A complex, but still elementary model

1. TWO-COUNTRY STOCK-FLOW-CONSISTENT MACROECONOMICSUSING A CLOSED MODEL WITHIN A DOLLAR EXCHANGE REGIME

2. A complex, but still elementary model • The simplifying assumptions are enormous. • There is no domestic or foreign investment in fixed or working capital • No holdings of financial assets by firms; • No wage inflation • No commercial banking • No “hot money”. • The treatment of expectations is rudimentary. Yet the model contains nearly 90 equations!

3. What is new relative to the simple two-country open model ? • Gold reserves are replaced by interest-generating dollar reserves • Households hold foreign financial assets • There are (several) price indices and real quantities • Prices are endogenous, and depend on exchange rates • Imports depend on income and relative prices • Overall, the model mixes trade theory and international finance

4. The model has several variants • The main variant is a fixed exchange rate regime, with fluctuating (endogenous) reserves • An alternative closure is a flexible exchange rate regime • Another possible closure is to assume that the deficit country lets interest rates move freely, while keeping a fixed exchange rate without losing reserves • A final closure would be to assume an endogenous fiscal policy whereby the deficit country reduces government expenditures to keep a fixed exchange rate without losing reserves

5. Notations • # stands for Japanese/UK • $ stands for American • Where an asset is issued by one country and held in another, the first term in the suffix refers to the country where the asset is held, the second to the country where it was issued; thus (for instance) B#$ describes a bill owned by a Japanese household but issued in the US.

6. Balance sheet of US country The net worth of the US central bank has to be zero (all profits are distributed to government, and the price of gold in dollars is assumed constant).

7. Balance sheet of the Japan/UK country The net worth of the Japan central bank may become positive, because The central bank can achieve a capital gain when the $ currency Appreciates, that is when the number of yens per dollar xr$ goes up

8. Trade prices • pm# = µ0 - µ1. xr# + (1 - µ1).py# + µ1.py$ • 0 < µ1 < 1 • px# = 0 - 1.xr# + (1 - 1).py# + 1.py$ • 0 < 1 < 1 • where pm is import prices, px is export prices, py is the GDP deflator, while bold characters denote natural logs of these variables.

9. Why? (1 - µ1).py# + µ1.py$ • If there were a simultaneous addition of some given amount to domestic inflation in both countries with no change in the exchange rate, then there would be an equivalent addition to export and (therefore) import prices in each country – hence the constraint that the coefficients on domestic and foreign inflation sum to unity.

10. Why ? µ1. xr# + µ1.py$ • If depreciation were exactly paralleled by a simultaneous and equal addition to domestic inflation, it is reasonable to expect that import prices would rise by the full amount of the depreciation – hence the sum of the coefficients on the exchange rate and domestic inflation must also sum to unity

11. Trade flows • x# = 0 - 1(pm$-1 - py$-1) + 2.y$ • im# = 0 - 1(pm#-1 - py#-1) + 2.y# • First equation says that the volume of Japanese exports (x#) responds with an elasticity of 1 with respect to the price of $ imports relative to that of $ domestic prices and 2 with respect to domestic output (y$). • Second equation says that Japanese imports (im#) respond with elasticities 1 with respect to import prices (pm#) relative to domestic prices (py#) and 2 with respect to domestic output (y#).

12. Marshall-Lerner conditions ? • It is worth pointing out, since it is so often assumed that the sum of the elasticities with respect to relative prices must sum to at least one if the trade balance is to improve following devaluation (the Marshall-Lerner condition), that in verity the sum of these elasticities need be no greater than the elasticity of terms of trade with regard to devaluation. For instance, if the deterioration in the terms of trade were 20% of the devaluation, then the sum of the price elasticities need be no more than 0.2. If there were no change at all in the terms of trade following devaluation – not an impossible outcome – the sum of the elasticities need be no greater than positive for the balance of trade to improve.

13. The consumption function • Households are assumed to make their real consumption decisions on the basis of their real (Haig-Simons) disposable income and on the basis of their past real wealth. • The implicit wealth to income ratio is assumed to be positively influenced by higher interest rates

14. Pricing • ps# = (1 + ).(W#.N# + IM#)/s# • ps$ = (1 + ).(W$.N$ + IM$)/s$ • The price level of sales ps is determined as a markup on unit costs. • This is a standard Kaleckian assumption.

15. Portfolio demand of Japanese households B##d = V#e.(10 + 11.r# - 12.(r$ + dxr$e) - 13.YD#e/V#e) B#$d = V#e.( 20 - 21.r# + 22.(r$ + dxr$e) - 23.YD#e/V#e) H#d = V#e.( 30 - 31.r# - 32.(r$ + dxr$e) + 33.YD#e/V#e) dxr$e is the expected rate of change

16. US-issued assets demanded by the private sector • Money: • H$s = H$h • Foreign demand for US T-bills • B#$s = B#$d.xr# • Domestic demand for US T-bills • B$$s = B$$d • All assets are supplied on demand • Symmetric for assets supplied by Japan

17. The Fed constraints • Standard balance sheet constraint • H$s = Bcb$d + or$.pg$ • The demand for bills by the Japanese central bank is: • Bcb#$s = Bcb#$d,xr# • the value of US bills supplied to the US central bank is pinned down to: • Bcb$s = B$s - B#$s - B$$s - Bcb#$s • To control interest rate, the Fed must take the residual amount of bills: • Bcb$d = Bcb$s

18. There are two equations with the same variable on the left-hand side • H$s = H$h • H$s = Bcb$d + or$.pg$ • One of the two must be dropped (and become the hidden equation). It will be the first one, which basically says that that money supply is endogenous and determined by money demand

19. The value of US Treasury bills, measured in Japanese currency, which the Japanese central bank acquires, is: • Bcb#$d = H#s - Bcb#d - or#.pg# + xr$.Bcb#$s-1 • This equation is saying that unless the Japanese bank buys gold, it must settle any residual discrepancy between the country’s current account balance and net private purchases of foreign issued assets by accumulating reserves in the form of US Treasury bills. Alternatively expressed, it describes the purchases of US Treasury bills which the Japanese central bank must make in order to prevent its exchange rate from floating up.

20. The evolution of foreign reserves of the # country  reserves = (Bcb#$d) + (or#.pg#) = (xr$.Bcb#$s) + (or#.pg#) = Bcb#$s.xr$ + xr$.Bcb#$s-1 + or#.pg# + pg#.or#-1 The terms on the right are capital gains.

23. Similarities There are no Rules of the game: the money stock does not change A twin surplus arises in the steady state There is a compensation mechanism at work: the rise in CB reserves is compensated by the fall in domestic credit Differences The current account surplus and the govt budget surplus are not constant anymore They both grow at the rate of the interest rate In the case of the deficit country, the US, there is no limit to this process: there is no fall in the Fed reserves, since the US dollar is the international currency Comparision with simplest model

24. Contradicting received opinion • Alan Greeenspan has been saying that Chinese accumulation of US Treasury bills is making it difficult for them to manage their monetary policy; but the above analysis strongly suggests that he is mistaken. • Mainstream authors would say that the Japanese (or the Chinese) central bank of our model is “sterilizing” foreign reserves, by selling domestic Treasury bills on the open market. In a way, it is true. But this is not the result of any intentional policy, where central bankers are actively intervening in financial markets. • The Japanese (Chinese) central bank, just like the US one, is simply attempting to keep interest rates constant. Bills are provided to those who demand them at the set rate of interest. The central bank provides cash on demand to its citizens.

25. Flexible exchange rates closure • To transform the model into a flexible exchange rate model, we must inverse or « bump » a small series of equations, because reserves cannot change anymore. • Eventually one equation becomes: • xr# = B$#d/B$#s • The endogeneity of the exchange rate only finds itself expressed in one single equation. But the effect works its way round so that the supply and demand for all assets are all brought into equivalence at (and by) the new exchange rate, until all stock changes revert to zero

27. What is meant here by the « balance of payments » is really the current account balance, which goes back towards zero

28. Closure with endogenous interest rates in the deficit country • Essentially we start from the flexible exchange rate model, but impose upon it that the exchange rate must remain constant. Hence another variable must become endogenous – the rate of interest on bills of the deficit country

30. Interest rate adjustments bring in instability • Interest rate adjustments will only keep the asset market in equilibrium for a single period. If the “UK” goes on having an external deficit, there will have to be a further rise in the UK interest rate, to induce foreign inflows of capital and a positive capital account. As there is no mechanism in play to correct the deficit,we end up with an unstable situation – the interest rate has to go on rising for ever. Meanwhile, the balance of trade remains negative, while the current account balance keeps getting worse, due to the rising burden of interest payments that need to be made abroad. • The model is in an explosive mode.