1. The basic model

Consider a small open economy inhabited by rational, infinitely-lived individuals that formulate optimal intertemporal plans for consumption of an imported good so as to maximize expected lifetime utility. Preferences are represented in the standard isoelastic, time-separable form:

where C is a vector that represents the intertemporal allocation of consumption, β is the subjective discount factor, and γ is the coefficient of relative risk aversion (i.e. 1/γ is the intertemporal elasticity of substitution).

The production technology adopts the simple form of a perfectly durable asset that yields a stochastic, nonstorable return each period, as in the partial-equilibrium models of savings by Phelps (1962) and Levhari and Srinivasan (1969) and in Lucas’ (1978) general-equilibrium model of asset pricing. The return is an exportable commodity that agents exchange for importable goods in a perfectly competitive world market. The relative price of imported goods in terms of exports is also subject to random disturbances. Markets of contingent claims are incomplete, and hence households cannot insure away country-specific shocks resulting from changes in real returns or the terms of trade. Thus, households maximize utility subject to a period-by-period resource constraint of the form:

Given A₀>0. A_t is the stock of wealth in units of exportables, R_t is the gross domestic rate of return on savings, and p_t is the relative price of imports in terms of exports, or the reciprocal of the terms of trade tot_t= p_t^-1. R_t and p_t are non-negative random variables such that the consumption-based interest rate r_t≡R_tP_t/P_t+1 is a log-normal i.i.d. process. Thus, Ln(r_t) is i.i.d. with mean μ and variance σ², and hence the mean and variance of r_t are μ_r≡exp(μ+σ²/2) and σ_r²≡μ_r² (exp(σ²-1)) respectively. At each date t, p_t is known but R_t and p_t+1 are unknown. ^2/

2. Free trade competitive equilibrium

Under free trade, the optimal intertemporal consumption allocation C^* is the one that maximizes (1) subject to (2). This maximization problem has the following dynamic programming representation:

The first-order conditions are the constraint (2) and the Euler equation:

The problem is solved by guessing that V(.)= B(A_t/P_t)^1-γ, for some constant B, and that C_t is a time-invariant fraction λ of wealth A_t/P_t. Optimal savings and consumption plans are:

Where

And the explicit solution of the value function is:

The constant λ is the marginal propensity to consume with respect to wealth (i.e. 1-λ is the saving rate). Under the condition that E[r_t^1-γ]<β^-1, (5) implies that consumption in each period is a positive fraction of the real value of asset holdings in units of importables, and (6) states that savings are a positive fraction of the gross return on initial asset holdings. Because the terms of trade are known but the return on exportables is unknown at the time C_t is chosen, the actual realization of R_t does not affect consumption, while the actual realization of p_t does.

Following Phelps and Levhari and Srinivasan, it is easy to show that increased risk in real asset returns (measured as a mean-preserving increase in σ_r² due to increased variability in either the domestic rate of return on exportables or the terms of trade) leads to a reduced saving rate as long as the coefficient of relative risk aversion is higher than 1 (γ>1), or the intertemporal elasticity of substitution in less than 1 (1/γ1), and that an increase in the mean return has the opposite effects. These results are derived by expressing λ as a function of μ_r and σ: ^3/4/

3. Equilibrium with permanent tariffs and lump-sum rebates

Suppose the government imposes a time-invariant import tariff τ, the revenue of which is rebated to consumers as a lump-sum transfer T_t. Households maximize (1) subject to the following budget constraint:

In equilibrium, T_t=p_t^τC_t. Thus, the optimality conditions for this maximization exercise are the same as in the case of free-trade competitive equilibrium, and hence consumption and savings plans are as in (5) and (6). This is because rebates prevent the tariff from affecting wealth, and because the tariff is time-invariant, so there is no intertemporal price-distortion. ^5/

4. Equilibrium with permanent tariffs and no rebates

If tariff revenue is not rebated but the tariff is still time-invariant, the Euler equation (4) is unchanged, but a wealth effect resulting from the crowding-out of consumption to finance unproductive government expenditures is introduced. The budget constraint is:

The guess is now that consumption is a constant fraction of post-tax wealth A_t/(l+τ)p_t. Optimal consumption and savings plans are:

And lifetime utility is:

The superscript τ is used to distinguish these allocations from those of the free-trade and tariff-rebates economies—λ is the same in the three cases.

1. Competitive equilibrium

Households maximize (1) subject to the following constraints:

Taking as given A₀>0, τ, and T_t. In equilibrium, the government’s budget constraint, T_t=τp_tC_t, holds for all states of nature in which tariffs are levied. Thus, for all dates and all states of nature, whether tariffs are present or not, the equilibrium resource constraint is the same as in (2)—i.e. the resource constraint is that of the free-trade economy because of the rebates. There is, however, a distortion affecting the intertemporal relative price of consumption depending on the date considered. There is no distortion at any date other than 0, regardless of whether tariffs are present, and hence the Euler equation is like (4). At t=0, however, the Euler equation is:

Thus, the expected marginal gain of an extra unit of savings in the period of the credibility test is affected by the tariff. Lack of credibility acts like a tax on the return of savings that distorts intertemporal relative prices in favor of current consumption. This is a general result that can be obtained with conventional lifetime utility functions and standard resource constraints. However, without the structure on preferences, technology, and uncertainty introduced in the last section, it is difficult to obtain closed-form solutions.

Since π is time-invariant, and hence independent of realizations of r_t, we rewrite (16) as follows:

Thus, the rate of the credibility tax is determined by both the size of the expected tariff, τ, and the subjective probability of policy reversal, π.

A simple backward-solution technique allows us to solve for the competitive equilibrium. ^6/ Optimal plans for t=0 are:

With

The superscript π, T is used to denote that these are allocations for the economy with uncertain duration of the trade reform and tariff rebates. Optimal plans for any date t>1 are given by (5) and (6) updated to the corresponding date and taking A₁ from (19). Lifetime utility as of the date the reform is announced is:

Equations (18)-(21) provide the framework for examining effects of imperfect credibility and the interaction of these effects with real shocks. η represents the distortion introduced by policy uncertainty. Clearly, η(0, τ) = 1, and hence a perfectly credible reform produces the free-trade competitive equilibrium. In general, however, for 0 < π < 1, η is a positive fraction in the range (1+r)^-1/γ < η < 1, and hence consumption at date 0 exceeds the level of consumption for the same period under credible free trade or under a regime of permanent, rebated tariffs.^7/ Since η is decreasing in π, it also follows that increased policy uncertainty (i.e. higher π) induces a stronger increase in consumption and a sharper decline in savings. This result reflects the prediction that the surge in consumption is stronger the shorter the duration of a trade reform obtained in the perfect-foresight credibility literature (Calvo (1987)). Note also that, contrary to van Wijnbergen (1992), C₀^{π, T} > C₀^τ or C₀^* regardless of the degree of risk aversion.^8/ Moreover, considering (9), one can show that, for any given π, a rise in σ² (fall in μ_r) leads to a rise in imports and a decline in savings as long as γ>1. Thus, a widening trade deficit and a falling saving rate may reflect lack of credibility, but can also reflect changes in the riskiness of savings.

2. Cyclical effects of imperfect credibility

In order to characterize formally the cyclical effects of uncertain duration of reform, and their interaction with real shocks, we provide an explicit definition of business cycles based on deviations from trend measured as logarithmic first differences. Since consumption fluctuates randomly around an average growth rate given by (1-λ)μ_r, logarithmic first-differences render the consumption process stationary. Denote the log first-difference of consumption as ΔC_t≡Ln(C_t)-Ln(C_t-1), and define Ln(r_t) ≡μ+ϵ_t, so that ϵ_t is the period-1 deviation of the log of the real interest rate from its mean. Then, at any date before the reform is introduced or after policy uncertainty is resolved, ΔC_t is:

The first two terms in the right-hand side of (22) define the trend of ΔC_t and the error term is the cyclical component. The variance of deviations from trend in consumption is given by σ². Equation (22) also describes consumption cycles in the free-trade economy, or in the economy with permanent tariffs and rebates. Thus, deviations from trend in consumption at t=-1, or before, and t=2, or later, are determined only by real uncertainty. Note also that although whether γ is greater or less than 1 determines if changes in μ_r or σ² have positive or a negative effects on the level of consumption, an increase in μ_r always induces an increase in the trend growth rate, regardless of the size of γ, and an increase in σ² induces faster consumption growth as long as γ> 2. Moreover, when γ > 2 an increase in risk increases growth but, since welfare is declining in σ², welfare in high-risk, fast-growing economies is lower than in low-risk, slow-growing economies.^9/

Consumption behavior in periods affected by policy uncertainty is:

Thus, at the two dates affected by lack of credibility, deviations from trend in consumption are jointly determined by real shocks and policy uncertainty. Real- and policy-uncertainty components of business cycles are clearly identified in (23) and (24). Real-uncertainty components are ϵ_-1, and ϵ₀, while policy-uncertainty components are the terms that include η. The credibility component is independent of the mean and variance of real shocks at date 0, but not at date 1, since λ is a function of μ_r and σ². Moreover, if a trade reform coincides with changes in μ_r and σ², there are also changes affecting the trend level of consumption growth.

ΔC₀ and ΔC₁ in (23)-(24) produce five important results:

(i) Policy uncertainty induces a boom-recession cycle (i.e. a boom at t=0 and a recession at t=1), regardless of the size of γ and of whether the reform succeeds or fails. This follows from the feasibility constraint η>λ and the fact that, unless π=0, 0<η<1.

(ii) The boom is weaker than the recession. η>λ and 0<η<1 imply that -Ln(η), which measures the boom as a deviation from trend in percent, is smaller than -Ln((η-λ)/(1-λ)), which is the absolute value of the recession.

(iii) The higher the probability of policy reversal, the larger the amplitude of the credibility-induced cycle (i.e. the stronger the boom and the deeper the recession). This is because η is decreasing in π.

(iv) The higher the degree of risk aversion γ, or the lower the intertemporal elasticity of substitution 1/γ, the smaller the amplitude of the credibility-induced cycle. This is because η is increasing in γ.

(v) The noncredible reform is always socially costly, compared to either the free-trade regime or the regime with permanent tariffs. This is demonstrated by recalling that permanent, rebated tariffs reproduce the free-trade equilibrium, differentiating (21) with respect to η, and noting that η is decreasing in π. The intuition is that the boom induces excessive consumption at t=0, relatively to Pareto-optimal plans in (5)-(6), and hence savings are insufficient to finance optimal consumption in the future.

3. Credibility effects and real uncertainty

In order to examine the link between real uncertainty and policy uncertainty, we study ex-ante and ex-post implications of the equilibrium laws of motion (23)-(24). Ex-ante, we consider a policymaker planning to introduce a trade reform with knowledge of the mean and risk characteristics of real asset returns and the structure of preferences and technology, but not knowing the subjective probability attached to policy reversal. Expected values of (23)-(24) provide a framework for analyzing how changes in and μ_Γ affect credibility effects. In this ex-ante environment, there are two results linking credibility effects to real uncertainty:

(vi) An increase in μ_r associated with a trade reform increases expected consumption growth via its positive effect on the trend components of (23)-(24), but it does not affect the deviation from trend at t=0. In contrast, the recession at t=1 is affected by the rise in μ_r because λ is part of the credibility component of the cycle and λ depends on μ_r. The direction of the effect depends on the size of γ. The recession is weaker (stronger) if γ>1 (γ<1) because the marginal propensity to consume falls (rises) when μ_r rises, and the credibility-induced recession is positively related to the propensity to consume.

(vii) An increase in risk (i.e. a rise in σ²), increases trend consumption growth if γ>2 and reduces it otherwise. The credibility boom at t=0 is independent of, σ² but the recession at t=1 is affected by the increase in risk because σ² alters the credibility component of the cycle via its effect on λ. The recession is stronger when γ>1 and weaker if γ<1. The intuition is similar to that for the case of a rise in μ_r.

Thus, (vi) and (vii) show that, for the realistic case in which the intertemporal elasticity of substitution is less than unitary (i.e. γ>1), an increase in mean returns (i.e. a permanent productivity gain or an improvement in the long-run growth of terms of trade) weakens the recession induced by a noncredible trade reform, while an increase in risk (i.e. a mean-preserving increase in the variability of domestic productivity or the terms of trade) strengthens it.

It is of interest to consider also the possibility that the probability of success of a trade reform may depend on the properties of real domestic or external shocks hitting the economy. In particular, if π is a decreasing function of mean returns and an increasing function of risk (i.e. π(μ_r, σ₂), with π₁<0 and π₂>2), the results are altered as follows. Since the magnitude of the credibility distortion falls as π falls, the fall in π associated with an increase in μ_r would reduce the amplitude of the credibility-induced cycle. Moreover, at t=1 the rise in μ_r has an additional effect on the credibility component of the cycle via its impact on the marginal propensity to consume, as described in Result (vi) above. If γ>1, the weakening of the recession due to the fact that η rises as π falls is reinforced by the fall in λ. A similar analysis applies for the case of a reduction in risk (i.e. a fall in σ²). Thus, if agents’ perception of the risk and return characteristics of domestic investments improve in response to exogenous developments or to the introduction of trade reforms, and if this improvement lends credibility to the reforms, credibility-induced cycles are weaker than in economies where the probability of reversal is independent of μ_r and σ².

The link between real and policy uncertainty also has important implications for ex-post measurement of credibility effects. Consider a researcher who has been given data on consumption for countries undertaking trade reforms, as well as information on terms of trade and real domestic rates of return, and who has been asked to assess the credibility of reforms. The issue is to determine whether observed differences in consumption fluctuations are an indicator of lack of credibility. Assume the researcher knows preference and technology parameters with precision, so the problem is to map unambiguously observed consumption patterns into measures of credibility (i.e. values of π).

Given data on real returns, the researcher computes μ_r and σ₂, and, given estimates of β and γ, he uses (22)-(24) to construct estimates of that portion of fluctuations in consumption determined by real uncertainty—i.e. he isolates the component of fluctuations driven by “fundamentals.” Define this component as ΔC_t^F. Then, it follows from (22) that for all t<0 and t>1 ΔC_t^F=ΔC_t, and from (23)-(24) and Result (i), if π>0, it follows that ΔC₀^F<ΔC₀ and ΔC₁F>ΔC₁. Thus, if the reform lacks credibility, consumption growth exceeds that predicted by fundamentals at the date the reform is introduced, followed by a fall below the level indicated by fundamentals at the date policy uncertainty is resolved. Moreover, using (20) and (23), and since τ is known, the researcher can reconstruct π from the observed ΔC₀ and the estimated ΔC₀^F. In particular, if ΔC₀ and ΔC₀^F are small, π is:

This expression indicates, as shown earlier, that larger deviations of consumption growth above the level attributed to fundamentals reflect a higher probability of policy reversal. The expression also shows that if the researcher only looked at the actual magnitude of the consumption boom at date 0, the resulting estimates of π would be biased upwards. The fraction of the business cycle attributed to real uncertainty must be taken into account in order to measure lack of credibility with accuracy. Among two economies undertaking trade reforms, one may display a stronger consumption boom than the other simply because its terms of trade are more volatile, and not because reforms are less credible.

Differences in realizations of terms-of-trade or productivity shocks, represented by ϵ in (23) and (24), that hit reforming economies at the time of implementing trade liberalizations may also bias measures of lack of credibility that do not separate real- and policy-uncertainty components. The bias is different depending on the duration of the shocks, as the following results show:

(viii) A transitory fall in the terms of trade, or an increase in p_o (i.e. a negative shock ϵ_-1 and a positive shock ϵ₀)^10/ shortens the amplitude of deviations from trade during an uncertain trade reform. ϵ_-1<0 weakens the boom at t=0 and ϵ₀>0 weakens the recession at t=1.

(ix) A permanent fall in the terms of trade, or an increase in p_t for all t≥0 (i.e. ϵ_-1<0 but ϵ_t for t≥0 and μ_r unchanged) reduces the boom but does not affect the subsequent recession.

(x) A secular decline in terms of trade that starts at t=0,^11/ or an increase in the rate of growth of p (i.e. ϵ_-1<0 coincides with a decline in μ_r for all t≥0) weakens the boom at t=0 because ϵ_-1<0 reduces the real-uncertainty component of the business cycle. At t=1, the fall in μ _r affects the business cycle via its impact on the size and direction of the credibility effect, which in turn depends on whether γ is greater or less than 1 (see Result (vi)). The fall in μ_r also reduces the trend growth rate.

4. Numerical results

We now undertake some numerical experiments to study the potential magnitude of the effects examined above. The model is calibrated to create a benchmark economy that conforms roughly to some empirical evidence for Latin America. Parameters are set as follows: σ=0.10, γ=2.33, β=0.95, and μ_r = 1.07. The value of γ is the estimate obtained by Ostry and Reinhart (1992) for Latin America in an optimizing model. β=0.95 is the value that Lucas (1986) used to calculate welfare losses of consumption instability. We use it so as to compare some of our results with his, although evidence from Ostry and Reinhart (1992) suggests that it may be biased downwards. Increasing β does not affect significantly our results, except for estimates of welfare costs that are sharply increased as β rises. Thus, a lower β provides optimistic scenarios in terms of welfare analysis.

The value of σ is the standard deviation of the log of the terms of trade for Latin American countries reported in Mendoza (1992). The real interest rate at 7 percent reflects historical evidence documented in Mehra and Prescott (1985) for the mean real interest rate on risky assets. Combining (22) with these parameters, and some slight variations, we produce average growth rates of consumption between 1 and 2 percent, with a standard deviation around 10 percent, roughly consistent with the Latin American experience regarding real per-capita consumption growth over the last 30 years in units of importables (see Mendoza (1994)). In the benchmark case we also set τ=0.3 and realizations of real shocks at t=0 and t=1 to zero.

Table 1 lists deviations from trend in consumption during a trade reform of uncertain duration for the benchmark case and alternative parameter structures, assuming different values of π. The first column reports results for the benchmark economy. If the reform is perfectly credible there are no fluctuations in consumption because, as (18) and (20) show, a credible reform does not distort consumption plans since η(0, τ)=1, and also because there are no real shocks occurring at dates 0 and 1. As π rises, credibility-induced cycles appear. Considering that, given σ=.1, deviations from trend driven by terms-of-trade shocks of up to 20 percent are a two-sigma event (i.e. they are within the 98 percent confidence interval), credibility-induced cycles—with booms between 2.5 and 11.3 percent and recessions between -2.7 and -11.9 percent depending on the size of π—are not unusually large.

Table 1.

Fluctuations in Consumption During a Trade Reform in the Economy with Tariff Rebates

(Deviations from trend in percent)

^1/Transitory deterioration of the terms of trade by 5 percent at t = 0 (i.e. P_o = P (1-0.05) where P is the average of the terms of trade).

^2/Permanent deterioration of the terms of trade by 5 percent (i.e., P₁ = P_o= P(1-0.05)).

^3/Secular decline in the terms of trade that starts with a 5 percent fall at t=0 and continues at an annual rate of 1 percent (μ_r = 1.0593 = 1.07 × 0.99).

Table 1.

Fluctuations in Consumption During a Trade Reform in the Economy with Tariff Rebates

(Deviations from trend in percent)

Probability of reversal (Π)	Benchmark economy		Low risk aversion (γ=½)		High risk aversion (γ=5)		High tariff (ø=0.7)		Low tariff (ø=0.1)		Higher mean returns (µr= 1.1)		Higher risk (σ=0.2)		Transitory shock 1/ ϵ -1=-0.05 ϵ 0= 0.05		Permanent shock 2/ ϵ -1=-0.05 ϵ 0= 0		Secular decline 3/ ϵ -1=-0.05 μ r =1.0593
	t=0	t=1	t=0	t=1	t=0	t=1	t=0	t=1	t=0	t=1	t=0	t=1	t=0	t=1	t=0	t=1	t=0	t=1	t=0	t=1
0.00	—	—	—	—	—	—	—	—	—	—	—	—	—	—	-5.0	5.0	-5.0	—	-5.0	—
0.25	2.55	-2.69	11.88	-12.37	1.19	-1.24	4.66	-4.92	0.99	-1.04	2.55	-2.74	2.55	-2.64	-2.45	2.31	-2.45	-2.69	-2.45	-2.68
0.50	5.26	-5.56	24.52	-25.58	2.45	-2.56	9.89	-10.47	2.00	-2.11	5.26	-5.65	5.26	-5.45	0.26	-0.56	0.26	-5.56	0.26	-5.53
0.75	8.16	-8.63	38.01	-39.79	3.80	-3.98	15.85	-16.81	3.03	-3.20	8.16	-8.77	8.16	-8.45	3.16	-3.63	3.16	-8.63	3.16	-8.58
1.00	11.26	-11.92	52.47	-55.14	5.25	-5.49	22.77	-24.20	4.09	-4.32	11.26	-12.13	11.26	-11.67	6.26	-6.93	6.26	-11.93	6.26	-11.85

^1/Transitory deterioration of the terms of trade by 5 percent at t = 0 (i.e. P_o = P (1-0.05) where P is the average of the terms of trade).

^2/Permanent deterioration of the terms of trade by 5 percent (i.e., P₁ = P_o= P(1-0.05)).

^3/Secular decline in the terms of trade that starts with a 5 percent fall at t=0 and continues at an annual rate of 1 percent (μ_r = 1.0593 = 1.07 × 0.99).

View Table

Table 1.

Fluctuations in Consumption During a Trade Reform in the Economy with Tariff Rebates

(Deviations from trend in percent)

Probability of reversal (Π)	Benchmark economy		Low risk aversion (γ=½)		High risk aversion (γ=5)		High tariff (ø=0.7)		Low tariff (ø=0.1)		Higher mean returns (µr= 1.1)		Higher risk (σ=0.2)		Transitory shock 1/ ϵ -1=-0.05 ϵ 0= 0.05		Permanent shock 2/ ϵ -1=-0.05 ϵ 0= 0		Secular decline 3/ ϵ -1=-0.05 μ r =1.0593
	t=0	t=1	t=0	t=1	t=0	t=1	t=0	t=1	t=0	t=1	t=0	t=1	t=0	t=1	t=0	t=1	t=0	t=1	t=0	t=1
0.00	—	—	—	—	—	—	—	—	—	—	—	—	—	—	-5.0	5.0	-5.0	—	-5.0	—
0.25	2.55	-2.69	11.88	-12.37	1.19	-1.24	4.66	-4.92	0.99	-1.04	2.55	-2.74	2.55	-2.64	-2.45	2.31	-2.45	-2.69	-2.45	-2.68
0.50	5.26	-5.56	24.52	-25.58	2.45	-2.56	9.89	-10.47	2.00	-2.11	5.26	-5.65	5.26	-5.45	0.26	-0.56	0.26	-5.56	0.26	-5.53
0.75	8.16	-8.63	38.01	-39.79	3.80	-3.98	15.85	-16.81	3.03	-3.20	8.16	-8.77	8.16	-8.45	3.16	-3.63	3.16	-8.63	3.16	-8.58
1.00	11.26	-11.92	52.47	-55.14	5.25	-5.49	22.77	-24.20	4.09	-4.32	11.26	-12.13	11.26	-11.67	6.26	-6.93	6.26	-11.93	6.26	-11.85

^1/Transitory deterioration of the terms of trade by 5 percent at t = 0 (i.e. P_o = P (1-0.05) where P is the average of the terms of trade).

^2/Permanent deterioration of the terms of trade by 5 percent (i.e., P₁ = P_o= P(1-0.05)).

^3/Secular decline in the terms of trade that starts with a 5 percent fall at t=0 and continues at an annual rate of 1 percent (μ_r = 1.0593 = 1.07 × 0.99).

Lowering γ to 1/2 (i.e. rising the intertemporal elasticity of substitution to 2) increases significantly the amplitude of the credibility-induced cycles relative to the benchmark, by a factor of about 4.5, while setting γ=5 (i.e. 1/γ=0.2) reduces the amplitude of the cycles by a factor of approximately 0.45. For π>1/2, the low risk-aversion case produces cycles larger than those generated by real shocks, which are between -20 and 20 percent with a probability of 0.98. Note also that consumption fluctuations are markedly more sensitive to reductions in γ than to increases when γ is initially around 2. Given the controversy in the econometric literature surrounding estimates of γ, this result suggests that economies may display more consumption instability because agents may be less risk averse, even if only marginally, than in other economies, and not necessarily because trade reforms are less credible. Thus, parameter uncertainty may play an important role.

High- and low-tariff simulations illustrate a similar point. When initial tariffs are high the economy displays larger credibility-induced cycles than when tariffs are low. A country with τ=.7 and π=.25 displays cycles about as large as those of an economy with τ=.1 and π=1. Thus, given the dispersion of existing tariffs among reforming countries, actual differences in the level of the tariffs being removed may also introduce noise into tests of lack of credibility based exclusively on the magnitude of consumption booms.

Simulations for economies with higher mean returns and higher risk illustrate that, since real and policy uncertainty are independent of each other, and the latter is resolved in one period, the effects of changes in μ_r and σ on credibility-induced cycles are small. As shown before, the credibility component of the boom at date 0 is independent of changes in μ_r and σ, but that component in the recession at date 1 is not. However, the impact on the recession is small because, although changes in risk and mean returns affect λ, the impact of the change in λ on the credibility effect λ/η depends on how close η is to 1. The closer η is to 1, the smaller the distortion induced by lack of credibility, and hence the smaller the effects of changes in λ on the credibility component of the business cycle. The benchmark values of γ and τ imply that the lowest value of η is 0.89, when π=1. Moreover, since η is decreasing in π, it also follows from this reasoning that the increase in μ_r (σ²) has a larger negative (positive) effect on consumption cycles relative to the benchmark the higher is π.

Consider now the implications of realizations of terms-of-trade shocks that coincide with trade reforms. Table 1 examines the three cases discussed earlier; a transitory decline in terms of trade that rises p_o only (i.e. a decline in ϵ_-1 and an increase in ϵ₀), a permanent decline in terms of trade rising p_t for all t (i.e. a decline in ϵ_-1 that leaves ϵ₀ unchanged), and a secular deterioration of terms of trade that starts at 0 and continues permanently (i.e. a decline in ϵ_-1 that coincides with a fall in μ_r). In the first two cases, terms-of-trade shocks are set to 5 percent, which is a small number given that shocks of up to 20 percent are a two-sigma event. In the third case the initial shock is also 5 percent, and the secular decline continues at 1 percent per annum.^12/ These shocks induce consumption fluctuations via the real component of deviations from trend ϵ, and not via credibility effects (except for the case of the secular terms-of-trade deterioration in which μ_r alters the credibility effect in (24)).

The transitory terms-of-trade shock reduces the amplitude of the business cycle in the period of policy uncertainty. This shock has an adverse effect on consumption at t=0 since it lessens the value of wealth in units of importables, but it also has a positive effect on consumption growth at t=1 because it increases the return on savings in units of importables between those two dates (since the price of importables is expected to fall). These effects are quantitatively important because an economy undertaking a trade reform with a probability of failure as high as 50 percent would not display the booming behavior normally attributed to lack of credibility. Even when the boom is present, the surge in consumption in an economy where π=1 and there is a transitory terms-of-trade shock is similar in magnitude to that of an economy with stable terms of trade and π=0.5. The same is true for economies experiencing a permanent terms-of-trade deterioration, except that a permanent shock does not have the weakening effect on the recession at t=1—relative to the benchmark—that is observed when the shock is transitory. The secular fall in trade relative prices has the same large adverse effects of a transitory shock on the deviation from trend in consumption at date 0, but at date 1 it results in a modest increase in consumption growth induced by the effect of μ_r on λ and hence η. Thus, the results of these exercises suggest that effects of real shocks that coincide with noncredible trade reforms need to be carefully considered in order to assess credibility on the basis of observed consumption behavior, even when the two sources of uncertainty are independent and policy uncertainty is resolved in one period.

The next task is to examine some welfare implications. However, welfare assessments need to be viewed with caution given the existing theoretical evidence showing that costs of credibility tend to be marginal unless durable goods or other persistence mechanisms are considered (see Calvo (1988)). Tables 2a and 2b report results of welfare analysis. Table 2a examines costs of higher risk on real asset returns and costs of realizations of terms-of-trade shocks at t=0 under alternative scenarios for π. The first case illustrates overall welfare costs of consumption instability driven by real uncertainty. The second set of estimates quantifies costs of one-period realizations of real shocks that serve as a better point for comparison with costs of policy uncertainty, which is also resolved in one period.^13/

Table 2a.

Welfare Costs of Real Uncertainty in the Economy with Tariff Rebates

(In percent of stationary consumption in the risk-free economy) ^1/

^1/A minus denotes a welfare gain and a terms of trade improvement.

Table 2a.

Welfare Costs of Real Uncertainty in the Economy with Tariff Rebates

(In percent of stationary consumption in the risk-free economy) ^1/

Overall Risk			Terms-of-trade Deterioration at t=0
σ	Welfare cost	Average growth	ϵ	Welfare costs
				Π=0	Π=0.25	Π=0.5	Π=0.75	Π=1
0.0	0.0	0.70	-0.10	-0.52	0.50	-0.48	-0.46	-0.44
0.025	1.18	0.75	-0.05	-0.26	-0.25	-0.24	-0.23	-0.22
0.05	4.84	0.82	-0.025	-0.13	-0.13	-0.12	-0.12	-0.11
0.075	11.44	1.08	0.00	0.00	0.00	0.00	0.00	0.00
0.1	21.86	1.38	0.025	0.13	0.13	0.12	0.12	0.11
0.125	37.75	1.76	0.05	0.26	0.26	0.25	0.24	0.23
0.15	62.17	2.22	0.10	0.53	0.52	0.50	0.48	0.46

^1/A minus denotes a welfare gain and a terms of trade improvement.

View Table

Table 2a.

Welfare Costs of Real Uncertainty in the Economy with Tariff Rebates

(In percent of stationary consumption in the risk-free economy) ^1/

Overall Risk			Terms-of-trade Deterioration at t=0
σ	Welfare cost	Average growth	ϵ	Welfare costs
				Π=0	Π=0.25	Π=0.5	Π=0.75	Π=1
0.0	0.0	0.70	-0.10	-0.52	0.50	-0.48	-0.46	-0.44
0.025	1.18	0.75	-0.05	-0.26	-0.25	-0.24	-0.23	-0.22
0.05	4.84	0.82	-0.025	-0.13	-0.13	-0.12	-0.12	-0.11
0.075	11.44	1.08	0.00	0.00	0.00	0.00	0.00	0.00
0.1	21.86	1.38	0.025	0.13	0.13	0.12	0.12	0.11
0.125	37.75	1.76	0.05	0.26	0.26	0.25	0.24	0.23
0.15	62.17	2.22	0.10	0.53	0.52	0.50	0.48	0.46

^1/A minus denotes a welfare gain and a terms of trade improvement.

Table 2b.

Welfare Costs of Policy Uncertainty in the Economy with Tariff Rebates

(In percent of stationary consumption in the economy with perfect credibility)

^1/A minus denotes a welfare gain.

^2/A minus denotes a terms-of-trade improvement

Table 2b.

Welfare Costs of Policy Uncertainty in the Economy with Tariff Rebates

(In percent of stationary consumption in the economy with perfect credibility)

	Welfare Cost of Trade Reform 1/
	Benchmark Economy			High Risk Aversion γ=5			High Tariff ø=0.7
π	ϵ=-0.1 2/	ϵ=0.0	ϵ=0.1	ϵ=0.1 2/	ϵ=0.0	ϵ=0.1	ϵ=-0.1 2/	ϵ=0.0	ϵ=0.1
0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
0.2	0.017	0.003	-0.011	0.015	0.001	-0.017	0.034	0.009	-0.017
0.4	0.039	0.011	-0.017	0.032	0.004	-0.033	0.089	0.038	-0.014
0.6	0.069	0.026	-0.017	0.053	0.010	-0.046	0.174	0.095	0.016
0.8	0.107	0.049	-0.009	0.076	0.018	-0.057	0.297	0.189	0.079
1.0	0.155	0.082	0.007	0.102	0.030	-0.064	0.472	0.334	0.193

^1/A minus denotes a welfare gain.

^2/A minus denotes a terms-of-trade improvement

View Table

Table 2b.

Welfare Costs of Policy Uncertainty in the Economy with Tariff Rebates

(In percent of stationary consumption in the economy with perfect credibility)

	Welfare Cost of Trade Reform 1/
	Benchmark Economy			High Risk Aversion γ=5			High Tariff ø=0.7
π	ϵ=-0.1 2/	ϵ=0.0	ϵ=0.1	ϵ=0.1 2/	ϵ=0.0	ϵ=0.1	ϵ=-0.1 2/	ϵ=0.0	ϵ=0.1
0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
0.2	0.017	0.003	-0.011	0.015	0.001	-0.017	0.034	0.009	-0.017
0.4	0.039	0.011	-0.017	0.032	0.004	-0.033	0.089	0.038	-0.014
0.6	0.069	0.026	-0.017	0.053	0.010	-0.046	0.174	0.095	0.016
0.8	0.107	0.049	-0.009	0.076	0.018	-0.057	0.297	0.189	0.079
1.0	0.155	0.082	0.007	0.102	0.030	-0.064	0.472	0.334	0.193

^1/A minus denotes a welfare gain.

^2/A minus denotes a terms-of-trade improvement

The first panel in Table 2a shows that variability in domestic asset returns or in the terms of trade is very costly, even though it induces faster growth. As σ varies from 0 to 15 percent, the average growth rate increases from 0.7 percent to 2.2 percent, but welfare costs rise from 0 to around 62 percent. Thus, in this example a high-risk economy grows faster than a low-risk economy, but faster growth represents lower welfare. σ=.025 induces a 1.2 percent welfare cost, and a more realistic σ=.1 results in a cost about 1/5 of the trend level of consumption in a risk-free economy.

These costs of consumption instability are significantly larger than those obtained by Lucas (1987). Some of the difference is accounted for by the smaller standard deviations in Lucas’ experiments. However, most of the difference is due to the fact that consumption is modelled here as a competitive equilibrium stochastic process in which uncertainty affects not just fluctuations of consumption around trend, but the trend growth rate itself. Lucas’ computations, in contrast, are not based on a solution of the competitive equilibrium and abstract from growth effects of σ.

The second panel in Table 2a reports costs of realizations of terms-of-trade shocks at t=0 ranging from -10 to 10 percent for various values of π. In general, these shocks produce welfare costs between -0.52 and 0.53 percent, and the costs are only marginally affected by the degree of policy uncertainty—by about as much as 1/10 of a percentage point as π rises from 0 to 1 and the shock moves between -0.1 and 0.1. This weak dependence on π reflects the fact that the processes driving real and policy uncertainty are independent. At the same time, however, this illustrates that even when the two uncertainties are independent, there is a link between costs of real uncertainty and lack of credibility. Note also that when the terms-of-trade shock is positive, the welfare loss is smaller the higher π because the credibility tax reduces the intertemporal relative price of consumption at t=0, and hence offsets the effect of the terms-of-trade deterioration.

Table 2b reports welfare costs of policy uncertainty. Costs of credibility-induced cycles in the benchmark economy for different realizations of terms-of-trade shocks and different values of π are reported, as well as those for economies where τ=0.7 and γ=5. The small magnitude of the costs reported in this Table, compared to those reported in the second panel of Table 2a, suggests that credibility is less costly than real shocks. This is true even in economies with a higher degree of risk aversion and higher initial tariffs than the benchmark. While costs resulting from terms-of-trade shocks range between -0.5 and 0.5 percent, those induced by policy uncertainty are only between -0.01 and 0.16 percent in the benchmark case depending on realizations of real shocks. A higher γ results in even smaller welfare costs of policy uncertainty, while a higher τ results in larger costs, but comparable in size to those induced by real shocks only when π approaches 1 and terms of trade either improve or remain constant. Real shocks have a small effect on welfare costs of credibility, reflecting again the independence of the two sources of uncertainty. Note, however, that terms-of-trade declines that coincide with noncredible reforms offset the cost of credibility and weaken the credibility-induced boom because they make current consumption more expensive. For low values of π, welfare may even improve slightly.

1. Competitive equilibrum

Consider now an economy where a trade reform is announced under the same conditions as before, except that tariff revenue is not to be rebated but used to finance unproductive government expenditures. The competitive equilibrium is the solution to this dynamic programming problem:

Where V^*(A₁, p₁) and V^τ (A₁, p₁) are given by (8) and (14) updated one period respectively. If the reform prevails, optimal plans for all t>0 are as in (5)-(6), and if it fails plans are (12)-(13). ^14/ At t=0 optimal plans are:

Where:

The superscript π, NT denotes that these solutions correspond to the regime of a noncredible reform without rebates. θ(π,τ) is the term that introduces the distortion due to lack of credibility (θ(0,τ)=1). The solutions (27)-(28) can be combined with (8) and (14) to produce a closed-form solution for (26):

These results are compared to those for the regime with permanent tariffs, not against the free-trade regime. When tariff revenue is rebated this distinction is irrelevant because free trade and permanent tariffs result in identical equilibrium allocations. In the case without rebates, however, comparing allocations under imperfect credibility against free-trade allocations produces misleading results, specially with regard to the role of the intertemporal elasticity of substitution in determining the direction of credibility effects. In particular, after some manipulation one can show that C₀^π,NT>C₀^τ, regardless of the value of γ, while C₀^π,NT>C₀^* only if γ>1. Thus, consumption under a temporary trade reform always exceeds consumption under a permanent tariff, but it exceeds free-trade consumption only if the intertemporal elasticity of substitution is less than unitary. A trade reform of uncertain duration always induces a boom if the economy starts from a regime with tariffs; contrary to the result in van Wijnbergen (1992), which depends on whether γ is greater or less than 1.

2. Cyclical effects of imperfect credibility

Proceeding as before, we focus on deviations from trend in consumption. At any date t<0 or t>1, cycles of consumption in this economy are the same as in the case of the economy with rebates (given by equation (22)) because the tariff is time-invariant and, although the nonrebated tariff has a negative wealth effect, the valuation of wealth A_t/p_t is affected uniformly by τ at any point in time. At t=0, when the reform is implemented, ΔC₀ is:

The first three terms in the right-hand side of this expression represent the real component of consumption growth; the first two define the trend and the third is the cycle. These three real elements have the same form as in the economy with rebates—except that μ_r is reduced by the effect of the permanent tariff. The last two terms represent deviations from trend due to policy uncertainty, which are different from those obtained with rebates.

At date 1, when policy uncertainty is resolved, ΔC₁ adopts one of two forms depending on whether the reform is reversed or not. In particular:

The expected value of ΔC₁ conditional on the realization of r₀ is:

Credibility and real-uncertainty effects are once again clearly identified in equations (32)-(34).

Given (31)-(37), six results can be established: ^15/

(i) Imperfect credibility induces a boom at t=0 regardless of the size of γ. This boom embodies a positive wealth effect resulting from tariff reduction, represented by Ln(l+τ), and an intertemporal substitution effect captured by -Ln(θ+λ(1-θ)). The latter is always negative if γ>1, but it can be positive if γ<1 and θ is low enough so that θ+γ(1-θ)<1. Overall, however, it can be proved that the wealth effect always dominates.

(ii) At t=1 imperfect credibility induces a boom or a recession depending on whether the reform is reversed or not and on the size of γ. If tariffs are reinstated there is a recession, regardless of the value of γ. This follows from the negative wealth effect induced by the reintroduction of tariffs, which dominates the substitution effect. The magnitude of the recession depends on γ; if γ>1, the recession is weaker than the boom at t=0, if γ<1 the opposite is true, and if γ=1 the boom and the recession are identical. If free trade prevails at t=1 and γ>1, the boom started at t=0 continues because there is no negative wealth effect and the substitution effect favors the expansion of consumption.^16/

(iii) In terms of expected deviations from trend at t=1 conditional on the realization of real shocks (i.e. (34)), credibility induces a recession if γ≤1, but, as we show numerically later, for γ>1 there are combinations of γ, π, and τ such that credibility effects induce a consumption boom. However, γ>1 is not sufficient to guarantee an expected boom.

(iv) Since θ is increasing in π when γ>1 and decreasing in π when γ<1 (see (29)), an increase in the probability of reversal has different effects on the amplitude of credibility-induced cycles depending on γ. For γ>1, an increase in π reduces the boom at date 0, weakens the recession at date 1 if tariffs return, and strengthens the boom at date 1 if tariffs do not return. There are two effects operating at date 1; the increase in π assigns more probability to the recession scenario of the policy reversal, while it also increases the magnitude of the boom in case free-trade continues. The first effect is associated with wealth, and hence tends to dominate.

(v) Given that θ is increasing in γ, an increase in γ (i.e. a decline in the intertemporal elasticity of substitution) has a positive effect on deviations from trend at date 1, regardless of whether the reform fails or not. At date 0 there are two offsetting effects because higher γ induces, in addition to an increase in θ, a fall in λ, and the credibility effect at t=0 is a function of θ and λ. For γ>1, the credibility effect is weaker the larger is γ, so the boom falls as risk aversion rises. Thus, an increase in γ tends to reduce the amplitude of credibility-induced cycles.

(vi) Welfare of the reforming economy, as given by (30), is decreasing in π. However, because of the wealth effect induced by the absence of rebates, trade reforms of uncertain duration are not always socially costly, compared to the level of welfare of the economy with permanent tariffs. γ>1 is sufficient for welfare under the uncertain trade reform to exceed that of the regime with permanent tariffs.

These results illustrate sharp differences in consumption dynamics between regimes with and without rebates. Impact effects at date 0 are qualitatively similar under the two regimes—both produce booms regardless of the degree of risk aversion. However, the presence of wealth effects in the economy without rebates tends to induce stronger booms than in the case with rebates. At date 1, when policy uncertainty is resolved, the two economies may display very different behavior; in particular, while the economy with rebates experiences a recession milder than the initial boom, regardless of the actual outcome of the trade reform and regardless of the risk aversion parameter, the economy without rebates may experience a boom or a recession depending on both whether the reform prevails and whether γ is greater or less than 1. Even if we compare against expected growth conditional on the realization of r₀, ΔC₁ in the economy without rebates may be stronger or weaker than in the economy with rebates. Welfare implications are also different. While welfare with or without rebates is decreasing in π, there are temporary reforms that improve welfare relative to an initial regime with permanent tariffs when revenue is not rebated. When revenue is rebated this cannot occur because the regime with permanent tariffs reproduces the allocations of the free-trade equilibrium.

3. Credibility effects and real uncertainty

Consider now effects of changes in the risk and return characteristics of domestic assets when tariff revenue is not rebated:

(vii) An increase in μ_r has positive growth effects at t=0,1 as in the case with rebates. The timing of cyclical effects, however, is reversed. There is no cyclical effect at date 1, as μ_r does not affect credibility components in (32)-(34), but at t=0 the increase in μ_r affects the credibility-induced boom via its effect on λ. If γ>1 (γ<1) the boom is stronger (weaker) because λ is decreasing (increasing) in μ_r.

(viii) An increase in risk (i.e. an increase in σ²) has trend effects on ΔC at t=0, 1 depending on whether γ>2 (as before, γ>2 implies that growth effects are positive). As in the case of the change in μ_r an increase in risk affects credibility effects at date 0, but not at date 1. If γ>1 (γ<1) the boom is weaker (stronger) because λ is increasing (decreasing) in σ².

For the researcher attempting to document evidence on credibility from data on consumption and real asset returns, the situation is also different without rebates. The “fundamental” component of business cycles driven by real factors, ΔC^F, is once again given by (22). Equation (31), together with Result (i), implies that ΔC₀>ΔC₀F for economies introducing trade reforms at date 0. However, (32)-(34) and Result (ii) imply that, even with real uncertainty unchanged, the data may show ΔC₁ greater or lower than ΔC₁^F depending on the final outcome of the trade reform and on the degree of risk aversion. In countries where the reform is reversed ΔC₁<ΔC₁^F for any value of γ, but in countries where free trade is maintained the opposite is observed if γ>1. Thus, if econometric estimates suggest that γ>1, the researcher should find booms in excess of those explained by fundamentals at dates 0 and 1 in free-trade economies, while in economies where reforms failed a boom-recession cycle should be observed.

As before, the researcher can also use the data to reconstruct the value of π associated with a particular pattern of consumption behavior. In particular, given an economy where the trade reform was abandoned at t=1, the following relationship holds: ^17/