Lecture 23 Monetary Policy. Noah Williams

Lecture 23 Monetary Policy Noah Williams University of Wisconsin - Madison Economics 702

Fed Policy Instrument Main instrument of conventional policy is the Federal Funds rate. An extremely short-term interest rate: the rate on overnight loans from one bank to another. Uses as implicit means of changing money supply. Policy carried out via open market operations by trading desk at New York Fed. Buy and sell government securities so that market for overnight cash clears at the target rate. Again in response to recent crisis and recession, direct lending and other purchases of assets have become an important component of policy response. Unconventional monetary policy.

Policy Interest Rates Discount Rate (DISCONTINUED) Primary Credit Rate Federal Funds Target Range - Upper Limit Federal Funds Target Range - Lower Limit Federal Funds Target Rate (DISCONTINUED) 7 6 5 (Percent) 4 3 2 1 0-1 2000 2002 2004 2006 2008 2010 2012 2014 2016 research.stlouisfed.org

Other Policy Instruments Also can adjust reserve requirements, minimum fraction of each type of deposit that a bank must hold as reserves. In recent years banks have held excess reserves at the Fed, and the Fed pays interest on them. Discount window lending: lending reserves to banks so they can meet depositors demands or reserve requirements, interest rate on such called the discount rate, role of lender of last resort. A discount loan increases the monetary base, increases in discount rate discourage borrowing, reduce the monetary base. In past, Fed discouraged banks from borrowing from the discount window. Instead, banks borrow from each other in the Federal funds market. Interest rate is the Fed funds rate. In the crisis the Fed encouraged discount window borrowing.

1 Discount Window includes primary, secondary and seasonal credit programs. Federal Reserve Bank of New York December 2008 Forms of Federal Reserve Lending to Financial Institutions Term Securities Single-Tranche Term Discount Term Auction ABCP Money Money Market Term Asset-Backed Primary Dealer Transitional Credit Reciprocal Currency Term Securities Commercial Paper Discount Securities Lending Facility OMO Program Window Program Facility Market Fund Investing Funding Securities Loan Credit Facility Extensions Arrangements Lending Facility Funding Facility Regular OMOs Window 1 Lending Options Program 4 Liquidity Facility Facility Facility 5 (announced (announced (announced (announced (announced (first announced (announced (announced (announced (announced (announced (announced March 7, 2008) August 17, 2007) December 12, 2007) March 16, 2008) 2 September 21, 2008) December 12, 2007) 3 March 11, 2008) 2 October 7, 2008) July 30, 2008) September 19, 2008) 2 October 21, 2008) November 25, 2008) U.S. and London brokerdealer subsidiaries of bank holding companies, Eligible Money Market All U.S. persons that Select central banks Despository institutions, Who can Depository Primary credit-eligible Primary credit-eligible participate? Primary dealers Primary dealers Primary dealers to lend on to banks Primary dealers Primary dealers institutions depository institutions depository institutions Goldman Sachs, Morgan Primary dealers U.S. branches and agencies Eligible CP issuers 6 Mutual Funds 7 own eligible collateral in their jurisdiction Stanley, Merrill Lynch 3 of foreign banks What are they Funds and Funds Funds Funds Funds Funds Funds Funds U.S. Dollars U.S. Treasuries U.S. Treasuries U.S. Treasuries Funds Funds Funds borrowing? subordinated note U.S. Treasuries, Full range of Schedule 1: U.S. Treasuries, U.S. Treasuries, Central banks pledge foreign Newly issued 3-month U.S. dollar-denominated Full range of What collateral agencies, Full range of Full range of Full range of Discount Window agencies, agency MBS Schedule 2 unsecured and assetbacked CP from eligible U.S. dollar-denominated certificates of deposit, bank Recently originated currency and lend against agencies, Discount Window U.S. Treasuries can be pledged? agency MBS, Discount Window Discount Window tri-party repo collateral First-tier ABCP notes and commercial paper eligible collateral in but typically collateral collateral collateral system collateral 9,10 Schedule 2: Schedule 1 plus all TSLF collateral agency MBS 8 issued by highly rated and tri-party repo their jurisdiction U.S. issuers AAA ABS 11 invesment grade debt securities agency MBS system collateral 10 9 financial institutions Is there a No (loans are No (loans are No (loans are reserve impact? Yes Yes Yes Yes Yes Yes Yes Yes Yes bond-for-bond) bond-for-bond) bond-for-bond) Yes Yes Yes Typically overnight, What is the Typically, term is Typically ABCP maturity date 28 days but up to Up to 90 days 15 28 days or 84 days 13,16 Overnight 28 days term of loan? overnight 14 days 12 13 Overnight Overnight Overnight to 3 months 13 2 weeks or less several weeks 17 (270-day maximum) 3 months N/A At least one year 14 Is prepayment allowed if term No No Yes Yes No N/A N/A No N/A No No No N/A N/A Yes is greater than overnight? Which Reserve Banks conduct FRBNY FRBNY All All All FRBNY FRBNY FRBNY FRBNY FRBNY FRBNY FRB Boston FRBNY FRBNY FRBNY operations? How frequently Typically on schedule with FRBNY Schedule 1: Every other As requested Every other week, (standing facility) or as necessary Daily week is the program Typically once As requested As requested As requested TAF auctions or as requested As requested As requested As requested Typically weekly As necessary accessed? or more daily (standing facility) 16 (standing facility) (standing facility) 18 Monthly by central banks Schedule 2: Weekly (standing facility) (standing facility) (standing facility) Where are Temporary statistics reported OMO activity 19 publicly? Temporary H.4.1 - Factors H.4.1 - Factors OMO activity 19 Affecting Reserve Affecting Reserve Balances 20 Balances 20 TAF Activity 19 H.4.1 - Factors Affecting Reserve Balances 20 H.4.1 - Factors Affecting Reserve Balances 20 H.4.1 - Factors Affecting Reserve Balances 20 Securities lending activity Term securities lending facility activity 19 Term securities lending facilty options program activity 19 H.4.1 - Factors Affecting Reserve Balances 20 H.4.1 - Factors Affecting Reserve Balances 20 H.4.1 - Factors Affecting Reserve Balances 20 TALF activity 19 2 The PDCF, TSLF and AMLF will remain in operation through April 30, 2009 as announced on December 2, 2008. 3 ECB and SNB created December 12, 2007; BOC, BOE, and BOJ created September 18, 2008; RBA, Sveriges Riksbank, DNB, and Norges Bank created September 24, 2008; Reserve Bank of New Zealand created October 28, 2008; Banco Central do Brazil, Banco de Mexico, Bank of Korea, and Monetary Authority of Singapore created October 29, 2008 4 TOP auctions are sales of options granting the right to enter into TSLF borrowing. 5 The TALF is expected to go live around February 2009. The Federal Reserve reserves the right to review and make adjustments to these terms and conditions including size of program, pricing, loan maturity, and asset and borrower eligibility requirements consistent with the policy objectives of the TALF. 6 Through the CPFF the FRBNY provides financing to an SPV that purchases eligible three-month unsecured and asset-backed commercial paper from eligible issuers. 7 Through the MMIFF the FRBNY will provide senior secured funding to a series of private sector SPVs to finance the purchase of certain money market instruments from eligible investors. 8 Reverse repos are collateralized with U.S. Treasuries. 9 PDCF and TSLF collateral expanded on September 14, 2008. 10 Includes non-u.s. dollar denominated securities. 11 Includes auto loans, student loans, credit card loans, or small business loans guaranteed by the U.S. SBA 12 Open market operations are authorized for terms of up to 65 business days. 13 28-day and 84-day terms may vary slightly to account for maturity dates that fall on Bank holidays. 14 Primary credit loans are generally overnight. Loans may be granted for term beyond a few weeks to small banks, subject to additional administration. 15 Maximum maturity of term increased from overnight to 30 days on August 17, 2007, and to 90 days on March 16, 2008. 16 Foward selling TAF auctions announced on September 29, 2008 will be conducted in November with terms targeted to provide funding over year-end. 17 Loans are targeted to span potentially stressed financing dates, such as quarter-ends. 18 TOP auctions may be conducted on multiple dates for a single loan and may be conducted well in advance of a loan period. 19 Data only available on days when operations are conducted. 20 Data published on Thursday, as of close of business on Wednesday.

Policy Decisions and Conduct FOMC meets 8 times per year to set target rate. Directives from Congress to pursue price stability and full employment. Prior to meetings intensive staff briefings, laying out policy options, scenarios, and likely effects. For many years the Fed resisted committing to an explicit inflation target. Now explicitly 2%. Fed has become much more transparent in recent years, releasing forecasts.

Last Update: March 21, 2018 PDF March 21, 2018 Federal Reserve issues FOMC statement For release at 2:00 p.m. EDT Share Information received since the Federal Open Market Committee met in January indicates that the labor market has continued to strengthen and that economic activity has been rising at a moderate rate. Job gains have been strong in recent months, and the unemployment rate has stayed low. Recent data suggest that growth rates of household spending and business fixed investment have moderated from their strong fourth-quarter readings. On a 12-month basis, both overall inflation and inflation for items other than food and energy have continued to run below 2 percent. Market-based measures of inflation compensation have increased in recent months but remain low; survey-based measures of longer-term inflation expectations are little changed, on balance. Consistent with its statutory mandate, the Committee seeks to foster maximum employment and price stability. The economic outlook has strengthened in recent months. The Committee expects that, with further gradual adjustments in the stance of monetary policy, economic activity will expand at a moderate pace in the medium term and labor market conditions will remain strong. Inflation on a 12-month basis is expected to move up in coming months and to stabilize around the Committee's 2 percent objective over the medium term. Near-term risks to the economic outlook appear roughly balanced, but the Committee is monitoring inflation developments closely. In view of realized and expected labor market conditions and inflation, the Committee decided to raise the target range for the federal funds rate to 1-1/2 to 1-3/4 percent. The stance of monetary policy remains accommodative, thereby supporting strong labor market conditions and a sustained return to 2 percent inflation. In determining the timing and size of future adjustments to the target range for the federal funds rate, the Committee will assess realized and expected economic conditions relative to its objectives of maximum employment and 2 percent inflation. This assessment will take into account a wide range of information, including measures of labor market conditions, indicators of inflation pressures and inflation expectations, and readings on financial and international developments. The Committee will carefully monitor actual and expected inflation developments relative to its symmetric inflation goal. The Committee expects that economic conditions will evolve in a manner that will warrant further gradual increases in the federal funds rate; the federal funds rate is likely to remain, for some time, below levels that are expected to prevail in the longer run. However, the actual path of the federal funds rate will depend on the economic outlook as informed by incoming data. Voting for the FOMC monetary policy action were Jerome H. Powell, Chairman; William C. Dudley, Vice Chairman; Thomas I. Barkin; Raphael W. Bostic; Lael Brainard; Loretta J. Mester; Randal K. Quarles; and John C. Williams. Implementation Note issued March 21, 2018

Release Date: December 16, 2008 For immediate release The Federal Open Market Committee decided today to establish a target range for the federal funds rate of 0 to 1/4 percent. Since the Committee's last meeting, labor market conditions have deteriorated, and the available data indicate that consumer spending, business investment, and industrial production have declined. Financial markets remain quite strained and credit conditions tight. Overall, the outlook for economic activity has weakened further. Meanwhile, inflationary pressures have diminished appreciably. In light of the declines in the prices of energy and other commodities and the weaker prospects for economic activity, the Committee expects inflation to moderate further in coming quarters. The Federal Reserve will employ all available tools to promote the resumption of sustainable economic growth and to preserve price stability. In particular, the Committee anticipates that weak economic conditions are likely to warrant exceptionally low levels of the federal funds rate for some time. The focus of the Committee's policy going forward will be to support the functioning of financial markets and stimulate the economy through open market operations and other measures that sustain the size of the Federal Reserve's balance sheet at a high level. As previously announced, over the next few quarters the Federal Reserve will purchase large quantities of agency debt and mortgagebacked securities to provide support to the mortgage and housing markets, and it stands ready to expand its purchases of agency debt and mortgage-backed securities as conditions warrant. The Committee is also evaluating the potential benefits of purchasing longer-term Treasury securities. Early next year, the Federal Reserve will also implement the Term Asset-Backed Securities Loan Facility to facilitate the extension of credit to households and small businesses. The Federal Reserve will continue to consider ways of using its balance sheet to further support credit markets and economic activity. Voting for the FOMC monetary policy action were: Ben S. Bernanke, Chairman; Christine M. Cumming; Elizabeth A. Duke; Richard W. Fisher; Donald L. Kohn; Randall S. Kroszner; Sandra Pianalto; Charles I. Plosser; Gary H. Stern; and Kevin M. Warsh. In a related action, the Board of Governors unanimously approved a 75-basis-point decrease in the discount rate to 1/2 percent. In taking this action, the Board approved the requests submitted by the Boards of Directors of the Federal Reserve Banks of New York, Cleveland, Richmond, Atlanta, Minneapolis, and San Francisco. The Board also established interest rates on required and excess

Figure 1. Medians, central tendencies, and ranges of economic projections, 2018 20 and over the longer run Percent Change in real GDP Median of projections Central tendency of projections Range of projections 3 Actual 2 1 2013 2014 2015 2016 2017 2018 2019 2020 Longer run Percent Unemployment rate 7 6 5 4 3 2013 2014 2015 2016 2017 2018 2019 2020 Longer run Percent PCE inflation 3 2 1 2013 2014 2015 2016 2017 2018 2019 2020 Longer run Note: Definitions of variables and other explanations are in the notes to the projections table. The data for the actual values of the variables are annual.

Figure 2. FOMC participants assessments of appropriate monetary policy: Midpoint of target range or target level for the federal funds rate Percent 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 2018 2019 2020 Longer run Note: Each shaded circle indicates the value (rounded to the nearest 1/8 percentage point) of an individual participant s judgment of the midpoint of the appropriate target range for the federal funds rate or the appropriate target level for the federal funds rate at the end of the specified calendar year or over the longer run. One participant did not submit longer-run projections for the federal funds rate.

Inflation and Unemployment in the U.S. 12.5 Gross Domestic Product: Implicit Price Deflator Civilian Unemployment Rate (Percent Change from Year Ago), (Percent) 10.0 7.5 5.0 2.5 0.0 1960 1970 1980 1990 2000 2010 2014 research.stlouisfed.org

Rules, Discretion, and US Inflation Explicit model helps explain US inflation history. Argument due to Kydland and Precott (1977). Extended by Barro and Gordon (1983). Version of model with Fed learning studied by Sargent (1999), Cho-Williams-Sargent (2002), Sargent-Williams-Zha (2006). Start with an expectations augmented Phillips curve, π t = πt e + a(y t Yt T ), motivated by the Lucas misperceptions model, where π t is inflation, πt e is expected inflation, Y t is output, and Yt T is trend output. The central bank cares about price stability and output. min πt 2 + ω(y t Yt ) 2 Y t,π t The first term represents the price stability goal. The second term represents the output gap.

Policy Problem Represent the central bank s problem as a Lagrangian: L(Y t, π t ) = π 2 t + ω(y t Y t ) 2 + λ ( π e t + a(y t Y T t ) π t ) The first order conditions are 2π t λ = 0 and 2ω(Y t Y t ) + λa = 0 or ω(y t Y t ) + aπ t = 0 Eliminate Y t using the Phillips curve constraint: ( π t = πt e +a Yt a ) ω π t Yt T π t = ω( πt e + a(yt Yt T ) ) ω + a 2

Exploiting the Phillips Curve Assume Y t > Y T t, so π t > ωπe t ω + a 2. Suppose in 1960, people expected price stability, π e 1960 = 0. The central bank decides to exploit the Phillips curve. π 1960 > 0 and Y T 1960 < Y 1960 < Y 1960. In the short-run, this makes people better off. But in a few years, people figure out what is happening. Adaptive expectations: π e 1965 = π 1960 > 0. Exploiting the Phillips curve requires still higher inflation. π 1965 > π e 1965, Y T 1965 < Y 1965 < Y 1965. Eventually expectations again catch up with reality.

This process stops only when π t = π e t. πt e = ω( πt e + a(yt ω + a 2 Y T t ) ) π t = πt e = ω(y t Yt T ) a Moreover, since π t = πt e, Y t = Yt T as well. In the long-run, this yields higher inflation with no output gain. Known as the time-consistency problem. Under rational expectations, this process occurs immediately. If π e t < ω(y t Y T t ) a, households expect π t > π e t. This is inconsistent with rational expectations. But this requires households to understand Fed s incentives.

Remedies How can the Fed reduce inflationary expectations? Adaptive expectations: stop trying to exploit Phillips curve. Rational expectations: commit not to exploit the Phillips curve. Isolate the Fed from pressure to make Y t > Y T t. Appoint conservative central bankers. Force the Fed to follow a narrow set of rules. Reputation may substitute for explicit commitment. Reality probably lies somewhere in between adaptive and rational It is possible but costly to simply lower money growth. Disinflation is less costly if it is credibly pre-announced.

The Taylor Rule Most influential policy rule due to John Taylor (1993). Simple rule for setting interest rate based on output gap, inflation target π = 2%, R = 4%. R t = R + 1.5(π t π ) + 0.5x t Originally proposed as an explanation of Fed behavior. Since has been shown to work well in a variety of models. Much academic literature focuses on the optimal design of interest rate rules similar to this. Even though Fed not explicitly rule based, analysis of rules is a key input in policy process.

27_05 INTEREST RATE (PERCENT) Monetary policy rule in a graph Monetary policy rule 7 6 5 Interest rate when inflation is on target 4 3 2 1 Inflation target 0 1 2 3 4 5 6 INFLATION RATE (PERCENT)

Monetary Trends - Monetary Aggregates and Their Components: Policy Based Inflation Indicators Monetary Trends Monetary Aggregates and Their Components https://research.stlouisfed.org/datatrends/mt/page10.ph Federal Funds Rate and Inflation Targets 0% 1% 2% 3% 4% Effective Federal Funds Rate 7.5 5.0 2.5 (Percent) 0.0-2.5-5.0 2000 2002 2004 2006 2008 2010 2012 2014 2016 1960 research.stlouisfed.org Federal Funds Rate and Inflation Targets shows the observed federal funds rate, quarterly, and the level of the funds rate implied by applying Taylor s (1993) equation to five alternative target inflation rates, π= 0, 1, 2, 3, 4 percent, where ft* is the implied federal funds rate, πt 1 is the previous period s inflation rate (PCE) measured on a year-over-year basis, yt 1 is the log of the previous period s level of real gross domestic product (GDP), and yt 1P is the log of an estimate of the previous period s level of potential output. ft* = 2.5 + πt 1 + (πt 1 π)/2 + 100 (yt 1 yt 1P)/2 1 of 6 4/11/2016 11:08 AM

Monetary Trends - Monetary Aggregates and Their Components: Policy Based Inflation Indicators Actual and Potential Real GDP https://research.stlouisfed.org/datatrends/mt/page10.ph Billions of Chain-Weighted 2009 Dollars Real Gross Domestic Product Real Potential Gross Domestic Product 17,000 (Billions of Chained 2009 Dollars) 16,000 15,000 14,000 13,000 12,000 2000 2002 2004 2006 2008 2010 2012 2014 2016 2025 research.stlouisfed.org Potential Real GDP is estimated by the Congressional Budget Office (CBO). 2 of 6 4/11/2016 11:08 AM

Monetary Trends - Monetary Aggregates and Their Components: Policy Based Inflation Indicators PCE Inflation https://research.stlouisfed.org/datatrends/mt/page10.ph Percent change from year ago Personal Consumption Expenditures: Chain-type Price Index 4 3 (Percent Change from Year Ago) 2 1 0-1 2000 2002 2004 2006 2008 2010 2012 2014 Source: US. Bureau of Economic Analysis research.stlouisfed.org 3 of 6 4/11/2016 11:08 AM

Taylor Rules A larger literature has now developed that has estimated the Taylor Rule, or similar simple rules, for a variety of countries and time periods. For example, Clarida, Galí, and Gertler (2000) do so for the Federal Reserve, the Bundesbank, and the Bank of Japan. Estimates for the United States reported by Judd and Rudebusch (2000). In general, the basic Taylor Rule, when supplemented with the lagged nominal interest rate, does quite well in matching the actual behavior of the policy interest rate. The argument for simple rules relies not on their optimality but on their simplicity; they useful benchmark for policy or aid in promoting policy transparency. Recent legislation proposed which would require Fed to consult Taylor rule

How are Changes in Policy Transmitted? Fed funds rate is very short term. In itself has little effect, as long-term rates are key determinant of spending decisions. But long rate depends on future path of short rate. So not just current policy matters, but expected future policy matters. Modern theory emphasizes the role of nominal rigidities. Some prices and wages are pre-set in nominal terms. So in short run Fed has some influence over aggregate demand. By lowering rates, it makes borrowing cheaper for households which boosts aggregate demand. Raising rates opposite. But prices and wages set understanding Fed behavior, hence importance of expectations.

Monetary Trends updated through 04/17/12 CPI Inflation and 1-Year-Ahead CPI Inflation Expectations Percent 6 5 4 Humphrey-Hawkins CPI Inflation Range CPI Inflation 3 2 1 0-1 -2 University of Michigan Federal Reserve Bank of Philadelphia 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 The shaded region shows the Humphrey-Hawkins CPI inflation range. Beginning in January 2000, the Humphrey-Hawkins inflation range was reported using the PCE price index and therefore is not shown on this graph. 10-Year Ahead PCE Inflation Expectations and Realized Inflation Percent 8 6 4 2 Realized Expected 0 65 70 75 80 85 90 95 00 05 10 See the notes section for an explanation of the chart. Treasury Security Yield Spreads Yield to maturity 4 10-Year less 3-Month T-Bill Real Interest Rates Percent, Real rate = Nominal rate less year-over-year CPI inflation 4

updated through 04/17/12 Implied One-Year Forward Rates Percent 7 6 5 4 3 2 1 0 Week Ending: 04/15/11 03/16/12 04/13/12 2y 3y 5y 7y 10y Monetary Trends Rates on 3-Month Eurodollar Futures Percent, daily data 0.53 Jun 2012 0.51 0.49 0.47 0.45 Apr 2012 0.43 May 2012 0.41 02/13 02/20 02/27 03/05 03/12 03/19 03/26 04/02 04/09 04/16 Rates on Selected Federal Funds Futures Contracts Percent, daily data 0.15 Rates on Federal Funds Futures on Selected Dates Percent 0.16 0.14 Jun 2012 0.15 04/02/2012 0.13 0.12 0.11 Apr 2012 May 2012 0.14 0.13 0.12 0.11 03/02/2012 02/03/2012 02/13 02/20 02/27 03/05 03/12 03/19 03/26 04/02 04/09 04/16 Apr May Jun Jul Aug Sep Contract Month Inflation-Indexed Treasury Securities Weekly data Inflation-Indexed Treasury Yield Spreads Weekly data Percent 4.00 1.67 Percent 4.00 1.67-0.67-3.00 2010 2011. 2012 2013 Note: Yields are inflation-indexed constant maturity U.S. Treasury securities Inflation-Indexed 10-Year Government Notes 5 10 15 20 Maturity -0.67-3.00 2010 2011 2012 5 2013 Inflation-Indexed Williams 10-Year Economics Government 702 Yield Spreads. 10 15 20 Horizon Note: Yield spread is between nominal and inflation-indexed constant maturity U.S. Treasury securities.

An Optimizing Model with Nominal Rigidities The original Keynesian model was based on some prices or wages being fixed, but firms did not take that into account. Modern New Keynesian theory considers dynamic GE models with nominal rigidities. The model consists of households who supply labor, purchase goods for consumption, and hold money and bonds, and firms who hire labor and produce and sell differentiated products in monopolistically competitive goods markets. The basic model of monopolistic competition is drawn from Dixit and Stiglitz (1977). Each firm set the price of the good it produces, but not all firms reset their price each period. Households and firms behave optimally: households maximize the expected present value of utility and firms maximize profits.

Price Adjustment Each period, the firms that adjust their price are randomly selected: a fraction 1 ξ of all firms adjust while the remaining ξ fraction do not adjust. The parameter ξ is a measure of the degree of nominal rigidity; a larger ξ implies fewer firms adjust each period and the expected time between price changes is longer. For those firms who do adjust their price at time t, they do so to maximize the expected discounted value of current and future profits. Profits at some future date t + s are affected by the choice of price at time t only if the firm has not received another opportunity to adjust between t and t + s. The probability of this is ξ s.

Basic New Keynesian Model of Transmission Can be derived from primitives: household consumption decisions, firm pricing decisions. Assumes monopolistic competition, sticky prices. Only labor input, C t = Y t. Unlike old Keynesian literature, assumes rational expectations. When firms set prices, forecast future demand and policy. Households also forecast future conditions when choosing consumption. Basic model has 2 key equations: a Euler equation which gives an IS relation between output and interest rates, and a Phillips curve which results from price setting decisions. Gives a relation between output and inflation. Along with a specification of monetary policy, these determine the evolution of output, inflation, and interest rates.

Basic Model Clarida-Gali-Gertler (1999), Woodford (2003). Let π t be inflation, E t π t+1 expected inflation, x t = y t y p t the output gap (deviation of output from potential ), R t the nominal interest rate. First equation relates output gap to real interest rate: x t = φ(r t E t π t+1 ) + E t x t+1 + g t Linearized consumption Euler equation/is curve. Second equation is the New Keynesian Phillips curve relating inflation and real activity: π t = κx t + βe t π t+1 + u t Linearized pricing decisions of firms with staggered price setting.

g t and u t are exogenous shocks. Demand (such as government spending) and cost-push (such as wage or markup fluctuations) Assume they re serially correlated: g t = ρ g g t 1 + ɛ g t u t = ρ u u t 1 + ɛ u t Note that timing of Phillips curve is different from previous expectations-augmented (Lucas suprise model): here inflation is fully forward looking. Can close model via an LM curve once we specify money demand. But since we ll analyze policy via setting interest rate R t, this will only pin down the stock of money.

Policy Implications of Price Stickiness Models that combine optimizing agents and sticky prices have very strong policy implications. When the price level fluctuates, and not all firms are able to adjust, price dispersion results. This causes the relative prices of the different goods to vary. If the price level rises, for example, two things happen. 1 The relative price of firms who have not set their prices for a while falls. They experience in increase in demand and raise output, while firms who have just reset their prices reduce output. This production dispersion is inefficient. 2 Consumers increase their consumption of the goods whose relative price has fallen and reduce consumption of those goods whose relative price has risen. This dispersion in consumption reduces welfare.

Optimal Policy The solution is to prevent price dispersion by stabilizing the price level. What is critical for this result is that nominal wages are assumed to be completely flexible. But the same argument would apply if wages are sticky and prices flexible. With sticky wages and flexible prices, monetary policy should stabilizes the nominal wage.

Cost Shocks Now assume π t = κx t + βe t π t+1 + u t where u t represents an inflation or cost shock, which is serially correlated: Then u t = ρ u u t 1 + ɛ u t π t = κ β i E t x t+i + β i E t u t+i i=0 i=0 Cannot keep both x and π equal to zero. Trade-offs must be made.