In English, the “second derivative” measures how the rate of change of a quantity is itself changing.

I know, still confusing.

Let’s run an example:

As Government spending grows sequentially larger, each additional round of expenditures will have less and less impact on the total. Going back to 2016, not including the CARES Act, the Government increased spending by roughly $50 billion each quarter on average. If we run a hypothetical model of Government expenditures at $50 billion per quarter, you can see the issue of the “second derivative.”

In this case, even though Federal expenditures are increasing at $50 Billion per quarter, the rate of change declines as the total spending increase.

More Leads To Less

The next chart shows how the “second derivative” is already undermining both fiscal and monetary stimulus. Using actual data going back to the Q1-2019, Federal Expenditures remained relatively stable through Q1-2020, along with real economic growth. However, in Q2-2020, with our estimates for Q3 and Q4, Federal Expenditures will almost double. However, the economy will not return to positive growth.

The chart below shows the inherent problem. While the additional fiscal stimulus may help stave off a more in-depth economic contraction, its impact becomes less over time.

However, this is ultimately the problem with all debt-supported fiscal and monetary programs.

Still In A Recession

As stated, even with the additional stimulus package, the outcome will be muted. If we assume our current estimates for GDP growth over the next 2-quarters, which align with mainstream consensus, we will still be in a recession.

At first glance, it appears that after one negative quarter of GDP, the economy is well back on track to normalcy. However, such an assumption would be incorrect. Given that we measure economic growth on an annualized basis, the three-quarters of positive change following such a steep decline still leaves the economy in a recession.

Yes, add a couple of more quarters of economic growth, and you will eventually be back into positive territory. However, therein lies an even bigger problem.

Dollars Of Growth Deteriorate

As noted above, it requires increasing levels of debt to generate lower rates of economic growth. The chart below shows the previous and estimated CARES Acts and their impact on GDP growth.

To understand this better, we can view it from how many dollars it requires to generate $1 of economic growth. Following the economic shutdown, when economic activity went to zero, each dollar of input had a more considerable impact as the economy restarted. However, in Q4, economic activity has already recovered and begun to stabilize at a slightly lower level than seen previously.