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### Sacrifice Ratios in Closed vs. Open Economies: An Empirical Test

Aggregate Supply and Potential Output

- The tradition in the monetary literature is that inflation is primarily affected by: (i) economic slack; (ii) expectations; (iii) supply shocks; and (iv) inflation persistence.
- The paper extends the standard New- Keynesian aggregate supply relationship to include also fluctuations in potential output, as an additional determinant of the relationship. It discusses whether potential output could be made a target for optimizing interest rules.

Aggregate Supply and Potential Output

The New-Keynesian aggregate supply derives from micro-foundations an inflation-dynamics model very much like the tradition in the monetary literature.

Inflation is primarily affected by: (i) economic slack; (ii) expectations; (iii) supply shocks; and (iv) inflation persistence.

This paper extends the New Keynesian aggregate supply relationship to include also fluctuations in potential output, as an additional determinant of the relationship.

Optimizing Monetary Rules

Consider a micro-based loss function which is the discounted value of a weighted sum of squared deviations of inflation from a zero level (so as to minimize distortion price dispersions among firms of identical technologies and demand schedules), the squared deviations in output from target output, and the level of the output target. The target output level is likely to be different from potential output under monopolistic competition because of the existence of a wedge between the marginal productivity of labor and the leisure/consumption marginal rate of substitution.

A quadratic-linear optimal problem:

minimize a micro-based loss function, subject to the constraints: (1) Aggregate supply relationship; (2) Government debt dynamics, and 3) the dynamic low governing the potential accumulation of the stock of capital.

Conjecture: Optimizing interest rules would respond to potential output changes in addition to inflation surprise and output gap.

Literature

Understanding why nominal changes have real consequences (why a short run aggregate supply relationship exists) has long been a central concern of macroeconomic research. Lucas (1973) proposes a model in which the effect arises because agents in the economy are unable to distinguish perfectly between aggregate and idiosyncratic shocks. He tests this model at the aggregate level by showing that the Phillips curve is steeper in countries with more variable aggregate maximal demand. Following Lucas, Ball, Mankiw, and Romer (1988) show that sticky-price Keynesian models predict that the Phillips curve should be steeper in countries with higher average rates of inflation and that this prediction too receives empirical support. Loungani, Razin, and Yuen (2001), and Razin and Yuen (2001) show that both Lucas’s and Ball-Mankiw-Romer’s estimates of the Phillips curve slope depend on the degree of capital account restrictions.

C is the Dixit-Stiglitz (1977) index of household consumption, P the Dixit-Stiglitz price index:

Log-linearized Model

log-linearize the marginal cost function around the deterministic steady state equilibrium:

Log-linearizing the two price-setting equations ,

the investment rule, [equation (7)], and using equation (8), yields:

Conclusion

The paper demonstrates that potential output improves the inflation-output gap trade-off.My intuition is that the task of the monetary authority, which trades off inflation and output gaps is facilitated if they target potential output, as well as the inflation fluctuations and the output gaps.

In so doing the monetary authority should be independent, so as not to get trapped in Barro-Gordon dynamic inconsistencies. A Taylor-like rule makes interest rate respond not only to the fluctuations in inflation rates and output gaps, but also the fluctuations in potential output is bound to raise the measure of consumer.

Elasticity of marginal product of

labor wrt output

Elasticity of wage demands,

wrt to output, holding

marginal utility of income

constant

Partial-equilibrium relationship?

Closing the trade account:

Prakash Loungani, Assaf Razin, and Chi-Wa Yuen

Background

Lucas (1973) proposed a model in which the effect arises because agents in the economy are unable to distinguish perfectly between aggregate and idiosyncratic shocks; he tested this model at the aggregate level by showing that the Phillips curve is steeper in countries with more variable aggregate demand. Ball, Mankiw and Romer (1988) showed that sticky price Keynesian models predict that the Phillips curve should be steeper in countries with higher average rates of inflation and that this prediction too receives empirical support

The data used in the regressions reported in this paper are taken from Ball (1993, 1994) and Quinn (1997).

Sacrifice ratios and their determinants: Our regressions focus on explaining the determinants of sacrifice ratios as measured by Ball. He starts out by identifying disinflations, episodes in which the trend inflation rate fell substantially. Ball identifies 65 disinflation episodes in 19

OECD countries over the period 1960 to 1987. For each of these episodes he calculates the associated sacrifice ratio. The denominator of the sacrifice ratio is the change in trend inflation over an episode. The numerator is the sum of output losses, the deviations between output and its trend (“full employment”) level.

Sacrifice ratios and their determinants: Our regressions focus on explaining the determinants of sacrifice ratios as measured by Ball. He starts out by identifying disinflations, episodes in which the trend inflation rate fell substantially. Ball identifies 65 disinflation episodes in 19 OECD countries over the period 1960 to 1987. For each of these episodes he calculates the associated sacrifice ratio. The denominator of the sacrifice ratio is the change in trend inflation over an episode. The numerator is the sum of output losses, the deviations between output and its trend (“full employment”) level.

For each disinflation episode identified by Ball, we use as an independent variable the current account and capital account restrictions that were in place the year before the start of the episode. This at least makes the restrictions pre-determined with respect to the sacrifice ratios, though of course not necessarily exogenous.

Quinn (1997) takes the basic IMF qualitative descriptions on the presence of restrictions and translates them into a quantitative measure of restrictions using certain coding rules. This translation provides a measure of the intensity of restrictions on current account transactions on a (0,8) scale and restrictions on capital account transactions on a (0,4) scale; in both cases, a higher number indicates fewer restrictions. We use the Quinn measures, labeled CURRENT and CAPITAL, respectively, as our measures of restrictions.

Conclusion

In our earlier work we showed that restrictions of capital account transactions were significant determinants of the slope of the Phillips curve, as measured in the studies of Lucas (1973), Ball-Mankiw-Romer (1998), and others.

The findings of this note lend support to this line of work, in particular to the open economy new Keynesian Phillips curve developed in Razin and Yuen (2001). We find that sacrifice ratios measured from disinflation episodes depend on the degree on restrictions on the current account and capital account. Of course, to be more convincing this finding will have to survive a battery of robustness checks, such as sub-sample stability, inclusion of many other possible determinants (such as central bank independence) in the regressions, and using instruments to allow for the possible endogeneity of the measures of openness.

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