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Final Exam Study Guide

Some post-midterm review questions:


1. In a given economy, the money supply is acyclical, the price level is countercyclical, and technology and wages are procyclical. Which business cycle theory or theories could explain this outcome?

Answer: According to Williamson, only the RBC model fits the model. A money-driven model, on the other hand, would not account for countercyclical prices. See Williamson, table 11.1 (p. 409) and table 11.3 (p. 432).

If money is acyclical (or fixed), then in an RBC model, prices should be countercyclical. It comes from the Equation of Exchange: MV=PY. If M and V are fixed, then a rise in Y (due to technology) must cause a fall in P. The same turns out to be true for the coordination failure story.


2. In a flexible-price cash-in-advance economy such as that in Williamson’s Macroeconomics, what are the two financial assets that the representative agent chooses between?

Answer:The representative agent chooses between bonds and currency. Currency can be withdrawn from the bank account at the beginning of the day or accessed through debit card or check throughout the day. Assuming the consumer faces a positive nominal interest on bonds, the consumer will not leave any idle cash in the bank account at the beginning of the day, choosing to either buy more bonds with it or withdraw it as currency to spend on consumption goods. Mc = M– + B–c (1+R–) + PY – PC – Bc – PT – PH(X) (note: Mc the "c" is subscript, M- the "-" is a superscript, B-c the "-" is superscript and the "c" is a subscript, R- the "-" is a subscript, Bc the "c" is subscript)


3. In a world where the pure expectations theory of the term structure holds, when happens to today’s rate on five-year bonds when:

Answer: As per Campbell's paper the formula is: Current Yield on Long-term Bond = Average short rate over the period of the long bond.

a. The current and future one-year rates are all 4% per year. A: The five year rate will also be 4% b. The 3rd-year rate rises from (a) to 10% A: The five year rate will be 5.5% c. The 4th year rate rises from (a) to 10% A: The five year rate will be 5.5%


4. In a world where the pure expectations theory of the term structure holds, when the spread between the five-year rate and the one-year rate widens, then what have we learned about future interest rates?

Answer: That future short-term (1 year) rates are also going to increase; additionally, short-term rates will increase faster than long-term in order to decrease the yield spread. Page 137 at the bottom, Campbell article.


5. In a world where either the pure expectations theory of the term structure or the term-premium version of the expectations theory holds, when the spread between the five-year rate and the one-year rate widens, then what is the complete set of possible explanations for this phenomenon?

Answer: When the spread between the long-term bond yield and the current short-term bond yield increases, that means that people have rational expectations that the average short-term rates over the life of the long-term bond are going to increase. This is another way of saying that people expect interest rates to increase in the future. This is often the case when large amounts of economic growth are expected (they expect the Fed to cause interest rate increases to "cool down" the economy when it's expanding). Thus, expected economic growth is a possible explanation of the spread.

Other explanations include: 2. expected inflation increases, which increases the future short term yields. 3. An increase in the Risk Premium for future short term yields. Although the pure-expectations theory does not take risk premiums into account the term-premium version of the expectations theory does.


6. Stagflation: High inflation and a negative GDP gap combined. This happened in the U.S. during much of the 1970’s and it happened in some Asian economies during their financial crises. What does the Taylor Rule recommend in such a situation? Using the benchmark parameter values of the Taylor Rule, give some quantitative examples of situations where the central bank cuts real interest rates in response to stagflation.

Answer:

This is a straightforward application of the Taylor Rule. For the benchmark case set real interest rate to 2% (you can set to anything as long as you're consistent), set inflation to 2% and set GDP Gap to zero [note that this is just to make the numbers simple]. The benchmark case results in a 4% suggested nominal interest rate. Now increase inflation to 3%, keep real interest rates the same and make the GDP Gap negative 3%. The suggested nominal interest rate goes to 3% a full percentage point cut from the benchmark case. This is an empirical example of the Taylor Rule resulting in interest rates being cut to respond to stagflation.


7. What do the RBC model and the New Keynesian model each predict about the time path of the real interest rate? What do I need to believe about the key source of shocks in a New Keynesian model to get a procyclical real interest rate?

Answer: The RBC model predicts that the real interest rate lags the business cycle and is countercyclical. This assumes that the direct effect of an increase in TFP on the supply of goods is larger than the effects of future rises in TFP on the demand for goods. Otherwise, the time trend in the real interest rate is uncertain. In contrast, the New Keynesian model with monetary shocks predicts the real interest rate leads the business cycle and is countercyclical. The New Keynesian model with investment or demand shocks predicts the real interest rate lags the business cycle and is procyclical. So, in order to obtain a procyclical real interest rate in a New Keynesian model, the shocks must be investment or demand shocks, rather than monetary shocks.


8. What’s the best way to solve a time consistency problem? Yes this is an essay question, and yes you need to argue a case convincingly to get full credit.

Answer: One approach to solve inconsistency problem is to have monetary policy determined by rules rather than discretion. Inflation targeting or Friedman’s k percent money growth rule are examples to these rules. It is important that rules are binding in this case.If the monetary gives up to ability to determine the money supply in order to to stimulate the economy, then public expects low inflation in the future. Problem with this method is that, rules can not account for completely unexpected circumstances. In an unanticipated event, it is socially more optimal to for government to have the flexibility to react to that event. A second affective to solve the problem would be to delegate policy to individuals who do not share the public’s view about the relative importance of output and inflation. The idea, due to Rogoff is simple: inflation and hence expected inflation is lower when monetary policy is controlled by someone who is known to be especially averse to inflation( Conservative Central Banker theory). Another suggestion by Blinder is; he thinks it is not necessary to to find a truly conservative banker as Rogoff is suggesting but instead you can direct the central bank to behave as if they really are inflation averse. He thinks central bankers set aside their own personal beliefs about what is best for society and adopt instead parameter values that lead them to do their duty. He calls this solution ‘’ responsible behaviour’’


9. Empirically, is there a free lunch when it comes to reducing the variance of inflation and output? Theoretically is there such a free lunch?

Answer: With Rogoff’s Conservative Central Banker, one cannot fully eliminate the inflation bias as long as weight is placed on unemployment. In that case, one can only achieve a lower inflationary at the expense of a higher unemployment variance. Empirically, this is not what is observed. It appears as though there is no significant tradeoff between the two.


10. How can delegating to an irrational person solve a time consistency problem? What particular kinds of irrationality can solve such a problem?


11. Why does Alan Blinder think that the time consistency literature is a waste of time? What issues does he think monetary economists should actually be working on?

  • Answer: Alan believes that in rational expectations world, it is ridiculous to waste time on the non-existent problem of time consistency for two reasons. First, central banks do not appear empirically to have an inflationary bias. Second, the description of central bankers behavior and objectives is inaccurate. Central Bankers are not tempted to move up the short-run Phillips curve in order to lower the rate of unemployment below the natural rate, they are actually concerned about the opposite that inflation would push unemployment too low. In reality, the Fed targets the natural rate of unemployment, suggesting that the time inconsistency problem that results from a target below the natural rate as suggested by Barro-Gordon is wrong. Governments have developed pre-commitment rules that are even better than Rogoff’s conservative central banker solution in achieving the desired outcome. Blinder suggests that academics focus on real world issues, such as the problems inherent in a central bank that follows the markets too closely. He also suggests that economist should develop an empirically coherent analysis of the term structure of interest rate, model the central bank as a committee, investigate the robustness of Brainard’s conservatism principle, and study the conditions that make either “opportunistic” or “disinflation” the preferred strategy. (DS) See Drazen Page 120

12. Name three elements of the “common core of practical macroeconomics.”

Short Answer: The participants in the AER symposium on the core of usable macroeconomics were Robert Solow, John Taylor, Martin Eichenbaum, Alan Blinder, and Olivier Blanchard. Within this group of five, there was some strong agreement, but there was a wide range of additional principles and caveats mentioned. Here are the main, most universal principles:

(a) The trend movement in output is predominantly driven by the supply of factors of production and total factor productivity. (b) There is no long-term trade-off between the rate of inflation and the rate of unemployment. (c) There is a short-run trade-off between inflation and unemployment, or at least in their variabilities. (d) Peoples' expectations matter and are highly responsive to policy.


Long Answer: Solow says the trend movement in output is predominantly driven by the supply side of the economy (the supply of factors of production and total factor productivity) and that the appropriate vehicle for analyzing the trend motion is some sort of growth model. He feels that short-term fluctuations, however, are demand-shock-driven, not supply-shock-driven, in constrast to the RBC-ers. Two approaches for modeling aggregate demand in the short-run are either (1) "opportunistically," i.e., in which functions should look as if they arose from reasonable micro-level behavior, or (2), imposing the intertemporal utility maximization from the start, in which we're essentially aggregating first-order conditions from household optimization. Solow thinks the expectations, beliefs and perceptions work is still too conjectural, and can be used to explain anything.

Taylor gives five principles: (1) Over the long term, labor productivity growth depends on the growth of capital per hour of work and on the growth of tech., or more precisely, on movements along as well as shifts of a production function. (2) There is no long-term trade-off between the rate of inflation and the rate of unemployment; a corollary is that a shift by the central bank to a higher rate of money growht will simply result in more inflation, and will not change unemployment; thus the Fed should just pick an inflation target and stick with it. (3) There is a short-run trade-off between inflation and unemployment, or at least their variabilities. (4) Peoples' expectations are highly responsive to policy, and thus, expectations matter for assessing the impact of monetary and fiscal policy. The most feasibly modeling of this is with the rational-expectations approach. (5) When evaluating monetary and fiscal policy, one should not think in terms of a one-time isolated change in the instrumetns of policy, but rather as a series of changes linked by a systematic process or policy rule.

Eichenbaum approaches the question from the perspective of stabilization policy. So, he agrees there's a core macro of practical macro. He thinks most stabilization policy has been learned in the past 28 years as the profession sifted through Friedman's 1968 AEA address. His principles are: First, monetary policy is neutral in the long run. At the very best, the Phillips curve is neutral. More likely it slopes the wrong way. Second, persistent inflation is always a monetary phenonomon. Third, monetary policy is not neutral in the short run. Fourth, most aggregate economic fluctuations are not due to monetary policy shocks.

Blinder says there are practical elements that macroecoomicsts agree on, and also critical failings of the standard macro model with need work. Overall, he says (1) prices and wages are largely predetermined in the short run and evolve according to Phillips-type equations. (2), output is demand-determined in the short run. (3) aggregate demand responds directly to fiscal policy and is interest-senstive, and thus resonsive to monetary plicy, which sets short-term interest rates. (4) Okun's law links output growth to changes in the unmemployment rate.

Blanchard says there is a core macro, and that it's very close to what Paul Samuelson identified by 1955 as the "neo-classical synthesis." It's based on two propositions: (1) In the short run, movements in economic activity are dominated by movements in aggregate demand. (2) Over time, the economy tends to return to a steady-state growth path. Together these two propositions explain the effects of shocks and of macroeconomic policy.


13. The Gold Standard and the Great Depression. How did the Gold Standard make it difficult for the U.S. to pursue a non-deflationary monetary policy in the Hoover years (1929-1932)?

Answer: Romer, The Nation in Depression: The tight monetary policy of 1928 was partly aimed at stopping gold outflow. The Federal Reserve was less able to respond to financial panic in 1931 because expansionary monetary policy would have led to serious loss of gold.

Temin, Transmission of the great depression: The gold outflow was a prominent determinant of the policy change, even though it was tiny relative to the U.S. reserves. The Fed's primary aim in 1928 and 1929 was to curb speculation on the stock exchange while not depressing the economy. It failed on both counts. Even though this policy did not impede stock-market speculation, it reduced the rate of growth of monetary aggregates and caused the price level to turn down. The monetary stringency was even tighter than it seems from examining the aggregate stock of money, because the demand for money to effect stock-market transactions rose, leaving less for other activities. The choice of deflation over devaluation-was the most important factor in the international transmission of the Great Depression.

The Federal Reserve raised interest rates sharply in October 1931 to protect the dollar-in the midst of the greatest depression the modern world economy has ever known. This action was not a technical mistake or simple stupidity; it was the standard response of central banks under the gold standard. It shows how the gold standard-working through an international financial panic-transmitted and intensified the Great Depression.


14. What are the raw facts about bank runs and collapses during the U.S. Great Depression?

Answer: The crash triggered banking panics and worsened the depression. Bank panics cause a fall in money supply (reduction of borrowings), increased interest rates. Moreover it enhances pessimism and reduces again consumption. When a bank fails, all the long term relationships and informations are lost. This loss of information causes agency costs to rise and the result is credit rationing that makes (especially for small investors) investments more difficult. Romer, The Nation in Depression, pg 32-4


15. Do M2 and nominal GDP still have a strong empirical relationship in most countries, or has that fallen apart due to financial innovation, government regulation, etc.?

Answer: Refer to Hafer's "What Remains of Monetarism? " pg. 20-30, Table 1, 2, &3

  • Short answer:

This evidence indicates not only that there is a positive correlation between money growth and nominal income growth but also that this correlation increases as the time interval increases. This outcome also is consistent with the proposition that income growth and money growth are positively related.

  • Long answer:

Fifteen countries (developed and undeveloped) were sampled and it suggests that average nominal GDP growth across the sample is closer to money growth than is inflation or real GDP growth.

  • As a first approximation, these data suggest a closer relation between money and nominal income than between money and inflation or money and real output.
  • Empirical Test:

A hypothesized relationship is used to examine an important monetarist proposition—namely, that there exists a positive connection between changes in the stock of money and the level of nominal income. To further check whether money growth can serve as an indicator of nominal income growth, this analysis employs so- called Granger causality tests.

  • 1) The hypothesis that M2 growth does not cause GDP growth is rejected in eight instances, and in seven cases the hypothesis that GDP growth does not cause M2 growth is rejected. These results suggest that the choice of the monetary aggregate has some effect on the test outcome.

Results: Overall, the results in Table 3 indicate that there is a causal link from money growth to nominal income in many countries.

  • 2) An even more restrictive hypothesis can be tested: Does money have a unidirectional effect on nominal GDP?

Results: Unidirectional causation from M2 to income cannot be rejected for about half of the countries. (Table 3)

  • 3) Conversely, is evidence of unidirectional causation running from GDP growth to money growth? Such a finding is most damaging to the idea that monetary aggregates are useful in setting policy because it signals that money growth is not exogenous to changes in income growth. (Table 3)

Results: With M2 it leads to the following out-comes: the hypothesis that GDP growth unidirectionally causes M2 is not rejected for Iceland, Malta, Pakistan, and South Africa at the 10 percent level. Bidirectional causation is not ruled out for Denmark, Japan, and the United States. The remaining countries indicate no reliable statistical relation.

  • The fact that the GDP-to-money causation is relatively weak across most countries suggests that money may possess potentially useful policy information.
  • The data from a variety of economies indicate that money growth is directly related to nominal income growth and inflation. Moreover, the evidence suggests a weaker relation between money growth and real output growth in the long run
  • As a side note:

• Policies that increase money growth are more likely, over time, to generate increased inflation, not faster growth in the production of goods and services. • The array of economic experiences captured by this subsample of countries suggests that the money-income relation does not hold only for certain types of economies.


16. What are DeLong’s types of monetarism, and which were most successful? Which policy messages or factual messages have made it into the new Keynesian synthesis, according to DeLong?

Answer: There are four types of monetarism:

1. First Monetarism --> (Fisher's MV=PY neutrality) 2. Old Chicago Monetarism --> Unstable Velocity, and friction in banking reserve make control on money supply difficult 3. Classic Monetarism --> stable Md, limit of stabilization policy (lags), rule based policy, and money supply is useful for short run stabilization (output change) 4. Political Monetarism --> Classic Monetarism redux --(stripped down version of more nuanced classic monetarism into merely discussions on money growth, stable velocity, and easy control for money supply). All economic problem becomes a matter of money supply growth controlled by Central Bank.

Most successful: Classic Monetarism

Factual Message for New Keynesian synthesis --> Money supply matters in short run stabilization policy (not neutral in SR); frictions gives slope to Aggregate Supply (sticky wages AS Keynesian curve), and fluctuations is about trend (not RBC below potential).

Monetarism shares insights with Keynesianism


17. Consider a Cagan money demand model where gamma = 0.5. If there’s a 100% probability that the money supply will double in 5 periods, what happens to the price level today? If there’s a 50% chance?

Answer: Remember pt=mt+gammat*mut. With the 100% probability, we have mu=0.2, and so pt=mt+0.5*0.2=1+0.1=1.1. Thus 10% return.

If the probability that money doubles is 50%, then mu=0.1. Now, pt=mt+0.5*0.1=1+0.05=1.05. Thus 5% return.


18. In an unpleasant monetarist arithmetic model, the money supply is stable but prices are rising. What do I know about the true underlying model (Cagan or Monetarist?) and about the size of the nation’s present and future deficits?

Answer: If money supply is stable and prices are rising it means that government debt is rising toward its limit (Sargent Wallace); in the future the government will recur to seignorage and there will be inflation. But the private sector ‘s expectations anticipate this effect of future higher money supply. This is a little tricky question because it seems to me to be both a Cagan + Sargent Wallace world.


19. In an unpleasant monetarist arithmetic model, the money supply is rising and inflation is growing at the same rate. What do I know about the true underlying model and what do I know about the sustainability of the nation’s deficits? This is a little bit of a trick question.

Answer: In the unpleasant monetarist model, when inflation is rising at the same rate than money, this means that the government has reached the debt threshold and growth is zero. But the debt can be sustained only if g > r ! So we are in a condition with negative real interest rate which is quite unusual. I think this is the “trick”, but I’m not so sure, so please check it again and let me know if I wrote down something very stupid and forget it !!!


20. According to Christina Romer, what ended the Great Depression? Answer:

    • According to C. Romer, an unusual rise in money supply for the period 1933 1937 due to the shift from a deflationary policy to devaluation and to an inflow of international capital from Europe (due to political instability in Europe and to the consequent Roosvelt’s administration choice to not sterilize that inflow) caused a fall in the interest rate and stimulated aggregate demand. The same explanation applies for the 1942 recovery.

21. Tell a Mishkin/Bernanke/Fisher story about how balance sheet problems worsened the Great Depression.

Answer: Mishkin- Fisher Story: In a deflationary period when the money supply falls: When prices fall, borrowers are hurt because they have to pay their nominal contracts with scarce dollars. So borrowers, both firms and households may go bankrupt because of nominal debt contracts. Mishkin presents a model of consumer "distress" to analyze the role of debt deflation in reducing consumer durables demand. He argues that consumers value "liquidity" (that is, holding wealth in assets that do not suffer distress-sale discounts due to asymmetric information about their true value).So, exogenous shocks to consumer liquidity will lead consumers to reduce their demand for illiquid consumer durables as they try to rebuild their stock of liquid assets. This framework served as the basis for Mishkin's study of the effects of changes in the household balance sheet and consumer expenditures during the Depression. According to Mishkin (1976), the changing distribution of wealth, not just aggregate wealth, should matter for aggregate consumption. Mishkin (1978) argued that in addition to the depressive effect of aggregate wealth reduction on consumption in the 1930s, the debt deflation (a reallocation of wealth away from indebted consumers) reduced aggregate consumption demand. Bernanke argues that in the presence of capital market imperfections, the destruction of intermediaries and the reduction in borrowers' net worth reduced investment in the 1930s by increasing the marginal cost of external financing. So when money supply falls and bankruptcies increase, both firms and consumers, banks will go bankrupt too. Debt deflation erodes the net worth of banks, causing some banks to fail, and others to tighten their credit standards to avoid runs by depositors. If banks go bankrupts then skilled knowledge within the bank is scattered (Lost human capital). When banks go bankrupt and real rates increase, only big firms can get loans sell commercial paper for financing but small firms will not be able to get loans from banks due to asymmetric information and lost human capital. They will not able to sell commercial paper too.( Flight to quality theory). Mishkin argues that reductions in stock prices and increases in quality spreads in bond markets are best viewed as the result of financial-market disruption and reductions in internal funds available to firms.


22. Does Bernanke think that the fall in the money supply during the Depression is a sufficient explanation for the Great Depression? Why or why not?

Answer: Uncertain. Gold standard created deflation (money supply low). Borrowers suffer. Large borrowers suffer most. Banks are large borrowers. When old banks went out of business, lost human capital with knowledge of 1) market and risk of investment, 2) knowledge of how to evaluate risk of borrowers. New banks less willing to lend - required higher compensation to lend. Large firms could still go to money market. Small borrowers cannot borrow, go out of business. Not the high-powered money that is problem, but the money multiplier controlled by the Fed. Fall in money supply results in a decrease in the velocity of money. Reduction of velocity is result of decreased availability of credit, which reinforces decrease in fall in money supply.

Another answer: Pg. 68 Calomiris No, capital market imperfections, specifically, debt deflation had a large impact by causing the destruction of intermediaries and the reduction in a borrower’s net worth. This instigated a huge banking failure which, in turn, sparked a financial collapse. According to Bernanke, fall in the money supply was importantand had long run effects because they affected the institutional structure of credit markets and the balance sheets of borrowers.


23. Did real wages rise or fall in the ‘29-‘32 period in the U.S.? Is this consistent with a real business cycle story? A Keyesian sticky nominal-wage story?

Real wages rose during the period. Inconsistent with RBC story - RBC says when you have a depression, result of "technological shock" (z). Reduces MPl, therefore w decrease. Is consistent with Keynesian sticky price. if prices are sticky and don't adapt to business cycle.

Answer: Margo Paper: It is not consistent with the RBC story, because real wages are procyclical in RBC model but is consistent with the Keynesian sticky nominal-wage story since real wages are countercyclical in that model.


24. According to Bernanke’s estimates, did the NIRA have a large negative impact on employment, as Cole and Ohanian appear to say? Can you find a way to reconcile their two stories? This is not a trick question, but it might take some thinking. Answer: (see Margo for Bernanke) Cole and Ohanian - NIRA allowed for creation of cartels in exchange for guarantees that firm would pay higher wages. Result is non-price competition for high wage jobs in cartelized industries - non-price competition took form of potential employees continuing job search (i.e., remained unemployed)instead of taking lower wage job. Bernanke says

Another answer: Pg. 48 Margo No, in fact it had a positive effect on employment although modest. (not sure how to reconcile) No it didn’t. According to Weinstein and Bernanke, working hours decreased(work sharing) during this period partly independent of NIRA. Bernanke shows that, as weekly hours are reduced beyond a certain point, hourly earnings rise. He finds that, as real wages increased during this period, firms cut back their labor demand, weekly hours fell, and so the hourly wages rose and so did employment. So NIRA by lowering the weekly hours raised weekly earnings and employment although the effects were modest. Cole and Ohanian did not take the positive effect of decreased weekly hours of work on the wage levels

Question from Rizal: " He finds that, as real wages increased during this period, firms cut back their labor demand, weekly hours fell, and so the hourly wages rose and so did employment..", I don't understand this. Please kindly elaborate. If labor demand cut, weekly hours fell, wages (may rose up to certain point) but employment declines, no? Or employment with shorter hours?


25. Rubin and Weisberg: Be able to tell me 1 story per chapter that has something to do with time consistency, optimal capital taxation, credibility, delegation, pooling versus separating equilibria, the implicit models (apparently) underlying Rubin’s worldview, the term structure of interest rates, sticky prices, etc.


26. You’ll notice that this second half of the course has fewer explicitly mathematical questions. HW 4-type questions are fair game, of course, and much of the pre-midterm material appearing on the final will be explicitly mathematical, but overall, the post-midterm material will be less explicitly mathematical than before. That said, be ready for mathematical questions about the major post-midterm models:

Time Consistency (with or without shocks, and know the guts of the “escape clause” story).

Answer There are 4 time consistency models that we have discussed: 1. Kydland & Prescott - This model attempts to minimize a loss function:

    L = 1/2(y-y*)^2 + 1/2a(pi-pi*)^2
  Subject to the Phillips curve:
    y = y(natural) + b(pi - pi(expected))
  If the government can commit, then pi = pi* = pi(expected) and 
    y = y(natural).
  If the government cannot commit, then:
    pi = pi* + b/a(y*-y(natural)) and again y = y(natural)

2. Drazen's Formal Demonstration (p.111 - 112) - For a world with one agent and a government and the utility function u(k,T), the order of who picks their variable, k or T, first does not matter. However, in a world where there a multiple agents with an identical utility function ui(ki,kaverage,T). The outcomes changes when the government picks T first versus when the agents pick their ki first.

3. Capital Taxation - There are only two periods. In period one, an agent has and income endowment which he breaks down into consumption and capital accumulation (savings):

    y = c1 + k2

In period two, the agent works, the government makes purchases, and there is a linear production function:

    c2 + g = al + Rk2

The consumer optimizes his intertemporal utility function:

    omega = ln(c1) + beta[ln(c2) + delta*ln(1-l) + gamma*ln(g)]

The optimums here are known as the "first best" or "command optimum" solutions. They work because the government uses a lump sum tax, which doesn't influence the agent's behavior.

If the gov't switched to taxes on K and L, distortions arise. The agent's decision on how much to save and work becomes a function of the taxes on K and L. The government will promise a low tax on K in an effort to get the agent to accumulate a lot of K in period 1. Then, the government will tax K highly, despite its promise, in period two because the agent will no longer be able to alter his amount of K. Anticipating this, the agent choses a lower amount of K in period one. The equilibria in this scenario will not be "first best" or "command optimum"

4. Barro & Gordon - Similar to Kydland and Prescott, Barro & Gordon are trying to minimize a loss function subject to a phillips curve. However, B&G have added stochastic shocks as part of their phillips curve. This has the same set-up as Rogoff's "Conservative Central Banker" framework, and it leads us into escape clauses.

Escape Clauses - When a government sets a rule, pi = 0, it generally improves the results from the loss function than when the government uses its discression. However, occasionally there is such a large shock to the economy that the government needs to be let out of the rule. This is an escape clause.

In order to enforce the escape clause, there is a stiff penalty, zeta, for when the government uses its discression. So, the government must determine the point where the cost of the shock, epsilon, exceeds the zeta. It sets the loss function of following the rule equal to the loss function of breaking the rule and solves for epsilon. The resulting epsilon is the magnitude of the shock nexessary to deviate from pi = 0.

Unpleasant Monetarist Arithmetic Answer Assume no population or GDP growth. The real government budget:

    Dt = Bt - Bt-1(1+ Rt-1) + (Ht - Ht-1)/Pt
    and
    Pt = (1/h)Ht where h is some constant

Here, the goevernment can finance the deficit through new bonds (debt) or money growth (seignorage). The government wants low inflation so it sets money growth, Ht - Ht-1, at som elow rate, theta. Eventually, at time T, the government can no longer carry anymore debt. The budget becomes:

    Dt = -Bt*Rt + (Ht - Ht-1)/Pt

Here, the governemtn has no choice but to finance the deficit through seignorage. As Ht - Ht-1 rises to cover the deficit, P because it has a fixed ralationship, 1/h, to H.

The basics of Williamson’s cash-in-advance model (the default money/macro model) Answer There is a consumer who starts his day with some amount of money and bonds plus the interest on those bonds:

    M + B(1+R)

The consumer goes to the ATM where he withdraws some of this money, but also uses it to pay nominal taxes and buy new bonds:

    WD = M + B(1+R) - PT - Bnew

WD is his cash on hand. He also has the option throughout the day of using checks and debit cards (bank services) to withdraw whatever nominal income he has received, PX. His nominal consumption will be:

    PC = M + B(1+R) - PT - Bnew + PX

However, the bank services he uses to get X out of the bank have a cost, H(X), and the cost increases as X increases. Here lies the consumer's problem, how much X should he consume? He could keep the cost of H(X) down by buying fewer bonds and carrying more cash, but then he would give up the interest, R on the bonds. So, he sets the marginal benefit of buying new bonds, P(1+R) to the maginal cost of H(X), P+PHx.

    solution:  Hx = R

The firm faces a similar dilema of how many bonds to buy versus how much banking to use. However, the firm is using it's cash for nominal investment, PI, not consumption, PC. The firm's solution is the same as the consumer's:

    Hx = R

This tell us that the amount of X for the consumer and the firm are the same.

When this fact it run through the government's budget and the national accounting identity and solve for M, we get:

    money demand: M = PL(Y,R) where M increases with Y and decreases with R

The equation of exchange: MV=PY in growth rates and logs as well Answer

Money supply x velocity = prices x GDP

Money supply is exogenously set by the government Velocity is assumed ot be constant Prices vary endogenously to hold the equation equal GDP is determined by A, K and alpha and not dependent on money

This holds the "classical dichotomy" of money not affecting real variables.

Natural logs: ln(MV) = ln(PY) can also be written as:

    m + v = p + y

Also,

    %change M + %change V = %change P + %change Y

Becasue V is fixed and M doesn't change Y

    %change M = %change P 

Theories of the term structure Answer 1. Pure Expectations Theory Interest rates on long bonds equal the average of interest rates of present and future short term notes.

    i2,t = (i1,t + i1,t+1)/2

Here, given that we know both current short term and long term rates, we can deduce the short term future rate.

2. Expectations or Term Premium Theory Interest rates on long bonds equal the average of interest rates of present and future short term notes plus some term premium, alpha.

    i2,t = (i1,t + i1,T+1)/2 + alpha

Alpha is the cost associated with borrowing for longer than one period.


27. What Summers hated about RBC and your favorite line from his paper.

Answer: Summers main critics to RBC are:

1) the parameters are questionable especially:

a) the share of time devoted to market activities; RBC level is too high !

b) the intertemporal elasticity of substitution in labor supply is too high !

2) the measure of the tech shocks is questionable: for example much of the Solow residual can be explained in terms of labor hoarding

3) is a free-price model where nominal and real magnitudes are completely mixed and undistinguishable

4) there is no consideration for exchange failures and sticky prices (also because point 3)

My favorite line is that about how much is useless for an applied economist to worry about the behaviour of stochastic Robinson Crusoes … tell me, how much do you feel stochastic today ???


28. Lucas’s model of monetary non-neutrality–what kinds of knowledge imperfections are crucial to his model?

Answer:Incomplete knowledge about price movements (i.e., prices determined in a way other than through a Walrasian auctioneer) and incomplete knowledge of the money supply.

Lucas’s model shows the following 3 things: 1. if the monetary increase is given lump sum regardless of labor product, the result is an inflation tax 2. if the monetary increase is tied to production, then the result is monetary neutrality 3. if the monetary increase occurs in the current period, but knowledge of how much of an increase is delayed to the market participants until some future period, the market participants will increase output as a hedge against uncertainty.


29. Stories about sticky prices–in theory and practice; especially the role of monopolistic competition. Price stickiness means prices are resistant to change even when underlying values and/or costs have changed. This is one reason why the short-run aggregate supply curve in the economy may not be vertical.

Answer: Prices in monopolistic competition or oligopoly can often be considered sticky-upward. In monopolistic competition or oligopoly, firms are mutually interdependent, and their control over the price is determined by the level of coordination among them. A mutually interdependent firm realizes that its price drops are more likely to be matched by rivals than its price increases. This implies that an oligopolist will try to maintain current prices, since price changes in either direction can be harmful, or at least nonbeneficial. Consequently, there is a kink in the demand curve because there are asymmetric responses to a firm's price increases and to its price decreases; that is, rivals match price falls but not price increases. This leads to "sticky prices," such that prices in an oligopoly turn out to be more stable than those in monopoly or in competition; that is, they do not change every time costs change. There is an elastic price elasticity of demand above the current market clearing price, and inelastic price elasticity below it which requires firms to match price reductions by their competitors to maintain market share. Associated with the kink in thet demand curve is a jump discontinuity in the marginal revenue curve. In this case, the firm's marginal costs could change without necessarily changing the price or quantity.

Note, however, that game theory and models of strategic interaction have largely replaced kinked demand to explain price dislocations and slowly adjusting prices. Four additional possible reasons for price stickiness are: menu costs, money illusion, imperfect information with regards to price changes, and fairness concerns. Robert Hall also cites incentive and cost barriers on the part of firms to help explain stickiness in wages. Mankiw cites "menu costs and aggregate-demand externalities," "the staggering of price," "coordination failure," and "efficiency wages."


30. According to the equation of exchange under flexible prices, if the money supply rises by 100%, what happens exactly to real output and the price level? Is this a good description of what appears to happen in the long run around the world?

Answer:The literal answer to this question is that we are not sure. The equation of exchange is just a tautology, not a theory. Now, if we assume that V is constant and Y is constant, then we have the "quantity theory of money." Now we can say something. In this case, all changes in M are passed into P, and Y is unchanged. Yes, this is a good description of what appears to happen in the long-run around the world. Lucas' paper presents two clear graphs (Figures 1 and 2) to show this. In Figure 1, there appears to be a 1-for-1 move in money growth and the inflation rate (it's a 95% correlation). In Figure 2, there appears to be no relationship between money growth and real output growth. [Note: Figure 1 plots the average of 30 years (1960-1990) for 110 countries. Figure 2 plots the average over the same 30 years, for the 100 IMF contries.]

In the short-run, however, much of the rise in M may go to Y rather than to P. That is, while money seems neutral in the long-run (i.e., the classical dichotomy), in the short-run, there may be real effects during the adjustment process. The theoretical reason for the short-term effects, i.e., the description of the adjustment process, could be Keynesianism, or it could be Monetarism, or other theories. This can be seen in Lucas' Figure 3, which shows only short spans of years on the graphs, rather than all 30 years at once.

Still, Lucas states, "The prediction that prices respond propotionally to changes in money in the long run, deduced by Hume in 1752 (and by many other theorists, by many different routes, since), has received ample - I would say, decisive - confirmation, in data from many times and places."


Other info:

Williamson, Notes, Chapters 1 and 3 (except for the Bellman Equation)

Williamson, Macroeconomics, Chapters 4, 5, 8.

Davis and Haltiwanger, “Gross Job Flows,”

Hazlitt, Economics in One Lesson, Chapters 1 and 2.



back to Macroeconomic Theory I, Econ 715

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