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Robustness of Equations of the Process of Economic Growth - Robustezza delle equazioni del processo di crescita economica

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  • Qayum, Abdul

    ()
    (Portland State University Economics - Liberal Arts & Sciences)

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    Abstract

    Economic growth is driven by the process of accumulation of the dominant resource expressed by an ordinary differential equation. This equation is studied in the models of Harrod (1939), Solow (1956), Lucas (1988), Romer (1990), and Grossman and Helpman (1991). The equations of the first three are robust, but not of the last two. The paper suggests an essential correction and a uniform procedure for formulating the equations. The paper also considers endogeneity in the first two models, with capital as the dominant resource, and empirical robustness of the last three with human capital and knowledge as the dominant resources. An economic growth model with the long run growth rate given from outside is considered as exogenous. It is defined as endogenous when the longrun rate of growth is determined from within by the solution of the system of equations of the model which describe the sources and causes of growth. Among these, there is usually one dominant source which is the main driving force in the process of growth. This may be physical capital, physical capital per effective worker, human capital, knowledge, or number of innovations. The equation of the process of economic growth expresses the process of accumulation of the variable representing the dominant source of growth by an ordinary linear differential equation. This paper studies the equations of the process of economic growth in the five outstanding contributions by Harrod (1939), Solow (1956), Lucas (1988), Romer (1990) and Grossman and Helpman (1991). Of these the first two contributions are not known as presenting endogenous models. It is argued here that the model in the first contribution is as endogenous as any other model and in the second, the model is not as exogenous as it has been made out to be. The models in the first two contributions do not express specifically the equations of the process of growth, but they can be tracked easily. The third contribution by Lucas presents a plausible equation of the process of growth with the possibility of being empirically verified. The equations in the last two contributions by Romer and Grossman and Helpman are not theoretically plausible or empirically verifiable. The aim of this paper is to point out the flaw in the formulation of the equation of the process of growth in the models of these two contributions and to suggest much needed correction to make them theoretically plausible and to set them free from the possibility of their being highly explosive and unstable. - La crescita economica è guidata dal processo di accumulazione della “risorsa dominante” espresso da un’equazione differenziale lineare ordinaria. Tale equazione è stata studiata nei modelli di Harrod (1939), Solow (1956), Lucas (1988), Romer (1990) e Grossman e Helpman (1991). Nei primi tre casi le equazioni risultano essere robuste, non così per Romer e per Grossman e Helpman. In questo studio si suggerisce una modifica essenziale e una procedura uniforme per la formulazione di queste equazioni. Nei primi due modelli, inoltre, viene considerata l’endogenicità e il capitale è assunto come “risorsa dominante”, mentre per gli altri tre viene considerata la robustezza empirica, con capitale umano e conoscenza come “risorse dominanti”. Un modello di crescita economica con tasso di lungo periodo dato dall’esterno è considerato esogeno. Si parla invece di modello endogeno quando tale tasso è determinato tramite la soluzione di un sistema di equazioni che descrivono le fonti e le cause che originano la crescita. Tra queste generalmente una è dominante e traina il processo di crescita. Tale fonte può essere il capitale, il capitale fisico per lavoratore, il capitale umano, la conoscenza o l’innovazione. L’equazione della crescita esprime il processo di accumulazione della variabile che rappresenta la fonte dominante della crescita stessa, tramite un’equazione differenziale lineare ordinaria. Questo studio esamina le equazioni dei processi di crescita descritte nei cinque importanti lavori di Harrod (1939), Solow (1956), Lucas (1988), Romer (1990) e Grossman e Helpman (1991). Tra questi, è noto che i primi due non presentano modelli di tipo endogeno. Nel nostro studio sosteniamo che in Harrod il modello è endogeno come qualunque altro modello, mentre il modello di Solow non è in realtà esogeno come generalmente ritenuto. Questi due modelli non esprimono specificamente le equazioni della crescita, sebbene esse si possano facilmente intuire. Il contributo di Lucas presenta un’equazione plausibile che, inoltre, può essere empiricamente verificata. Le equazioni di Romer e di Grossman e Helpman non sono teoricamente plausibili né empiricamente verificabili. Lo scopo di questo studio è evidenziare le criticità presenti nelle equazioni della crescita formulate da Romer e da Grossman e Helpman e suggerire le modifiche necessarie per renderle teoricamente plausibili e prive dei problemi di esplosività e di instabilità.

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    Bibliographic Info

    Article provided by Camera di Commercio di Genova in its journal Economia Internazionale / International Economics.

    Volume (Year): 63 (2010)
    Issue (Month): 4 ()
    Pages: 407-421

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    Handle: RePEc:ris:ecoint:0604

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    Keywords: Dynamic Equations; Equilibrium Growth; Steady State; Human Capital; Knowledge Capital; Innovations;

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    1. Romer, Paul M, 1987. "Growth Based on Increasing Returns Due to Specialization," American Economic Review, American Economic Association, vol. 77(2), pages 56-62, May.
    2. Jones, Charles I, 1995. "Time Series Tests of Endogenous Growth Models," The Quarterly Journal of Economics, MIT Press, vol. 110(2), pages 495-525, May.
    3. Paul M Romer, 1999. "Increasing Returns and Long-Run Growth," Levine's Working Paper Archive 2232, David K. Levine.
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