4 Solution method and calibration
5.1 Benchmark results
Table 2 shows the results for the benchmark model. There are several interesting results.
First, we …nd that the optimized exchange rate rules lead to lower standard deviations of nominal depreciation ( et), compared to the optimized interest rate rules, regardless of the degrees of openness. This result is consistent with the …ndings of McCallum (2006, 2007). Second, like McCallum (2006, 2007), we …nd that an exchange rate rule can deliver lower volatility of output, compared to an interest rate rule, when the degree of openness is high. The standard deviation11 of GDP is 1.79% for the optimized exchange rate rule (with = 3:0, GDP = 1:0) compared to 2.30% for the optimized interest rate rule (with
= 1:8, GDP = 0) for the high openness economy. In contrast, for the low openness economy, the standard deviation of GDP is higher, at 2.56%, for the optimized exchange rate rule (with = 3:0, GDP = 0:8), compared to 2.15% for the optimized interest rate rule (with = 2:9, GDP = 0). Third, unlike McCallum (2006, 2007), we also …nd that the optimized exchange rate rule delivers a lower (2.00%) standard deviation of domestic …nal goods price in‡ation ( t) compared to the optimized interest rate rule (2.86%), when the degree of openness is high.12 However, when the degree of openness is low, the optimized
11Standard deviations reported in this paper are in terms of log deviation of variables from their steady state values.
12In contrast, McCallum (2006, 2007) …nd that the standard deviation of tis higher for an exchange rate rule, even though the di¤erence relative to an interest rate rule becomes smaller as the degree of openness increases.
exchange rate rule leads to a higher (2.54%) standard deviation of domestic …nal goods price in‡ation compared to the optimized interest rate rule (0.87%).
(Table 2 about here)
Why does the optimized exchange rate rule deliver lower standard deviations of GDP and domestic …nal goods price in‡ation when the degree of openness is high? The intuition can be inferred from the standard deviations of nominal depreciation and import price in‡ation ( mt Ptm=Pt 1m ). As noted above, the optimized exchange rate rule delivers a lower standard deviation of nominal depreciation compared to the optimized interest rate rule, regardless of the degree of openness. This can a¤ect the volatility of GDP and domestic …nal goods price in‡ation through two channels. On the one hand, the nominal exchange rate can play the role of shock absorber. This means that the less variable and hence less ‡exible nominal exchange rate for the optimized exchange rate rule restricts the ability of nominal exchange rate to stabilize GDP through expenditure switching e¤ects. On the other hand, the lower standard deviation of nominal depreciation leads to a lower standard deviation of import price in‡ation for the optimized exchange rate rule since there is full exchange rate pass through into the import price. Since the imported goods are inputs in the production process, the import price in‡ation can be thought of as a supply shock. Hence, the lower standard deviation of import price in‡ation tends to lead to lower standard deviations of domestic …nal goods price in‡ation and GDP. When the degree of openness is high (so that imported input as a share of gross output is high), the pass-through e¤ect dominates, which leads to lower standard deviations of GDP and domestic …nal goods price in‡ation for the optimized exchange rate rule. When the degree of openness is low, the shock absorber role of nominal exchange rate dominates, so the standard deviations of GDP and domestic
…nal goods price in‡ation for the optimized exchange rate rule is higher, compared to the optimized interest rate rule.
For the high openness economy, the lower standard deviation of domestic …nal goods price in‡ation ( t) leads to a lower mean resource cost of price dispersion (ut), for the optimized exchange rate rule (0.09% versus 0.18% for the optimized interest rate rule). However, sur-prisingly, despite the lower mean resource cost of price dispersion, the optimized exchange rate rule leads to much higher welfare cost compared to the optimized interest rate rule. The welfare cost of the optimized exchange rate rule is 0.34% of steady state consumption while it is -0.31% for the optimized interest rate rule. The welfare di¤erence of 0.65% of steady state consumption is large in the realm of business cycle analysis.13 The better performance of the optimized interest rate rule seems to stem from the terms of trade e¤ect. The expected value14 of terms of trade, St, for the optimized interest rate rule (3.24%) is higher than that of the optimized exchange rate rule (1.28%). The more favorable terms of trade for the op-timized interest rate rule stems from its higher volatility of nominal depreciation. A higher volatility of nominal depreciation leads to a more favorable terms of trade since it induces exporters to set higher export price to compensate for the exchange rate uncertainty. The more favorable terms of trade for the optimized interest rate rule in turn allows the represen-tative household to consume more and work less, compared to the optimized exchange rate rule.15 Hence, the optimized interest rate rule delivers higher mean consumption (2.01%), lower mean labor hours (-1.33%) and hence lower welfare cost (-0.31%), compared to the optimized exchange rate rule (0.97%, -0.54% and 0.34%, respectively).
For the low openness economy, in addition to the lower expected value of terms of trade, the optimized exchange rate rule leads to a higher mean resource cost of price dispersion, since
13For comparison, the classic estimate of welfare cost of business cycle in Lucas (1987) is 0.17% for a coe¢ cient of risk aversion, , of 20, while = 2 in our model.
14Expected value of a variable is reported in terms of log deviation from its steady state value in this paper.
15Using a simpler model for which imported goods are not inputs into the production of intermediate goods but combine with a composite domestic goods to form a constant elasticity of substitution composite …nal goods, Sutherland (2006) show that the mean terms of trade can increase or decrease the welfare depending on the parameter values. However, the model in this paper cannot be directly compared with Sutherland (2006) since the production structure is di¤erent.
it leads to a higher standard deviation of domestic …nal goods price in‡ation as mentioned above. The less favorable terms of trade and the higher mean resource cost of price dispersion both lead to a higher welfare cost for the optimized exchange rate rule.
5.2 High elasticity of substitution for export
The subsection above has shown that under the benchmark model, an optimized exchange rate rule is welfare inferior to an optimized interest rate rule, regardless of the degrees of openness. This is true even though the optimized exchange rate rule delivers lower standard deviations of GDP and domestic …nal goods price in‡ation for the high openness economy.
The reason is that an optimized exchange rate rule delivers lower volatility of nominal depre-ciation and hence less favorable mean terms of trade, compared to an optimized interest rate rule. Since the terms of trade e¤ect plays an important role in the results, it is natural to ask whether the results will continue to hold for alternative parameterization of the model, for which the terms of trade e¤ect might play a smaller role.
A parameter that is important for the magnitude of the terms of trade e¤ect is the elasticity of substitution for export, . When the elasticity of substitution for export is high, exporters might be less willing to charge a higher export price to cushion for the exchange rate uncertainties since the demand is more sensitive to the price. This would make the terms of trade e¤ect to vary less with exchange rate volatility. In the subsection above, the elasticity of substitution for export, , is set to 0.6 following McCallum (2006, 2007) and Kollmann (2002). However, there are a lot of uncertainties regarding the empirical value of . For instance, using data from a panel of developed and developing countries, Lai and Tre‡er (2002) …nd that the estimates for the elasticity of substitution for aggregate manufacturing are between 5 to 8. Using disaggregated data from US and 5 other countries, Hummels (2001) …nds that the elasticities of substitution range from 3 to 8 for most goods but can be as high as 79 for some goods. In light of these empirical evidences, we will …rst check
the robustness of the results in detail for a high elasticity of substitution for export, = 10, followed by more robustness checks for other values of .16
Table 3 shows the results for the case of = 10. Similar to the results in Table 2, for the high openness economy, the optimized exchange rate rule delivers lower standard deviations of GDP and domestic goods price in‡ation, compared to the optimized interest rate rule. Therefore, the optimized exchange rate rule leads to a lower mean resource cost of price dispersion. However, unlike the results in Table 2, for the high openness economy, the optimized exchange rate rule entails a lower welfare cost compared to the optimized interest rate rule when = 10. The intuition for this result can be found in Table 3. When
= 10, while the optimized interest rate still delivers a higher mean terms of trade (0.25%
vs. 0.11% for the optimized exchange rate rule), the di¤erence in the mean terms of trade is much smaller compared to the benchmark results for which = 0:6 (3.24% vs. 1.28%
for the optimized interest rate rule and the optimized exchange rate rule, respectively). As mentioned above, the reason behind this pattern is that when the elasticity of substitution for export is high, exporters will be less willing to charge a higher price to cushion for the exchange rate volatility and hence the mean terms of trade will vary less with exchange rate volatility. Therefore, the welfare di¤erence between the optimized exchange rate rule and the optimized interest rate rule depends mostly on the mean resource cost of price dispersion.
Since the optimized exchange rate rule leads to a lower (0.03%) mean resource cost of price dispersion compared to the optimized interest rate rule (0.20%), the optimized exchange rate rule is welfare superior to the optimized interest rate rule.
(Table 3 about here)
16Another parameter that might a¤ect the magnitude of the terms of trade e¤ect is the elasticity of substitution between domestic value added and imported inputs, #. However, we do not investigate the robustness of the results for alternative values of # in this paper because for the model in this paper, a change in # would also a¤ect the steady state import to GDP ratio, making it impossible to disentangle the e¤ects of # and the degree of openness for the model.
Interestingly, unlike the results in Table 2, when = 10, the optimized exchange rate rule is also welfare superior to the optimized interest rate rule for the low openness economy. Like the case of high openness, the di¤erence in mean terms of trade is smaller for the case of low openness when = 10. In addition, the optimized exchange rate also delivers lower standard deviations of GDP and domestic goods price in‡ation for the case of low openness, when
= 10. This is because when the elastcity of substitution for export is high, export demand is sensitive to the export price, so exporters will try to make their export prices more stable, leading to more stable export demand. A more stable export demand in turn leads to more stable domestic …nal goods price in‡ation and GDP through the linkages between export demand, GDP, and factor prices. The lower standard deviation of domestic …nal goods price in‡ation leads to a lower mean resource cost of price dispersion for the optimized exchange rate rule. The lower resource cost of price dispersion translates into a smaller welfare cost for the optimized exchange rate rule.
(Figure 1 about here)
In order to investigate further the robustness of the results for di¤erent values of , we plot the welfare costs for the exchange rate rules and interest rate rules, for between 0.6 to 20 in Figure 1. For both types of monetary policy rules, we …x at 3 and GDP at 0 for all values of . As can be seen from the …gure, for the case of high openness, the exchange rate rule is welfare superior to the interest rate rule for > 2. For the case of the low openness, the exchange rate rule is welfare superior to the interest rate rule for > 7.
These values are within the range of the empirical estimates of the elasticity of substitution.
Hence, the results in this paper suggest that high degree of openness by itself does not make an exchange rate rule to be welfare superior to an interest rate rule, when the expected utility of the representative household is used as the welfare criterion. In contrast, for high elasticity of substitution for export, an exchange rate rule can be welfare superior to an
interest rate rule, regardless of the degrees of openness. It is also worthwhile to note that the welfare costs of interest rate rules increase very rapidly as elasticity of substitution for export increases, especially for the case of high openness, while the welfare costs of exchange rate rules change by less as elasticity of substitution for export changes.
6 Conclusion
In this paper, we compare the welfare performances of exchange rate rules with interest rate rules. We develop a New Keynesian small open economy DSGE model for the analysis. We depart from the existing studies on exchange rate rules by using the expected lifetime utility of the representative household as the welfare criterion. We …nd that while an exchange rate rule delivers lower standard deviations of GDP and in‡ation compared to an interest rate rule when the degree of openness is high, an exchange rate rule is welfare inferior to an interest rate rule under benchmark parameterization. This is because an exchange rate rule delivers lower mean terms of trade, which leads to lower mean consumption and higher mean labor hours. However, for high elasticity of substitution for export, an exchange rate rule is welfare superior to an interest rate rule, regardless of the degree of openness, as the di¤erences in mean terms of trade for the two classes of rules become smaller.
The results in this paper suggest that elasticity of substitution for export, which can be thought of as the degree of competition in the export market, is more important than the degree of openness in deciding the welfare ranking between exchange rate rules and interest rate rules. They also suggest that an exchange rate rule can be a better monetary policy rule than an interest rate rule for a country that faces intense competition in the export market, which should be relevant for most emerging economies.
We conclude this paper by discussing the directions for future research. First, the paper can be extended to allow for incomplete pass-through of exchange rate. Studies such as
Devereux and Engel (2003) and Corsetti and Pesenti (2005) have shown that incomplete pass-through can alter the welfare ranking of monetary policy regimes. Second, the paper can be extended to incorporate "balance sheet e¤ects". Elekdag and Tchakarov (2007), for example, have shown that balance sheet e¤ects associated with liability dollarization can make it bene…cial for emerging markets to stabilize the exchange rate.
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Table 1
Benchmark parameter values for high-openness economy
Benchmark parameter values for high-openness economy