ESTRATEGIA DE LOS ACTORES MÉTODO MACTOR

fundamentals) tends to have an additional independent effect apart from the effect exercised by the lagged level of the fundamentals.

The analysis by Prati and Sbracia (2002) suffers from two shortcomings. The first shortcoming is its application to a small sample of countries all af- fected by the East Asian financial crisis in 1997-98. Second, given that Prati and Sbracia (2002) model a static global game, an analysis emphasizing the cross sectional variation between countries seems more appropriate than the time series analysis conducted. To overcome these shortcomings in the present analysis, I work with a much larger set of countries, emphasizing the cross- sectional variation between countries by estimating pooled probit regressions controlling for time effects.

2.2

Theoretical Background

This section presents a coordination game model on the occurrence of sudden stops. The model is based on the framework presented in Calvo (1998b) and Calvo (2003). I extend the original Calvo setup by introducing a continuum of infinitely many identical firms of mass one. In a first step, I set up a coordination game with common knowledge. In a second step, in section 2.4 I extend the setup further by introducing private signals on the fundamentals.

2.2.1

The Firms

Following Calvo (1998b) and Calvo (2003), each of the infinitely many firms produces tradable output with a linear homogeneous production function, in which tradable capital is the only production factor. Capital is fully interna- tionally mobile ex ante but immobile after investment.

The firms maximize their value by choosing between constant growth paths. The value of a firm is defined as the sum of discounted future cash flows until infinity. Due to the linear production function, the rate of investment or capital accumulation equals the rate of output growth. In their optimization, firms consider the technology parameter, the tax rate, and the international interest

can be found.7

Vi ₌ α(1−τ)−zi

(r−zi₎ (2.1)

Vi _{represents the firm value, αis the productivity factor, τ is the constant}

output tax rate,zi _{is the investment rate that the firm can choose. rrepresents}

the constant international interest rate. Optimizing the value of the firm with respect to the rate of investment or capital accumulation leads to:

∂Vi ∂zi =

α(1−τ)−r

(r−zi₎2

The model delivers corner solutions. If the after-tax return on capital,

α(1−τ) exceeds the international interest rate r, it is optimal for a firm to

invest as much as possible and thus grow as fast as possible. If the return on capital is lower than the interest rate, the firm does not accumulate capital at all. Such a firm would even borrow as much capital as possible and invest it

abroad. For the model to deliver a sensible outcome, the parameter zi _must

be restrained to finite ’corners’. Following Calvo (2003), the value of zi _is

restricted to an interval [0, z] withz < r, in which the lower bound ensures that

capital cannot be unbolted. The upper bound stands for reasonable outcomes

with respect to the valuation of the firms. In particular, as zi _{signifies the}

constant growth path of the firm, by bounding it, I rule out the possibility that the firm can outgrow the world market in the infinite horizon.

A firm would never invest if this investment had a negative effect on the

value of the firm. Hence, it suffices to consider the sign of the derivative of Vi

with respect to zi_{. If the sign is positive, the agent invests as much as possible}

(restricted toz < r in this model); if negative, investment equals zero.

sgn∂Vi

∂zi = sgn[α(1−τ)−r] (2.2)

7_{For a detailed derivation, please see Appendix 2.10. The firms expect the tax rate}

to be constant, because a sudden stop is unexpected to them. In the light of possible growth collapses and ensuing sudden stops, a different tax policy τt might be optimal for

the government. Therefore, firms would expect the tax rate to change once a crisis occurs. Calvo (2003) shows that growth collapse and sudden stops also occur in the case when they are foreseen by the firm. Therefore, I do not consider the case of an anticipated crisis here.

2.2. THEORETICAL BACKGROUND 47

2.2.2

The Government

The government inherits a stock of debt D, which must be financed by an

output tax. The tax rate is set so that the future discounted tax revenues cover the amount of debt. This is possible, assuming full capital market access by the government. D=ατ Z _∞ 0 K_tecone−rtdt= ατ r−zecon (2.3) with zecon = R₁ 0 K˙idi R₁ 0 Kidi = K˙ econ Kecon

The superscriptecon_{indicates that a variable refers to the economy and not}

to an individual i.

2.2.3

The Reduced Form Game Between Firms

The mechanical way in which the government sets the tax rate introduces strategic complementarity between the firms into the model. The profit of investment for an individual company positively depends on the rate of invest-

ment of all other firms. This can be shown by solving Equation (2.3) forτ and

plugging it into Equation (2.2):

sgn∂V

i

∂zi = sgn[α−D(r−z

econ_{)−r] (2.4)}

The return on investment is a positive function of zecon_{. This results from}

the burden of debt repayment being carried by more firms. Through the tax- setting mechanism, the investment decision of each firm depends negatively on the state of the fundamentals.

The main mechanism underlying the interaction of firms is therefore: If growth is high, the government sets a low tax rate, which in turn sustains high growth. Similarly, if growth is low, the government sets a high tax rate, holding firms off investing, which in turn further induces low growth.