Appendix: I. Bankruptcy
The probability of bankruptcy, as defined in expression (3), depends on the chosen level of inputs (I). The effect of an increase in I on pr(I) is:
where H is the cumulative distribution function of P. Since f(0) = 0 and f is concave, pr’(I) is always positive. Furthermore:
The first term is positive as long as long as h′(Pb)>0. This is the case, for example, if
This expression is positive if f” is sufficiently negative.
II. Input Choices
The responsiveness of private firms’ optimal input choices (Iv) to changes in input cost (w) and entry cost (C) is:
The numerators in expressions (21) and (22) are positive, while the denominators in both are negative if pr″(I) is positive.
SOEs’ optimal input choice responds to w in the following way:
III. Real Depreciation of the Domestic Currency
The change in SOEs’ input choice resulting from an exogenous depreciation of the domestic currency (a rise in e) is:
The input choice of private firms, on the other hand, responds as follows:
Since the last term in curly brackets in the denominator is positive while the entire denominator is negative (in keeping with the assumption of pr″(I) <0):
As long as h′(Pb) > 0, we have:
The term in the square brackets of the numerator in (27) exceeds unity if there is positive value added in the production process. Hence:
Finally, if f‴ < 0, then:
Aghevli, B. B. Khan M. S. and Montiel P. J. (1991), “Exchange Rate Policy in Developing Countries: Some Analytical Issues” International Monetary Fund Occasional Paper 78 March.
Goldfeld, S. M. and Quandt R. E. (1988) “Budget Constraints, Bailouts, and the Firm under Central Planning” Journal of Comparative Economics Vol. 12 pp. 502–20.
Goldfeld, S. M. and Quandt R. E. (1990) “Output Targets, the Soft Budget Constraint and the Firm under Central Planning” Journal of Economic Behavior and Organization Vol. 14 pp. 205–22.
Han, D. S. (1992) “Credit-Constrained Enterprises and Incentive Schemes During the Transition to a Market Economy” mimeo University of Pennsylvania August.
Hardy, D. C. (1992) “Soft Budget Constraints, Firm Commitments, and the Social Safety Net” Staff Papers, International Monetary Fund Vol. 39 pp. 310–29.
Hemming, R. and Mansoor A. M. (1988) “Privatization and Public Enterprises,” International Monetary Fund Occasional Paper 56 January.
Hillman, A. L. Katz E. and Rosenberg J. (1987) “Workers as Insurance: Anticipated Government Assistance and Factor Demand” Oxford Economic Papers Vol. 39 pp. 813–20.
Husain, A. M. and Sahay R. (1992) “Does Sequencing of Privatization Matter in Reforming Planned Economies?” International Monetary Fund Working Paper WP/92/13 forthcoming in Staff Papers.
I am indebted to Elhanan Helpman for very useful suggestions. Comments by Carlos Asilis, Malcolm Knight, Ceyla Pazarbasioglu, Carlos Vegh, and seminar participants at the IMF are gratefully acknowledged. Any remaining errors are my own.
State support for SOEs is also common in developed market economies, as well as in developing countries. The analysis here also applies to these cases, especially in economies where SOEs produce a significant share of total output.
C may be interpreted as the cost of purchasing the firm’s capital stock, which is firm-specific and has no scrap value.
All variables are in real terms. Input supply and input market interactions are analyzed below. Each firm takes w as given, but in equilibrium w equates input demand with supply.
Labor, particularly skilled labor, serves as a good example of a nontraded factor of production. In addition, the analysis can also apply to manufactured intermediate goods. Distortions associated with the intermediate goods market are beyond the scope of this paper; they are analyzed in Husain and Sahay (1992).
Private firms are assumed to be able to meet their immediate costs in the event of bankruptcy. Relaxing this assumption would make the comparison with SOEs more complex. Suppliers of inputs, for example, would demand a higher price from private firms than from SOEs in order to compensate for the possibility of nonpayment, or partial payment. The effect of SOEs on the input cost faced by private firms, however, would still be similar to what is captured here.
Conditions under which this holds are derived in the Appendix. The assumption allows us to capture a “bankruptcy aversion” effect that induces a private firm to choose a lower input level than it would if it were unconcerned about bankruptcy. The purpose here is to use this effect to distinguish between private firms and SOEs, and to study their responses to policy changes.
For simplicity, future profits are not discounted in this formulation. All the results presented here can easily be replicated for discount rates within the interval (0,1].
Recall that the expected value of P is normalized to unity.
These derivations are relegated to the Appendix.
SOEs need not produce the same good as private firms, although this assumption is made here for convenience. The results derived below continue to hold as long as both types of firms experience similar shocks and use the same inputs.
This assumption allows for a simple yet appealing analysis of the behavior of SOEs. Managerial inefficiencies that induce excessive employment of inputs could also be added to the framework.
Note that since all private firms are identical, they all produce at the same scale. Similarly, all SOEs produce at the same scale. The scale of production of SOEs and private firms, however, differs.
While the model does not formally address exit decisions of private firms, the reduction in n may be interpreted as a situation in which fewer new firms replace firms that shut down in response to a low price shock.
The purpose here is not to discuss what policies lead to a depreciation of the equilibrium real exchange rate. Rather, the analysis has to do with the effects of such a depreciation. A discussion on the impact of various policy changes, including trade liberalization and fiscal reform, on the equilibrium real exchange rate may be found in Aghevli, Khan, and Montiel (1991).
For analytical convenience, the fixed cost of entry (C) is assumed to be in foreign currency units. The results are similar even if C is partly or entirely denominated in home currency units.
Derivations of the change in optimal input choices of both private and state-owned firms are contained in the Appendix. It is shown, under fairly general assumptions about the production function and the probability density function of the (foreign) price level, that the increase in input demand by private firms in response to a real depreciation of the domestic currency exceeds that of public firms. This implies that the “bankruptcy effect”--the effect of a decline in the probability of bankruptcy-- induces private firms to increase production in response to a real depreciation.
Note that this holds if and only If the elasticity of w with respect to e is less than one.
The results may also be interpreted more generally. If, for example, there are several inputs--some traded and some nontraded--the real depreciation not only improves competitiveness but also alters firms’ desired input mix. In such a case, the ensuing change in total output also depends on the degree of substitutability between traded and nontraded inputs.
While a complete analysis of the role of credit policy would include a discussion of the allocation of credit as well as the design of incentive-compatible repayment mechanisms, the objective here is to focus on the potential output effects of a lower entry cost (C), in the absence of incentive problems. Such a reduction in C may, inter alia, be associated with an improvement in the efficiency of credit markets. Han (1992) studies incentive-compatible tax/subsidy schemes designed to induce productive but credit-constrained SOEs to expand production while encouraging less productive SOEs to reduce their scale of operation.
The case in which a reduction in C leads to a decrease in n is exactly analogous to the case of a real depreciation of the domestic currency illustrated in Figure 4.
In their study of SOEs and privatization, Hemming and Mansoor (1988) review the problems associated with government ownership and observe that “a growing body of evidence claims to show that when the public and private sectors can be compared in terms of the cost of producing similar outputs, the private sector outperforms the public sector.”