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In a nutshell, we argue that shifts in income distribution may have contributed to the pre-crisis macroeconomic instabilities and current account imbalances in the following ways: In the USA, the functional income distribution has remained roughly stable, but top-end household income inequality has increased dramatically. This has triggered very substantial expenditure cascades all the way down the income ladder.

Emulation in consumption is very strong as a result of the institutional specificities of the labour market high labour mobility, weak precautionary saving , the educational system private schools and the financial system poor regulation, easy access to credit. It would certainly be misleading to qualify emulation as irrational or to attribute it to an excessive desire for luxury goods. Rather, applied to the US context, the relative income hypothesis highlights the difficulties faced by the middle and upper-middle class in providing for what they perceive as basic needs in the face of rising inequality at the top of the distribution.

Such goods can be qualified as positional goods, because their value is determined by relative rather than absolute consumption. In the face of declining relative incomes, households below the top of the distribution opted to reduce their saving a non-positional good and increase consumption and debt in an attempt to keep up with the rising spending patterns of households at the top.

This has contributed to the increasing current account deficit and the debt crisis starting in In Germany, the shares of wages and household income in national income have strongly decreased, with the result of reduced private household spending and aggregate demand. By contrast, top household income shares have not increased very much, partly because corporations have chosen to accumulate large net financial savings within firms rather than raising top management pay to US levels.

Expenditure cascades have been limited as a result of relatively stable top income shares, but also due to a rather different institutional setting low labour mobility, publicly financed education system, etc. In China, both the functional income distribution lower household income and the personal income distribution rising top-end inequality changed considerably prior to the Great Recession.

The former effect has weakened private household spending and thus aggregate demand. At the same time, expenditure cascades have been limited due to an underdeveloped financial system which has limited the access to personal credit. In both Germany and China, the rise in the current account balance stems to a large extent from the higher saving of the non-household sectors, i.

Compared to the USA, the relative income hypothesis and upward-looking status comparisons have played less of a role in determining macroeconomic trends. By contrast, the shift in the functional distribution at the expense of households and towards higher corporate net saving has weakened aggregate demand and contributed to the increasing current account surpluses. The remainder of the paper is structured as follows.

Section 2 discusses empirical facts on income distribution, household debt and the current account for the USA, Germany and China. Section 3 presents the main building blocks of the model, and Section 4 discusses the calibration of the model. Section 5 presents numerical simulations. In Section 6, we discuss the contribution and the limitations of the paper in relation to the existing literature, and Section 7 concludes. The full set of model equations is provided in an Appendix. We argue that changes in functional and personal income distribution may have contributed to the build-up of macroeconomic instability in a number of relevant countries prior to the Great Recession.

Among the most important indicators of financial fragility are excessive household leverage ratios and current account imbalances. A compelling explanation of these trends is one of upward-looking status comparisons, or expenditure cascades Frank et al. The degree to which expenditure cascades occur likely depends on the specific nature of inequality as well as country-specific institutions. Our preference for the expenditure cascades model is based on the observation that it fits very well with the pre-crisis macroeconomic patterns of a number of countries, most prominently the USA.

According to this view, households just below the top of the distribution have reduced their saving in order to try to keep up with the spending patterns of households at the top. This, in turn, may have also increased the pressure on the lower middle and lower classes to increase spending relative to their incomes. Ultimately, therefore, the rising standard of living at the top of the distribution has affected the consumption norms of the entire income distribution.

Evidence in favour of the above explanation of the decrease in the US household saving rate can be provided based on micro data.

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In this way, the rise in top-end income inequality seems to have contributed in an important way to the rise in the consumption-to-GDP ratio and to the decrease of net exports prior to the Great Recession, while the financing of private household expenditure increasingly relied on foreign borrowing van Treeck and Sturn, On the other hand, there is evidence that a decrease in the wage share or an increase in the corporate financial balance leads to an increase in the current account Lavoie and Stockhammer, ; Behringer and van Treeck, Further empirical evidence suggests that a change in the fiscal balance also significantly affects the current account, ceteris paribus e.

Chinn and Ito, ; Behringer and van Treeck, Clearly, to the extent that corporate wealth is highly unequally distributed but retained corporate profits are not counted as household income, top household income shares may underestimate the degree of top-end inequality in countries where retained profits increase at the expense of household income. But the rise in retained corporate profits also restrains domestic demand if the investment spending of firms does not increase proportionally to the rise in retained profits.

Finally, and perhaps paradoxically, the rise in corporate saving may limit the pressure for the middle class to engage in debt-financed consumption, because rich households which can be seen as the reference group for the middle class do not increase their spending in proportion with the rising profits of the corporations, of which they are the owners, but rather increase their saving rate indirectly through corporate net saving.

In this way, the rise in corporate income at the expense of household income weakens private consumption, domestic demand and imports, thereby contributing to the rise in net exports. Excess domestic savings will be reflected in a current account surplus. For further discussion of the empirical evidence, see van Treeck and Sturn Figures 1 to 3 illustrate these empirical findings in a descriptive manner for the USA, Germany and China.

The share of private consumption in GDP increased by almost 10 percentage points from to , and residential investment added a further two percentage points of GDP to private household expenditures. While the adjusted wage share decreased somewhat, the share of disposable household income in national income remained roughly constant.

The financial balance of the corporate sector increased slightly. In Germany, by contrast, top household income shares remained almost constant until the Great Recession Figure 2 , even though the rise in the Gini coefficient of household income since the mids was similar to the rise in the USA OECD, However, the functional income distribution in Germany showed a marked shift to the expense of wages and household disposable income throughout the s and the s, i.

Note that the decline in the adjusted wage share was significantly more pronounced than the decline in household disposable income. This may reflect government transfers, but also the importance of unincorporated businesses in Germany. During both the s and s, the increase in the current account was driven by the rise in the corporate financial balance. Note that the weak domestic demand was not due to low private business investment in either period, contrary to an argument routinely made by the Organisation of Economic Cooperation and Development OECD, , Rather, the rising net exports were the result of weak private consumption and residential investment expenditure and low public investment, especially in the s.

The increase in the current account balance was primarily driven by the rise in corporate net lending and the reduction in the government deficit, but also by the increase in the private household financial balance, at least in the s. Household leverage decreased during the s, following the rise during the s after reunification. The case of China is in some respects similar to that of Germany Figure 3.

Although data reliability is a notorious problem, there was a clear and very pronounced downward trend of the share of private consumption in GDP. This was only partly compensated by the increase in residential investment. The shares of wages and, even more so, household income in national income have declined spectacularly since the late s.

At the same time, top household income shares as well as the Gini coefficient of household incomes have risen substantially. The rise in the current account balance since the mids was driven by the increase in corporate and government net lending. In this section we present the accounting structure and discuss the most important behavioural equations of our model.

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Space constraints force us to focus only on the key assumptions that drive the main results of the model, but we refer interested readers to an Appendix for the complete model. Despite the large size of the model, some of our modelling choices are somewhat simplistic from a theoretical perspective. This is true especially for the modelling of capital investment, asset prices rates of return and exchange rates. Since these parts of the model are not our main focus of attention but are notoriously difficult to model, we attempted to find a reasonable compromise in our modelling strategy.

Although the specifications are simple, many parameters and exogenous variables are time varying in our model and calibrated to real-world data in our simulations. We thus go beyond most existing SFC models, which often rely on relatively arbitrary and time-invariant values for parameters and exogenous variables. Other parts of the model are specified in far greater detail. This is true especially for the modelling of income distribution and consumption.

The household sector of each country is divided into ten segments deciles , which allows us to calibrate the personal income distribution for each country in a realistic way using actual data. Moreover, we construct quantitative measures to capture heterogeneous cross-country emulation behaviour in private household consumption. A discussion of the limitations of the model with respect to existing literature is provided in Section 6. Appendix A contains a full list of variables and parameters. The full set of model equations is provided in Appendix B.

Table 2 shows the balance sheet matrix for the three model economies as a single complete system. Variables without the superscript i denote sector aggregates. In each country there are three sectors: households, firms and banks. Households hold two types of assets: domestic bank deposits, m h j and domestic corporate equity, e d j p e j where e d j is the number of shares and p e j is the price per share. On the liability side, households have loans, l h j from domestic and foreign banks in domestic currency.

Firms issue equities and take on loans, l f j from domestic banks. Cross-border lending and borrowing is limited to consumer loans, so that the current account is the sum of net exports and net interest payments received on consumer loans. Trade linkages are modelled in the following simple way. While we do not pretend to have a good theory of exchange rate determination, exchange rates are calibrated using time-varying real-world data see Section 4. For our purposes, the use of exogenous exchange rates does not seem to be too far from reality. Because in our model only households can lend and borrow internationally, we also assume that total imports are a function of household consumption:.

To a large extent, this modelling choice is based on the empirical observation that the decrease of US net exports as a percentage of GDP since the early s was reflected in the simultaneous rise in the private consumption-to-GDP ratio. Both private investment and government final demand remained relatively stable as a percentage of GDP over that period see Section 2.

Similarly, in China, the increase of net exports as a percentage of GDP during the s was accompanied by a decrease of the consumption-to-GDP ratio, whereas the other components of aggregate demand remained relatively constant as a percentage of GDP. Nevertheless, our specification of imports is certainly not entirely realistic. A considerable part of total US imports are investment goods. The fact that international financial transactions are limited to borrowing by households is also not realistic, but it accounts for the fact that the credit-based private consumption in the USA required an increasing amount of foreign financing prior to the Great Recession.

Note that capital flows play no active role in determining the current account except for interest payments on personal loans. Notice also that we abstract from other real supply-side factors that can have important implications for exports and imports. Such factors include unit labour costs, technological catching-up or non-price competitiveness.

Instead, our model highlights the potential relevance of one determinant of trade and current account imbalances, i. A further simplifying feature of the model is that international trade is limited to three countries, whose trade and current account balances must necessarily sum to zero. Thereby, the analysis is reduced to the three countries with the largest pre-crisis current account imbalances. That is, firms distribute a fixed fraction of expected total profits net of interest payments see Godley and Lavoie, A.

Expectations are modeled in a simple backward-looking fashion, with g j being the growth rate of the economy. In our calibration and simulation exercises, we will adjust the corporate retention rate in each country in order to control for the different patterns of wage income and household income.

Interest rates are exogenous but time variant. Aggregate household disposable income is equal to the sum of the wage bill and interest and dividend payments received from banks minus interest paid on consumer loans. Aggregate household disposable income is distributed across deciles in the following way:. The calibration of personal income distribution requires us to specify the distribution of wages and household net worth as well as interest rates and corporate saving rates in each country.

Stock prices simply follow a random walk. The specification of the consumption function is an extension of the expenditure cascades model proposed by Frank et al. It is assumed that households in the top income decile consume only on the basis of their own disposable income and accumulated wealth, which may be interpreted as a variant of the life-cycle model:. Similar specifications for aggregate consumption are proposed by Godley and Lavoie A.

The lower deciles emulate the consumption of their reference group. Following the behavioural insight that status comparisons are predominantly upward looking, we define the social reference group of each decile as the next highest decile in the income distribution. The desired consumption of the bottom nine deciles is then given by:. These include in particular the financing of public goods education, health care, etc.

For instance, households with highly firm-specific skills, weak female labour force participation and a large gender pay gap, prevalent in Germany, may react to rising inequality with higher precautionary savings Carlin and Soskice, Similarly, the passivity of monetary and fiscal policies in the face of business cycle downswings in Germany, which increases the risk of long-term unemployment and hysteresis effects, adds to the perceived need for precautionary saving and hence reduces consumption emulation.

Besides, the much more extensive state-funded provision of public goods in Germany, compared to the USA, limits the room for positional arms races because the limited scope of private education or health care markets reduces the degree of price differentiation. The precise construction of country-specific emulation behaviour is, of course, open to debate.

For instance, one might ask why Germans will not channel their funds into more positional differentiation on, say, cars or fashion instead of education and health care. The response to this is that households with relatively low incomes will accept low saving rates and high leverage ratios only if this is necessary for them to acquire such positional goods that are perceived as especially important in terms of the social status that they stand for. To give an example, most households wish to maintain healthy balance sheets through adequate saving and low debt levels, but they also seek to send their children to the best schools possible.

This can be achieved both through paying high tuition fees, and by living in those expensive neighbourhoods where the best schools are located. When income inequality increases and rich households spend more money on housing and schooling, households below the top of the distribution face a difficult trade-off between saving less and borrowing more on the one hand and sending their children to lower-quality schools on the other hand. In the USA, many households with falling relative incomes seem to have chosen the first option prior to the Great Recession see Frank et al.

In Germany, the pressure for households to trade off healthy personal finances for basic middle-class needs such as decent education, housing or health care is certainly weaker. Despite our efforts to provide some empirical backing for the country-specific emulation parameters, the exact size of the emulation parameters is difficult to determine with certainty. Therefore, in our simulations we will perform a sensitivity analysis using different emulation rates for each country. Clearly, the ability of the middle class in China, but also in Germany, to engage in debt-financed consumption is restricted by the more conservative bank lending practices in these countries, compared to the USA.

In sum, while the consumption function is simple, it encompasses different theories of consumption, including Keynesian, life-cycle and relative income theories. The total credit demand of households is given by. That is, we link borrowing to consumption in a very simple fashion 3 and we assume that the only cross-border borrowing activity is related to financing consumption. Again, the starting point for this way of reasoning is the observation that the relative strength of domestic demand in the USA was due to relatively strong consumer demand which was in large part financed by credit and led to a current account deficit that also required foreign financing.

We assume that households face a financing constraint beyond which the banking sector will restrict its provision of credit for consumption purposes. This is formalised by means of indicator functions: z 1 i , j which take a value of 1 when the finance constraint is not binding and a value of 0 once it becomes binding, and z 2 i , j which work the other way around. Specifically, once the leverage ratio of a given household decile reaches a certain threshold, the finance constraint becomes binding.

Additionally, we require that households service their debt at all times out of their disposable income. It is only when leverage exceeds the maximum level accepted by banks that consumption is reduced. According to our specification, banks will still allow households to consume in accordance with a measure of their lifetime budget constraint reflected by current income and wealth. But they are no longer willing to finance expenditures that go beyond this level. We assume that lending rates are equal to deposit rates, i. Interest rates are exogenous, but time varying.

Because banks make consumer loans internationally, non-zero capital account balances are possible and intermediated through the banking system, but they are fully driven by the current account. Firms can finance their investment expenditures in three ways. They can retain profits, f U j issue new equities, e s j or borrow from domestic banks, l f , d j The dividend decision is formalised in Equation 3. Furthermore, following a standard practice in the SFC literature Godley and Lavoie, A , we assume that a constant fraction of investment is financed via new equity issues.

Finally, the remaining financing gap is closed by borrowing from the banks. The simplicity of the investment function may be justified by the observation that current account imbalances were mainly driven by different trends in private household expenditure across countries, and less by corporate investment. In our calibration and simulations we use an empirical measure for the rate of utilisation, to ensure that it remains within a realistic range. In this section we describe a relatively simple way of calibrating the model to real-world data, including the starting values of the endogenous variables as well as the exogenous variables and parameters.

Figures 4 to 6 show the components of GDP, the functional income distribution, sectoral financial balances and debt-income ratios for the three model economies. In contrast to Section 2, macroeconomic variables are now adjusted to match the accounting setup of the theoretical model. For instance, we do not explicitly model the government sector but distinguish only the household sector and the non-household sector, as we discuss below.

The basic procedure is as follows: First, model-adjusted data helps define the parameters and the starting values of the endogenous variables. We then run the model and follow the trajectory of the most important endogenous variables as a baseline scenario. If the model produces a realistic baseline simulation, it can also be employed for scenario analysis. We can then ask how specific variables of interest, in particular the current account and household debt, would have developed, if shocks to the functional and personal income distribution had not occurred. A further motivation for choosing different starting dates is that inequality has started to increase strongly in the early s in the USA, but only since the mids in Germany and China.

In contrast to much of the open economy SFC literature, we do not model the public sector explicitly because our main focus is on private sector behaviour and the demand for private consumption including residential investment. This also means that we do not model central bank interventions in international capital flows, which in our model result only from private trade balances and interest payments on outstanding private debt.

Separating the government and corporate sectors is one of the possible extensions left for future research. Net exports are taken directly from the national accounts. Household disposable income is calculated as the sum of the household financial balance from the national accounts and our measure of consumption. Corporate disposable income is then calculated as the sum of the corporate financial balance and our measure of investment as defined above.

As a matter of simplification we chose an initial net foreign position of zero for all countries. Furthermore, GDP equals national income. Stocks of decile-specific assets and liabilities are calculated as follows. These are multiplied with our decile-specific measures of disposable income, giving us the starting values for the decile-specific stock of debt. The aggregate stock of household debt in each country is obtained as the sum of debt of the household deciles.

The stock of aggregate and decile-specific assets is calculated in a similar fashion. First, we multiply aggregate net-worth-to-income ratios with our measure of disposable income to obtain the aggregate net worth. To obtain the household-level measures of net worth, we use information on the wealth distribution from Wolff , for the USA and our own calculations based on SOEP for Germany. Aggregate deposits held by households are computed as the sum of outstanding domestic consumer and business loans, taken from the Flow of Funds.

For China we use data from Zhong et al. We use exogenous but time-varying interest rates. Due to time-series limitations, time mapping was used to fill the entire simulation period with data. The exchange rates used for the simulations are based on bilateral exchange rates and the special drawing rights SDR held with the IMF. This allows us to use exogenous but time-variant exchange rates in a comparable manner. These penalty terms are subtracted from the natural rate to yield the effective rate of imitation.

The penalty term for the rate of imitation in a given country is normalised to the unit interval. It is constructed as follows:.

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Data sources and sample periods are summarised in Appendix C. By backward calculation we obtain a natural rate of imitation equal to 0. Clearly, our construction of the imitation parameters is only approximative and far from the statistical validity of a properly specified regression. In particular, our choice of proxies may be subject to a selection bias and the direction of cause and effect we assume in the following is not indisputable.

Referring to the existing literature, our choice of proxies can be motivated as follows:. The computation of the country-specific penalty terms rests on two pillars: 1 labour market arrangements Carlin and Soskice, and 2 public infrastructure Frank et al. The first pillar describes labour market mobility and firm-specific skills using data on the incidence of long-term unemployment and average job tenure in each country.

As firm-specific skills put an obstacle to matching workers quickly to appropriate jobs, we expect workers with more highly firm-specific skills and lower employment mobility to save a higher proportion of their income during times of rising income inequality, as this increases the risk of persistent status loss. Hence, a more flexible labour market e. USA compared to Germany is expected to reduce the penalty term for the rate of imitation. High long-term unemployment may also be due to a lack of aggregate demand and passive monetary and fiscal policies causing unemployment hysteresis.

The second pillar is public infrastructure, which we approximate with health care expenditures, social transfers, the number of private schools per one million population and the level of education tuition fees. For instance, the lower public per capita expenditures on health care, the lower the penalty term for the rate of consumption imitation. On the other hand, the number of private schools per one million inhabitants and annual tuition fees are positively related to emulation. According to Figure 4 , the maximum debt-to-income ratio of all household deciles in the USA in is 2.

Hence we multiply all values from the IMF database with 2. This allows us to consider country-specific degrees of financial market development and deregulation. In this way we obtain a constant threshold of 2. For China, we obtain relatively low values. Here, the threshold increases from 0. Clearly, our simple specification of the maximum debt-to-income ratio is far from being the only possible calibration.

This choice may be seen as oversimplifying, but we do believe it constitutes progress compared to purely theoretical SFC models. Equity prices are determined by a random walk with relatively low volatility. A possible extension of the model would be the inclusion of more complex and realistic stock price mechanisms. However, in this paper we do not address such issues as excess volatility or asset price inflation.

We use standard values of the portfolio choice parameters, following Dallery and van Treeck The rate of capacity utilisation affects the rate of capital accumulation via the investment function in Equation Equation A. The latter is calculated as the average of actual unemployment between and We thus obtain baseline values for potential output which we can then use as an exogenous variable for the scenario analysis. With the rate of capacity utilisation endogenous, the expansionary output effects of a fall in e. The purpose of the following simulations is to analyse the quantitative effects of rising inequality, both personal and functional, on the current account in different institutional environments.

In particular, we shock the following variables according to data taken from the national accounts and household surveys:. The distribution of the wage bill : Although survey data is often not fully comparable and different reference years have to be used, we have reliable survey data for the shares of all income deciles for at least two data points in all countries Figures 4 — 6.

We can thus shock the entire personal income distribution 10 in each of the three countries. Compare the parameter list in Appendix A for the changes of the entire distributions. Distributed profits : We shock the share of profits which is distributed to households in such a way as to partly adjust for the different trends of wages and household disposable income observed in the data Figures 4 — 6.

The accumulation rate : As a matter of comparability, we have to make sure that the national GDPs do not vary widely between the baseline scenario and the alternative scenario. This requires corrections of autonomous capital stock growth of —0. Figures 7 — 9 as well as Appendix D present the simulation results. Both illustrations include scenario values following income shocks. On the one hand, this is to compare the scenario values with the model-adjusted data and thus to determine if the model can replicate the stylised facts from Section 2 Appendix D.

On the other hand, a scenario analysis is conducted to investigate how the relevant macroeconomic variables would have changed in the absence of income shocks Figure 7 — 9. Germany, deviation between scenario values and baseline; Upper left: GDP expenditure approach; Upper right: Sectoral financial balances; Lower left: GDP income approach; Lower right: Debt-income ratios for selected deciles. China, deviation between scenario values and baseline; Upper left: GDP expenditure approach; Upper right: Sectoral financial balances; Lower left: GDP income approach; Lower right: Debt-income ratios for selected deciles.

The saddle paths, in particular in Appendix D, do not always show smooth convergence towards the steady-state solution, as is usually the case in theoretical SFC models. The following reasons can be mentioned for this: first, the amount of time-variant parameters loaded into the model such as interest and exchange rates. In most of the existing SFC literature, some of the parameters are chosen to guarantee strict convergence. While our emphasis is on bringing parameters closer to observable data, we accept a higher degree of under- or overshooting. This certainly does not mean that we allow for explosive paths.

Finally, the implementation of financing constraints for consumers, if it becomes binding, can produce temporary non-linearities on the saddle paths. We first compare the model-adjusted data from Figures 4 — 6 with the scenario values from our simulations Appendix D. The results from the scenario analysis will be reported and discussed in detail in Subsection 5. It should be emphasised at the outset that the model cannot be expected to replicate perfectly the real-world data from Figures 4 — 6 for the simple reason that our model treats the three economies as a single closed system.

For example, the model forces the current account balances of the three countries to sum to zero, whereas this is obviously not the case in the real world. With this caveat in mind, the following observations can be made cf. Appendix D. While the US consumption-to-GDP ratio is slightly overestimated and the investment-to-GDP ratio slightly underestimated by the model, the current account deficit matches very well with the data, especially at the end of the simulation period.

The same applies for the Chinese investment-to-GDP ratio. Only at the end of the simulation period does the model underestimate the Chinese current account surplus, which at the same time requires a small overestimation of the Chinese consumption-to-GDP ratio. Importantly, the US household financial balance is replicated closely and turns negative in the course of the simulation period. The level of the corporate financial balance is slightly underestimated. With the exception of the German household financial balance, which is continuously overestimated, all other sectoral financial balances of the model match very well with the data.

Note that the overestimation of the German household financial balance is in accordance with the overestimation of the current account and thus can be traced back to GDP differentials in the three-country model. In accordance with real-world data, simulated household debt-to-income ratios are highest in the USA, at least at the end of the simulation period, and lowest in China with the somewhat puzzling exception of the tenth decile.

Yet, one has to admit that the simulated debt-to-income ratios are not realistic throughout; see Figures 10 — Besides using a wide definition, Piketty employed the terms "wealth" and "capital" as interchangeably. What are the implications of doing that for economic growth and distribution theory? In second place, even though using neoclassical tools, would be possible to incorporate Piketty's main points in a heterodox structure in order to do not throw the baby out with the bath water? The distinction between financial and productive assets is relevant and consistent with the Post-Keynesian paradigm.

Being so, from a Post-Keynesian perspective, Piketty's hypothesis is wrong. The paper is divided in three sections besides this introduction. In the second section we revisited Piketty's main considerations and its reception in the economic literature. In third section we revisited Kaldor, Pasinetti and Foley models showing our main points about the relation between r, i and g.

The last section brings our conclusions. In terms of the history of economic thought, Piketty's book goes back to an analytical tradition where history, theory and polities were combined in the study of economic phenomena. His strategy begins with a panoramic reading of data, picturing the history of the trajectory of wealth or of capital in France, U. As suggested by the title, "capital" is at the centre of the stage.

The increase in inequality is said to have been generated mostly by the great and increasing domination of income from capital. Piketty's controversial argument does not issue simply from his conclusions, but begins with the very definition of the term he is using. Capital is defined as " the sum total of nonhuman assets that can be owned and exchanged on some market " p. Two fundamental problems descend from this definition and a third one is added during construction of the argument 2. First of all, all forms of property, whether real or financial, are included without any distinction between them.

We show in the next section that this distinction is unfortunately very important in the light of the financial fragility of capitalist economies. Next, as already pointed out by Piketty himself and various authors e. It is not clear whether and when Piketty refers to one or another 3. While authors like Solow, consider that in the long run there are no big problems in treating "capital" and "wealth" as interchangeable terms, we believe that this distinction is also important when constructing a growth and distribution theory that leads to aspects of the capitalist financial fragility.

Moreover, as pointed out by Patnaik, , a third problem emerges from the fact that Piketty's theory is based on the neoclassical theoretical paradigm. Uncritical use of the marginalist approach in determining the profit rate demonstrates how a valid and critical theoretical framework can be submerged, misunderstood and forgotten in the social sciences 4 Aspromourgos, At any rate we do not tackle this issue as it has been discussed at length in the literature e.

Capital in the Twenty-First Century focuses on the process of income concentration in favour of capital, enabled by the apparently capacity of the economy to absorb increasing quantities of capital without a significant fall in interest rates. All theory that relies on a neoclassical production function to account for income distribution relies crucially on the substitution elasticity between capital and labour and it is not different in this case.

In Piketty's model the rate of profit is related to the marginal productivity of capital. We can see this point using a CES production function where the relation between the profit share and the capital-output ratio is given by:. In terms of growth rates we have that:. This expression allows us to see in a very pedagogical way the main elements behind the mechanism describe in the book. Piketty argues that in the long run, a rate of return on capital systematically higher than the rate of growth of the economy implies that capital or rather, wealth grow more rapidly than output and income.

In order to close the argument he states that:. Piketty reverts to the neoclassical model of distribution of income by relying on a high value of the elasticity of substitution between capital and labour. Finally the book presents a complementary explanation for the recent increase in inequality that relies inside the wage structure. Piketty points out that the excessively high rewards to managers could also contribute in explaining the phenomenon of rise in inequality. Aspromourgos, shows that although the argument is valid, if we assume a production function with constant returns to scale, it is not possible to maintain a neoclassical theory of marginal productivity to explain profits and at the same time reject it when it comes to explaining wages.

Piketty stresses the relevance of socioeconomic forces in determining distributive dynamics, but his theoretical reference leaves very little space for it. Despite its hypotheses and conclusions, Capital in the Twenty-First Century shows that in a sense we are coming back to the XIX century not only in terms of inequality levels but also in terms of a return to "patrimonial capitalism" Krugman, What are the implications of the alternative definition used by Piketty for a theory of distribution?

14.5 Government Policies to Reduce Income Inequality

Or do his main results survive if the more conventional definition of capital is used? The fundamental result of the Harrod-Domar model is that a stable growth path with full employment is mathematically possible but extremely unlikely Oreiro, Despite its intuitive insights, Kregel, argues that Harrod's model is " general accepted to contain an anomaly or a problem, viz the knife edge " p. In a very simple way, the warranted output growth rate in steady-state is unstable and any shock generates an explosive growth path or its collapse to zero Fazzari et al.

Since those predictions are not verified during the period of the Golden Age , Post-Keynesian authors like Nicholas Kaldor and Luigi Pasinetti developed long run growth models with full employment. For doing that it was necessary to develop a new theory for the functional distribution of income in which the profit share would be the variable of adjustment between the decisions of investment and savings Harcourt, ; Oreiro, A significant number of authors have modified Harrod's original model in order to "correct" its intrinsic instability 7.

Shaikh, proposes an adjustment process that stabilizes the warranted growth path. Skott, also discusses the mechanisms that can stabilize models in Harrods tradition in the long run. Fazzari et al. In the ceiling the economy cannot growth explosively because is limited by the supply side. In the floor the instability is solved by the introduction of an autonomous demand component. In this section we will focus on the original models of Kaldor and Pasinetti since they are sufficient to study the relation between r and g.

In the preface of his Magnus Opus, Principles of Political Economy and Taxation , Ricardo considers that the laws that regulate distribution are " the principal problem in Political Economy " Kaldor, , p. Effectively, one of the theoretical assumptions in Post-Keynesian analytical models is that the functional distribution of income has a fundamental importance for the long run economic growth since it influences the investment decision. Post-Keynesian theory has its beginning with Nicholas Kaldor in a seminal paper published in the Review of Economic Studies , not because he was the first- this position corresponds to Kalecki - but because he is the most known Harcout, The "Cambridge Equation" was first established by Kaldor, and Pasinetti extend his initial results.

Kaldor calls his theory "Keynesian" for at least three reasons Harcourt, First because he situates it in the "widow's cruse" analogy made by Keynes in A Treatise on Money. Second because he considers that investment precedes savings. Being so, while investment determines the level of income and its distribution, savings works as an adjustment variable. Finally he extends the Keynesian multiplier principle to the long run in determination of prices and wages.

Where Y corresponds to the level of income, W corresponds to the total of wages and P to the total of profits. Investment and savings are representing by I and S , respectively. Savings are divided between savings that come from wages, S w , and profits, S p. In an economy with two social classes output is divided between those who receive wages and profits. In the other hand, total savings is a formed by savings that come from wages and savings that come from profits.

Notice that we do not refer to workers or capitalist savings. This differentiation will be done explicitly by Pasinetti. Finally, investment equals savings. Departing from these identities, Kaldor finds the profit share and the profit rate of the economy:. Where S p and S w correspond to the marginal propensity to save from profits and wages, respectively.

Equation 3 shows that the profit share is a function of the investment level and the propensity to save from wages and profits. The higher the investment level, higher will be the profit share. Also, the higher is the propensity to save out of profits and lower is the propensity to save out of wages, higher will be the profit share. Equation 4 gives the profit rate as a function of the investment level and the propensities to save. Here appears for the first time a relation between growth rate and profit rate. In the other hand, the higher is capital's productivity, lower will be the profit rate.

Once again, the higher the propensity to save out of profits and lower the propensity to save out of wages, the higher would be the profit rate. This condition does not depend on the existence of different social classes and instead is related with the nature of entrepreneur's income Oreiro, This happens because firms have a higher incentive to save since i there is a need of continuous expansion of productivity capacity that would make be possible if part of the funding comes from retaining profits and ii the existence of increasing returns make firms competitive position dependent of its market share.

Kaldor calls the sensibility coefficient of distribution. Given a change in investment it would determine how much income distribution would change. The model still operates under two restrictions. Equation 3. The Cambridge Equation postulates that the capital's profitability is determined through the equilibrium growth path independently from capital's productivity.

Another way to see this result is presented as follow. Combining Harrod's condition with both Kaldor's restrictions we have that:. Piketty argues that a profit rate systematically superior to the output's growth rate is responsible for the increase in income inequality in capitalism. In fact he affirms that:. Being so, a special tax regime on the capital's profitability in order to revert the increasing inequality will be desirable. However, in the light of Kaldor's model this alternative does not seem viable from an economic point of view.

The model presented in the last section ignores that workers can save and being so have property of part of the capital stock. Pasinetti then showed that the Cambridge Equation could also be obtained without any reference to the propensity to save out of wages Oreiro, To demonstrate the validity of this affirmative lets considerer an economy where workers save a fraction Sw of their income so that - supposing that capital is the only asset of the economy - a share of the capital stock belongs to workers.

In this context a share of the profits generated in the production process would belong to workers that will also receive wages W. Let P p be the amount of profits that belongs to capitalists, P w the profits that belongs to workers, s w the propensity to save of workers and s p the ropensity to save of capitalists. We have then the follow system of equations:. Let be K w the capital stock that belongs to workers. We will suppose that workers "lend" this capital to capitalists receiving an interest rate of r. In steady state we can show that the capital share of workers is given by:.

Equation 13 shows that the distribution of wealth between social classes is stable in the long run. Making the profit rate equals the ratio between the total profit and the capital stock 8 and after some algebraic manipulations, Pasinetti finds that capital profitability is given by:. Equation 15 is again the famous Cambridge Equation. We establish that the profit rate is determined by the natural growth rate and the savings propensity from profits.

The great challenge that the Cambridge Equation had put to the neoclassical theory was in its degree if generality Oreiro, In fact it is valid for any production function. In this way a systematically superior capital's return rate in relation to outputs growth rate is not responsible for an increase in inequality. Passinetti's model shows that capitalist economies does not have an inexorable tendency to an increase in inequality of income and wealth. In order to have a better understand of this point let us make a numerical simulation.

Keynesian economics - Aggregate demand and aggregate supply - Macroeconomics - Khan Academy

We consider an economy in which labor force growth rate of 1. Let's suppose that the normal capacity utilization rate is equal to 0. Finally taking the propensity to save from capitalists equals to 0. In order to capture technological progress and following Kaldor, and Verspagem, we take a technological function in this format:. Where the productivity growth rate, , depends on the capital's growth rate, g , the labor force growth rate, n , and the technological gap, G.

We also have that is a parameter that intends to capture learning capacitys. Finally q 0 and q 1 are constants. In our simulation the coefficient represents the part of technological progress that is disembodied and equals 0. The values for the output's growth rate, the profit share and the wealth share from the capitalists can be visualized in the figure bellow:. Source: Authors own elaboration. In the right vertical axe we have the natural growth rate, while in the left we have the profit share and wealth that belongs to capitalists.

All this variables depend non-linearly of the technological gap, represented in the horizontal axe. Pasinettian model shows us that capitalist economies do not have an inexorable tendency to increase income and wealth inequality. Minsky belongs to a tradition of authors for which there is no capitalist economy without banks, without credit and without debt instruments Deos, Accordantly to Vercelli, , the structural instability in authors as Marx, Schumpeter, Keynes and Minksy himself comes exactly from the properties of money and credit.

Minskyan analysis departs from an economy where each agent is characterized by his portfolio, formed by assets and liabilities. Part of the assets, being longlasting and demanding an expressive sum of resources to be acquired, has to be financed. Financial liabilities are generated exactly in order that the assets can be pursued.

They create future financial commitments that have to be met. That is why a Minskyan economy is by its nature a speculative economy Minsky, ; Deos, The deep global recession that started in the financial market revived a strong interest in the explanation and policy implications of financial crashes Sordi and Vercelli, Both, Keynes see for example the G. The differentiation between profit rate and interest rate is not obvious. Foley, develops a mathematical representation of the Minskyan regimes Hedge, Speculative and Ponzi modifying the last version of Taylor and O'Connel, Minsky saw a tendency of the agents that make the spending decisions - especially those who hold capital assets 9 - of becoming progressive more indebted in prosperity times, increasing in this way their vulnerability to financial crises.

Financial fragility is a result of the firms practice to get into debt to finance production. The FIh is related to the conception of capitalism as an inherent unstable system Keen, , It establishes a link between credit expansion with the increase in asset's prices and the inherent fragility of an economy Grasselli and Costa Lima, The fragility of economic units fluctuates pro-cyclical with economic fluctuations, increasing the danger of severe financial crises after a boom phase.

The original and traditional approach deals with non-financial firms financing investment, even thought there is in the literature references to household's debt. Where Re corresponds to the firm's revenue, D corresponds to the loans taken by the firms, I once again is investment and V is given by the debt service. So we have that the sum between revenue and loans have to be equal to the sum between the investment and the service debt payments. Net worth, PL , equals the difference between assets, A , and debts, B. Differentiating identity V in time we get the relation the links identities IV and V:.

Minsky identifies tree possible financial postures for the firm. In the first one, called Hedge , revenues are sufficient to cover the total of investment and the debt service. An agent has a Hedge or secure posture when its expected income allows him to meet all his financial commitments in a finite time horizon.

In the second state, the firm can meet the debt service with its own revenues, but cannot do it with the principal. If for some periods the financial commitments are higher than the expected income, then agent has a Speculative structure. The debtor and creditor speculate about the possibility that the debtor will be able to refinance its debt in the future.