Lifetime investment hypothesis

Last odd thought before sleep.  What if we think of investment as a lifetime investment function akin to the lifetime incomes hypothesis?  How would that change the standard view on corporate income tax and investment rates?

Let us assume that investment is a constant function of output.  Thus investment today is a function of long term output growth in each sector.  This fits the facts: in Canada manufacturing investment is pretty stable around 4 and 5.5 % of output over the last thirty years.  Let us also assume that investment is not directly related to profits.  This also fits the facts as investment as a percent of profits is highly volatile and negative.  What then accounts for the fluctuation in investment rates as a percent of output?

If as I have above that investment is a near constant of output then we might be tempted to write:

I = A + q * 1-Y

Where I is investment, A is a fixed independent part (the amount that needs to be invested to maintain medium run growth rates) q is a proportional share of un-anticipated output growth (Y) for the sector.

This tells us a couple of things.  Investment decisions today are determined by commitments made at t-1 and the actual level of output growth realized from those investments.  So if present realized output levels are higher then expected investment levels increase, if lower than expectations they decrease.

This is a nice formulation because it actually gives a material explanation to investment rates with respect to output and anticipations.

But what does all this have to do with corporate taxes.  Quite a bit.  Given capital depreciations allowances, corporations can write-off investment in plant and equipment and as such their decision to invest in expanding production is only tenuously related to tax rates.  What however will induce corporations to invest is an exogenous increase in demand for the sectors output given by q * 1-Y.

Within limits, corporate tax rates are therefore of little consequence on investment decisions.

Update to conclusion: If CIT cuts permanently increased demand then they would lead to a permanent increase in investment.