The Investment Equation

1. By effectively setting the rate at which people borrow and lend in financial markets, the Fed exerts a substantial influence on the level of economic activity in the short run • The IS curve captures the relationship between real interest rates and output in the short run • An increase in the interest rate will decrease investment, which will decrease output: Y = C + I + G + NX • The decrease in output is normally a multiple of the decrease in investment I down  Y down  C down  Y and C down yet more • In Jones’ freshwater world, however, C depends on permanent income and doesn’t respond to changes in short-run output and income • Changes in I do not lead in multiplicative changes in Y • The IS Curve shows activity decreasing when interest rates rise and investment spending declines

2. CHAPTER 10 The IS Curve

3. The national income accounting identity implies that the total resources available to the economy (domestic production, Y, plus imports, IM) equal total uses (consumption, C, investment, I, government purchases, G, and exports, EX) • The national income identity is one equation with six unknowns: Yt = Ct + It + Gt + EXt - IMt • Thus we need five additional equations to solve the model • consumption, government purchases, exports, and imports each depend on the economy’s potential output which is given exogenously • each of these components of GDP is a constant fraction of potential output – where the fraction is a parameter

4. The Investment Equation • The equation includes one term accounting for the share of potential output that goes to investment, parameter aibar • It also includes a term weighting the difference between the real interest rate Rt, and the marginal product of capital, r bar • the MPK, r bar, is an exogenous parameter and is time invariant • When the MPK is low relative to the real interest rate, firms should save their money • However, if the MPK is high relative to the real interest rate, firms should borrow and invest in capital • The sensitivity to the changes in the interest rate is denoted by parameter b bar • in the short-run, the MPK and the real interest rate can be different because installing new capital to equate the two takes time • For now we take the real interest rate, R, as given

6. Deriving the IS Curve 1. divide the national income accounting identity by potential output: 2. substitute the five equations into this equation:

7. 3. recalling the definition of short-run output, this simplifies to the equation for the IS curve:

8. The gap between the real interest rate and the MPK matters for output fluctuations • firms can always earn the MPK on new investments • note as well that the parameter will equal zero when potential output is equal to actual output • the parameter is the sum of the aggregate demand parameters for consumption, investment, government purchases, exports and imports minus one and is thus called the aggregate demand shock

9. when the aggregate demand shock parameter equals zero, the IS curve has a short-run output of 0 where the real interest rate is equal to the long-run value of the MPK • when the real interest rate changes, the economy will move along the IS curve • an increase in the interest rate causes the economy to move up the IS curve and short-run output will decline • the higher interest rate raises borrowing costs, reduces demand for investment, and reduces output • if the sensitivity to the interest rate were higher, the IS curve would be flatter and a given change in the interest rate would be associated with larger changes in output • the higher interest rate raises borrowing costs, reduces demand for investment, and therefore reduces output below potential

10. when the aggregate demand shock parameter equals zero, the IS curve has a short-run output of 0 where the real interest rate is equal to the long-run value of the MPK • when the real interest rate changes, the economy will move along the IS curve • an increase in the interest rate causes the economy to move up the IS curve and short-run output will decline • the higher interest rate raises borrowing costs, reduces demand for investment, and reduces output • if the sensitivity to the interest rate were higher, the IS curve would be flatter and a given change in the interest rate would be associated with larger changes in output • the higher interest rate raises borrowing costs, reduces demand for investment, and therefore reduces output below potential

12. An Aggregate Demand Shock • suppose that information technology improvements create an investment boom: • the aggregate demand shock parameter will increase • output is higher at every interest rate and the IS curve shifts right • for any given real interest rate Rt, output is higher when increases

14. A Shock to Potential Output • short-run output is unaffected by a change in potential output • shocks to potential output change actual output by the same amount in our setup • however, some shocks to potential output, such as an earthquake, may change other parameters in addition to potential output • the earthquake example reduces actual and potential output by the same amount, but leads to an increase in short-run output because it also increases the MPK Other Experiments • imagine that Japan enters into a recession and reduces her imports • This, of course, is contrary to Jones’ assertion that (Japan’s) aim bar is a parameter …but it makes more sense than assuming Japan’s imports are insensitive to her short-run output and income • the aggregate demand parameter for our exports, aex bar, declines and our IS curve shifts to the left • thus the Japanese recession has an international effect • we could shock any of the other aggregate demand parameters that are a part of a bar

15. Microfoundationsof the IS Curve Consumption • people seem to prefer a smooth path for consumption to a path that involves large fluctuations in consumptions • the permanent-income hypothesis concludes that people base their consumption on an average of their income over time rather than on their current income • the life-cycle model of consumption suggests that consumption is based on average lifetime income rather than on income at any given • when young, people borrow to consume more than their income • as income rises over a person’s life, consumption rises more slowly and individuals save more • during retirement, individuals live off their accumulated savings • the life-cycle/permanent-income (LC/PI) hypothesis implies that people smooth their consumption relative to their income • this is why Jones sets consumption proportional to potential output rather than actual output • a strict version of the LC/PI hypothesis implies that predictable movements in potential output should also be smoothed

16. the life-cycle model of consumption: • when young, people borrow to consume more than their income • as income rises over a person’s life, consumption rises more slowly and individuals save more • during retirement, individuals live off their accumulated savings CHAPTER 10 The IS Curve

18. Multiplier Effects • we can modify the consumption equation to include a term that is proportional to short-run output: • solving for the IS curve yields an equation that is similar to the previous result, but that now includes a multiplier on the aggregate demand shock and interest rate terms: • the multiplier is larger than one • aggregate demand shocks will increase short-run output by more than one-for-one in the presence of the multiplier • if one section of the economy is shocked, it will “multiply” through the economy and will result in a larger effect…if short-run output falls, consumption falls, which leads to short-run output falling and consumption falls again in a “vicious circle”

19. Investment • at the firm level, the gap between the real interest rate and the MPK determines investment • in a simple model, the return on capital is the MPK minus depreciation • a richer framework includes corporate income taxes, investment tax credits, and depreciation allowances

20. a second determinant of investment is the firm’s cash flow, which is the amount of internal resources the company has on hand after paying its expenses • it is more expensive to borrow to finance investment because of agency problems • agency problems are when one party in a transaction has more information than the other party

21. adverse selection is the idea that if a firm knows it is particularly vulnerable, it will want to borrow because if the firm does well it can pay back the loans. If it fails, the firm cannot pay back the loan but will instead declare bankruptcy • moral hazard is the idea that a firm that borrows a large sum of money may undertake riskier investments because if it does well, it can repay, while if it fails it can declare bankruptcy

22. the potential output term in the investment equation incorporates cash flows to a degree • cash flow effect can be seen in the presence of potential output • if we wish to add short-run output , it would provide additional justification for a multiplier

23. Government Purchases • government purchases can be a source of short-run fluctuation or an instrument to reduce fluctuations • discretionary fiscal policy includes purchases of additional goods in addition to the use of tax rates • for example, the government can use the investment tax credit to encourage investment today rather than later

24. transfer spending often increases when an economy enters into a recession • automatic stabilizers are programs where additional spending occurs automatically to help stabilize the economy • welfare programs and Medicaid are two such stabilizer programs that receive additional funding when the economy weakens

25. fiscal policy’s impact depends on two things: 1. The problem of timing may make it such that discretionary changes are often put into place with significant delay. 2. The no-free-lunch principle implies that higher spending today must be paid for, if not today, some point in the future. Such taxes may offset the impact of the discretionary spending adjustment.

26. the permanent-income hypothesis says that what matters for consumption today is the present discounted value of your lifetime income, after taxes • Ricardian equivalence is the idea that what matters for consumption is the present value of what the government takes from the consumers rather than the specific timing of the taxes CHAPTER 10 The IS Curve

27. an increase in government purchases financed by an increase of taxes of the same amount will have a modest positive impact on the IS curve and will raise output by a small amount in the short-run • an increase in spending today financed by an unspecified change in taxes and/or spending at some future date will shift the IS curve out by a moderate amount – perhaps as much as 25 to 50 cents for each dollar CHAPTER 10 The IS Curve

28. Net Exports if the trade balance is a deficit, the economy imports more than it exports if the trade balance is in surplus, the economy exports more than it imports • the trade balance is the main way that foreign economies influence the U.S. economy in the short-run an increase in the demand of U.S. goods in foreign countries stimulates the U.S. economy by an outward shift of the IS curve if Americans shift their demands to imports, the IS curve shifts left and reduces short-run output

29. 10.6 Conclusion • higher interest rates raise the cost of borrowing to firms and households and thus reduce the demand for investment spending – lowering short-run output CHAPTER 10 The IS Curve

30. Summary 1. The IS curve describes how output in the short run depends on the real interest rate and on shocks to the aggregate economy. 2. When the real interest rate rises, the cost of borrowing faced by firms and households increases, leading them to delay their purchases of new equipment, factories, and housing. These delays reduce the level of investment, which in turn lowers output below potential. Therefore, the IS curve shows a negative relationship between output and the real interest rate. CHAPTER 10 The IS Curve

31. 3. Shocks to aggregate demand can shift the IS curve. These shocks include (a) changes in consumption relative to potential output, (b) technological improvements that stimulate investment demand given the current interest rate, (c) changes in government purchases relative to potential output, and (d) interactions between the domestic and foreign economies that affect exports and imports. 4. The life-cycle/permanent-income hypothesis says that individual consumption depends on average income over time rather than current income. This serves as the underlying justification for why we assume consumption depends on potential output. CHAPTER 10 The IS Curve

32. 5. The permanent-income theory does not seem to hold exactly, however, and consumption responds to temporary movements in income as well. When we include this effect in our IS curve, a multiplier term appears. That is, a shock that reduces the aggregate demand parameter by 1 percentage point may have an even larger effect on short-run output because the initial reduction in output causes consumption to fall, which further reduces output. CHAPTER 10 The IS Curve

33. 6. A consideration of the microfoundations of the equations that underlie the IS curve reveals important subtleties. The most important are associated with the no-free-lunch principle imposed by the government’s budget constraint. The direct effect of changes in government purchases is to change . However, depending on how these purchases are financed, they can also affect consumption and investment, partially mitigating the effects of fiscal policy on short-run output CHAPTER 10 The IS Curve