Can Price-Level Targeting Reduce Exchange Rate Volatility?

Abstract

Previous studies have shown that, under certain conditions, a central bank can achieve a better trade-off between inflation and output volatility by replacing its inflation target with a price-level target. This article studies whether a Taylor rule that targets the price level instead of the inflation rate can reduce nominal and real exchange rate volatility without compromising the goals of inflation and output stability. The results indicate that supply shocks cause less nominal and real exchange rate volatility under price-level targeting. However, in the case of demand shocks the results depend on the persistence of the shocks.

Appendices

Appendix

This appendix describes the log-linearized model. Lower-case variables are percentage deviations of the variables from their steady-state values. Nominal prices with ~ indicate that they are divided by the consumer price index to convert them into (stationary) real variables.

The households’ utility maximization problem yields the aggregate labor supply, the Euler equation (which depends on the marginal utility of consumption), and the real interest parity condition.

$$\omega n_{t} + z_{t}^{n} = - \left( {c_{t} - \eta c_{t - 1} } \right)\frac{\sigma }{1 - \eta } + \tilde{w}_{t}$$

(50)

$$\lambda_{t} = E_{t} \lambda_{t + 1} + r_{t} - E_{t} \pi_{t + 1}$$

(51)

$$\lambda_{t} = z_{t}^{c} - \left( {c_{t} - \eta c_{t - 1} } \right)\frac{\sigma }{1 - \eta }$$

(52)

$$E_{t} {rer}_{t + 1} - {rer}_{t} = r_{t} - E_{t} \pi_{t + 1} - \left( {r_{t}^{F} - E_{t} \pi_{t + 1}^{*} } \right)$$

(53)

Total labor supply is divided between the traded and non-traded sectors.

$$n_{t} = \gamma n_{t}^{NT} + (1 - \gamma )n_{t}^{H}$$

(54)

The capital stock in each sector (j = NT, H) evolves according to (55). The investment decision is determined by (56), and the value of installed capital is given by (57).

$$\delta i_{t}^{j} = k_{t}^{j} - (1 - \delta )k_{t - 1}^{j}$$

(55)

$$q_{t}^{j} = \lambda_{t} + \phi \left( {z_{t}^{i} + i_{t}^{j} - i_{t - 1}^{j} } \right) - \beta \phi E_{t} \left( {z_{t + 1}^{i} + i_{t + 1}^{j} - i_{t}^{j} } \right)$$

(56)

$$q_{t}^{j} = \left( {1 - \beta (1 - \delta )} \right)E_{t} \left( {\lambda_{t + 1} + \tilde{r}_{t + 1}^{j} } \right) + \beta (1 - \delta )E_{t} q_{t + 1}^{j}$$

(57)

The rental price of capital in each sector depends on their marginal product of capital.

$$\tilde{r}_{t}^{j} = \tilde{p}_{t}^{j} + z_{t}^{a} + \left( {\alpha - 1} \right)\left( {k_{t - 1}^{j} - n_{t}^{j} } \right)$$

(58)

Output and marginal cost in each sector are determined by the following equations:

$$y_{t}^{j} = z_{t}^{a} + \alpha k_{t - 1}^{j} + (1 - \alpha )n_{t}^{j}$$

(59)

$$\widetilde{mc}_{t}^{j} = \alpha \tilde{r}_{t}^{j} + (1 - \alpha )\tilde{w}_{t}^{{}} - z_{t}^{a}$$

(60)

The demand for each type of good is given by

$$x_{t}^{NT} = - \zeta \tilde{p}_{t}^{NT} + x_{t}$$

(61)

$$x_{t}^{H} = - \zeta \tilde{p}_{t}^{T} - \zeta_{T} (\tilde{p}_{t}^{H} - \tilde{p}_{t}^{T} ) + x_{t}$$

(62)

$$x_{t}^{F} = - \zeta \tilde{p}_{t}^{T} - \zeta_{T} \left( {\tilde{p}_{t}^{F} - \tilde{p}_{t}^{T} } \right) + x_{t}$$

(63)

$$x_{t} = \frac{C}{X}c_{t} + \frac{G}{X}z_{t}^{g} + \frac{I}{X}i_{t}$$

(64)

$$i_{t} = \gamma i_{t}^{NT} + (1 - \gamma )i_{t}^{H}$$

(65)

The demand for exports is

$$x_{t}^{H*} = \nu x_{t - 1}^{H*} + (1 - \nu )\left( {\zeta_{X} z_{t}^{x*} - \zeta_{T} \left( {\tilde{p}_{t}^{H} - {rer}_{t} } \right)} \right)$$

(66)

Non-traded output equals domestic spending on non-traded goods, while the home traded good is sold domestically and exported.

$$y_{t}^{NT} = x_{t}^{NT}$$

(67)

$$y_{t}^{H} = \left( {1 - \frac{EX}{Y}\frac{1}{1 - \gamma }} \right)x_{t}^{H} + \frac{EX}{Y}\frac{1}{1 - \gamma }x_{t}^{H*}$$

(68)

Price stickiness and partial price indexation imply the following hybrid New Keynesian Phillips curves for domestic goods and for imports:

$$\pi_{t}^{NT} = \frac{(1 - \beta \theta )(1 - \theta )}{\theta (1 + \beta \mu )}\left( {\widetilde{mc}_{t}^{NT} - \tilde{p}_{t}^{NT} + z_{t}^{u} } \right) + \frac{\beta }{1 + \beta \mu }E_{t} \pi_{t + 1}^{NT} + \frac{\mu }{1 + \beta \mu }\pi_{t - 1}^{NT}$$

(69)

$$\pi_{t}^{H} = \frac{(1 - \beta \theta )(1 - \theta )}{\theta (1 + \beta \mu )}\left( {\widetilde{mc}_{t}^{H} - \tilde{p}_{t}^{H} + z_{t}^{u} } \right) + \frac{\beta }{1 + \beta \mu }E_{t} \pi_{t + 1}^{H} + \frac{\mu }{1 + \beta \mu }\pi_{t - 1}^{H}$$

(70)

$$\pi_{t}^{F} = \frac{{(1 - \beta \theta^{F} )(1 - \theta^{F} )}}{{\theta^{F} (1 + \beta \mu^{F} )}}\left( {\widetilde{mc}_{t}^{F} - \tilde{p}_{t}^{F} } \right) + \frac{\beta }{{1 + \beta \mu^{F} }}E_{t} \pi_{t + 1}^{F} + \frac{{\mu^{F} }}{{1 + \beta \mu^{F} }}\pi_{t - 1}^{F}$$

(71)

$$\widetilde{mc}_{t}^{F} = {rer}_{t} + z_{t}^{f}$$

(72)

The following two equations are used to calculate the consumer inflation rate:

$$\pi_{t} = \gamma \pi_{t}^{NT} + (1 - \gamma )\pi_{t}^{T}$$

(73)

$$\pi_{t}^{T} = \kappa \pi_{t}^{H} + (1 - \kappa )\pi_{t}^{F}$$

(74)

The following equations describe how relative prices change over time:

$$\tilde{p}_{t}^{NT} = \tilde{p}_{t - 1}^{NT} + \pi_{t}^{NT} - \pi_{t}$$

(75)

$$\tilde{p}_{t}^{H} = \tilde{p}_{t - 1}^{H} + \pi_{t}^{H} - \pi_{t}$$

(76)

$$\tilde{p}_{t}^{F} = \tilde{p}_{t - 1}^{F} + \pi_{t}^{F} - \pi_{t}$$

(77)

$$\tilde{p}_{t}^{T} = \tilde{p}_{t - 1}^{T} + \pi_{t}^{T} - \pi_{t}$$

(78)

In models with price-level targeting, there is one additional equation describing the evolution of the consumer price level:

$$p_{t} = p_{t - 1} + \pi_{t}$$

(79)

The interest rate at which the country borrows or lends internationally depends on the exogenous world interest rate and the net-foreign-assets-to-GDP ratio.

$$r_{t}^{F} = z_{t}^{r*} - \psi by_{t}$$

(80)

The net-foreign-asset position evolves according to Eq. (84), which is derived from the country’s budget constraint. The country accumulates assets when exports are larger than imports. The last term reflects the fact that the ratio of net foreign assets to nominal GDP can also evolve due to the interest on existing assets/debt, changes in the nominal exchange rate, inflation, and GDP growth.

$$\begin{aligned} by_{t} & = by_{t - 1} + \frac{EX}{Y}\left( {\tilde{p}_{t}^{H} + x_{t}^{H*} - \tilde{p}_{t}^{Y} - y_{t} } \right) - \frac{IM}{Y}\left( {\widetilde{mc}_{t}^{F} + x_{t}^{F} - \tilde{p}_{t}^{Y} - y_{t} } \right) \\ & \quad + \,BY\left( {\Delta s_{t} - \pi_{t}^{Y} - y_{t} + y_{t - 1} + r_{t - 1}^{F} } \right) \\ \end{aligned}$$

(81)

The change in the nominal exchange rate depends on the change in the real exchange rate and on the inflation differential.

$$\Delta s_{t} =\Delta {rer}_{t} + \pi_{t} - \pi_{t}^{*}$$

(82)

Aggregate output, its price index, and its inflation rate are given by

$$y_{t} = \gamma y_{t}^{NT} + (1 - \gamma )y_{t}^{H}$$

(83)

$$\tilde{p}_{t}^{Y} = \gamma \tilde{p}_{t}^{NT} + (1 - \gamma )\tilde{p}_{t}^{H}$$

(84)

$$\pi_{t}^{Y} = \gamma \pi_{t}^{NT} + (1 - \gamma )\pi_{t}^{H}$$

(85)

Monetary policy is conducted with a Taylor rule that targets expected inflation (Eq. 86) or the expected price level (Eq. 87).

$$r_{t} = \lambda_{r} r_{t - 1} + (1 - \lambda_{r} )(\lambda_{\pi } E_{t} \pi_{t + 1} + \lambda_{y} y_{t} ) + z_{t}^{r}$$

(86)

$$r_{t} = \lambda_{r} r_{t - 1} + (1 - \lambda_{r} )(\lambda_{p} E_{t} p_{t + 1} + \lambda_{y} y_{t} ) + z_{t}^{r}$$

(87)

Finally, all exogenous variables (h = c, i, g, a, u, n, r, r*, x*, f) evolve according to an AR(1) process, where $\varepsilon_{t}^{h}$ is an i.i.d. shock .

$$z_{t}^{h} = \rho^{h} z_{t - 1}^{h} + \varepsilon_{t}^{h}$$

(88)

Notes

• 1. An overview of inflation-targeting practices around the world can be found in Little et al. [2008].

• 2. The large holdings of foreign exchange reserves in these three Latin American countries and their occasional foreign exchange interventions support that view.

• 3. Such measures are not always motivated by the desire to reduce exchange rate volatility. A fixed exchange rate may also be motivated by the need for a credible commitment to lower money growth.

• 4. Although this is not always the case: exchange rates may also act as “shock-absorbers” and dampen a rise (or fall) in those variables.

• 5. For that reason some authors prefer the term “price-path target.”

• 6. To be clear, the price level would be trend-stationary if the price-level target is regularly updated (price-path target) and stationary is the price-level target is never adjusted.

• 7. To be precise, the nominal exchange rate would only become trend-stationary if both countries adopt a price-level target and the real exchange rate is stationary.

• 8. With a Taylor rule the central bank adjusts the money supply so that, given the money demand, the equilibrium nominal interest rate equals its desired rate.

• 9. If the country is a net debtor then B ^F < 0 and households pay interest to the rest of the world.

• 10. Since all households are identical, households’ subscripts are dropped from now on.

• 11. The aggregate capital stock available in sector j at time t is determined at time t − 1 and denoted by K ^j _t−1 . However, the capital that intermediate firm f in sector j rents at time t is determined at time t and denoted by $K_{t}^{j} \left( f \right)$.

• 12. This friction is equivalent to the debt-elastic interest rate studied by Schmitt-Grohé and Uribe [2003].

• 13. OECD’s Quarterly National Accounts, 1992–2014.

• 14. OECD’s Quarterly National Accounts. Data are available starting in 1997. Therefore, I use the value for 2003 rather than the average between 1992 and 2014.

• 15. This statistic is obtained from the OECD’s Trade in Value Added (TiVA) database (2005–2009) and is better than gross imports over GDP because it excludes imports that are re-exported.

• 16. Smets and Wouters [2003] discuss this methodology. The model is estimated and simulated using DYNARE 4.0.4.

• 17. The volatilities of consumption growth and the real exchange rate’s appreciation rate are linked by Eq. (5).

• 18. In the log-linearized model lower-case letters indicate percentage deviations from their steady-state values. The exceptions are the interest rate and the inflation rate, where the difference is used: $r_{t} \equiv R_{t} - \bar{R}$, $\pi_{t} \equiv \varPi_{t} - \bar{\varPi }$.

• 19. The price-level targeting rules include the possibility that the price-level target is updated every quarter by a fixed rate (price-path target). However, the log-linearization of the model makes a fixed price-level target and a price-path target equivalent. With a fixed price-level target the steady-state value of the price level is constant. With a price-path target that steady-state value grows at a constant rate. But the dynamics of the price level around its steady-state value are the same. Similarly, there is no need to specify the inflation target in the inflation-targeting rules because such target affects the steady-state rate of inflation but not the log-linearized model.

• 20. The standard deviation of these shocks does not affect the comparison between Taylor rules.

• 21. The real interest rate is defined as the nominal interest rate minus expected (rather than actual) inflation.

• 22. These equations use the fact that p _t  = p _t−1 + π _t , s _t  = s _t−1 + Δs _t , E _t−h (p _t–h ) = p _t–h , and E _t−h (s _t−h ) = s _t−h .

• 23. Notice that the standard deviations shown in this section’s tables correspond to the standard deviation of the forecast errors when the horizon goes to infinity.

• 24. The impulse-response functions depict percentage deviations from the steady-state values of those variables. The nominal and real exchange rates are defined so that an increase represents depreciation. The responses of the price level and the nominal exchange rate (which are non-stationary under an inflation target) are constructed using the responses of the inflation rate and the rate of nominal appreciation.

• 25. Notice that, although the shock’s effect on inflation is temporary, under an inflation target it causes a permanent change in the price level and the nominal exchange rate.

• 26. The real interest rate differential also depends on the exogenous foreign interest rate r _t * and the risk premium. The foreign interest rate does not change in response to supply and demand shocks. The risk premium does, but its change is similar across Taylor rules. Therefore, the main driver of the real interest rate differential is the change in the domestic real interest rate.

• 27. One factor that attenuates that difference is the increase in the risk premium, which depreciates the currency (and increases real exchange rate volatility) in the case of inflation targeting and reduces the appreciation (and decreases real exchange rate volatility) in the case of price-level targeting.

• 28. Taylor rules imply a linear relationship between the interest-rate and the targeted economic variables (e.g., the output gap and the expected inflation rate or price level). Optimal monetary policy rules like the one used by Svensson [1999] are derived from the minimization of a loss function that depends on the targeted economic variables. They imply a nonlinear relationship between the interest rate and those variables. For a discussion of optimal monetary policy see, for example, Clarida et al. [1999].