Autonomous demand and technical change: exploring the Kaldor–Verdoorn law on a global level

This paper aims to explain labour productivity through the lens of a Kaldorian perspective. To assess the relationship between output, demand, capital accumulation, and labour productivity, we apply Panel Structural Vector Autoregressive (P-SVAR) modelling to a dataset of 52 countries observed over a long-time span as provided by the Penn World Table. Findings validate the Kaldorian perspective and show that demand shocks—measured by government expenditures and exports—produce positive and persistent effects on labour productivity. Findings are confirmed even when the full sample is broken down to consider developed and developing countries separately.


Introduction
Usually regarded as one of the main causes of slacking economic growth, the prolonged stagnation of productivity in recent decades has been a concern for several advanced economies. This interpretation is grounded on a theoretical approach where economic growth is explained in terms of and limited by both the growth of the factors of production, labour and capital, and technical progress. From this perspective, there is a long-run path in which the system gravitates towards positions of full employment and the constraints to an increasing output are the growth 1 3 in productive efficiency and the accumulation of productive resources. In a situation where all resources are fully utilised, labour productivity growth is interpreted as an improvement in technical efficiency and is ascribed exclusively to supply-side factors such as a change in endowments or production techniques.
By contrast, in a demand-led growth theoretical approach, no automatic mechanism ensures a tendency towards full employment of productive resources, and economic growth is interpreted as fundamentally determined by aggregate demand. In this approach, the actual path of the economy, which is determined by demand, influences the trajectory of its growth: supply conditions define the path of potential output in a way that is not independent of the actual path of output determined by demand. Consequently, labour productivity is seen as largely endogenous to aggregate demand, which thus constitutes a constraint on both output and productivity growth. As postulated by the Kaldor-Verdoorn law, a stable long-run relationship between output and labour productivity exists, whereby output growth determines productivity growth. Market expansion becomes a necessary condition for activating those technological and organisational factors which favour productivity growth, such as incentives to the introduction of organisational improvements and more efficient employment of inputs, changes in the sectoral composition of output and employment, static (linked to the indivisibility of the production process) as well as dynamic (involving innovative activities and learning-by-doing) economies of scale, and increased investment that incorporates technical progress (Kaldor, 1957(Kaldor, , 1966Verdoorn, 1949). Over the years, several studies have been carried out and have found empirical confirmation of a positive relationship moving from output to productivity (for a detailed review, see Deleidi et al., 2020bDeleidi et al., , 2021bMcCombie et al., 2002). The Kaldor-Verdoorn law thus constitutes empirical evidence for interpreting labour productivity dynamics as predominantly endogenous to aggregate demand. Specifically, in his analysis of the determinants of productivity growth from 1970 onwards, Kaldor (1975a) attributes a crucial role to the exogenous components of demand and, in particular, to export growth. The external demand for manufactured products is interpreted as an exogenous factor that can activate the cumulative expansion of manufacturing output and productivity (Kaldor, 1975a(Kaldor, , 1977. 1 Based on these premises, in this paper, we analyse the relationship described by the Kaldor-Verdoorn law by introducing the intuition developed by Kaldor (1975a) and thus focusing on the effects of autonomous demand components on labour productivity dynamics. To do this, we theoretically merge the standard Kaldor-Verdoorn law with a demand-led model of growth based on the notions of 1 Another strand of literature explains the stagnation of productivity dynamics through the concept of 'Structural Change'. According to this perspective, which starts with Baumol's (1967) seminal work, economies would experience stagnating productivity due to an expansion of the service sector-compared to other economic sectors-which is associated with lower productivity dynamics and potential productivity gains compared to other sectors (e.g., the manufacturing sector) (Storm, 2017;Szirmai and Verspagen, 2015). However, such a perspective has been critically discussed by Deleidi et al. (2020b) who have proved that stagnating productivity is mainly ascribable to a slowdown in aggregate demand rather than shifts toward the service sector, and Fontanari and Palumbo (2022) who have also emphasized the role of stagnating wages.

3
The interpretation of Kaldor-Verdoorn's law also has essential theoretical reference in the analysis of Adam Smith, describing the phenomenon of increasing returns as the result of an increase in the division of labour. Smith (1776) argued that the growth of labour productivity is due to an increase in the division of labour and productive specialisation. Both these mechanisms originate from the expansion of the market. Processes of productive specialisation can take place both between an increasing number of firms, favouring productive diversification and the creation of new firms or industries, and within firms through an increased fragmentation of operations, favouring processes of concentration and growth in size (see Kaldor, 1966;Smith, 1776;Sylos Labini, 1984). Hence, static and dynamic economies of scale are associated with increasing returns to scale, whereby increased production leads to savings in input per unit of output (Kaldor, 1966). According to Kaldor, the development of economies of scale is peculiar to the manufacturing sector, which he considers to be the engine of economic growth. Dynamic economies of scale enhance returns as output increases through the accumulation of experience and knowledge, fostering innovative activity (Arrow, 1971). Static economies of scale, on the other hand, operate even in the absence of technological progress: the return per unit of labour grows as the size of production increases for technical and organisational reasons due, for example, to the presence of indivisibility in the production process (see Kaldor, 1957Kaldor, , 1966Kaldor & Mirrlees, 1962).
It is worth noticing that interpreting productivity growth as endogenously determined by output growth does not exclude that a reverse influence might also exist, namely from productivity growth to output growth. Indeed, Kaldor's analysis highlights the existence of a virtuous circle linked to a cumulative causation process, according to which output growth favours productivity growth, which in turn leads to further increases in output through the positive effect of productivity on external competitiveness (see Kaldor, 1970Kaldor, , 1972. Increased competitiveness would favour exports, which, according to Kaldor, are the main driver of economic growth as a truly autonomous component of demand (Palumbo, 2009). Moreover, the rise in productivity can reduce the propensity to import and, by lowering relative prices, increase the propensity to consume (Cesaratto et al., 2003). Exports would thus have the dual role of fuelling the virtuous circle of growth and, by financing imports, relieving the possible constraint that trade imbalances can place on output growth (Thirlwall, 1979).
The relationship outlined by the mechanisms mentioned above is shown, in its simplest version, in Eq. (1), generally known as Verdoorn's law: where l p represents the rate of growth of labour productivity; ̇y is the rate of growth of output; represents the pace of exogenous technical progress; and measures the relationship between ̇y and l p . From now on, we shall refer to the parameter as the Verdoorn effect.
(1) lp = +̇y When addressing the second mechanism concerning the effect of technical progress embodied in newly installed capital goods, 2 Kaldor (1957) includes the capital-labour ratio in his analysis. As shown in Eq. (2), Kaldor's original technical progress function postulates the existence of a positive relationship between the growth rate of labour productivity ( l p ) and the growth rate of the capital-labour ratio ( ̇k ): Since "the use of more capital per worker inevitably entails the introduction of superior techniques" (Kaldor, 1957, p. 595), the growth of the capital-labour ratio aims to capture the effect on technical progress of "the speed with which innovations are introduced" (Lavoie, 2015, p. 429). We shall thus refer to the parameter as the capital accumulation effect.
Starting with Michl (1985), the two effects on labour productivity growth described are combined in a single relationship reported in Eq. (3) (see also Antenucci et al., 2020;Deleidi et al., 2021b): where labour productivity growth ( l p ) is affected by both the rate of growth of output ( ̇y ) and the rate of growth of the capital − labour ratio ( ̇k ). Equation (3) thus combines the Verdoorn effect ( ) with the effect of capital accumulation ( ) described in Kaldor's technical progress function (Kaldor, 1957).
The Kaldor-Verdoorn law has been extensively studied within the post-Keynesian or demand-led growth theoretical framework, which underlines the central role of demand in determining both output and productivity growth. Therefore, in this perspective, the Verdoorn effect formalised in the Kaldor-Verdoorn law can be interpreted as the effect of changes in aggregate demand on productivity. Recent theoretical contributions have nested the Kaldor-Verdoorn law inside the supermultiplier model of growth (Deleidi & Mazzucato, 2019;Nah & Lavoie, 2019). According to the supermultiplier model, GDP growth is driven both in the short-and long-run by the evolution of the non-capacity creating autonomous components of demand, namely export, government expenditure, and autonomous consumption (Cesaratto et al., 2003). 3 These components are defined as autonomous and non-capacity creating since they neither depend on the current level of income nor directly affect productive capacity (Serrano, 1995). Specifically, government expenditure is determined by fiscal policy decisions; exports depend on the level of foreign demand; and autonomous consumption is financed through bank loans created through an endogenous money creation process or accumulated wealth (Barbieri Góes & Deleidi, (2) lp = +̇k (3) lp = +̇y +̇k 1 3 2022). 4 Following the supermultiplier model of growth, the relationship between the rate of growth of output ( ̇y ) and the autonomous components of demand ( ̇z ) can be written as in Eq. (4): where m is the supermultiplier, ̇y is the rate of growth of output, and ̇z is the rate of growth of autonomous components of demand. By substituting Eq. (4) into Eq. (3), we obtain Eq. (5) where labour productivity growth ( l p ) is determined by both the rate of growth of autonomous components of demand ( ̇z ) and the rate of growth of the capital-labour ratio ( ̇k ). It is worth noting that the combination of the supermultiplier model with the Kaldor-Verdoorn law is entirely in line with the Kaldorian perspective: "I would now place more, rather than less, emphasis on the exogenous components of demand, and in particular on the role of exports, in determining the trend rate of productivity growth in the United Kingdom in relation to other industrially advanced countries" (Kaldor 1975a, p. 896). 5 Furthermore, Eq. (5) also considers the level effects that different supermultipliers may produce on the average growth rate of output and labour productivity, by affecting permanently their levels. In other words, while the size of the supermultipliers does not affect the trend growth rate of output and productivity, different supermultipliers can produce different level effects during the adjustment process from a fully adjusted position to another one, thus producing different average growth rates of output and productivity. Since the size of the market is determined both by the rate of growth of autonomous components of demand ( ̇z ) and the magnitude of the supermultiplier ( m ), then, assuming a constant ̇z , the greater m the larger the expansion of the market.
In the current paper, by applying P-SVAR techniques to a panel dataset of 52 countries observed over a long-time span, we validate Eqs. (3) and (5). When considering Eq. (5), we also estimate the effect of different components of autonomous demand by breaking down autonomous expenditures into government spending and exports. Finally, as explained in the following sections, the use of autonomous demand will allow us to overcome potential empirical issues related to the identification of demand shocks.

Empirical literature
Although the empirical literature on the factors enhancing productivity growth is extremely vast, we focus on empirical evidence in favour of a positive effect on labour productivity growth associated with output growth and capital accumulation. After the initial estimations by Verdoorn (1949), who estimated a Verdoorn effect of 0.45, and by Kaldor (1966), who assessed a dynamic version of Verdoorn's law for which an additional percentage point of output growth leads to a 0.5% increase in productivity, several studies contributed to validate the Verdoorn law. An extensive review of those empirical investigations can be found in McCombie (1983), Thirlwall (1983), andMcCombie et al. (2002).
In recent contributions, the Kaldor-Verdoorn law has been empirically verified both in country-specific studies and through cross-country analyses. Among the formers, Bianchi (2002), Ofria (2009) 2021) have found that results are positive and significant even when controlling for institutions and inequality in the case of Brazil (at the municipal level). They tested the direct and indirect impacts of institutions on productivity growth, controlling for human and physical capital, as well as for demand growth. They found that in municipalities with inclusive institutions and higher human capital, productivity growth responds more strongly to demand growth. Nassif et al. (2022) find results that validate the Kaldor-Verdoorn law also for the case of Brazil. Concerning panel analysis, Knell (2004) Gabrisch (2021) applied the model to a panel of Central and Eastern European countries; the author finds that slower productivity growth is not due to 'adverse technological progress' but to weakening external and domestic demand. Deleidi et al., (2020aDeleidi et al., ( , 2020b validated the Verdoorn law for the manufacturing sector in nine Eurozone countries by using an ARDL model and autonomous components of demand, while Carnevali et al. (2020) estimated a positive 'Smith effect' in the Euro area manufacturing industries within the context of Sylos Labini's productivity equation (Sylos Labini, 1984). 6 Regarding the effect of capital per unit of labour on productivity dynamics, several works have demonstrated the positive role of capital accumulation in fostering productivity. In this paradigm, labour productivity growth is typically decomposed into the contributions of two components: capital deepening and total factor productivity. Among these, the process of increasing capital per unit of labour has a positive and significant effect on productivity according to a number of authors, including Kumar and Russell (2002), who estimate a contribution of capital accumulation to productivity growth of 77% for a panel of 57 countries, as well as Jorgenson et al. (2008) and Foda (2017), who estimate a contribution of capital accumulation to productivity growth for the US economy of about 53 and 45%, respectively. Sichel and Oliner (2002) analyse the influence of ICT investment on productivity growth in the post-1995 period in the US nonfarm business sector and they find a contribution of ICT to the growth of labour productivity of 42% and a contribution of other forms of capital of 7%. Van Ark et al. (2008) evaluate the productivity gap between Europe and the US estimating a positive contribution of capital service per hour worked to average productivity growth of 1 and 1.3% points for the EU and the US. Borsato and Lorentz (2022) incorporate the notion of robotisation into the analysis; the authors find that a higher degree of robotisation strengthens the mechanism that links labour productivity growth at the industrial level to the macroeconomic level.
Closely related to the purposes of this paper are the results obtained by Michl (1985), who was the first to estimate an extended version of Kaldor's technical progress function, finding a Verdoorn coefficient of 0.54 and a capital accumulation coefficient of 0.40 for eight advanced countries for the period 1950-1983. More recently, Antenucci et al. (2020) have estimated a positive capital accumulation coefficient and a positive Verdoorn coefficient for G7 countries, while Deleidi et al. (2021b) have obtained confirmation of the extended version of Kaldor's technical progress function at the Italian regional level. 7 To sum up, the empirical literature largely confirms the existence of a positive effect of output growth and capital accumulation on labour productivity growth. Estimated coefficients vary depending on the methods used and the temporal-spatial level of the analysis. Following part of the recent literature (Antenucci et al., 2020;Deleidi et al., 2020bDeleidi et al., , 2021b, in this paper, we use P-SVAR modelling to validate Eqs. (3) and (5). The employed method allows us to consider and overcome a long-debated problem in the relevant literature, namely the endogeneity of investment to output growth. The novelty of this paper lies in the use of autonomous components of aggregate demand as a proxy for the Verdoorn effect, and the application of P-SVAR techniques to a dataset of 52 countries. The use of demand 1 3 Economia Politica (2023) 40:57-80 components-namely government expenditure, export, and their sum-will allow us to identify demand shocks using P-SVAR techniques, that is shocks that can be associated with "a distinct economic interpretation" (Kilian & Lütkepohl, 2017, p. 209), and then assess whether these shocks produce any effects on labour productivity. The identification of demand shocks using autonomous components of demand and P-SVAR modelling is particularly relevant in this field of research since it would allow us to solve a twofold shortcoming in the considered empirical literature. First, the use of structural models to validate the Kaldor-Verdoorn law (Antenucci et al., 2020;Deleidi et al., 2021b), employing output growth rather than autonomous demand components, does not provide a meaningful economic interpretation of identified shocks because shocks associated with output can be theoretically ascribed to both supply and demand factors. Secondly, introducing demand components in a single equation modelling (Deleidi et al., 2020a(Deleidi et al., , 2020b implies assuming the exogeneity of autonomous demand components, which would allow us to neither estimate structural shocks nor assess the dynamic evolution of demand shocks on labour productivity dynamics and therefore assess its persistence. The current paper aims to improve the recent empirical analysis by overcoming the limitations mentioned above.

Data
The source of all our data is the Penn World Table v. 10.0 (Feenstra et al., 2015). From the whole database, we set a minimum limit of 30 observations per country, thus reducing the usable data to a set of 52 countries. 8 From this database, we can construct the GDP level ( Y ), government consumption ( G ) and exports ( EXP ). In line with the supermultiplier literature, we sum G and EXP to obtain autonomous expenditure ( Z ). On the other hand, we construct a series of the capital-labour ratio ( k ) and labour productivity ( LP ). Both the capital-labour ratio and productivity are built considering the hours worked (and not the number of workers). In this way, we can adjust the series to exclude short-run cyclical fluctuations due to changes in capacity utilisation from LP and k , typically described by the mechanism underlying Okun's law. According to Okun's law, an increase in output leads to productivity gains in cyclical phases of the economy because the change in the degree of capacity utilisation gives firms an incentive to vary the working time of existing workers rather than the number of workers. 9 All variables are transformed into logarithms. Additional details are reported in Appendix A.
To provide a complete picture, we split the dataset into developed ( n = 25 ) and developing ( n = 27 ) countries using the United Nations methodology (UN, 2020, pp. 165-166). Of the 3089 annual observations, 1625 refer to developed countries, whereas 1464 observations refer to developing ones. Using this dataset-which considers a set of heterogeneous countries-we can determine how the various sources of demand differently affect productivity growth in economies at different stages of development.

Methods
To assess the validity of the Kaldor-Verdoorn law, we make use of the Panel Structural Vector Autoregressive (P-SVAR) methodology (Pedroni, 2013). This usefully considers responses to both idiosyncratic and common shocks while permitting full cross member heterogeneity of the response dynamics (Pedroni, 2013, p. 180). The advantage of this methodology is that it allows us to consider the existing heterogeneity within individual countries of the panel and cross-sectional dependence that is likely to arise from the fact that individual countries of the sample respond not only to their own member-specific idiosyncratic shocks but also to shocks that are shared across countries within the panel (Pedroni, 2013, p. 181). 10 A P-SVAR can be summarised as in Eq. (6): where B 0i is the matrix of contemporaneous coefficients, x is the vector of considered variables, B i (L) is the matrix of lagged coefficients, and w i,t is the vector of estimated structural shocks. 11 P-SVAR modelling allows us to estimate w i,t by imposing suitable restrictions on the B 0i matrix derived from the considered economic theory (Kilian & Lütkepohl, 2017). Once restrictions are imposed and structural shocks estimated, impulse response functions (IRFs) are computed to evaluate the dynamic effects produced by a shock on the variables included in the model. IRFs are reported with 95% confidence interval bands estimated by bootstrapping standard errors. All models include two lags for each variable estimated through the GTOS (general-to-specific) criteria (Pedroni, 2013). Additionally, we estimate the cumulative effects computed by dividing the cumulated response of labour productivity to In the current paper, we do not want to focus on the cyclical fluctuations of labour productivity as instead postulated by Okun's law. However, for an in-depth analysis of this topic, see, Okun (1962), Jeon and Vernengo (2007) and Fontanari et al. (2020), among others. 10 For the sake of simplicity, IRFs corresponding with composite shocks are reported in Sect. 5, while those associated with common and idiosyncratic shocks are available upon request. 11 All variables are taken at levels to preserve any cointegrating or long-run relationship that may exist among the considered variables (Auerbach and Gorodnichenko, 2012, ft. 6;Kilian and Lütkepohl, 2017). the corresponding impulses (Deleidi et al., 2021a;Spilimbergo et al., 2009). Since models are in log-level, estimated IRFs and cumulative effects are elasticities.
We estimate three different models. In Model 1, vector x includes [Y;k;LP] , namely variables reported in Eq. (3), Sect. 2. However, as argued in Sect. 3, the use of GDP as a determinant of productivity cannot shed light on an important point backed by several supporters of the Kaldor-Verdoorn law: whether demand shocks affect labour productivity dynamics. Indeed, the shock extrapolated by the output equation cannot be directly associated with a demand shock because supply factors may also determine it. To overcome this issue, we use variables that can be theoretically associated with a demand shock. To do this, the vast literature on fiscal policy (see, among others, Auerbach & Gorodnichenko, 2012;Blanchard & Perotti, 2002;Deleidi et al., 2020aDeleidi et al., , 2021aDeleidi et al., , 2021c, as well as the one on the supermultiplier (Barbieri Góes & Deleidi, 2022;Cesaratto et al., 2003;Freitas & Serrano, 2015;Serrano, 1995) allow us to define a demand shock. Specifically, in our models, demand shocks are identified employing the notion of autonomous demand ( Z ), government expenditure ( G) , and export ( EXP ). Once innovations to demand are obtained, we aim to assess the effect of Z and its components ( G and EXP ) on productivity dynamics. To do this, we estimate Models 2 and 3. While Model 2 includes [Z;k;LP] and output Y is replaced by autonomous demand Z , Model 3 considers G and EXP separately. Indeed, Model 3 includes the following variables: [EXP;G;k;LP].
The theoretical intuition developed by Michl (1985) and the identification strategies employed by Antenucci et al. (2020) and Deleidi et al. (2021b) are used to estimate Models 1, 2, and 3. Specifically, structural shocks are obtained using shortrun restrictions and a Cholesky factorisation. In the case of Model 1, we assume the identification summarised in (7) where ' − ' indicates an unrestricted parameter and '0' represents a zero restriction: The identification reported in Eq. (7) assumes that GDP affects labour productivity and the capital-labour ratio within the contemporaneous relationship. On the contrary, the output is not affected by labour productivity or the capital-labour ratio within the contemporaneous relationship. In the last row of Eq. (7), labour productivity is assumed to be affected by both the capital-labour ratio and output dynamics within the contemporaneous relationship (see also Eq. (3) in Sect. 2). 12 When moving to the identification of Model 2, output ( Y ) is replaced by autonomous demand ( Z ). In line with the supermultiplier literature considering autonomous demand as the driver of GDP and labour productivity growth (Deleidi & Mazzucato, 2019), Z is assumed independent from labour productivity and the capital-labour ratio within the contemporaneous observation, while k and LP are ordered as in Eq. 7.
Finally, as shown in Eq. (9), the identification employed in Model 3 is similar to the one used in Model 2. Following Barbieri Góes and Deleidi (2022), we assume that export ( EXP ) is more exogenous than government expenditure ( G ) within the contemporaneous relationship. However, to provide a clear picture, a robustness check is carried out by assuming an additional identification for Model 3 where government expenditure ( G ) is considered more exogenous than export ( EXP ) within the contemporaneous relationship. Findings and the corresponding identification strategy used for this robustness check are reported in Appendix B.

Findings
In this section, we plot the IRFs estimated for Models 1, 2 and 3. In particular, we report findings of estimated models by showing both IRFs and cumulative effects.
IRFs are reported in Figs. 1, 2, and 3 and correspond to the estimates obtained for Model 1, 2, and 3, respectively. IRFs are highly persistent as they remain positive throughout the whole twenty-year period. When considering the Verdoorn effect, IRFs show that a rise in output ( Y in Fig. 1), autonomous demand ( Z in Fig. 2), and its components considered separately ( G and EXP in Fig. 3) produces long-lasting effects on labour productivity ( LP).
The persistence of these effects is also detected when analysing the capital accumulation effect. Indeed, an increase in capital-labour ratio k leads to a persistent rise in labour productivity in Model 1, 2 and 3 (see Figs. 1, 2, and 3). Such evidence is also confirmed when breaking down the sample into developed and developing countries.
The cumulative effects are reported in Table 1. When considering all countries in Model 1, the Verdoorn effect is almost equal to 1%, whereas the capital accumulation effect is lower and equal to 0.138% on average. This means that a 1% change in output leads to a roughly proportional increase in labour productivity, while 1% increase in the capital-labour ratio raises labour productivity by 0.138%. By replacing the growth of output with the growth of autonomous demand ( Z ) in Model 2, the Verdoorn effect falls compared to Model 1, as a 1% increase in demand ( Z ) is followed by a labour productivity increase of 0.323% on average. Conversely, the capital accumulation effect estimated for Model 2 is higher than that obtained for Model 1: a unitary rise in the capital-labour ratio raises labour productivity by 0.281% on average. One possible explanation for the lower effect of autonomous demand could lie in the fact that ( Z ) excludes the impact of investment, which is instead partially captured by the growth of output; this would also explain the lower coefficient of the capital-labour ratio in Model 1, where the Verdoorn coefficient would partially capture the effect of embodied technical progress. The size of the estimated coefficient for the capital accumulation effect remains nearly unchanged in Model 3, where autonomous demand ( Z ) is broken down into government expenditure and export. When evaluating the effect of different demand components, government expenditure ( G ) produces larger effects on labour productivity than export ( EXP ) in all samples, assuming an average value of 0.314 and 0.135%, respectively. These results shed light on the role of autonomous demand components in determining productivity growth: while Kaldor (1977) emphasised the role of exports as the main driver, our results show a considerably higher impact of government spending. Findings obtained for Model 3 are also robust to a different identification strategy. Indeed, the IRFs and cumulative effects reported in Appendix B are in line with the results reported in this section.
When breaking down the sample into developed and developing countries, the estimates of Model 1 confirm a Verdoorn effect of around 1% for both subgroups. However, as autonomous demand is introduced in Model 2, results show that demand shocks produce different effects on the two groups of countries: while in developed countries, an increase in demand produces an average response of labour productivity of 0.334%, in developing countries such a response is equal to 0.436%. This could result from different stages of development; possibly, during the early stages of development, where sectors such as textiles are developing, productivity gains may be higher in these sectors (Magacho & McCombie, 2018). Ultimately, this result could be a consequence of the composition of output, something that should be analysed at the sectoral level and is beyond the scope of this paper. Going further, Model 3 allows us to observe the differences between countries according to the source of demand. As we have seen, on average, the impact of government spending is more important than exports for labour productivity growth, and this is true for both developed and developing countries. The impact of public spending on output and productivity growth is in line with our theoretical assumptions, whereby the government, by stimulating demand, creates room for market size to increase and this allows economies of scale to deepen, leading to productivity growth. Comparing the two groups, we observe that the average effect of government expenditure on productivity is greater in developing countries, while the average impact of export is greater in developed ones. The latter result is in line with Kaldor's idea that exports are especially crucial to those countries that have a more advanced manufacturing sector and which, because of this, would be able to offer industrial products at lower costs, attract more demand for their manufactured goods and, thus, 1 3 gain further productivity benefits (Kaldor, 1975b;Palumbo, 2009). 13 Finally, the capital accumulation effect is larger in developing countries than in developed ones in all estimated models. Focusing on Model 2 and 3, the impact of capital accumulation ranges between 0.463 and 0.521% for developing countries and between 0.133 and 0.168% for developed countries. The larger effect of capital accumulation in developing countries may be related to a composition effect of investment. Indeed, this larger coefficient could capture the impulse, in developing countries, to adopt production methods with a higher capital endowment per worker, which stimulates higher productivity growth (as in the case of the manufacturing sector), while in developed countries a larger share of investment is directed to services where productivity gains are smaller. Furthermore, it is worth noticing that, in Model 2, demand shocks produce greater effects than capital accumulation on productivity when considering developed countries, while developing countries experience a slightly higher relevance of the capital accumulation effect. Model 3 shows that the most relevant impact on productivity for developed countries is the one generated by government expenditure, while it is again the accumulation of capital for developing countries.

Conclusions and policy implications
The slowdown in productivity growth during the last decades is one of the most important issues to be explained and solved by economists and policymakers nowadays. In neoclassical growth models, productivity growth is considered one of the main drivers of long-run economic growth. According to this strand of thought, productivity and then economic growth are stimulated by the so-called supplyside factors, such as endowments and techniques of production. On the contrary, in demand-led growth models and notably the Kaldor-Verdoorn law (Kaldor, 1966;Verdoorn, 1949), the relationship between labour productivity and economic growth is reversed: a more sustained output growth-driven by aggregate demand expansion-leads to an increase in labour productivity. In this framework, the expansion of the market, determined by higher demand and thus by a higher level of production, stimulates innovation through: (1) incentives to improve organisational aspects and use inputs more efficiently; (2) changes in the sectoral composition of output and employment; (3) static and dynamic economies of scale; and (4) growth in investment embodying more advanced technological goods.
In the current paper, we have endorsed a Kaldorian perspective from a theoretical and empirical standpoint. Theoretically, we have followed the intuition developed by Kaldor (1975a), according to whom the exogenous components of demand  (Pedroni, 2013) to calculate Impulse Response Functions (IRFs) and quantify the dynamic effects of capital-labour ratio, output, autonomous demand and its components on labour productivity. To do this, we have applied P-SVAR modelling to a dataset provided by the Penn World Table  composed of 3089 observations, divided into 52 countries observed over a long-time span. We have estimated three different models. In Model 1, we have assessed the standard Kaldor-Verdoorn law augmented by the capital-labour ratio and-with the introduction of autonomous demand in Model 2 and its breakdown into government expenditure and exports in Model 3-we have also been able to verify whether demand and fiscal policy shocks can exert positive and persistent effects on labour productivity dynamics. Additionally, our models have also been estimated on subsamples considering 'developed' and 'developing' countries separately to provide a complete picture. Findings have validated the Kaldor-Verdoorn law for the full sample and when the 52 considered nations are classified as 'developed' and 'developing' countries. We have shown that an autonomous demand shock positively affects labour productivity. Furthermore, when autonomous demand is broken down into government expenditure and export, government expenditure ( G ) produces larger effects on labour productivity than export ( EXP ), assuming an average value of 0.314 and 0.135%, respectively, both when the full sample is considered and when developed and developing countries are considered separately. It is worth noticing that, when comparing the two groups of countries, the effect produced by export is relatively higher in developed countries than in developing ones. In contrast, government expenditure exerts greater effects on productivity in developing countries than in developed ones. Finally, the capital accumulation effect positively influences labour productivity in all the estimated models. This effect is even higher than the one produced by demand shocks in developing countries. When looking at developed countries, the impact of demand on productivity-especially the one determined by government expenditure-is always predominant compared to the capital accumulation effect.
In conclusion, demand management policy seems to represent an appropriate tool to stimulate innovation and labour productivity. One of the main policy implications of our findings is that public expenditure and particularly expansionary fiscal policies can boost innovation and labour productivity. Thus, our results are in line with some of the policy prescriptions advocated in the recent Fiscal Monitor released by the International Monetary Fund (IMF, 2020): a well-designed fiscal policy plan can stimulate the structural transformation of the economy and foster productivity growth. This result is particularly relevant nowadays if policy prescriptions aimed at allowing countries to emerge from the stagnation generated by the COVID-19 pandemic and the one experienced after the Great Recession are to be formulated.

Appendix B
A robustness check is carried out on Model 3 by assuming a different identification strategy shown in Eq. (10), where government expenditure is considered more exogenous than export in the contemporaneous relationship. Estimated IRFs and cumulative effects are reported in Fig. 4 and Table 2, respectively. As in the main model specification, IRFs are highly persistent as they remain positive throughout the 20-year period. Furthermore, cumulative effects are similar to the findings obtained in Sect. 3, thus showing that findings are robust to different model specifications.