Stock Market Valuation in a Dynamic Monopolistically Competitive by yxm80800


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

Università degli Studi di Bari, 15 May 2008, 15 May 2008
           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?

Università degli Studi di Bari, 15 May 2008
           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
           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

Università degli Studi di Bari, 15 May 2008
           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.

Università degli Studi di Bari, 15 May 2008
                          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.

Università degli Studi di Bari, 15 May 2008
                         differentiated input         Final good industry
                                firms                         P.C.
                                 Firm 1

                                  kn,t,ln, t                                             Ct
             Kt                                qn,t         CES
                                 Firm n                  aggregation          Yt


                                Firm N

                                                                   All income returns to HH
                         regulated by wt, it
                                                                   as wage, rental or profits;
                           generates n, t
                                                                      asset markets open
Università degli Studi di Bari, 15 May 2008
           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.

Università degli Studi di Bari, 15 May 2008
           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
              100% rate of depreciation of capital.

Università degli Studi di Bari, 15 May 2008
             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
                 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
                 all agents are at an optimum:
Università degli Studi di Bari, 15 May 2008
              households are maximising their intertemporal
              all firms, IIF and final good industry, are maximising
               profits (face a static problem),
              households want to hold 100% of the stocks of
           Households’ equilibrium allocation is symmetric.

Università degli Studi di Bari, 15 May 2008
               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.

Università degli Studi di Bari, 15 May 2008
                        Anticipated future gains in
           Anticipated gains in sectorial or individual
                 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.

Università degli Studi di Bari, 15 May 2008
           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?

Università degli Studi di Bari, 15 May 2008
           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

Università degli Studi di Bari, 15 May 2008
           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!

Università degli Studi di Bari, 15 May 2008

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