OPTIMAL INFLATIONARY AND RESERVE REQUIREMENT POLICIES: A STUDY OF AN ECONOMY WITH AN INFORMAL SECTOR

Governments in developing economies often resort to taxing bank money balances through imposition of high reserve requirements and also by relying on seigniorage to finance their deficits. In the context of those practices, this research reported in this paper attempts to answer the following questions: First, why do developing economies with an informal sector resort to inflationary measures to finance their activities? Second, how does a government induce an agent to choose the formal economy? It is demonstrated, for the first question, that in the trade-off between inflation and reserve requirements, the optimal policy is maximum inflation and minimum reserve requirements that will increase the steady-state utility of an optimizing agent. Regarding the second question, the agents prefer the informal economy if policy relies on a maximum reserve requirement.


Introduction 1
This paper addresses the unintended consequences of the regulations on bank reserve and infl ation fi nancing on the informal and formal sectors of an economy. Such regulations are often observed in several developing countries. As a matter of public policy, the terms "informal sector" and "informal economy" are synonymous, and they refer to a marginally unregulated economy that sometimes not only subordinates itself to the formal economy, but also provides income and a safety net for the economic agent (ILO, 2003;ILO, 2005;Castells & Portes, 1989). These informal economic arrangements are a rational response by micro-entrepreneurs to defeat over-regulation by the government (de Soto, 2000). Moreover, greater shares of national wealth in developing countries are uncounted; the average size of the informal sector i n developing economies is 41 percent of gross national in come (GNI) (Schneider, 2002). Effectively, it can be noted that there is an increasing interdependence between the formal and the informal sectors, because the policy designed to target the formal sector has broader implications for the social welfare of the economic agents in the informal sector.
In addition, governments in developing economies with informal sectors often resort to taxing money balances through imposition of high reserve requirements on bank deposits; they also rely on seigniorage to fi nance their defi cits. 2 So, to fi nance its expenditures, the government uses either bank reserves or seigniorage. However, a higher reserve requirement implies crowding-out of private capital while by using seigniorage the government creates money from thin air, which drives infl ationary pressure. In such policy trade-offs, there is a continuous tension between the macroeconomic stability programmes advised by th e IMF and the domestic needs of the developing economies to meet their social and economic obligations. Consequently, countries are trapped in cycles of severe reserve requirements and anti-infl ationary measures that have unintended consequences for economic growth and development. Therefore, the conventional prescriptions derived from neo-liberal policies have failed to address the existence of the informal economy and the ways in which it complicates a government's fi scal and monetary options and further represses the fi nancial sector.
The fi rst attempt to address this fi nancial repression was made by McKinnon and Shaw (1973), who defi ned fi nancial repression as the set of regulatory restrictions that limited the capacity of the fi nancial intermediaries to achieve their full potential. However, fi nancial development is important in promoting economic growth (Stiglitz & Uy, 1996;Levine, 1997;Beck, Levine & Loayza, 2000). For example, based on the fi ndings from surveys of formal and informal fi nancial institutions in Ghana, Malawi, Nigeria, and Tanzania, Nissanke and Aryeetey (2006) stated that the continuous poor performance of fi nancial systems could be partly explained by the high degree of fi nancial market fragmentation. On the basis of the evidence in a recent study by Lu and Yao (2009), it has been argued that the rise of privileged and unprivileged sectors in the economy can be regarded as a consequence of fi nancial repression. Any government action has implications for the welfare of the agent when the government fi nances its defi cits through money creation and reserve requirements. Steel, Aryeetey, Hetige and Nissanke (1997) have contended that informal fi nancial institutions are an important vehicle for mobilizing household savings, and this study has recommended that informal fi nance be better integrated into fi nancial development strategies. Freeman (1987), and Freeman and Haslag (1993), have used an overlapping generation framework in a fi nancially-repressed environment, which provides an important baseline for subsequent theoretical research on optimal reserve requirements. This paper extends Freeman's and Haslag's models into the fi nancially repressive dual economy model to answer the following questions: First, why do developing economies with informal sectors resort to infl ationary measures to fi nance their activities? Secondly, how does a government induce the agent to choose the formal economy? In our case, the model is applied to an environment in which homogenous agents hold different assets in two markets-formal and informal-allowing the government to fi nance defi cits through a reserve requirement and money creation or seigniorage.
Consistent with the fi ndings of Freeman and Haslag (1993), we demonstrate that for the fi rst question, on the trade-off between infl ation and reserve requirements, the optimal policy is maximum infl ation and minimum reserve requirements that will increase the steady-state utility of an optimizing agent. Regarding the second question, the agents prefer the informal economy if the policy relies on a maximum reserve requirement. Therefore, the government is not only optimizing the infl ationary policy but also inducing the agent to favour the forma l economy by minimizing the reserve requirement. The agent uses the storage technology in the informal sector because the optimizing agent predicts that the government is inclined to regulate and suppress fi nancial intermediaries.
The best response of the agent in the informal sector is to hide some goods, because the agents do care about the weighted average rate of return on the assets. In a dual economy with formal and informal sectors with an expanding nominal stock of money, the reserve requirement not only serves as a tax on deposits, but also keeps the agent from using the most productive capital to match the return from the informal sector. The reserve requirements will not induce growth in the fi nancial sector. Instead, it does the opposite and promotes the informal sector. The heavier the degree of fi nancial regulation, the bigger the scope of the informal economy, and the less seigniorage the government can collect.
We use a relatively simple model expounded in section 2 to arrive at the conclusions. Section 3 describes the maximization of welfare, and examines policy analysis. Section 4 discusses the steady states under different policy regimes, and section 5 is the conclusion of this paper.

The Model
This model is an overlapping-generation model following Eastman op cit. We provide an appendix that includes further details on the model derivation. There are three types of assets: money, capital, and informal goods. Assets are held either because they are required (money balances) or because they have a high rate of return (capital). We describe the evolution of the economy from time t = 1 onwards. The economy is populated by agents who each live for two periods.
In each period t , 1  t N two-period-living agents are born. We assume that for each period , t where n is population growth with a positive constant and implying that total endowment of the economy grows at this rate.
Agents maximize the twice-continuously differentiable additive utility function

Asset Allocation Decisions
There is storage technology in the informal sector. An agent stores t h 2 of his savings in the informal sector at time t and returns ) h ( f t 2 units of goods at 1  t . The minimum requirement to invest in capital technology is y k  . This assumption forces the agent to use intermediation; if the rate of return on capital is x and by assumption ) ( n x  , the return on capital is higher than the money rate of return. If the economy is growing, then money supply should grow and the rate of return of intermediated capital x should grow even faster as well (Champ & Freeman, 1994).
We assume that the current old generation holds the fi at money, which is an intrinsically worthless piece of paper. The monetary authority can determine the growth of the money supply: z is the rate of growth of the fi at money. The government uses seigniorage to fi nance its expenditures. The government requires that a fi xed fraction  of all deposits at fi nancial intermediaries must be held as a reserve of fi at money.

Behaviour of Young Agents
Taking the price level sequence   t p , as given, we defi ne t t h h 2 1 , as the value of agents (fi at money and intermediated capital) and stored goods in the informal sector respectively. Young agents at each date t choose t t h h 2 1 , to maximize: The stock of fi at money available in this intermediated economy is where gh 1t is required reserve and N t gh 1t is aggregate reserve. The price sequence evolves over time to keep up with infl ation. Given that the intermediated stock of fi at money is nominal, it was multiplied by the price sequence to obtain the real value of money (Champ and Freeman 1994). M is the nominal stock of fi at money.

Competitive Equilibrium
The agent's problem can be transformed as follows; the young agent allocates his endowment, and diversifi es the allocation of assets in formal and informal markets, because the agent cares about the weighted rate of returns. The entire endowment is allocated for current consumption when young, and saving when old, in the informal and formal markets. Let t t h h 2 1 , denote the total savings of a young agent at time t in the formal and informal sectors, so that the young agent chooses The fi rst-order condition: In the competitive equilibrium, the agent equalizes the marginal rate of substitution to the rate of return in both economies. Given ), ( 1  t h any policy that lowers the rate of return has a negative implication for the welfare of the agent, which requires further characterization to the welfare property of our model.

Characterization of Stationary Equilibrium
The market-clearing condition is the real rate of return on fi at money using equation (3): Under the assumption ( . x n  ), if money is not dominated in the rate of return, then the agent has no reason to use the storage technology in the informal sector. Moreover, no agent or intermediary will choose to hold more fi at money than legally required. The rate of return on saving is the weighted average of the rates of return on money and capital in the formal economy: We can deduce from this equation the following rules: x. This simply means that if z = 0, the rates of return in the formal and informal sectors are the same. If the fi at money is not growing, then the government is running a balanced budget, and the agent is indifferent and will allocate its endowment to either market. However, the government does create money as a device to alter the welfare and asset allocation between the formal and informal markets. Also from equations (7), and (9) we defi ne the rate of return in the informal sector: Finally, the government's budget constraints require that The deduction from the government budget constraints has greater public policy implications as the result of corner solutions. 4 For equation (11), the deduction, if z = 0  g = -∞ is unrealistic, so we make further assumptions to maximize the welfare of the future generation of the current young by setting   z 1 to optimize in equation (12) as a counter-reaction of the agent to the government's action. The government is always faced with trade-offs between infl ation and reserve requirements, as a matter of public policy. Our response to our research question-which policy maximizes the welfare of the economic agent?-is that excessive infl ationary policy is preferred to extreme reserve requirements. It is true that the extreme cases remain as extreme, and they rarely occur; the bottom line is that infl ationary policy is the second-best public policy.

Maximizing the Welfare of the Future Generation
The future generation chooses   , 1  z to maximize its welfare. (12) The economy on the right side of the Laffer curve, conducting monetary policy through reserve requirements to gain seigniorage, will lower the rate of return in money.
Given that the government fi nances its expenditures through money creation, equation (13) shows the steady-state utility of the agent under an infl ationary policy regime. Since we defi ne   z 1 , for simplicity, we need to defi ne     to determine the sign of equation (13). After cancelling the terms out in further equations, we get equation (15): Using  from equation (13) in equation (15), we obtain equation (16): (16) For the government to fi nance its expenditures, the optimal repression is to set  as low as possible, which is to say, zero, i.e., Given that the level of current government expenditure is constant, the optimal policy is to set   z , which will relax the constraint on reserve requirements and create more opportunity for the agent to obtain the most productive capital in the formal sector. The optimal seigniorage should be obtained by the policy that minimizes the reserve requirements and maximizes infl ation, which is consistent with the fi ndings of Freeman and Haslag.

Policy to Induce Agents into the Formal Sector
The agent's criteria to choose either sector depend on the rate of return  and ) , the agent will prefer the formal sector to the informal economy. If , the agent will prefer the storage technology in the informal economy to saving in the formal economy. Conducting the policy experimentation as shown in Table 1, we consider the extreme case of conducting monetary policy and its implication for the rate of return in both sectors. The government monetary policy will change the composition of the assets held by the agent in both markets through the rate of return.
Using the rate of return in the informal economy in equation (10) we obtain equation (17): Solving for government expenditure in terms  , and setting either maximum reserves or minimum reserves, we obtain the comparative results in Table 1 below:

The Steady State under Policy Regimes
From Table 1 we conclude that for the government to induce agents to hold assets in the formal sector, the optimal policy is a combination of infi nite infl ation and minimum reserve requirements. However if the government conducts its policy International Journal of Banking and Finance, Vol. 8, Iss. 1 [2011], Art. 2 towards maximum reserve requirements, such a policy promotes the informal sector, because the agent will favour storing his/her goods rather than allocating one's portfolio in the formal economy with a lower rate of return. Most governments of developing economies do not rely heavily on reserve requirements, in order to avoid further growth of the informal sector. Promoting the size of the informal economy is not in the interest of the government; this could be one of the reasons that developing economies use the infl ationary policy. We might say that the IMF prescription for holding maximum reserve requirements is not really helpful to the economies that rely on seigniorage as their main source of revenue. This could be one of the sources of the resistance and tension between the global institutional demand and what country-level policymakers need.

Conclusions
In economies with developed fi nancial intermediation, where the size of the informal sector is small to be negligible, the agents prefer the informal economy if the policy relies on a maximum reserve requirement. The government that minimizes the reserve requirements is not only optimizing the infl ationary policy but also inducing the agent to favour the formal economy. In searching for Pareto improvement, using the open-market operations remains a reasonable mechanism designed to offset the transfers of wealth between generations when the government is paying a return on reserves. Open-market operations will reward deposit in the formal economy and mitigate the need to use the informal economy unless the rate of return is equalized between the two sectors. This issue is left for future research.
The stock of fi at money available in this economy is

Competitive Equilibrium
The agent's problem can be transformed as follows. Let t t h h 2 1 , denote the total savings of a young agent at time t in the formal and informal sectors, so that the young agent chooses The fi rst-order condition:

Characterization of Stationary Equilibrium
The market clearing condition is the real rate of return on fi at money from (3): International Journal of Banking and Finance, Vol. 8, Iss. 1 [2011], Art. 2

Optimal Infl ationary and Reserve Requirement Policies: A Study of an Economy with an Informal Sector: 21-34 31
Also from equations (6) and (7) we defi ne the rate of return in the informal sector: x z Finally, the government's budget constraints require that

3.
Maximizing the Welfare of Future Generations Using the envelope theorem we cancel out the following terms: From equation (9) we get Since the government fi nances its expenditures through money creation, equation (19) shows the steady-state utility of the agent under this policy regime.