Exchange Rate Flexibility, Volatility, and Domestic and Foreign Direct Investment

Joshua Aizenman

doi:10.5089/9781451930825.024.A006

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Exchange Rate Flexibility, Volatility, and Domestic and Foreign Direct Investment

Author: Mr. Joshua Aizenman¹

¹ 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

Publication Date:: 01 Jan 1992

eISBN:: 9781451930825

Language:: English

Keywords:: SP; exchange rate; price level; regime employment; productivity shock; risk diversification motive; aggregate investment; Exchange rate flexibility; Employment; Foreign direct investment; Global

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The impact of exchange rate regimes on domestic and foreign investment in the presence of a short-run Phillips curve is investigated. Producers may diversify internationally to increase the flexibility of production, thereby diversifying country-specific productivity and monetary shocks. Aggregate investment is shown to be higher under a fixed exchange rate than under a flexible exchange rate for both productivity and monetary shocks. Welfare is not, however, necessarily higher under either regime: a flexible exchange rate stabilizes employment in the presence of real shocks at the cost of reduced expected GNP and investment.

Abstract

This paper analyzes the implications of exchange rate flexibility for the patterns of domestic and foreign direct investment. The past two decades have been characterized by the growing integration of capital markets and a substantial increase in the importance of gross foreign direct investment flows. ¹ Most of these flows have been associated with cross-hauling—the simultaneous export and import of capital. On balance, the industrialized countries have experienced a negative net flow of foreign direct investment, the magnitude of which has been small relative to the gross flows. These developments are consistent with a trend toward a much greater international diversification of productive capacity by multinationals.

This period has also been characterized by the co-existence of various types of exchange rate regimes. The European countries adopted policies aimed at minimizing fluctuations of their bilateral exchange rates, whereas the United States, Japan, and Canada have stayed with a flexible exchange rate system. Most developing countries have adopted a fixed exchange rate or a crawling peg.

The proliferation of exchange rate systems suggests that further attention should be given to the degree to which these regimes influence flows of domestic and foreign direct investment. Should countries wishing to encourage foreign flows of investment increase the flexibility of their exchange rates, or adopt a fixed exchange rate regime? Some studies have investigated the impact of exchange rate volatility on investment and international trade, but not enough attention has been given to the more fundamental forces that determine the evolution of prices, exchange rates, and the volume of trade.² Because investment, exchange rates, and the volume of international trade are endogenous variables that adjust to various shocks, their behavior can be better understood if the underlying forces affecting each economy are traced. A macroeconomic modeling strategy, where the exchange rate, prices, employment, and investment are endogenously determined may provide a more coherent interpretation of the observable correlations. In this paper such a model is used to identify the dependency on the composition of shocks of the correlations among observable variables, and to investigate the impact of exchange rate regimes on the behavior of investment.

Most of the theoretical research on foreign direct investment has been conducted in the context of real international trade and has focused on its microfoundation. In these models the risk diversification motive and the internalization of externalities or market imperfections have been offered as explanations for foreign direct investment.³ Obviously, these models are silent regarding the macroeconomic dimensions of foreign investment flows and the relevance of the choice of exchange rate regime for the patterns of these flows. This paper bridges this gap by studying the behavior of foreign direct investment in a world economy characterized by the presence of a short-run expectations-augmented Phillips curve. In such an economy, unanticipated monetary shocks may be transmitted into the real economy, generating a reallocation of resources. Hence, the choice of the exchange rate regime may affect the patterns of the foreign investment flows. The modeling strategy is to place the insights from the micro literature in a macro context, in order to capture the impact of the existence of a Phillips curve on the patterns of investment, and thus derive the linkages between the shocks affecting producers and the corresponding macroeconomic adjustment of the nominal and the real exchange rate, prices, and real wages.

To isolate the role of exchange rate regimes, one may consider the case where there is no impedence to international trade in goods or to foreign direct investment and where agents are risk neutral. Thus, the potential role of commercial policy and transportation costs may be disregarded as reasons for foreign direct investment flows, as well as the possibility that the degree of risk aversion plays a role in determining the pattern of investment. Labor is assumed to be immobile, and installed capital is location- and sector-specific. There is a one-period lag between the implementation of investment in productive capital and the availability of the productive capacity. The economy is subject to productivity and monetary shocks, and the supply side is characterized by the presence of a short-run Phillips curve. Foreign direct investment is motivated by the producer’s attempt to increase flexibility of production: being a multinational enables producers to reallocate employment and production toward the more efficient or cheaper plant. This flexibility gives the producer the option to adjust its international production pattern to the realization of shocks, at the cost of carrying the extra productive capacity.⁴ To address the implications of the exchange rate regime for the pattern of direct investment, an economy is constructed characterized by monopolistic competition, where production at a given period requires investment in the productive capacity in the preceding period.⁵ The investment is implemented by risk-free entrepreneurs, who face the option of operating as multinational or as nondiversified national producers. Free entry is also assumed, and, hence, equilibrium carries the requirement that expected economic rent is dissipated.⁶

The key outcome is that a fixed exchange rate regime is more conducive to both domestic and foreign direct investment, relative to a flexible exchange rate; this conclusion applies for both productivity shocks and monetary shocks. It is shown that the resultant investment—domestic and foreign—is higher in a fixed exchange rate regime. In the case of monetary shocks, the concavity of the production function implies that volatile monetary shocks will reduce expected profits under a flexible exchange rate regime. Fixed exchange rates are better at insulating real wages and production from monetary shocks, and are thus associated with lower volatility and, thereby, higher expected profits. The higher expected income, in turn, supports higher domestic and foreign direct investment. In the case of productivity shocks, flexible exchange rates tend to foster lower volatility of employment and lower expected profits. The reason is that in a country experiencing a positive productivity shock the exchange rate tends to appreciate, both nominally and in real terms, which will moderate (and may even eliminate) the resultant employment expansion. Under a fixed exchange rate system, the nominal appreciation mechanism does not work; hence, in the presence of a positive productivity shock, employment will tend to expand more than it does under a flexible rate. The employment expansion that follows a positive productivity shock with a fixed exchange rate increases expected profits, thereby raising domestic and foreign direct investment.⁷

The model is described in Section I, Section II characterizes the equilibrium, and Section III derives the closed-form solution for a simple example. Section IV compares the various possible regimes, and Section V offers conclusions.

I. The Model

Consider a minimal model with two countries, two periods, and two classes of goods. In the first period entrepreneurs face the investment decisions, determining the productive capacity of the economy in the second period. Starting in period 1 with a given endowment of good Y, denoted by , which serves as both the consumption and the investment good in the first period, an entrepreneur may invest in one of the two countries (operating as a nondiversified producer), or in both countries (operating as a multinational). Following the capacity decisions of the first period, entrepreneurs will use the services of labor in the second period toward the production of differentiated products, denoted by D and indexed by i. The key behavioral assumptions of the model are defined in the following subsections.

Preferences

The utility of the representative agent is given by

\begin{matrix} U = Y_{1} + \frac{D_{2} + g (L)}{1 + ρ}, & (1) \end{matrix}

where L denotes labor, g’ < 0, g” < 0, and Y₁ is consumption of the homogeneous good at period 1. The subjective rate of time preference is reflected by p, and the disutility from labor is captured by g(L). The utility derived from consuming d varieties of the differentiated products is given by D₂:

\begin{matrix} D_{2} = {[\sum_{i = 1}^{d} {(D_{2, i})}^{α}]}^{1 / α}, & for 0 < α < 1 . & (2) \end{matrix}

The term D_{2, i} is the consumption level of variety i in period 2, Agents in the foreign country have the same utility.

Production

The production of the differentiated product in plants located in the home and the foreign economy, respectively, is given by a Cobb-Douglas function:

\begin{matrix} D_{2, i}^{s} = \frac{1}{a} {(L)}^{γ}, & D_{2, i}^{s *} = \frac{1}{a *} {(L *)}^{γ}, & for 0 < γ < 1 . & (3) \end{matrix}

To deal with macro issues, a short-run Phillips curve is modeled, whereby monetary disturbances are transmitted into the real economy in the short run. The model incorporates the Fischer-Gray formulation of labor contracts, where labor is employed subject to nominal contracts⁸. The wage for period 2 is preset at level W_o, so that the expected employment equals the employment target, .⁹ Within the second period, employment is demand-determined: producers demand labor so as to maximize their profits. Henceforth, foreign values are indexed by an asterisk.

Investment, Uncertainty, and the Producer’s Problem

Producers may prefer to operate as multinationals producing in both countries in an attempt to diversify their exposure to country-specific shocks. Returns to scale can exist as long as some of the fixed inputs are shared by several plants—and. hence, the capacity cost of two plants is lower than twice the capacity cost of one plant. The diversification motive will operate even if producers are risk neutral, as long as a variable input is used in the short run and the correlation among shocks affecting the two countries is less than unitary. This point is illustrated in Figure 1, which plots the production function of a multinational that uses labor as the variable input. Suppose that there are two possible states of nature—h and l—associated with high and low productivity, respectively. The corresponding production functions are D^s,h_i^** and D^s,l_i, respectively. In the absence of a variable input in the short run, the production process collapses into points A and B, respectively. Suppose that the correlation among productivity shocks in the two countries is negative, and the probability of the occurrence of each shock is one half. In the absence of a variable input, a multinational that invests in both countries will produce twice the output at K₂ (point K₂ is defined as half the distance between A and B). In this borderline case the multinational does not increase the expected output per plant by diversifying internationally. Rather, diversification stabilizes output, at the cost of doubling the productive capacity of the producer.

The situation is more complex when a variable input, like labor, is introduced. Note that the marginal product of labor is higher in the country operating in state h (point B), compared with the country operating in state l (point A). If the cost of labor is the same in both countries, the multinational will tend to expand employment in the first country, contracting employment in the second country. Such an adjustment will increase the multinational’s aggregate output by the difference between the marginal productivity of labor (per unit of employment reallocated in this way).¹⁰ Hence, the ability to adjust employment in these circumstances implies that a multinational more than doubles its expected output by investing in both countries. In this case, the diversification of production will tend to stabilize and increase the expected output. This example illustrates the potential advantage that the multinational operating in both countries derives from flexibility of production. Further insight will be gained when this situation is cast in a framework that derives prices, real wages, profits, and investment endogenously.

Investment is location- and product-specific, allowing production of the differentiated product, i, at the chosen location. An entrepreneur may invest in one of the two countries, at a cost of K. Alternatively, entrepreneurs may diversify their productive capacity by investing both at home and in the foreign country at a cost of K(1 + η), for η ≤ 1. A diversified producer operates as a multinational firm, having the capacity to produce in both countries.¹¹ Entrepreneurs are risk neutral, and there is free entry. The uncertainty pertains to the future productivity of labor and the supply of money in each economy. The joint distribution of shocks is symmetric, and is known to all agents in period 1. Investment is implemented in period 1, prior to the resolution of the uncertainty regarding productivity in period 2. A strategy of diversifying the investment could be to “buy” the option of channeling production to the more productive location. More formally, real gross profits (revenue minus the wage bill) of a diversified and a specialized producer can be denoted by π^d and π^nd, respectively. A nondiversified equilibrium, where all producers specialize in one location, can be characterized by

\begin{matrix} E [π^{n d}] = K (1 + ρ) & (4 a) \end{matrix}

\begin{matrix} E [π^{d}] < K (1 + ρ) (1 + η), & (4 b) \end{matrix}

where E stands for the expectations operator referring to the first-period expected level of second-period profits. Equation (4a) is generated by the free entry, implying the break-even condition. Condition (4b) implies that the marginal producer does not have an incentive to diversify internationally. Integrating the two conditions, one infers that a nondiversified equilibrium is stable if

\begin{matrix} \frac{E [π^{d}] - E [π^{n d}]}{E [π^{n d}]} < η . & (5) \end{matrix}

Equation (5) indicates that the (percentage) gain from diversification falls short of the percentage increase of costs. Applying the same logic, the diversified equilibrium is characterized by

\begin{matrix} E [π^{d}] = K (1 + ρ) (1 + η) & (6 a) \end{matrix}

\begin{matrix} E [π^{n d}] < K (1 + ρ), & (6 b) \end{matrix}

or, that¹²

\begin{matrix} \frac{E [π^{d}] - E [π^{n d}]}{E [π^{n d}]} > η & (7) \end{matrix}

The Money Market

To simplify exposition, this model uses the simplest specification of the demand for money: constant velocity where the demand for money equals a fraction, q, of nominal domestic gross national product (GNP); for the purposes of notation simplicity, q = 1. Under a fixed exchange rate regime, the national money markets are integrated into a unified international money market. The equilibrium is characterized by the equality of global demand and the supply of money, and the balance of payments mechanism generates the desirable distribution of money across countries. Under a flexible exchange rate system the money market is national, and domestic prices and the exchange rate are determined so as to equate the demand for and the supply of money in each country.

II. The Equilibrium

The equilibrium can be analyzed first by characterizing the behavior of consumers and producers, and then by describing the possible regimes.

Consumer Demand

Consumption in the second period is characterized by the solution to

\begin{matrix} \max {[\sum_{i = 1}^{d} {(D_{2, i})}^{α}]}^{1 / α}, & (8) \end{matrix}

subject to

\sum_{i = 1}^{d} P_{2, i} D_{2, i} = I N_{2},

where P_{2, i},IN₂ are the second-period money prices of good i and the second-period money income, respectively. The solution of the consumer’s problem is characterized by

\begin{matrix} D_{2, i} = {(\frac{{\bar{P}}_{2}}{P_{2, i}})}^{σ} \frac{I N_{2}}{{\bar{P}}_{2}}, & for σ = 1 / (1 - α) & (9) \end{matrix}

and

\begin{matrix} {\bar{P}}_{2} = {[\sum_{i = 1}^{d} {(P_{2, i})}^{- α σ}]}^{- 1 / (α σ)} . & (10) \end{matrix}

The overall price index of differentiated products is ₂. The consumer’s utility function (equation (1)) is additive in the consumption of the homogeneous good in period 1 and the consumption of the differentiated products aggregate, D₂. Applying equations (9) and (10), it follows that D₂=IN₂/₂. This implies that if an internal equilibrium is observed where goods are consumed in both periods, the real interest rate in terms of good Y must equal 1 + p. At that interest rate, consumers are willing to postpone consumption to the second period, and the aggregate saving is determined by the investment. Henceforth it is assumed that the supply of the homogeneous good is large enough to induce an internal equilibrium.¹³

Producer Pricing

The producer of a differentiated product, i, has market power facing a demand, the elasticity of which is σ (see equation (9)). Profits are maximized when the value of the marginal product of labor (marginal revenue times the marginal product of labor) equals the wage. Applying equations (3) and (9) yields the supply of the differentiated product and the demand for labor (denoted by D^s₂, and L^d₂, respectively):

\begin{matrix} D_{2, i}^{s} = a^{- 1 / (1 - γ)} {(\frac{αγ P_{2, i}}{W_{0}})}^{γ^{'}}, & L_{2, i}^{d} = {(\frac{αγ P_{2, i}}{a W_{0}})}^{1 / (1 - γ)}, & (11) \end{matrix}

where γ’=γ/(1-γ). Producers’ nominal profits (denoted by II_{2, i}) are

\begin{matrix} Π_{2, i} = (1 - αγ) P_{2, i} D_{2, i} . & (12) \end{matrix}

Next, the equilibria in a fixed and in a flexible exchange rate regime can be characterized. The two countries are identical ex ante; hence, the focus can be on the symmetric equilibrium. The exchange rate is normalized to unity, and transportation costs and commercial policy are assumed away. Thus, the price of the same variety of product is the same in both countries. (See the appendix for a characterization of the equilibria in fixed and flexible exchange rate regimes when all producers operate as multinationals and when all producers operate as nondiversi-fied firms.) In equilibrium the goods and money markets clear, the contract wage is preset at a level that is expected to generate the employment target, and free entry eliminates expected rents. Equilibrium in the goods market requires that the supply be equated to the sum of domestic and foreign demand. In regimes where the producers are not diversified, each variety is produced in only one country. Multinational suppliers will produce in both countries; thus, the supply of each good is the sum of the production in plants located in both countries.

Equilibrium in the money market is obtained by first characterizing the price level and nominal GNP, and then applying this information to the money market. A key difference between flexible and fixed exchange rate regimes is that under a flexible regime the money market is national; it is cleared separately in each country, determining the price levels in the two economies and, indirectly, the exchange rate. Under a fixed exchange rate regime, the money market is international—the global supply of money equals the global demand. The precise decomposition of the supply of money between the two countries is obtained through the balance of payment mechanism. The wage contract is set according to the Fischer-Gray formulation, which equates expected employment to the employment target, denoted by . Free entry implies the elimination of expected rents. The zero expected rent condition implies that for multinationals, profits derive from production in both locations, and that the cost of capital goes up (at a rate of η) due to needed investment in two plants. This condition is instrumental in determining the number of varieties and, indirectly, the equilibrium level of investment.

Although the identity of the exchange rate regime is policy determined, the nature of the diversification of production is established endogenously—producers decide whether to diversify or operate as multinationals. Hence, in addition to the conditions postulated by the systems defined in equations (28a)–(28f) through (31a)–(31f) in the appendix, stability conditions determine the nature of the regime. One may expect a nondiversified regime where all producers operate nationally if the marginal benefit from becoming multinational falls short of the extra capacity cost, and thus a version of equation (5) should be satisfied. Similarly, there will be a multinational equilibrium if producers do not benefit by switching to a nationalistic strategy, and thus a version of equation (7) applies.

III. Productivity Shock, Monetary Shocks, Volatility, and Investment

Further insight is gained by focusing on the simplest stochastic example: two states of nature, with a negative correlation between domestic and foreign shocks.¹⁴ Exposition is simplified further by a consideration of the extreme cases, where all shocks are either real or nominal. When these two extreme cases are understood, the analysis can be redone for the general case.

Productivity Shocks

Suppose, first, that volatility is due to productivity shocks, which can take the following values:

\begin{matrix} (\frac{1}{a}, \frac{1}{a *}) = {\begin{matrix} (1 + h, 1 - h) \\ or \\ (1 - h, 1 + h) \end{matrix} & (13) \end{matrix}

with equal probabilities (1 > h > 0). (See the appendix for a detailed solution for the case of real shocks.)

Fixed Exchange Rate Regime

Aggregate investment and aggregate employment in the nondiversified regime are given by

\begin{matrix} m K_{| F I, R, N} = {[\frac{\frac{1}{2} (1 - αγ) {(2 \bar{L})}^{γ}}{1 + ρ}]}^{a / [a (1 + γ) - 1]} \\ \begin{matrix} \cdot [\frac{{(1 + h)}^{α / (1 - αγ)} + {(1 - h)}^{α / (1 - αγ)}}{K}] & (14 a) \end{matrix} \end{matrix}

\begin{matrix} L_{2_{| F I, R, N}}^{d} = 2 \bar{L} {(\frac{1}{a})}^{a [1 - αγ]} \\ \begin{matrix} \cdot {[{(1 - h)}^{α / [1 - αγ]} + {(1 + h)}^{α / [1 - αγ]}]}^{- 1}, & (14 b) \end{matrix} \end{matrix}

where ∣FI, R, N stands for a fixed exchange rate, subject to real shocks, with nondiversified producers. If all producers diversify—that is, operate as multinationals—aggregate investment and employment are (see the appendix for further details)

\begin{matrix} \frac{1}{2} n K {(1 + η)}_{| F I, R, D} \\ = \frac{1}{2} {[\frac{(1 - αγ) {(2 \bar{L})}^{γ} {({(1 + h)}^{1 / (1 - γ)} + {(1 - h)}^{1 / (1 - γ)})}^{1 - γ}}{1 + ρ}]}^{α / [α (1 + γ) - 1]} \\ \begin{matrix} \cdot {[\frac{1}{K (1 + η)}]}^{[1 - αγ] / [α (1 + γ) - 1]} & (15 a) \end{matrix} \end{matrix}

\begin{matrix} L_{2_{| F I, R, D}}^{d} = 2 \bar{L} {(\frac{1}{a})}^{1 / [1 - γ]} {[{(1 - h)}^{1 / [1 - γ]} + {(1 + h)}^{1 / [1 - γ]}]}^{- 1}, & (15 b) \end{matrix}

where ∣FI, R, D stands for a fixed exchange rate, subject to real shocks, with diversified producers. It is henceforth assumed that the various heterogeneous goods are close substitutes and that the labor share is large enough that α(l + γ) > 1. This assumption is needed in order to ensure that a higher set-up cost, K, will reduce the number of varieties offered, and plays a role similar to the Marshall-Lerner condition in trade theory. ¹⁵ The condition determining the nature of the regime is obtained by applying equation (5); producers will operate as nondiversified if¹⁶

\begin{matrix} {[{(1 + h)}^{1 / (1 - γ)} + {(1 + h)}^{1 / (1 - γ)}]}^{α (1 + γ) / [1 - αγ]} \\ \begin{matrix} < (1 + η) \frac{1}{2} [{(1 + h)}^{α / (1 + αγ)} + {(1 - h)}^{α / (1 + αγ)}], & (16) \end{matrix} \end{matrix}

and diversification will occur if the opposite inequality holds.

There are two reasons for diversification : returns to scale, and the gains from reallocating production toward the more productive country. Internationally diversified capacity will allow production to be spread across several plants, lessening the impact of the diminishing marginal productivity of the variable inputs, at the cost of increasing capital expenditure by the factor η. If this cost is small enough, it will be worthwhile to invest in multiple plants. Formally, from equation (16), if, 2^{α(1-γ)/(1 - αγ)} - 1>η entrepreneurs will invest in two plants, even in the absence of shocks. In this case, in the absence of transportation costs the production location is undetermined. With low volatility, producers will prefer to diversify, reaping gains from international diversification of country-specific shocks, as well as from the smaller impact from diminishing marginal productivity.

If 2^{α(1-γ)/(1 - αγ)} - 1 > η < 1, international diversification will occur only if volatility (as measured by h) is high enough.¹⁷ Higher volatility increases the economic value of diversification by increasing the value of the option to reallocate production toward the more productive or cheaper country. Diversification will occur if the value of this option exceeds the extra cost of capital, as will occur if the inequality in (16) is reversed. Inspection of (16) shows that as long as 1 > η for a large enough h, producers will diversify internationally. Henceforth, it is assumed that 2^{α(1-γ)/(1 - αγ)} - 1 > η< 1. Thus, in the absence of uncertainty producers will specialize, and will produce only in one plant.

For further insight, the adjustment of labor in the nondiversified regime can be compared to that in the diversified regime (equations (14b) and (15b)). It follows that the elasticity of tabor adjustment with respect to a real shock is greater in the diversified regime:¹⁸

\begin{matrix} \frac{d \log (L^{d})}{d \log {(1 / a)}_{| F I, R, D}} > \frac{d \log (L^{d})}{d \log {(1 / a)}_{| F I, R, N}} > 0 . & (17) \end{matrix}

The economic factors determining the nature of the equilibria are illustrated in Figures 2 and 3. Figure 2 traces the marginal productivity of labor in the two states where curves MP^h_L and MPⁱ_L. correspond to states h and l, respectively. Employment in the nondiversified regime will fluctuate between L^h_N and L^l_N. Note that in states of nature where productivity abroad is higher than at home (as is the case in state l), a multinational benefits by shifting employment from the home economy to the foreign country.¹⁹ The benefit from the marginal unit of employment reallocation is measured by the difference between the marginal productivity of labor in the two countries, and is determined by the volatility of shocks (note that QQ¹ = 2hMP^o_L). Once the volatility of shocks is large enough, the benefits from diversification overwhelm the cost, and all producers will diversify. The diversification achieved with multinational production stabilizes the price of the various varieties. In the nondiversified regime the price level in the country experiencing the adverse shock will tend to rise, reducing the real wage and partially mitigating the drop in employment. This effect is absent in the diversified regime. Hence, employment fluctuates more in the diversified regime, as reported in equation (17). In Figure 2, employment drops to L^l_D and L^l_N in the country facing the adverse shock under diversified and nondiversified regimes, respectively. Employment increases to L^h_D and L^h_N in the country facing the favorable shock under diversified and nondiversified regimes, respectively.

Note that in the nondiversified regime employment is reallocated from the bad state of nature toward the good state (relative to the case of stable employment at L₀). Such an adjustment increases expected profits. This effect is more powerful, the greater is the volatility of the shocks. In Figure 2, in the nondiversified regime the expected output exceeds the output in the absence of shocks by half the dotted area. Recalling that profits are eliminated because of free entry, higher profits will attract new producers. Hence, a higher volatility of real shocks will increase aggregate investment. The same effect operates in an even more powerful way in the diversified regime.²⁰

In panel A of Figure 3, curve FI summarizes the patterns of investment under a fixed exchange rate regime as a function of the volatility of productivity shocks, measured by h.²¹ For low volatility, producers will operate as nondiversified, and the aggregate investment is traced by curve FI,N. When volatility rises, all producers will diversify, and the aggregate investment will be traced by FI,D. Curve FI is upward sloping, and the switch to the diversified regime is associated with higher volatility of employment as well as with a higher expected gross domestic product.

Flexible Exchange Rate Regime

In the case of a flexible regime subject to real shocks, the country experiencing the adverse shock will undergo a depreciation (see equations (30a)–(30f) and (31a)–(31f) in the appendix for technical details). If the adverse shock hits the home economy, prices, P_i, will increase. This result follows from the markup pricing rule and the decline in the demand for money resulting from the drop in output triggered by the adverse shock. The opposite adjustment occurs in the other country experiencing the favorable productivity shock. The adjustment of employment reflects two conflicting effects: the adverse productivity shock causes a drop in the demand for labor, whereas the higher price level mitigates the fall in employment because of the induced decline in the real wage. For the special case considered in this paper (where the elasticity of the demand for money with respect to output is unity), the two effects balance each other, and employment is completely stabilized. As depicted in Figure 2, employment in both countries is at level L₀. In the nondiversified regime output will fluctuate because of the impact of the productivity shock. The discrepancy between the marginal productivity of labor in the two countries generates an incentive to diversify, which depends on the volatility of shocks. With a high enough volatility, all producers will diversify. That diversification will stabilize the global output of each variety.²² A by-product of the stabilization of employment achieved with exchange rate flexibility is that the expected output under a flexible exchange rate regime is lower than the expected output under a fixed exchange rate.²³ Applying the procedure outlined in the appendix, one obtains

\begin{matrix} \begin{matrix} m K_{| F L, R, N} = {[\frac{\frac{1}{2} (1 - αγ) {(\bar{L})}^{γ}}{1 + ρ}]}^{α / [α (1 + γ) - 1]} \end{matrix} \\ \begin{matrix} \cdot {[\frac{{{(1 + h)}^{α} + {(1 - h)}^{α}}^{1 / [1 - αγ]}}{K}]}^{[1 - αγ] / [α (1 + γ) - 1]} & (18 a) \end{matrix} \end{matrix}

\begin{matrix} \frac{1}{2} n K {(1 + η)}_{| F L, R, D} \\ \begin{matrix} = \frac{1}{2} {[\frac{2 (1 - αγ) {(\bar{L})}^{γ}}{1 + ρ}]}^{α / [α (1 + γ) - 1]} {[\frac{1}{K (1 + η)}]}^{[1 - αγ] / [α (1 + γ) - 1]}, & (18 b) \end{matrix} \end{matrix}

where index ∣FL, R stands for a flexible exchange rate in the presence of real shocks. The inference that follows from applying (5) is that producers will operate as nondiversified if and only if h is small enough, in such a way that

\begin{array}{l} {[{(1 + h)}^{(1 - αγ) / (1 - γ)} + {(1 - h)}^{(1 - αγ) / (1 - γ)}]}^{α (1 - γ) / [1 - αγ]} \\ \begin{matrix} < (1 + η) \frac{1}{2} [{(1 + h)}^{α} + {(1 - h)}^{α}], & (19) \end{matrix} \end{array}

and diversification will occur if the opposite inequality holds. As with the case of the fixed exchange rate, the condition for observing a nondiversified regime in the absence of volatility is that 2α(1-γ)/(1-αγ) - 1 < η.

Applying equations (14), (15), and (18), it can be shown that

\begin{array}{l} m K_{| F L, R} < m K_{| F l, R} \\ \begin{matrix} \frac{1}{2} n (1 + η) K_{| F L, R} < \frac{1}{2} n (1 + η) K_{| F l, R \cdot} & (20) \end{matrix} \end{array}

These results are summarized in pane! A of Figure 3.²⁴ Volatile real shocks under a flexible exchange rate with nondiversifled producers induce output fluctuation, which in turn reduces expected profits and, hence, aggregate investment.²⁵ Once volatility reaches a high level, the market switches to the diversified regime, a switch that stabilizes the global output of each variety and eliminates the adverse consequences of any further increase in volatility.

Monetary Shocks

In the following subsections the adjustment to a monetary disturbance is evaluated. Suppose that the initial supply of money is given by

\begin{matrix} (M, M *) = {\begin{matrix} \begin{matrix} M_{0} (1 + h), & M_{0} (1 - h) \end{matrix} \\ or \\ \begin{matrix} M_{0} (1 - h), & M_{0} (1 + h), \end{matrix} \end{matrix} & (21) \end{matrix}

with equal probabilities, where M and M^* stand for nominal balances in the two countries.

Fixed Exchange Rate Regime

In a fixed exchange rate regime, the money market is international and the two shocks are diversified away. Hence, the aggregate supply of money is stable, and there is no transmission of the monetary instability to prices and output. Investment in the nondiversified and the multinational regimes is given by (see equations (28a)–(28f) and (29a)–(29f) in the appendix for the solution)

\begin{matrix} m K_{| F l, M, N} = {[\frac{\frac{1}{2} (1 - αγ) {(2 \bar{L})}^{γ}}{1 + ρ}]}^{α / [α (1 + γ) - 1]} {[\frac{2}{K}]}^{[1 - αγ] / [a (1 + γ) - 1]} & (22 a) \end{matrix}

\begin{matrix} \frac{1}{2} n K {(1 + η)}_{| F l, M, D} \\ \begin{matrix} = \frac{1}{2} {[\frac{2 (1 - αγ) {(\bar{L})}^{γ}}{1 + ρ}]}^{α / [α (1 + γ) - 1]} {[\frac{1}{K (1 + η)}]}^{[1 - αγ] / [α (1 + h) - 1]}, & (22 b) \end{matrix} \end{matrix}

where ∣FI, M stands for the fixed exchange rate, subject to monetary shocks. The condition determining the nature of the regime is obtained by applying equation (5); producers will operate as nondiversified if and only if 2α(1-γ)/(1-αγ) - 1 < η.

Flexible Exchange Rate Regime

Investment and employment in the nondiversified and the multinational regimes are given by (see equations (30a)–(30f) and (31a)–(31f) in the appendix for the solution)

\begin{matrix} m K_{| F L, M, N} = {[\frac{\frac{1}{2} (1 + αγ) {(\bar{L})}^{γ}}{1 + ρ}]}^{α/ [α (1 + γ) - 1]} \\ \begin{matrix} \cdot {[\frac{{{(1 + h)}^{αγ} + {(1 + h)}^{αγ}}^{1 / [1 - αγ]}}{K}]}^{[1 - αγ] / [α (1 + γ) - 1]} & (23 a) \end{matrix} \end{matrix}

\begin{matrix} L_{2_{| F L, R, D}}^{d} = \frac{M}{M_{0}} \bar{L} . & (23 b) \end{matrix}

An expansionary monetary shock at home will induce a higher price of domestic goods and a depreciation. The induced drop in real wages will expand employment and output. The opposite adjustment occurs in the foreign country. Although this adjustment is optimal from the point of view of each producer, the resultant equilibrium turns out to be associated with lower expected profits and, thereby, with lower investment. Inspection of equations (23a) and (23b) reveals that higher monetary volatility (higher h) depresses aggregate investment. This can be seen in Figure 1, where the production function in the absence of real shocks is given by D^s,o_i,. The impact of volatility due to monetary shocks in a flexible exchange rate system is that employment will fluctuate between L_l and L_h (where L_hi – = – L_t,). This will depress expected profits, from point K₂ to point K₃, and will ultimately reduce the aggregate investment.

The presence of these shocks induces disparities among the real wages in the two countries, generating an incentive to diversify the production process. If the volatility is large enough, all producers will operate as multinationals. The resultant aggregate investment and employment are (see appendix for details)

\begin{matrix} \frac{1}{2} n K {(1 + η)}_{| F L, M, D} \\ = \frac{1}{2} {[\frac{(1 - αγ) {(\bar{L})}^{γ} {{(1 + h)}^{γ} + {(1 - h)}^{γ}}}{1 + ρ}]}^{α/ [α (1 + γ) - 1]} \\ \begin{matrix} \cdot {[\frac{1}{K (1 + η)}]}^{(1 - αγ) / [α (1 + γ) - 1]} & (24 a) \end{matrix} \end{matrix}

\begin{matrix} L_{2_{| F L, R, D}}^{d} = \frac{M}{M_{0}} \bar{L}, & (24 b) \end{matrix}

where index ∣FL, M stands for the flexible exchange rate regime in the presence of monetary shocks. It follows from an application of equation (5) that producers will operate as nondiversified if and only if h is small enough, so that

\begin{matrix} {[{(1 + h)}^{(1 - αγ) γ / (1 - γ)} + {(1 - h)}^{(1 - αγ) γ / (1 - γ)}]}^{α (1 - γ) / (1 - αγ)} \\ \begin{matrix} < (1 + η) \frac{1}{2} [{(1 + h)}^{αγ} + {(1 - h)}^{αγ}], & (25) \end{matrix} \end{matrix}

and diversification will occur if the opposite inequality holds. As with the case of the fixed exchange rate, the condition for observing a nondiversified producer is that the international return to scale is not powerful, so that 2α(1-γ)/(1-αγ) - 1 < η. A comparison between equations (23) and (25) yields

\begin{array}{l} m K_{| F L, M} < m K_{| F l, M} \\ \begin{array}{l} \frac{1}{2} n (1 + η) K_{| F L, M} < \frac{1}{2} n (1 + η) K_{| F l, M} . & (26) \end{array} \end{array}

The behavior of the economy is summarized in panel B of Figure 3, showing that higher monetary volatility is associated with a drop in aggregate investment.²⁶

IV. Comparison Between Regimes

This section presents a graphic summary of the results and an economic interpretation of the findings. The regimes can be compared by an analysis of the dependency of aggregate investment on the volatility of shocks. The aggregate investment for each country is given by mK + (1/2)nK(1 + η), and the volatility measure by h. The assumption of risk-neutral entrepreneurs, and the fact that gross profits are a fraction 1 - αγ of revenue imply that the expected utility from consumption is²⁷

\begin{matrix} E [Y_{1} + \frac{D_{2}}{1 + ρ}] = \bar{Y} + \frac{αγ}{1 - αγ} [m K + \frac{1}{2} n K (1 + η)] . & (27) \end{matrix}

Consequently, tracing the behavior of aggregate investment provides information on the expected utility of consumption, or equivalently, the expected net present value of real consumption. Throughout this discussion, it is important to keep in mind that equation (27) represents only the consumption component of the expected utility. To obtain the expected utility, one must subtract the expected disutility from labor from (27). In the model here, trade accounts for half (on average) of GNP, and thus tracing the expected consumption also provides information about the average volume of international trade.

Figure 3 reveals that for a given volatility of shocks, a fixed exchange rate regime is associated with higher domestic and foreign direct investment than a flexible regime. Although Figure 3 represents the special example considered here, its underlying logic is more general. With free entry, the behavior of aggregate investment follows the behavior of gross profit, which, on average, is the return to capital. For a given volatility of shocks, a fixed exchange rate regime is associated with higher expected profits. If the shocks are monetary, employment will fluctuate more under a flexible exchange rate regime. (In fact, in the example used here, employment will be stable under a fixed exchange rate.) The volatility of employment and production under a floating exchange rate will depress expected profits, because in the absence of productivity shocks, monetary shocks will induce a move on a given production function (D^s,o in Figure 1). The diminishing productivity of labor implies that such volatility adversely affects expected profits (and, hence, aggregate investment).

The case of real shocks is more involved because the production function shifts around the nonstochastic production, fluctuating between D^s,h_i and D^s,l_i (Figure 1) in the states of high and low productivity, respectively. If producers diversify, under a fixed exchange rate regime employment will be reallocated from the less productive to the more productive country. This reallocation is smaller in a flexible exchange rate regime, because the country experiencing the more favorable realization of productivity will experience nominal and real appreciation, which will moderate (and potentially eliminate) the resultant expansion of employment. The heavier reallocation of employment to the more efficient country in a fixed exchange rate regime will tend to increase expected profits, thereby encouraging investment.²⁸ In terms of Figure 1, employment will fluctuate between L_t and L_h in a fixed exchange rate regime, and will stay at in a flexible exchange rate regime.

The reallocation of employment observed in a fixed exchange rate regime increases expected output (relative to the expected output level under a flexible exchange rate regime). To see this, note that the marginal product of labor at point B exceedsjhat at point A by a factor of 2h. Thus, starting with employment level in both countries under a fixed exchange rate regime, a marginal reduction of employment in the less productive country and a corresponding increase in employment in the more productive country will increase expected profits by the divergences in the marginal product of labor. The same logic applies to the consecutive reallocation of employment across countries, until this arbitrage opportunity is eliminated (that is, until one reaches a point like A´ and B´ where the marginal product is equal in the two countries). In terms of Figure 1, expected output, K₁ in a fixed exchange rate regime will exceed the expected output in a flexible exchange rate regime, K₂.²⁹

V. Concluding Remarks

The analysis presented here suggests that aggregate investment is higher under a fixed exchange rate regime than under a flexible exchange rate for both productivity and monetary shocks. Hence, the adoption of a fixed exchange rate could encourage flows of direct foreign investment. This result does not imply, however, that a fixed exchange rate is always superior to a flexible one. There is, in fact, a trade-off between the volatility of employment and expected income in the presence of real shocks—a flexible exchange rate stabilizes employment at the cost of reducing expected GNP and investment. Thus, relative welfare must be determined by a weighing of these two effects according to the degree to which agents dislike labor volatility. Such a comparison will also hinge on the relative importance of productivity versus monetary shocks. The results of this study suggest, however, that countries wishing to encourage foreign direct investment will benefit from a fixed exchange rate adopted in conjunction with policies that will improve the safety net for unemployment. Thus, these countries could reap the benefits of more investment and higher GNP, while protecting themselves partially against higher employment volatility.

Although this analysis focused on the case of monetary shocks that stemmed from the stochastic supply of money, the same analysis would apply if the volatility stemmed from the stochastic demand for money, or from “bubbles.”³⁰ These results suggest that attempts to minimize monetary shocks through the proper coordination of monetary policies can be beneficial, and that these benefits may occur indirectly by encouraging investment. In this paper risk neutrality was assumed, and thus none of the results relate to risk-averse behavior. Even with risk neutrality, volatility affects welfare because of the diminishing marginal productivity of variable inputs in the short run. Although the potential importance of risk aversion should not be dismissed, the risk-neutrality may be viewed as a useful benchmark that implies that all the results reported here would still hold even if producers had access to a forward exchange rate market. The results derived in this paper stem from the absence of complete markets in the presence of contracts that do not allow for complete contingent prices. The addition of forward coverage does not make the market complete, so all the paper’s results continue to hold.

This paper used a macroeconomic approach to address the behavior of foreign direct investment, building on the micro behavior of producers. Such an approach is useful for highlighting the feedback between shocks, the behavior of economic agents, and the adjustment of macro variables. A micro analysis of foreign direct investment leads to the conclusion that if fluctuations in the real exchange rate are large enough, a corporation will benefit by expanding production and employment in the country experiencing a decline in its real exchange rate. Thus, the corporation obtains a higher expected profit than it would have if it had not diversified internationally by foreign direct investment (for a review of this argument see Grubel (1988)). This argument suggests a positive correlation between real exchange rate flexibility and foreign direct investment, and may seem to differ from the prediction of the model presented here. However, it is important to keep in mind that the above results were derived in a micro model that did not consider the possibility of monetary shocks; rather, it focused on the adjustment of a given producer and overlooked the macro feedback effects triggered by the aggregate adjustment of producers.

The model showed that in the presence of a Phillips curve and monetary shocks the beneficial effects of a flexible exchange rate may backfire—efficient adjustment from the point of view of a given producer may be to minimize the losses stemming from a monetary shock.³¹ These losses may be eliminated under a fixed exchange rate, which prevents a spillover of disturbances in the money market into the real exchange rate.

In the presence of a Phillips curve, the flexibility of a nominal exchange rate may differ from the flexibility of the real exchange rate. Although such a distinction is of no relevance in a micro model, it does apply to a macro model. An example of this point is provided in the discussion in the paper on the adjustment to real shocks. The analysis demonstrated that such shocks require a greater adjustment of the real exchange rate under a fixed exchange rate than under a flexible rate—the stabilization of employment achieved under a flexible exchange rate regime reduces the supply gap between domestic and foreign products, and, hence, the real exchange rate will fluctuate less under a flexible exchange rate regime.³² Therefore, the logic of the macro approach is consistent with the micro analysis of foreign direct investment, as long as it is recognized that monetary shocks may lead to results that are outside the micro context, and that the flexibility of the real exchange rate may differ from that of the nominal exchange rate.

APPENDIX

Derivations and Solutions of Key Equations

This appendix lays out the simultaneous equation systems that characterize each regime, and derives the key equations used in the paper.

Fixed Exchange Rate

If all producers operate as nondiversified in a symmetric equilibrium, m producers specialize in the production of distinct varieties in each country, and the total number of goods is 2m. The domestic and foreign varieties are denoted by index i and j (1 ≤ i, J ≤ m), respectively. The symmetric framework implies that all varieties in a given country are characterized by similar equations. Hence, the concept of representative domestic and foreign varieties, denoted by r and r*, respectively, is used.

Nondiversified Producers

The equilibrium is characterized by the following conditions:

\begin{matrix} a^{- 1 / (1 - γ)} (\frac{{αγP}_{2. i}}{W_{0}})^{γ^{,}} & = & (\frac{\bar{P_{2}}}{P_{2. i}})^{σ} & \frac{{IN}_{2} + IN \overset{*}{2}}{{\bar{P}}_{2}}, \\ (a^{*})^{- 1 / (1 - γ)} (\frac{αγ P_{2. i}^{*}}{W_{0}})^{γ^{,}} & = & (\frac{\bar{P}}{P_{2, i}})^{σ} \frac{{IN}_{2} + {IN}_{2}^{*}}{{\bar{P}}_{2}}, & for 1 \leq i, j \leq m (28 a) \end{matrix}

\begin{matrix} {\bar{P}}_{2} = {(m)}^{- 1 / (σ σ)} {[{(P_{2, r})}^{- α σ} + {(P_{2, r^{*}})}^{- α σ}]}^{- 1 / (α σ)} & (28 b) \end{matrix}

\begin{matrix} I N_{2} = m P_{2, r} D_{2, r}^{s}, & I N_{2}^{*} = m P_{2, r^{*}} D_{2, r^{*}}^{s^{*}} & (28 c) \end{matrix}

\begin{matrix} I N_{2} + I N_{2}^{*} = M_{2}^{s} + M_{2}^{s^{*}} & (28 d) \end{matrix}

\begin{matrix} n E [L_{2, r}^{d}] = \bar{L}, & n E [L^{*}_{2, r^{*}}^{d}] = \bar{L} & (28 e) \end{matrix}

\begin{array}{l} E [(1 - α γ) \frac{P_{2, i} D_{2, i}^{s}}{{\bar{P}}_{2}}] = K (1 + p), \\ \begin{matrix} E [(1 - α γ) \frac{P_{2, j} D_{2, j}^{s}}{{\bar{P}}_{2}}] = K (1 + p), & for 1 \leq i, j \leq m . & (28 f) \end{matrix} \end{array}

Condition (28a) is the goods market equilibrium, equating the supply to the sum of domestic and foreign demand. In the regimes where the producers are nondiversified, the supply of each variety stems from one country (as is the case in system (28)). The money market equilibrium is obtained by first characterizing the price level and nominal GNP, and then applying this information to the money market. Condition (28b) is the consumer price index, obtained from equation (10), where r and r* stand for a representative variety produced at home and abroad. Nominal income equals nominal GNP, as given by condition (28c). The money market equilibrium can be characterized through information on the price level and nominal income. Assuming a unitary velocity, equilibrium in the money market is stated in condition (28d), where index s stands for the supply. Under a fixed exchange rate regime, the money market is international—the global supply of money equals the global demand, as is indicated by equation (28d). The precise decomposition of the supply of money in the two countries is obtained through the balance of payment mechanism.

The wage contract is set according to (28e), equating expected employment to the employment target, denoted by . Free entry implies that expected rents are dissipated, as postulated by (28f). This condition is instrumental in determining the number of varieties and, indirectly, the equilibrium level of investment.

Multinational Producers

If all producers are multinational, and there are n of them, the distinction between domestic and foreign variety disappears, and r is used as the representative variety:

\begin{array}{l} {(a)}^{- 1 / (1 - γ)} {(\frac{α γ P_{2, i}}{W_{0}})}^{γ′} + {(a^{*})}^{- 1 / (1 - γ)} {(\frac{α γ P_{2, i}}{W_{0}})}^{γ′} = {(\frac{{\bar{P}}_{2}}{{\bar{P}}_{2, i}})}^{σ} \frac{I N_{2} + I N_{2}^{*}}{{\bar{P}}_{2}}, \\ \begin{matrix} for i = 1, \dots, n . & (29 a) \end{matrix} \end{array}

\begin{matrix} {\bar{P}}_{2} = n^{- 1 / (α σ)} P_{2, r} & (29 b) \end{matrix}

\begin{matrix} I N_{2} = n P_{2, r} D_{2, r}^{s}, & I N_{2}^{*} = n P_{2, r} D_{2, r}^{s^{*}} & (29 c) \end{matrix}

\begin{matrix} I N_{2} + I N_{2}^{*} = M_{2}^{s} + M_{2}^{s^{*}} & (29 d) \end{matrix}

\begin{matrix} n E [L_{2, r}^{d}] = \bar{L}, & n E [L^{*}_{2, r}^{d}] = \bar{L} & (29 e) \end{matrix}

\begin{matrix} E [(1 - α γ) \frac{P_{2, r} {D_{2, r}^{s} + D^{*}_{2, r}^{s}}}{{\bar{P}}_{2}}] = K (1 + η) (1 + ρ) . & (29 f) \end{matrix}

The interpretation of the various equations in system (29) is similar to (28), with the needed modifications due to the diversified production. Multinational producers will produce in both countries; thus the supply of each good is the sum of the production in plants located in both countries (see equation (29a)). The zero expected rent condition recognizes that the multinational produces in both locations, and that the cost of capital goes up (at a rate of η) due to the needed investment in two plants (see (29f)).

Flexible Exchange Rate Regime

For the equations detailing the flexible exchange rate regime, the exchange rate is denoted by S, defined as the domestic currency price of a unit of foreign currency. The law of one price is assumed to hold for the same variety, and thus $P_{2, i} = S P_{2, i}^{*}$ , where $P_{2, i}^{*}$ stands for the foreign currency price of variety i abroad, The modified equilibrium conditions are as follows below.

Nondiversified Producers

\begin{array}{l} \begin{matrix} {(a)}^{- 1 / (1 - γ)} {(\frac{α γ P_{2, i}}{W_{0}})}^{γ′} = {(\frac{{\bar{P}}_{2}}{P_{2, i}})}^{σ} \frac{I N_{2} + S I N_{2}^{*}}{{\bar{P}}_{2}}, & i = 1, \dots, m \end{matrix} \\ \begin{matrix} {(a)}^{- 1 / (1 - γ)} {(\frac{α γ P_{2, j}^{*}}{W_{0}})}^{γ′} = {(\frac{{\bar{P}}_{2}}{S P_{2, j}^{*}})}^{σ} \frac{I N_{2} + S I N_{2}^{*}}{{\bar{P}}_{2}}, & j = 1, \dots, m & (30 a) \end{matrix} \end{array}

\begin{matrix} {\bar{P}}_{2} = {(m)}^{- 1 / (α σ)} {[{(P_{2, r})}^{- α σ} + {(S P_{2, r^{*}}^{*})}^{- α σ}]}^{- 1 / (α σ)} & (30 b) \end{matrix}

\begin{matrix} I N_{2} = m P_{2, r} D_{2, r}^{s}, & I N_{2}^{*} = m P_{2, r^{*}}^{*} D_{2, r^{*}}^{s^{*}} & (30 c) \end{matrix}

\begin{matrix} I N_{2} = M_{2}^{s}, & I N_{2}^{*} = M_{2}^{S^{*}} & (30 d) \end{matrix}

\begin{matrix} n E [L_{2, r}^{d}] = \bar{L}, & n E [L^{*}_{2, r^{*}}^{d}] = \bar{L} & (30 e) \end{matrix}

\begin{array}{l} E [(1 - α γ) \frac{P_{2, r} D_{2, r}^{s}}{{\bar{P}}_{2}}] = K (1 + ρ), \\ \begin{matrix} E [(1 - α γ) \frac{(S P_{2, r^{*}}) D_{2, r^{*}}^{s}}{{\bar{P}}_{2}}] = K (1 + ρ) . & (30 f) \end{matrix} \end{array}

A key difference between the exchange rate regimes is that under a flexible regime the money market clears in each country separately (as is reflected in equation (30d)), determining the price levels in the two economies and, indirectly, the exchange rate.

Multinational Producers

Equilibrium under a flexible exchange rate regime, where all producers are multinational, is characterized by

\begin{array}{l} {(a)}^{- 1 / (1 - γ)} {(\frac{α γ P_{2, i}}{W_{0}})}^{γ′} + {(a^{*})}^{- 1 / (1 - γ)} (\frac{α γ P_{2, i}}{S W_{0}}) = {(\frac{{\bar{P}}_{2}}{P_{2, i}})}^{σ} \frac{I N_{2} + S I N_{2}^{*}}{{\bar{P}}_{2}} \\ \begin{matrix} for 1 \leq i \leq n & (31 a) \end{matrix} \end{array}

\begin{array}{l} \begin{array}{l} \begin{matrix} {\bar{P}}_{2} = {(n)}^{- 1 / (α σ)} P_{2, r} & (31 b) \end{matrix} \end{array} \end{array}

\begin{matrix} I N_{2} = n P_{2, r} D_{2, r}^{S}, & S I N_{2}^{*} = n P_{2, r} D_{2, r}^{s^{*}} & (31 c) \end{matrix}

\begin{matrix} I N_{2} = M_{2}^{s}, & I N_{2}^{*} = M_{2}^{s *} & (31 d) \end{matrix}

\begin{matrix} n E [L_{2, r}^{d}] = \bar{L}, & n E [L^{*}_{2, r}^{d}] = \bar{L} & (31 e) \end{matrix}

\begin{matrix} E [(1 - α γ) \frac{P_{2, r} {D_{2, r}^{s} + D^{*}_{2, r}^{s}}}{{\bar{P}}_{2}}] = K (1 + η) (1 + ρ) . & (31 f) \end{matrix}

Solutions for the Combinations

Solving for the four combinations ((1) fixed exchange rate, nondiversified producers; (2) fixed rate, multinational producers; (3) flexible exchange rate, nondiversified producers; and (4) flexible rate, multinational producers) involves similar steps. The case of real shocks will be reviewed in detail. (The derivation of the equilibrium for monetary shocks follows similar steps and will be discussed briefly.)

Beginning with nondiversified producers under a fixed exchange rate regime, denote the global supply of money by ${\bar{M}}_{2}^{s}$ , which, in the absence of monetary shocks, is exogenously given. Hence, equation (28d) implies that the sum of nominal income equals the global supply of money, or $I N_{2} + I N_{2}^{*} = {\bar{M}}_{2}^{s}$ . Applying this condition to equation (28a) yields

\begin{matrix} a^{- 1 / (1 - γ)} {(\frac{α γ P_{2, r}}{W_{0}})}^{γ′} = {(\frac{{\bar{P}}_{2}}{P_{2, r}})}^{σ} \frac{{\bar{M}}_{2}^{s}}{{\bar{P}}_{2}} . & (32) \end{matrix}

Equivalently, multiplying both sides of (32) by P_{2, r}, and collecting terms yields

\begin{matrix} {(\frac{P_{2, r}}{a})}^{1 / (1 - γ)} {(\frac{α γ}{W_{0}})}^{γ′} = {(\frac{{\bar{P}}_{2}}{P_{2, r}})}^{σ α} {\bar{M}}_{2}^{s} . & (3 2^{'}) \end{matrix}

Dividing equation (28b) by P_{2, r} yields

\begin{matrix} \frac{{\bar{P}}_{2}}{P_{2, r}} = {(m)}^{- 1 / (α σ)} {[1 + {(\frac{P_{2, r}}{P_{2, r^{*}}})}^{α σ}]}^{- 1 / (α σ)} . & (33) \end{matrix}

Next, the price of the foreign relative to the domestic varieties is derived from the ratios of the equilibrium conditions in the goods market (the two equalities in (28a)):

\begin{matrix} \frac{P_{r *}}{P_{r}} = {(\frac{a^{*}}{a})}^{[1 - α] / [1 - α γ]} . & (34) \end{matrix}

Applying equation (34) to (33), using (13) yields

\begin{matrix} \frac{{\bar{P}}_{2}}{P_{2, r}} = {(m)}^{- 1 / α σ} {(\frac{1}{a})}^{[1 - α] / [1 - α γ]} {[{(1 - h)}^{α / [1 - α γ]} + {(1 + h)}^{α / [1 - α γ]}]}^{- 1 / α σ} . & (35) \end{matrix}

The price of domestic varieties as a function of the shocks is obtained by substituting equation (35) into equation (32′):

\begin{array}{l} {(\frac{P_{2, r}}{a})}^{1 / (1 - γ)} \\ \begin{matrix} = {(\frac{W_{0}}{α γ})}^{γ^{'}} \frac{1}{m} {(\frac{1}{a})}^{α / (1 - α γ)} {[{(1 - h)}^{α / [1 - α γ]} + {(1 + h)}^{α / [1 - α γ]}]}^{- 1} {\bar{M}}_{2}^{s} . & (36) \end{matrix} \end{array}

The demand for labor (equation (11) in the text) is given by

L_{2, i}^{d} = {(\frac{α γ}{W_{0}})}^{1 / (1 - γ)} {(\frac{P_{2, i}}{a})}^{1 / (1 - γ)} .

Substituting (36) into (11) gives the demand for labor:

\begin{matrix} L_{2, i}^{d} = (\frac{α γ}{W_{0}}) \frac{1}{m} (\frac{1}{a}) α / [1 - α γ] {[(1 - h^{α / [1 - α γ]} + {(1 + h)}^{α / [1 - α γ]})]}^{- 1} {\bar{M}}_{2}^{s} . & (37) \end{matrix}

Applying (37) to (28e) yields the level at which the contract wage is preset:

\begin{matrix} W_{0} = \frac{α γ {\bar{M}}_{2}^{s}}{2 \bar{L}} . & (38) \end{matrix}

The price of the domestic variety and the demand for labor are derived by substituting equation (38) into equations (36) and (37):

\begin{array}{l} P_{2, r} = {(\frac{1}{2 \bar{L}})}^{γ} m^{- (1 - γ)} {(a)}^{[1 - α] / [1 - α γ]} [{(1 - h)}^{α / [1 - α γ]} \\ \begin{matrix} {+ {(1 + h)}^{α / [1 - α γ]}]}^{- (1 - γ)} {\bar{M}}_{2}^{s} & (39) \end{matrix} \end{array}

\begin{matrix} L_{2, i}^{d} = 2 \frac{\bar{L}}{m} {(\frac{1}{a})}^{α / [1 - α γ]} {[{(1 - h)}^{α / [1 - α γ]} + {(1 + h)}^{α / [1 - α γ]}]}^{- 1} . & (40) \end{matrix}

Applying equations (32), (34), and (39), one can calculate expected profits. From E[(a)−α/[1−αγ]] = (1 − h)α/[1−αγ] + (1+ h) α/[1−αγ], and equations (11), (33), (35), and (39), expected profits may be given by

\begin{array}{l} E [(1 - α γ) \frac{P_{2, i} D_{2, i}^{s}}{{\bar{P}}_{2}}] \\ \begin{matrix} = \frac{1}{2} (1 - α γ) m^{[1 - α (1 + γ)] / α} {[{(1 - h)}^{α / [1 - α γ]} + {(1 + h)}^{α / [1 - α γ]}]}^{[1 - α γ] / α} {[2 \bar{L}]}^{γ} . & (41) \end{matrix} \end{array}

The equilibrium number of varieties is determined by the requirement that rents are dissipated, and, hence, equation (41) should equal the cost of capital, K(1 + ρ). Incorporating this term and solving for the equilibrium (m) and aggregate investment (mK) yields (14a) in the main text.

Applying the same procedure for the equations in system (29), one obtains the solution for diversified producers under a fixed regime. The only structural difference between this case and that of nondiversified producers is that the relative price of domestic to foreign varieties is 1, hence relative price effects are absent. It follows that employment is determined by

\begin{matrix} L_{2, i}^{d} = 2 \frac{\bar{L}}{n} {(\frac{1}{a})}^{1 / [1 - γ]} {[{(1 - h)}^{1 / [1 - γ]} + {(1 + h)}^{1 / [1 - γ]}]}^{- 1} & (42) \end{matrix}

(This is equation (15b) in the main text.)

For derivations of equilibria in the presence of real shocks under a flexible exchange rate regime, the analysis starts again with nondiversified producers. From the two equilibrium conditions in the goods market (equation (30a)), it can be inferred that

\begin{matrix} \frac{P_{r *}}{P_{r}} = {(S)}^{[1 - γ] / [1 - αγ]} {(\frac{a *}{a})}^{[1 - α] / [1 - αγ]} . & (43) \end{matrix}

Note that in the absence of monetary shocks the supply of money in each country is the same $(M_{2}^{s} = M_{2}^{s^{*}})$ . Applying this observation to equations (30c), (30d), and (30a), after collecting the various terms, yields

\begin{matrix} \frac{a *}{a} = \frac{P_{r *}}{P_{r}} . & (44) \end{matrix}

Combining equations (43) and (44) and solving for the exchange rate

\begin{matrix} S = {(\frac{a}{a *})}^{α} . & (45) \end{matrix}

Applying equations (45), (30b), (30d), $(M_{2}^{s} = M_{2}^{s^{*}})$ , and equation (30a) yields the price level (after the various terms are collected):

\begin{matrix} P_{2, r} = a {(\frac{W_{0}}{αγ})}^{γ} {(\frac{1}{m} M_{2}^{s})}^{1 / (1 - γ)} . & (46) \end{matrix}

Applying equation (46) to the demand for labor (equation (11)) yields

\begin{matrix} L_{2, i}^{d} = (\frac{αγ}{W_{0}}) \frac{1}{m} M_{2}^{s} . & (47) \end{matrix}

The flexibility of the exchange rate generates price and real wage adjustment, which stabilizes employment. Combining equations (30e) and (47) yields the contract wage, which is set according to

\begin{matrix} W_{0} = \frac{αγ M_{2}^{s}}{\bar{L}} . & (48) \end{matrix}

The rest of the derivation, which characterizes the investment equilibrium, follows the same steps described above for the case of a fixed exchange rate.

The derivation of equilibria for multinational producers follows the same procedure as for the nondiversified producers, using the equations in system (31). The results for the labor market are similar: the demand for labor is nonstochastic (equation (47), replacing m with n). The nominal exchange rate, S, is given by the productivity ratio (a/a^*). With diversification, the global supply of each variety is stabilized, whereas in the nondiversified regime it fluctuates. These results affect the assessment of the equilibrium investment in capital. Equation (18b) in the main text was derived by an application of the steps described above.

The characterization of equilibria in the presence of monetary shocks and a fixed exchange rate follows the steps already discussed before, with the additional understanding that the global nature of the supply of money eliminates the effects of negatively correlated monetary shocks.

The analysis of monetary shocks under a flexible exchange rate regime is more complex. Starting with the nondiversified regime and taking the ratio of the two equilibrium conditions in the goods market (equation (30a))

\begin{matrix} \frac{P_{r *}}{P_{r}} = {(S)}^{[1 - γ] / [1 - αγ]} . & (49) \end{matrix}

\begin{matrix} \frac{P_{r *}}{P_{r}} = {(\frac{M *}{M})}^{1 - γ} . & (50) \end{matrix}

Combining equations (49) and (50) and solving for the exchange rate

\begin{matrix} S = {(\frac{M}{M *})}^{1 - αγ} & (51) \end{matrix}

Applying equations (51), (30b), (30d), and the fact that $I N_{2} + S I N_{2}^{*} = M + S M *$ (that is, equation (30a)) and solving for the price level yields, after the various terms are collected)

\begin{matrix} P_{2, r} = {(\frac{W_{0}}{αγ})}^{γ} {(\frac{1}{m} M)}^{1 / (1 - γ)} . & (52) \end{matrix}

Applying equation (52) to equation (11) yields

\begin{matrix} L_{2, i}^{d} = (\frac{αγ}{W_{0}}) \frac{1}{m} M . & (53) \end{matrix}

Combining equations (30e) and (47) yields the contract wage, which is set according to

\begin{matrix} W_{0} = \frac{αγ M_{0}}{\bar{L}} . & (54) \end{matrix}

The rest of the derivation, characterizing the investment equilibrium, follows the same steps described above for the case of a fixed exchange rate.

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Joshua Aizenman is Professor of Economics at Dartmouth College and a Research Associate of the National Bureau of Economic Research.

He holds a Ph.D. from the University of Chicago. The research for this paper was conducted while he was a Visiting Scholar in the Research Department. He would like to thank Guillermo Calvo, John Huizinga, and participants in a seminar given by the Research Department.

World foreign direct investment flows (in the reporting economies) as a fraction of merchandise fob exports between 1965 and 1985 were 0.029. From 1985 this ratio has increased remarkably, and between 1986 and 1990 it reached 0.054 (see International Monetary Fund (various years)).

For a discussion regarding the factors affecting direct foreign investment in recent years and the implications of exchange rate volatility for investment, see Froot and Stein (1989), Edwards (1990), Klein and Rosengren (1990), and Goldberg (1990). For a discussion regarding the optimal currency area, see Mundell (1961), McKinnon (1963), Corden (1991), and Boughton (1991).

For a useful survey of the various approaches, see Grubel (1988).

A version of this model was used in Aizenman (1991) to evaluate the implications of restrictions on capital mobility on the welfare ranking of exchange rate regimes.

This construct is an intertemporal version of Dixit and Stiglitz’s (1977) monop-olistically competitive framework of the type applied by Helpman and Krugman (1989) in the international context. International transmission of disturbances in the presence of monopolistic competition and nominal rigidities has been dealt with by Dornbusch (1987), Aizenman (1989), and Svensson and van Wijnbergen (1989).

See Dixit (1989), Krugman (1989), and Baldwin and Krugman (1989) for related models that focus on the entry-exit decisions facing entrepreneurs in the presence of volatile exchange rates.

This analysis does not imply that a fixed exchange rate regime is superior to a flexible exchange rate system; for such a judgment, one would need to compare the behavior of employment across regimes, in addition to expected consumption. In a different context Aizenman (1991) has shown that this type of model implies that the literature of the 1980s overstated the case for a flexible exchange rate regime.

See Gray (1976) and Fischer (1977). For applications of the Fischer-Gray framework in an open economy, see Flood and Marion (1982), Turnovsky (1983), and Marston and Turnovsky (1985).

This employment target equals the expected employment level that will prevail in the absence of nominal contracts, and is determined by preferences and technology. The employment target is equivalent to the concept of the expected full-employment level. For the purposes here, is taken as given, assuming that it is not affected by the nature of the exchange rate regime. There are alternative ways of modeling the short-run Phillips curve that would produce similar results. An example is Lucas’s framework of incomplete contemporaneous information regarding the decomposition of the aggregate shock into the real and the nominal parts.

Starting with employment level in both countries, a marginal reduction of employment in the less productive country and a corresponding increase in the more productive country will increase the multinational’s expected profits by the divergences of the marginal product of labor at points B and A.

The value of 1 - η measures the returns to scale associated with the presence of fixed costs that may be shared by both locations. Entrepreneurs may also increase their production capacity by investing in two plants at home, at a capita) cost of K(1 + η) In the absence of transportation costs and uncertainty, producers will be indifferent between choosing to produce in two plants operating at home, or one operating at home and one abroad. A small uncertainty (as well as small transportation costs) will suffice, however, to brake this indifference: producers who operate with two plants prefer to diversify internationally, benefiting from both the extra capacity and the diversification of country-specific shocks (Section III discusses these points in further detail).

The intermediate case, where producers will be indifferent between the two investment strategies, will occur if all the inequalities in equations (4b) and (6b) are replaced with equalities.

Note that the assumption of risk-neutral entrepreneurs implies that investment I in period 1, generating nominal income, II₂, in the second period, will be undertaken if E[II2/₂] –I(1+ρ)⩾ 0 It can be shown that if the supply of Y is small enough, the Cobb-Douglas production function (defined by equation (3)) implies a corner solution where all Y is invested, and none is consumed in the first period. In such a case, the real interest rate is determined by the marginal productivity of capital. If the supply of Y is large enough to ensure positive consumption in period 1, the real interest rate is determined by preferences (that is, it is equal to 1 + ρ). In such a case, the actual investment is determined by the demand for investment at that real interest rate.

The simplicity of the example enables one to focus on a closed-form solution, dispensing with the need to use first-order approximations. Although it is a special example, it allows one to describe the economic forces at work. The results can be shown to apply to richer stochastic environments with any number of states of nature, and the analysis can be readily extended to the case of a positive correlation.

It can be shown that the elasticity of expected real profits with respect to the number of varieties is [1 - a(l + γ)] /α. If the demand for the various varieties is relatively inelastic, more varieties will reduce the labor employed in the production of a representative variety, thereby raising profits. This implies that profits will go up with the number of varieties, and that a higher set-up cost will imply more producers. The assumption that the varieties are close substitutes rules out this outcome.

In equation (5), E[π^nd]=E[(1-σγ)P_{2, i}D^s_{2, i}/₂ The value of E[π^d is obtained by calculating the profits that will occur to a marginal producer that will switch to a multinational strategy (assuming that all other producers behave as nondiversified).

This result follows from equation (16). Note that

0 < \frac{d (\frac{{[{(1 + h)}^{1 / (1 - γ)} + {(1 - h)}^{1 / (1 - γ)}]}^{a (1 - γ) / [1 - αγ]}}{[{(1 + h)}^{a (1 - γ) / [1 - αγ]} + {(1 + h)}^{a (1 - γ) / [1 - αγ]}]})}{d h}

Inspection of equation (16) reveals that, for η satisfying 2^{α(1-γ)/(1 - αγ)} - 1 > η< 1, (16) does not hold for h = 0, but does ho!d for h = 1.

This result follows from the fact that (1+h)^x/[(1+h)^x + (1+h)^x] increases with x. The corresponding values of x for the nondiversified and the diversified regimes are α/(1-αγ), and 1/(1 - γ). respectively.

Recall that there is no labor mobility. Hence, no labor crosses borders, and employment reallocation is achieved by changing the employment level in each country.

As was discussed above, in the diversified regime there is no adjustment of real wages, and, hence, the reallocation of employment is more pronounced.

FI is a plot of equations (14a) and (15a) as a function of the volatility, h; the switch from a nondiversified to a diversified regime is determined by equation (16).

This result follows from the fact that the flexibility of the exchange rate stabilizes employment in the presence of productivity shocks under both the nondiversified and the diversified regime. The stabilization of employment implies also the stabilization of the aggregate output of a multinational, because the shocks affecting the two countries are negatively correlated. Recall that complete employment stabilization is due to the unitary elasticity of the demand for money with respect to output. It can be shown that the stabilization of employment achieved by the flexibility of the exchange rate (relative to employment under a fixed exchange rate regime) holds for a general demand for money.

Following the logic of the previous discussion regarding Figure 2, the expected output difference between the fixed and flexible exchange rate regime, in the absence of diversification, is equal to half the dotted area in Figure 2.

Curve FL in panel A of Figure 3 is drawn by plotting equations (18a) and (18b) as a function of the volatility, h, recognizing that the switch from a nondiversifled to a diversified regime is determined by equation (19).

Although a higher volatility does not affect the expected output (because of the stabilization of employment), it will depress expected real profits because of the induced relative price adjustment. Note that the analysis here suggests that the correlation between the volatility of shocks and investment depends on the nature of shocks and the nature of the exchange rate regime. For example, whereas higher volatility of productivity shocks will increase investment under a fixed exchange rate regime, it will tend to depress investment under a flexible exchange rate.

FL is a plot of equations (23a) and (24a) as a function of the volatility, h; the switch from a nondiversified to a diversified regime is determined by equation (25). The international diversification achieved with multinationals shifts the supply of each variety from nationalistic to multinational sources, thereby stabilizing the aggregate output of each variety. Note that the labor market remains nationalistic, since monetary policy continues to affect real wages and employment. It can be shown that for large volatility the diversification partially lessens the impact of monetary shocks (that is, for a large enough h, FL,N in panel B of Figure 3 is below FL,D).

This result is obtained in several steps. First, note that the first-period budget constraint is Y₁, ¯Y - mK – ½nk/(1= + η). From equations (9) and (10) it can be inferred that D₂ = IN₂/

₂, where IN₂ is nominal GNP. Equation (27) is inferred by applying this result and the condition of zero expected rents—that is, the condition that

E [(1 - αγ) \frac{I N_{2}}{P_{2}}] = (1 + ρ) [m K + \frac{1}{2} n K (1 + η)] .

For further details, see equations (28f), (29f), (30f), and (31f) in the appendix.

The realiocation of employment between countries is achieved by adjusting the employment level in each country.

Note that the producer cares about expected real profits. In the monopolistic competitive framework used here, output and real profits are positively associated, and, hence, higher expected output also implies higher expected profits.

See Frankel and Froot (1990) for an analysis of bubbles as a potential driving force in the evolution of exchange rates.

In these circumstances, the higher volatility of monetary shocks under a flexible exchange rate may increase foreign direct investment and depress aggregate investment. Recall that the model predicted that volatile monetary shocks under a flexible exchange rate will lead to diversification. It can be verified that with volatile monetary shocks, welfare tends to be lower if producers are not allowed to operate as multinationals. In terms of Figure 3, for a large enough h, the curves associated with the nondiversified regime are below the curves associated with the diversified one. Thus, capital mobility works to lessen the adverse consequences of monetary shocks (for further details, see Aizenman (1991)).

Applying equations (34), (44), and (45) from the appendix, it follows that in the non diversified regime the elasticity of the real exchange rate with respect to productivity shocks is larger under a fixed exchange rate. Expressed formally, dlog[P_r/SP*]/d log(a/a^*) equals 1 - α under a flexible exchange rate regime, and (1 - α)/(l - αγ) under a fixed exchange rate. The reason is that the real exchange rate should clear the goods market. Hence, greater disparity of the supply adjustment across regimes will necessitate greater relative price adjustment. Exchange rate flexibility works to stabilize employment and to reduce the supply disparity across regimes, and, hence, it will require a smaller adjustment of the relative prices.

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IMF Staff papers: Volume 39 No. 4

Author: International Monetary Fund. Research Dept.

Volume/Issue:: Volume 1992: Issue 004

Publisher:: International Monetary Fund

ISBN:: 9781451930825

ISSN:: 1020-7635

Pages:: 260

DOI:: https://doi.org/10.5089/9781451930825.024

Keywords
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Output and Employment

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Margina! Productivity of Labor

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Effect of Shocks on Investment

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Countries

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About

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Abstract

I. The Model

Preferences

Production

Investment, Uncertainty, and the Producer’s Problem

The Money Market

II. The Equilibrium

Consumer Demand

Producer Pricing

III. Productivity Shock, Monetary Shocks, Volatility, and Investment

Productivity Shocks

Fixed Exchange Rate Regime

Flexible Exchange Rate Regime

Monetary Shocks

Fixed Exchange Rate Regime

Flexible Exchange Rate Regime

IV. Comparison Between Regimes

V. Concluding Remarks

APPENDIX

Derivations and Solutions of Key Equations

Fixed Exchange Rate

Nondiversified Producers

Multinational Producers

Flexible Exchange Rate Regime

Nondiversified Producers

Multinational Producers

Solutions for the Combinations

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