Stock Market Valuation in a Dynamic Monopolistically Competitive Economy

1. Stock Market Valuation in a Dynamic Monopolistically Competitive Economy Gabriel Talmain University of Glasgow

2. Motivation • Stock market rises with no corresponding change on the productivity side, • Nikkei early 90’s, • US stock market 1998-2000. • Talk about “new economy”: • future gains in productivity justify immediate increase in the valuation of firms. • It is clear that “good news” for a corporation makes its shares go up well before its profits increase. • Is this possible also at the aggregate level?

3. Two main approaches to valuation of the stock market: the Lucas asset pricing model and the one based on Tobin's q. • In Lucas asset pricing model, the fruit tree paradigm, e.g. Aiyagari and Gertler (RED 1999) or Greenwood and Jovanovic (AER 1999) or Hobjin and Jovanovic (AER 2001), the stream of earnings on the asset is exogenous. • In Tobin's q approach, e.g. Gilchrist and Leahy (JME 2002) or Danthine and Donaldson (RES 2002), the value of a firm is the present value of its installed capital.

4. Comparison • Tobin's q approach allows for aggregate economic conditions, such as the strength of the aggregate demand and the cost of the factors of production, to feed back in the earnings of the individual firm. • The fruit tree model captures the flavour of intangible assets which bear fruits beyond the corporation' investment in machinery, bricks and mortar.

5. Capturing both aspects • One would really want a model which includes the general equilibrium features of the Tobin's q approach, and which can spell out how each firm's competitiveness (the fruit bearing quality of the tree) translates into valuation. • This paper will concentrate on a firm's monopoly position as the source of its market value. • If a firm's monopoly profits were independent of all other variables in the economy, our model would reduce to the Lucas asset pricing model. • By letting general equilibrium determine these profits, our model also captures the feed-back from the aggregate economy onto the individual firm, one of the nice features of Tobin's q theory. • In addition, our model will feature heterogeneous and non-symmetric firms and we can derive a closed form solution for its equilibrium. • The heterogeneity will enable us to contrast the effect on the stock market of an anticipated increase of productivity at the aggregate level vs at the individual or sectorial level.

6. differentiated input firms M.C. Final good industry P.C. Firm 1 Ct kn,t,ln, t CES aggregation Kt qn,t Yt Firm n Kt+1 L Firm N All income returns to HH as wage, rental or profits; asset markets open regulated by wt, it generates n, t

7. Assumptions • Intermediate input firms (IIF) • heterogeneous, • monopolistic competitive on their supply market: the final good industry, • compete on the labour and physical capital markets, • distribute all profits as dividends (Modigliani-Miller environment), • shares traded on the stock market. • Households • homogenous, • supply labour inelastically to IIF, • expected utility maximisers, • CRAA felicity function, one argument: consumption of final good, • own all physical capital, rent it out to IIF, • own and trade all the shares of stock.

8. Final good industry • perfectly competitive, representative firm, • produce the final good which is used either for immediate consumption (perishable and homogenous commodity) or for capital in the next period, • 100% rate of depreciation of capital.

9. Equilibrium being considered • given the initial endowment of physical capital and distribution of share across households, • a set of intertemporal prices must: • temporary equilibrium: clear all markets in every period, • rational equilibrium: price realisations validate the households believes, • fundamental equilibrium: the price of a stock of share equates the value of the firm to the discounted value of the stream of dividends (in the metric induced by the utility of the households), • all agents are at an optimum:

10. households are maximising their intertemporal utility, • all firms, IIF and final good industry, are maximising profits (face a static problem), • households want to hold 100% of the stocks of shares. • Households’ equilibrium allocation is symmetric.

11. Increase in productivity and the stock market • instantaneous increases in productivity: • output increases, • in this framework, factor shares remain constant, • hence, stock market increase proportional to the increase in productivity. • anticipated future gains in productivity: • during 1998-2000 years, talk about a “new economy”: stock market was supposed to be reacting to future gains in productivity.

12. Anticipated future gains in productivity • Anticipated gains in sectorial or individual productivity: • the stocks of the firms expected to experience the gains do increase in value. • Anticipated gains in aggregate productivity: • no immediate effect on the values of shares, • at the time of the gain, shares’ value increase is proportional to the productivity gains.

13. Intuition • Aggregate profit share is a fixed proportion of the aggregate output, same for the share of rent; • the rate of return on physical capital and on the stock market portfolio are collinear: the interest rate is equal to the rate of return on the stock market portfolio; • the anticipated future increase in aggregate productivity will lift the forward interest rate for the period in question, but by how much?

14. Since the price of capital is fixed by the supply side (equal to the price of the final good), the forward rate of interest must leave today’s value of physical capital unchanged; • since the aggregate stock market is an asset collinear to physical capital, the increase in the forward rate leaves the value of the stock market unchanged.

15. Possible explanations for increase in stock market in response to anticipated future factors: • break in our assumptions, • this includes a bubble in stock market prices. • The share of GDP going to monopoly profits is anticipated to increase!