Monetary Policy, Market Structure and the Income Shares in the U.S

Abstract

A general equilibrium model of heterogeneous capital is employed to investigate whether, how and to what extent monetary policy and market structure may have contributed to the decline of the labor share in the U.S. in recent decades. By construction the model allows monetary policy to affect the labor share through two channels, i.e. one linking the policy rate to the real interest rate and another linking the latter to the useful life of producers’ goods, whereas regarding market structure, the more competitive the economy, the higher the labor share. From its solution using U.S. data over the period 2000–2014 it emerges that the persistent reduction in the policy rate on the one hand slowed down the decline in the labor share and on the other accelerated it, because the reduction in the policy rate was accompanied by a robust upward trend in the equilibrium real rate of interest, which increased the useful life of producers’ goods. In turn, to gauge the relative strength of these two opposite effects, the equation of the labor share is estimated by means of the autoregressive distributed lag method. The results show that the adverse effect of monetary policy through the useful life of producers’ goods was more than 12 times as strong as the favorable effect of the policy rate and on this ground I conclude that the monetary policy contributed to the decline of the labor share significantly, at least since 2000. As for the market structure, it is found that even if firms had and attempted to exercise monopoly power, it would be exceedingly difficult to exploit it because the demand of consumers’ goods is significantly price elastic.

Appendices

Appendix 1

1.1 Derivation of the money value of the depreciated capital stock

Observe from (5) in the text that the sum total R(υ, τ) of revenues minus operating expenses of a unit of producers’ goods from time τ to the rest of its useful life u is given by:

$$ R\left(\upsilon, \tau \right)={\int}_{\tau}^{\upsilon +u}\left[\frac{P\left(\upsilon \right)}{b\left(\upsilon \right)}{e}^{\mu \left(t-\upsilon \right)}-w\right]{e}^{-i\left(t-\upsilon \right)} dt. $$

(31)

Depreciation on the unit of producers’ goods of vintage υ from τ to time τ + 1 is defined as the decline in its worth during that year:

$$ D\left(\upsilon, \tau \right)=R\left(\upsilon, \tau \right)-R\left(\upsilon, \tau +1\right). $$

(32)

So, on the way to finding the expression for net income, let us derive the expression for R(υ, τ). With the help of (11) and (14), expression (8) simplifies into:

$$ \frac{P\left(\upsilon \right)}{b\left(\upsilon \right)}={we}^{-\mu u} $$

(33)

Substituting this into (31) and carrying out the integration gives the value of one unit of producers’ goods of vintage υ computed as of time τ:

$$ {\displaystyle \begin{array}{l}R\left(\upsilon, \tau \right)=w\left[{e}^{-\mu u}{\int}_{\tau}^{\upsilon +u}{e}^{\mu \left(t-\tau \right)-i\left(t-\tau \right)} dt-{\int}_{\tau}^{\upsilon +u}{e}^{-i\left(t-\tau \right)} dt\right]=\\ {}\kern2.75em =w\frac{ie^{-\mu \left(\upsilon +u-\tau \right)}-\mu {e}^{-i\left(\upsilon +u-\tau \right)}-\left(i-\mu \right)}{i\left(i-\mu \right)}.\end{array}} $$

(34)

Expression (13a) gives the units of all producers’ goods employed at time t. Hence, its value should be:

$$ Z\left(K(t)\right)=Z(t)={\int}_{t-u}^tR\left(\upsilon, \tau \right)S\left(\upsilon \right) d\upsilon . $$

(35)

In turn, by drawing on (13b) to write:

$$ S\left(\upsilon \right)={e}^{g\left(\upsilon -\tau \right)}S\left(\tau \right), $$

(36)

expression (35) can be transformed into:

$$ {\displaystyle \begin{array}{l}Z(t)={\int}_{t-u}^tR\left(\upsilon, \tau \right)S\left(\upsilon \right) d\upsilon =\\ {}\kern1.5em =\frac{\eta }{1+\eta}\frac{wS\left(\tau \right)}{i\left(i-\mu \right)}\left[{\int}_{t-u}^{\tau }{ie}^{-\mu \left(\upsilon +u-\tau \right)+g\left(\upsilon -\tau \right)}-\mu {e}^{-\mu \left(\upsilon +u-\tau \right)+g\left(\upsilon -\tau \right)}-\left(i-\mu \right){e}^{g\left(\upsilon -\tau \right)}\right] d\upsilon .\end{array}} $$

(37)

Upon evaluation of this integral and some re-arrangements of terms, we obtain the money value of the undepreciated capital stock as:

$$ {\displaystyle \begin{array}{l}\kern14em Z(t)=\frac{\eta }{1+\eta}\frac{w}{i} QS(t)\\ {}\mathrm{where}\\ {}\kern8em Q=\frac{{i e}^{-\mu u}}{\left(g-\mu \right)\left(i-\mu \right)}+\frac{\mu {e}^{- iu}}{\left(i-g\right)\left(i-\mu \right)}-\frac{i\mu {e}^{- gu}}{g\left(g-\mu \right)\left(i-g\right)}-\frac{1}{g}.\end{array}} $$

(38)

Expression (38) gives the value of the undepreciated capital stock on which interest is due and paid to the owners of the corresponding money capital.

Appendix 2

1.1 Data used in the computations of the model and the statistical analysis

Table 3 Estimates of certain key variables and parameters of the model

Table 4 Series of computed and reported variables of interest

Table 5 Share of labor from various sources