Chapter 4: Government Money with Portfolio Choice

• Introduction
  
  Model PC (Portfolio Choice) introduces government bills, interest payments and the central bank into model SIM.
  Households may now hold money or bills.
  Money+Bills = Private Debt
  Net Worth of Households = Net Worth of Private Sector
  Counterpart to Private Sector: Public Debt
  Public Debt = Outstanding Bills issued to Households and the Central Bank by Government
  Assets of Central Bank: Government Bills. Liabilities: Money provided to households.
  The current account of the central bank describes the inflows and outflows from current operations. The capital account describes any changes in the central bank’s balance sheet.
  
  Equation of model PC
  
  The main assumption in Model PC is that producers sell whatever is demanded.
  -Production = consumption + government expenditure.
  -Disposable income increased by interest on government debt.
  -Taxable income increases with interest payments on bills held by households.
  
  Portfolio Decision
  The household sector makes decisions in two stages. Firstly, households decide how much to save and then how to allocate their wealth. The difference between disposable income and consumption is equals the change in total wealth and the new consumption function now contains total wealth.
  
  Households hold some of their wealth in the form of bills and some in the form of money. The proportion held in the form of bills is negatively related to the interest rate and positively related to the level of disposable income. The interest rate must equalize the supply and demand for bills. Holdings of money are the difference between total household wealth and their demand for bills
  
  The Endogeneity of the Money Supply
  
  The government budget constraint represents total government expenses less government revenues. The capital account of the central bank states that additions to the stock of high powered money equal the additions in the demand for bills. The central bank purchases the bills issued by government that households are not willing to hold given the interest rate (residual purchaser).
  
  Expectations
  
  If realized disposable income is greater than expected, the additional disposable income will be saved in the form of cash money balances. Money balances provide flexibility in a monetary system of production and act as a buffer to absorb unexpected cash flows. Households invest in bills on the basis of the expectations they make in relation to their disposable income at the start of the period.
  
  The Steady State Solution
  
  In Model PC, the interest rate plays a greater role. Higher interest rates induce households to hold more interest paying bills. This decrease in the liquidity preference of households leads to an increase in national income as the issuance of more bills means government debt has increased. Therefore, higher interest rates generate higher economic activity. This contradicts previous economic thought that high interest rates stunt economic growth.
  
  Results
  
  An increase in the permanent level of government spending increases the stationary level of income and disposable income; dY*/dG >0. Any permanent decrease in the overall tax rate Q has the same effect; dY*/dQ <0.>0 where a3 = (1-a1)/ a2. Thus if households decide to save larger amounts of both their current income and past wealth than what is consumed then the level of steady state income will be higher.
  
  These results contradict a ‘paradox of thrift’ that has been put forth by Keynesians for years. Keynesians stated that higher saving levels lead to higher stationary levels of income because households were seeking a higher overall wealth target for a given income. However, this implies higher interest payments on government debt and thus a higher steady state income has been achieved.
  
  
  Graphical Analysis
  
  The effect of an increase in the propensity to consume out of disposable income is that GDP increases in the short run but decreases in the long run leading to a lower steady state.
  
  The behaviour of national income can be explained as follows. As households increase consumption out of current income there is an initial increase in national income due to an increase in aggregate demand. However, savings decrease, depleting the stock of wealth. This eventually overtakes the positives of higher levels of consumption out of current income. Wealth and consumption drop until national income reaches a new lower steady state level.
  As households are spending more government tax revenues increase and the government goes into a surplus allowing them to pay off some of their debt.
  
  Figure 4.7 shows the effect of an increase in the rate of interest set by the central bank. Any increase in the rate of interest or the tendency to consume leads to a temporary increase in disposable and national incomes. The target level of wealth also increases, suggesting an increase in savings and demand for bills by households. In the next period, consumption and income rises leading to a higher steady state.
  
  Figure 4.8 shows the effect of a decrease in the tendency to consume. Here, the target wealth to income ratio would rise. There would be an initial fall in national income but there would also be a discrepancy between current wealth and target levels of wealth, enticing households to purchase bills.
  
  The Puzzling Impact of Interest Rates Reconsidered
  
  Here we assume the MPC is not constant, and assumes a value which depends negatively on the interest rate on bills. The initial impact of the increased interest rate on the economic activity is negative, causing a fall in consumption, disposable income and national income.
  
  A reduction in the MPC increases the target wealth to income ratio, leading to an increase in the stock of wealth. If households’ wealth keeps increasing consumption demand is lower than disposable income.
  
  There is also an increase in government debt. The short term recession caused by the negative impact of the higher interest rates forces government tax revenues down. This negative effect is reinforced by an overall increase in government expenditures as a result of the higher cost of servicing their debt. The total effect is a government deficit. This shrinks as government expenditures and taxes continue to increase up to stationary level. Here the government budget is balanced, and eventually the deficit flow is wiped out by rising consumption expenditures.
  
  
  A Government Target for the Debt to Income Ratio
  
  Relative amount of Public Debt = V/Y (Wealth of Households/GDP)
  The steady-state wealth to disposable income ratio is determined by the behavior of households, which equals the α3 ratio. Governments can do nothing to alter the debt to disposable income ratio. Government and credit rating agencies are more concerned with public debt as a ratio of GDP, which is easier to modify. If households are targeting too high a wealth ratio, the government can reduce its stationary debt to GDP ratio. If government wishes to decrease this, they need to increase tax rates or reduce interest rates, resulting in a reduced level of stationary income. Thus, the debt to income ratio must be disregarded to sustain full employment income.