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The Weekend Quiz – August 20-21, 2016 – answers and discussion

Here are the answers with discussion for this Weekend’s Quiz. The information provided should help you work out why you missed a question or three! If you haven’t already done the Quiz from yesterday then have a go at it before you read the answers. I hope this helps you develop an understanding of modern monetary theory (MMT) and its application to macroeconomic thinking. Comments as usual welcome, especially if I have made an error.

Question 1:

Central banks provide reserves to the commercial banking system at some penalty rate. However, by standing ready to act as the lender of last resort to the commercial banks, the central bank’s capacity to control bank lending and target a given monetary policy rate is compromised.

The answer is True.

The facts are as follows. First, central banks will always provide enough reserve balances to the commercial banks at a price it sets using a combination of overdraft/discounting facilities and open market operations.

Second, if the central bank didn’t provide the reserves necessary to match the growth in deposits in the commercial banking system then the payments system would grind to a halt and there would be significant hikes in the interbank rate of interest and a wedge between it and the policy (target) rate – meaning the central bank’s policy stance becomes compromised.

Third, any reserve requirements within this context while legally enforceable (via fines etc) do not constrain the commercial bank credit creation capacity. Central bank reserves (the accounts the commercial banks keep with the central bank) are not used to make loans. They only function to facilitate the payments system (apart from satisfying any reserve requirements).

Fourth, banks make loans to credit-worthy borrowers and these loans create deposits. If the commercial bank in question is unable to get the reserves necessary to meet the requirements from other sources (other banks) then the central bank has to provide them. But the process of gaining the necessary reserves is a separate and subsequent bank operation to the deposit creation (via the loan).

Fifth, if there were too many reserves in the system (relative to the banks’ desired levels to facilitate the payments system and the required reserves then competition in the interbank (overnight) market would drive the interest rate down. This competition would be driven by banks holding surplus reserves (to their requirements) trying to lend them overnight. The opposite would happen if there were too few reserves supplied by the central bank. Then the chase for overnight funds would drive rates up.

In both cases the central bank would lose control of its current policy rate as the divergence between it and the interbank rate widened. This divergence can snake between the rate that the central bank pays on excess reserves (this rate varies between countries and overtime but before the crisis was zero in Japan and the US) and the penalty rate that the central bank seeks for providing the commercial banks access to the overdraft/discount facility.

So the aim of the central bank is to issue just as many reserves that are required for the law and the banks’ own desires.

Now the question seeks to link the penalty rate that the central bank charges for providing reserves to the banks and the central bank’s target rate. The wider the spread between these rates the more difficult does it become for the central bank to ensure the quantity of reserves is appropriate for maintaining its target (policy) rate.

Where this spread is narrow, central banks “hit” their target rate each day more precisely than when the spread is wider.

So if the central bank really wanted to put the screws on commercial bank lending via increasing the penalty rate, it would have to be prepared to lift its target rate in close correspondence. In other words, its monetary policy stance becomes beholden to the discount window settings.

The best answer was True because the central bank cannot operate with wide divergences between the penalty rate and the target rate and it is likely that the former would have to rise significantly to choke private bank credit creation.

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Question 2:

If inflation is stable and maintained at a rate equal to the interest rate, then the government deficit as a proportion of GDP could double (say from 2 to 4 per cent) without pushing up the public debt ratio.

The answer is True.

Again, this question requires a careful reading and a careful association of concepts to make sure they are commensurate. There are two concepts that are central to the question: (a) a rising fiscal deficit – which is a flow and not scaled by GDP in this case; and (b) a rising public debt ratio which by construction (as a ratio) is scaled by GDP.

So the two concepts are not commensurate although they are related in some way.

A rising fiscal deficit does not necessary lead to a rising public debt ratio. You might like to refresh your understanding of these concepts by reading this blog – Saturday Quiz – March 6, 2010 – answers and discussion.

While the mainstream macroeconomics thinks that a sovereign government is revenue-constrained and is subject to the government fiscal constraint, MMT places no particular importance in the public debt to GDP ratio for a sovereign government, given that insolvency is not an issue.

The mainstream framework for analysing the so-called “financing” choices faced by a government (taxation, debt-issuance, money creation) – the government budget constraint – is written as:
gbc

Which you can read in English as saying that Budget deficit = Government spending + Government interest payments – Tax receipts must equal (be “financed” by) a change in Bonds (B) and/or a change in high powered money (H). The triangle sign (delta) is just shorthand for the change in a variable.

Remember, this is merely an accounting statement. In a stock-flow consistent macroeconomics, this statement will always hold. That is, it has to be true if all the transactions between the government and non-government sector have been corrected added and subtracted.

So from the perspective of Modern Monetary Theory (MMT), the previous equation is just an ex post accounting identity that has to be true by definition and has not real economic importance.

For the mainstream economist, the equation represents an ex ante (before the fact) financial constraint that the government is bound by. The difference between these two conceptions is very significant and the second (mainstream) interpretation cannot be correct if governments issue fiat currency (unless they place voluntary constraints on themselves to act as if it is).

That interpretation is inapplicable (and wrong) when applied to a sovereign government that issues its own currency.

But the accounting relationship can be manipulated to provide an expression linking deficits and changes in the public debt ratio.

The following equation expresses the relationships above as proportions of GDP:

debt_gdp_ratio

So the change in the debt ratio is the sum of two terms on the right-hand side: (a) the difference between the real interest rate (r) and the GDP growth rate (g) times the initial debt ratio; and (b) the ratio of the primary deficit (G-T) to GDP. A primary fiscal balance is the difference between government spending (excluding interest rate servicing) and taxation revenue.

The real interest rate is the difference between the nominal interest rate and the inflation rate. If inflation is maintained at a rate equal to the interest rate then the real interest rate is constant.

A growing economy can absorb more debt and keep the debt ratio constant or falling. From the formula above, if the primary fiscal balance is zero, public debt increases at a rate r but the public debt ratio increases at rg.

So if r = 0, and g = 2, the primary deficit ratio could equal 2 per cent (of GDP) and the public debt ratio would be unchanged. Doubling the primary deficit to 4 per cent would require g to rise to 4 for the public debt ratio to remain unchanged. That is entirely possible.

So a nation running a primary deficit can obviously reduce its public debt ratio over time or hold them constant if growth is stimulated. Further, you can see that even with a rising primary deficit, if output growth (g) is sufficiently greater than the real interest rate (r) then the debt ratio can fall from its value last period.

Furthermore, depending on contributions from the external sector, a nation running a deficit will more likely create the conditions for a reduction in the public debt ratio than a nation that introduces an austerity plan aimed at running primary surpluses.

Clearly, the real growth rate has limits and that would limit the ability of a government (that voluntarily issues debt) to hold the debt ratio constant while expanding its fiscal deficit as a proportion of GDP.

The following blog may be of further interest to you:

Question 3:

The wage share in national income in many nations has fallen over the neo-liberal period. However, a declining wage share does not mean the real standard of living for workers is falling.

The answer is True.

The wage share in nominal GDP is expressed as the total wage bill as a percentage of nominal GDP. Economists differentiate between nominal GDP ($GDP), which is total output produced at market prices and real GDP (GDP), which is the actual physical equivalent of the nominal GDP. We will come back to that distinction soon.

To compute the wage share we need to consider total labour costs in production and the flow of production ($GDP) each period.

Employment (L) is a stock and is measured in persons (averaged over some period like a month or a quarter or a year.

The wage bill is a flow and is the product of total employment (L) and the average wage (w) prevailing at any point in time. Stocks (L) become flows if it is multiplied by a flow variable (W). So the wage bill is the total labour costs in production per period.

So the wage bill = W.L

The wage share is just the total labour costs expressed as a proportion of $GDP – (W.L)/$GDP in nominal terms, usually expressed as a percentage. We can actually break this down further.

Labour productivity (LP) is the units of real GDP per person employed per period. Using the symbols already defined this can be written as:

LP = GDP/L

so it tells us what real output (GDP) each labour unit that is added to production produces on average.

We can also define another term that is regularly used in the media – the real wage – which is the purchasing power equivalent on the nominal wage that workers get paid each period. To compute the real wage we need to consider two variables: (a) the nominal wage (W) and the aggregate price level (P).

We might consider the aggregate price level to be measured by the consumer price index (CPI) although there are huge debates about that. But in a sense, this macroeconomic price level doesn’t exist but represents some abstract measure of the general movement in all prices in the economy.

The real wage (w) tells us what volume of real goods and services the nominal wage (W) will be able to command and is obviously influenced by the level of W and the price level. For a given W, the lower is P the greater the purchasing power of the nominal wage and so the higher is the real wage (w).

We write the real wage (w) as W/P. So if W = 10 and P = 1, then the real wage (w) = 10 meaning that the current wage will buy 10 units of real output. If P rose to 2 then w = 5, meaning the real wage was now cut by one-half.

So the proposition in the question – that a declining wage share does not mean the real standard of living for workers is falling – true.

Irrespective of what happens to the wage share, as long as the real wage is rising, material standards of living will be rising (other things equal). That is, a declining wage share per se doesn’t denote a decline in workers’ living standards.

What it tells us is that a rising proportion of national income is going to profits (non-wages). But that rising proportion could be in relation to an overall expanding pie.

A declining wage share is consistent with growth in the real wage which is slower than the growth in labour productivity. If the real wage is growing but labour productivity is growing faster, then the wage share will fall.

A declining wage share driven by a real wage falling (and labour productivity at least not falling by as much) would signify a decline in living standards but that is because the real wage is falling.

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    This Post Has One Comment
    1. re q1)-” If the commercial bank in question is unable to get the reserves necessary to meet the requirements from other sources (other banks) then the central bank has to provide them.”-
      Has this ever happened? a new bank has created a loan,been unable to secures reserves to settle payments from the private sector. But then subsequently been loaned uncollateralised reserves from the CB at an interest rate which makes the initial loan profitable for the bank.

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