So far, the simplest possible form of price stickiness – the simultaneous re-negotiation of all non-tradables’ prices every second period – has been as-sumed. This allowed to derive the consumption, real exchange rate and cur-rent account dynamics analytically. This section shows that the model’s main results remain valid when assuming overlapping price contracts `a la Taylor (1979, 1980), that is, multi-period nominal contracts with only a fraction of prices re-negotiated each period.21 The motivation for this extension is twofold: First, it enables me to show that the model’s results do not hinge on a restrictive assumption about price setting. Second, Taylor pricing generates richer dynamics, as it imparts both forward- and backward-looking aspects to non-tradables’ prices and the real exchange rate.
To develop a simple example, each producer of intermediate goods is as-sumed to set his price for two periods, with a fraction α of intermediate goods’
producers adjusting in periods t + i, i = {0, 2, 4, 6, ..}, and a fraction (1 − α) in periods t + i + 1. Price setters of the first group are characterized by the superscript I, those of the second group by the superscript II.
A group I producer sets his price pN,t(z) = pN,t+1(z) such that the present value of his profits over periods t and t+1 is maximized, that is, he maximizes
21Another widely-used variant of price adjustment has been proposed by Calvo, 1983.
He assumes that every individual firm adjusts its price with a constant, exogenously given probability each period. For open economy models with partial adjustment, see for example Ambler and Harb, 1999 and Kollmann, 1997. Introducing partial adjustment of prices would not change my model’s main results.
the following function:
As in the previous section, yN,t is given by the final good producer’s demand for non-tradable intermediate goods, equation (3.13). The only difference to the profit maximization problem considered in the previous section is that period t and t + 1 aggregate non-tradables’ prices now also depend on the price set by group II producers.
Profit maximization yields pIN,t(z) as
pIN,t(z) = θ−1M C where, as in the previous section, it is assumed that each individual producer ignores the effect of his price on aggregate prices and output. The above equation shows that all group I producers charge the same price, that is,
PN,tI = pIN,t(z) ∀ z.
The period t price of non-tradable final goods is given as a geometric average of the prices charged by group I and group II producers. Group I producers charge t. Group II producers, who must hold their price constant over periods t − 1 and t, charge the price set in period t − 1. PN,tis thus given as
PN,t= (pIN,t)α(pIIN,t−1)1−α (3.38) and the period t + 1 price level as
PN,t+1 = (pIN,t)α(pIIN,t+1)1−α. (3.39) Substituting PN,tand PN,t+1 with the expressions implied by the above equa-tions, and Pt and Pt+1 with equation (3.11), equation (3.37) yields pIN,t as
pIN,t(z) =
where Φ is defined as Φ ≡ θ−1γ−1(1 − γ)1−γ1M C. Note that, when the price of tradable goods and those set by group II are constant, pIN is constant and equal to
Profit maximization of group II producers yields pIIN,t−1(z) as
pIIN,t−1(z) = Substituting equations (3.40) and (3.41) in equation (3.38) yields the period t price level of non-tradable goods as
PN,t = Φ1−α(1−γ)1 h
and the relative price of tradable goods as PT,t
In what follows, Proposition 2 will be reproduced in the above model-ing framework with Taylor-pricmodel-ing. Since the real exchange rate depends on lagged and future prices in a complex manner, real exchange rate dynamics are solved numerically.22 The parameter values are chosen as follows: α, the fraction of firms setting prices in even periods, is set to equal 0.5. Following Mendoza and Uribe (1999b), γ, the share of tradables in total consumption, was set to 0.5. This is in line with Mexican and Brazilian data, where the weights of non-tradable goods in the CPI equal 0.6 (see Mendoza, 2000:6) and 0.46, respectively.23 The value of θ = 45 is taken from Blanchard and Kiotaki (1987); the real interest rate r = 6.5 percent from King, Plosser and Rebelo (1988). The path of the nominal exchange rate is set such that the nominal devaluation in the aftermath of stabilization amounts to 30 percent. It is assumed that the implementation of the period t∗ exchange rate reduction is publicly announced at the beginning of period t∗ − 1, that is, price setters in period t∗ − 1 are the first to take into account the future reduction and ensuing increase in the nominal exchange rate.
Given the exogenously assumed nominal exchange rate path, (relative) non-tradables’ prices and the real exchange rate can be numerically solved.
A graphic exposition of the exogenously imposed path of PT and the resulting paths of PN and the real exchange rate are presented in appendix 3.6.3 to this chapter; the implied rates of real appreciation are reported in table 3.1 (on page 116). They give evidence of a real exchange rate appreciation of almost 13 percent in the period preceding the peg’s breakdown, followed in period t∗+ 1 by a real depreciation of 16.66 percent. Thereafter, the real exchange rate converges quickly to its long-run value.
Of course, given the relatively simple modeling setup, these values are not fit for a direct comparison with actually observed dynamics during ERBS.
This would require extending the model, for instance by a further endogeni-zation of labor supply and production decisions and more sophisticated for-mulations of the consumption basket, exchange rate policy and the formation
22Note that Y
e N,t+1
YN,t is a function of pIN,t: YN,t+1e
YN,t
= CN,t+1e CN,t
= pα(1−γ)N,t p(1−α)γN,t−1 p−(1−α)N,t+1 p−α(1−γ)N,t+2
PT ,t
PT ,t−1
γ
.
Due to the way the PN enter the enumerators of the second and third terms of these equations, logarithmic versions of equations (3.42) and (3.43) cannot be solved analytically for PN,t or PPN,t
T ,t (nor be transformed into linear functions in non-tradables’ prices).
23See Chapter 2.
Period Real Appreciation (-)/Depreciation Rate (in percent)
t∗− 1 2.05
t∗ -12.98
t∗+ 1 16.66
t∗+ 2 -3.87
t∗+ 3 0.40
t∗+ 3 0.02
t∗+ 4 0.001
Table 3.1: The real appreciation in the model with Taylor pricing of exchange rate expectations.24 Despite these caveats, the model’s results are not too far from what has been witnessed during the Mexican ERBS which lasted from February 1988 to November 1994: During this program – which was followed by an annual devaluation rate of 90 percent – the real exchange rate appreciated by 32.6 percent.