Growth Rate Analysis of GDP and GNP
in Six Industrial Countries (1981-2004)

Tommy Eshleman
Vani Kotcherlakota
University of Nebraska at Kearney

Introduction
     The main objective of this paper is to analyze the growth rates of Gross Domestic Product (GDP) and Gross National Product (GNP) for the six largest industrial countries for the period from 1981-2004.  The time period of the study allowed the comparison of growth rates of selected sub-periods to determine any major changes in the relationship between GDP and GNP over time.  The countries chosen for the analysis were, on average, the six largest economies in the world over the time period of study; Canada, France, Germany, Japan, the United Kingdom and the United States.  China currently has the sixth largest economy in the world, but this was not the case over most of the time period of the study. 
     The paper is presented in three sections.  In the first section GDP, GNP, and NPI (Net Primary Income from Abroad) are defined, and general comparisons among the six countries are made.  The second section presents the data and methodology used in the study.  The third section analyzes the growth rates of GDP and GNP for the selected countries.  Conclusions are given in the end.
Section 1.  GDP and GNP
     The main difference between GDP and GNP lies in the treatment of corporate profits, interest, income and wages.  GDP measures the market value of labor and property output generated within the borders of a country regardless of whether the labor and property are provided by residents of that country or foreigners.  GNP measures the market value of labor and property output provided by a country's residents regardless of whether the labor and property are located in that country or abroad.  As such, GDP is a more accurate measure of a country's domestic production, as it excludes income generated abroad.
     The Commerce Department of the United States began emphasizing GDP over GNP as the preferred measurement of economic activity in 1991 1.  That year, U.S. GNP in the second quarter dropped at an annual rate of .1%, while GDP rose at an annual rate of .8% for the same time period.  It was determined that the rise in GDP was a more accurate gauge of the economy at that time than the drop in GNP, so the GDP measure was emphasized.  Another advantage of using GDP is that it helps in making international comparisons, since most countries emphasize GDP as their measure of economic activity.
     Table 1 compares GNP and GDP data for the six selected countries for 2004, the most recent data used in the analysis.  The difference between GNP and GDP is called the Net Primary Income from Abroad (NPI), which is defined below.

Using the U.S. as an example, Net Primary Income from Abroad is defined as follows:
A = U.S. production of goods and services within the U.S.
B = U.S. production of goods and services abroad.
C = Foreign production of goods and services within the U.S.
so
GNP = A + B
GDP = A + C
and
NPI = GNP - GDP = (A+B)-(A+C) = B-C

U.S.  Net Primary Income from Abroad is U.S. production abroad minus foreign production in the U.S. 
     A positive NPI for a country indicates that residents and businesses in that country have expanded their economic activities in foreign countries to a greater extent than foreign countries have expanded into that country.  In this case, GNP would be larger than GDP.  A negative NPI indicates just the opposite. 
     A cursory look at Table 1 shows that the current NPI for Canada, Germany, and the U.S. is negative.  The current NPI for France, Japan, and the U.K. is positive.  The NPI for Japan was positive for every year of the study period except the first year, 1981.  This accounted for widespread concern over Japanese encroachment into the U.S. in the 80’s and early 90’s.  That sentiment has waned over the last decade with economic problems in Japan, even though their NPI continues to be positive. 
     The main question addressed in this study is whether one country’s expansion of economic activities in foreign countries is especially beneficial to the economic growth of that country as measured by the real growth in both GDP and GNP.  While one could make a general observation on the impact of a positive or negative NPI on the health of an economy in terms of economic growth, we will attempt to examine the percentage change in a country’s NPI over time to determine if this characteristic has any relationship with the economic growth of that country.  
Section 2.  Data and Methodology
     Data for this analysis was collected from the International Financial Statistics Yearbook2 for the six selected countries.  The GDP and GNP of each country are measured in its own currency:  Canadian Dollars, French Francs (Euro equivalent starting in 1993), German Deutsche Marks (Euro equivalent starting in 1993), Japanese Yen, British Pounds, and U.S. Dollars. The focus of the study is on the analysis of the differences in growth rates in GDP and GNP, and the relationship between this characteristic and growth in general for each country.  The GDP and GNP data were adjusted by each country’s GDP price index to reflect real production changes.
     A semi-log model was used to analyze the data, and OLS was used in the estimation.  The model took the form:

log GDPi = ai + biT.
log GNPi  = ci + diT

where

log GDPi = logarithmic values of GDP for country i
log GNPi = logarithmic values of GNP for country i
ai, ci = intercepts
bi = percentage growth rates of GDP in country i
di = percentage growth rates of GNP in country i
T = time period (1981-1992) and (1993-2004)

     The slope coefficient of the semi-log model measures the constant proportional or relative change in the dependent variable for a given absolute change in the time variable T.  This model is often referred to as a (constant) growth model3, and can be used to measure the average annual growth in GDP and GNP over a given time period. 
Section 3.  Results and Analysis
     The data and regression equations are given in the appendix.  The growth rates obtained for the semi-log model are given in Table 2.  The study period was divided into two 12-year time periods, 1981-1992 and 1993-2004, to compare changes in the economic growth measures over time, and also due to data considerations in obtaining continuous price index numbers and Euro conversion rates for France and Germany.
     The table shows that only Japan and Germany experienced greater growth in GNP than in GDP (greater growth in NPI) over the 1981-1992 time period, while all countries except Germany had greater growth in GNP than in GDP for the 1993-2004 time period.  All countries except Germany and Japan experienced an increase in the average annual growth of both GNP and GDP for the 1993-2004 time period vs. the 1981-1992 time period. 
     To determine if greater growth in NPI is associated with greater growth in both GNP and GDP, a correlation analysis was run on the data in Table 2 to measure the correlation between the growth in NPI (GNP growth rate – GDP growth rate) and the growth rate of both GNP and GDP.  Table 3 shows the correlation matrix for the 1981-1992 time period and for the 1993-2004 time period.
     The Pearson correlation coefficients can take a value between -1 and 1, with 1 indicating a perfect positive correlation and 0 indicating no correlation4.  In time period 1993-2004, the correlation coefficient between the difference in growth rates (GNP-GDP) and GDP growth is .610124, and between the difference in growth rates and GNP it is .677618.  These coefficients are positive and closer to 1 than to 0, suggesting that when growth in GNP is greater than growth in GDP, that both GNP and GDP tend to grow at a greater rate.  This relationship is even stronger in the 1981-1992 time period, with correlation coefficients of .847196 and .876104, respectively.  A positive correlation between two variables does not suggest that an increase in one variable causes an increase in the other, but only that the two variables tend to change in the same direction.  The observation that can be made from this analysis is that when a country has expanded its economic activities in foreign countries at a greater rate than foreign countries have expanded into that country, it tends to experience greater economic growth as measured by both GDP and GNP. 
     This relationship does not hold for every situation or for every country.  A good example is Japan, which continues to show very high growth in NPI in the most recent time period from 1993-2004, while at the same time experiencing among the lowest average annual economic growth rates in GDP and GNP of the six countries in the study.  Still, the positive relationship noted above appears strong for most other countries in the study.
     As a spot check of the positive relationship between growth in NPI and growth in both GDP and GNP, an analysis of the sub-period from 1993-2000 was performed.  This period represented a time of tremendous growth and prosperity for the U.S., which ended with the terrorist attacks and recession of 2001.  Table 4 shows the same GDP-GNP variables used above for the 1993-2000 time period.
     During this period of high economic growth in the U.S., GNP grew at an average annual rate of nearly one-half of a percentage point higher than GDP, a far greater difference than any other country in the study.  Average annual economic growth in the U.S. measured by GDP and GNP was the highest of the six countries as well.
Summary and Conclusions
     The main objective of this paper was to analyze and compare growth rates of GDP and GNP in the six major industrial countries.  A semi-log (constant growth) model estimated with OLS was used for the analysis.
     The main conclusion from the empirical work is that of the six largest industrial countries in the world over the time period 1981-2004, when a country experiences expanded economic activity abroad at a greater rate than foreign expansion within their own country (Positive Net Primary Income Abroad), economic growth as measured by both real GDP and real GNP is greater as well.  Japan appears to be the major exception to this relationship, as it’s growth in GNP is greater than growth in GDP during periods of high and low economic growth. 
     In addition, while all nations currently emphasize GDP as their primary measure of economic activity and growth, GNP may be a more accurate indicator of the economic health of a nation in terms of  growth potential

Table 1.  GNP, GDP, and NPI, in Billions of Currency Units, 2004

Source:  International Financial Statistics Yearbook, 20052

Table 2.  Growth Rate Percentages from Semi-Log Model

All variables are significant at the 5% confidence level.

Table 3.  Correlation Matrix of Variables from Table 2

Table 4.  Growth Rate Percentages from Semi-Log Model

APPENDIX 1:  GDP, GNP, and Price Index Data, by Country, 1981-2004

Source:               (1993-2004)      International Financial Statistics Yearbook, 2005
                          (1981-1992)      International Financial Statistics Yearbook, 1996

APPENDIX 2:  Semi-Log Model Estimates, OLS