Income Distribution in a Stock-Flow Consistent Model with Education ...

Eastern Economic Journal, 2011, 37, (134–149) r 2011 EEA 0094-5056/11 www.palgrave-journals.com/eej/

Income Distribution in a Stock-Flow Consistent Model with Education and Technological Change Stephen Kinsellaa, Matthias Greiff b and Edward J. Nellc a

Kemmy Business School, Department of Economics, University of Limerick, Co. Limerick, Limerick, Ireland. E-mail: [email protected] b Institute of Institutional and Innovation Economics, Faculty of Economics and Business Studies, Hochschulring 4, D-28359 Bremen, Germany. c Department of Economics, New School for Social Research, 6 East 16th Street, New York, NY, 10003, USA.

We model a macroeconomy with stock-flow consistent national accounts built from the local interactions of heterogenous agents (households, firms, bankers, and a government) through product, labor, and money markets in discrete time. We use this model to show that, without any restrictions on the type of interactions agents can make, and with asymmetric information on the part of firms and households in this economy, power-law dynamics with respect to firm size and firm age, income distribution, skill set choice, returns to innovation, and earnings can emerge from multiplicative processes originating in the labor market. Eastern Economic Journal (2011) 37, 134–149. doi:10.1057/eej.2010.31 Keywords: inequality; agent-based macroeconomics; econophysics JEL: C63; C15

INTRODUCTION [W]hat markets do y is to generate the pressures that increase productivity y these pressures bring about innovations, organizational innovations as well as new technologies, which markets then diffuse throughout the system by the force of competition. Market adjustment — the price system — mobilizes the profits to underwrite the investment in these innovations, making the diffusion possible. This means that markets pick winners and losers, which is, indeed, a rough sort of allocation [Nell 1998]. In this paper, we claim the market system generates inequality endogenously, producing the ‘‘rough sort of allocation’’ described in the quote above. In markets characterized by decentralized traders interacting locally with other traders, and globally as members of a ‘‘sector,’’ rewards accrued by the successful benefit the rewarded, and losses hurt the losers. This modeling structure allows us to replicate observed empirical regularities of income distribution, educational levels, and firm sizes, and allows us to contribute to several literatures at once.1 We model the simple insight of the market as an allocative mechanism between winners and losers using a four sector macrodynamic model comprised of firms, households, banks, and a government. Gains and losses are induced by market trading of heterogeneous agents for goods, better jobs, and risky assets, and innovative products. Initially, each agent in our model is given randomly allocated resources and abilities (households) or productivities (firms), which define a reservation wage for an individual household, and a basic cost structure for a firm. The corresponding gains from trade in goods and services (there is both labor and rental income

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generated in this model) go to those who ‘‘won’’ at the end of each trading sequence, creating an ‘‘allocative’’ market. Winners win, and losers lose, although a loss in one period does not necessarily ‘‘kill’’ the losers, thanks to a government transfer to the newly unemployed or disenfranchised in the form of a dole. The system carries on as an allocative mechanism — not of resources, but of relative wealth, and the result is a complex system2 exhibiting many of the regularities found in the empirical literature, as wealth, in the form of claims, is transferred from agent to agent in a bidding process which we can see and track in this agent-based model. Those households that do not find jobs in the labor market do not die: a ‘‘dole’’ is provided for them by a government, allowing them to survive until the next period. This creates the ‘‘tail’’ of the distribution we see in empirical studies of income distribution [Sinha 2006; Yakovenko 2009]. We make a twofold contribution in this paper. First, our model contains no representative agent, no utility function, no production function, and no rational expectations. We assume individual behavior is unpredictable — that individuals follow simple rules. We are not interested in discerning the outcome of these rules at the individual level. We begin from the premise of indeterminacy of individual choice at the micro level, which we instantiate as random selection from a given distribution. The action of any two agents are almost independent of each other, that is, there are a large number of degrees of freedom at the micro level. We do not look for a deterministic equilibrium but for a statistical equilibrium, defined as unregulated micro fluctuations with stable macro regularities [Foley 1994, 1999]. Second, our model generates observed empirical regularities in a parsimonious and easily extensible way, including income distribution, firm size distribution, business cycles, and other fat tailed distributions. We are keen to distribute the model, created in Mathematica, to allow others to extend the model. Economics has studied ‘‘fat tailed’’ or power-law distributions which characterize firm size and income distributions since the 19th century [Pareto 1896, 1965; Champernowne 1998; Gabaix et al. 2003; Yakovenko 2009]. The existence of these power laws has also been demonstrated in the econophysics, industrial organization, and finance literatures in recent work.3 Models of interaction between heterogeneous agents which generate these dynamics are also beginning to become widespread.4 Our model contributes to the literature on agent-based computational economics by combining the insights of transformational growth [Nell 1998], with modern simulation methods and modeling. The rest of this paper is laid out as follows. We describe the model in detail in the following section. We describe and discuss the results of our simulation study in the subsequent section. We conclude with a blueprint for further work on this model in the final section.

MODEL We first describe the characteristics of each set of economic agents in the model. Households Each household i is a productive unit, delimited by the following criteria: available resources in money units, mi, ability (normalized between 0 and 10), yH i , a savings Eastern Economic Journal 2011 37


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rate si randomly drawn from the uniform [Angle 2006] distribution, and an age for each period t. The initial age of each household is drawn from a [Pareto 1896, 1965; Spence 1973; Singh and Maddala 1976; Ijiri and Simon 1977; Nell 1998; Gabaix et al. 2003; Kleiber and Kotz 2003; Taylor 2004; Wright 2005; Godley and Lavoie 2006; Sinha 2006; Hu et al. 2008; Gatti et al. 2008; Gonzalez-Estevez et al. 2008; Lorentz and Savona 2008; Yakovenko 2009] uniform distribution. Each year the household’s age increases; at the age of 75 years the household dies, and gets replaced by a newborn household. The newborn household inherits the wealth of its parent, but has a different ability. For simplicity there is no inheritance tax. Households work until the end of their days, so there is no retirement. Households save, not for retirement but for future consumption, investment in education, and for bequests. We assume that innate abilities are uniformly distributed. High innate ability means the cost of acquiring skills in terms of time and resources will be low, whereas low innate ability means the cost of acquiring skills in terms of time and resources will be high. What households bring to market are innate talents, which they can augment by further learning into more marketable skill sets. We assume at any moment in the model the skills of a household can be summed up in a measure of the household’s productivity, yH. The higher this is, the better the job the household is qualified for, and therefore the higher pay the household can bargain for in the labor market. Firms, on the other hand, will have installed, and will be operating, a technology, with a rated productivity, yF. When a household’s productivity is suboptimal, yHoyF, the household will perform inadequately (causing accidents, slowdowns, and damage to the productive process), so the actual productivity of the firm will be lower than its rated or optimal productivity at any moment. When yFoyH, there is no impact of better households on the productivity of the firm. The households are not working at their highest remuneration, however, and will likely move on. Only when yFpyH i for all employees i do we have a firm working at its highest potential output. If the firm wishes to raise yF, it can invest in innovation, which we describe in ‘Introduction’ section. This process is risky, as many innovations can fail. For example, say the firm hires only 75 percent of its ideal workforce, but the remaining quarter of its workforce are substandard for its uses. We will then assume the actual productivity of the firm is a simple average of the productivities of its households for a given technology, and that the firm will wish to hire new workers once the substandard workers’ contracts are up to close the gap between its actual productivity and its highest level of productivity. Individual workers may increase their productivity by augmenting their innate abilities with education and training.

Ability and education Education transforms ability into marketable skills. Education is not directly related to households ability and households learn on the job. This is a simplifying assumption but it is in line with the literature on signaling in the labor market [Spence 1973]. By spending money on education households can obtain a degree which acts as a signal to potential employers who cannot observe the household’s ability. The households degree is public information while ability is private information. This does not mean that households do not learn anything in getting their education. Of course, someone who has taken exams in a foreign language at school is better at speaking Eastern Economic Journal 2011 37


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that language than someone who has never learned that particular language. This difference, however, only matters if the language is part of the job requirement, which would be a rare coincidence from which we abstract. Rather it is the case that someone who learned a language at school signals their willingness and persistence in completing a specific task. Households borrow from banks, and spend their saved incomes to afford increased levels of education. At each point in time household i’s ability is given by yH i (t). Over time ability changes. The household’s ability increases from learning by doing and from spillover effects. We write: H F H yH i ðt þ 1Þ ¼ a1 yi ðtÞ þ a2 maxðye ðtÞ; yi ðtÞÞ

ð1Þ

þ a3 maxðmax yFe0 ; yH i ðtÞÞ 0 e

where a1 þ a2 þ a3 ¼ 1. Here we assume ability is non-decreasing in y, where yFe (t) is the productivity of household i ’s employer. We assume each household is, to some degree, capable of learning on the job, such that over time the counter maxe0 yFe0 will pick out the highest productivity of all firms via a series of spillover effects from firms of higher productivity to firms of lower productivity, via churning in the labor market. Each household’s ability is private information, that is, it is unknown to firms. Firms, however, observe the household’s degree, which acts as an imperfect proxy for ability. Each household has either no degree (dg ¼ 1) or one of the following four degrees: college, B.A., M.A., Ph.D. (dg ¼ 2, dg ¼ 3, dg ¼ 4, dg ¼ 5, respectively). In order to receive a degree a household must have both, a specific level of ability (0oyCollegeoyB.A.oyM.A.oyPh.D.) and some money which can be spend on education (spCollege, spB.A., spM.A., spPh.D.). With each degree a pair (sp,y) is associated. This means the household’s ability has to be above some threshold yCollege (this ability is needed to get into college, pass qualifying exams y) and in addition she has to have enough money cover the expenses associated with getting education (e.g., college expenses and tuition). 8 5 if spXspPh:D: and yH XyPh:D: > > > > H > > < 4 if spXspM:A: and y XyM:A: H dg ¼ 3 if spXspB:A: and y XyB:A: > > > > 2 if spXspCollege and yH XyCollege > > : 1 else This allows for poor households with high abilities but no degree since they cannot afford the cost of education. And rich households are more likely to get the degrees since they are in a position to pay for education. Also, a Ph.D. is not necessarily smarter than a M.A. since the M.A. could have very high ability but no money. In the labor market, matching degree will play a role since ability is not directly observable (Figure 1). Firms Firms are characterized by their monetary resources, their productivity (normalized between 0 and 10) and their productive capacity k. Each firm is owned by a single capitalist household; there are no stocks and no joint ownership. Firms hire house Eastern Economic Journal 2011 37


138 ability PhD MA degree BA degree college degree no degree spending on education

Figure 1. Degree as a function of ability and spending on education.

holds P for a wage, w. The total wage bill for the economy at time t will be W ¼ ni¼1 wi ðtÞ. The firms produce output in the form of goods and services. All goods and services are sold to households (consumption) and firms (intermediate inputs, capital replacement, and innovation), as described in more detail below. Firms use their profits to replace depreciated capital goods, expand capacity, and to innovate. Investment and innovation The firm which decides to invest faces two choices. First, it can invest in an increase of productive capacity (a new factory, a new service, same productivity), which changes the scale of the firm’s processing abilities, and no more. This is assumed to be riskless — the firm in this model would not make such a commitment unless it perceived strong demand for its products and services going forward. After spending I units of money on new capital goods the firm’s productive capacity changes as described in the next equation (dp1 is depreciation). ð2Þ

kðt þ 1Þ ¼ ð1 dÞkðtÞ þ I

A second option the firm may choose is to innovate, that is, to attempt to produce wholly new products and services. The firm takes a gamble when deciding to innovate. The gamble may not pay off, and the firm may lose out, perhaps even going out of business. We assume firms always invest their profits in additional productive capacity, unless they decide to do an innovation. Each period a coin is tossed and the firm invests in productive capacity with probability 0.8 and innovates with probability 0.2. If they decide to invest, firms will use their profits, but they will also have to borrow. This captures the intuition that expanding existing capacity is relatively easy, whereas completely new productive processes generated by innovation require much larger (and riskier) investments. When firms invest in an innovation, they have to pay the costs of innovation which is fixed in our model. The firm will place an order for new fixed capital goods, asking the producers to modify the new set of goods. They will therefore have to scrap their old set of goods. In our vertically integrated system, innovations in yF raise the coefficients of production for productive processes. Households then need to learn how to use this new technology.5 The firm’s productivity at any moment is given by yF. The effect of innovation on F y is to raise or lower it incrementally according to the outcome of the largely Eastern Economic Journal 2011 37


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stochastic process of innovation. If the innovation results in a complete failure the firm’s productive capacity decreases, yF(t þ 1) ¼ 0.9yF(t). If the innovation is not a complete failure, productive capacity increases according to ð3Þ

yF ðt þ 1Þ ¼ ð1 bÞyF ðtÞ þ b10

(We use 10 as an upper bound on productivity, and also as an upper bound on households’ abilities since some kind of normalization is required.) The variable b is a random variable drawn from a half-normal distribution with mean 0.2 (and variance p2/50) reflecting the fact the incremental innovations are way more likely than excellent innovations where the firm breaks the mould and produces something truly new and exciting. Workers can also play a role here, where high ability workers can generate ‘‘learning by doing,’’ where workers with higher ability change the probability of success by narrowing the difference between yF and yH. Say a firm fails utterly in one period’s innovation. They will have to pay back any monies they have borrowed, and their equity price will slide. Their workers, however, are more experienced, and still as productive. Now there are more workers who are above the firm’s level of productivity, and it will be more likely that the next innovation will be more successful. Pricing The ‘‘consumer good’’ which each household works to consumer is produced by both labor and capital goods, including unfinished goods-in-process, which in turn have been produced be an even ‘‘earlier’’ stage, using labor and capital goods to work on even more rudimentary goods-in-process. The same holds for capital goods. Final goods are the results of stages of intermediate processing. Wages will therefore be thought of as a ratio of payment in consumption goods to labor, measured in consumption goods, and analogous to the rate of profits on capital. Both elements entering into production, capital and labor, are produced. Neither is ‘‘scarce’’; neither is ‘‘given,’’ in the textbook sense. The absence of nominal prices is a common assumption on the econophysics literature (see, e.g., Yakovenko [2009] or Wright [2005]). Our model’s focus is on transfers of money and the distribution of money which emerges from the interactions of the various actors in the system. We do not keep track of what kind of goods and services are delivered, because all that matters is the money transfer. One reason for that is that money is the only quantity that is conserved, while many goods and services are intangible or disappear after consumption. In principle, it would be possible to compute nominal equilibrium prices and let exchange take place at these prices. The absence of nominal prices is a strength of our model, since it allows exchanges to take place at out-of-equilibrium prices which can be far from equilibrium prices. The particular purchases of each agent are not explicitly modeled, but aggregated into a single amount that represents the agent’s total expenditure. Total expenditure can represent multiple small purchases, a single large purchase, or a fraction of a purchase amortized over several periods. The interpretation is deliberatively flexible. The only relevant information is that expenditure cannot exceed the agent’s money holdings. Individual commodity types are not modeled. A firm’s revenue is proportional to its productivity and number of workers, so larger firms and firms with higher productivity will receive higher Eastern Economic Journal 2011 37


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revenues. Since we do not compute nominal prices in the goods market a transfer from a household to a firm is measured only by the amount of money transferred and can represent multiple separate transactions or fractions of a large single transaction. It is true that firms differ in their productivity but this is no problem since on average more productive firms will receive a larger share of spending. Although demand is calculated probabilistically, more productive firms and firms with more workers will receive a larger share of total demand, as we see in ‘‘Demand’’ section. Labor market In the labor market unemployed households are randomly matched with firms. Firms have a reservation wage wF which indicates the firm’s willingness to hire a household of a particular type. Households come to the labor market and offer their services for a reservation wage wH. Provided that the firm has enough money it is willing to hire the household at the household’s reservation wage if wHpwF. We assume that there is a standard basket of commodities defining a socially determined normal wage which we call w. The socially determined wage is a nominal quantity and is given by the total quantity of money per agent. A firm’s reservation wage is a function of w, the firm’s money and productivity. The reservation wage, that is the maximum amount of money firm j is willing to pay, is given by ð4Þ

wFj ¼

mpej wminðdg; lÞ mpe

where mpej is money per employee for firm j and mpe is the average amount of money per employee over all firms; dg is a variable indicating the potential employees type as observed by the firm (no degree: dg ¼ 1, college degree: dg ¼ 2, B.A.: dg ¼ 3, M.A.: dg ¼ 4, Ph.D.: dg ¼ 5) and l is a variable corresponding to the firm’s productivity in the following way. 8 > 1 if yFj oyCollege > > > > > > 2 if yCollege pyFj oyB:A: > < l ¼ 3 if yB:A: pyFj oyM:A: > > > > 4 if yM:A: pyFj oyPh:D: > > > > :5 y F Ph:D: pyj Putting l into the firms’ reservation wages ensures that firms do not pay higher wages for overqualified workers. This means that McDonalds is willing to hire Ph.D.s but is not going to pay them more than the wage they pay for the employee with no degree since the burger-flipping skills of both are probably the same. Household i ’s reservation wage is a function of their wealth, measured by money, their ability (both relative to average money and abilities), their degree, and a variable ui. The variable ui fluctuates between zero and one and reflects the household’s bargaining power. If the household is unemployed ui decreases by 10 percent per period (but does not fall below zero) and if the household is employed it increases by ten percent (but does not rise above one). In this way, the household adjusts their reservation wage depending on their situation. Through the variable ui households adjust their reservation wages so that in a situation of high unemployment Eastern Economic Journal 2011 37


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wages will fall and when the labor market is tight wages will rise. ð5Þ

wH i

g mi yH i ¼ ui t þ ð1 tÞ H wdg i m y

denotes agent i ’s money relative to households’ average money holding where mi/m and yH is the average ability of households in that particular class (e.g., the average ability of households with bachelor’s degrees). There is a firing rule, also: if a firm does not have enough money to pay the wage bill for the remaining employees, the last in is let go, and so on, until profitability is restored. They then return to the labor market. Employees either receive their wages or a dole payment in each period. If no job can be found, or if the individual is fired, the individual receives a dole of 30 percent of the socially determined normal wage. Demand After the matching in the labor market, in which money is transferred from firms to households, households begin to demand consumption of goods and services. Each household spends a fraction 1s of their income on consumption goods. Using yi for household i’s income, the total amount of expenditure on consumption P is given by C ¼ i (1si)yi. Since consumption is taxed by the government, a fraction, tr, of each household’s income goes to the government as taxes, thus T ¼ tr C. The remaining money in the system at the end of a period ((1tr)C) goes to firms as profits. The probability that a particular firm, say firm Pj, is the recipient of household i’s expenditure is proportional to ljZk1Z , where lj ¼ min(yH, yFj ) (the j sum over all the firm’s employees’ abilities) and here kj is the firm’s productive capacity. way we can also compute an index of real GDP, which is given by PIn Zthis 1Z ). Assuming for a moment that firms’ productive capacities are fixed j (lj kj (at some kind of steady state of capital accumulation) real GDP would be at its maximum if all firms would have the highest possible productivity and all households would be employed and have the highest possible ability. Since both firms’ productivity and households’ abilities are bounded from above, the only way to increase GDP would be by building up higher productive capacities. We find that real GDP changes faster if households’ abilities and/or firms’ productivities increase faster, that is if workers learn faster and if innovation is cheaper. If depreciation is higher it is harder for firms to build up productive capacity and we observe less fluctuations in real GDP since the changes in productive capacity are slower. In the absence of any changes in productive capacity real GDP declines if existing firms go bankrupt, and get replaced by new firms with lower productivity, or if high-ability households die, and get replaced by descendants with lower abilities. Banks There is a fixed number of retail banks operating on a simple principle: charge more for loans than deposits. Agents, both households and firms, can take a loan to invest in education or innovation. We assume that firms reinvest all their profits, so only households put money in a bank account, which is automatically opened for them. of their deposits as reserves. This The banks are required to hold some fraction (rr) Eastern Economic Journal 2011 37


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increases the total quantity of money through a multiplier effect, but due to the short duration on loans the money multiplier will be smaller than the standard multiplier We assume an interest rate on deposits which is exogenously fixed, but banks 1/rr. set the interest rate on loans according to a simple markup rule. The interest rate on loans will vary but it will always be above the interest rate on deposits in order to cover defaults. Banks adjust the interest rate on loans following a similar rule to the government’s rule for the adjustment of the tax rate, described in section 7. For banks there are two limits, blower thresholdpbupper threshold. If the bank’s interest payment on deposits exceeds its income from interest earned on loans, or if the bank’s capital exceeds bupper threshold, the interest rate on loans is decreased. Vice versa, the bank increases its interest rate on loans if it makes a surplus or if its capital is below blower threshold. Our central bank is a passive agent. The central bank lends money to the government or to banks if necessary. It acts as a lender of last resort by offering fixed-rate loans at the discount window. Retail banks are forced to borrow from the discount window when they lack the excess reserves to honor demand deposit withdrawals.6 By setting the central bank’s discount rate to zero we ensure that no money will escape our closed financial system (consisting of households, firms, retail banks and the government). If the government runs a deficit for a couple of successive periods it is possible that it runs down all its money if it cannot adjust the tax rate fast enough. In order to make the dole payments the government has to borrow money from the central bank’s discount window. Banks have simple lending criteria. Banks will lend to any household or firm if its net wealth is positive. We begin by setting the term structure of the loan at one period. Firms and households pay back the principal plus the interest rate in the next period. If they can repay interest but not the principal, the debt is rolled over. If the agent however cannot pay interest their debt increases and eventually becomes ‘‘bad debt’’ when the agents goes bankrupt. By borrowing money debt increases. When the interest on the loan cannot be paid the agent’s debt increases, that is, the agent borrows more money to pay interest on her loans. To avoid Ponzi schemes we have to ensure that this does not go on forever. By setting an upper bound for households’ and firms’ negative money (ponziH, ponziF) borrowing without bounds is precluded. If an agent’s negative money ( ¼ debt) is equal or above this limit the agent goes bankrupt. When firms go bankrupt and households become unemployed and therefore run down their surpluses and repayment capacities, their outstanding debts become ‘‘bad debts,’’ and the banks have to generate enough interest to themselves stay afloat. Banks have to set their interest rates, ib, to cover the probability (which they cannot know, we assume Knightian uncertainty) of firms and households defaulting, which allows us to model credit-crunch type scenarios in this model. Households’ and firms’ bankruptcies represent a loss for the banking sector. When a household goes bankrupt its net wealth (money holdings and bank accounts) is restored to zero. When a firm goes bankrupt it is replaced by a new firm who gets some amount of money from the government as a subsidy. The money supply, which is endogenous, fluctuates out of sync with the business cycle we see generated by the information asymmetry in the labor market. We model debt as negative money, but preclude unlimited borrowing via the Ponzi-limits mentioned above. In addition the total amount of debt allowable in the system is limited through the minimum reserve requirement, so MpMB/1rr, Eastern Economic Journal 2011 37


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the required reserve ratio and MB the monetary base. In the absence of with rr borrowing from the central bank the monetary base will stay constant. Government The government is a passive actor in our model. The government puts a tax on consumption, so we have T ¼ tr C, where C is the amount of money spend by all households, and T is the total amount of taxes. The government adjusts its tax rate via simple rules of thumb. If the government runs a growing deficit (the government is indebted and current expenditure exceeds tax income) it increases the tax rate by 1 percent. If it runs a growing surplus (positive money and tax income higher than expenditure) it decreases the tax rate by one percent. Since in this model the governments only expenditure is the dole the tax rate will usually be very low. The government has a level of money that it wants to maintain in order to meet its obligations to pay out the dole without having to go into debt. We call this level gthreshold. The government adjusts the tax rate according to the following rule: decrease the tax rate if tax income is larger than government expenditure or if the government’s monetary resources are above gthreshold; increase the tax rate if tax income is less than government expenditure or if the government’s monetary resources are below gthreshold. This implies that the tax rate stays the same if the government makes a loss (surplus) but its monetary resources are above (below) gthreshold. The total model is summarized in Figure 2. Social accounts

investment

banking

consumption

Time

labor market

Fundamentally our macroeconomy consisting of a set of social accounts within a stock-flow consistent framework in the tradition of Godley and Lavoie [2006] and Taylor [2004]. Our vertically integrated economy is constrained by accounting

Firms (F)

Households (H)

hire workers and produce output

work or unemployed

sell output to households

pay interest on loans, pay back loan

borrow money

invest in capacity, buy intermediate goods (inputs)

Banks (B)

make deposit, withdraw money or borrow money

Money Flows

F

wage

G

dole

pay dole

consumption

pay interest on loans, earn interest on deposits, pay back loans

Government (G)

H

F

cons.

G

taxes

collect taxes

interest payments

H

F interest

B

H

educ

spend money on education

F

H inputs

Figure 2. Structure of the model. Eastern Economic Journal 2011 37


144 Table 1 Social accounting matrix for the model

Consumption Wages Taxes Investment Profits Equity Loans S

Households

Firms

C +W TH IH

+C W TF IF +P +Eq +LF 0

Eq LH 0

Government

Banks

+T +I P

0

L 0

S 0 0 0 0 0 0 0

relationships. Following Godley and Lavoie [2006] and Taylor [2004], we list the economic agents in the columns, and their various activities in the rows. Columns represent stocks, rows represent flows. The households consume a fraction of their wages þ W, and decide whether to invest their savings (income minus consumption this period) in education, IH to improve their productivity, or continue saving, which will form part of their bequest fund or finance future consumption. The firms pay wages, W, and derive profits, þ P from their activities, which they use to either invest in simple increases in productive capacity (a new factory, say, or more services for customers), IF or risk their saved earnings by innovating. The firms will face increases or decreases in the value of their equity Eq, held by households, on the basis of the success or failure of the innovation process, described above, summarized in the investment, equity, and loans rows. Note that Eq can fluctuate from period to period as a result of these innovations. The firms and households may take out loans from the banks, þ LF,H, and pay them back next period. The government, as mentioned above, is a passive actor, redistributing taxes on consumption T at a rate T ¼ tr C þ tresP to those without wage income in a particular period, and always runs a balanced budget, period by period, because the government borrows from the central bank to fund its deficit. Deficits are repaid in future periods. The government does not invest its surplus, it only spends money on the dole. If the government runs a surplus it lowers taxes. We implicitly assume that households are the owners of the firms. Each firm is owned by exactly one capitalist household; there are no stocks or joint ownership (Table 1).

SIMULATION RESULTS The structure of the model and the money flows between households, firms, banks, and the government are represented in Figure 2.7 In the labor market, firms hire households for a wage and unemployed workers get a dole from the government. Firms produce consumption goods which they sell to households. All households — employed and unemployed — spend a fraction (1s) of their income on consumption goods. Since consumption is taxed a fraction of households’ spending goes to the government. Households put the remaining fraction s of their incomes into a bank account at a randomly chosen bank. If households have deposits or loans from the period before they receive or pay interest, which changes their income. Firms also pay interest on their loans. Households and firms repay a loan if they have money left after consumption (households) and wage payments (firms). Otherwise the debt is rolled over. Eastern Economic Journal 2011 37


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Households and firms can also decide to get a new loan or withdraw money from their bank account. With a certain probability (sH and sF, respectively) households and firms borrow money. Households use their loans and withdrawals to invest in education. Firms use their loans to invest in productive capacity or innovation. Our model represents a closed system of randomly interacting agents. Global macroscopic patterns, such as the distribution of incomes, stability in economic production and employment emerge from the local interactions of heterogeneous agents. Figures 3 and 4 show these emergent patterns from a representative simulation run.8 We group the graphical results of our simulation in Figures 3 and 4. Figure 3(a) shows that our economy provides a relatively stable income to households, which varies counter-cyclically with unemployment. We can see from Figure 3(b) that unemployment and the tax rate move together. This is evidence for the government increasing (decreasing) the tax rate in response to higher (lower) expenditure relative to tax income, and shows the ‘‘passive’’ nature of the government as a simple automatic stabilizer in our model: the tax rate cycles pro-cyclically with the unemployment rate. Figures 3(c) and (d) show consumption and investment. In Figure 3(d), we observe that investment is relatively volatile, which reflects the fluctuations in profit income and the riskiness of innovative activity. Several studies note the emergence of a Boltzmann–Gibbs distribution within agent-based models.9 Our model pulls out a gamma or exponential distribution of income over time with respect to wage and profit income. At the top 5 percent of

a

b

Dole, Wage

c

Unempl. and tax rate

Consumption

350000 250000

0.5 300000

200000

0.4

250000

150000

0.3

100000

200000

0.2

50000 50

100

150

200

150000

20

Time

40 60 Time

d

P(m)

800000

100

150

200

Time

e Investment

50

80 100

{Histogram-points and fit to gamma distribution}

600000 400000 200000

50

100 150 Time

200

500

1000

1500

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Figure 3. Graphical output of simulation results, 1. (a) Wage income (solid line) and dole income (dotted line); (b) Taxes (above) and income supports (below) are clearly pro-cyclical with the business cycle, reflecting the passive nature of the government in this model. Solid line is five-period moving average; (c) Consumption; (d) Investment; (e) Distribution of majority of incomes and fit to gamma distribution with parameters 1.24 and 414.6, significant at 10 percent level (Kolmogoroff–Smirnov test). Eastern Economic Journal 2011 37


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a

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Figure 4. Graphical output of simulation results, 2. (a) Real GDP clearly shows business cycles, black line is a five-period moving average; (b) Top 5 percent of the income distribution, Pareto distributed with a ¼ 1.51, tested with Kolmogorov–Smirnov tests in line with Clauset et al. [2009].

income, our model pulls out a Pareto distribution. At the lowest 95 percent of income, the model replicates the gamma distribution, rather than the standard lognormal distribution we see in studies within the inequality literature [Cowell 1998]. Figure 3(e) shows the overall distribution of households’ incomes, and the fit to the gamma distribution. Again, the money supply in our model is endogenous, and varies also with the business cycle. At the beginning of the simulation, the money supply declines sharply and stabilizes slightly above the monetary base, indicating a small size of the multiplier. We believe that this results from a decline in households deposits. During the first periods of the simulation households’ expenditures exceed incomes, and hence there is an outflow of money from the household sector. Since in our model households are the only agents who provide deposits, the money supply operates at a lower level. As mentioned in the ‘‘Introduction’’ section,10 our model is capable of generating endogenous business cycles, as Figure 4(a) shows. The solid line is a moving average. We clearly see a change in real GDP as the economy moves through employment, investment, and consumption cycles, driven by endogenous forces within the system. In addition, the top 5 percent of income-earners do form a Pareto distribution. Most studies find top incomes are Pareto distributed with a slope of 1.45–2.1 [Kleiber and Kotz 2003], and from our model we get a slope of 1.51, as we show in Figure 4(b), tested with Kolmogorov–Smirnov tests and significant at the 10 percent level. For example, Wright [2005] finds an income distribution at the top 5 percent to be Pareto distributed with slope 1.3. Discussion Our model contains some interesting features worth discussing further. Money is ‘‘locally’’ conserved in our model, following Yakovenko [2009]. We assume an economy with a large number of agents — households, firms, banks, and a government — interacting simultaneously. Because our model does not have the traditional closure of utility maximizing households vying against firms facing given production functions, we make the assumption that money is conserved in the economy in any period. This is a plausible assumption for ‘‘ordinary’’ economic agents, who merely transmit money to Eastern Economic Journal 2011 37


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and from one another in a voluntary bargaining process, and who cannot create or destroy money, thus conserving it. For example, if agent i pays some amount Dm to another agent j for goods and services, the money balance of the system as a whole will be maintained, because in sum mi Dm ¼ mj þ Dm, which is a strict accounting identity we observe through out the model, and this permeates the structure of our national accounts system described in section 8. Only governments and banks have the ability to create money, and the government in our model is assumed to be a passive actor, only taking taxes to redistribute income to the less fortunate in the labor market bargaining process. Banks ‘‘create’’ money through the fractional reserve process, making the quantity of money endogenous to the system. The process of injection of money into the economic system is equivalent, physically, to the increase in the level of energy of a system coming from an external source. As long as the rate of money flowing into (or out of) the economy is slow relative to the relaxation processes ongoing in the economy (to avoid hyperinflation), then the system will remain quasi-stationary and in a quasi-statistical equilibrium [Foley 1994] with slowly changing parameters.11 Debt in this model is characterized as ‘‘negative money,’’ where the bank gets a debt obligation (plus some interest next period) in exchange for providing the firm or household with money to pursue their various activities, thus increasing their cash balances in this particular period [Braun 2001]. Debt in our model changes the boundary conditions for each economic agent, but does not violate the assumption of conservation of money, which feeds directly into our description of firm size and age dynamics, and income inequality dynamics [Angle 2006].

CONCLUSION In this paper, we develop a model of endogenous inequality, based on the idea that simple parameters applied multiplicatively over many generations can give us a good idea of how the distribution of income between persons has evolved up to now. Our model is Borgesian in temperament, and in the vein of Champernowne and Gibrat, addressing inequality as a multiplicative phenomenon. We apply an agent-based model of the transformation of a society from material equality in initial conditions to distorted income distributions. We show how and where the model was losing it’s equality, and showed a redistributive policy to counteract it. Someone has already thought of giving the poor money, however. The effects of ‘‘tuning’’ this inequality distribution are also shown. This is a transformational growth theory of markets, writ large. If inequality is generated by the Market (with a capital ‘‘M’’), then ‘‘class’’ is just the name given to a socially generated partition of certain collections of certain bins in the histogram of overall earnings at some period of time. In this study, we aver that markets do not exist primarily to allocate resources efficiently markets represent the ebb and flow of goods and services to winners and losers over time. Through competition in all its forms, markets generate surpluses that go to the successful, who carry these gains forward through time and use them to their own advantage. These knock-on effects alter the distribution of wealth in the system, especially when we take account of the presence of inter-sectoral feedbacks. Trading behavior makes markets unstable because of the ever-present cost pressures from competing economic entities, which, although richer traders are partially insulated from these cost problems in the short run, will affect all members of the sector eventually. Eastern Economic Journal 2011 37


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Notes 1. In particular, we use a stock-flow consistent macro framework in the tradition of Taylor [2004] and Godley and Lavoie [2006], the model generates observed empirical regularities such as persistent, endogenously generated dispersions of income in the tradition of Nell [1998] and Angle [2006], and our relates directly to the literature on computational-agent-based macroeconomics, in the vein of Dosi et al. [2006], Gatti et al. [2008], Lorentz and Savona [2008] and Ciarli et al. [2010]. The paper by Ciarli, Lorentz, Savona, and Valente clearly focuses on intra-sectoral dynamics, so it is not very close to our model technically, but has the same spirit. Similarities exist between our paper and Dosi et al. [2006], as well as Lorentz and Savona [2008], with respect to technology. In all papers, innovation and the diffusion of technology shocks are modeled in a similar way. Wright [2005] has a similar model, with no prices and wages drawn from a given distribution, but no banking sector, no government, no education and innovation. Our work is related to agent-based approaches via the assumption of heterogeneous agents, and through the use of simulation to uncover ‘‘emergent’’ phenomena, such as endogenously generated business cycles. Our simple model replicates many of the findings of these agent-based papers, for example, firm size distribution and wealth distributions. 2. Where a complex system is defined as the simple macroscopic regularity resulting from the interaction of many agents in decentralized exchange [Foley 2003; Angle 2006]. 3. See Singh and Maddala [1976], Ijiri and Simon [1977], Kleiber and Kotz [2003], Cingano and Schivardi [2004], Sinha [2006] and Coad [2008] for summaries of recent work in these diverse fields. 4. See Dosi et al. [2006], Gatti et al. [2008], Lorentz and Savona [2008] and Ciarli et al. [2010] for survey of such models and related literatures. 5. There is a risk that new technologies cannot be utilized by the existing workforce, which require retooling, re-skilling, and perhaps new households. 6. Clearly, when bupper threshold, and blower threshold are set high enough, the government and banks almost never have to borrow from the central bank. 7. For this set of runs, we set the number of agents as: 500 households, 150 firms, 75 banks. We posit initial amounts of money as: 1,000 for each household and each firm, 10,000 for each bank, 1,000 for the government. The required reserve ratio is rr ¼ 0.1, which implies a monetary base of MB ¼ 14,01,000.The tax rate is initially set at 10 percent and interest rate for loans is fixed at 1 percent. We parameterize other variables as follows: d ¼ 0.1, Z ¼ 0.7, t ¼ 0.5, g ¼ 1, a1 ¼ 0.7, a2 ¼ 0.2, a3 ¼ 0.1, sH ¼ 0.5, sF ¼ 0.5, spCollege ¼ 100, spB.A. ¼ 300, spM.A. ¼ 500, spPh.D. ¼ 800, yCollege ¼ 2, yB.A. ¼ 4, yM.A. ¼ 6, yPh.D. ¼ 8, ponziF ¼ 10,000, ponziH ¼ 1,000, gthreshold ¼ 2,000, bupper threshold ¼ 1,000, blower threshold ¼ 500. We performed standard robustness checks on our parameters, they did not change the results significantly. 8. An animation of the money flows between sectors and a dynamic Social Accounting Matrix (www.stephenkinsella.net/research) are available from the authors upon request. 9. See Gonzalez-Estevez et al. [2008] and Hu et al. [2008] for surveys and references. 10. We thank an anonymous reviewer for the suggestion to discuss the business cycle facet of our model more completely. 11. Yakovenko [2009] gives the example of a kettle on a gas stove heating slowly, where the kettle has a well defined, but slowly increasing amount.

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