Managing Growth in Miniature: Solow's Model as an Artifact by Verena Halsmayer

The aim of this paper is to analyse Solow's model, introducing the consideration that steady state labour productivity (in efficiency units) and its determinans are not constant values, for a country over a given period of time. They are, in fact, time series with unit roots. First, the paper shows that Solow's model can be interpreted as an error correction model and it could be consistent with the stochastic nature of the variables. Secondly, implications about integration and coinstegration of the relevant series are tested. We use data coming from four countries over the period 1960-88. The error correction mechanism implied by Solow's model never appers to have been operative: convergence of current productivity towards its (stochastic) steady state path does not emerge in any considered case.

The subject of this research is the Solow Growth Model. The relevance is substantiated by the fact that the Solow Growth Model is conceptually simple, and simultaneously it can be complicated with clarifications and additions. The authors believe that one of such clarification is consideration of the demand as a stochastic variable. The goal of this research is to propose a model that takes into account the random nature of consumer demand based on the Solow Growth Model. The article aims to examine the Solow Growth model; conduct a literature overview of the most common modifications of the model; analyze the well-known modifications and complications of the model; outline the methods of such modifications and complications; offer Solow Growth Model supplemented with microeconomic substantiation with consideration of the stochastic demand. The article employs the methods of analysis, synthesis, comparison, and differential calculus. The novelty lies in the statement  that consumption depends on demand; it is intuitively obvious that demand can be considered as stochastic variable. This is explained by the individual traits of the consumers. Therefore, the demand can be described via stochastic differential equation based on the standard Wiener process (analogy with Brownian motion). The article offers a stochastic differential equation of demand. The Solow Growth Model is supplemented with the stochastic differential equation of demand. In conclusion, the authors determine the key modification and complication trends of the Solow Growth Model; developed the model based on the Solow Growth Model with the stochastic differential equation of demand as its addition. Further research should be aimed at solution of the obtained mathematical model supplemented with the stochastic differential equation of demand.

PurposeThe principal aim of this paper is to review three basic theoretical growth models, namely the Harrod-Domar model, the Solow model and the Ramsey model, and examine their implications for economic policies.Design/methodology/approachThe paper utilizes a positivist research framework that emphasizes the causal relationships between the variables in each of the three models. Mathematical methods are employed to formulate and examine the three models under study. Since the paper is theoretical, it does not use any empirical data although numerical illustrations are provided whenever they are appropriate.FindingsThe Harrod-Domar model explains why countries with high rates of saving may also enjoy high rate of economic growth. Both the Solow and Ramsey models can be used to explain the medium-income trap. The paper examines the impact of Covid shocks on the macroeconomy. While the growth rate can be recovered, it may not always possible to recover the output level.Research limitations/implicationsFor the Harrod-Domar model, the public spending decreases the private consumption at the period 1, but there is no change in the capital stock and hence the production in subsequent periods. For the Ramsey model with AK production function, both the private consumption and the outputs will be lowered. In both the Harrod-Domar and Ramsey models with Cobb-Douglas production function, if the debt is not high and the interest rate is sufficiently low, it is better to use public debt for production rather than for consumption. If the country borrows to recover the Total Factor Productivity after the Covid pandemic, both the Harrod-Domar and Ramsey models with Cobb-Douglas production function show that the rate of growth is higher for the year just after the pandemic but is the same as before the pandemic.Practical implicationsThe economy can recover the growth rate after a Covid shock, but the recovery process will generally take many periods.Social implicationsThis paper focuses on economic implications and does not aim to examine social implications of policy changes or Covid-type shock.Originality/valueThe paper provides a comparison of three basic growth models with respect to public spending, public debts and repayments and Covid-type shocks.

Investigating the factors effective on economic growth is of great importance for most economists. Although lots of studies have been done on economic growth in the world, it has less been regarded in Iran. In this article, by estimating growth regression, we attempt to investigate the supply side of economic growth in Iran. Then we compare the predictive results of Fuzzy-logic, Neural-Fuzzy and Solow models. The results show that there was negative significant relationship (i.e.–0.035) between unstable policy and economic growth rate in Iran during investigation period (1959–2001). In this model, the effect of expenses used by government is positive (i.e. 0.01). Furthermore, the estimated results of long term relationship show that the variable coefficients of capital, labor power, exportation, and inflation are 0.319, 0.016, 0.001, and–0.001, respectively. And also by comparing the predictive results of models for the average percent of annual growth, it is predicted that the average percent of Solow, Neural-Fuzzy, and Fuzzy-logic models are 7.17%, 5.92%, and 6.46% for 2002–2006, respectively. Evaluation of results from the models on the basis of criteria shows that model Neural-Fuzzy predicts better than Fuzzy-logic and Solow models. In other words, forecasting by the model Neural-Fuzzy is recommended.

This paper provides evidence of a problem with the influential testing and assessment of Solow's (1956) growth model proposed by Mankiw et al. (1992). It is shown that when the assumption of a common rate of technical progress is relaxed in the neoclassical model, the goodness of fit of Mankiw et al.’s equation improves dramatically. However, and more importantly, it is shown that this result, as well as the magnitude of estimates obtained, merely reflects a statistical artifact. This has serious implications for the possibility of actually testing Solow's growth model.

We discuss the role of the elasticity of substitution in the local determinacy properties of a steady state or a stationary balanced growth path in a general multisector economy with CES technologies. Our main results are the following: We give some sufficient conditions for the occurrence of local indeterminacy in exogenous and endogenous growth models. We show that local indeterminacy takes place even without a capital intensity reversal from the private to the social level if the productive factors are weakly substitutable. Moreover, we show that the conditions for local indeterminacy in exogenous growth models and in endogenous growth models may be qualitatively different.

This paper examines the implications of a monetary human capital investment endogenous growth model for aggregate economic fluctuations. In addition, an exogenous growth model with a similar human capital investment specification is included in the analysis to compare the business cycle properties of the endogenous growth model with that of the exogenous growth model. The money introduced into the models allows for the liquidity effects. It is found that both the endogenous and exogenous human capital investment growth models are able to capture the business cycle properties of U.S. data closely. Some sensitivity analysis results are provided. The theory predicts that the stochastic properties of the human capital shocks affect the ability of the models to generate the business cycle facts.

After more than forty years studying growth, there are two classes of growth models that have emerged: exogenous and endogenous growth models. Since both try to mimic the same set of long-run stylized facts, they are observationally equivalent in some respects. Our goals in this paper are twofold. First, we discuss the time-series properties of growth models in a way that is useful for assessing their fit to the data. Second, we investigate whether these two models successfully conform to post-war U.S. data. We use cointegration techniques to estimate and test long-run capital elasticities, exogeneity tests to investigate the exogeneity status of TFP, and Granger-causality tests to examine temporal precedence of TFP with respect to infrastructure expenditures. The empirical evidence is robust in confirming the existence of a unity long-run capital elasticity. The analysis of TFP reveals that it is not weakly exogenous in the exogenous growth model. Granger-causality test results show unequivocally that there is no evidence that TFP for both models precede infrastructure expenditures not being preceded by it. On the contrary, we find some evidence that infrastructure investment precedes TFP. Our estimated impact of infrastructure on TFP lay roughly in the interval (0.19, 0.27).

After Harrod and Domar independently developed a dynamic Keynesian circular flow model to illustrate the instability of a growing economy, mainstream economists quickly reduced their model to a supply side-only growth model, which they subsequently rejected as too simplistic and replaced with Solow's neoclassical growth model. The rejection process of first diminishing the model and then replaced it with a neoclassical alternative was similar to how the full Keynesian macroeconomic paradigm was diminished into IS-LM analysis and then replaced by a simplistic neoclassical framework that largely ignored the demand side of the economy. Furthermore, subsequent work by mainstream economists has resulted in a logically inconsistent framework for analyzing economic growth; the popular endogenous growth models, which use Schumpeter's concept of profit-driven creative destruction to explain the technological change that Solow left as exogenous, are not logically compatible with the Solow model.

The relevance of the study is to identify the accuracy of the estimate obtained by the A2C algorithm, as well as the need for verification of reinforcement learning when working with optimization of economic processes. The purpose of the study was to analyze the effectiveness of the A2C algorithm, along with the specifics of its implementation, in solving optimization economic problems. The tasks considered were maximizing consumption in the Solow, Romer and Schumpeterian models of endogenous economic growth, and maximizing per capita income in the latter two, according to the consumption rate (in the latter two – saving rate) and the share of scientists in the economy, respectively. The results showed that for deterministic models (Solow model, Romer model), the variance of the parameter estimate is minimal and the average differs from the value obtained analytically by no more than a thousandth part with a sufficiently high number of time periods in the model. Nevertheless, in stochastic models (the Schumpeterian model), firstly, a high number of time periods in the model is required to match the estimate to the value obtained analytically, and secondly, the estimate obtained in this way, although biased by no more than a thousandth of a fraction, has a high variance.

The two‐level CES aggregate production function—that nests a CES into another CES function—has recently been used extensively in theoretical and empirical applications of macroeconomics. We examine the theoretical properties of this production technology and establish existence and stability conditions of steady states under the Solow and Diamond growth models. It is shown that in the Solow model the sufficient condition for a steady state is fulfilled for a wide range of substitution parameter values. This is in sharp contrast with the two‐factor Solow model, where only an elasticity of substitution equal to one is sufficient to guarantee the existence of a steady state. In the Diamond model, multiple equilibria can occur when the aggregate elasticity of substitution is lower than the capital share. Moreover, it is shown that for high initial levels of capital and factor substitutability, the effect of a further increase in a substitution parameter on the steady state depends on capital–skill complementarity.

Previous frequentist research exploring the Solow growth model and its MRW specification has grappled with persistent challenges such as multicollinearity and reverse causality inherent in neoclassical growth models. This study aims to showcase the Bayesian approach’s advantages in determining whether the Solow or MRW model better explains income variations across advanced countries. To this end, we apply a hybrid Metropolis-Hastings algorithm within the Bayesian non-linear framework to a panel of 38 advanced countries from 1970 to 2019. The results yield significant insights: Firstly, by integrating informative priors that capture prior beliefs on variable interactions, Bayesian inference effectively addresses potential multicollinearity and reverse causation. Secondly, Bayesian estimation introduces valuable shrinkage effects that enhance estimation accuracy. When subject to Bayesian shrinkage, broad capital elasticities more closely align with true values, highlighting the influence of technological advancement and latent factors often overlooked by traditional observation. Lastly, our analysis reveals that the augmented MRW model, accounting for heterogeneous technology growth and depreciation rates, is the best fit. This study provides a reliable empirical foundation for shaping comprehensive policies aimed at fostering sustained economic growth through technological progress alongside the accumulation of physical and human capital.

We extend the Solow growth model with human capital and migration flows by introducing public capital subjected to congestion as an essential input in the production function. This is an important novelty given that population variation induced by migration affects factors productivity and, hence, growth. We show that, in general, the impact on physical and public capital growth induced by migration is ambiguous and depends on the degree of public capital congestion. As regards the human capital growth rate, not only does it depends on the congestion externality linked to public capital, but also on the relative human capital endowment of migrants with respect to resident population. Moreover, the long-run per capita growth rate coincides with the exogenous technological progress growth rate only when public capital is not congested. In the general case in which congestion affects public capital, the long rungrowth rate differs from the traditional Solow model and could even be negative. Finally, we analyse the transitional dynamics and derive the conditional convergence equation for the growth rate of per capita income.

본 논문은 유사한 재난발생이라도 국가에 따라 상이한 경제적 영향을 미칠 수 있음에 주목하고 그 거시적 메커니즘을 이론적으로 규명하고 있다. 재난이 국가나 지역의 경제상황에 따라 다른 파급영향을 미칠 수 있음에 착안하여, 대표적인 경제성장분석모형인 솔로우 성장모형을 통해 재난 발생이 국가나 지역의 경제성장에 어떤 영향을 미치는지 고찰한다. 본 연구의 방법론으로 활용된 솔로우 성장모형은 대표적인 신고전적 성장이론의 하나로서, 재난이 국가나 지역경제에 미치는 영향을 시 공간적 맥락에서 구조적으로 파악하기에 유용한 틀을 제시해줄 수 있다고 판단하였다. 솔로우 모형에서 경제성장은 자본의 증가, 노동투입 증가 그리고 기술 진보라는 세 가지 핵심 요소에 의해 이루어진다고 가정한다. 솔로우 모형을 통해 재난이 국가나 지역의 경제성장에 미치는 영향을 단순화시키고 핵심 요소들이 시공간적으로 어떻게 변화하는지 살펴본다. 솔로우 모형 적용결과 재난 이후 저축률 감소와 재난의 시공간적 불평등성이 발생하고, 경제수준에 따른 빈곤의 덫이 존재하는 것으로 나타났다.This article attempts to examine the impacts of disasters on economic growth with the application of the Solow growth model. The paper employs the Solow growth model as a methodology, which represents a neoclassical growth theory in economics. The key idea of this research begins with the assumption that the degree of disaster damage differs across the countries as they have different socioeconomic systems in the spatiotemporal context. In the Solow growth model, it is assumed that there are three main causes of economic growth; increase in the stock of capital, growth in labor input and technological progress. This research has a theoretical basis on the hypothesis that disasters have a strong influence on the national or regional economic system. The results support that the disastrous effects on economic growth depend on the economic status of countries or regions. In addition, the Solow growth model reveals economic inequality in the impacts of disasters.

The dynamics of capital accumulation in Marx and Solow