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Understanding how price responds to costs and production
Carnegie-Rochester Conference Series on Public Policy 52 (2000) 79-85 North-Holland www.elsevier.nYlocate/econbase
Understanding how price responds to costs and production A comment Susanto Basu University of Michigan and National Bureau of Economic Research
The Bils/Chang paper contributes to understanding an issue of first-order i m p o r t a n c e - - w h e n a shock to supply or demand in a market is cushioned by the price system and has relatively little effect on output, and when such a shock affects mostly output and leaves prices basically unchanged. Studies of business cycles have not located significant sources of large, exogenous shocks that cause most output fluctuations. Thus, business-cycle theory has focused on developing amplification and propagation mechanisms whereby small shocks can have large output effects (and thus small price effects). However, such a program runs into the problem that not all shocks have small effects on prices, even in the short run. For example, the oil price shocks of the 1970s were associated with large increases in inflation that were more or less contemporary. So business-cycle theorists need to go beyond models in which all small shocks have small effects on prices. Instead, they need to build models where only some shocks have large output effects, while others have large price effects. T h a t is, their amplification and propagation mechanisms need to be strongly "shock-dependent." Bils and Chang are attempting to contribute to this research program. I disagree, however, with an interpretation they advance for this research. In their introduction, Bils and Chang argue that if some shocks can be shown to have large price effects, it must be the case that costs of nominal price adjustment are not important for understanding business cycles. But it has been known for a long time that plausible nominal costs of price adjustment can explain sizable output fluctuations (e.g., in response to monetary policy shocks) only if powerful mechanisms amplify and propagate the shocks. 1 1Ball and Romer (1990). In the New Keynesian literature, these mechanisms are typi0167-2231/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S0167-2231(00)00017-8
However, since Bils and Chang want to argue that these mechanisms do not operate in response to some shocks, what they really mean is that nominal rigidities by themselves cannot halt quick price adjustment in response to all shocks. But this does not mean that nominal rigidities are always unimportant-they will matter for the shocks that do induce amplification and propagation. The first component of the paper attempts to establish that the price response does indeed depend on the source of the shock. Bils and Chang then present two firm-level pricing models that try to reproduce the facts they find in their empirical investigation. The models are interesting, whether or not they can explain the empirical findings. I discuss them after investigating the robustness of the empirical results.
A n alternative derivation Here I present a different way of deriving an equation that is very similar to the Bils-Chang estimating equation. This method emphasizes that the regression they run is very close to an identity. Since the national income accounts require that national income be the same whether computed from the product side or from the income side, it must be true that for a firm or industry P Y - PMM + W N + PKK,
(1)
as long as PK is defined as nominal payments to capital divided by K. Now take logs and differentiate:
+ t - s ,(r M +
+
+
+ KCtK + k),
(2)
where, e.g., PMM PY (Note that this is the quick way to prove that for any consistent system of national accounts, the standard primal Solow residual must identically equal the dual cost-based Solow residual-just group the quantity terms on one side of equation (2) and the price terms on the other.) Rearranging, we find: 8M Z - -
~
(SM?~'~ -J#-8 N ~ "~- 8 K k -- y ) "~- 8 M p M "~- 8N~l) -~ 8 K p K
=
- T $ ' P + 8 M P M "~" 8N~] + 8 K p K .
(3)
cally termed "real rigidities." Kimball (1995) shows that the Ball-Romer result holds in a dynamic setting.
80
So far this is only accounting, but note that the resulting equation is already very close to equation (6) in the paper. Now assume PK comprises both the required return to capital, R, and the rate of pure economic profit (if any): PK = R + H. Then we can split the return to capital into two parts: Ar =_ - T . P P + 8Mp M ~- 8N ~ + 8R~" "~- 8K PK"
(4)
Note that I have not written the equation in terms of the log change in profit. Since profit can be zero or negative, its log change may not be well-defined. Now for the first time I introduce economics into the derivation by assuming that the entity in question is a cost-minimizing firm facing input prices W, PM, and R. Then, using the Bils and Chang separability and CES assumptions, we can substitute out for R: Ar = - T F P + SM~M + SN~V+ SR[~ + l(fia -- ~)] ÷ SK'pK
Ar - T F P + SM~M + (SN "Jr 8R)~l) ÷
(~2 -- k) ÷ 8 K PK"
Comparing this equation to (6) in the paper shows that log price change is related to the same four observed variables, but with somewhat different coefficients. As the derivation makes clear, the one substantive assumption is that the data describe the behavior of a cost-minimizing firm with a separable value-added production function. Parenthetically, I am somewhat skeptical of the exact form of equation (6) in the paper. Since that equation should hold for all #, it must hold in the case of perfect competition, where # = 1 and/2 -- 0. But then their equation (6) holds without error (assuming no measurement error, so e = 0). However, in my equation (5) the change in the profit rate appears in the error term even with perfect competition. (For example, changes in output will cause variations in pure profits in a competitive model with an exogenously fixed number of firms producing with diminishing returns to scale.) Since my derivation is much more general (almost all of it comes from differentiating an identity), I am inclined to believe that equation (6) in the paper must be due to additional assumptions which are not clearly spelled out.
Discussion of empirical results The key to understanding the empirical part of the Bils-Chang paper is to note that it is a model of omitted variable bias---nonstructural estimation 81
of the extent to which the omitted variable (change in pure profit) changes the coefficient on the four included right-hand-side variables. If the change in profit is negatively correlated with changes in wages but not with changes in materials prices (for example), it indicates that the firm does not pass through wage changes to prices but does pass through materials cost changes to prices (holding demand constant). A reason to be wary of the empirical results in the paper is that they are likely to be extremely sensitive to errors in variables. In industry data, many of the outputs of the industry are also its inputs-that is, the outputs of many firms are inputs of other firms within the same industry. This fact implies that the industry's output price is also approximately its input price. Thus, as we increase the variance of the noise relative to that of the signal in all the variables in the Bils and Chang regression, the coefficient of the 15M variable is biased towards 1 while all the other coefficients are biased towards zero. (Another way to put it is that even with measurement error, PM retains its ability to predict 15, since they share the same measurement error, but all the other variables lose that ability.) I confirmed that 15and 15i are highly correlated by examining two-digit manufacturing data from the data set assembled by Jorgenson et al. (1987); in these data the two price series have an average correlation (across industries) of 0.96. This reflection is interesting for two reasons. First, the predicted results are close to what Bils and Chang find. Their Table 1 shows that the coefficient on the materials price is robustly close to 1, while the other coefficients are always smaller than their expected values. Second, the four-digit ASM data they use is subject to large measurement errors (see, Norrbin, 1993). Bils and Chang make intelligent choices to address some of the known problems, such as the lack of nonproduction-worker hours, but these cannot make up for fundamental flaws in data construction. In particular, I am concerned that their industry data do not necessarily fit the accounting identity, my equation (1), especially after their imputations of nonproduction-worker hours. 2 Since the estimating equation is so close to an identity, errors in data construction are likely to cause large changes in the estimated coefficients. This point is reinforced by the fact that the correlation between I5 and iSM is SO large. In this case, the regression is likely to "fixate" on the useful variable iSM and mostly ignore the others. In order to assess the likely importance of these data construction issues, I run the Bils and Chang basic regression, equation (6), using the Jorgenson data set, which is constructed to be as conformable to economic theory as 2An easy diagnostic for this problem is to estimate equation (3). If the data axe constructed to obey the accounting identity (1), then (3) should fit perfectly.
82
the available data allow. I find (standard errors in parentheses): 15 =
-0.76TFP
(.011)
-b
1.07SM15M "b 0.87(SN + sR)lb
(.012)
(.022)
1.02SR(~ --/¢).
(.051)
These results are directly comparable to the two-digit results in Column 4 of Table 1 in the paper. I find coefficients on TFP and capital's rental rate that are 50 percent larger, closer to their predicted values. The coefficients on the wage and on the materials price are also closer to their predicted value of 1 than in the paper. This regression gives only mild support to the paper's contention that changes in marginal cost do not affect price for given factor prices. In particular, the results are quite consistent with a standard Cobb-Douglas production function for value added (a = 1). This result is important, because the unrealistically high estimates of a in Table 1 and Tables 5-6 motivate Bils and Chang to develop their second model of countercyclical markups, but that model generates no markup variation if a = 1. I also find that instrumenting the right-hand-side variables with standard business-cycle instruments often increases the coefficients even more, especially those on TFP and the wage change variables, as one would predict if the major problem with the regression were errors in variables.
D i s c u s s i o n o f t h e theoretical m o d e l s
My results indicate that there is not much direct empirical motivation to develop the limit-pricing and marketing models in the paper. However, from the standpoint of developing more propagation mechanisms for the macroeconomist's toolbox, new models of countercyclical markups are always welcome. The marketing model is particularly interesting and innovative. However, I suspect that the ability of the models to explain what Bils and Chang believe to be the empirical results depends importantly on an unrealistic element in their calibration. Note from equation (5) that, absent measurement error, the only way to explain a coefficient different from 1 on all four right-hand-side variables is to have large absolute changes in pure profits that are correlated with changes in the included variables. Furthermore, the omitted variable is multiplied by capital's revenue share. Unrealistically, Bils and Chang simulate their models assuming a markup of 1.5. 3 This has two effects. First, it leads to large absolute variations in pure profit in response 3Such a high markup implies either that returns to scale must be about equally large or that the rate of pure profit must be very high. Basu and Fernald (1997) find no evidence that either is true. Their evidence suggests that the maximum plausible markup on value added is about 1.1 in an average industry. 83
to output fluctuations. Second, it increases capital's revenue share to an unrealistic level. For their assumed value of the cost share of capital of 1/3, the revenue share is about 55 percent These two elements in conjunction imply a large omitted variable bias that might explain the results that Bils and Chang find. However, using better data I find empirical results that are much closer to their predicted values. Thus such unrealisticcalibration is not needed to explain the sort of results I find. A n open question is whether the interesting countercyclicality of the markup in the two models is also eliminated if one assumes a more realisticlevel of the markup. Equation (29) in the paper appears to indicate that this is not the case in the simple two-firm marketing model. If that result is generally true, then Bils and Chang have contributed a valuable model of cyclical markup variation.
84
References
Ball, L. and Romer, D., (1990). Real Rigidities and the Non-Neutrality of Money. Review of Economic Studies, 57: 183-203. Basu, S. and Fernald, J. G., (1997). Returns to Scale in U. S. Production: Estimates and Implications. Journal of Political Economy, 105: 249-83. Jorgenson, D. W., Gollop, F., and Fraumeni, B., (1987). Productivity and U.S. Economic Growth. Cambridge: Harvard University Press. Kimball, M. S., (1995). The Quantitative Analytics of the Basic Neomonetarist Model. Journal of Money, Credit, and Banking, 27: 1241- 77. Norrbin, S. C., (1993). The Relation between Price and Marginal Cost in U.S. Industry: A Contradiction. Journal of Political Economy, 101:1149-64.
85
Understanding how price responds to costs and production A comment Susanto Basu University of Michigan and National Bureau of Economic Research
The Bils/Chang paper contributes to understanding an issue of first-order i m p o r t a n c e - - w h e n a shock to supply or demand in a market is cushioned by the price system and has relatively little effect on output, and when such a shock affects mostly output and leaves prices basically unchanged. Studies of business cycles have not located significant sources of large, exogenous shocks that cause most output fluctuations. Thus, business-cycle theory has focused on developing amplification and propagation mechanisms whereby small shocks can have large output effects (and thus small price effects). However, such a program runs into the problem that not all shocks have small effects on prices, even in the short run. For example, the oil price shocks of the 1970s were associated with large increases in inflation that were more or less contemporary. So business-cycle theorists need to go beyond models in which all small shocks have small effects on prices. Instead, they need to build models where only some shocks have large output effects, while others have large price effects. T h a t is, their amplification and propagation mechanisms need to be strongly "shock-dependent." Bils and Chang are attempting to contribute to this research program. I disagree, however, with an interpretation they advance for this research. In their introduction, Bils and Chang argue that if some shocks can be shown to have large price effects, it must be the case that costs of nominal price adjustment are not important for understanding business cycles. But it has been known for a long time that plausible nominal costs of price adjustment can explain sizable output fluctuations (e.g., in response to monetary policy shocks) only if powerful mechanisms amplify and propagate the shocks. 1 1Ball and Romer (1990). In the New Keynesian literature, these mechanisms are typi0167-2231/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S0167-2231(00)00017-8
However, since Bils and Chang want to argue that these mechanisms do not operate in response to some shocks, what they really mean is that nominal rigidities by themselves cannot halt quick price adjustment in response to all shocks. But this does not mean that nominal rigidities are always unimportant-they will matter for the shocks that do induce amplification and propagation. The first component of the paper attempts to establish that the price response does indeed depend on the source of the shock. Bils and Chang then present two firm-level pricing models that try to reproduce the facts they find in their empirical investigation. The models are interesting, whether or not they can explain the empirical findings. I discuss them after investigating the robustness of the empirical results.
A n alternative derivation Here I present a different way of deriving an equation that is very similar to the Bils-Chang estimating equation. This method emphasizes that the regression they run is very close to an identity. Since the national income accounts require that national income be the same whether computed from the product side or from the income side, it must be true that for a firm or industry P Y - PMM + W N + PKK,
(1)
as long as PK is defined as nominal payments to capital divided by K. Now take logs and differentiate:
+ t - s ,(r M +
+
+
+ KCtK + k),
(2)
where, e.g., PMM PY (Note that this is the quick way to prove that for any consistent system of national accounts, the standard primal Solow residual must identically equal the dual cost-based Solow residual-just group the quantity terms on one side of equation (2) and the price terms on the other.) Rearranging, we find: 8M Z - -
~
(SM?~'~ -J#-8 N ~ "~- 8 K k -- y ) "~- 8 M p M "~- 8N~l) -~ 8 K p K
=
- T $ ' P + 8 M P M "~" 8N~] + 8 K p K .
(3)
cally termed "real rigidities." Kimball (1995) shows that the Ball-Romer result holds in a dynamic setting.
80
So far this is only accounting, but note that the resulting equation is already very close to equation (6) in the paper. Now assume PK comprises both the required return to capital, R, and the rate of pure economic profit (if any): PK = R + H. Then we can split the return to capital into two parts: Ar =_ - T . P P + 8Mp M ~- 8N ~ + 8R~" "~- 8K PK"
(4)
Note that I have not written the equation in terms of the log change in profit. Since profit can be zero or negative, its log change may not be well-defined. Now for the first time I introduce economics into the derivation by assuming that the entity in question is a cost-minimizing firm facing input prices W, PM, and R. Then, using the Bils and Chang separability and CES assumptions, we can substitute out for R: Ar = - T F P + SM~M + SN~V+ SR[~ + l(fia -- ~)] ÷ SK'pK
Ar - T F P + SM~M + (SN "Jr 8R)~l) ÷
(~2 -- k) ÷ 8 K PK"
Comparing this equation to (6) in the paper shows that log price change is related to the same four observed variables, but with somewhat different coefficients. As the derivation makes clear, the one substantive assumption is that the data describe the behavior of a cost-minimizing firm with a separable value-added production function. Parenthetically, I am somewhat skeptical of the exact form of equation (6) in the paper. Since that equation should hold for all #, it must hold in the case of perfect competition, where # = 1 and/2 -- 0. But then their equation (6) holds without error (assuming no measurement error, so e = 0). However, in my equation (5) the change in the profit rate appears in the error term even with perfect competition. (For example, changes in output will cause variations in pure profits in a competitive model with an exogenously fixed number of firms producing with diminishing returns to scale.) Since my derivation is much more general (almost all of it comes from differentiating an identity), I am inclined to believe that equation (6) in the paper must be due to additional assumptions which are not clearly spelled out.
Discussion of empirical results The key to understanding the empirical part of the Bils-Chang paper is to note that it is a model of omitted variable bias---nonstructural estimation 81
of the extent to which the omitted variable (change in pure profit) changes the coefficient on the four included right-hand-side variables. If the change in profit is negatively correlated with changes in wages but not with changes in materials prices (for example), it indicates that the firm does not pass through wage changes to prices but does pass through materials cost changes to prices (holding demand constant). A reason to be wary of the empirical results in the paper is that they are likely to be extremely sensitive to errors in variables. In industry data, many of the outputs of the industry are also its inputs-that is, the outputs of many firms are inputs of other firms within the same industry. This fact implies that the industry's output price is also approximately its input price. Thus, as we increase the variance of the noise relative to that of the signal in all the variables in the Bils and Chang regression, the coefficient of the 15M variable is biased towards 1 while all the other coefficients are biased towards zero. (Another way to put it is that even with measurement error, PM retains its ability to predict 15, since they share the same measurement error, but all the other variables lose that ability.) I confirmed that 15and 15i are highly correlated by examining two-digit manufacturing data from the data set assembled by Jorgenson et al. (1987); in these data the two price series have an average correlation (across industries) of 0.96. This reflection is interesting for two reasons. First, the predicted results are close to what Bils and Chang find. Their Table 1 shows that the coefficient on the materials price is robustly close to 1, while the other coefficients are always smaller than their expected values. Second, the four-digit ASM data they use is subject to large measurement errors (see, Norrbin, 1993). Bils and Chang make intelligent choices to address some of the known problems, such as the lack of nonproduction-worker hours, but these cannot make up for fundamental flaws in data construction. In particular, I am concerned that their industry data do not necessarily fit the accounting identity, my equation (1), especially after their imputations of nonproduction-worker hours. 2 Since the estimating equation is so close to an identity, errors in data construction are likely to cause large changes in the estimated coefficients. This point is reinforced by the fact that the correlation between I5 and iSM is SO large. In this case, the regression is likely to "fixate" on the useful variable iSM and mostly ignore the others. In order to assess the likely importance of these data construction issues, I run the Bils and Chang basic regression, equation (6), using the Jorgenson data set, which is constructed to be as conformable to economic theory as 2An easy diagnostic for this problem is to estimate equation (3). If the data axe constructed to obey the accounting identity (1), then (3) should fit perfectly.
82
the available data allow. I find (standard errors in parentheses): 15 =
-0.76TFP
(.011)
-b
1.07SM15M "b 0.87(SN + sR)lb
(.012)
(.022)
1.02SR(~ --/¢).
(.051)
These results are directly comparable to the two-digit results in Column 4 of Table 1 in the paper. I find coefficients on TFP and capital's rental rate that are 50 percent larger, closer to their predicted values. The coefficients on the wage and on the materials price are also closer to their predicted value of 1 than in the paper. This regression gives only mild support to the paper's contention that changes in marginal cost do not affect price for given factor prices. In particular, the results are quite consistent with a standard Cobb-Douglas production function for value added (a = 1). This result is important, because the unrealistically high estimates of a in Table 1 and Tables 5-6 motivate Bils and Chang to develop their second model of countercyclical markups, but that model generates no markup variation if a = 1. I also find that instrumenting the right-hand-side variables with standard business-cycle instruments often increases the coefficients even more, especially those on TFP and the wage change variables, as one would predict if the major problem with the regression were errors in variables.
D i s c u s s i o n o f t h e theoretical m o d e l s
My results indicate that there is not much direct empirical motivation to develop the limit-pricing and marketing models in the paper. However, from the standpoint of developing more propagation mechanisms for the macroeconomist's toolbox, new models of countercyclical markups are always welcome. The marketing model is particularly interesting and innovative. However, I suspect that the ability of the models to explain what Bils and Chang believe to be the empirical results depends importantly on an unrealistic element in their calibration. Note from equation (5) that, absent measurement error, the only way to explain a coefficient different from 1 on all four right-hand-side variables is to have large absolute changes in pure profits that are correlated with changes in the included variables. Furthermore, the omitted variable is multiplied by capital's revenue share. Unrealistically, Bils and Chang simulate their models assuming a markup of 1.5. 3 This has two effects. First, it leads to large absolute variations in pure profit in response 3Such a high markup implies either that returns to scale must be about equally large or that the rate of pure profit must be very high. Basu and Fernald (1997) find no evidence that either is true. Their evidence suggests that the maximum plausible markup on value added is about 1.1 in an average industry. 83
to output fluctuations. Second, it increases capital's revenue share to an unrealistic level. For their assumed value of the cost share of capital of 1/3, the revenue share is about 55 percent These two elements in conjunction imply a large omitted variable bias that might explain the results that Bils and Chang find. However, using better data I find empirical results that are much closer to their predicted values. Thus such unrealisticcalibration is not needed to explain the sort of results I find. A n open question is whether the interesting countercyclicality of the markup in the two models is also eliminated if one assumes a more realisticlevel of the markup. Equation (29) in the paper appears to indicate that this is not the case in the simple two-firm marketing model. If that result is generally true, then Bils and Chang have contributed a valuable model of cyclical markup variation.
84
References
Ball, L. and Romer, D., (1990). Real Rigidities and the Non-Neutrality of Money. Review of Economic Studies, 57: 183-203. Basu, S. and Fernald, J. G., (1997). Returns to Scale in U. S. Production: Estimates and Implications. Journal of Political Economy, 105: 249-83. Jorgenson, D. W., Gollop, F., and Fraumeni, B., (1987). Productivity and U.S. Economic Growth. Cambridge: Harvard University Press. Kimball, M. S., (1995). The Quantitative Analytics of the Basic Neomonetarist Model. Journal of Money, Credit, and Banking, 27: 1241- 77. Norrbin, S. C., (1993). The Relation between Price and Marginal Cost in U.S. Industry: A Contradiction. Journal of Political Economy, 101:1149-64.
85