




































American Economic & Social Review; Vol. 3, No. 1; 2018  

ISSN 2576-1269   E-ISSN 2576-1277 

Impact Factor: 3.9 

                                            Published by Centre for Research on Islamic Banking & Finance and Business, USA 

 

 

18 

 

Testing the Validity of the Solow Growth Model: Empirical 

Evidence from Cross-Country Panel Data 
 

 

 
Chigozie Nelson Nkalu

1
, Richardson Kojo Edeme

1
 & Queen O. Chukwuma

1 

 

 
1
Department of Economics, University of Nigeria, Nsukka Enugu State, Nigeria 

 

Correspondence: Chigozie Nelson Nkalu, Department of Economics, University of Nigeria, Nsukka Enugu State, 

Nigeria. Email: nkaluconnection@gmail.com, Phone: +2348066884155 

 

To cite this article: Nkalu, C. N., Edeme, R. K., & Chukwuma, Q. O. (2018). Testing the Validity of the Solow 

Growth Model: Empirical Evidence from Cross-Country Panel Data. American Economic & Social Review, 3(1), 

18-22. Retrieved from http://www.cribfb.com/journal/index.php/aesr/article/view/197 

 

 

Received: November 2, 2018      Accepted: November 8, 2018           Online Published: November 11, 2018          

    

Abstract 

This study seeks to test for the validity of the Solow growth model using cross-country panel data. Panel OLS 

analysis was adopted following an extensive review of recent and related literature with output-side of the real GDP 

as the dependent variable with other variables like population, capital stock and employment as the independent. 

However, population and capital stock are positively impacting the output with statistically significant value, while 

employment is not an important variable in the model even though it exhibits a negative and statistically significant 

effect to the output. In conclusion, the estimation result conforms the postulations of the basic Solow and augmented 

Solow growth model thereby validating the Solow model across-countries.  

 

Keywords: Solow Model, Cross-Country, Panel OLS, Growth Theories, Output-side of RGDP. 

 

JEL: A10, A20, C01, C15, C87  

1. Introduction 

One of the greatest challenges in economic growth and development policy is the persistent and significant 

differences and ranges of standards of living across countries. Different growth theories have evolved over the years 

starting from classical theories of growth to endogenous and neoclassical growth theories. All the growth theories 

strive to account for the differences in growth experiences across countries, and why the growth changes over time.  

However, growth theory analyzes the relationship between the macro-dynamics and technological change and over 

the years, different growth models have been developed to account for and sustain the emergence and diffusion of 

technical change effects and the acceleration of economic growth, employment dynamics, capital stock among 

others (Llerena & Lorentz, 2004). 

World Bank (1993) pointed out that endogenous growth models laid emphasis on international trade posits posit that 

due to diffusion of knowledge already existing in developed countries, high productivity growth is feasible in 

initially developing economies. However, the relatively underdeveloped resources in developing countries offer an 

opportunity to be exploited. In the newly industrialized Asian countries, faster capital growth otherwise known as 

accelerated growth could be accounted for by closing the gap between best and actual practice. 

In basic Solow model, there has been a long run constant growth rate with stable equilibrium. However, the 

assumption of neoclassical analytical representation of production function comprises Inada conditions, diminution 

marginal return to all input, and constant returns to scale and other levels of substitution among them. In the 



www.cribfb.com/journal/index.php/aesr                 American Economic & Social Review                Vol. 3, No. 1; 2018 

19 

 

inception of the Solow model, the technological growth and population growth rate were simply exogenous, taken 

for example a constant savings rate with the propensity that every economy always trades in the path of Iso-savings 

curve (Milton, Ricardo, & Eliezer, 2005). 

Despite the novelty of Solow growth model, it has some shortcomings, one of the significant limitations of the 

model is its premise or assumption of a closed economy with the convergence assertion or hypothesis that 

presupposes a group of heterogeneous countries with no type of interrelationship. Even though it has been argued 

that there is no model with no untrue assumption, but this can be verifiable if the end result of such model can 

validate the basic and working assumption. In addition to the proposition of the Solow growth model with a closed 

economy assumption, Barro, Mankiw and Sala-Martin (1995) made some significant attempt in construction an 

open economy growth model.  

Another notable shortcoming of the Solow growth model implicitly divergence of income share from capital from 

the output of the estimated model and national account information. That is, the unsynchronized share of income 

from capital and the national accounting information, however, this was the brain behind the attempt by Lucas 

(1988) to eliminate this problem by incorporating both physical and human (like education) resources into the 

concept of capital. Thirdly on the limitations of Solow growth model lies the infinitesimal low estimated 

convergence rate, though the convergence rate has been impacted by the modification of the Solow growth model by 

an open economy version of the model such as Ramsy-Cass-Koopmans model with relatively augmented 

convergence rate. The fourth and final shortcomings of the Solow growth model is that technological progress is the 

ultimate factor in determining the level of growth equilibrium of relevant variables in the model (Milton, Ricardo, & 

Eliezer, 2005). 

Nevertheless, given the shortcomings of the Solow growth model, the model laid a strong foundation of growth 

theories in the economic literature with emphasis on the behavior of income growth across countries. Therefore, this 

study utilizes data from cross-country panel to study to verify the validity the Solow growth theories across 

countries as well as ascertain the magnitudes of population, employment and capital stock of growth. On that note, 

this study is organized as follows. Section 1 presents the introductory of dynamics of economic theories; section 2 

presents a brief empirical literature review and underlying analytical underpinning of the current study. Section 3 

discusses the theoretical framework with a model specification, and Section 4 presents the result and discussions 

with a conclusion.  

2. Brief Review of Related Literature 

Many researchers have attempted to test for the validity of the Solow neoclassical growth model in recent times, and 

notable among them is work of Mankiw, Romer, and Weil (1992). This study pointed out that with the introduction 

of the human capital variable in the model, the data will be well fitted with lend credence to the divergence in 

income disparities across countries. This study utilized new econometric methodology to provide new evidence on 

the behavior of income disparities across countries using time series data. Just as Romer and Weil (1992), Hoeffler 

(2002) used cross-country panel with OLS and fixed effect model to test for the validity of Solow growth model. 

The study also employed instrumental variables (IV), system and first-differenced GMM technique, the study 

revealed that the augmented Solow model is better explained by system GMM estimator, and thus concluded that 

poor growth performance of Sub-Saharan Africa is completely accounted for by augmented Solow model.  

Durlauf, Kourtellos and Minkin (2001) in testing for the validity of Solow growth model using a general growth 

function or equation highlighted that the assumption of identical Cobb-Douglas production technology is 

unsatisfactory when analyzing cross-country. Related to this findings is Duffy and Papageorgiou (2000) who found 

alternative production function more satisfactory than the standard Cobb-Douglas production. However, Durlauf et 

al. (2001) also noted that strong heterogeneity is more evidenced in poorer countries in comparison with other richer 

countries with high tendencies of omitted variables in the nonlinear growth process. The result also revealed that 

higher income per capita countries is associated or linked with the highest coefficient which is evidenced in the 

unstable physical capital. The estimation result equally showed low values in growth rate in poor countries as a 

result of some omitted variables that was not captured by Solow model specification.  

Murthy and Chien (1997) in the empirics of economic growth for OECD countries extended the Solow model by 

reexamining the augmented Solow model and adding a better measure of human capital, physical capital, and 

advancement in technological variables. This study showed that there is a high rate of convergence in OECD 

countries when optimal policies in human capital development and trade are enacted with a concomitant increase in 

savings. Similar to this study is Lee and Smith (1997) who employed panel data econometric analysis in 

investigating the empirical study of stochastic Solow model with emphasis on growth and convergence of multiple 

economies. However, the study showed that technical issues that are inherent in cross-sectional approach can be 

solved by panel analysis. Also evidenced in the study is the conclusion of heterogeneous convergence speed and 

inconsistent parameter in growth effects when a dynamic panel is utilized. 



www.cribfb.com/journal/index.php/aesr                 American Economic & Social Review                Vol. 3, No. 1; 2018 

20 

 

Nevertheless, Easterly & Levine (2001) in analyzing the stylized facts of growth models using growth accounting 

method found a high variation in the residuals of Solow model with relevance of efficiencies in the government 

policy, instrument framework vis-à-vis other structural and social infrastructures as prerequisites for cross-country 

accumulation of capital variation. Moreover, Ding and Knight (2009) studied the validity of the augmented Solow 

model in relation to economic growth in China using cross-country panel data of 146 countries. The estimation 

result from the GMM adopted showed that the augmented Solow growth model with structural change and human 

capital development impact significantly on economic growth. Laying more emphasis on the Chinese economy, the 

study equally revealed that rapid growth rate in China is attributable to huge investment in the physical capital with 

a concomitant change in employment and structural output and policy of low population growth.  

Sumer (2012) tested for the joint validity of economic growth models introduced by Solow, Harrod-Domar, Barro 

and Romer using seemingly unrelated regression (SUR) model in Turkey with annual data ranging from 1980 to 

2010. This study revealed that public expenditure is one of the major sources of economic growth in Turkey. The 

study validated the Barro model in Turkish economy by concluding that government intervention, public demand, 

and efficient economic structures stimulate economic growth towards steady-state.  

3. Methodology 

Solow (1956) theoretically nested the basic growth framework of which recent studies on growth models are built 

upon. Also, Romer, Mankiw, and Weil (1992) augmented the basic Solow growth model by introducing human 

capital into the Model. However, highlights of the basic and augmented Solow models are presented below.  

The basic Solow growth model employed the neoclassical production function which state that per capita income 

growth is caused by the physical stock of capital (K), the stock of labour (L), and technological change (A) as 

represented in equation 1.1 below.with an exogenous growth rate of labour n as represented in equation 1.1 and 1.2 

respectively. 

   

where: Y is output, K is capital, L is labour and A is knowledge or effective labour. 

Note that the growth rate of labour n is exogenous as in equation 1.2 below: 

n

L

L




 …………………………………………………………………..…………………………..1.2 

Also, the amount of national income save which equals investment is known as physical capital stock as shown in 

equation 1.3 below: 


K (t) = S(t) –  K(t) …………………………………………………………..………………….1.3 

where: 


K (t) is the growth rate of capital stock, S(t) is the savings, K(t) is the actual capital stock, and α is the 

capital depreciation rate.  

However, adding technological shift into production function gives equation 1.4 which shows further growth in per 

capita income can be stimulated in an economy that has reached steady-state through incorporating technological 

progress. 

 )()()()( 1 tAtLtKtY    ……………….………………………………………………1.4 

where: o<α<1, A(t) captures technical shift and it is assumed to be exogenous at the growth rate of g.  

Therefore, the central logarithmic equation of the basic Solow model is given in equation 1.5 as follows: 

gtoALgnLSLtYL nnnn 





 )()(
11

)( 







…………….………………..1.5 

The above equation 1.5 states that the depreciation rate (ɑ), the labour exogenous growth rate (g), the initial state of 

technology A(o) and the savings rate (s) determine the growth rate of per capita income. 

Romer, Mankiw and Weil (1992) in their augmented Solow growth model modified the equation 1.5 by including 

the human capital into the aggregate production function as shown in equation 1.6 below: 

)()()()( 1 tAHtLtKtY B  …………………………………………………………….1.6 

While the physical capital per capita growth is shown as: 

           )()()()( tKrgntYStK k   …………………………………………………………..1.7 

 where: SK = is the income share of physical capital production and r is the rental rate of capital. Therefore, the 

logarithmic transformation of the function of augmented Solow growth model is given in equation 1.8 below: 



www.cribfb.com/journal/index.php/aesr                 American Economic & Social Review                Vol. 3, No. 1; 2018 

21 

 

         )(
1

rgnLSL nkn 






………………………………………………………………1.8 

Given the above theoretical framework based on basic and augmented Solow growth model, this study shall employ 

the following modified model to test for the validity of the Solow model using cross-country panel data: 

         itititititn CKEMPPOPRGDPOL   3210 ……………...………………….1.9 

Where: RGDPO is the output-side of the real GDP, POP is the population, EMP is the employment, and CK is 

capital accumulation. Also, Ln is the natural logarithm and  is the stochastic error term, while the subscript it 

represents the time series panel. The study will employ panel OLS random effect to test for the validity of the Solow 

growth model using cross-country annual panel data.  

4. The Result, Discussion, and Conclusion 

This section presents the result, analyze and discuss the output from the estimation. Before the result is presented, it 

is imperative here to present the summary statistics of variables of interest as specified in the empirical model 

(equation 1.9) above.  

 

Table 1.The Summary Statistics of Variable of Interest 

Variable Mean Std. Dev. Min Max Observations 

rgdpo overall 242850.9 902614.9 122.2258 1.32e+07 N = 6535 

between 902614.9 122.2258 1.32e+07 n = 6535  

within 0 242850.9 242850.9 T = 1  

pop overall 32.16035 118.4157 .040731 1324.353 N = 6535 

between 118.4157 .040731 1324.353 n = 6535  

within 0 32.16035 32.16035 T = 1  

emp overall 14.8108 59.87839 .023815 784.4269 N = 6040 

between 59.96964 .023815 784.4269 n = 6021  

within .0792873 13.32098 16.25312 T = 1.00316  

ck overall 696684.4 2744717 60.60447 4.53e+07 N = 6535 

between 2744717 60.60447 4.53e+07 n = 6535  

within 0 696684.4 696684.4 T = 1  

Source: Computed by the Author Using STATA 13.0 Econometric Software 

 

The Table 1. above is self-explanatory showing the overall variables of interest with the corresponding mean, 

standard deviation, minimum, maximum and observation within and within values.  

 

Table 2. The Estimation Output of the Panel Regression 

rgdpo Coef. Std. Err. t P>t [95% Conf. Interval] 

pop 1266.085 83.22248 15.21 0.000 1102.94 1429.231 

emp -847.8773 173.9049 -4.88 0.000 -1188.793 -506.9613 

ck .3058931 .000823 371.66 0.000 .3042796 .3075065 

_cons 688.5399 2164.773 0.32 0.750 -3555.191 4932.271 

R-Squared = 0.97     Adjusted R-Squared = 0.97     Prob>F = 0.000 

Source: Computed by the Author Using STATA 13.0 Econometric Software 

 

From the estimated output in Table 2, the result shows that all statistics/variables conform to the expectations of the 

Solow growth model. The population growth and capital stock are all positively impacting on the output. The 

employment variable is not positive and negatively affecting the output of the estimation though it is not an 

important variable in the model as pointed out in the theoretical framework of the Solow growth model. Also, the 

values of R-Squared and Adjusted R-Squared reveal relatively best fit, but not necessary while dealing with panel 

analysis. Consequently, despite the fact that all other variables conform to the Solow theoretical apriori expectation, 

with employment influencing the growth negatively, the result still validates the postulations of the Solow growth 

model.   

 

 



www.cribfb.com/journal/index.php/aesr                 American Economic & Social Review                Vol. 3, No. 1; 2018 

22 

 

References 

Barro, R. J., Mankiw, G. N. and Sala-I-Martin, X. (1995). Capital Mobility in Neoclassical Models  of 

Growth,  American Economic Review, 85, 103 – 15. 

Ding, S. and Knight, J. (2009). Can the augmented Solow Model explain China’s remarkable economic 

growth? A Cross-Country Panel Data Analysis. Journal of Comparative  Economics, 37, 432-452. 

Duffy, J. and Papageorgiou, C. (2000). A Cross-Country Empirical Investigation of the  Aggregate Production 

Function Specification. Journal of Economic Growth, 5, 87-120. 

Durlauf, S. N., Kourtellos, A. and Minkin, A. (2001). The local Solow growth model. European  Economic 

Review, 45, 928 – 940. 

Easterly, W. and Levine, R. (2001). It is not factor Accumulation stylized facts and growth models. 

 Working Papers Central Bank of Chile. 

Hoeffler, A. (2002). The augmented Solow model and the African growth debate. Oxford Bulletin of Economics 

and Statistics, 64, 135 – 158. 

Llerena, P., and Lorentz, A. (2004). Alternative Theories of Economic Growth and Co-Evaluation of Macro-

Dynamics and Technological Change: A Survey. Laboratory Economics and  Management (LEM), 

Working Paper Series.  

Lucas, R. (1988). On the Mechanics of Economic Development, Journal of Monetary Economics,  22, 3–42. 

Mankiw, N. G., Romer, D., and Weil, D. N. (1992). A Contribution to the Empirics of  Economic Growth, 

Quarterly Journal of Economics, 58, 407–437. 

Milton, B. F., Ricardo, G. S., and Eliezer, M. D. (2005). The Empirics of the Solow Growth  Model: Long-

term evidence. Journal of Applied Economics, Vol. 8(1), 31-51 

Murthy, V. N. and Chien, I. (1997). The Empirics of Economic Growth for OECD Countries:  Some New 

Findings. Economics letters, 55, 425 – 429. 

Sumer, K. K. (2012). Testing the Validity of Economic Growth Theories with Seemingly  Unrelated Regression 

Models: Application to Turkey in 1980-2010. Applied Econometrics and International Development, 

12(1), 63 – 72. 

 

 

 

Copyrights 

Copyright for this article is retained by the author(s), with first publication rights granted to the journal. 

This is an open-access article distributed under the terms and conditions of the Creative Commons Attribution 

license (http://creativecommons.org/licenses/by/4.0/) 

 


