The Cyclical Behavior of the Price-Cost Markup

1. The Cyclical Behaviorof the Price-Cost Markup By Christopher J. Nekarda and Valerie A. Ramey

2. Role of Markups in New Keynesian Models • The key transmission mechanism in the NK model is sticky prices and variable markups. • A positive demand shock (e.g. monetary or government spending) leads output and MC to increase. Prices don’t adjust, so the markup falls. • A positive technology shock lowers MC and raises output. Prices don’t adjust, so the markup rises.

3. A Contractionary Monetary Shock in the NK Model • A contractionary monetary shock decreases demand because prices don’t fall. • Nominal MC falls with output. Thus, real MC falls. • Since the markup is the inverse of real MC, the markup is countercyclical. From Smets-Wouters (2003). “MC” is real marginal cost.

4. Effects of Government Spending Neoclassical: ↑G → ↑L → ↓ MPL → ↓ W/P New Keynesian ↑G → ↑L, ↓ MPLand ↓ μ→ ↑ W/P (μ is the markup)

5. Findings of this paper • Markups are procyclical • observed both in aggregate and industry data • Aggregate Evidence • Markups trough during recessions and peak in the middle of expansions • Markups are procyclical in response to monetary shocks • Not sensitive to average-marginal cost distinction • Industry Evidence • Markups are procyclical in response to government-spending induced increases in shipments in detailed industries

6. Outline • Theoretical framework for measuring markups • Aggregate Evidence • Data • Creation of wage factor • Assessment of unconditional cyclicality • Monetary VARs • Industry Evidence • Data • Regressions

7. Theoretical Framework Theoretical Markup: • Key points for measuring marginal cost MC: • A cost-minimizing firm should equalize the marginal cost of raising output across all possible margins. • 2. Inputs with adjustment costs have more complicated marginal cost structures. • 3. Thus, we focus on the input that the empirical evidence suggests has negligible adjustment costs: average hours per worker, h.

8. Cost Minimization Minimize h = average hours per worker N = number of workers Ω(Ws,h) = wage function Y = output A = labor-augmenting technological progress subject to

9. Marginal Cost The standard procedure is to use the average wage as the marginal cost of an extra hour. Bils (1987) observed that because of overtime hours, the average wage per hour differs from the marginal wage per hour. The problem is that we observe the average wage, not the marginal wage.

10. Deriving Marginal Hours Costs:The Wage Function Consider the following wage function: Suppose:

11. Linking Average and Marginal Wages Marginal cost of raising average hours per worker (Bils’ “marginal wage”) Thus, the relationship between average wages and marginal wages is:

12. Thus, marginal cost becomes: WA is available data. I will discuss below how we measure the factor multiplying WA. But, first we need to derive a specification for marginal productivity in the denominator.

13. Measuring Productivity Cobb-Douglas CES σ is the elasticity of substitution between capital and labor

14. Measuring Markups Average Markup, Cobb-Douglas Marginal Markup, Cobb-Douglas Marginal Markup, CES s = labor share =

15. Aggregate Analysis • We first construct the marginal-average wage adjustment factor. • We then combine that variable with standard government data to derive series on markups. • The only other complicating factor is the CES specification, which requires a measure of technology.

16. Measuring v/h • There is readily available CES data on average hours and overtime hours for manufacturing. • But manufacturing was only 26 percent of GDP at its post WWII peak and is now only 11 percent. • Also, Deleire et al (2002) show that the CES overcounts overtime hours – implies that those who work overtime hours work 25 hours per week. • We construct new series on average hours and overtime hours for the entire civilian economy using a previously unexploited data source.

17. Source of hours data for entire economy • The BLS Employment and Earnings publication provides data on persons at work and average hours of persons at work (Cociuba, Prescott, Ueberfeldt (2009)) • E & E also reports persons at work by ranges of hours of work, such as 35-39 hours per week, etc. • We constructed series on the number of hours worked in excess of 40 hours per week. We call those “overtime hours,” although they do not necessarily command a premium.

18. Average Weekly Hours, Aggregate EconomyCPS

19. Average Weekly Hours, ManufacturingCES

20. Estimating Use difference approximation Bils allowed ηt to depend on cubics in ht and time trends. We determined that a state-space model was best for estimating the time-varying coefficient. Thus, we estimate the equation above along with the transition equation:

21. Estimated dv/dh

22. Overtime Premium, ρ • Statutory overtime premium is 50%. • Mitigating factors: • Trejo (1991), Hamermesh (2006) – effective rate is around 25% • CES overtime hours for manufacturing are defined as those that command a premium. Our aggregate economy hours are simply hours worked above 40. According to May CPS, between 25% and 35% of worker who work more than 40 hours per week actually receive overtime pay.

23. Estimated

24. Aggregate Average Markups

25. Marginal Markups, Aggregate Economy

26. Marginal Markups, Manufacturing

27. Cyclicality of Markups Correlation of HP filtered components with GDP

28. Cyclicality of Markups Dynamic Correl. of HP filtered components with GDP

29. CES Production Function • Requires estimate of technology A. • We use 2 approaches 1. Bivariate SVAR 2. HP filter – A is the HP trend • Correlation of markup with cyclical component of GDP (premium = 25%) SVAR: 0.040 HP: 0.424

30. Implications of Procyclical Markups for NK Models • As discussed above, the NK model predicts procyclical markups in response to technology shocks, but countercyclical markups in response to demand shocks. • Thus, unconditional countercyclical markups are potentially consistent with the NK model if technology shocks are the main cyclical force. • Thus, it is important to look at the cyclicality of the markup conditional on demand shocks in order to test the NK model.

31. Effects of Monetary Shocks on Markups • We estimate a standard VAR on quarterly data from 1960:III – 2008:IV. • Variables: log real GDP, log commodity prices, log GDP deflator, log markup, federal funds rate. • A shock to the federal funds rate, ordered last, is the monetary policy shock.

32. Effect of a Contractionary Monetary Shock

33. Relation to the New Keynesian Phillips’ Curve Literature Xt = output gap mc = real marginal cost = labor share = 1/markup The reason that the output gap enters with the wrong sign but mc enters with the right sign is that mc and x are negatively correlated. That means the markup and the output gap are positively correlated.

34. Relation to Rotemberg and Woodford (1999) Recall that labor share is the inverse of the average markup. Their graph implies a procyclical markup.

35. Relationship to Bils (1987) Our adjustments are an extension of Bils’ framework. Why does he conclude that markups are countercyclical? The key is the details of implementation

36. Re-estimation of Bils (1987)All specifications use 2-digit manufacturing industry data

37. Relation to the Literature • Inventory-Sales Ratios

38. Why We Also Do an Industry Analysis • It is always useful to see whether aggregate results hold at a more disaggregated level. • We can construct a highly relevant demand instrument • We can construct markups using gross output. Basu and Fernald argue value added is not a natural measure of output, and that it only makes sense when markups are constant at unity.

39. Data Construction • NBER-CES Manufacturing Industry Database Annual data from 1958-1996 on 4-digit SIC manufacturing industries Data on hours, employment, payrolls, shipments, capital • Benchmark Input-Output Tables that use SIC codes 1963, 1967 1972, 1977, 1982, 1987, 1992 Traces interindustry linkages, including final shipments to the government

41. Data Construction (cont.) • Merging and matching industries yields 272 4-digit industries • Although only the benchmark years are available, their timing is very fortuitous – they correspond to peaks and troughs of military spending • Our instrument:

42. Construction of Wage Conversion Factors • The NBER database contains data on total hours of production workers and the number of production workers employed. • From this we construct average hours per worker. • We use estimates of the relationship between overtime hours and average hours in CES 2-digit data to construct these for the associated 4-digit data.

43. Estimated equation Let μ = ln(Markup), s = labor share Average Markup Marginal Markup Estimating Equation

44. First-Stage Regressions using Government Demand Number of observations = 1,631 R-squared = 0.495 F-statistic on Δ5GY = 239.7

45. Regression of Markup on Gross Shipments (Coefficient on Gross Shipments) Specifications with industry and time fixed effects.

46. Regression of Markup on Value Added (Coefficient on Value Added) Specifications with industry and time fixed effects.

47. Robustness • Concern about technological change • We tried excluding computer industries, using only direct government demand, and using only lagged Y in the denominator of the demand instrument. • All of the coefficient estimates were similar.

48. Conclusions • We find no evidence of countercyclical markups, for the entire economy, for aggregate manufacturing, or for detailed industries. • Our results are robust to adjustments of average wages to marginal wages. • Our results hold unconditionally as well as conditional on demand shocks. • More research is needed to see whether basic mechanism of the New Keynesian model actually holds.