*by Menzie Chinn, Econbrowser.com*

*Originally posted at Econbrowser 14 November 2013.
*

**1.** From my (undergraduate) Economics 390 “Topics in Macro” midterm:

Consider this statement:

“Borrowing and spending by the public sector will crowd out investment and growth in the private sector.”

Paul Ryan, “Path to Prosperity” (April 2012).

For larger image see first graph in post below.

**1.1** In a standard IS-LM model, where investment spending is given by:

(7′)* I = b0 – b2i*

Will higher government spending crowd out investment? Use a graph to help explain your answer.

**Answer:** The increase in government spending shifts the IS curve out by α‾ΔGO ; aggregate demand would rise to Y’0, except for the increase in interest rates – associated with the higher money demand arising from higher income – decreases investment. [α‾ ≡ (1-c1(1-t1))-1]. Hence, there is crowding out of investment of:

* Δ I = -b 2 Δ i < 0*

The distance Y’0-Y1 is the amount of income crowded out.

**1.2** Suppose instead investment spending is given by:

(7)* I = b0 + b1 Y – b2 i *

Do we know if government spending will result in reduced investment? Use a graph to help explain your answer.

**Answer:** The increase in government spending shifts the IS curve out by α ‾ Δ GO ; aggregate demand would rise to Y’0, except for the increase in interest rates – associated with the higher money demand arising from higher income – decreases investment. [Now α ‾ ≡ (1-c1(1-t1)-b1)-1]. Hence, there is crowding out of investment of:

*ΔI = b1Δ Y – b2Δ i ? 0*

The distance Y’0-Y1 is the amount of income crowded out.

**1.3** If the economy starts out in a liquidity trap, what is the impact of an increase in government spending on investment (assuming equation 7)? Use a graph to help explain your answer. Be careful to state your assumptions.

**Answer:** Assuming the economy ends up in a liquidity trap, then investment will increase.

Recall:

*ΔI = b1 ΔY – b2Δi *

As long as interest rates stay at zero, then

*ΔI = b1 ΔY > 0 *

Where by *α‾ΔGO = ΔY* and *α‾ ≡ [1-c1 (1-t1 )-b1]-1*

**1.4** Consider problem 1.3 again, but assume:

Where *MB* is money base [*B* is government bonds], and the price level is held fixed. Use a graph to help explain your answer. Be careful to state your assumptions.

**Answer:** The correct answer depends upon whether interest rates remain at zero. In this case with the revised money demand equation, the LM curve will shift up due to the increase in government spending (as long as the initial budget balance was zero or less).

If the interest rate does rise (as in the figure above), then investment might or might not fall. Otherwise, investment will increase.

**Relation to Current Conditions**

I can hear now certain individuals (the usual suspects) muttering about ivory tower economics and the irrelevance of such concepts to real world conditions. Hence, it’s interesting to see what Goldman Sachs sees as important to investment behavior. From D. Mericle, “Capex: The Fundamentals Remain Strong,” Goldman Sachs 11/12/2013 [not online]:

Business investment has been weak so far this year and grew a disappointing 1.6% in Q3. But it is not surprising that businesses have been hesitant about investing in a year that included a $200bn tax hike hitting consumers and a large drop in government spending.- Our investment growth model suggests that consumer demand is the missing piece of the capex puzzle. In contrast, the other fundamental drivers of business investment growth remain strongly supportive. Profit rates are high, lending standards continue to ease, and the starting level of investment remains low.
- We expect capital spending to strengthen next year, with an added boost if consumption recovers in line with our forecast. This reinforces our view that private sector spending should accelerate in 2014, pushing GDP growth into the 3-3.5% range.

*(emphasis added – mdc)*

I think it’s of particular note that output (consumption in particular) is seen as a critical driver of investment; crowding out due to high interest rates — current or incipient — is nowhere to be seen.

Profits (which are correlated with economic activity) are another positive. This also suggests the accelerator effect is more important than the dreaded crowding out effect due to fiscal policy.

By the way, despite the recent increase in long rates, the real ten year interest rate in October is just now reaching levels last seen in mid-2011 (and is much below levels recorded before the recession).

**Figure 1:** Ten year constant maturity TIPS yields (blue) and real ex ante yields calculated as difference between ten year constant maturity nominal yields and mean expected ten year inflation from Philadelphia Fed Survey of Professional Forecasters. NBER defined recession dates shaded gray. Source: Fed via FRED, Philadelphia Fed, NBER, and author’s calculations.

The astute observer will note that in 2009-2010, as the American Recovery and Reinvestment Act was implemented, real interest rates declined even as spending rose and peaked.