Consumers’ preferences, number of firm dynamics and the factor shares evolution

1. Consumers’ preferences, number of firm dynamics and the factor shares evolution Alexander Osharin and Valery Verbus NRU HSE – Nizhny Novgorod

2. The motivation To investigate the capabilities of the extended two-factor ZKT model in explaining some observations concerning factor shares dynamics, markup movements and asymmetry of the business cycle.

3. Some papers on factor shares 1. Bentolila (2003): Explaining Movements in the Labor Share. 2. Jalava, Pohjola, Ripatti and Vilmunen (2005): Biased Technical Change and Capital-Labor Substitution in Finland, 1902-2003. 3. Матвеенко (2008):Ресурсы, институты, инновации и экономический рост: двойственный подход. 4. Ripatti , Vilmunen (2010): Declining labor share – Evidence of a change in the underlying production technology? 5. Tipper (2011): One for all? The capital-labor substitution elasticity in New Zealand. 6.Raurich, Sala, Sorolla (2011): Factor shares, the Price Markup, and the elasticity of Substitution between Capital and Labor.

4. Empirical evidence on factor shares dynamics Decline of labor share since the mid-1980s in most of the OECD countries.

5. Empirical evidence on labor share short and medium run movements (1)

6. Empirical evidence on labor share short and medium run movements (2)

7. Empirical evidence on labor share short and medium run movements (3)

8. Empirical evidence on labor share short and medium run movements (4)

9. Empirical evidence on labor share short and medium run movements (5)

10. The Labor Share and Real Wages in 12 OECD countries

11. Raurich, Sala, and Sorolla (2011) findings: 1. The elasticity of substitution between capital and labor is larger than one in Spain and smaller than one in the U.S. 2. In Spain the labor income share (LIS) has decreased while the ratio of capital to GDP has increased. 3. In contrast, both the ratio of capital to GDP and the LIS have decreased in the U.S., which implies an elasticity of substitution lower than one. 4. Consideration of the price markup drives the value of the elasticity of substitution away from one and, therefore, provides a further cause of rejection of the Cobb-Douglas (CD) specification. This result holds both for Spain and the U.S. but goes in opposite direction: it yields an upward bias in Spain and a downward bias in the U.S. 5. Price markup accounts for 63% of the LIS evolution in Spain and 57% in the US, whereas the elasticity of substitution explains, respectively, 27% and 39% of its variation. 6. Price markup time series in both countries is countercyclical.

12. Mark-ups and return to capital in Spain

13. Mark-ups and return to capital in the USA

14. How markups move, in response to what, and why, is however nearly terra incognita for macro. . . . We are a long way from having either a clear picture or convincing theories, and this is clearly an area where research is urgently needed. Blanchard (2008)

15. Markupsand firm entry and exit decisions literature Jaimovichz (2003): Firm Dynamics, Markup Variation and the Business Cycle. Jovanovic (2005): Asymmetric Cycles. Jaimovichz, Floetotto (2008): Firm dynamics, markup variations, and the business cycle. Floetotto, Jaimovichz, Pruitt (2009): Markup Variation and Endogenous Fluctuations in the Price of Investment Goods. Li, Mehkari (2009): Expectation Driven Firm Dynamics and Business Cycles. Nekarda, Ramey (2010): The Cyclical Behavior of the Price-Cost Markup. Cheremukhin, Tutino (2012): Asymmetric Firm Dynamics under Rational Inattention.

16. Empirical evidence on asymmetry of business cycle, markupsand firm entry and exit decisions Business cycle is asymmetric. The economy tends to alternate between long periods of slow expansion and short periods of sharp contraction. Markups lag the business cycle. Lagged markups are countercyclical. Firm exit is at list 30% more volatile than firm entry. Firm exit is strongly countercyclical and asymmetric. Firm entry is procyclical and symmetric.

17. Empirical evidence on firm entry and exit rates (Nekarda and Ramey, 2010)

18. Two-factor model of monopolistic competition Preferences of consumers are additively separable (as in ZKT) and utility maximization has the form: where is the demand of a consumer, is the variety price vector and is the individual expenditure, which is supposed to be constant, is the mass of varieties.

19. Goods market Each firm produces a unique variety and solves the following profit maximization problem: where is the output of a firm, and are the marginal and constant production cost, which are identical across firms.

20. Goods market SR equilibrium Since all firms are identical, there exist a continuum of the symmetric short-run equilibriums with where is the relative love for variety, and are the equilibrium levels of price and output of a firm.

21. Capital and labor markets To get an equilibrium on capital and labor markets each firm solves the following profit maximization problems: where and are the nominal wage and interest rate of capital, and are capital and employment of a firm.

22. Capital and labor market SR equilibrium SR - equilibrium profit as a function of labor and capital cost: where is a markup of a firm, is a production function of a firm.

23. Capital and labor shares (1) For the Cobb-Douglas (CD) production function the capital and labor shares equal to Where is a constant.

24. Capital and labor shares (2) For the CES production function where is a parameter, related with capital- labor substitution by , , the capital and labor shares equal to where is a constant.

25. Substitution between capital and labor • When is negative, , then • and • In this case capital and labor are technical complimentsand labor share will increase with increasing relation. • When is positive, , then and • In this case capital and labor are technical substitutes andlabor share will decrease with increasing relation.

26. Constant absolute risk aversion (CARA) utility function The following constant absolute risk aversion (CARA) utility function has the relative love for variety (RLV) with . The more is the more risk aversive is the consumers.

27. SR equilibrium price and mark-up as a function of the mass of the firms Price level for CARA utility function and mark-up in the SR-equilibrium are inversely dependent on the mass of the firms: which corresponds to the pro-competitive behavior of the equilibrium price.

28. Mark-ups counter-cyclical behavior (1) Since real aggregate income equals to and , where is the total nominal expenditure level (assumed to be constant in the model), we have It means that mark-ups are countercyclical (at list towards the shocks changing the number of the firms). The key question for us: whether the real GDP is increased or decreased in the period when labor share decreased?

29. Mark-ups counter-cyclical behavior (2) Let and is shocked, and is increased, then for mark-ups while for the total real income It means that mark-up is countercyclical.

30. De-trended GDP for the USA (1950-2005)

31. De-trended GDP for France (1950-2005)

32. De-trended GDP for Germany (1970-2005)

33. De-trended GDP for the United Kingdom (1950-2005)

34. The key question for us: what is going with the number of firms ? If the number of monopolistically competitive firms on the market increase, then the mark-ups fall and labor income share increases. If the number of monopolistically competitive firms on the market decrease, then the mark-ups rise and labor income share decreases.

35. LR equilibrium price and mark-up as functions of the exogenous parameters Price level for CARA utility function in the LR equilibrium Mark-up level for CARA utility function in the LR equilibrium

36. Profit as a function of the number of firms

37. Profit as a function of the number of firms Since (as it is stated in ZKT), theright hand side sign depends on the signof the RLV derivative

38. Profit as a function of the number of firms In the price-decreasing (pro-competitive) case: In the price-increasing (anti-competitive) case: The sign of the initial value of the profit:

39. Profit as a function of the number of firms in the pro-competitive case

41. Thank you for rational attention!