The gravity model in international trade

CASE STUDY FOR CROATIA

AUTHORS: Lander Bijnens Louis Claes d’Erckenteel Peter Filipic Benjamin Kardum Robine Van Campen

Table of contents 1. THEORETICAL POINT OF VIEW OF GRAVITY MODEL ......................................................................... 2

2. GRAVITY MODEL OF INTERNATIONAL TRADE ................................................................................... 4

2.1 Gold medal ........................................................................................................................................ 4

2.2. Silver medal ..................................................................................................................................... 4

2.3 Bronze medal .................................................................................................................................... 4

2.4 Fixed country effects ........................................................................................................................ 5

2.5 Fixed and variable trade cost ........................................................................................................... 5

3. TRADE OVERVIEW CROATIA ............................................................................................................... 6

4. ECONOMETRIC ANALYSIS ................................................................................................................... 8

4.1 Model for year 2002 ..................................................................................................................... 8

4.2 Model for year 2007 ..................................................................................................................... 9

4.3 Model for year 2014 ................................................................................................................... 11

5. CONCLUSION ..................................................................................................................................... 12

1. THEORETICAL POINT OF VIEW OF GRAVITY MODEL The gravity model of trade is used to predict the bilateral trade flows based on the economic

sizes and distances between two countries. The basic model for trade between two countries

(i and j) is based on the law of gravity in physics, which states that the force of gravity between

two objects is proportional to the product of masses of the two objects divided by the square

of the distance between them. In symbols:

Fij=GMi

β1Mj

β2

Dijβ3

In this equation F is the trade flow between countries i and j (or the force of the gravity), Mi

and Mj are the masses of each country, Dij is the distance between the two countries and G is

a constant. So according to this model the exports from country i to country j are explained

by their economic sizes, population, direct geographical distances and some dummy variables

incorporating institutional characteristics common to specific flows.

This standard gravity model can be augmented with several variables to test whether they are

relevant in explaining trade, this is called the augmented gravity model. Infrastructure

endowments (subsidies), squared differences in capita per income and real exchange rates

are examples of these variables.

The model was first used in 1962 by the dutch economist Jan Tinbergen. Also Pöyhönen (1963)

and Linnemann (1966) proposed and tested similar models to analyze international trade

flows. In 1970 Leamer and Stern provided some foundations with their book on quantitative

international economics. This is based on the ‘potluck assumption’, which means that all of

the goods produced in the nations are thrown in a ‘pot’ and each country draws its

consumption out of the pot in proportion to its income. The expected value of the

consumption of country i produced by country j will be equal to the product of the share of

world GDP of country i times the share of world GDP of country j. This means that the bilateral

trade is in proportion to the GDP shares. In 1979 Anderson was the first to formulate a gravity

equation from a model that considered product differentiation. The next theoretical

foundations of the gravity equation came when Bergstrand explored the theoretical

determination of bilateral trade in which gravity equations are related to simple monopolistic

competition models. Krugman and Helpman worked with a differentiated product framework

with enlarging returns to scale to justify the gravity model in 1985. Deardorff verified in 1995

that the gravity equation characterizes a lot of models and can be explained from different

standard trade models. More recently Anderson and Van Wincoop published a theory close

to Anderson’s theory from 1979: the main value added is the derivation of a practical way of

using the full expenditure system to estimate key parameters on cross-section data.

Recent years a lot of papers are published by empirical trade economists, the methodological

advances in these papers have been generally ignored in wider literature as they are typically

viewed as contributions to narrow empirical topics.

The popularity of the model is based on three pillars:

1. There is a demand for knowing what normal trade flows should be (international key

flows are a key element in all economic relationships).

2. The date to estimate the normal trade flows are easily accessible to all researchers.

3. The several high profile papers have formed the respectability of the gravity model and

have created a set of practices that any empirical researcher needs to make empirical

choices.

The gravity model estimates the pattern of international trade and has been used to test

hypotheses implanted in pure economic theories of trade. In this case trade will be based on

relative factor abundances, the Heckscher-Ohlin model is an example of such a model. The

model essentially says that nations will import goods that are produced with scarce factor(s)

and export products that use abundant and cheap factor(s). This model builds on Ricardo’s

theory of comparative advantage, which says that a firm, individual or nation has an

comparative advantage over another if he can produce a good at a lower relative opportunity

cost. There are several reasons why the gravity model is more successful as the other ones:

- A number of results of studies do not match the expectations of the comparative

advantage theories. E.g. the US (most capital intensive country in the world) exports

more in labor intensive industries.

- Countries with similar levels of income trade more, which indicates that these

countries are trading in differentiated goods because of their similarities. This is the

opposite of what the Heckscher-Ohlin model states.

2. GRAVITY MODEL OF INTERNATIONAL TRADE As mentioned in the previous section the gravity model is based on the law of gravity in

physics. Further in-depth analysis shows that the gravity equation in its core is an expenditure

equation due to the estimation of bilateral trade. With some mathematical manipulation we

can observe the following transformation of the physics concept towards the economics

concept:

𝑏𝑖𝑙𝑎𝑡𝑒𝑟𝑎𝑙 𝑡𝑟𝑎𝑑𝑒 = 𝐺𝑌1𝑌2

𝑑𝑖𝑠𝑡12𝑒𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦−1 ; 𝐺 ≡

1

Ω𝑜

1

𝑃𝑑1−𝑒𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦 (1)

With difference to physics gravity constant in economic models occurs un-constant regarding

to GDP’s which varies over time. The concept of the above equation is based on two important

parameters: Ω measures openness of a nation (nations export and import to world markets),

and P measures prices (price indices or costs). The equation shows great importance of

interpretation of the gravity un-constant since it is the source of large number of errors in

estimation.

Furthermore, during the estimation process of the gravity model we meet several potential

“traps” which can lead researchers to wrong results and false conclusions. Economic literature

(Baldwin & Taglioni, 2006) defined them as gold, silver and bronze medals.

2.1 Gold medal The gold medal problem is referred to the bias which occurs when we estimate the gravity

model with the standard OLS procedure. This is due to fact that omitted terms are correlated

with the trade and cost terms. One of the standard OLS assumptions is that 𝑝𝑙𝑖𝑚𝑗 → 𝛽𝑗, but

in many cases the estimations become biased due to violating the previously mentioned

condition. In our estimation the expression becomes 𝑝𝑙𝑖𝑚𝑗 → 𝛽𝑗 + 𝛾𝛿. Researchers can

avoid gold medal by including dummy variables (sometimes in the literature referred as trade

resistance term) and estimating whole process with fixed effects estimator or LSDV.

2.2. Silver medal The silver medal problem is defined as the problem of calculation of averages of the bilateral

flows. The theory tells us that averaging should be done after taking logs not before regarding

calculations because the sum of logs is just approximately log of the sum (Σ log ≈ log Σ). And

when we have unbalanced trade this differences become larger. This is an important issue for

the states like Croatia which have unbalanced trade flows.

2.3 Bronze medal The bronze medal problem occurs when we compare the price indices of different countries.

The consequence is incorrect deflation of bilateral trade. It has severe impact on the

impetration of the results.

2.4 Fixed country effects The economics literature defined a special group of models called fixed-effects models. Their specification allows us to define a special variable for unobserved or misspecified factors that explain the trade volume between two countries. In most cases the economic literature still provides the GDP as proxy for expenditure on tradable goods.

2.5 Fixed and variable trade cost In international trade research the economics literature has made clear that tariffs or institutional barriers are a crucial impediment for firms to export their goods abroad. One reason for the increase in trade in the recent years is that there has been enormous decline in international trade costs. We have a wide range of trade cost components. Not just the transportation costs and tariffs as two main categories of trade costs, but also other components such as language barriers, informational costs and red tape. In that manner we can distinguish between fixed and variable trade costs. Fixed trade costs are those that are independent of the quantity. While on the other hand we have variable trade costs that change with quantity (in literature sometimes referred to as Ad-Valorem costs – According to the value). In particular, fixed export costs are those which firms have to overcome before they are able to sell on the foreign markets. For example, in a recent study of 15,000 firms in 7 European countries (Navaretti et al., 2010) estimate that big firms (>249 employees) are between 20 and 40 %-points more likely to engage in exports than small firms (with <10 employees).

3. TRADE OVERVIEW CROATIA From 2002 until the financial crisis, Croatia’s GDP has been growing steadily. A maximum GDP

of approximately 70 billion USD was reached in 2009. Since then it declined a little, today

Croatia’s GDP is at 57,22 billion USD. Croatia is a country that gains income mainly from a

service-based economy. Tourism is the most important sector, followed by manufacturing,

and also international trade is a relevant contributor. Croatia’s top 20 main trading partners

are listed below. This trade consists mainly of industrial goods, this is the case for import as

well as export.

1 Italy 11 Poland

2 Germany 12 United States of America

3 Russian Federation 13 United Kingdom

4 China 14 Spain

5 Slovenia 15 Turkey

6 Austria 16 Netherlands

7 France 17 Japan

8 Hungary 18 Switzerland

9 Bosnia and Herzegovina 19 Serbia

10 Czech Republic 20 Belgium

Since 2004 Croatia has been candidate to enter the EU. SAA (Stabilisation and Association

Agreement) was a first attempt to improve trade between Croatia and the EU. On the 29th of

October 2001 Croatia was the second Balkan country that signed the SAA. This is a sort of

agreement between the EU and the Balkan countries that is adapted for each different

member. The main target of SAA is to create free trade between EU and the member counties.

But it also supports common political and economic goals and encourages regional co-

operation. After Croatia signed the SAA in 2001 it still had to wait until February 2005 for the

agreement to get into force. The SAA had a substantially positive influence on Croatia’s trade.

A second factor that changed Croatia’s trade substantially is the CEFTA 2006 also known as

Central European Free Trade Agreement. The first CEFTA was actually signed in 1992 in

Poland. It was a free trade agreement between non-EU countries in South-east Europe. As by

2006 many of the former members became part of the EU they had to finally leave the CEFTA.

Because of this in 2006 CEFTA had to be reformed, new countries entered the agreement. One

of them was Croatia that joined “CEFTA 2006” in 2007. From 2007 to 2013 this free trade

agreement helped Croatia to expand its international trade. It eliminates trade barriers,

provides appropriate intellectual property protection, it also created stable rules. In 2013

Croatia left the CEFTA because it became member of the EU. Once member of the EU, a lot of

trade complications disappeared.

4. ECONOMETRIC ANALYSIS

GDP €106 lngdp Import from Export to Distance

Mean 1464303 13,11093 767403,8 362692,5 2056,803 Standard error 528849,2 0,393707 160153,4 104744,3 641,5497 Median 540855,4 13,19295 388349,5 144988 963,323 Standard deviation 2365085 1,760712 716227,9 468430,8 2869,098 Sample variance 5,59E+12 3,100106 5,13E+11 2,19E+11 8231721 Kurtosis 12,48747 -0,15152 2,06503 3,020161 2,46151 Skewness 3,287556 -0,52642 1,696761 1,870022 1,969221 Range 10567742 6,84333 2505721 1707322 9087,428 Minimum 11283,02 9,331054 207403 14474 180,3356 Maximum 10579025 16,17438 2713124 1721796 9267,764 Sum 29286057 262,2186 15348075 7253850 41136,06 Sample size 20 20 20 20 20

The table above contain the descriptive statistics for the twenty best trade partners of Croatia

in 2007. There are some important things to notice. Firstly, the sample size n=20 is pretty low

for an econometric analysis. Due to this small sample size, it could be that some results are

not externally valid and reliable. Second, it is important to notice that there is a large

difference between the means and medians of all continuous variables. This is an indication

that these variables are not normally distributed but the distribution is skewed and contains

outliers. Therefore the natural logarithms are computed. In the example above, de mean and

median of lngdp are much closer to each other which indicates that this was indeed the right

decision.

4.1 Model for year 2002

(1) (2)

VARIABLES lnimport lnexport

lngdp 0.615*** 0.492 (0.197) (0.362)

lndistance -0.937** -1.404**

(0.354) (0.504)

1.SAA -0.274 0.00984

(0.358) (0.669) Constant 11.36*** 14.81***

(0.955) (2.437)

Observations 20 20 R-squared 0.450 0.465

Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

Based on the trade flows of Croatia with 20 other trade partners, respectively their GDP, geographical distance between the trade countries and dummy variable for SAA, the results of the econometric analysis suggest the folowing conclusions. R-squared which measures the goodnes of fit of the model is 0.45 and 0.465, respectively, which can be interpreated that nearly half of the variation in overall data is explained with the above model. This is a pretty good result considering the models for other time periods. Furthermore, the values of explanatory variables are in the logarithmic form. It follows that the variables lngdp and lndistance are in agreement with economic theory. In general, higher GDP for the origin country reflects the positive outcome for Croatia in 2002, and more distant country reflects in negative sign. If we take, for example, lngdp for import which is significant on the 95% interval we can interpret that result as if the GDP of the other tradable country with Croatia raise by 10%, then import to Croatia will increase by 6.15%. The lnexport variable for export is not significant, so we can not make any conclusion. The last is the estimation of SAA (Stabilization and Assocation Agreement) dummy variable which was signed in 2001 is more tricky to intrepret. The t-values for lnexport and lnimport variables are also insignificent and have different signs. However, we have to take into account that we have a relatively small sample of only 20 observations. With a larger sample we might have come to more significant conclusions.

4.2 Model for year 2007

(3) (4)

VARIABLES lnimport lnexport

lngdp 0.558* 1.161***

(0.274) (0.214)

lndistance -0.772* -1.902***

(0.372) (0.271)

1.SAA -0.527 -0.774*

(0.400) (0.375)

1.FTA 0.256 2.964***

(0.635) (0.726)

Constant 11.46*** 10.07***

(1.726) (2.018)

Observations 20 20

R-squared 0.264 0.781

Robust standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

To start off, the import part will be discussed. The explanatory variables ‘lngdp’ and

‘lndistance’ are significant on a 90% level, meaning that the null hypothesis of no relation

between ‘lnimport’ and those two variables individually can be rejected with a 90 percent

certainty. The R-Squared of 0.264 indicates that this model explains 26,4% of the total

variation in imports of Croatia in 2007. This is relatively low compared to the other models.

Quite surprisingly, the dummy variables FTA and SAA, respectively indicating whether Croatia

has a free trade agreement and stabilisation and association agreement with the trade

partner, are not significant. A possible explanation could be that the sample size is too small.

Only two countries in dataset were part of the CEFTA and had therefore a FTA with Croatia.

Another, but more unlikely explanation is that those trade agreements don’t affect the

imports of Croatia. Assuming this is not very realistic.

Since the parameters of the dummies on the import part are not significant, they cannot be

properly discussed. On the other hand, the coefficients of lngdp and lndistance both have

expected signs: positive for lngdp and negative for lndistance. This indicates that if the

distance between Croatia and its trade partner is higher, there will be less imports. if the gdp

of the trade partner is higher, Croatia will ceteris paribus import more goods from that

country.

The values for both parameters lie within one standard deviation from the aggregated data,

so our findings are in line with earlier statistical evidence. Since the estimated model in in the

log-log format, the interpretation of the coefficients is quite straightforward. It goes as

follows: if the gdp in the origin country rises with ten percent, the Croatian imports for that

country will rise with 5,58%. This interpretation is analogue for all logged variables.

On the export side, the FTA and SAA dummies are significantly different from zero with a

respective significance level of .01 and .1. Furthermore, the gravity model for export in 2007

explains a lot more variation (78,1%) than it does for the imports. This is probably because the

exports were already to the EU were already totally liberalised but the imports went to a

transition period. The interpretation of the dummy parameters are not straightforward

anymore. For instance, to get the meaning of the FTA parameter, following equation has to

be computed: (e2.964-1)*100=1837.53%. Since this is an enormously high figure, it’s better not

to interpret it directly because that would mean that joining the CEFTA increases exports from

Croatia to that country with almost twentyfold. This outcome is not realistic. What is

important here is that the FTA has a positive impact on trade between countries. The SAA

coefficient has a contra intuitive sign due to the small sample size.

In comparison with 2002 the parameters on the import side remain approximately the same

while on the export side the absolute effects of gdp and distance become slightly larger and

therefore more elastic in 2007.

4.3 Model for year 2014

(1) (2)

VARIABLES lnimport lnexport

lngdp 0.560*** 0.450*

(0.187) (0.244)

lndistance -1.751*** -1.526***

(0.437) (0.403)

1.Diagcum -1.623 -0.513

(0.977) (1.193)

1.Eumember 0.591 -0.433

(0.479) (0.879)

Constant 18.59*** 17.68***

(2.338) (2.594)

Observations 20 20

R-squared 0.680 0.635

As for the 2014, Croatia had experienced the first year of being a member of the EU which reflected on its import and export. Model analysis shows that the R-squared indicator 0.680 in 2014 which presents 68% of the total variation in imports and its the highest R-square of all three observed models in this paperwork. Following dummy variables that have been used in the model diagcum and Eumember didn’t show any significance which was unexpected since the theory alludes advantages and benefits of economic integration (implying on Eumemeber dummy variable). This, third analysis has even more confirmed the doubt that the sample size isn’t good enough to get true results. Furthermore, coefficients of lngdp and lndistance behave as they should, positive sign for lngdp and negative for lndistance. Positive indicator shows that if the GDP of specific Croatia’s trade partner is higher Croatia will do more import from it, under the condition that nothing changes. As for the lndistance which has a negative sign, this can only mean the longer distance is the less import will be done. Coefficient interpretation would go for an example: if the gdp in the origin country changes for a positive one percent the Croatian import for that specific country will be increased by 0.56%. Third gravity model for 2014 shows that there are almost no differences between import (68%) and export (63%) sides. (not sure! Because you were saying when there are three *** then it is 1% etc...)

5. CONCLUSION The gravity model of the trade is used to predict trade flows between some specific countries

based on the size and distance between them. Usually the basic model uses two countries as

the example that are marked with “i” and “j” and it has been established on the law of gravity

in physics, furthermore that means that the gravity between two objects is proportional to

the product of masses of two objects divided by the square of the distance that is between

them. The first use of the econometrical model was used in 1962 by the dutch economist Jan

Tinbergen, among him there are Pöyhönen (1963) and Linnemann (1966) who have proposed

and tested similar models into their analysis in international trade flows. Recent years a lot of

papers are published by empirical trade economists, the methodological advances in these

papers have been generally ignored in wider literature as they are typically viewed as

contributions to narrow empirical topics.

As it has been mentioned in the paperwork, gravity model contains famous gold, silver and

bronze medal mistakes. The gold medal mistake refers to a mistake that comes out from

correlation of the variables that have been left out and so called trade cost. The silver medal

mistake is defined through the problem of average calculation of the bilateral flows, so

practically this theory points out that averaging should be done after taking particular logs and

not before regarding calculations, because the sum of logs is just approximately log of the

sum. Bronze medal mistake is the kind of the “problem” that happens when the prices of

different countries are compared, which has severe impact on the impetration of the result.

Croatia’s GDP has been growing steadily from 2002 until the financial crisis, where the

maximum of the GDP was reaches in 2009 which was approximately 70 billion USD. Since that

time Croatia has faced many problem and rapidly declined over the years, today’s GDP is

around 57,22 billion USD. Croatia is a country that gains income mainly from a service based

economy which is actually the source of problems, for the example tourism is the most

important sector followed by manufacturing and international trade as third most important

element and very relevant contributor in development.

Econometric analysis included the sample size of twenty countries (n=20) which is pretty low

for doing a structural and valid analysis. Due to this small sample size there is a high possibility

that some of the results are not valid and reliable as the would when the sample size would

be e. g. over 50 countries. Another noticeable thing is that there is a large difference between

the means and medians of all continuous variable which points out on indication that these

variable are not normally distributed but the distribution is skewed and contains outliers.