### Quantity-Expectations Parity: A Real-time Exercise

In 2018 I began to develop the framework of Quantity Expectations Parity (QEP).  Quantity-Expectations Parity is a framework for understanding the linkages between expectations,
the real economy, and financial markets. It explicitly calls for the intersection of all three components in order to understand how the economy and financial markets work at a high-level. I refrain from calling it a theory because it explicitly rejects the idea of strict equalities. The economy and financial markets are living organisms. That doesn’t mean that there aren’t testable implications, on the contrary, the framework is built upon empirical observation. Everything is meant to be falsified by the data. The main aim is to disentangle the numerous correlations that shock and drive researchers.

That is what the “Parity” focuses on. The parities are the key to breaking down the correlations. Another lesson of the QEP framework is that by creating a daisy-chain of parity relationships, it will tell you the order of integration necessary for the parity to ‘cointegrate’. For example, QEP states the AAA-10Y spread is related to the 1st difference in debt-to-GDP, not log-levels as some authors have suggested. QEP explicitly throws out the idea that expectations are useless. It embraces expectations. It assumes the proper expectations horizon is an empirical question as opposed to a pre-determined theoretical guided choice.

I hope to convey a few key ideas:

– Economic incentives are separate from financial incentives, but both matter for the aggregate flows of debt and money within our economy. The Federal Reserve is just force linking the real economy to the financial markets. Another force is the Federal Government.
– The only way to study all these major topics is jointly.

All balance sheet financial quantities are going to reflect incoming and outgoing cash flows. This creates the endless vortex of correlation between all financial, real economic, and debt quantities.

The Basic Idea

Each person in the economy today is receiving some level of income, $Y_{t}$. Income is a flow. They expect that this level of income is going to increase or remain unchanged for the foreseeable future. They are making decisions today based on their current position that will impact them in the future. The expectation made one year ago is $E_{t-1}[Y_t]$. Today the expectation is, $E_{t}[Y_{t+1}]$. Each person behaves according to some variant of
$$E_{t-1}[Y_t]\approx\Delta^n Cash_{t-1,t} + E_{t}[Y_{t+1}]$$
The number of differences, $n$, is left open. This identity states that if expectations for future income are less than they were last year, people make up the difference by raising cash. In order for expectations to change, there must be a change in economic reality.
$$E_{t-1}[Y_t] - E_{t}[Y_{t+1}]\approx Y_{t -1} - Y_{t}$$
The expectations that people form are primarily determined by the economic reality of the day. This implies that most of the future is predetermined by what has already happened. Consider the ISM which is damn near correlated with every asset price and the difference between short-term and long-term expected GDP growth. Real outcomes drive expected ones and vice-versa, and both feed into asset prices.
$${{ISM_t^{Man} - 50}\over{10}} \approx E_t[\Delta NGDP]^{ST(<=1y)} - E_t[\Delta NGDP]^{LT(>1yr)} \\ corr = 67\%$$

The change in expected income will lead to changing Treasury yields
$$y^{10}_{t}= y^{10}_{t-1}+(E_{t}[Y_{t+1}]-E_{t-1}[Y_t])$$
Therefore financial incentives to borrow and refinance old debts vary directly with the economic incentives as reflected in changing expectations.
$$y^{10}_{t}-y^{10}_{t-1}= (E_{t}[Y_{t+1}]-E_{t-1}[Y_t])$$
If $y^{10}_{t}-y^{10}_{t-1}= (E_{t}[Y_{t+1}]-E_{t-1}[Y_t]) < 0$, then the financial incentives to issue new debt and refinance old debts are greatest just when the economic incentives to raise cash are the largest. The financial incentive is greatest when bond risk premium is at its lowest.
$$E_t[\overline{ret}_{t+1}]= \bar y_t + (\bar y_t - E_t[\bar y_{t+1}])$$
The economic and financial incentives are felt by corporations, households, and the Federal Government all at the exact same time. Taking on new debt or refinancing old debts are both viable ways to raise the cash needed to equate last year's expectations with today's outcome.
$$\Delta Cash_{t-1,t}=\Delta New Debt/Refi_{t-1,t}$$
$$E_{t-1}[Y_t]\approx\Delta New Debt/Refi_{t-1,t} + E_{t}[Y_{t+1}]$$
Substituting $Y_t$ for $E_{t}[Y_{t+1}]$ we easily see that changes in the amount of debt outstanding and equivalently cash balances (also possibly arising from refinancing old debt) are the result of forecasting errors made about future income growth.
$$E_{t-1}[Y_t] - Y_{t}\approx\Delta New Debt/Refi_{t-1,t}$$
In fact, if we divide through by prices we see that forecasting errors about real income growth drive real debt and money balances. A change in new debt or refinancings is closely related to the second difference in the stock of debt.
$$E_{t-1}[{Y\over{P}} ] - {Y\over{P}} =\Delta^2 {Debt\over{P}}$$

So where are we today? There has undoubtedly been a short-fall in real labor income.  This represents the economic incentives to raise cash, withdraw home equity, and refinance past debts.
Concurrently, the fall in the level of expected income, as measured by trend nominal GDP per capita, has mirrored the fall in yields.
QEP states that financial incentives mirror economic ones, and when both converge as they do now, this leads to dramatic changes in debt. It is in this environment that all the actors face the same incentives to refinance and issue new debts.

Financial and real economic incentives weigh in on households to refinance past mortgage debts, leading to a flood of new Agency MBS issuance.
Households also have also resorted to home equity withdrawals to meet their cash needs.

The basic measure of financial incentive is the negative of the past years change in the 10-yr Treasury rate,
$$FinancialIncentive^{Rates} = - \Delta y^{(10)}_{t-250,t}$$
Households have reacted strongly to financial incentives.
Across-the-board financial actors are faced with the same incentives. Municipalities have the incentive to refund past debts.
Changing financial incentives permeate throughout the entire capital market. This is highlighted in the chart below which shows the 12m change in non-Treasury issuance as a fraction of GDP against the negative of the 12m change in the 10-yr Treasury yield. Non-Treasury issuance is defined here as the sum of Agency MBS, corporate bond and stock, and municipal issuance.
Whenever income falls below expectations, economic actors are faced with the real economic incentive to raise cash. For households, this is labor income; for corporations, it is nominal profits; and for State and Local Governments, it's tax revenue.  In order to stay afloat, debt-laden entities must raise cash whenever cash flow falls short of expectations.  This often comes in the form of refinancing past debts.  If credit markets seize and financing becomes unavailable, then firms and households are faced with bankruptcy.

QEP fundamentally combines quantities and expectations with real economic outcomes. Nominal profit expectations drive asset prices. Corporate cash flows are after all nominal. Debts are nominal.  QEP leverages these basic facts and explicitly seeks to explain correlations.  The table below shows that both economic and financial incentives factor into capital market issuance.
Direct Linkages Between Economic and Financial Incentives

It is of course of interest to understand why and how "financial and real economic incentives coincide". These are directly linked through the Federal Reserve's policy function. In this function, economic incentives, such as a fall in employment or inflation are directly translated into a financial incentive.

The Federal Reserve has been mandated to follow a policy which seeks to maximize full employment and deliver stable prices. The set of inputs that most track the Fed's behavior are listed on the right-hand side of the standard "Taylor rule" named after John Taylor's original 1993 formulation of the Fed's policy rule (Taylor, 1993). A standard Taylor rule can be found in (Orphanides, 2007) (see equation 8):

i=(1-\theta_{i})(r^*+\pi^*)+\theta_{i}{i_{t-1}}+\theta_{\pi}(\pi-\pi^*)+\theta_{q}(q-q^*)+\theta_{\Delta q}(\Delta q-\Delta q^*)
\label{eq:taylorrule}

Where, $(\pi-\pi^*)$ is the inflation gap or deviation from target, $\pi^*$. The output gap is $(q-q^*)$ and $(\Delta q-\Delta q^*)$ accounts for changes in the output gap. The real equilibrium rate of interest is $r^*$. When $theta_{i} > 0$ allows for inertia (i.e persistence in rates and therefore expectations), which is a key feature of the actual behavior of interest rates and inflation. The nominal interest rate set by the Fed is $i$. The important takeaway is that this rule describes how the Fed has historically reacted (i.e. *in the past*) to deviations in output and inflation from their target levels. A regression-based estimate of this rule, or a similar rule, would be characterized as the Econometricians expectation of the nominal short-term rate.
We can immediately see that the Federal Reserve helps households to meet their cash flow needs through discount rate policy and balance sheet policy. For example, by holding mortgage-backed securities they support housing markets and make it easier for homeowners to refinance. Discount rate policy, while directly impacting the term-structure also has an impact on equity prices.

Although Fed policy is discretionary, the Federal Governments's automatic stabilizers are not. A fall in economic growth is mechanically linked to more borrowing. Also, layoffs translate into cash payouts in the form of unemployment insurance, which must also be financed. There are also Keynesian policies that are enacted in response to recessions. These stabilizers provide a floor for economic growth.

For a fall in payrolls, there will be two effects:

1). The Federal Reserve will lower interest rates.

2). The Federal Government will borrow more.

Lower interest rates and increased borrowing. It is not that lower interest rates lead to increased borrowing, it is instead the effects of the real economy on interest rates and government borrowing. Without this, we may well see a positive correlation between government borrowing and interest rates. Stimulus packages, automatic stabilizers like unemployment insurance, and the drop in tax revenues have all converged to increase Treasury issuance.

Expectations Linkages to Financial and Economic Incentives

Expectations drive asset prices. This statement is uncontroversial. Changing expectations about real growth and inflation lead to variation in asset prices. This leads to the cycle in real economic activity. Price expectations influence the direction of interest rates and nominal profits.

We have just witnessed how changing financial incentive bring capital market participants to the markets. Yet expectations as reflected in commodity markets are no doubt connected to this phenomenon. In particular, price expectations drive nominal profit expectations and therefore help drive asset prices.

To illustrate, we know that the prices that businesses charge roughly equates to their economic incentives. For manufacturers, we can represent the economic incentive by

\Delta {Inventories \over{New\ Orders}} \approx - \Delta^{2} Prices^{ISM}
.
In this case, when manufacturers have a high level of inventories-to-new orders, they expect prices to come down. There is a relatively high correlation between the inventories-to-new orders ratio and the prices expected by manufacturers.

Forces Converge on The Primary Dealer

Quantities and expectations converge on the primary dealers to create the asset prices we see in the market.  The primary dealer balance sheet takes the force of issuance and expectations and what comes out is asset price volatility.  I have done this deep dive and those interested can find my paper here. In short, since issuance comes all at once, dealers must decide how to price assets to fix their desired inventories.  Their net positioning in Treasuries is often driven by movements in yields themselves (which reflect expectations).  It is exactly when Treasury and Agency MBS issuance spike that yields themselves are falling.  These facts help to explain the high correlations found between many variables in macro-finance.