For $x>0$,

$\dfrac{\partial C(\Delta,f,..)}{\partial f}>0$

(iv) By using envelop theorem, I can get how the change in $r_{1}$ affects
procurement costs

$\dfrac{\partial C(\Delta,f,..)}{\partial