Empirical evidence of Goodwin’s growth cycle in

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1. Introduction

Employment is an important determinant in the macroeconomic theories of growth and the distribution cycle. While the classical economy is considered capital scarce from the perspective of Leontief, it is seen as labour constrained in the Marxian view (Barrales‐Ruiz, Mendieta‐Muñoz, Rada, Tavani, & Von Arnim, 2021). In this context, the share of income between capitalists and labourers is an important aspect of economic distribution. The level of employment increases wages bill and reduces the share of profit. Therefore, wage share and employment rate are important constituents in determining distribution in the growth cycle. A theory based on these attributes would thus significantly contribute to our understanding of the dynamics of capitalist economies.

Goodwin (1967), the main proponent of the growth cycle, was inspired by Marx’s writing on “The General Law of Capitalist Accumulation” in Capital Vol. 1. The constant conflict between wage and profit, and the complementarity of labour with capital determines the growth cycle. This bi-variate relationship between employment rate and wage share leads to the establishment of a profit-led growth cycle. Furthermore, the determination of the periodic movement between the employment rate and wage share depends on some specific variables, namely labour productivity, workforce and capital-income ratio.

Several seminal works on the Goodwin cycle have served to further strengthen the theoretical research on this phenomenon (Skott, 1989; Desai, Henry, Mosley, & Pemberton, 2006; Veneziani & Mohun, 2006; Sasaki, 2013; von Arnim & Barrales, 2015; Dávila-Fernández & Libânio, 2016). However, most empirical works have mostly been dedicated to analysing advanced nations (Harvie, 2000; Grasselli & Maheshwari, 2018; Barrales & von Arnim, 2017; Flaschel, 2010). Harvie (2000) studied 10 OECD countries to find that the results of the original Goodwin model deviated from the empirical estimations. However, Grasselli and Maheshwari (2018) relaxed one specific assumption of the Goodwin model – the unitary investment to profit ratio. Subsequently, they estimated the modified Goodwin model in 10 OECD countries and found the results of the neo-Goodwin model to be closer to the empirical estimates. However, empirical study on the Goodwin cycle in relation to emerging countries is scanty (García Molina & Herrera Medina, 2010; Moura & Ribeiro, 2013). Both the studies based on Harvie (2000) method found that the original Goodwin model was not a true predictor of the data drawn from developing nations. There are two plausible reasons for this. First, the theoretical assumption of the Goodwin model considers a unitary investment to profit ratio. In other words, this model assumes that while all profits are invested, producers may retain some of it and invest the rest. Grasselli and Maheshwari (2018) named this the capital accumulation rate and incorporated this variable into their model. This neo-Goodwin (modified) model was able to truly predict the actual data in 10 OECD countries. Second, this model is applicable in the capitalistic nature of economy. However, the institutional setup for capitalism in the emerging economies is highly diverse. As a result, it is not astonishing that the capitalistic mode of production and distribution is not fully mature in emerging economy like India. This is because a considerable amount of the labour force in these countries is engaged in the agriculture sector, which is not a capitalistic mode of production, be it in terms of ownership or market exposure (Basu & Das, 2016). Moreover, the Indian industrial sector is dominated by the unorganised sector, which contributes a massive share of home production and family labour (Marjit & Kar, 2009). However, the fact that capitalism has not fully grown in the country does not mean it is trivial in India. For instance, the organised manufacturing sector in India, which is a subset of the capitalistic set up, comprises 10 million labourers employed in 2,22,120 factories that produced 10% of the Indian GDP in 2013, indicating that the country became more capitalistic during the neo-liberal regime post-1991 (Basu & Das, 2018). The service sector cannot considered because Barrales-Ruiz et al. (2021) have the opinion that labourers in the service sector are not labourers from the Marxian view, which can only earn wages and this model is based on Marxian idea (Goodwin, 1967).

The theoretical underpinnings, empirical differences and capitalistic nature of Indian organised manufacturing industries, as described above, motivated us to examine the Goodwin cycle in terms of the Indian economy. For this purpose, data were derived from the Annual Survey of Industries in the Indian economy from 1980 to 2018. Subsequently, although the empirical results were found to deviate from the main Goodwin model, they were closer to the neo-Goodwin model. The labour market-led and cost (supply-side) effect conditions of the Goodwin cycle were also verified. Lastly, the profit-led regime of the Goodwin cycle was confirmed through graphical depiction.

The rest of this paper is organised as follows: Section 2 explains Goodwin’s theory, presents an overview of the empirical literature and identifies the relevant research gaps. Section 3, explains mathematical model and econometric methodology used for the computation of the Goodwin model. Section 5 describes the data and analyses the empirical result. Lastly, Section 6 offers the concluding remarks.

2. Literature review

The literature review consists of the theoretical foundation and empirical findings of the Gooodwin model. The theoretical background of Goodwin's growth cycle is derived from Marx's Capital Vol. 1. It is a periodic relationship between labourers and wages. Literature of the Goodwin cycle is proceeded by the extension of the theoretical model. The empirical literature computed the Goodwin model through different mathematical and econometrics techniques.

2.1 Goodwin’s theory

The theoretical motivation of Goodwin cycle draws on the classical growth cycle. It originates from “The General Law of Capitalist Accumulation” of Marx’s Capital Vol. 1, where the cyclical relationship between wage and labourers is described by Marx as follows: “the general movements of wages are exclusively regulated by the expansion and contraction of the industrial reserve army, and these again correspond to the periodic changes of the industrial cycle” (Marx, 1887, p. 446). The industrial cycle’s periodic movement, involving expansion and contraction phases, is dependent on the wages of workers and the profit from capital. The mechanism of the growth cycle arises from the concept of the distribution of income between capital and labour, which was described by Marx as follows: “In consequence of favourable circumstances…. profits in it, being greater than the average profits, attract additional capital, of course the demand for labour rises and wages also rise. The higher wages ….. glutted with labour power, and wages at length fall again to their average level or below it, ….. It gives place to their emigration” (Marx, 1887, p. 447).

In simpler words, greater profit motivates producers to pursue capital accumulation, which, in turn, requires the employment of labourers in industries. This leads to an increase in wage, which will contribute to reducing the capitalistic share (profit) at the cycle’s peak. Meanwhile, decrease in profits disincentives the capitalist from capital accumulation. Subsequently, employment decreases and wages follow suit till the point where profits again start getting the largest share in the distribution of income, which signifies the trough of a growth cycle. Effectively, this periodic movement continues to operate over time.

In the book titled “Socialism, Capitalism and Economic Growth (1967)”, Goodwin defines the growth cycle as the complementarity of capital to workers, while also describing the inherent class conflict between profit and wages. Higher profitability sows the seeds of one’s own destruction – it leads to an increase in capital, employment and output, which, in turn, strengthens the bargaining power of workers during the upswing of the growth cycle. Subsequently, rising real wages reduces profits, which leads to decreases in capital, employment and output. This represents a downswing, where labour productivity is greater than the real wage rates.

2.2 Empirical literature

Since most studies on the Goodwin growth cycle are an extension of his theoretical model (Skott, 1989; Desai et al., 2006; Veneziani & Mohun, 2006; Sasaki, 2013; von Arnim & Barrales, 2015; Dávila-Fernández & Libânio, 2016), there is a paucity of empirical studies specifically investigating the Goodwin model (Harvie, 2000; Grasselli & Maheshwari, 2018; Barrales & von Arnim, 2017; Flaschel, 2010; García Molina & Herrera Medina, 2010; Moura & Ribeiro, 2013). The econometric estimation of the growth cycle was initially attempted by Harvie (2000), who conducted a study covering 10 OECD countries where the wage share and employment rates were computed and then compared with the data estimates. The growth rates of variable are estimated through log-linear OLS regression and Phillips curve is computed through ARDL model. The results identified a large error in the wage share and employment rate, with the aforementioned variables displaying an anti-clockwise movement in the employment rate and wage share bi-sphere plane. This anti-clockwise movement signifies that the Goodwin cycle follows a profit-led regime. Harvie’s (2000) model was further extended by Grasselli and Maheshwari (2018), who computed a modified wage share and employment rate model. The wage share was modified by the inclusion of the capital accumulation rate, while the employment rate was deflated by 100 in the estimations. They applied same log-linear OLS regression and ARDL model as applied by Harvie (2000). Subsequently, the results showed that the error between the data and the model had reduced substantially. Some researchers also investigated the different regimes of growth cycles, namely the wage-led and profit-led regimes. For instance, Barrales-Ruiz et al. (2021) studied the US economy in terms of the wavelet phase difference and the VAR impulse response function. They identify a negative effect of wage share on economic activity (output gap and employment rate), implying the existence of a profit-led regime and the positive effect of economic activity (output gap and employment rate) on wage share, which symbolises a wage-led regime. Furthermore, Barrales and von Arnim (2017) expanded the existing literature in their study on the US economy, whose major contribution was establishing a distinction between short- and long-run growth cycles, wherein the former analyses the cyclical component of any variable denoting economic activity, but the latter explores the trend component of the same variables. Apart from this, the wavelet analysis conducted in this study and identified a negative covariance between economic activity and wage share. In addition, the phase diagrams of the short-run growth cycle confirmed anti-clockwise movement in the economic activity and wage share in their bi-sphere plane. However, the long-run growth cycle initially moved anti-clockwise (i.e. profit-led regime), and then followed a clockwise movement. Similarly, Flaschel (2010) studied short- and long-run Goodwin’s cycles in US economy through Hodrick and Prescott (HP) filter techniques and two stage least square regression method. The HP filter result showed seven short-run growth cycles in a 50-year period, while the long-run growth cycle exhibited anti-clockwise movement in the employment rate and wage share in the bi-sphere plane. Further, regression result indicate labour market-led and cost-effect condition hold which support existence of Goodwin cycle’s condition in the US economy. Recent literature on Goodwin cycle was contributed by Cauvel (2022) and Bailly, Mortier, and Giraud (2023). Cauvel (2022) investigated the neo-Goodwin model by splitting wage share into wage rate and productivity. The VAR impulse response function result suggest that shock to utilisation rate (output gap) positively affect wage share and shock to wage share negatively affect utilisation rate (output gap). However, Bailly et al. (2023) extended Goodwin cycle with the incorporation of debt to output ratio on the US economy through bootstrap simulation method. The result found that Goodwin cycle exist with the incorporation of debt to output ratio.

Though most of these studies were based on advanced nations, some attempts were made to assess emerging economies. For instance, García Molina and Herrera Medina (2010) studied sets of developed and developing economies using the Harvie (2000) based regression (log-linear OLS and ARDL) model. They noted significant disparity between the data and the model estimates of wage and employment rate. In this context, it should be noted that there are three kinds of movement in the growth cycle – Keynesian (clockwise movement), Goodwin (anti-clockwise movement) and atypical (inconsistent with clockwise and/or anti-clockwise movement). Moura and Ribeiro (2013) studied the Brazilian economy by applying Gompertz–Pareto distribution (GPD) method, and found that although the model value deviated from the data, anti-clockwise movement was observed in the employment rate and wage share bi-sphere plane.

At the same time, while few studies have been conducted on the distribution of income and employment growth in the Indian economy, they are not accordance with the Goodwin cycle theory. For instance, Kannan and Raveendran’s (2009) study of the manufacturing sector revealed that the purchasing power and wage share of workers had shrunk at the expense of an increase in the emoluments of managers. Furthermore, after spending half a decade in the neo-liberal regime, decreases in employment growth and increases in capital intensity were observed. Basu and Das (2018) who applied mathematical model of profit rate decomposition and argued that profit share increased, while the wage share reduced along with the purchasing power and bargaining power of labourers under the neo-liberal regime (1991 onwards). In spite of the wide range of investigations carried out by these studies, the literature is still lacking in a few aspects. First, the periodic movement of the distribution of income in relation to the employment rate has not been explored yet. Second, organised manufacturing industries are considered here because Basu and Das (2018) found that Indian organised manufacturing industries have capitalistic features, and Goodwin (1967) argued that this model is suitable for the capitalistic character of a sector or economy. Hence, this analysis has been conducted on the phases of the growth cycle in Indian industries, which are either wage-led or profit-led. Addressing these research gaps, this papers aims to explore the Goodwin growth cycle in the context of the organised manufacturing industries in India.

3. Mathematical model and econometric methodology

Goodwin defined the growth cycle through a bi-variate differential equations to explain the interdependence between wage share and employment rate. The modified Goodwin model is also introduced through the inculsion of investment to profit ratio. The mathematical model is applied through different econometrics methods like log-linear regression and the Autoregressive distributed lag model.

3.1 Goodwin’s mathematical model

Goodwin’s model represents the bi-variate differential relationship between wage share and employment rate in terms of a given sets of variables. It can be estimated by following equations [1]:(1) $a = a_{0} e^{α t}$ (2) $N = N_{0} e^{β t}$ (3) $σ = \frac{K}{Y}$ (4) $u = \frac{w L}{Y} = \frac{W}{Y}$ (5) $\dot{K} = (1 - u) Y$ (6) $v = \frac{L}{N}$ (7) $\dot{\frac{w}{w}} = - γ + ρ v$

All quantities noted above are expressed in their real and net terms. Furthermore, $a$ refers to labour productivity, that is output to labour ratio; $N$ is the total workforces; $w$ indicates the wage rate, that is wages to labourers ratio; $W$ is the total wage bills; $L$ refers to labourers employment; $v$ is the labourers employment rate; $u$ indicates the labourers share; $1 - u$ is the capitalists share; and $K$ is the capital; $Y$ indicates income; dot refers to change in the variables with time and t is time.

All the above equations are based on assumptions made by Goodwin. Equation (1) represents steady disembodied technical (productivity) growth, Equation (2) refers to the steady growth of workforce, Equation (3) is the constant capital to output ratio, Equation (5) indicates the only two factors of production (capital and labour), with their returns as all wages are consumed and all profits are invested. Equation (7) represents the linear approximation of the Phillips curve, where the real wage rates increase in the neighbourhood of full employment. Notably, Expression (4) and (6) refer to identities.

Subsequently, the growth rates of wage share and employment are expressed as [2]:(8) $\dot{u} = [- (α + γ) + ρ v] u$ (9) $\dot{v} = [\frac{1 - u}{σ} - (α + β)] v$

Furthermore, the partial derivation of change in the wage share and employment rate in Equations (8) and (9) are conducted in the form of a Jacobian matrix, based on the trivial solution of wage-share and employment rate are represented by $u^{*}$ and $v^{*}$ respectively [3].(10) $u^{*} = 1 - (α + β) σ$ (11) $v^{*} = \frac{(α + γ)}{ρ}$

The modified (neo) Goodwin model.

The assumption of Equation (5) – all wages are consumed and all profit are invested – does not hold true in the real world. In other words, the ratio of the investment to the profit does not reach unity, but is mostly less than unity. This means that some portion of the profit is retained by the capitalist. Grasselli and Maheshwari (2018) introduced this concept in the Goodwin model for empirical estimation, naming it the capital accumulation rate. The capital accumulation rate refers to the investment (capital formation) to profit ratio, which lies between 0 to 1. Following Grasselli and Maheshwari (2018), this study introduced the real capital accumulation rate ( $λ$ ) in the calculation of the growth rate of employment, which is subsequently reflected in the wage share.

Hence, the change in employment rate will be ${\dot{v}}^{'}$ , expressed as:(9M) ${\dot{v}}^{'} = [\frac{λ (1 - u)}{σ} - (α + β)] v$

Furthermore, the modified position for the equilibrium wage share will be $u^{#}$ :(10M) $u^{#} = 1 - \frac{(α + β) σ}{k}$ In addition, conditions for the Goodwin cycle were investigated in terms of the bi-variate linear relationship between wage share and employment rate. The positive sign of employment rate in Equation (8) and the negative sign of wage share in Equation (9) confirm the existence of the Goodwin cycle. The alternate sign in this bi-variate cross relationship arises from the off-diagonal elements of the Jacobian matrix in Equation (4A), noted in Appendix.

From Equation (8), the growth rate of the wage share is found to be a positive linear function of the employment rate.(12) $\frac{\dot{u}}{u} = + ρ v$

Moreover, the results of Equation (12) are similar to those of the Phillips curve in Equation (7) [4]. Furthermore, the positive sign of the employment rate is a result of the dominance of real wage movement over nominal wage, which is integral to the functioning of the labour market. Flaschel (2010) used the term labour market-led situation to define such circumstances, where wages share increase as a result of full employment.

On the other hand, from Equation (9), the growth rate of employment rate is found to be a negative linear function of the wage share.(13) $\frac{\dot{v}}{v} = - \frac{1}{σ} u$

The negative sign of the wage share results from the rising wage bill (share), which increases production costs, that ultimately contributes to reduced investment, production and, subsequently, employment. This is referred to as the cost effect by Flaschel (2010). Notably, Goodwin and his followers believe in this supply side (cost effect) idea.

3.2 Econometric methodology

The positions of equilibrium wage share, employment rate were estimated by a given sets of six parameters: $α, β, σ, γ, ρ$ and $λ$ . These parameters were calculated econometrically, after which these are utilised to compute the equilibrium wage share, employment rate. This is called the model estimate of wage share $(u^{*}$ ), modified model wage share $(u^{#})$ and employment rate ( $v^{*}$ ). Moreover, the mean value of the wage share ( $\bar{u})$ and employment rate $(\bar{v})$ across time can also be calculated from the data. Notably, the relative error of the wage share and employment rate are $(u^{#} - \bar{u}) / \bar{u}$ and $(v^{*} - \bar{v}) / \bar{v}$ , respectively.

Parameters estimation.

The exponential disembodied labour productivity growth $α$ in Equation (1) is estimated using the log linear ordinary least squares (OLS) regression method.(1E) $\ln a_{t} = {l n a}_{0} + α t + ε_{a t}$

The same method is applied to Equation (2) for estimating the exponential total labour force growth $β$ :(2E) $\ln N_{t} = {l n N}_{0} + β t + ε_{N t}$

Following this, the constant capital-output ratio of equation (3) is calculated by averaging the capital-output ratio at each time period. This can be expressed as:(3E) ${σ = T}^{- 1} \sum_{t = 1}^{T} (\frac{K_{t}}{Y_{t}})$

Furthermore, the Phillips curve relationship between real wage rate and employment rate of equation (7) is estimated using the ARDL model suggested by Harvie (2000). This model, in particular, is applied because the variables used the current study are a mixture of stationary and non-stationary variables. For instance, the growth of real wage rate $\dot{w_{t}}$ is a stationary variable, while the employment rate $v_{t}$ is a non-stationary one (see Table 1).(7E) ${(\frac{\dot{w}}{w})}_{t} = - γ + ρ v_{t} + \sum_{i - 1}^{m} ϑ_{i} ∆ {(\frac{\dot{w}}{w})}_{t - i} + \sum_{i - 0}^{m} {φ_{i} ∆ v}_{t - i} + ε_{w t}$ where, $γ$ and $ρ$ are the long-run parameters, $ϑ_{i}$ and $φ_{i}$ are the short-run parameters, $m$ represents the numbers of lags and $ε_{w t}$ refers to the error term. Moreover, it is considered that $ρ > 0$ , meaning that the real wage rate increases at the neighbourhood of full employment. Following Harvie (2000), we also take into consideration of long run parameters $γ$ and $ρ$ in our analysis.

The labour market-led situation and cost effect of the growth cycle, investigated through Equations (12) and (13), were estimated using the ARDL model. This is because the dependent variables, which are the growth rates (growth rate of wage share and growth rate of employment rate), are stationary, while the independent variables (employment rate and wage share) are non-stationary (see Table 1).

Drawing on Equation (12), the growth rate of wage share is positive function of employment rate and it can be expressed as:(12E) ${(\frac{\dot{u}}{u})}_{t} = b + π v_{t} + \sum_{i - 1}^{m} ϴ_{i} ∆ {(\frac{\dot{u}}{u})}_{t - i} + \sum_{i - 0}^{m} {η_{i} ∆ v}_{t - i} + ε_{e t}$

Drawing on Equation (13), the growth rate of employment rate is negative function of wage share and it can be expressed as:(13E) ${(\frac{\dot{v}}{v})}_{t} = c + τ u_{t} + \sum_{i - 1}^{m} μ_{i} ∆ {(\frac{\dot{v}}{v})}_{t - i} + \sum_{i - 0}^{m} {ψ_{i} ∆ u}_{t - i} + ε_{c t}$ where $π > 0$ in equation (12E) confirms a labour market-led situation and $τ < 0$ in equation (13E) ensures the cost effect. Both of these long-run parameters are take into consideration to infer about condition for Goodwin cycle (labour market-led and cost effect), $ε_{e t}$ and $ε_{c t}$ are the error terms.

Furthermore, the Goodwin cycle can be distinguished into short-run and long-run cycles. While the short-run growth cycle involves the cyclical components of variables, the long-run growth cycle involves the trend of the variables (Barrales & von Arnim, 2017; Flaschel, 2012). These trend and cyclical components were extracted using the time-based Hodrick and Prescott (1997) filter. Notably, the trend refers to a growth component that changes smoothly over time and is defined as the sum of squares to the second difference. Meanwhile, the cycle indicates deviation of a trend from the actual time series – its mean closes to zero over the time period. The smoothing parameter $г$ is taken as 6.25 for the annual data.(14) $a_{t} = \min \sum_{t = 1}^{t} {[c}_{t}^{2} + г {((g_{t + 1} - g_{t}) - (g_{t} - g_{t - 1}))}^{2}$ (15) $c_{t} = a_{t} - g_{t}$ where $a_{t}$ refers to the actual time series, $g_{t}$ indicates growth, $c_{t}$ is the cycle and t = 1,2,3,……,T i.e. time periods.

4. Data and empirical result

This section describe the data sources, time periods and choice of the variables. It also discuss the empirical finding and different conditions for the Goodwin cycle.

4.1 Data descriptions

The data of all the variables are obtained from the Annual Survey of Industries (ASI), except for the price index, the values for which is acquired from the database of Reserve Bank of India (RBI). The selected time period of 1980 to 2018 is specifically chosen due to constraints related to the availability of reliable data for periods before and after it. All variables were deflated by their respective prices to convert them into real terms. For instance, the wages were deflated by the consumer price index of industrial workers CPI(IW) at base year 2004, net capital stocks were deflated by the wholesale price index of manufacturing products WPI(MP) at base year 2004 and net income was deflated by the wholesale price index of all commodities WPI(ALL) at base year 2004. The common base year for the price is thus considered as 2004.

For the total workforce, the calculation of the total person engaged accounts for the workers, managers and unpaid family members. For calculations related to labourers employment $(L)$ denotes the number of workers.

Hence, employment rate $v = \frac{L}{N} = \frac{numbers of workers}{total persons engaged}$

For calculating the wage rate $w$ , wages to workers is chosen as labourers’ income is the main element of this theory.

Therefore, real wage rate $w = \frac{w a g e s t o w o r k e r s / C P I (I W)}{n u m b e r s o f w o r k e r s}$

The growth rate of real wage rate is the first log difference in the real wage rate, that is expressed as $\dot{w} = \ln w_{t} - \ln w_{t - 1}$ or, alternatively, $\frac{{w_{t} - w}_{t - 1}}{w_{t - 1}}$

For the calculation of output or income $Y$ , the net income is selected as it only consists of wage and profit, which is more consistent with the assumptions in Equation (5). For labour productivity, the net real income is divided by the number of workers.

Thus, labour productivity $a = \frac{n e t i n c o m e / W P I (A L L)}{n u m b e r s o f w o r k e r s}$

Furthermore, the net real capital stock is recursively estimated by the perpetual inventory method, as presented below: $K_{t} = K_{t - 1} + (I_{t} - D_{t}) / P_{t}$ where $K_{t}$ is the net real capital stock at the current time period, $K_{t - 1}$ refers to the depreciated real fixed capital at a pervious time period, $I_{t}$ is the gross capital formation at the current time period, $D_{t}$ refers to the depreciation at the current time period and $P_{t}$ is the wholesale price index of manufacture products at the current time period. This same method is implemented by Kannan and Raveendran (2009) and Basu and Das (2018) applied to the ASI data to estimate the net real capital stock in this study. Moreover, the selection of variables is also dictated by these authors. The reason for selecting the fixed capital and gross capital formation is that it has a boarder scope than gross fixed capital formation. As a result, it is capable of capturing all kinds of capital.

Effectively, the capital output ratio $σ = \frac{n e t r e a l c a p i t a l s t o c k}{n e t i n c o m e / W P I (A L L)}$

Lastly, the real capital accumulation rate $(λ)$ is the capital formation to profit ratio.

Hence, $λ = \frac{capital formation}{Profit}$

4.2 Empirical result

The descriptive statistics of the analysis conducted in this study are presented in Table 1, which shows that the growth rate of wage share is negative, while the growth rate of employment rate is at its minimum. Moreover, the standard deviation of wage share and growth rate of wage share exhibit one of the highest values in the table, coming only after the capital-income ratio. The maximum and minimum values indicate fluctuation in the variables. Large fluctuations are observed in the growth rate variables. Furthermore, the Augmented Dickey Fuller (ADF) test for non-stationarity of the variables shows that all the growth rate variables are stationary.

The results of the econometrically estimated parameters and the deduced values are shown in Table 2. The estimated parameters are computed using Equations (1E) to (7E), while the deduced values, which represent the model estimates of wage share, employment rate, are calculated by Equations (10), (11), (10M). These model estimates are based on the six given parameters, while the data estimates are acquired by considering the average of the available variables.

The results presented in Table 2 indicate that the labour productivity growth is 5.14% and capital-income ratio is 5.854, but the workforce growth is at 1.77%. In other words, high labour productivity growth and capital-income ratio accompanied by less workforce growth indicates that workers are being substituted by capital. The Philips curve’s coefficient result shows that with a 1 unit increase in employment rate, growth rate of the real wage rate increased by 1.34%. This direct relationship between the growth rate of real wage rate and the employment rate in the Phillips curve arises because when there is high employment, employers have difficulty hiring suitable labourers as they have to pay higher wages to attract (and retain) workers in the industry. Furthermore, the capital accumulation rate is 57%, meaning that approximately two-third of the whole profit is invested in real terms. Moreover, while the data estimate of wage share is 29% and the model estimate of wage share is 59%, calculating the modified wage share by including the capital accumulation rate decreases it to 29%, which is closer to the data estimate of 29%. Meanwhile, the data estimate and model estimate of employment rate are 77% and 80%, respectively, which is quite close to each other. Moreover, the employment rate is very high compared to the wage share. This indicates that although workers’ contribution to the production is significantly high, their income share is squeezed thin, thus favouring the capitalists class. The relative error between the data estimate and model estimate of modified wage share $(u^{#} - \bar{u}) / \bar{u}$ and employment rate $(v^{*} - \bar{v}) / \bar{v}$ are approximately 2% and 3.6% respectively. However, relative error between the data estimate and model estimate of orginal wage share $(u^{*} - \bar{u}) / \bar{u}$ is 100%. In other words, minimal deviation is observed between the data and the modified model, which suggests that this data is a good fit for the modified (neo-Goodwin) model rather than the original Goodwin one. By relaxing the assumption of unitary capital accumulation rate (investment to profit ratio) in the Goodwin model, the modified model reaches closer to the real data.

Furthermore, the bi-variate cross relationships between wage share and employment rate are estimated using Equations (12E) and (13E), as presented in Table 3. The positive sign in equation (12E) and negative sign in equation (13E) are expected to validate the existence of a labour market-led situation and the cost effect, respectively.

The results presented in Table 3 indicate that with a 1 unit increase in the employment rate, the growth rate of wage share increased by approximately 2.64%. This positive partial effect of the employment rate on wage share confirms the existence of a labour market-led situation in Indian organised manufacturing industries. In addition, this positive relationship shows that real wage is an important determinant of the Goodwin model compared to nominal wage. This is similar to Phillips curve. The only difference between Phillips curve of equation (7) and labour market-led situation of equation (11) is that wage is divided by the number of labourers (wage rate) in the former, while wage is divided by income (wage share) in the latter. If there is negative sign of employment rate then it indicates price movement dominated on real wages and this represents a goods market-led situation. On the contrary, with 1 unit increase in wage share, the growth rate of the employment rate decreased by 0.01%. This negative partial effect of wage share on employment rate verifies the existences of the cost effect condition. This negative relationship indicates that rise in wage share increases the input cost of producers, leading to less hiring of labourers for the production process. If there is positive sign of wage share then it indicates increasing wage bill (share), which, in turn, will increase the purchasing power of labourers. Higher purchase of goods motivates producers to invest more. Subsequently, this will result in more production and hiring of workers. This is defined as the purchasing power effect. These contrasting signs, as shown in Table 3, fulfil the conditions (labour market-led situation and cost-effect) of the Goodwin cycle which is similar to finding of Flaschel (2010).

The different diagnostic tests are conducted for the error term of ARDL regression to check models’ validation for all three equations, i.e. 7E, 12E and 13E. In Breusch-Godfrey Serial Correlation LM Test, the null hypothesis is absence of any serial correlation. In the Jarque-Bera test for error normality, the null hypothesis is that error is normally distributed. In the Breusch-Pagan-Godfrey test for Heteroscedasticity, the null hypothesis is the constant variance of error. CUSUM and CUSUM of square of residual are for stability of the model. Table 4 shows that the p-value of all tests is greater than 0.1 implying acceptance of all the null hypotheses. Thereby it can be inferred that there is no serial correlation, error is normally distributed and absence of heteroscedasticity. CUSUM and CUSUM-square test indicates that the parameter is stable over time. Further, the bound tests of ARDL co-integration in Table 3A of Appendix show that the F-statistic is greater than the upper bound I(1) for all three equations (7E, 12E and 13E). This suggests that co-integration exists and ARDL is an appropriate method.

Consistent with Harvie (2000), after investigating the growth cycle based on the quantitative method, the qualitative approach was also employed to describe its profit-led distribution. The qualitative approach is the graphical depiction of employment rate and wage share, which is applied by Harvie (2000). The anti-clockwise movement of the growth cycle in the employment rate-wage share bi-sphere plane over the selected time period was explored. In addition, the cyclical relationship was investigated using a bi-dimensional diagram of employment rate and wage share, with the horizontal axis displaying the former and the vertical axis indicating the latter. The growth cycle can also be distinguished between the short-run and long-run cycles – the former deals with cyclical component and the latter with the trend of the variables. These trend and cyclical component are extracted using a time-based HP filter. The short- and long-run growth cycles based on the data in this study are depicted in Figures 1 and 2 respectively.

It is observed that the short-run growth cycle spans 6–7 years in the whole 39-year period, which is consistent with Flaschel (2010). The short-run growth cycles are nearly closed orbits depicting anti-clockwise movement in the employment rate and wage share bi-sphere plane. Specifically, two periods – 1980 to 86 and 1987 to 1992 – exhibit clockwise movements in the employment rate and wage share bi-sphere plane because prior to 1991 Indian economy is state control planned economy. However, apart from these two periods, all others present an anti-clockwise movement, pointing at profit-led distribution. This means that in four out of six short-run cycles, the Goodwin growth cycle exists. This anti-clockwise movement in short-run growth cycles are observed from the 1991 onwards, during the neo-liberal regime in India when economy got capitalistic orientation. Meanwhile, the long-run growth cycle spanning a 39 years period covers half of the closed orbit of the anti-clockwise movement in the employment rate and wage share bi-sphere plane. In this cycle, the wage share declines continuously, while the labourers employment rate remains stagnant. This suggests the erosion of labour income share in the whole income, leading to wage-squeezed distribution. The cross mark in the long-run growth cycle graph indicates the co-ordinate of the average employment rate and wage share.

All of these indicators show that the neo-Goodwin growth cycle exists and that the capitalist imprint is expanding in the organised manufacturing sectors of India. The high employment rate and less wage share indicate that income distribution mainly favours the capitalists class. Drawing on this result, the policy suggestion for the manufacturing sector of the Indian economy is to conduct redistribution of income by enforcing a ceiling for the maximum salary for managers and a floor for the minimum wages of workers (upper and lower bounds for salaries and wages, respectively). The ceiling of managers’ salary is required because distribution of income goes in favour of large part of workforce (labourers) rather than its smaller counterpart (managers). On the contrary, minimum wages of workers ensure equity between their contribution in the production process as input and their remuneration of income, i.e. marginal contribution of workers equal to wages.

5. Conclusion

The previous empirical studies on the Goodwin model do not match data estimates for developed and developing economies. However, the Goodwin model is modified by relaxing the unitary investment-to-profit ratio assumption and incorporating it into the model. Hence, the neo-Goodwin model estimates close to data estimates for developed countries. However, the capitalistic nature of this model is not explored in the emerging country like India. Hence, the aim of the paper is to investigate Goodwin’s growth cycle in the Indian context by employing the annual data of Indian industries from 1980 to 2018. The econometric results indicate that the original Goodwin model estimates deviate form data but modified (neo) Goodwin model estimates close to data estimates of both wage share and employment rate. The bi-variate relationships between wage share and employment rate confirm the existence of a labour market-led situation and the cost effect. Furthermore, it is observed that the short-run and long-run growth cycles move in an anti-clockwise direction in the employment rate and wage share bi-sphere plane. That symbolises distribution of income goes in favour of capitalist class.

All these findings indicate that the neo-Goodwin growth cycle exists in the Indian economy for the organised manufacturing industries. The policy suggestion based on empirical finding is that redistribution of income by enforcing a ceiling for the maximum salary for managers and a floor for the minimum salary of workers. The scope for future research on this area of study can be extended to exploring non-linear estimation techniques and the demand side of the growth cycle by incorporating Kaldorian investment and saving, Kaleckian demand and supply of investment, Keynesian marginal efficiency of capital, Schumpeterian innovation or Shaikh’s Humbug Production Function (1974).

Notes

1.Equation (1) represent main mathematical equation; Equation (1E) denotes empirically estimated equation from Equation (1), Equation (1M) represent modified equation of Equation (1) and lastly Equation (1A) refers Appendix’s equation.

2.Systematic derivation conducted by Harvie (2000) in his Appendix.

3.The derivation is given in Appendix.

4.The only difference between Phillips curve of equation (7) and labour market-led situation of equation (11) is that wage is divided by the number of labourers (wage rate) in the former, while wage is divided by income (wage share) in the latter.

Availability of data and material: All materials and datasets are collected from public domain and available on request.

Competing interests: No potential competing interest of any form reported by the authors.

Funding: The present research work did not receive any grant or funding from any sources.

Figure 1

Short-run growth cycle

[Figure omitted. See PDF]

Figure 2

Long-run growth cycle

[Figure omitted. See PDF]

Figure 1A

CUSUM and CUSUM of squares of error

[Figure omitted. See PDF]

Table 1

Descriptive statistics

	Mean	Std. Dev	Maximum	Minimum	ADF
Labour productivity growth	0.0466	0.0934	0.2135	−0.1486	5.498709***
Workforce growth	0.0191	0.0505	0.1253	−0.1522	−3.1344
Capital income ratio	5.8540	1.4819	10.1024	3.3238	−2.5620
Real wage rate growth	0.0115	0.0461	0.0811	−0.1850	−6.0534***
Employment rate	0.7690	0.0114	0.7861	0.7410	−2.1565
Employment rate growth	0.0005	0.0111	0.03636	−0.0261	−3.4132*
Wage share	0.2915	0.1402	0.5194	0.1296	−1.6441
Wage share growth	−0.0350	0.1013	0.1714	−0.2860	−5.4797***

Note(s): ***, ** and * indicate the statistical significance at the 1, 5 and 10% levels, respectively