Banking and Lending/Investment. How Monetary Policy Becomes Decisive? Some Branching Rumination.

Among the most notoriously pernicious effects of asset price inflation is that it offers speculators the prospect of gain in excess of the costs of borrowing the money to buy the asset whose price is being inflated. This is how many unstable Ponzi financing structures begin. There are usually strict regulations to prevent or limit banks’ direct investment in financial instruments without any assured residual liquidity, such as equity or common stocks. However, it is less easy to prevent banks from lending to speculative investors, who then use the proceeds of their loans to buy securities or to limit lending secured on financial assets. As long as asset markets are being inflated, such credit expansions also conceal from banks, their shareholders and their regulators the disintermediation that occurs when the banks’ best borrowers, governments and large companies, use bills and company paper instead of bank loans for their short-term financing. As long as the boom proceeds, banks can enjoy the delusion that they can replace the business of governments and large companies with good lending secured on stocks.

In addition to undermining the solvency of the banking system, and distracting commerce and industry with the possibilities of lucrative corporate restructuring, capital market inflation also tends to make monetary policy ineffective. Monetary policy is principally the fixing of reserve requirements, buying and selling short-term paper or bills in the money or inter-bank markets, buying and selling government bonds and fixing short-term interest rates. As noted in the previous section, with capital market inflation there has been a proliferation of short-term financial assets traded in the money markets, as large companies and banks find it cheaper to issue their own paper than to borrow for banks. This disintermediation has extended the range of short-term liquid assets which banks may hold. As a result of this it is no longer possible for central banks, in countries experiencing capital market inflation, to control the overall amount of credit available in the economy: attempts to squeeze the liquidity of banks in order to limit their credit advances by, say, open market operations (selling government bonds) are frustrated by the ease with which banks may restore their liquidity by selling bonds or their holdings of short-term paper or bills. In this situation central banks have been forced to reduce the scope of their monetary policy to the setting of short-term interest rates.

Economists have long believed that monetary policy is effective in controlling price inflation in the economy at large, as opposed to inflation of securities prices. Various rationalizations have been advanced for this efficacy of monetary policy. For the most part they suppose some automatic causal connection between changes in the quantity of money in circulation and changes in prices, although the Austrian School of Economists (here, here, here, and here) tended on occasion to see the connection as being between changes in the rate of interest and changes in prices.

Whatever effect changes in the rate of interest may have on the aggregate of money circulating in the economy, the effect of such changes on prices has to be through the way in which an increase or decrease in the rate of interest causes alterations in expenditure in the economy. Businesses and households are usually hard-headed enough to decide their expenditure and financial commitments in the light of their nominal revenues and cash outflows, which may form their expectations, rather than in accordance with their expectations or optimizing calculations. If the same amount of money continues to be spent in the economy, then there is no effective reason for the business-people setting prices to vary prices. Only if expenditure in markets is rising or falling would retailers and industrialists consider increasing or decreasing prices. Because price expectations are observable directly with difficulty, they may explain everything in general and therefore lack precision in explaining anything in particular. Notwithstanding their effects on all sorts of expectations, interest rate changes affect inflation directly through their effects on expenditure.

The principal expenditure effects of changes in interest rates occur among net debtors in the economy, i.e., economic units whose financial liabilities exceed their financial assets. This is in contrast to net creditors, whose financial assets exceed their liabilities, and who are usually wealthy enough not to have their spending influenced by changes in interest rates. If they do not have sufficient liquid savings out of which to pay the increase in their debt service payments, then net debtors have their expenditure squeezed by having to devote more of their income to debt service payments. The principal net debtors are governments, households with mortgages and companies with large bank loans.

With or without capital market inflation, higher interest rates have never constrained government spending because of the ease with which governments may issue debt. In the case of indebted companies, the degree to which their expenditure is constrained by higher interest rates depends on their degree of indebtedness, the available facilities for additional financing and the liquidity of their assets. As a consequence of capital market inflation, larger companies reduce their borrowing from banks because it becomes cheaper and more convenient to raise even short- term finance in the booming securities markets. This then makes the expenditure of even indebted companies less immediately affected by changes in bank interest rates, because general changes in interest rates cannot affect the rate of discount or interest paid on securities already issued. Increases in short-term interest rates to reduce general price inflation can then be easily evaded by companies financing themselves by issuing longer-term securities, whose interest rates tend to be more stable. Furthermore, with capital market inflation, companies are more likely to be over-capitalized and have excessive financial liabilities, against which companies tend to hold a larger stock of more liquid assets. As inflated financial markets have become more unstable, this has further increased the liquidity preference of large companies. This excess liquidity enables the companies enjoying it to gain higher interest income to offset the higher cost of their borrowing and to maintain their planned spending. Larger companies, with access to capital markets, can afford to issue securities to replenish their liquid reserves.

If capital market inflation reduces the effectiveness of monetary policy against product price inflation, because of the reduced borrowing of companies and the ability of booming asset markets to absorb large quantities of bank credit, interest rate increases have appeared effective in puncturing asset market bubbles in general and capital market inflations in particular. Whether interest rate rises actually can effect an end to capital market inflation depends on how such rises actually affect the capital market. In asset markets, as with anti-inflationary policy in the rest of the economy, such increases are effective when they squeeze the liquidity of indebted economic units by increasing the outflow of cash needed to service debt payments and by discouraging further speculative borrowing. However, they can only be effective in this way if the credit being used to inflate the capital market is short term or is at variable rates of interest determined by the short-term rate.

Keynes’s speculative demand for money is the liquidity preference or demand for short-term securities of rentiers in relation to the yield on long-term securities. Keynes’s speculative motive is ‘a continuous response to gradual changes in the rate of interest’ in which, as interest rates along the whole maturity spectrum decline, there is a shift in rentiers’ portfolio preference toward more liquid assets. Keynes clearly equated a rise in equity (common stock) prices with just such a fall in interest rates. With falling interest rates, the increasing preference of rentiers for short-term financial assets could keep the capital market from excessive inflation.

But the relationship between rates of interest, capital market inflation and liquidity preference is somewhat more complicated. In reality, investors hold liquid assets not only for liquidity, which gives them the option to buy higher-yielding longer-term stocks when their prices fall, but also for yield. This marginalizes Keynes’s speculative motive for liquidity. The motive was based on Keynes’s distinction between what he called ‘speculation’ (investment for capital gain) and ‘enterprise’ (investment long term for income). In our times, the modern rentier is the fund manager investing long term on behalf of pension and insurance funds and competing for returns against other funds managers. An inflow into the capital markets in excess of the financing requirements of firms and governments results in rising prices and turnover of stock. This higher turnover means greater liquidity so that, as long as the capital market is being inflated, the speculative motive for liquidity is more easily satisfied in the market for long-term securities.

Furthermore, capital market inflation adds a premium of expected inflation, or prospective capital gain, to the yield on long-term financial instruments. Hence when the yield decreases, due to an increase in the securities’ market or actual price, the prospective capital gain will not fall in the face of this capital appreciation, but may even increase if it is large or abrupt. Rising short-term interest rates will therefore fail to induce a shift in the liquidity preference of rentiers towards short-term instruments until the central bank pushes these rates of interest above the sum of the prospective capital gain and the market yield on long-term stocks. Only at this point will there be a shift in investors’ preferences, causing capital market inflation to cease, or bursting an asset bubble.

This suggests a new financial instability hypothesis, albeit one that is more modest and more limited in scope and consequence than Minsky’s Financial Instability Hypothesis. During an economic boom, capital market inflation adds a premium of expected capital gain to the market yield on long-term stocks. As long as this yield plus the expected capital gain exceed the rate of interest on short-term securities set by the central bank’s monetary policy, rising short-term interest rates will have no effect on the inflow of funds into the capital market and, if this inflow is greater than the financing requirements of firms and governments, the resulting capital market inflation. Only when the short-term rate of interest exceeds the threshold set by the sum of the prospective capital gain and the yield on long-term stocks will there be a shift in rentiers’ preferences. The increase in liquidity preference will reduce the inflow of funds into the capital market. As the rise in stock prices moderates, the prospective capital gain gets smaller, and may even become negative. The rentiers’ liquidity preference increases further and eventually the stock market crashes, or ceases to be active in stocks of longer maturities.

At this point, the minimal or negative prospective capital gain makes equity or common stocks unattractive to rentiers at any positive yield, until the rate of interest on short-term securities falls below the sum of the prospective capital gain and the market yield on those stocks. When the short-term rate of interest does fall below this threshold, the resulting reduction in rentiers’ liquidity preference revives the capital market. Thus, in between the bursting of speculative bubbles and the resurrection of a dormant capital market, monetary policy has little effect on capital market inflation. Hence it is a poor regulator for ‘squeezing out inflationary expectations’ in the capital market.

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Principal Bundles Preserve Structures…

A bundle P = (P, M ,π; G) is a principal bundle if the standard fiber is a Lie group G and ∃ (at least) one trivialization the transition functions of which act on G by left translations Lg : G → G : h ↦ f  g . h (where . denotes here the group multiplication).

The principal bundles are slightly different from affine bundles and vector bundles. In fact, while in affine bundles the fibers π^-1(x) have a canonical structure of affine spaces and in vector bundles the fibers π^-1(x) have a canonical structure of vector spaces, in principal bundles the fibers have no canonical Lie group structure. This is due to the fact that, while in affine bundles transition functions act by means of affine transformations and in vector bundles transition functions act by means of linear transformations, in principal bundles transition functions act by means of left translations which are not group automorphisms. Thus the fibers of a principal bundle do not carry a canonical group structure, but rather many non-canonical (trivialization-depending) group structures. In the fibers of a vector bundle there exists a preferred element (the “zero”) the definition of which does not depend on the local trivialization. On the contrary, in the fibers of a principal bundle there is no preferred point which is fixed by transition functions to be selected as an identity. Thus, while in affine bundles affine morphisms are those which preserve the affine structure of the fibers and in vector bundles linear morphisms are the ones which preserve the linear structure of the fibers, in a principal bundle P = (P, M, π; G) principal morphisms preserve instead a structure, the right action of G on P.

Let P = (P, M, π; G) be a principal bundle and {(U_α, t_(α)}_α∈I a trivialization. We can locally consider the maps

R^(α)_g : π^-1(U_α) → π^-1(U_α) : [x, h]_(α) ↦ [x, h . g]_(α) —– (1)

∃ a (global) right action R_g of G on P which is free, vertical and transitive on fibers; the local expression in the given trivialization of this action is given by R^(α)_g .

Using the local trivialization, we set p = [x, h]_(α) = [x, g_(βα)(x) . h]_β following diagram commutes:

which clearly shows that the local expressions agree on the overlaps U_αβ, to define a right action. This is obviously a vertical action; it is free because of the following:

R_gp = p => [x, h . g]_(α) = [x, h]_(α) => h · g = h => g = e —– (2)

Finally, if p = [x, h₁]_(α) and q = [x, h₂]_(α) are two points in the same fiber of p, one can choose g = h₂^-1 . h₁ (where · denotes the group multiplication) so that p = R_gq. This shows that the right action is also transitive on the fibers.

On the contrary, that a global left action cannot be defined by using the local maps

L^(α)_g : π^-1(U_α) → π^-1(U_α) : [x, h]_(α) ↦ [x, g . h]_(α) —– (3)

since these local maps do not satisfy a compatibility condition analogous to the condition of the commuting diagram.

let P = (P, M, π; G) and P’ = (P’, M’, π’ ; G’ ) be two principal bundles and θ : G → G’ be a homomorphism of Lie groups. A bundle morphism Φ = (Φ, φ) : P → P’ is a principal morphism with respect to θ if the following diagram is commutative:

When G = G’ and θ = id_G we just say that Φ is a principal morphism.

A trivial principal bundle (M x G, M, π; G) naturally admits the global unity section I ∈ Γ(M x G), defined with respect to a global trivialization, I : x ↦ (x, e), e being the unit element of G. Also, principal bundles allow global sections iff they are trivial. In fact, on principal bundles there is a canonical correspondence between local sections and local trivializations, due to the presence of the global right action.