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Increasing returns to scale and sticky prices: are they important for real exchange rates?
Carnegie-Rochester Conference Series on Public Policy 43 (1995) 103-110 North-Holland
Increasing returns to scale and sticky prices: are t h e y i m p o r t a n t for real exchange rates? A comment Mary G. Finn* Federal Reserve Bank of Richmond
Beaudry and Devereux (1995) advance the idea that increasing returns to scale in conjunction with sticky prices are important for understanding real exchange-rate behavior. They argue that in the presence of both increasing returns to scale and sticky prices, monetary shocks significantly affect the real exchange rate in a fashion that is consistent with the stylized facts. The present discussion further analyzes their idea. It is organized into four parts. Part 1 considers the increasing returns to scale assumption. Part 2 discusses the assumption of sticky prices. Part 3 evaluates the model. Part 4 concludes the discussion.
1
I n c r e a s i n g r e t u r n s to scale
A key model assumption is increasing returns to scale (IRS) in production. IRS are not only a central feature of the model's propagation mechanism but also the source of equilibrium indeterminacy. Indeterminacy of equilibrium, in turn, provides the avenue for introducing another key assumption, the assumption of sticky prices. That is, the sticky-price assumption is the equilibrium selection device. IRS together with sticky prices contribute to the conditions under which money is strongly nonneutral. IRS take the form *Special thanks go to Zvi Hercowitz for many helpful conversations. I also thank Michael Dotsey, Marvin Goodfriend, Jeremy Greenwood, and Peter Ireland for their comments. The views expressed here do not necessarily reflect the views of the Federal Reserve System or the Federal Reserve Bank of Richmond. 0167-2231/95/$09.50/© 1995 - Elsevier Science B.V. All rights reserved. SSDI 0167-2231(95)00041-W
of an externality that, in equilibrium, magnifies the parameters in the relationships between aggregate outputs and aggregate inputs. More exactly, the production function for a domestic intermediate goods firm (ignoring fixed costs for simplicity) is: xi =
'[ki~/~2/~l-c~l-c~2)]A.-~rn-~j--, "--
0 < 0(1, C~2 < 1
(1)
where xi is the output of firm i, kix, kim, and li are domestic and foreign capital and domestic labor employed by firm i, A is the externality, and al,C~2 are parameters. This production function exhibits constant returns to scale in the firm's inputs. The externality is determined by: A = []gxa]~y/(1-al-a2)] "y-l,
'~ :> 1
(2)
where k~, kin, and l are the economy wide averages of kix, ki,~, and li, respectively, and ~ is the IRS parameter. In the symmetric equilibrium, all domestic intermediate goods firms are identical. It follows that, in equilibrium, the relationship between aggregate domestic output and aggregate domestic inputs is: x = [k; 1
(3)
where x is the economywide average of xi. Since "/ > l, the presence of the externality increases the parameters in this relationship. A similar relationship obtains between aggregate foreign output and aggregate foreign inputs. The following two issues arise.
1.1
What are the microeconomic foundations of Ills q.
In particular, what is the rationale for assuming the existence of an externality that depends on a flow aggregate economy variable, namely, aggregate labor input? This type of externality magnifies labor input's exponent, ( 1 - - Ot I - - C ~ 2 ) ~ , in the aggregate production function, thereby strengthening the economy's contemporaneous responses to shocks. An answer to the above question seems necessary if one is to take seriously the argument that IRS are important for understanding real exchange rates.
1.2
Extraordinary sensitivity to changes in the magnitude of IRS
Beaudry and Devereux's theory crucially depends on the size of the IRS parameter, % This dependence is explained as follows. A necessary condition for the indeterminacy of equilibrium is that, at the aggregate level, the marginal productivity of labor is increasing in labor, that is: (1 -
-
104
>
1
(4)
or
3`>!,
7_=1/(1-al-c~2)
(5)
For example, taking Beaudry and Devereux's calibrated value of (1 - ch - c~2), 0.70, this necessary condition becomes 3' > 1.43. When 3' < ~_, the equilibrium in Beaudry and Devereux's model world economy is a determinate one with flexible prices. In this equilibrium, monetary shocks are an insignificant source of volatility in real variables, including the real exchange rate. For a value of 3' sufficiently higher than 2, equilibrium becomes indeterminate. That is, there exists a multiplicity of equilibria. One of these equilibria features sticky prices. In the sticky-price equilibrium, monetary shocks cause substantial volatility in the real exchange rate and other real variables. But, this volatility is decreasing in the size of 3' (see Beaudry and Devereux's Tables 2 and 3). Intuitively, an increase in ~, exerts two opposing forces on volatility. First, for any given change in the amounts of employed capital and labor, an increase in 3` implies a bigger change in output and most other real variables. Second, at higher values of ~,, the aggregate marginal productivity of labor rises more quickly with increases in labor. Consequently, smaller changes in labor, and hence capital, output and most other real variables are needed to equilibrate the economy in response to shocks. It turns out that the second force is the dominant one, so that volatility decreases as 3' increases. The upshot of these considerations is that confidence in Beaudry and Devereux's quantitative theory of the linkage between money and the real exchange rate requires confidence that "), lies in a narrow range above 3', which in their case equals 1.43. It is difficult to acquire such confidence. Existing empirical evidence on the value of 3' is far from being precise. Studies by Hall (1990), Baxter and King (1991), Caballero and Lyons (1992), Eden and Griliches (1993), and BasH and Fernald (1994) given point estimates of 3' ranging anywhere from one to ten. 2
Sticky prices
The assumption of sticky or predetermined goods prices at any point in time is also a prominent model assumption. It is essential for why significant monetary nonneutrality obtains. A unique feature of this assumption is that it is made at the last stage of the modelling procedure. It is only when the indeterminacy of equilibrium arises that the sticky-price assumption is made, thereby rendering the equilibrium determinate. Costs and benefits accompany the sticky-price assumption. Because of the unique feature, one cost is that to arrive at the point of making the assumption requires, as indicated earlier, a strong stand both on the nature 105
and magnitude of IRS. Secondly, the assumption is made at the expense of being an extreme abstraction from reality - it rules out any response of all goods prices in the world economy to contemporaneous events. The sticky-price assumption has the advantage of being consistent with optimizing behavior on the part of all agents. More precisely, the prices chosen by the monopolistically competitive firms always solve the purely intratemporal profit maximization objectives of those firms. Nonetheless, a curious outcome of the unique feature of the sticky-price assumption is that it is possible to imagine that those prices were set one period in advance, i.e., prices are predetermined because firms never want to adjust prices to contemporaneous shocks. Another advantage of the sticky-price assumption is that when it is combined with the IRS and transactions cost assumptions, it turns out to be effective in achieving the goal of specifying a model with significant monetary nonneutrality. An intuitive discussion of how the nonneutrality works follows. It focuses on the effects on the domestic economy of a permanent increase in the domestic money stock at time t(Nt). First, consider the effects occurring at time t. Since the time-t domestic price level (Pt) is predetermined, the impact effect of the increase in Nt is an increase in time-t domestic real money balances (Nt/Pt). The rise in (Nt/Pt) reduces the marginal transactions cost of hiring domestic production factors, thereby leading to a rise in the employment of those factors and, thus also, in time-t domestic aggregate output (Xt). The increase in Xt is absorbed by increases in both consumption (C,:t) and investment at time t. Due to the presence of IRS in production, these expansions in employment, output, consumption, and investment are all quite sizeable. C,:t rises relative to time-t consumption of foreign output (Cmt). The real exchange rate equals the ratio of the two consumptions: = Cx /Cm
(6)
where et is the domestic currency price of one unit of foreign currency at time t and Pt* is the time-t foreign price level. With both Pt and Pt* predetermined, et increases to effect an increase in (ctP~)/Pt that matches the rise in Cxt/Cmt. That is, the nominal and real exchange rate both depreciate by the same amount. Notice what happens at the level of the individual monopolistically competitive domestic firms. Their optimal intratemporal price-setting behavior is captured by a constant markup of price over marginal cost:
pit = (1/p)MCit
(7)
where pit and MCit are firm i's price and marginal cost at time t and p is a parameter. Marginal cost depends on an index of factor prices and the 106
externality:
a / ~ l / n b*~2 d/(1-~1-42) MCit
=
~.*~t
I,~tlct ]
At
,, t
(8)
where/)t, (et, RA.t), and l/Vt are the rental time-t prices of domestic and foreign capital and domestic labor, in domestic currency units, and A is a parameter. Since, by assumption, goods prices cannot respond to current shocks, pit does not respond to the increase in Nt. From the markup rule it follows that neither does MCit; thus, the factor price index rises to exactly match the rise in the externality. Firms willingly accommodate the time-t monetaryinduced expansions in employment and demand for their goods at constant prices and marginal costs. Over time prices can change, but they do so gradually. The time-(t + 1) domestic price level is essentially determined by the condition for domestic money-market equilibrium at time t: PtC~t
.
1 + ¢,(Nt/Pt, Xt) =/3Et[pt+-~t+ ' ]
(9)
where ¢1 is the first-order partial derivative of the transaction cost function with respect to its first argument, Et is the expectations operator conditioned on time-t information, /3 is a parameter (and fixed costs are ignored for simplicity). This condition states that Nt/Pt is an increasing function of Xt and a decreasing function of time-t domestic nominal rate of interest /3(Pt+lCxt+l)/(PtCxt). While Pt+I can change in response to the rise in Nt, there are two reasons why it changes by a negligible amount. First the expansion in Xt is sufficiently large relative to that in Nt/Pt so as to create a small incipient excess demand for real money balances. Second, at the given interest-rate elasticity, the small rise in (Cxt+~/Cxt) causes a small rise in the real and nominal interest rate that is enough to ensure money-market equilibrium. Consequently, there is no need for a discernible change in Pt+l. The new steady-state values of all real (nominal) variables are invariant (equiproportionate) to the permanent increase in Art. But, because of capital accumulation and IRS, the higher values of employment, output, consumption, investment, and the real exchange rate, relative to the steady state, persist for some time. It is only after about four quarters, as growth in consumption of the domestic good becomes negative, that P eventually and slowly increases. At any point of time, the increase in P works to keep the domestic nominal interest rate approximately constant in face of the small negative consumption growth rates. A constant nominal interest rate is sufficient to ensure domestic money-market equilibrium. Meanwhile, previous P increases engineer the reductions in N / P that, each period, closely match declines in X as the economy returns to the steady state. These movements of P equal those of p since in the symmetric equilibrium P = p. The path 107
of the real exchange rate essentially reflects that of Cx. Therefore, not only does the real exchange rate slowly return to its original steady-state value but it also breaks away from e, which rises to its new and higher steady-state value.
3
Model evaluation
Some model predictions are consistent with empirical regularities. Particularly, the model captures the high volatility of nominal and real exchange rates relative to the volatility of price levels, the strong comovement between the rates of change of nominal and real exchange rates, and the persistency of real exchange-rate movements that characterize real world data. But, the model also has a number of predictions for key variables that sharply contrast with the facts.
3.1
Output
The model has strong implications for the magnitude of output responses to monetary shocks. It is difficult to precisely evaluate this implication since the model is calibrated so as to impose a value for the standard deviation of real output. However, some evaluation is possible by examining the impulse response analysis portrayed in Beaudry and Devereux's Figure 6a. This figure shows that a one-percentage-point increase in the domestic money stock contemporaneously causes a seven-percentage-point rise in domestic real output. An output response of this magnitude seems too big for two reasons. First, Sims' (1980) evidence for the U.S. economy over the period 1948-1978 shows that a one-percent money-stock innovation within the same period causes a 0.42-percent increase in real output. Second, in a simple cashin-advance model economy with a predetermined price level, a one-percent monetary innovation would simultaneously cause only a one-percent output increase.
3.2
Nominal interest rate
The model predicts that essentially no nominal interest-rate movements result from monetary shocks. This implication seems counterfactural, too. There is strong evidence documenting the liquidity effects on nominal interest rates exerted by changes in the money supply (for example, see Cochrane, 1989). 108
3.3
Real and nominal exchange rates
In the model, the standard deviation of the real exchange rate is less than one half of the standard deviation of output. The facts are different. Backus, Kehoe, and Kydland (1994) and Mendoza (1995) provide evidence that the standard deviation of the real exchange rate is greater than that of output for many countries, often by a factor of two or three. As mentioned above, the model's nominal and real exchange rates exhibit strong high-frequency covariation. In this regard the model mimics the empirical evidence. But this model feature is not so much a prediction as it is an assumption. That is, by assumption all prices are predetermined for one period and, therefore, nominal exchange-rate changes must entirely cause the real exchange-rate responses to contemporaneous shocks. Another empirical regulary characterizing nominal and real exchange rates is that their levels move very closely together (see Stockman, 1987). This fact suggests that the strong comovement between nominal and real exchange rates occurs at high, medium, and low frequencies. The impulse response model analysis, portrayed in Beaudry and Devereux's Figure 2a, shows the paths of the nominal and real exchange rate breaking apart just a few quarters after the monetary shock. Thus, it seems that the model is not consistent with the significant medium and low frequency comovement that is apparent in real world nominal and real exchange rates.
4
Conclusion
Beaudry and Devereux's idea that increasing returns to scale and sticky prices are key elements for explaining real exchange rates is interesting. But it is not convincing. Substantive issues concerning the justification of the nature and magnitude of increasing returns to scale would first need to be addressed. Also, it is difficult to accept the sticky-price assumption as a useful abstraction. The assumption that all goods prices in the world economy are sticky is not only an extreme one but also, by definition, it assumes the answer to one of the most puzzling aspects of real exchange-rate behavior: the high covariation between the rates of change of nominal and real exchange rates. Moreover, the fashion in which the assumptions of increasing returns to scale and stocky prices are combined seems to be at the heart of the counterfactual effects of monetary shocks. The assumption of sticky prices is the means of resolving the indeterminacy of equilibrium arising from increasing returns to scale. The counterfactual effects of monetary shocks include massive output and virtually no nominal interest-rate responses. The upshot is that the combination of increasing returns to scale and sticky prices of the type found in Beaudry and Devereux is unlikely to be important for promoting an understanding of real exchange rates. 109
References
Backus, D., Kehoe, P., and Kydland, F., (1994). International Business Cycles: Theory and Evidence. Frontiers of Business Cycle Research. Manuscript, (ed.) T. Cooley. Basu, S. and Fernald, J., (1994). Constant Returns and Small Markups in U.S. Manufacturing. Board of Governors of the Federal Reserve System, International Finance Discussion Paper, 483. Baxter, M. and King, R., (1991). Productive Externalities and Business Cycles. Federal Reserve Bank of Minneapolis, Institute for Empirical Macroeconomics Discussion Paper, 53. Beaudry, P. and Devereux, M., (1995). See this volume. Caballero, R. and Lyons, R., (1992). External Effects in U.S. Procyclical Productivity. Journal of Monetary Economics, 29: 209-226. Cochrane, J., (1989). The Return of the Liquidity Effect: A Study of the Short-Run Relation Between Money Growth and Interest Rates. Journal of Business and Economic Statistics, 7: 75-83. Eden, B. and Griliches, Z., (1993). Productivity, Market Power, and Capacity Utilization When Spot Markets are Complete. American Economic Review, 83: 219-223. Hall, R., (1990). Invariance Properties of Solow's Productivity Residual. Growth/Productivity/Unemployment, (ed.) P. Diamond. Cambridge: MIT Press. Mendoza, E., (1995). The Terms of Trade and Economic Fluctuations, International Economic Review, forthcoming. Sims, C., (1980). Comparison of Interwar and Postwar Business Cycles: Monetarism Reconsidered. American Economic Review, 70: 250-257. Stockman, A., (1987). The Equilibrium Approach to Exchange Rates. Federal Reserve Bank of Richmond Economic Review, 73/2.
110
Increasing returns to scale and sticky prices: are t h e y i m p o r t a n t for real exchange rates? A comment Mary G. Finn* Federal Reserve Bank of Richmond
Beaudry and Devereux (1995) advance the idea that increasing returns to scale in conjunction with sticky prices are important for understanding real exchange-rate behavior. They argue that in the presence of both increasing returns to scale and sticky prices, monetary shocks significantly affect the real exchange rate in a fashion that is consistent with the stylized facts. The present discussion further analyzes their idea. It is organized into four parts. Part 1 considers the increasing returns to scale assumption. Part 2 discusses the assumption of sticky prices. Part 3 evaluates the model. Part 4 concludes the discussion.
1
I n c r e a s i n g r e t u r n s to scale
A key model assumption is increasing returns to scale (IRS) in production. IRS are not only a central feature of the model's propagation mechanism but also the source of equilibrium indeterminacy. Indeterminacy of equilibrium, in turn, provides the avenue for introducing another key assumption, the assumption of sticky prices. That is, the sticky-price assumption is the equilibrium selection device. IRS together with sticky prices contribute to the conditions under which money is strongly nonneutral. IRS take the form *Special thanks go to Zvi Hercowitz for many helpful conversations. I also thank Michael Dotsey, Marvin Goodfriend, Jeremy Greenwood, and Peter Ireland for their comments. The views expressed here do not necessarily reflect the views of the Federal Reserve System or the Federal Reserve Bank of Richmond. 0167-2231/95/$09.50/© 1995 - Elsevier Science B.V. All rights reserved. SSDI 0167-2231(95)00041-W
of an externality that, in equilibrium, magnifies the parameters in the relationships between aggregate outputs and aggregate inputs. More exactly, the production function for a domestic intermediate goods firm (ignoring fixed costs for simplicity) is: xi =
'[ki~/~2/~l-c~l-c~2)]A.-~rn-~j--, "--
0 < 0(1, C~2 < 1
(1)
where xi is the output of firm i, kix, kim, and li are domestic and foreign capital and domestic labor employed by firm i, A is the externality, and al,C~2 are parameters. This production function exhibits constant returns to scale in the firm's inputs. The externality is determined by: A = []gxa]~y/(1-al-a2)] "y-l,
'~ :> 1
(2)
where k~, kin, and l are the economy wide averages of kix, ki,~, and li, respectively, and ~ is the IRS parameter. In the symmetric equilibrium, all domestic intermediate goods firms are identical. It follows that, in equilibrium, the relationship between aggregate domestic output and aggregate domestic inputs is: x = [k; 1
(3)
where x is the economywide average of xi. Since "/ > l, the presence of the externality increases the parameters in this relationship. A similar relationship obtains between aggregate foreign output and aggregate foreign inputs. The following two issues arise.
1.1
What are the microeconomic foundations of Ills q.
In particular, what is the rationale for assuming the existence of an externality that depends on a flow aggregate economy variable, namely, aggregate labor input? This type of externality magnifies labor input's exponent, ( 1 - - Ot I - - C ~ 2 ) ~ , in the aggregate production function, thereby strengthening the economy's contemporaneous responses to shocks. An answer to the above question seems necessary if one is to take seriously the argument that IRS are important for understanding real exchange rates.
1.2
Extraordinary sensitivity to changes in the magnitude of IRS
Beaudry and Devereux's theory crucially depends on the size of the IRS parameter, % This dependence is explained as follows. A necessary condition for the indeterminacy of equilibrium is that, at the aggregate level, the marginal productivity of labor is increasing in labor, that is: (1 -
-
104
>
1
(4)
or
3`>!,
7_=1/(1-al-c~2)
(5)
For example, taking Beaudry and Devereux's calibrated value of (1 - ch - c~2), 0.70, this necessary condition becomes 3' > 1.43. When 3' < ~_, the equilibrium in Beaudry and Devereux's model world economy is a determinate one with flexible prices. In this equilibrium, monetary shocks are an insignificant source of volatility in real variables, including the real exchange rate. For a value of 3' sufficiently higher than 2, equilibrium becomes indeterminate. That is, there exists a multiplicity of equilibria. One of these equilibria features sticky prices. In the sticky-price equilibrium, monetary shocks cause substantial volatility in the real exchange rate and other real variables. But, this volatility is decreasing in the size of 3' (see Beaudry and Devereux's Tables 2 and 3). Intuitively, an increase in ~, exerts two opposing forces on volatility. First, for any given change in the amounts of employed capital and labor, an increase in 3` implies a bigger change in output and most other real variables. Second, at higher values of ~,, the aggregate marginal productivity of labor rises more quickly with increases in labor. Consequently, smaller changes in labor, and hence capital, output and most other real variables are needed to equilibrate the economy in response to shocks. It turns out that the second force is the dominant one, so that volatility decreases as 3' increases. The upshot of these considerations is that confidence in Beaudry and Devereux's quantitative theory of the linkage between money and the real exchange rate requires confidence that "), lies in a narrow range above 3', which in their case equals 1.43. It is difficult to acquire such confidence. Existing empirical evidence on the value of 3' is far from being precise. Studies by Hall (1990), Baxter and King (1991), Caballero and Lyons (1992), Eden and Griliches (1993), and BasH and Fernald (1994) given point estimates of 3' ranging anywhere from one to ten. 2
Sticky prices
The assumption of sticky or predetermined goods prices at any point in time is also a prominent model assumption. It is essential for why significant monetary nonneutrality obtains. A unique feature of this assumption is that it is made at the last stage of the modelling procedure. It is only when the indeterminacy of equilibrium arises that the sticky-price assumption is made, thereby rendering the equilibrium determinate. Costs and benefits accompany the sticky-price assumption. Because of the unique feature, one cost is that to arrive at the point of making the assumption requires, as indicated earlier, a strong stand both on the nature 105
and magnitude of IRS. Secondly, the assumption is made at the expense of being an extreme abstraction from reality - it rules out any response of all goods prices in the world economy to contemporaneous events. The sticky-price assumption has the advantage of being consistent with optimizing behavior on the part of all agents. More precisely, the prices chosen by the monopolistically competitive firms always solve the purely intratemporal profit maximization objectives of those firms. Nonetheless, a curious outcome of the unique feature of the sticky-price assumption is that it is possible to imagine that those prices were set one period in advance, i.e., prices are predetermined because firms never want to adjust prices to contemporaneous shocks. Another advantage of the sticky-price assumption is that when it is combined with the IRS and transactions cost assumptions, it turns out to be effective in achieving the goal of specifying a model with significant monetary nonneutrality. An intuitive discussion of how the nonneutrality works follows. It focuses on the effects on the domestic economy of a permanent increase in the domestic money stock at time t(Nt). First, consider the effects occurring at time t. Since the time-t domestic price level (Pt) is predetermined, the impact effect of the increase in Nt is an increase in time-t domestic real money balances (Nt/Pt). The rise in (Nt/Pt) reduces the marginal transactions cost of hiring domestic production factors, thereby leading to a rise in the employment of those factors and, thus also, in time-t domestic aggregate output (Xt). The increase in Xt is absorbed by increases in both consumption (C,:t) and investment at time t. Due to the presence of IRS in production, these expansions in employment, output, consumption, and investment are all quite sizeable. C,:t rises relative to time-t consumption of foreign output (Cmt). The real exchange rate equals the ratio of the two consumptions: = Cx /Cm
(6)
where et is the domestic currency price of one unit of foreign currency at time t and Pt* is the time-t foreign price level. With both Pt and Pt* predetermined, et increases to effect an increase in (ctP~)/Pt that matches the rise in Cxt/Cmt. That is, the nominal and real exchange rate both depreciate by the same amount. Notice what happens at the level of the individual monopolistically competitive domestic firms. Their optimal intratemporal price-setting behavior is captured by a constant markup of price over marginal cost:
pit = (1/p)MCit
(7)
where pit and MCit are firm i's price and marginal cost at time t and p is a parameter. Marginal cost depends on an index of factor prices and the 106
externality:
a / ~ l / n b*~2 d/(1-~1-42) MCit
=
~.*~t
I,~tlct ]
At
,, t
(8)
where/)t, (et, RA.t), and l/Vt are the rental time-t prices of domestic and foreign capital and domestic labor, in domestic currency units, and A is a parameter. Since, by assumption, goods prices cannot respond to current shocks, pit does not respond to the increase in Nt. From the markup rule it follows that neither does MCit; thus, the factor price index rises to exactly match the rise in the externality. Firms willingly accommodate the time-t monetaryinduced expansions in employment and demand for their goods at constant prices and marginal costs. Over time prices can change, but they do so gradually. The time-(t + 1) domestic price level is essentially determined by the condition for domestic money-market equilibrium at time t: PtC~t
.
1 + ¢,(Nt/Pt, Xt) =/3Et[pt+-~t+ ' ]
(9)
where ¢1 is the first-order partial derivative of the transaction cost function with respect to its first argument, Et is the expectations operator conditioned on time-t information, /3 is a parameter (and fixed costs are ignored for simplicity). This condition states that Nt/Pt is an increasing function of Xt and a decreasing function of time-t domestic nominal rate of interest /3(Pt+lCxt+l)/(PtCxt). While Pt+I can change in response to the rise in Nt, there are two reasons why it changes by a negligible amount. First the expansion in Xt is sufficiently large relative to that in Nt/Pt so as to create a small incipient excess demand for real money balances. Second, at the given interest-rate elasticity, the small rise in (Cxt+~/Cxt) causes a small rise in the real and nominal interest rate that is enough to ensure money-market equilibrium. Consequently, there is no need for a discernible change in Pt+l. The new steady-state values of all real (nominal) variables are invariant (equiproportionate) to the permanent increase in Art. But, because of capital accumulation and IRS, the higher values of employment, output, consumption, investment, and the real exchange rate, relative to the steady state, persist for some time. It is only after about four quarters, as growth in consumption of the domestic good becomes negative, that P eventually and slowly increases. At any point of time, the increase in P works to keep the domestic nominal interest rate approximately constant in face of the small negative consumption growth rates. A constant nominal interest rate is sufficient to ensure domestic money-market equilibrium. Meanwhile, previous P increases engineer the reductions in N / P that, each period, closely match declines in X as the economy returns to the steady state. These movements of P equal those of p since in the symmetric equilibrium P = p. The path 107
of the real exchange rate essentially reflects that of Cx. Therefore, not only does the real exchange rate slowly return to its original steady-state value but it also breaks away from e, which rises to its new and higher steady-state value.
3
Model evaluation
Some model predictions are consistent with empirical regularities. Particularly, the model captures the high volatility of nominal and real exchange rates relative to the volatility of price levels, the strong comovement between the rates of change of nominal and real exchange rates, and the persistency of real exchange-rate movements that characterize real world data. But, the model also has a number of predictions for key variables that sharply contrast with the facts.
3.1
Output
The model has strong implications for the magnitude of output responses to monetary shocks. It is difficult to precisely evaluate this implication since the model is calibrated so as to impose a value for the standard deviation of real output. However, some evaluation is possible by examining the impulse response analysis portrayed in Beaudry and Devereux's Figure 6a. This figure shows that a one-percentage-point increase in the domestic money stock contemporaneously causes a seven-percentage-point rise in domestic real output. An output response of this magnitude seems too big for two reasons. First, Sims' (1980) evidence for the U.S. economy over the period 1948-1978 shows that a one-percent money-stock innovation within the same period causes a 0.42-percent increase in real output. Second, in a simple cashin-advance model economy with a predetermined price level, a one-percent monetary innovation would simultaneously cause only a one-percent output increase.
3.2
Nominal interest rate
The model predicts that essentially no nominal interest-rate movements result from monetary shocks. This implication seems counterfactural, too. There is strong evidence documenting the liquidity effects on nominal interest rates exerted by changes in the money supply (for example, see Cochrane, 1989). 108
3.3
Real and nominal exchange rates
In the model, the standard deviation of the real exchange rate is less than one half of the standard deviation of output. The facts are different. Backus, Kehoe, and Kydland (1994) and Mendoza (1995) provide evidence that the standard deviation of the real exchange rate is greater than that of output for many countries, often by a factor of two or three. As mentioned above, the model's nominal and real exchange rates exhibit strong high-frequency covariation. In this regard the model mimics the empirical evidence. But this model feature is not so much a prediction as it is an assumption. That is, by assumption all prices are predetermined for one period and, therefore, nominal exchange-rate changes must entirely cause the real exchange-rate responses to contemporaneous shocks. Another empirical regulary characterizing nominal and real exchange rates is that their levels move very closely together (see Stockman, 1987). This fact suggests that the strong comovement between nominal and real exchange rates occurs at high, medium, and low frequencies. The impulse response model analysis, portrayed in Beaudry and Devereux's Figure 2a, shows the paths of the nominal and real exchange rate breaking apart just a few quarters after the monetary shock. Thus, it seems that the model is not consistent with the significant medium and low frequency comovement that is apparent in real world nominal and real exchange rates.
4
Conclusion
Beaudry and Devereux's idea that increasing returns to scale and sticky prices are key elements for explaining real exchange rates is interesting. But it is not convincing. Substantive issues concerning the justification of the nature and magnitude of increasing returns to scale would first need to be addressed. Also, it is difficult to accept the sticky-price assumption as a useful abstraction. The assumption that all goods prices in the world economy are sticky is not only an extreme one but also, by definition, it assumes the answer to one of the most puzzling aspects of real exchange-rate behavior: the high covariation between the rates of change of nominal and real exchange rates. Moreover, the fashion in which the assumptions of increasing returns to scale and stocky prices are combined seems to be at the heart of the counterfactual effects of monetary shocks. The assumption of sticky prices is the means of resolving the indeterminacy of equilibrium arising from increasing returns to scale. The counterfactual effects of monetary shocks include massive output and virtually no nominal interest-rate responses. The upshot is that the combination of increasing returns to scale and sticky prices of the type found in Beaudry and Devereux is unlikely to be important for promoting an understanding of real exchange rates. 109
References
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