In this paper we compute the foreign trade multiplier on Romanian exports and imports data during 1990-2008. Our motivation comes from the need to determine the trade performance and trade efficiency using proper indicators The multiplier of foreign tradeforeign trade multiplier, open economy, marginal propensity of imports

Pop-Silaghi Monica Ioana

English

Research Papers in Economics

230 
 
FOREIGN TRADE MULTIPLIER IN ROMANIA BEFORE AND AFTER ACCESSION 
TO THE EUROPEAN UNION 
 
Pop-Silaghi Monica Ioana  
Babe -Bolyai  University  Faculty  of  Economics  Cluj-Napoca,  Romania  Email: 
monica.pop@econ.ubbcluj.ro Phone: 0040722837987 
 
In this paper we compute the foreign trade multiplier on Romanian exports and imports data during 1990-
2008. Our motivation comes from the need to determine the trade performance and trade efficiency using 
proper indicators The multiplier of foreign trade is highly quoted in the literature but little empirical work 
–even the easiest one- is done particularly in the case of Romania. We compare direct calculus based on 
time series data and simple regression analysis results. Based on these results, we conclude that foreign 
trade multiplier proves to be difficult in explaining correctly the relationship between trade and income for 
the Romanian case. 
 
Keywords: foreign trade multiplier, open economy, marginal propensity of imports 
 
JEL Code: F10 
 
1. Introduction 
The multiplier became of great importance in economic literature, especially after Keynes has 
discussed it in his famous book “General Theory of employment, interest and money” in 1936. 
The author sees the theory of multiplier as an integral part of his conception of employment. In 
his opinion, the multiplier tells that when an increase of global investments occurs, the income 
will grow with the level of multiplier of investments [5]. 
Harrod developed a multiplier for the foreign trade, on the same principles as the ones of Keynes 
multiplier of investments [2]. The multiplier of foreign trade shows how much increases the 
national income at a one-unit growth of exports [1]. But can we rely on this indicator when 
characterizing the trade performance of a country? 
As studies like [1] and [6] argues on the importance of computing the multiplier of foreign trade 
when characterizing the trade performance, the objective of this paper will be to compute the 
trade multiplier and interpret the results on the empirical data of the Romanian economy. Our 
motivation toward this study comes also from the general task of finding the most suitable tools 
for empirically analyse the trade performance and efficiency for Romania.  
To pursue our goal that consists in trying to compute the multiplier, we will calculate it in a 
deterministic  way.  We  will  investigate  how  the  multiplier  performs  on  the  Romanian  case, 
considering yearly data from 1990 to 2008. Results are helpful to see the impact of trade upon the 
economic growth of Romania particularly through the multiplier indicator. This indicator is much 
discussed from the theoretical perspective but we found very little empirical work, particularly 
for the case of Romania or other emergent countries.   
The  paper  develops  as  follows.  Section  2  introduces  the  formalization  of  the  foreign  trade 
multiplier. Section 3 computes the multiplier using the direct way supplied by the multiplier 
formula, for successive years. Section 4 tries to estimate the indicator for the whole period of 
study, using the regression technique from econometrics. Section 5 will discuss the results and  
conclude the paper. 
 
2. Foreign trade multiplier: theoretical aspects 
We will present the derivation of the foreign trade multiplier as in [1]. Reviewing [2] is useful for 
a  reader  interested  how  the  debate  over  the  indication  evolved,  when  Keynes  and  Harrod 
proposed their ideas. 231 
 
Richard Kahn (1931) was the first who generated a formal idea of a multiplier, applied for the 
economic topic of employment. He made the assumption that there is a distinction between wage 
goods  and  capital-intensive  goods  industries.  Later,  Keynes  (1936)  developed  an  income 
multiplier. We will shortly review the formal derivations toward the formula of the multiplier. 
In a closed economy, the Keynesian equation of income states that, where Y is the income, C the 
consumption, I the investments and G the government consumption. The consumption can be 
expressed as a function of the level of the income  cY C = , where c is marginal propensity to 
consumption. Furthermore, the marginal propensity to consumption can be stated as  c s - =1 , 
where s is the marginal propensity to savings. We should note that  c
Y
C
=
¶
¶
 with  0 >
¶
¶
Y
C
. If the 
assumptions that consumption is endogenous is made and we consider that it depends on income; 
investments and government consumption thus the equation of the income can be rewritten as 
G I cY Y + + = . Therefore, we can infer that 
( ) ( ) G I
s
G I
c
Y + = +
-
=
1
1
1
 (1) 
which represents the equation for the multiplier of investments. Therefore, the multiplier effect of 
investments to income is directly proportional to the marginal propensity of consumption. If the 
propensity to saving lowers to zero, the multiplier tends to infinite and if it is equal to 1, there is 
no consumption and the multiplier becomes 1.  
Considering an open economy, the Keynesian model is extended as  X C M Y + = + , where M 
represents the imports and X the exports. If we assume that investments are exogenous and we fix 
them at a given level  0 I I = , the global demand is  0 0 I cY C C + + =  where  0 C  represents the 
autonomous consumption. By replacing the global demand in the above-mentioned equation, we 
obtain 
) (
1
1
0 0 M X I C
c
Y - + +
-
=  (2) 
If we are interested how the national income varies at a growth of exports, we can compute the 
partial derivative of income with respect to exports, in an open economy,  c X Y - = ¶ ¶ 1
1 / . 
Assuming that imports vary linear with the levels of national income,  mY M M + = 0  - with m 
the marginal propensity to import, we can derive the formula of the trade multiplier: 
m c
M x + -
=
1
1
 (3) 
The  multiplier  of  exports  has  a  low  value  as  the  marginal  propensity  of  imports  is  high, 
respectively as the degree of openness of the country based on imports is higher. It also depends 
directly with the marginal propensity to consumption.  
 
3. Direct estimation of the foreign trade multiplier 
A first handy calculus for estimating the foreign trade multiplier is based on the above-mentioned 
formulas where  
0 1
0 1
Y Y
M M
Y
M
m
-
-
=
D
D
=  and 
0 1
0 1
Y Y
C C
Y
C
c
-
-
=
D
D
=  (4) 
where indices 0 and 1 represents 2 successive periods of time.  
Simply applying the formulas (3) and (4) for two successive periods of time for the Romanian 
data from 1990 to 2008, we obtained the results of table 1. 
 232 
 
Table 1 Multiplier of exports (or foreign trade) on the period 1990-2008, computed for 
every two successive periods of time 
Year  Multiplier  
1990  - 
1991  2.176103 
1992  1.596276 
1993  2.156263 
1994  2.227097 
1995  1.960436 
1996  1.837958 
1997  2.345988 
1998  4.5226 
1999  1.79271 
2000  1.588561 
2001  1.634728 
2002  1.461164 
2003  1.501683 
2004  0.816769 
2005  -2.19231 
2006  1.219734 
2007  0.781878 
2008  0.91956 
Mean  1.574844 
SOURCE: Own calculus on data from Statistical Yearbook of Romania, 2007, Eurostat, World 
Bank indicators for years 2007 and 2008 
 
We observe that the values obtained are high and very unstable, fact that determines us to be  
strongly uncertain in what concerns the relevance of this indicator. We can evaluate the results, 
for examples stating that in the year 1992 with respect to the year 1991, the national income grew 
for 1.59 times at a unit grow of exports. An interesting value is that obtained for the year 2005, 
when the propensity to consumption exceeded 1. During this year, a high number of loans were 
given and the consumption increased a lot. This fact meant that the multiplier effect of exports on 
income vanished. The situation came to normal in the year 2006 when income grew 1.21 at a unit 
growth of exports. However, we can see that the accession of Romania to the European Union 
did not bring a very positive impact if we observe solely the multiplier indicator of foreign trade 
performance. A detailed analysis in the structure of exports would give us a more specific view 
on this aspect. The complete liberalisation of foreign trade after the year 2004 when Romania 
became  a  full  member  of  the  European  Union  meant  the  increasing  of  exports  but  also  the 
increase  in  imports.  Much  of  these  imports  were  consumption  oriented  and  this  is  revealed 
through the negative sign of the indicator in 2005 and small values in the next years. As a policy 
recommendation,  we  would  state  here  that  in  order  to  achieve  a  better  trade  performance, 
Romania should focus on importing more technological goods and exports more value added 
products. In this way, steps to diminish the gap between Romania and the other old members of 
the European Union would certainly being taken.   
It is difficult to express a general opinion about this indicator, as the values are calculated in 
chain,  but  we definitely  can  say  that  for  Romania  the  instability  is  highly  expressed  by  the 
multiplier of foreign trade. 
More, if we want to assess a value for the overall study period, the only alternative is to consider 
the mean of the values which  is 1.57 When we computed the standard deviation, we, however 233 
 
obtained a high value for these values so there is no doubt that another techniques of computing 
the multiplier are required. 
 
4. Regressions for assessing the multiplier of foreign trade 
The idea of computing the multiplier with regressions comes from the formulas (4) by passing 
them to limit. Therefore,  
dy
dm
m =  and 
dy
dc
c =  (5) 
Therefore, equations (6) can be derived.  
0
0
C cY C
M mY M
+ =
+ =
 (6) 
Regressions can be employed directly with these equations, or considering their log form. Bairam 
(1997)  specified  in  a  similar  way  the  multiplier  of  foreign  trade,  while  Ghani  used  those 
specifications to compute the multiplier for more than 60 countries [4].  
We will consider therefore, the following regressions: 
M M mY M e + + = 0  (7.1) 
C C cY C e + + = 0  (7.2) 
m m Y m M e + + = 0 log log  (7.3) 
c c Y c C e + + = 0 log log  (7.4) 
We will try to estimate the parameters m and c by simple linear regression, during 1990-2008, for 
the case of Romania. As we have only 18 observations we intend to test the stability of the 
multiplier, by removing out of the model the first and the last statistical observations. Therefore, 
we  will employ  the  analyses  on  3 samples:  1990-2008,  1991-2008  and  1990-2008.  We  will 
estimate the multiplier both using the equations (6) and using the log forms of those equations. 
Table 2 depicts the results. 
  
Table 2. Estimating parameters m and c using linear regressions 
Equation  m/c  F stat  T stat  DW 
statistic 
7.1  0.42  8687.315  93.2  1.24 
7.2  0.67  329.6809  18.15  1.076 
7.3  1.076  5848.332  103.2  1.83 
7.4  0.99  9259.222  96.22  0.83 
SOURCE: Own calculus on data  
 
As we can see from table 2, t statistics for all coefficients is high enough in order to pass the 
Student test for the significance of the regression coefficients. Therefore, the hypothesis that the 
regressions coefficients do not differ significantly from 0 is rejected. In order to determine if the 
exogenous variable (in our case Y) influences in a significant way the values of endogenous 
variables (in our case M and C) we employed the variance method, by applying the F-test. As we 
can see, the computed F statistics is high, which express the fact that, based on the sample data, 
the exogenous variable influences in a significant way the dependent one. The Durbin Watson 
statistic  shows that  in  the  case  of the  log  regression  for  m  we  can  for  sure accept  the  null 
hypothesis of no autocorrelation of errors.  
In order to validate the regressions, we need to perform tests on the residuals. A first test is the 
one of the normality of the residuals. As we have a small sample (with only 19 observations), 
have applied the Lilliefors test [3]. The results of the Lilliefors tests showed us that we can rely 234 
 
on log versions of the data as residuals are smaller than in case of using real levels. We also 
performed  stability  tests  which  revealed  that    log  regressions  are  more  stable  than  direct 
regressions.  Therefore,  we  have  another  reason  to  consider  log  regressions  as  being  better 
estimators for the marginal propensity to consume and to import indicators
113.  
Table 3 depicts the values of the foreign trade multiplier, computed with both methods, with log 
regressions and with direct regressions. We can observe that lower values are obtained with 
regression techniques than when computing the multiplier on two successive years.  
 
Table 3. The foreign trade multiplier 
Equations 
Multiplier value 
7.1, 7.2  1.33 
7.3, 7.4  0.92 
 
A value of 0.92 of the multiplier of foreign trade, states that an increase with one unit of exports 
leads towards a smaller increase in the income.  
 
5. Conclusion 
In this paper we tried to compute the Harrod multiplier of foreign trade for the case of the 
Romanian economy. Our motivation was to check if the multiplier could be used as a valid 
indicator for characterizing the trade performance of a country.  
We started the paper by formalizing the multiplier of foreign trade. Therefore, we presented and 
computed the multiplier using two techniques: one based on the successive yearly data, and one 
based  on  the  regression  technique.  The  study  period  was  between  1990  and  2008  and  we 
considered  nominal  values  in  national  currency  for  the  GDP,  imports  and  the  national 
consumption. The critical years that changed more the situation were years 2004, 2005 when 
since Romania was full member of the European Union. 
Starting from the theoretical presentation of the multiplier developed in section 2, this indicator 
was conceived for characterizing the influence of the foreign trade on the income of a country for 
two successive periods of time. Therefore, probably, the results of section 3 are the ones that 
come closer with the economical theoretical foundation of the multiplier. But, as the values vary 
substantially from year to year on the study period, this indicator cannot represent a reliable one 
for our purpose of characterizing the relation between external trade and the income, before and 
after accession to the European Union. We can notice that for the first half of the period the 
multiplier values are around 2, and for the second half of the period, the values are about 1.5. It 
follows that for the period of transition, with high inflation and quite high economical instability 
high values of the multiplier are obtained. As the economy gets more stable, the values of the 
multiplier are lower.  
Computing the multiplier using regressions, we concluded that using log values of the data is 
more significant than using direct nominal values. We performed tests for the regression residuals 
and, under some small concerns we can say that the regressions are valid. Although statistically 
we can base only on the log computations, the obtained value is far apart from the values of table 
1.  The overall value of the multiplier is smaller than in the case when using successive periods 
estimations. Therefore, the conclusions do not remain the same. Even more, if no log data would 
be considered for the regressions, the overall results come closer with the reality. But, in this 
case, the statistical tests are not any more fulfilled, due to high variability of the input data.  
Relying on the overall multiplier value computed with regressions, we can infer a lower influence 
of foreign trade on the gross domestic product. Anyway, the value we obtained is comparable 
                                                       
113 Table with results on Liliefors test and stability test can be provided upon request 235 
 
with the ones of [4], which reports a wide range of values for the Harrod foreign trade multiplier 
for different countries. Reviewing the findings of [4], no inference pattern can be drawn out, as 
between less developed and developing countries with a high value for the multiplier (like Brazil, 
Panama, Dominican Republic etc.) we can find countries with a good welfare as South Korea, 
Ireland,  Italy  etc.  Developed  countries  like  Austria,  Germany,  US,  Spain,  Sweden  have  a 
multiplier around unity, but in this category there are countries like Argentina, Uruguay, Nepal, 
Nigeria etc.  
Based on our analysis, we can conclude that the Harrod foreign trade multiplier is not a good 
indicator for characterizing trade performance. Regarding this direction, our results could be 
influenced  by  the  fact  that  we  had  only  19  yearly  data available  for  analysis.  Probably,  the 
equations used for estimating the propensity to consumption and to imports  should be more 
specified, and other relationships or supplemental variables need to be adopted for this. 
 
References 
1. Gilbert Abraham-Frois, Economics, (Romanian translation), Humanitas, Bucharest, 1994 
2. Daniele Besomi, On the Spread of an Idea: The Strange Case of Mr. Harrod and the Multiplier, 
History of Political Economy, 32:2, 2000 
3. Ioan Florea, Statistics, (Romanian), Babes-Bolyai University Press, Cluj-Napoca, 2000 
4. Gairuzazmi Ghani, Levels of Economic Development and the Dynamic Harrod Foreign Trade 
Multiplier: A Re-examination of Empirical Evidence, International Trade Economics Working 
Papers Archive at WUSTL, University of South-Carolina, 2004 
5. John Maynard Keynes, The General Theory of Employment, Interest and Money, Macmillan 
Cambridge University Press, 1936, www.marxists.org edition 
6. Gheorghe Popescu, International Trade Models, (Romanian), Ed. Corvin, Deva, 2001 
   

Economics, (Romanian translation),

International Trade Models,

Keynes, The General Theory of Employment, Interest and Money,

Levels of Economic Development and the Dynamic Harrod Foreign Trade Multiplier: A Re-examination of Empirical Evidence, International Trade Economics Working Papers Archive at WUSTL,

On the Spread of an Idea: The Strange Case of Mr. Harrod and the Multiplier, History of Political Economy,

FOREIGN TRADE MULTIPLIER IN ROMANIA BEFORE AND AFTER ACCESSION TO THE EUROPEAN UNION

http://steconomice.uoradea.ro/anale/volume/2009/v1-international-relations-and-european-integration/35.pdf

FOREIGN TRADE MULTIPLIER IN ROMANIA BEFORE AND AFTER ACCESSION TO THE EUROPEAN UNION

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