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# A Human Capital Based Growth Model with Environment and Corruption

*Journal of Economic Structures*
**volume 3**, Article number: 10 (2014)

## Abstract

In this paper, we present a simple overlapping-generations model with human capital, pollution, and political corruption to consider problems related to sustainable growth. In many growth models that incorporate the environment, it is assumed that there exists an altruistic government that enforces the environmental policy to maximize the utility of households or social welfare. The conditions for sustainable growth are derived based on this assumption. However, the assumption that the government implements appropriate policies might be overly optimistic. Bribes, political donations, and corruption might taint and skew government policy. This paper also considers politico-economic problems. We assume that environmental policy is determined endogenously through a process of bargaining between the government and the firm (or interest group). Corruption relaxes environmental standards, lowers the long-run growth rate, and might cause economic stagnation. The long-run growth rate might become negative if the economy is rife with corruption.

**JEL Classification:** O44, P48, Q20.

## 1 Introduction

As described in this paper, we present a simple overlapping-generations model with human capital, pollution, and political corruption to consider problems related to sustainable growth.

In earlier studies, for example, John and Pecchenino ([1994]), John et al. ([1995]), and Bovenberg and Heijdra ([2002]) extend the model of Diamond’s ([1965]) OLG model and examine the relation between growth and the environment. Stokey ([1998]), Aghion and Howitt ([1998]) also examine the relation between economic growth and the environment.^{Footnote 1}These studies assume that the government is altruistic. Results obtained using such models suggest that environmental externalities should be internalized by environmental policies. These studies do not consider politico-economic problems. Moreover, the assumption that the government implements appropriate policies might be overly optimistic. Bribes, political donations, and corruption might taint and skew government policy. Negotiation and compromise between parties might occur when the government executes policies. Furthermore, not only government but also the private sector might use political power to head off the introduction of strict environmental policies if such policies reduce their profits.^{Footnote 2}

In this paper, we will consider how political corruption affects economic growth and the environment. To highlight the dynamic features of economic activities, we use the ideas of human capital. Human capital accumulation is one of the most important factors when we consider long-run growth (Lucas [1988]). Some insist that R&D and innovation exert an important role in long-run growth (Romer [1990]; Aghion and Howitt [1992]). We can construct a growth model with R&D and innovation instead of human capital. However, we can derive similar results even if we introduce R&D. So, we assume that human capital accumulation becomes an engine of productivity improvement.

Lopez and Mitra ([2000]) consider the relation between pollution and growth. The amounts of donations and pollution level (environmental standard) are determined endogenously through a process of bargaining between the government and the firm. They show that corruption does not affect the sustainability of economic growth, although the economy emits more pollution than under the social optimum.

Our model might be interpreted as an extension of Lopez and Mitra ([2000]). A salient difference is that we construct a dynamic OLG model rather than a static model (Lopez and Mitra [2000] construct a static model). By constructing an OLG model, we can derive the different results from Lopez and Mitra ([2000]). It can be demonstrated that corruption relaxes environmental standards and lowers the long-run growth rate. Results show that the growth rate might become zero or negative if the government and/or public sector are corrupt to such a degree. Our paper specifically examines the case in which the government colludes with the entrepreneur. Their utility will increase at the expense of the laborer. In this sense, an implicit conflict exists between entrepreneurs and laborers.^{Footnote 3}

This paper is organized as follows. In Sect. 2, the basic setting of this paper is described. In Sect. 3, we consider environmental policy. In Sect. 2 and Sect. 3, we do not take bribes or political donations into consideration. In this case, the long-run growth rate becomes positive and the environment improves over time if certain conditions are met. In Sect. 5, problems related to political corruption are introduced. The entrepreneurs offer political donations to the government if such donations can increase their profits to a great extent. However, the government accepts donations if the net benefit of taking political donations is positive. We assume that the amount of donations and the pollution level (environmental standards) are determined endogenously through a process of bargaining between the government and the entrepreneur. In this case, the government and the firm try to arrive at a cooperative outcome through mutual agreement. We show that this interlocking relation between entrepreneurs and government lowers the growth rate. The economy might stagnate if the economy is heavily tainted by corruption.

## 2 The Model

First, we will analyze the final goods sector. The market for final goods is assumed to be perfectly competitive. A continuum of firms exists. Because the technology displays constant returns to scale, the precise number of firms is irrelevant. For simplicity, we will take their total mass to be one. Following Copeland and Taylor ([1994]) and Stokey ([1998]), we assume that the output of the final good can be written as a function of pollution and effective input (in our model, human capital). We establish the production function of the final good as

where ${Y}_{t}$ is the aggregate output,^{Footnote 4}*A* denotes the productivity parameter, ${H}_{t}$ represents the human capital, and ${D}_{t}$ signifies the pollution. The parameter *α* is assumed as $0<\alpha <1$. Presuming that the government distributes permits uniformly across firms and then allows a secondary market in those permits, then those firms maximize their profits at each date, taking the wage rate ${w}_{t}$ and the price of permit ${\tau}_{t}$ as given. The profit of the firm is given as

Here $\stackrel{\u02c6}{{D}_{t}}$ denotes the numbers of permits that the government supplies to each firm. From the firms’ profit maximization (evaluated market equilibrium), we can obtain

Presuming that the market for permits clears at every moment: ${D}_{t}={\stackrel{\u02c6}{D}}_{t}$ for all *t*. Then ${\pi}_{t}={\tau}_{t}{D}_{t}=A(1-\alpha ){H}_{t}^{\alpha}{D}_{t}^{1-\alpha}$.^{Footnote 5}

Let us consider consumers. Generation *t* is defined as the people who are born in period *t*. We assume that individuals live for two periods and that each has one child. Without loss of generality, we assume that the number of each generation is unity. During the period of youth, individuals accumulate human capital and do not work. The production function of human capital of generation *t* is specified as

where *B* is the parameter and $0<\beta <1$. The ${H}_{t}$ on the right-hand-side denotes positive externalities from the human capital of parents (generation $t-1$), and ${z}_{t}$ is the educational outlay from the parents. Education cost of young people (generation *t*) is paid by their parents (generation $t-1$). Note also that there is no decision making when they are young.

Each individual can only work during the second period of life. They supply human capital inelastically, earn a wage, and allocate their income to consumption and education outlay of their children. It is assumed that the labor market clears at every moment. We also assume that utility of the representative individual depends on consumption and the parents’ education expenditure on the child.^{Footnote 6}We specify the expected utility of an individual in generation *t* (which is represented as ${U}_{t}^{I}$) as

where ${c}_{t}$ signifies consumption and ${z}_{t}$ denotes the education outlay to their children. Also, ${\varphi}_{1}$ ($0<{\varphi}_{1}<1$) and ${\varphi}_{2}$ (${\varphi}_{2}>0$) are the parameters.

In addition, ${E}_{t}$ represents the environmental quality. We assume that the dynamic behavior of environmental quality is specified as

where ${b}_{1}>1$ and ${b}_{2}>0$. The stock of the environmental good has the ability to renew itself. The rate of renewal is given as function ${b}_{1}{E}_{t}$. However, pollution causes environmental damage. One unit of pollution spoils ${b}_{2}$ units of environmental quality. Therefore, the net rate of change of the stock of the environment is given as (6).

Let us consider generation $t-1$. They accumulate their human capital in period $t-1$ and work in period *t*. Their budget constraint is given as ${w}_{t}{H}_{t}={c}_{t}+{z}_{t}$. Individuals maximize their utility (5) ^{Footnote 7}subject to the budget constraint, taking ${E}_{t}$ as given. From the individuals’ utility maximization, we can obtain

From Eqs. (2), (4), and (8), we can obtain the following:

Next, we will specifically examine the entrepreneur.^{Footnote 8}We assume that the utility of the entrepreneur in period *t* depends only on the profit of the firm in period *t* (we implicitly assume that entrepreneurs are short lived). We specify the utility of entrepreneur (${U}_{t}^{F}$) as

## 3 Environmental Policy

In this section, we consider government policy. A government supplies a permit to control the pollution. We assume that the government is short-lived and that its objective is to maximize utility (${U}_{t}^{G}$), which is defined as

where ${U}_{t}^{I}$ and ${U}_{t}^{F}$ are defined in the previous section. Also, ${M}_{t}$ signifies the political donation and $f({M}_{t},{Y}_{t})$ denotes the net benefit of such a donation. In this section, we specifically examine the case in which ${M}_{t}=0$. In other words, we analyze the case in which no political corruption exists. Therefore, the utility of the government in this is given as ${U}_{t}^{G}={U}_{t-1}^{I}+{U}_{t}^{I}+{\varphi}_{3}{U}_{t}^{F}$ because we assume $f(0,{Y}_{t})=0$. In Sect. 4, we will discuss problems related to political corruption in detail. Parameter ${\varphi}_{3}$ is the relative weight that the politicians assign to the utility of the entrepreneur. The following equations must hold:

The government in period *t* looks ahead to the subsequent period because the utility of each young voter depends on ${c}_{t+1}$ and ${E}_{t+1}$. Following Verbon and Verhoeven ([1992]), Meijdam and Verbon ([1997]), and Ono ([2005]), this paper assumes rational expectations and myopic decision making. Rational expectations mean that the short-lived government can estimate the environmental tax rate in the subsequent period accurately. Myopic decision making implies that the government does not consider the impact of current policies on future political decisions. These assumptions imply that the government chooses a level of pollution ${D}_{t}$, taking the level of pollution in the next period ${D}_{t+1}$ as given.

Let us consider the impact of the relaxation of environmental regulations (the increase in the supply of the emissions credits). First, it raises the wages and consumption of elderly worker. This effect increases the utility of each old voter. Second, it drives up profits of the firm. This effect improves the utility of each entrepreneur. Third, it increases the consumption of period $t+1$ because human capital in period $t+1$ will drive up by such deregulation. This effect increases the utility of each young voter. Fourth, the environmental quality decreases in period $t+1$. Each young voter will be worse off by this effect.

The condition for the maximum is given as

where ${\varphi}_{4}\equiv (1-\alpha )(1+{\varphi}_{3}+\alpha (1-\beta ))$. Then we can express the level of pollution (denoted as ${D}_{t}^{\ast}$) as

The level of pollution will be higher when individuals do not care about the environment (lower ${\varphi}_{2}$), when the regenerative ability of the environment is high (higher ${b}_{1}$), when pollution does not severely affect the environment (lower ${b}_{2}$), when the profit rate is high (lower *α*), and when the relative weight the politicians attach to the utility of entrepreneur is high (higher ${\varphi}_{3}$). From Eqs. (6) and (13), we obtain

Here we define ${g}^{\ast}\equiv \frac{{b}_{1}{\varphi}_{2}}{{\varphi}_{2}+{\varphi}_{4}}$. The growth rate of ${E}_{t}$ is ${g}^{\ast}-1$ for all *t*. It is assumed that ${g}^{\ast}>1$. That is, ${E}_{t}$ improves over time. Furthermore, from Eqs. (9) and (13), we obtain

We define $\frac{{H}_{t}}{{E}_{t}}\equiv {q}_{t}$. Equations (14) and (15) imply that

The dynamic behavior of ${q}_{t}$ is given as (16). We can show that ${q}_{t}={q}_{t+1}$ in the long run because $0<1-(1-\alpha )(1-\beta )<1$ (see Fig. 1). This steady state is unique and stable. In the steady state, $\frac{{H}_{t+1}}{{H}_{t}}={g}^{\ast}$. Therefore, the growth rate of the final good is also given by ${g}^{\ast}$. The initial values of ${q}_{t}$ do not play an important role in our model.

We have not considered the range of ${D}_{t}$ until this point. However, as pointed out by Copeland and Taylor ([1994]), and Stokey ([1998]), the contribution of ${D}_{t}$ to ${Y}_{t}$ must be limited by a ceiling. Suppose that ${D}_{t}\le \overline{d}{Y}_{t}$. Copeland and Taylor ([1994]), and Stokey ([1998]) make similar assumptions. We assume that $\overline{d}$ is relatively large and the existence of this assumption does not affect our results thus far.

We can show that human capital accumulation is necessary for $\frac{{Y}_{t+1}-{Y}_{t}}{{Y}_{t}}>0$ if we assume ${D}_{t}\le \overline{d}{Y}_{t}$. To prove this, suppose that $B=0$ and $\beta =1$. Then ${H}_{t}={H}_{0}$ for all *t*. Suppose also that $\frac{{b}_{1}{\varphi}_{2}}{{\varphi}_{2}+{\varphi}_{4}}>1$ (see Eq. (14)). In this case the ${D}_{t}$ come at $\overline{d}{Y}_{t}$ (note that ${D}_{t}/\overline{d}{Y}_{t}={D}_{t}^{\alpha}/A{H}_{0}^{\alpha}$) and the growth rates of ${Y}_{t}$ and ${E}_{t}$ become 0 in the long run. Human capital accumulation play an essential role in our model when ${D}_{t}\le \overline{d}{Y}_{t}$. In this paper, we would like to analyze how political corruption affects growth rate and environment. So, considering the human capital accumulation is necessary in our model.

## 4 Corruption and Political Donation

In the analysis presented above, we did not take political corruption into consideration. Several studies have, however, pointed to the possibility that political problems are detrimental to economic growth. For example, Krusell and Rios-Rull ([1996]) argue that an important role is played by vested interests in determining policies. They show that knowledge related to cottage technology sometimes blocks the adoption of new technology. Ehrlich and Lui ([1999]) construct a model in which each agent invests in political capital that affects income distribution. However, investment in political capital does not contribute to production or productivity increases, it counts for nothing from a social point of view. Acemoglu et al. ([2006]) show that interlocking relations among existing low-skilled managers (which can be interpreted as low productivity industries), capitalists (which can be interpreted as owners of the firms or financial sectors), and government might bring about the delay of changes in the industrial structure. In these models, corruption tends to affect the steady state of the economy. However, these models do not consider environmental problems or bargaining between government and the private sector to affect environmental policies.

In this section, we introduce an interest group that offers a political donation to a government to head off the introduction of a strict environmental policy. Here, we assume that the entrepreneurs can form an interest group and affect government policies.^{Footnote 9}The net profit of entrepreneurs is given as $(1-\alpha ){Y}_{t}-{M}_{t}$ (where ${M}_{t}$ denotes the political donation). Therefore, the utility of representative entrepreneur is given as $log[(1-\alpha ){Y}_{t}-{M}_{t}]$. The utility of the government is defined as

In that equation, $f({M}_{t},{Y}_{t})$ represents the net benefit of political donation.^{Footnote 10}We assume that $f(0,{Y}_{t})=0$ for all ${Y}_{t}$. In Sects. 2 and 3, we do not consider political donations (that is, ${M}_{t}=0$). If ${M}_{t}=0$, Eq. (17) is equivalent to ${U}_{t}^{G}={U}_{t-1}^{I}+{U}_{t}^{I}+{\varphi}_{3}{U}_{t}^{F}$. It is also assumed that a risk of taking a donation exists because a collusive relation between the interest group and government might not be supported by voters. We assume that the risk of accepting a donation increases with ${Y}_{t}$. Economic development increases the government’s risk of taking a donation: we assume $\frac{\partial f}{\partial M}>0$ and $\frac{\partial f}{\partial Y}<0$. The donation might be regarded as a bribe. In many countries, bribes are illegal in general. Bribery scandals might engender a change of government. The government officials might be arrested for corruption.

Figure 2 shows a positive correlation between per-capita GDP^{Footnote 11}and corruption perceptions index (CPI) published by Transparency International a non-governmental organization that monitors corporate and political corruption in international development (Transparency International [2009]). Corruption is defined as the abuse of entrusted power for private gain. A higher score of the index indicates less corruption. The highest (lowest) value is defined as 10 (0). The results show that seven out of every ten countries (and nine out of every ten developing countries) have an index of fewer than 5 points out of 10. We present a plot showing the data of 168 countries in Fig. 2.

Lambsdorff ([2007]) shows that an improvement in the CPI by one point increases average income by 4 percentage points because appropriate institutions increase capital inflows and raise productivity.^{Footnote 12}

This might imply that rich countries tend to have cleaner government, fair institutions, and appropriate laws. If so, the risk of taking political donations might increase with per-capita income because citizens in the developed countries call on the rectitude of government. To reflect this point, we assume that the net benefit of political donation increases with ${M}_{t}$ and decreases with ${Y}_{t}$. In this paper, we assume that $f({M}_{t},{Y}_{t})\equiv \gamma \frac{{M}_{t}}{{Y}_{t}}$. Therefore, the utility of the government is given as ${U}_{t}^{G}={U}_{t-1}^{I}+{U}_{t}^{I}+{\varphi}_{3}{U}_{t}^{F}+\gamma \frac{{M}_{t}}{{Y}_{t}}$.

We assume that ${M}_{t}$ and ${D}_{t}$ are determined endogenously through a process of bargaining between the government and the private firm. In this case, the government and the firm try to arrive at a cooperative outcome through mutual agreement. Available to them are a set of outcomes from which they can choose and a disagreement outcome, i.e., the outcome that is obtained when the government and the firm fail to arrive at an agreement (see Nash [1953] and Osborne and Rubinstein [1990]). In this paper, the bargaining solution is to determine ${\tau}_{t}$ and ${D}_{t}$ to maximize

where $\mathrm{\Delta}{U}_{t}^{F}$ and $\mathrm{\Delta}{U}_{t}^{G}$ are defined as

Therein, ${D}_{t}^{\ast}$ is given as (13). The conditions for the maximum are expressed as

which suggests that

where ${D}_{t}^{1}$ is the pollution discharged in this situation. The pollution is more emitted (and differs from the optimal values) when the marginal benefit of the political donation is high (larger *γ*) and profit rate is high (lower *α*). In this case, dynamic behavior of ${E}_{t}$ is given as

Here ${g}^{1}\equiv \frac{{b}_{1}{\varphi}_{2}}{{\varphi}_{2}+{\varphi}_{4}+\gamma {(1-\alpha )}^{2}}$. In the steady state, the growth rates of ${E}_{t}$, ${H}_{t}$, ${Y}_{t}$ are the same and are denoted as ${g}^{1}-1$. From Eqs. (14) and (24), we know that ${g}^{\ast}>{g}^{1}$.

The intuition behind these results is as follows. Corruption increases the total amount of pollution because the government accepts political donations in exchange for the extra issuance of permits. An increase in pollution bumps the total output because ${Y}_{t}$ is positively correlated with ${D}_{t}$ (see Eq. (1)). So, corruption allows the economy to grow faster in period *t*. However, environmental stock decreases because ${E}_{t+1}$ is negatively correlated with ${D}_{t}$ (see Eq. (6)). So corruption has two opposite effects on ${D}_{t+1}$. First, corruption tends to increase ${D}_{t+1}$ because the government issues more permits for a given ${E}_{t+1}$. On the other hand, corruption in period *t* decreases ${E}_{t+1}$ and this reduces ${D}_{t+1}$ (see Eq. (23)). The latter negative effects predominate eventually and the growth rate settles down at a lower steady state rate.

Figure 3 shows the relation between ${g}^{1}$ and *γ*. ${g}^{1}$ is correlated negatively with *γ*. The growth rate is positive if *γ* is small, although the growth rate is lower than ${g}^{\ast}$. However, ${g}^{1}$ becomes smaller than 0 if $\gamma >\stackrel{\u02c6}{\gamma}$, where $\stackrel{\u02c6}{\gamma}$ is defined as follows:

The growth rates of ${Y}_{t}$, ${H}_{t}$, and ${E}_{t}$ are given by ${g}^{1}$. In fact, ${g}^{1}$ becomes positive (negative) if and only if $\gamma <\stackrel{\u02c6}{\gamma}$ ($\gamma >\stackrel{\u02c6}{\gamma}$). Political corruption engenders economic stagnation. Therefore, preventing politicians’ or government officials’ unfair meddling in government affairs might be necessary to achieve sustainable growth. Lopez and Mitra ([2000]) also assume that environmental policy and the amount of political donations are determined by bargaining between firms and government. In their model, corruption is unlikely to preclude the possibility of sustainable growth, although the pollution levels corresponding to corrupt behavior are always above the socially optimal level. In our model, this is no longer true. The long-run growth rate might become negative if the economy is rife with corruption.

Hall and Jones ([1999]) insist that the difference in output per worker and per-capita income are driven by differences in social infrastructure across countries. They define social infrastructure as institutions and government policies that determine economic environment within which individuals accumulate skills, firms accumulate capital and engage in product activity. They conclude that per-capita output is positively related with social infrastructure. If we can relate uncorrupt government (in this case, *γ* is small) to one feature of desirable social infrastructure, then our results might support the contention of Hall and Jones ([1999]).

## 5 Concluding Remarks

In this study, we extend a simple overlapping-generations model to consider the sustainability of growth. Our model includes environmental problems and political corruption. In many growth models that incorporate the environment, it is assumed that there exists an altruistic government that enforces the environmental policy to maximize the utility of households or social welfare. In many previous studies, the conditions for sustainable growth are derived based on this assumption.

In the first part of this paper, we assumed that no political corruption exists. In this case, output per worker, human capital, and environmental quality grow at a positive rate in the steady state. Next, we integrated the politico-economic problems into the model because many earlier studies that examine environment and economic growth do not address political problems. We analyze the case in which the government accepts a political donation and relaxes an environmental regulation. We assume that environmental policy is determined endogenously through a process of bargaining between the government and the entrepreneur. This paper showed that the interlocking relations between the government and the interest group lower the growth rate and might cause economic stagnation. Lopez and Mitra ([2000]) show that corruption is unlikely to preclude the possibility of sustainable growth, although the pollution levels corresponding to corrupt behavior are always above the socially optimal level. In our model, this is no longer true. The long-run growth rate might become negative if the economy is rife with corruption.

## Notes

- 1.
- 2.
- 3.
- 4.
Subscript

*t*represents the level in period*t*throughout this paper. - 5.
See Stokey ([1998]). In her model, the profits are allocated to households because the firms are owned by households. However, the profits become entrepreneur’s income in our model. We will explain this point later in detail.

- 6.
- 7.
Note that the utility of an individual in generation $t-1$ is given as

$${U}_{t-1}^{I}={\varphi}_{1}log{c}_{t}+(1-{\varphi}_{1})log{z}_{t}+{\varphi}_{2}log{E}_{t}.$$ - 8.
Acemoglu et al. ([2006]) describe a model in which collusion between capitalists and entrepreneurs undermines the economy.

- 9.
Grossman and Helpman ([1994]) consider the effect of the interest groups. Acemoglu et al. ([2006]) consider the case in which old low-skill managers and capitalists entered into a collusive agreement. Ehrlich and Lui ([1999]) discuss the situation in which each agent (individuals or bureaucrat) invests not only in human capital but also in political capital, which affects income redistribution. Aidt et al. ([2008]) construct a model in which the government sets a tax rate to maximize its net benefit. In his model, raising the tax rate increases the share that the government can obtain, but it decreases the tax base because some workers begin to move to the informal sector.

- 10.
Downs ([1957]) assumes that the sole motive behind government policy formulation is the winning of elections. He did not consider rent-seeking behavior of the government.

- 11.
We use data obtained from the World Bank ([2011]).

- 12.

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## Acknowledgements

This work was supported by JSPS KAKENHI Grant Number 25245042. I am grateful to Keisuke Osumi, Hikaru Ogawa, Kenichiro Ikeshita, Masayuki Sato, Shintaro Nakagawa, and two anonymous referees for their helpful comments. I would also like to express my appreciation to the participants in some conferences (The 9th World Congress of the Regional Science Association International held at Timisoara, Romania, and Seminars held at Kagoshima University and Japan Women’s University) who made valuable suggestions on earlier versions of this paper. Needless to say, all remaining errors are mine.

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Ikazaki, D. A Human Capital Based Growth Model with Environment and Corruption.
*Economic Structures* **3, **10 (2014). https://doi.org/10.1186/s40008-014-0010-3

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### Keywords

- Political corruption
- Sustainable growth
- Human capital
- Environment