Question Details

[answered] Macroeconomic Models: With the description of various inter

4.Historically( that is, prior to 2008) the Fed directly influenced only short-term interest rates( for example, the federal funds rate and short term Treasury security rate) through its purchase and sale of short-term Treasury securities. Discuss how the direct actions on short-term rates translate into effects on other interest rates( when interest rates are not at the zero lower bund); in particular

(Notes 3)

1 Use the term structure of interest rates to discuss how the direct action of the Fed can affect market( or nominal) rates on long-term Treasury securities.

2. Use the risk structure of interest rates to discuss how the direct action can affect market rates on corporate bonds and on home mortgages.

5.Suppose the Fed recently released the following hypothetical announcement; although we expect the economy to be doing a lot better in about a year from now. As a result, we plan on keeping the federal fund rate and short-term Treasury interest rates at term interest rates. We plan on keeping short rates high for some time thereafter to over the last several years. Also we understand that our current policy of very low short-term interest rates has led to increased uncertainty about inflation prospects over the coming years. We are confident that our new policy strategy will reduce the nervousness in financial markets and reduce inflation uncertainty immediately.

  • Based on theories of the term structure of interest rates, give a detailed answer explaining what you think would happen to the slope of the Treasury yield curve if everyone believes the Fed?s announcement.
  • In general we have observed over at least the past 50 years that current short

Term interest rates display more variation (up and down) than current long-term interest rate. Explain why? Also discuss whether the Fed?s (hypothetical) policy announcement variation in short-term and long-term interest rates.

6.Suppose that the economy is shocked from an initial position of long-run equilibrium and that, as a result, we observe an immediate (i.e short,-run) increase in potential output but a decline in actual outputs and inflation. The Fed announces that it has not altered its target rate of inflation

  • Use the model of aggregate demand and aggregate supply developed in class (assuming adaptive adjustment of inflation expectations) to explain what set of factors could have caused these observation and why.
  • Given your answer to the previous part, explain what happens to the real interest rate and to exchange rate (in units: foreign currency per dollar) in the short run
  • Suppose that the nominal or market interest rate moves in the same direction as the real interest rate in your answer to part2, Discuss what must have happened to the price of existing(coupon or zero-coupon) bonds using formulas presented in this course( carefully define each variable)

7. Suppose the Fed issues the following hypothetical announcement:

? We now plan on using a policy rule in which the real interest rate depends only on the expected rate of price inflation as opposed to depending on the actiial current rate of inflation( relative to target) and the level of output( relative to potential output) More precisely, our new rule r = r0+r?e where r is a positive constant.?

What could justify the Fed?s change in focus from actual current inflation to expected future inflation?

Assume that our classroom macroeconomic model is exactly same as always expect for substitution of the new monetary policy rule, given this alternative macro model, what are the impacts in the short run f a positive shock in aggregate demand, such as an increase in government expenditures, G?? You answer should clearly indicate the impact in the short run of an exogenous increase in G on the (1) new MP curve, (2) IS curve (3) new AD curve, and (4) AS curve of an exogenous increase in G; in so doing, indicate the short-run impact on (5) inflation (6) output, and (7) the real interest rate ( Hint: the effect of the new policy rule on the MP and AD curves is tricky, so be careful)

What happens to expected inflation, output and the real interest rate in the long run? In qualitative terms, how does your answer differ, I at all from the answer in the case of our standard classroom model?

8.Suppose that the current yield to maturity of 3-year, 6 year and 9year Treasury securities is 3%, 6% and 9%respectively ( all yield are expressed at annual rates).Using the expectations theory of the term structure, calculate the following implicit expected annual interest rates.

I: the implicit expected annual rate on a 3 year bond purchased 3 years in the future (3 year from today)

II: the impact expected rate on a 6 year bond purchased 3years in the future.

III: Finally assume that the term premium on a 9 year bond is 2%( perineum) use the liquidity premium theory of the term structure of interest rate to calculate:

The implicit expected rate on a 6-year bond purchased 3 years in the future.

Macroeconomic Models:


With the description of various interest rates and financial institutions as background, we


now turn to development of macroeconomic models that will provide us with the


theoretical basis to understand developments in the economy, including the macro effects


of monetary policy and of the collapse of housing prices in late 2006.


IS-MP-AS macroeconomic framework (based on work of Professor David Romer at UC


Berkeley; also partly covered in Cecchetti/Schoenholtz textbook.)


Market in New Goods and Services


1. Current real consumption of domestically-produced or foreign-produced goods and


services depends on current real after-tax income and on expected future real after-tax


income. (It also depends on other factors discussed in points 2, 3, and 4 below.) There


are two main pieces to understanding the basics of modern models of consumption.


First, consumption ?smoothing? over one?s lifetime is approximately optimal. That is if a


person expects to live T periods, then C1 = C2 = ?= CT is approximately optimal. This


follows from the key assumption of diminishing marginal utility of consumption. For


example, over two periods with a total of 20 units of consumption, reallocating one?s


consumption from a smooth (10, 10) to a choppy (5, 15) lowers utility on balance


because reducing consumption by 5 units (in period one) lowers utility more than raising


consumption 5 units (in period two) boosts utility; thus smooth or equal consumption is


optimal (there are some exceptions, discussed in class and briefly below).


Second, under modern models, consumption in every period of life depends on an


individual?s expected lifetime resources, not just today?s resources. Think of this as the


total of your current and expected future after-tax wage income (we will discuss the


impact of non-human wealth below). This has implications for temporary vs. permanent


changes in income.


For example, if a person unexpectedly receives $1 on a temporary or transitory


basis?either because of a one-time wealth transfer or a temporary tax cut?and if the


person allocates the income evenly to consumption in each period of their lifetime (as


should be the case given the point made above), then consumption rises by (1/T) dollars


each period starting immediately. That is, the marginal propensity to consume out of


temporary income?defined as the increase in current consumption for a small change in


temporary income?is (1/T). If T is 33 years, then the one-time $1 boost to income raises


consumption 3 cents per year (relative to baseline) starting immediately. As a topical


application, an exogenous decline in house prices resulting in a $1 fall in household


wealth would reduce total consumer spending by 3 cents (and, in fact, empirical evidence


supports a decline of 3 cents on the dollar in the aggregate).


By contrast, if the person unexpectedly receives an additional dollar every period,


so that the income rise is permanent, lifetime resources rise by $33 and consumption rises


by $1 per year (relative to baseline) starting immediately. Thus the marginal propensity


to consume out of permanent income is 1. [Notice I have described the increase in either


temporary or permanent income as "unexpected." What would happen to the path of


consumption if income increases and if the increase were fully expected, such as an 2


increase in income when you move from college to a job or from your working years to




Implicitly, the prior analysis assumes perfect capital (borrowing and lending) markets so


that an individual can borrow against their expected future income. If the government


announces a permanent tax cut of $1000 per person to take effect in two years then


individuals must be able to borrow against that expected future boost to after-tax income


(or draw down existing savings). Otherwise, consumption smoothing starting today--at


the new higher level of consumption--would not be possible.


To summarize at this point, households will choose the optimal level of current


consumption given today?s expectations of current and future after-tax income, etc. (i.e.,


given today?s view about lifetime resources). They will (approximately) maintain this


level of consumption for the rest of their lifetime unless something unexpected happens


that alters today?s expectations of current and future income, etc. For example, an


unexpected boost to lifetime resources would lead to an immediate increase in


consumption to a new level that would remain constant ("smoothed") until the next


unexpected change in lifetime resources occurs.


2. consumer durables (e.g., autos, computers) provide services over time and thus have an


investment (as well as a consumption) component; thus as the real interest rate?viewed


as the real cost of borrowing?rises, demand for durables falls.


a. real interest rate = r = i - ?e where i is the nominal or market rate of interest




and ? is the expected rate of price inflation. Notice that we are not using the actual (or


realized) rate of inflation but rather the rate that borrowers and lenders expect will occur


as of today when decisions are made. This is called the ex ante real interest rate.


3. Households are believed to display a ?positive rate of time preference,? meaning that


they would prefer to consume now rather than in the future, all else equal. The household


choice between present and future consumption (and hence the decision about saving or


foregone current consumption) depends on the strength of time preference versus the


relative price of future consumption [1/(1+r)]. If the real interest rate changes, there is a


substitution (or incentive) and an income (also called a target-wealth effect) effect that


work in opposite directions. Under the former, a higher rate of return on saving, r,


provides an incentive to save more today or, put another way, to substitute future for


current consumption (for a given rate of time preference). By contrast, saving will fall


(current consumption rise) to the extent that the higher rate of return does not require as


much saving to achieve a target level of wealth in the future (say at retirement). Based on


empirical evidence on aggregate consumption behavior, we assume that the substitution


effect dominates so that higher r means lower current consumption and hence higher


household saving. This effect can alter the above result on consumption smoothing.


4. There are a few other important determinants of consumption. As suggested above,


consumption depends on a household?s net non-human wealth?the value of its stocks


and bonds and houses, etc. minus the value of its debts. The idea is that (net) assets


generate a stream of current and future non-wage income which provides resources (in 3


addition to wages) that support consumption over one?s lifetime. Also, the state of


consumer confidence matters for consumption.


Taken together, the previous points imply that current consumption depends on


current (after-tax) wage income, expected future (after-tax) wage income, non-human


wealth, real interest rates, and consumer confidence. As discussed at length later in the


course, wealth is inversely related to interest rates as well as having an exogenous


component such as the price of housing (assumed exogenous in this course). These


separate factors can replace non-human wealth in the expression for current consumption.


5. Real investment in plant and equipment and software by businesses and in new homes


(i.e., residential construction) by households varies inversely with real borrowing costs,


i.e., with the real interest rate. Also, real business investment depends on business


optimism/pessimism as well as on expectations of future demand for their products (i.e.,


expected future sales).


6. Real U.S. imports depend on our current and expected future income and, hence, real


U.S. net exports (i.e., exports minus imports) vary inversely with domestic income. Also,


real U.S. net exports tend to fall as the dollar rises relative to other currencies (i.e., as the


dollar appreciates). The exchange rate, ex, is denominated in the units: foreign currency


per dollar, so that an increase (decrease) in "ex" denotes an appreciation (depreciation) of


the dollar. In addition, the value of the dollar tends to rise as domestic (i.e. U.S.) interest


rates rise relative to those abroad. This is because higher U.S. rates provide an incentive


for worldwide investors to increase the demand for dollars to buy dollar-denominated


interest bearing securities, which in turn pushes up the value of the dollar. Thus higher


domestic interest rates reduce U.S. net exports (and equivalently boost foreign saving in


the U.S.)


7. Y = C + I + G + X ? IM or, equivalently, I = Shh + Sbus + Sgov + Sfor .


These two equations define equilibrium in the market for new goods and services. The


second equation explains why goods market equilibrium is sometimes called the IS (or


more accurately, I = S) relation.


The full set of equations defining the goods market is presented next:


1. Y = C + I + G + X ? M


2. C = C0 + cy(Y ? T) + cye(Y ? T)e -cr r


3. I = I0 + iy Y + iye Ye - ir r


4. NX = N0 - ny Y - nyeYe - ne ex


5. ex = e0 + er (r ? rf) 4


Notice that the equations are linear in the variables. A list of variables contained in the


model follows:


Y denotes real output or income (basically, real GDP)


C denotes real private consumption expenditures


I denotes real private investment expenditures (business plus residential)


G denotes real government expenditures (not including transfer payments)


NX = X-IM denotes real exports less imports


T denotes taxes minus transfer payments, real


Y ? T, Ye ? Te denote real current and expected future disposable income, respectively


r denotes the real interest rate


rf denotes the real foreign interest rate


ex denotes the exchange value of the dollar (expressed in units of foreign currency per




Shh, Sbus, Sgov, Sfor denote household, business, gov?t, and foreign saving, respectively


All intercepts terms and slope coefficients are taken as constant unless otherwise noted.


Examples of slope coefficients are:


cy = dC/d(Y-T) = marginal propensity to consume out of current real disposable income.


iy = dI/dY = marginal propensity to invest out of real income


By substituting equations 2 ? 5 into equation 1 and solving the result for r as a function of


Y, we get the following linear equation that mathematically defines the IS curve:


r = (messy negative slope coefficient) Y + (messy intercept term)


Conclusion: higher domestic real interest rates are negatively related to aggregate


demand in goods market equilibrium; this is because C, I, and NX are each inversely


related to real interest rates (be certain that you understand the economics behind this


fundamental point). The downward sloping curve in (y, r) space that captures all


combinations of real interest rates and GDP consistent with equilibrium in the market for


goods and services is called the IS curve. A simple way of thinking about why the IS


curve is downward sloping follows: because Y = C+I+G+NX, an increase in Y must be


matched by an increase in C+I+G+NX, which requires a reduction in r. Also, the curve


shifts to the right (or upward) with increases in current G, improved consumer or business


confidence, increased foreign demand for U.S. goods?in short, it shifts with changes in


any exogenous variable appearing in the ?messy intercept term.? The effect of tax cuts


on current consumption and, hence, aggregate demand is ambiguous; they boost current


disposable income but reduce future disposable income if the current cuts are expected to


be financed by future tax hikes.


An aside on curve shifting: Recall the equation for a straight line, Y = mX + b. Here, Y


is the variable on the vertical axis, X is the variable on the horizontal axis, ?m? is the


slope of the line, and ?b? is the Y-intercept. Generally in this course, important curves


(such as the IS curve) will be straight lines, so the above formula applies. The curve


shifts if and only if ?b? changes (of course, ?b? may be a complicated linear combination 5


of several exogenous variables, so ?b? will change if any of its components change).


Finally, if Y changes but ?b? does not then we are talking about movement along the


curve rather than a shift of the curve. What happens to the curve when ?m? changes?


Monetary Policy


1. r = M (? ? ?*, Y ? Yp) = r* + r?(? ? ?*) + ry(Y ? Yp)


The Fed is assumed to raise real interest rates when price inflation on goods and services,


?, rises relative to its target, ? *, and when the output gap (difference between actual and


potential GDP) rises. I have linearized the M function after the second equals sign; in


this expression, r* is a constant, although it depends on a host of factors in more


complicated formulations. Also, r? and ry are constants. For example, ry = dr/d(Y ? Yp)


and is interpreted as the impact of a change in the output gap on the real interest rate. In


class, I will set ry = 0, to simplify the analysis.


This monetary policy ?rule? can be described as ?leaning against the wind.? The idea


intuitively is that if ? rises or if Y rises, an increase in the real interest rate by the Fed


reduces aggregate demand (through the channels discussed above) and puts downward


pressure on inflation and output; conversely, if ? falls or if Y falls, a reduction in the real


interest rate by the Fed boosts aggregate demand and puts upward pressure on inflation


and output. Notice that when Y = Yp and ? ? ?*, the Fed sets the real rate equal to r*.


The rate, r*, is called various names, including the "natural," the "neutral," and the


"equilibrium" level of the real interest rate. Suppose we start with: Y = Yp and ? ? ?*; in


this case, r = r* and policy is said to be neutral. From this situation if output and inflation


were to decline (possibly as a result of a negative aggregate demand shock) then r < r*


and policy is said to be stimulative. Similarly, if r > r* policy is said to be contractionary.


The rule is deceptively simple, masking a host of important issues, including:


a. for stability, Fed must target the real interest rate-- if ? rises and i goes up (recall that


"i" is the nominal or market rate of interest), but less than point-for-point, the real interest


rate falls and aggregate demand rises and hence ? rises even more, leading to unstable




b. Can the Fed affect real interest rates? Yes, if ? is sticky in the short run, as evidence


strongly suggests (especially the experience during the late 1970s and early 1980s).


c. Which goal is more important to the Fed? Are the goals of low inflation and high


output complementary?this is an extremely important issue that is discussed later.


d. Should arguments of the M function be the expected future values of ? and y, rather


than current values? Arguably, by cutting interest rates through the early stages of the


financial crisis the Fed appeared to respond to their forecast or expectation that the


housing/financial market mess would hurt the future level of overall economic activity. 6


e. Should the Fed respond to movements in ?headline? price inflation (e.g., the total CPI)


or in ?core? inflation (total CPI excluding food and energy prices)? Although households


obviously pay for food and energy?and so the total CPI matters to consumers?


movements of prices of these goods often are transitory (e.g., changing with the seasons).


Core prices are less volatile and generally provide a better short-run signal of underlying


trend movements in the cost of living. This view was called into question by events that


resulted in persistent increases in food and energy prices over the couple of years prior to


the fall of 2008.


It also is important to note that the Fed?s task is complicated by the fact that there


are several empirical measures of inflation, including the CPI; the Fed actually focuses on


the personal consumption expenditures price index, not the CPI.


f. Should asset prices?such as the prices of houses and stocks?be an argument of the


M function? The idea is that central banks perhaps should be concerned with the


development of asset price ?bubbles? in which asset prices rise in anticipation of further


asset price increases rather than on changes in underlying fundamentals. The Fed does


not react directly to movements in asset prices, only indirectly to the extent that asset


prices affect Y and ?. Former Chairmen Greenspan and Bernanke both have argued


against responding directly to asset price bubbles. They argue that in practice it is hard, if


not impossible, to identify bubbles as they are occurring. Further, even if they could be


identified, it is not obvious how to deflate bubbles. And, when bubbles burst, they have


argued that the Fed can deal with the fallout when it happens with the intention of


limiting collateral damage to the rest of the financial system and to the overall economy.


This perspective has been sorely tested by the housing/financial/macroeconomic crisis of


the past few years.


Professor Alan Blinder (of Princeton and also former Vice Chair of the Federal


Reserve) has offered an interesting appraisal of the conventional Fed view of intervening


in bubbles. He notes that the Fed executed a successful mop-up-after strategy when the


tech bubble popped in 2000. Despite the loss of roughly $8 trillion in wealth, not one


financial institution of any size failed and the ensuing recession was so mild in terms of


output loss that it was call ?the recessionette.? By contrast, perhaps because of the sheer


size of the subprime bubble bursting and associated financial crisis, the Fed?s mop-up


strategy seems not to have worked so well or quickly, as the financial system and


economy as a whole have improved very slowly.


Blinder argues that there are two types of bubbles and the Fed potentially can


intervene in one type while it is occurring. He calls this type a ?bank-centered bubble?


and is characterized by speculative excesses fueled by irresponsible bank lending. In this


case, the Fed?s role as a bank supervisor and regulator gives it extraordinary insight into


bank lending practices and arms it with several tools to address harmful lending practices,


such as outright prohibition of certain types of lending or other forms of regulatory


discipline. In contrast, Blinder argues that in the second type of bubble, such as stock


market bubbles, bank lending plays at best a minor role; in this case, the Fed is not well


positioned to intervene as the bubble is developing (the Fed has no tools aimed directly at


tech stocks and only limited ability to affect stock prices more broadly). 7


g. Zero bound on nominal interest rates: As noted in the first module of the course, the


Fed?s target level of the federal funds rate reached close to zero in late December 2008


and remains only slightly higher as of September 2016. The funds rate cannot go any


lower, so it appears that the Fed is out of its traditional ammunition. However, ?the real


interest rate? in the monetary policy rule should be interpreted as the interest rate relevant


for affecting macroeconomic behavior; in normal times it is reasonable to think of this as


the real federal funds rate because it is the rate targeted by the Fed and because other


interest rates more closely tied to macro behavior are indirectly related to it (in ways we


will discuss in detail later in the course). Currently, it is better to think of ?the real


interest rate? as longer term interest rates such as the long-term rate on Treasury


securities which is greater than zero; in the current environment the Fed has been trying


?evidently with some success?to bring down such longer-term interest rates directly.


h. In (y,r) space, the curve relating all values of r and y consistent with the monetary


policy rule is called the MP line. It is horizontal if r depends only on ?; it is upward


sloping if r depends on y. The idea is that if y falls (rises) the Fed leans against the wind


by reducing (increasing) the real interest rate. Also, the MP curve shifts up with higher


inflation: the idea is that, for a given y, higher inflation causes the Fed to boost the real


interest rate to fight the higher inflation. The curve shifts up (down) if the target rate of


inflation falls (rises). **To simplify the analytics for the rest of this module, we will set ry


=0, ignoring the impact of the output gap on interest-rate setting by the Fed; thus we


will consider only the case where the MP line is flat, shifting up or down with inflation.**


Aggregate Demand: IS-MP in (Y, ?) space


--As ? rises, r rises because of the Fed response; this leads to a reduction in the interestsensitive components of aggregate demand (AD). The curve relating all values of Y and


? consistent with goods market equilibrium subject to the Fed?s policy response function


is called the AD curve; it is downward sloping. The curve shifts upward or to the right


with higher values of current G, improved consumer/business confidence, and lower


taxes (subject to the earlier caveats), and higher values of the Fed?s target rate of inflation


(?*). [For certain former Econ 110 students, notice that this approach differs from the


IS-LM-AD approach because it focuses on price inflation rather than on the price level.]


Inflation adjustment/Aggregate Supply


We will introduce two characterizations of the supply side of the economy but then focus


on only one of them. Both approaches incorporate some ?stickiness? into the inflation


adjustment process, which is realistic for the U.S. economy. In the first approach,


inflation itself is assumed to have inertia or to be ?sticky? in the short run, in part because


of multi-year labor and supply contracts that fix the rate of increase of certain wages and


prices for a period of time. The CPI inflation rate, e.g., varies every month but usually


not by much, so this is not an unreasonable starting point. For the U.S. economy, this


case probably overstates the importance of inflation inertia and understates the extent to


which aggregate demand movements initially affect inflation. In the second approach,


inflation expectations are sticky; this probably understates the importance of inertia in


inflation itself but overstates the extent to which demand disturbances initially affect 8


inflation. The Fed staff tends to use variants of the second approach because of the


importance of inflation expectations to the price adjustment process in the United States;


we will focus on this approach below.


Define the actual rate of price inflation as the percentage change in the price level,


(Pt - Pt-1)/Pt-1 = ?Pt/Pt-1. For the sake of brevity let ?Pt/Pt-1 = ?t. In this definition, the


price level at time t (today) is Pt. The price level in period t-1 (last period) is Pt-1. Dating


of the other variables in the model is handled the same way.


The expected rate of price inflation also is an important concept. In particular, we can


ask: given all the information available to you last period, by how much did you expect


last period's price level, Pt-1, to increase this period (again, expressed as a percent of last


period's price level)? The answer is: ( Pet - Pt-1)/Pt-1. In this expression, Pet is the price


level that you expected last period to occur this period and ( Pet - Pt-1)/Pt-1 is known as the


expected rate of price inflation for period t, ?et. To drive home the point, the price level


that you expect this period to hold next period (in period, t+1) is given by, Pet+1.


The first key equation defining the inflation adjustment process is:


*** ?t = ?et + g (Yt - Yp) + ?s, where g is a positive constant. Equation S1 1. This equation is a standard expectations-augmented Philips curve (the simple


Philips curve relates inflation to the GDP gap only), also known as the aggregate supply


relation. Current inflation depends on expected inflation point-for-point; it varies


positively with the output gap (Y ? Yp); and it depends on ?inflation shocks,? denoted as


?s. For the moment, ignore these inflation shocks. The equation says that output is high


(exceeds the natural or potential rate, Yp) when inflation exceeds expected inflation, i.e.,


when the public has been surprised by the level of inflation. The idea is that if prices of


output are unexpectedly high, producers would desire to supply more output than


originally planned.


In this sense there is a tradeoff for the economy in the absence of inflation shocks


and for a given expectation of inflation: we can have more aggregate output (and lower


unemployment) if we are willing to accept higher price inflation or, conversely, we can


achieve lower price inflation only at the expense of less output. By contrast, if


expectations of inflation always equaled actual inflation, there would be no tradeoff. (As


we will see below, in our model there is a short-run tradeoff due to fixed inflation


expectations in the short...


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