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# economics ECO2023-0002

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This 14 page Bundle was uploaded by ew Notetaker on Monday November 16, 2015. The Bundle belongs to ECO2023-0002 at Florida State University taught by Joab Corey in Fall 2015. Since its upload, it has received 24 views. For similar materials see Principles of Economics: Microeconomics in Economcs at Florida State University.

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Notes for Monetary Economics PhD Course John H. Cochrane Fall 2004 1 1 Preliminaries 1.1 Class management Review course outline, website. Bring namecards. The course is based on problem sets, exam, class participation. I will call on you, and may ask for 10 minutes w. chalk. Register somehow. Participate in class. Don’t get lost either on history and jargon or on equations. I will never be mean on a class question — but I will be mean if you ask it after class! Will we do makeup tues before Thanksgiving? 1.2 Big Picture Tefusfecueiepillndhnei ﬂation. Money, monetary policy also associated with outputﬂuctuations, but they will be a lesser concern here. First things ﬁrst — we need to understand the price level before understanding its non neu- tralities. The ﬁscal theory high on my agenda. I think it may replace MV=PY and shake the foundations of monetary theory. We will mix theory, empirical work, histori- cal experience. As reading Sargent and Velde shows, our forebears were much better at remembering long historical experience. We need to broaden our horizons past 20 years of US time series. Monetary economics is to be taken seriously, as an understanding of the world around us, not as a game for writing clever equations. You should take that attitude in your own work. Money is hidden, which is why monetary economics is cool. Some people say “Eco- nomics is obvious,” and this is a good counterexample. Imagine an investigative reporter trying to understand ﬂation. He goes from the grocer to the wholesaler to the farmer to the seed supplier to the worker to the grocer...that (if!) money supply is the root cause is far from obvious! We’ll study lots of other far-from obvious things. 2 Overview: Theories of the price level 2.1 Commodity monies or standards. The most obvious theory of the price level derives from gold coins or a commodity standard. Gold nuggets, gold coins then fully redeemable tokens. The price level is obvious. It seems simple but...there is no real commodity use for money! Perhaps this is a commitment mechanism? Or perhaps we should understand it as an instance of the quantity theory (comes next), with nature giving us the limited supply? (Perhaps gold was worth a lot more when used as money than it would be in aﬁat money economy.) 2 The same basic economics applies now in pegged exchange rate or currency boards. (Though where base country price level comes from still to be determined, and the option to devalue the peg or abrogate the board make it interesting. ) 2.2 Monetarism: 20th century from Fisher to Friedman. - MV = PY. Read this causally from M to P, Y. “ Inﬂation is always and everywhere a monetary phenomenon.” - Read Friedman: How does M aﬀect Y then P. - Fiat money. Thus can apply to 20th century institutions in a way gold/commodity theory cannot. - Ingredients of the “quantity theory”: a) Money demand as an inventory for making transactions. You hold money despite interest loss, as you hold a peanut butter inventory. b) Money supply is limited. (Though it’s free for the government to print!) - There is much more to “monetarism.” Among other propositions: a) The Fed should pay attention to and control money supply. Period. 4% rule. tmaypektn ﬂation but really ignore output and interest rates. )TeFdnoteai”ndytoo ﬀset shocks. (4% because Friedman didn’t trust the Fed, not because a stochastic optimal policy exercise would yield 4%. There is a whiﬀ of commitment and rules vs. discretion here. ) c) Most output and inﬂation variability is due to Fed mistakes in controlling the money supply. (False, as we’ll see.) d) “Operating procedures” The Fed should focus on money supply, not interest rates as instrument, signal, etc. -Poem: a) The theory relies on a rigorous distinction between “money” and “non-money” assets. It has always foundered the question,What is money anyway? Cash, reserves, checking accts. (M1). Money market — can write checks but few do (and pays interest)? Unused credit card balances? Sweep accounts? The Marie Antoinette theory applies — there are a lot of liquid assets thatcould be used as money though their velocities are typically low.. A martian would think that actual institutions look much more like unlimited private banknotes or electronic accounting system of exchange than like the textbook base + checking accounts limited by reserve requirements vs non-transactions “bonds.” b) The theory requires government control of the monetary assets. For example, if people can issue circulating IOUs (banknotes) the price level is indeterminate.How 3 should the Fed control “money” Should it eliminateﬁnancial innovation? This also requires the government to rigorously control “money substitutes” such as privately- circulating IOUs (checks, banknotes), and to pass laws forbidding the use of other objects (foreign currency). If these are free, demand for government money can go to zero and the price level to inﬁnity. c) Theory requires that the Feddoes control the money supply. But in fact it pegs interest rates (for good reasons, “unstable money demand”) The theory no more applies to the current institutional setting than the gold standard theory applieﬁato a money setting. 2.3 “Fed view.” “Old-Keynesian” This is the view implicit in every statement by the Fed, newspapers, Op-ed, and most applied macroeconomists writing for non-professonal audiences. a) Fed controlsFederal funds rate. Not directly in US, but directly in some countries. This is the overnight rate for reserve requirements (in US) reserves (in other countries). b) The causal change to inﬂation: ﬀ → short term rates → long term rates → “de- mand” → “gaps” “unused capacity”→ “price pressure”→ inﬂation. (Since prices are stiky, control of nominalﬀ gives the fed control of real rates with a nominal lever) c) Price level determination?pt−1and stickiness determinesp t d) Problem: there is not a shred of evidence or theory for any step of the chain. This basic Keynesian “model” is still with us. All the discussion of Bush tax cuts is over taxes (if we give them an extra $600, how much will they spend?) not tax rates. More “spending” is thought to be good. The idea seems to be that C/Iﬀ aects Y. What is ”Aggregate demand”? Money vs “Credit”? How can consumption go up without investment going down? (The saving = investment condition seems to disappear.) 2.4 Fiscal theory money base + nominal debt price level = Epv future primary surpluses. This equation is in every model, including Friedman (46) - Sargent. It is often read as the “Government budget constraint” from left to right. The Fed sets P, base and debt are what they are, so this tells the treasury how much taxes to raise in order to payﬀo the debt. For example, if the Fed runs a deation, the treasury has to raise taxes to pay oﬀ henesdvueofomnlbns. In the ﬁscal theory, works from right to left, as expected present value determines the stock price (“money as stock.”) Both “readings” — “regimes” are possible. 4 - This can determine the price level with a) NO monetary frictions whatever b) Arbitrary private “moneys” (IOUs, banknotes, etc.) Unlike MV=PY only government liabilities are on the LHS,not M1) c) Arbitraryﬁnancial and transactions-technology innovation. If we all want to use debit cards, no problem. d) If the Fed pegs interest rates. (We’ll show that later.) Thus it applies transparently to the current institutional environment. It is also a natural “Frictionless benchmark” on which to build more complex theories. Allows us to start with a Chicago "free market" approach to money, and add frictions only if we need them. A few questions and objections right oﬀ the top: Q: What about helicopter drops? A: Helicopter drops do raise the price level in both quantity andﬁscal theories. It would be a “wealth” or “pigou” e ﬀect. Note that helicopter drops are aﬁscal operation. Accounting would say this is “spending”ﬁnanced by borrowing, and the Fed buys the bonds issuing money. Q: What about open market operations? A: the Fed does not do helicopter drops,the Fed does open market operations. In an open market operation, you get moneybut you give up the same amount of bonds. BIG QUESTION #1: Is an open market operation the same as a helicopter drop (money ﬁnanced deﬁcit)? Monetarists say YES. Really? This violates the MM theorem. (Equity-debt swap, or short vs. long term debt swap). Put that way, it’s not so obvious. Of course, it depends on the proposition that M is special. FT: NO. Open market operations make NO dﬀ ierence to LHS! Toﬁrst order, open market operations have no e ﬀect on the price level. (First order: no frictions. A maturity structure allows open market operations to a ﬀect the timing of inﬂation — “long term debt and theﬁscal theory”) Q: What about the “Stability of Money Demand”For example, From Lucas “Money demand in the united states: a quantitative review) 5 or Luas’ Nobel lecture A: Add to the theory MV = PY 6 Now we have two equilibrium conditions. Both hold. Causality can runM− >M V = PY − >P − >F T − > surplus.O rcra surplus− >FT − >P − >M V = PY − >M .M y demand stability does not mean that moneycausesinﬂation. Rich guys smoke cigars; smoking cigars will not necessarily make you rich. There is a deeper theorem which we will study: no test based on times series of M, B, P, Y, etc. can tell you which regime works. (Extra if there is time. The theories are really not all that distinct. Tﬁscalare underpinnings of even monetarism. Why does a peg or currency board work. If you have a peg or board (100% reserve peg), a strapped government will eventually raid the reserves and abandon the peg. OTOH, a government in good standing with no reserves anaasbrwthma dkepapg.Tusapgsumaya ﬁscal question, not a question of will. Even a gold standai just a peg with gold, and thus requires ﬁscal backing.) 2.5 Interest rate rules. Idmthe ﬁscal theory is not that popular. Most monetary economic discussion today is conducted in the context of “New Keynesian” models and the study ofinterest rate rules. This is thus the “standard theory” (Woodford’s book), all academic policy- oriented advice. “Optimal policy” is cast in terms of Taylor-rule cients. We have to face the fact: we live in an economy in which the Fed is pegging interest rates. We do not observe galloping ﬂation, so we need a theory of the price level that accommodates an interest rate rule. The classic criticism: an interest rate peg does not determine the price level. (Fried- man 68 stresses the experience of the Fed-Treasury accord.) New theoretical “solution:” Rather than aﬁxed peg, what if the Fedraises interest rates more than 1-1 with inﬂation. If inﬂation starts up, the Fed will then end up raising real rates which should driveﬂation back down again! Since we haveﬁat money and interest rate targets, this is the only viable theory other than FT that can be applied to the current institutional arrangement. (This one is also quite immune toﬁnancial innovation, the other problem with the quantity theory.) “Taylor rule” claims: a) If the fed raises r more than 1-1 witﬂation, the price level will be deter- minate (unlike classic interest rate pegs) b) 70s (most recent and vital history for US ﬂation): The Fed did not raise interest rates enough (estimates less than 1-1). In the 80s the Fed “learned”’ estimates give more than 1-1, this stoppedﬂation. 7 Important note: read Friedman, and see how vital it is for him to have a stylized story for recent events (great depression and deﬂation, post WWII inﬂation with Fed-Treasury accord, and, amazingly enough, the 70s’ stag ﬂation, which he called ahead of time.) A great part of Taylor rule success is this story for our most important recent episode. Issues: a) Empirical. Can we measure Taylor rule coe ﬃcients?(JC will argue no) Is there a 70-80 diﬀerence (Orhpanides paper will argue no, if you account for output right.) Is this really true of US? Or has the Fed just not faced a serious challenge like 73! With inﬂation 10% unemployment 8% will they really go to 20% interest rates? b) Theoretical. Is claim a) true? That will of course depend on the model of the economy you have in mind. i) It’s easy in old-keynesian models — but those have no economics, so it’s hard to call this a “theoretical” understanding of the price level. ii) Frictionless models rely on the threat of explosive in ﬂation, since the “raise real rates, open gaps, reduce inﬂation through the Phillips curve” channel does not exist. If inﬂation rises to 10%, and the Fed must then raise interest rates to 20%, the only way to do this is to raise in ﬂation to 20%-real rate. But then the Fed will have to raise inﬂation 40%,...Seriously, this is how the models work. The Taylor rule is π = φπ .fI φ> 1, the only “bounded solution” isπ =0 . T u,eTalrli t+1 t said to determine the price level. The words around this are that the threat of explosive inﬂation will “align expectations” in the right way. We have to study this and see if we believe it. iii) It’s a subtle issue in New-Keynesian models. In most such models, the timing conventions (does the output gap depend on πtvs. π t−1 or πtvs. E t t+1) mean they work like the frictionless model above. New Keynesian models All this leads us to studying New Keynesian models The central question is the Phillips curve, and central there is what is structural on the y axis. (Causality is also an issue — do gaps cause inﬂation or does inﬂation cause gaps) a) Historical correlation (left axis variableﬂation), b) Unexpected inﬂation, adaptive expectations(Friedman) c) Unexpected inﬂation, rational expectations (Lucas) d) New Keynesian models. Rational expec tations plus sticky prices. results in forward looking Phillips curve. Micro foundations are extremely spelled out, and satisfy the Lucas-Sargent challenge to old Keynesian macro in spades. From optimization, price = expected future price.Thsi ﬂation less expectedfuture inﬂation e) Mankiw thinks we should go back to mechanical expectations and Friedman 8 to better ﬁtt. Fact: NK timing means like frictionless models, the theory relies ono-equilibrium threats. As you see, I am still deeply sceptical that the New-Keynesian models plus Taylor rule can overturn the old proposition that interest rate pegging is not enough to determine the price level. If I’m right, theﬁscal theory is the only theoretically coherent way of understanding the price level in aﬁat money economy that is following an interest rate target. But this is just a conjecture, and iﬀ I’m working on now. 2.6 Commitment Central banks do a lot for “reputation,” “commitment,” “transparency” etc. Much of the “inﬂation targeting” and “rules-vs. discretion” is to get more “commitment” Why? Hwishsmprn? a) Old (Barro-gordon) — Iﬂation is like capital levy (precisely, inﬁscal theory!). We need commitment to keep them from in ﬂating away bonds after they are sold. b) More deeply now. Taylor rules rely on oﬀ-equilibrium threat explosions, so you have to make those never-observed oﬀ-equilibrium threats credible. 9 elbm aerpV The big point is the empirical question: What areeects of monetary policy?” Let’s stop theorizing and look at the data. It’s remarkably hard to do! We want to know the sign, size and duration of eﬀects. The point of CEE is to produce things likeﬁrst graph of impulse responses. (Show in class) These summarizehistorical experienceof postwar policymaking. “On average, 12 months after we tightened, what happened?” 3.1 Background Ways to quantify experience following monetary policy moves. P 1) Run regresisonst= ajmt−j+ εt(From Friedman and Schwartz; St. Louis Fed Equation). Use{a } to measure the eﬀects of monetary policy j 2) Tobin, Solow, etc. critiques: a) Does casualty run from m to y or from y to m? Maybe people are demanding more m in anticipation of y? b) Maybe this just reﬂects policy reactions? (CEE make this point, p. 4, pp.2). If t (exchange rates, say) induces the Fed to changt+1and yt+2you measure the eﬀect of exchange rates as aﬀect of monetary policy.” Example: weathert+1= a + b × weather forectst t+1 but shooting the weather man will not produce a sunny day. c) In a controlled system, you might see nothing. Think of the steering wheel analogy: as you drive down the road, the car stays in the middle, the steering wheel moves all over to counter the wind. You see nothing in the regression, though the wheel really does control the car. (This is the‘right hand variable correlated with error term since right hand variable is endogs problem. The former two are the “causal interpretation of regressions” problem.) 3) Sims/Granger: splitm = expected + unexpected, a “Rule” plus “shocks”:m = t f(xt)+ εt. t is not a response to current orPexpected fhnveey.T y following ε can measure ”eﬀect” of monetary policy. P = aj t+jis not aﬀePted by the above problem. Thus, proceed in two steps 1)m = bj t−j+ εt2) yt= aj t−ji equivalent to a VAR. Does this really work? When? What are the hidden assumptions? All good questions, coming later. 10 3.2 VAR procedure You have a vector of variablest nR zt= µ + A 1 t−1+ A 2 t−2+ ... +tε equation by equation OLS. (Theε are forecast errors, so ortgonal to right hand vari- ables.) Then simulate the system’s response to shocksε. For example, ∙ ¸ ∙ ¸∙ ¸ ∙ ¸ m t a1,mm a 1,my m t−1 εmt = µ + + .. + yt a1,ym a1,yy yt−1 εyt m t = µ +ma 1,mmm t−1+ a1,my t−1+ a2,mmm t−2+ ... + mt yt = µ +ya 1,ym t−1+ a1,yy t−1 a 2,ym t−2+ ... +yt The top equation is the "Fed rule." It decomposes m into an expected part, i.e. a part that is a response to the economy, and unexpected part; a shock, a part that is not a response to the economy. Then simulate forwards responses to shocks. Done. Orthogonalization There is a little issue. What ifm and εm are correlated? It doesn’t make sense to move one without the other. One solution is to incorporatecurrent y in the m equation, ∙ ¸ ∙ ¸∙ ¸ ∙ ¸∙ ¸ ∙ ¸ mt = µ + 0 a 0,my m t + a1,mm a1,my m t−1 + .. + εmt yt 00 yt a1,ym a1,yy yt−1 εyt mt = µ + a 0,my t a 1,mmmt−1 + a1,my t−1 a 2,mmmt−2 + ... +mt m yt = µ +y a1,ym t−1+ a1,yy t−1 a 2,ym t−2+ ... + yt Now ε and ε are uncorrelated, so it does make sense to move one without the other. mt yt (Why are they uncorrelated?ε is orthogonal to {m ,m ,...y ,y ,...}. ε = mt t−1 t−2 t t−1 yt yt− µ y a 1,ymm t−1− a1,yy t−1..is in t−1m t−2,...t t−1,... }.) Note this does aﬀect the IR. Now aεy shock will aﬀect m contemporaneously, but a m shock does not aﬀect y contemporaneously. Before, since the shocks were correlated adyuhadom vebhatne,ohm einepneoashk. Problem: there are two ways to do it. You’re making an assumption here. The as- sumption does not aﬀect the model’s ability to describe the data, so data can’t help. The assumption is only about theinterpretation of the resulting impulse response functions. The question is, does the contemporaneous m y correlation mean aects y in the month — and conversely that the Fed does not look at y when setting m — or does it mean y aﬀects m in the quarter —and conversely that the economy doesn’t react at all to policy 11 within the month. You may say neither assumption is plausible. That’sﬁne, and we’ll think about other ways to orthogonalize the VAR later. This is the “identiﬁcation problem” Note that it goes away if the shocks are not correlated. A more general version: Write the regressoin errors (with no contemporaneous right hand variables)ε and the underlying orthogonal shocksv (including the “monetary policy shock” we’re after), z = µ + A z + .. + ε t 1 t−1 t zt = µ + A z 1 t−1+ .. + Cvt I.e. ε = Cv .Teo ﬀ-diagonal elements ofC will capture the contemporaneous correla- t t tion ∙ ¸ ∙ ¸∙ ¸ ∙ ¸∙ ¸ m t = µ + a 1,mm a1,my m t−1 + .. + Cmm C my vmt yt a1,ym a1,yy y t−1 C ym C yy vyt and specify E(vv )= I. Now, how do we SpecifyC?W ened CIC = E(εε )= Ω That gives 3 conditions. We need one more condition — equivalent to which variable appears contemporaneously above. One way to do it is a zero restriction — that’s what we did above. (TheCholeski decomposition— matlab command choleski — canﬁnd the C matrix for you. Thus a common way to program VARs is to run the regression using only lagged variables and then use the choleski decomposition to spread the shocks across variables.) Other orthogolanization schemes are possible, and are far more attractive ways of “imposing theory” than the recursive scheme: -Long run restrictions. ChooseC so that the limiting response of y to an m shock is zero. (Blanchard and Quah) -Sign or shape restriction. ChooseC so that output always declines following a shock. “Use theory” (Uhlig) Again, I think much too much is made of this. Many people dismiss VAR evidence as a result. For example, “. . . with a speciﬁc parameterization of preferences the theory would place many restrictions on the behavoir of endogenous variables. But these predictions do not take the form of locating blocks of zeros in a VAR descrip- tion of these variables.” “Money and Interest in a Cash-in-Advance Economy,” Robert E. Lucas, Jr., and Nancy L. Stokey, p. 512. 12 (Quoted, and Bob and Nancy might say quoted a bit out of context and too harshly, in Fernandez-Villaverde, Rubio-Ramirez and Sargent“A,B,C, (and D)’s for Understanding VARs”.) As we will see, it is often the case that not much hinges on idenﬁication since the shocks are pretty orthogonal. (A LOT hinges on which variables you include). All VARs do is capture the autocovariance function; if you like second moments there is no reason not to like these! Impulse response, moving average representation and variance decomposition. The impulse-response function is the same as the moving average representation. You can view the simulation as just an easy way to calculate the moving average representa- tion. (As a simple example, suppose you start with a scalar AR(1), zt= φz t−1+ εt. 2 3 If you simulate the response to the shock you get1,φ,φ ,φ ... But these are exactly the coeﬃcients of the moving average representation X∞ zt= φ εt−j. j=0 That’s a lot easier than factoring and inverting lag polynomials!) Thu,ecnw eteIRormongargeeenaon X∞ z = µ + B v t j t−j j=0 Think of one line of this representation yt= µ y b 0ym mt+ b 0yy ytb 1ym mt−1 + b 1yy yt−1 ... All the shocks are orthogonal and unit variance, so we can write 2 2 2 2 var(yt)= b 0ym+ b 0yy+ b1ym + b1yy+ .. Finally, we can group the terms and express the variance oyf asepatdueom shocks” and the part “due to y shocks.” var(y )= {b2 + b2 + ...} + {b + b2 + ..} t 0ym 1ym 0yy 1yy = variance due to m shocks + variance due to y shocks (It’s common to divide byvar(y t) to express thepercent of variance due to the various shocks.) This is the variance decomposition. It is one way of quantitatively addressing Friedman’s question: how much volatility of output is due to monetary policy shocks? If we turned the shocks oﬀ and made monetary policy totally predictable, how much would output variance go down? 13 Thevariancehereisanin ﬁnite sum which may explode (especially if y is a level). For this reason we often calculate variance decompositions aierent horizons. How much of the k-step ahead forecast error variance of output is due to monetary policy shocks? To calculate this quantity start again with the moving average representation yt+k= µ +b 0ym mt+k+b 0yy yt+kb1ym mt+k−1 +b1yy yt+k−1...+bkym mtb kyy yt kym mt−1+b kyy yt−1... y Now, the shocks att and before are known at timet,o E t t+k= µybkym mt + bkyy ytb kym mt−1 + bkyy yt−1 ... and yt+k−E t t+k= b0ym mt+k+b 0yy yt+kb1ym mt+k−1+b 1yy yt+k−1....+k−1m mt+1 +bk−1y yt+1 var(y − E y )= b£2 + b2 + ... + b ¤ + b2 + b2 + .... + b ¤ t+k t t+k 0ym 1ym k−1m 0yy 1yy k−1y Again, I’ve grouped the coﬃcients into a part due to m and a part due to y. You could graph this as a function of k, and you can see how you can eyeball the results once you understand the impulse-response function. The AR(1) representation The AR(1) representation is really useful for programming. Write zt= A 1 t−1+ A2 t−2+ A 3 t−3+ εt as ⎡ ⎤ ⎡ ⎤⎡ ⎤ ⎡ ⎤ zt A 1 A 2 A3 zt−1 εt ⎣ zt−1⎦ = ⎣ 100 ⎦⎣ zt−2 ⎦ + ⎣ 0 ⎦ zt−2 010 zt−3 0 Now, the forward simulation just consists of for i=2:horizon; y=y; response(i,:) = y(1:nvars)’; end; 14

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