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Authorized for public release by the FOMC Secretariat on 1/10/2020 BOARD OF GOVERNORS OF THE FEDERAL RESERVE SYSTEM Division of Monetary Affairs FOMC SECRETARIAT Date: March 7, 2014 To: Research Directors From: Matthew M. Luecke Subject: Supporting Documents for DSGE Models Update The attached documents support the update on the projections of the DSGE models. 1 of 1 Authorized for public release by the FOMC Secretariat on 1/10/2020 System DSGE Project: Research Directors Drafts 0DUFK, 201 Page 1 of 68 Authorized for public release by the FOMC Secretariat on 1/10/2020 The Current Outlook in EDO: December FOMC Meeting (Class II – Restricted FR) Dario Caldara ∗ March 6, 2014 1 The EDO Forecast from 2014 to 2016 Given recent data (including expectations for the federal funds rate), EDO projects below-trend real GDP growth until the end of 2015while unemployment remains around 7 percent through 2016 (Figure 1).1 This subdued pace of real activity is accompanied by low inflation, which slowly rises from a low of 1.2 percent at 2014:Q1 to 1.8 percent by 2016. This baseline is heavily shaped by the model’s interpretation of the low level of interest rates. In particular, low interest rates over the projection reflect, according to the implementation used in the projection, both the drag on interest rates imparted by past and prospective weakness in activity and some degree of monetary accommodation, with the first factor the more important, largely by assumption (as fluctuations in risk premiums are the dominant factor in accounting for fluctuations in expected interest rates over history, and hence are also assumed to be important over the projection period). Because market expectations for low interest rates owe (in the model) importantly to weak expected demand, the model projects that the aggregate risk premium will return to its early 2012 levels, lowering GDP growth and boosting unemployment above its long-run level. But the negative impact of the rise in the aggregate risk premium is partly offset by expected unusually accommodative monetary policy in 2014. In addition, lower-than-expected labor productivity and surprisingly strong inflation since last year have led the model to infer a deterioration in aggregate supply conditions, which modestly reduces GDP growth early in the projection. ∗ Dario Caldara (dario.caldara@frb.gov) is affiliated with the Division of Research and Statistics of the Federal Reserve Board. Sections 2 and 3 contain background material on the EDO model, as in previous rounds. These sections were co-written with Hess Chung and Jean-Philippe Laforte. 1 The baseline forecast for EDO is conditioned on the staff’s preliminary March 2014 Tealbook projection through 2014:Q1 and market expectations that the federal funds rate will remain at its effective lower bound through the second quarter of 2015 (as indicated by OIS market prices). We do not impose an unemployment or inflation threshold on the monetary policy rule. The model’s static structural parameters have been re-estimated using data through 2013:Q3. In particular, the new estimates incorporate the latest comprehensive revision to NIPA data. For estimation, the observable corresponding to the model’s concept of investment excludes spending on intellectual property products. 1 Page 2 of 68 Authorized for public release by the FOMC Secretariat on 1/10/2020 Figure 1: Recent History and Forecasts EDO Projection Summary Real GDP Core PCE price index Percent change, a.r. 5 Percent change, a.r. 5 2.5 4 4 2.0 2.0 3 3 1.5 1.5 2 2 1.0 1.0 1 1 0.5 0.5 0 0 0.0 0.0 -1 -1 -0.5 -0.5 -2 -2 -1.0 -1.0 -3 -3 -1.5 -1.5 -4 -4 -2.0 2011 2012 2013 2014 2015 2016 2011 2012 2013 2014 2015 2016 2.5 -2.0 Federal Funds Rate Percent 5 5 4 4 3 3 2 2 1 1 0 0 -1 -1 -2 -2 -3 -3 -4 -4 -5 2011 2012 2013 2014 2015 2016 -5 2014 Q4/Q4 Real GDP (a) Credible set (c) Federal Funds Rate (b) Credible set (c) 2016 Q4/Q4 2.2 2.8 3.1 -1.0-4.9 .5-4.3 1.1-5.0 Core PCE Price index (a) 1.2 Credible set (c) 2015 Q4/Q4 .7-1.6 1.4 1.6 .7-2.1 .9-2.5 0.1 0.6 1.4 .0-1.2 .0-2.3 .2-3.1 (a) Q4/Q4 percent change, (b) Q4 level, (c) 68 percent Red, solid line -- Data (through 2014:Q1) and projections; Blue, solid line -- Previous projection (December, 2013, as of 2013:Q4); Black, dashed line -- Steady-state or trend values Contributions (bars): Red -- Financial; Blue -- Technology; Silver -- Monetary policy; Green -- Other Inflation is held below target by a combination of weak aggregate demand and muted pressure on wages in the labor market. Indeed, the unemployment rate rises through early 2015, driven largely by the aforementioned weak demand conditions. By the end of the forecast, however, a substantial portion of the elevated unemployment rate is accounted for the stickiness in wages and prices in EDO, which prevents the real wage from falling sufficiently to bring down unemployment; indeed, EDO estimates that the real wage must decline notably to clear the labor market.2 2 As discussed below, unemployment enters the EDO model through a new-Keynesian wage Phillips curve, without much specificity regarding structural labor-market features. As such, the primary role of unemployment is as a gauge of the degree to which real-wage adjustment impedes labor market clearing, and anomalously persistent and elevated rates of unemployment lead EDO to detect a decline in the real wage needed to clear the labor market. While most of the runup in unemployment since 2007 is driven by weak demand (in EDO), the model identifies a component of the increase in unemployment as due to a decline in the market-clearing real wage. Finally, as noted in the model description below, such a decline is implemented in the model by a shift in labor supply. 2 Page 3 of 68 Authorized for public release by the FOMC Secretariat on 1/10/2020 2 An Overview of Key Model Features Figure 2 provides a graphical overview of the model. While similar to most related models, EDO has a more detailed description of production and expenditure than most other models.3 Figure 2: Model Overview Specifically, the model possesses two final good sectors in order to capture key long-run growth facts and to differentiate between the cyclical properties of different categories of durable expenditure (e.g., housing, consumer durables, and nonresidential investment). For example, technological progress has been faster in the production of business capital and consumer durables (such as computers and electronics). The disaggregation of production (aggregate supply) leads naturally to some disaggregation of expenditures (aggregate demand). We move beyond the typical model with just two categories of (private domestic) demand (consumption and investment) and distinguish between four categories of private demand: consumer non-durable goods and non-housing services, consumer durable goods, residential investment, and non-residential investment. The boxes surrounding the producers in the 3 Chung, Kiley, and Laforte (2011) provide much more detail regarding the model specification, estimated parameters, and model propeties. 3 Page 4 of 68 Authorized for public release by the FOMC Secretariat on 1/10/2020 figure illustrate how we structure the sources of each demand category. Consumer non-durable goods and services are sold directly to households; consumer durable goods, residential capital goods, and non-residential capital goods are intermediated through capital-goods intermediaries (owned by the households), who then rent these capital stocks to households. Consumer non-durable goods and services and residential capital goods are purchased (by households and residential capital goods owners, respectively) from the first of economy’s two final goods producing sectors, while consumer durable goods and non-residential capital goods are purchased (by consumer durable and residential capital goods owners, respectively) from the second sector. In addition to consuming the non-durable goods and services that they purchase, households supply labor to the intermediate goods-producing firms in both sectors of the economy. This remainder of this section provides an overview of the key properties of the model. In particular, the model has five key features: • A new-Keynesian structure for price and wage dynamics. Unemployment measures the difference between the amount workers are willing to be employed and firms’ employment demand. As a result, unemployment is an indicator of wage, and hence price, pressures, as in Gali (2010). • Production of goods and services occurs in two sectors, with differential rates of technological progress across sectors. In particular, productivity growth in the investment and consumer durable goods sector exceeds that in the production of other goods and services, helping the model match facts regarding long-run growth and relative price movements. • A disaggregated specification of household preferences and firm production processes that leads to separate modeling of nondurables and services consumption, durables consumption, residential investment, and business investment. • Risk premia associated with different investment decisions play a central role in the model. These include A) an aggregate risk-premium, or natural rate of interest, shock driving a wedge between the short-term policy rate and the interest rate facing private decisionmakers (as in Smets and Wouters (2007)) and B) fluctuations in the discount factor/risk premia facing the intermediaries financing household (residential and consumer durable) and business investment. 2.1 Two-sector production structure It is well known (e.g., Edge, Kiley, and Laforte (2008)) that real outlays for business investment and consumer durables have substantially outpaced those on other goods and services, while the prices of these goods (relative to others) has fallen. For example, real outlays on consumer durables have far outpaced those on other consumption, while prices for consumer durables have been flat and those for other consumption have risen substantially; as a result, the ratio of nominal outlays in the two categories has been much more stable, although consumer durable outlays plummeted in the Great Recession. Many models fail to account for this fact. 4 Page 5 of 68 Authorized for public release by the FOMC Secretariat on 1/10/2020 EDO accounts for this development by assuming that business investment and consumer durables are produced in one sector and other goods and services in another sector. Specifically, production by firm j in each sector s (where s equals kb for the sector producing business investment and consumer durables sector and cbi for the sector producing other goods and services) is governed by a Cobb-Douglas production function with sector-specific technologies: 1−α Xts (j) = (Ztm Zts Lst (j)) α (Ktu,nr,s (j)) , for s = cbi, kb. (1) In 1, Z m represents (labor-augmenting) aggregate technology, while Z s represents (labor-augmenting) sector-specific technology; we assume that sector-specific technological change affects the business investment and consumer durables sector only; Ls is labor input and K u,nr,s is capital input (that is, utilized non-residential business capital (and hence the nr and u terms in the superscript). Growth in this sector-specific technology accounts for the long-run trends, while high-frequency fluctuations allow the possibility that investment-specific technological change is a source of business cycle fluctuations, as in Fisher (2006). 2.2 The structure of demand EDO differentiates between several categories of expenditure. Specifically, business investment spending determines non-residential capital used in production, and households value consumer nondurables goods and services, consumer durable goods, and residential capital (e.g., housing). Differentiation across these categories is important, as fluctuations in these categories of expenditure can differ notably, with the cycles in housing and business investment, for example, occurring at different points over the last three decades. Valuations of these goods and services, in terms of household utility, is given by the following utility function: E0 ∞ X cnn β t ς cnn ln(Etcnn (i)−hEt−1 (i))+ς cd ln(Ktcd (i)) t=0 +ς r ln(Ktr (i)) −ς cbi kb 1+ν l (Lt (i)+Lt (i)) 1+ν , (2) where E cnn represents expenditures on consumption of nondurable goods and services, K cd and K r represent the stocks of consumer durables and residential capital (housing), Lcbi + Lkb represents the sum of labor supplied to each productive sector (with hours worked causing disutility), and the remaining terms represent parameters (such as the discount factor, relative value in utility of each service flow, and the elasticity of labor supply). By modeling preferences over these disaggregated categories of expenditure, EDO attempts to account for the disparate forces driving consumption of nondurables and durables, residential investment, and business investment – thereby speaking to issues such as the surge in business investment in the second half of the 1990s or the housing cycle the early 2000s recession and the most recent downturn. Many other models do not distinguish between developments across these categories of 5 Page 6 of 68 Authorized for public release by the FOMC Secretariat on 1/10/2020 spending. 2.3 Risk premia, financial shocks, and economic fluctuations The structure of the EDO model implies that households value durable stocks according to their expected returns, including any expected service flows, and according to their risk characteristics, with a premium on assets which have high expected returns in adverse states of the world. However, the behaviour of models such as EDO is conventionally characterized under the assumption that this second component is negligible. In the absence of risk adjustment, the model would then imply that households adjust their portfolios until expected returns on all assets are equal. Empirically, however, this risk adjustment may not be negligible and, moreover, there may be a variety of factors, not explicitly modelled in EDO, which limit the ability of households to arbitrage away expected return differentials across different assets. To account for this possibility, EDO features several exogenous shocks to the rates of return required by the household to hold the assets in question. Following such a shock – an increase in the premium on a given asset, for example– households will wish to alter their portfolio composition to favor the affected asset, leading to changes in the prices of all assets and, ultimately, to changes in the expected path of production underlying these claims. The “sector-specific” risk shocks affect the composition of spending more than the path of GDP itself. This occurs because a shock to these premia leads to sizable substitution across residential, consumer durable, and business investment; for example, an increase in the risk premia on residential investment leads households to shift away from residential investment and towards other types of productive investment. Consequently, it is intuitive that a large fraction of the non-cyclical, or idiosyncratic, component of investment flows to physical stocks will be accounted for by movements in the associated premia. Shocks to the required rate of return on the nominal risk-free asset play an especially large role in EDO. Following an increase in the premium, in the absence of nominal rigidities, the households’ desire for higher real holdings of the risk-free asset would be satisfied entirely by a fall in prices, i.e., the premium is a shock to the natural rate of interest. Given nominal rigidities, however, the desire for higher risk-free savings must be off-set, in part, through a fall in real income, a decline which is distributed across all spending components. Because this response is capable of generating comovement across spending categories, the model naturally exploits such shocks to explain the business cycle. Reflecting this role, we denote this shock as the “aggregate risk-premium”. Movements in financial markets and economic activity in recent years have made clear the role that frictions in financial markets play in economic fluctuations. This role was apparent much earlier, motivating a large body of research (e.g.,Bernanke, Gertler, and Gilchrist (1999)). While the range of frameworks used to incorporate such frictions has varied across researchers studying different questions, a common theme is that imperfections in financial markets – for example, related to imperfect information on the outlook for investment projects or earnings of borrowers – drives a wedge between the cost of riskless funds and the cost of funds facing households and firms. Much of the literature on financial frictions has worked to develop frameworks in which risk premia fluctuate 6 Page 7 of 68 Authorized for public release by the FOMC Secretariat on 1/10/2020 for endogenous reasons (e.g., because of movements in the net worth of borrowers). Because the risk-premium shocks induces a wedge between the short-term nominal risk-free rate and the rate of return on the affected risky rates, these shocks may thus also be interpreted as a reflection of financial frictions not explicitly modelled in EDO. The sector-specific risk premia in EDO enter the model in much the same way as does the exogenous component of risk premia in models with some endogenous mechanism (such as the financial accelerator framework used Boivin, Kiley, and Mishkin (2010)), and the exogenous component is quantitatively the most significant one in that research.4 Figure 3: Unemployment Fluctuations in the EDO model Historical Decomposition for Unemployment Unemployment Rate Percent 10 10 8 8 6 6 4 4 2 2 0 0 -2 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 Black, solid line -- Data (through 2014Q1) and projections; Black, dashed line -- Steady-state or trend values Contributions (bars): Red -- Financial; Blue -- Technology; Silver -- Monetary policy; Yellow -- Labor supply; Green -- Other 2.4 Unemployment Fluctuations in the EDO model This version of the EDO model assumes that labor input consists of both employment and hours per worker. Workers differ in the disutility they associate with employment. Moreover, the labor market 4 Specifically, the risk premia enter EDO to a first-order (log)linear approximation in the same way as in the cited research if the parameter on net worth in the equation determining the borrowers cost of funds is set to zero; in practice, this parameter is often fairly small in financial accelerator models. 7 Page 8 of 68 -2 Authorized for public release by the FOMC Secretariat on 1/10/2020 is characterized by monopolistic competition. As a result, unemployment arises in equilibrium – some workers are willing to be employed at the prevailing wage rate, but cannot find employment because firms are unwilling to hire additonal workers at the prevailing wage. As emphasized by Gali (2010), this framework for unemployment is simple and implies that the unemployment rate reflects wage pressures: When the unemployment rate is unusually high, the prevailing wage rate exceeds the marginal rate of subsitution between leisure and consumption, implying that workers would prefer to work more. In addition, in our environment, nominal wage adjustment is sticky, and this slow adjustment of wages implies that the economy can experience sizable swings in unemployment with only slow wage adjustment. Our specific implementation of the wage adjustment process yields a relatively standard New-Keynesian wage Phillips curve. The presence of both price and wage rigidities implies that stabilization of inflation is not, in general, the best possible policy objective (although a primary role for price stability in policy objectives remains). While the specific model on unemployment is suitable for discussions of the links between unemployment and wage/price inflation, it leaves out many features of labor market dynamics. Most notably, it does not consider separations, hires, and vacancies, and is hence not amenable to analysis of issues related to the Beveridge curve. As emphasized above, the rise in unemployment during the Great Recession primarily reflected, according to the EDO model, the weak demand that arose from elevated risk premiums that depressed spending, as illustrated by the red bars in figure 3. Indeed, these demand factors explain the overwhelming share of cyclical movements in unemployment over the past two-and-a-half decades, as is also apparent in figure 3. Other factors are important for some other periods. For example, monetary policymakers lowered the federal funds rate rapidly over the course of 2008, somewhat in advance of the rise in unemployment and decline in inflation that followed. As illustrated by the silver bars in figure 3, these policy moves mitigated the rise in unemployment somewhat over 2009; however, monetary policy efforts provided less stimulus, according to EDO, over 2010 and 2011 – when the federal funds rate was constrained from falling further. (As in many other DSGE models, EDO does not include economic mechanisms through which quantitative easing provides stimulus to aggregate demand). The contribution of supply shocks – most notably labor supply shocks – is also estimated to contribute importantly to the low-frequency movements in unemployment, as shown by the yellow bars in figure 3. Specifically, favorable supply developments in the labor market are estimated to have placed downward pressure on unemployment during the second half of the 1990s; these developments have reversed, and some of the currently elevated rate of unemployment is, according to EDO, attributable to adverse labor market supply developments. As discussed previously, these developments are simply exogenous within EDO and are not informed by data on a range of labor market developments (such as gross worker flows and vacancies). 8 Page 9 of 68 Authorized for public release by the FOMC Secretariat on 1/10/2020 2.5 New-Keynesian Price and Wage Phillips Curves As in most of the related literature, nominal prices and wages are both “sticky” in EDO. This friction implies that nominal disturbances – that is, changes in monetary policy – have effects on real economic activity. In addition, the presence of both price and wage rigidities implies that stabilization of inflation is not, in general, the best possible policy objective (although a primary role for price stability in policy objectives remains). Given the widespread use of the New-Keynesian Phillips curve, it is perhaps easiest to consider the form of the price and wage Phillips curves in EDO at the estimated parameters. The price Phillips curve (governing price adjustment in both productive sectors) has the form: p,s p,s πtp,s = 0.22πt−1 + 0.76Et πt+1 + .017mcst + θts (3) where mc is marginal cost and θ is a markup shock. As the parameters indicate, inflation is primarily forward-looking in EDO. The wage (w) Phillips curve for each sector has the form: s s s w 4wts = 0.014wt−1 + 0.95Et 4wt+1 + .012 mrsc,l t − wt + θt + adj. costs. (4) where mrs represents the marginal rate of substitution between consumption and leisure. Wages are primarily forward looking and relatively insensitive to the gap between households’ valuation of time spent working and the wage. The middle panel of figure 1 presents the decomposition of inflation fluctuations into the exogenous disturbances that enter the EDO model. As can be seen, aggregate demand fluctuations, including aggregate risk premiums and monetary policy surprises, contribute little to the fluctuations in inflation according to the model. This is not surprising: In modern DSGE models, transitory demand disturbances do not lead to an unmooring of inflation (so long as monetary policy responds systematically to inflation and remains committed to price stability). In the short run, inflation fluctuations primarily reflect transitory price and wage shocks, or markup shocks in the language of EDO. Technological developments can also exert persistent pressure on costs, most notably during and following the strong productivity performance of the second half of the 1990s which is estimated to have lowered marginal costs and inflation through the early 2000s. More recently, disappointing labor productivity readings over the course of 2011 have led the model to infer sizeable negative technology shocks in both sectors, contributing noticeably to inflationary pressure over that period (as illustrated by the blue bars in figure 1), 2.6 Monetary Authority and A Long-term Interest Rate We now turn to the last agent in our model, the monetary authority. It sets monetary policy in accordance with an Taylor-type interest-rate feedback rule. Policymakers smoothly adjust the actual 9 Page 10 of 68 Authorized for public release by the FOMC Secretariat on 1/10/2020 interest rate Rt to its target level R̄t ρr Rt = (Rt−1 ) R̄t 1−ρr exp [rt ] , (5) where the parameter ρr reflects the degree of interest rate smoothing, while rt represents a monetary policy shock. The central bank’s target nominal interest rate, R̄t depends the deviation of output from the level consistent with current technologies and “normal” (steady-state) utilization of capital and labor (X̃ pf , the “production function” output gap) Consumer price inflation also enters the target. The target equation is: R̄t = X̃t pf ry Πc rπ t Πc∗ R∗ . (6) In equation (6), R∗ denotes the economy’s steady-state nominal interest rate, and φy and φπ denote the weights in the feedback rule. Consumer price inflation, Πct , is the weighted average of inflation in the nominal prices of the goods produced in each sector, Πp,cbi and Πp,kb : t t Πct = (Πp,cbi )1−wcd (Πp,kb )wcd . t t (7) The parameter wcd is the share of the durable goods in nominal consumption expenditures. The model also includes a long-term interest rate (RLt ), which is governed by the expectations hypothesis subject to an exogenous term premia shock: RLt = Et ΠN τ =0 Rτ · Υt . (8) where Υ is the exogenous term premium, governed by Ln (Υt ) = 1 − ρΥ Ln (Υ∗ ) + ρΥ Ln (Υt−1 ) + Υ t . (9) In this version of EDO, the long-term interest rate plays no allocative role; nonetheless, the term structure contains information on economic developments useful for forecasting (e.g., Edge, Kiley, and Laforte (2010)) and hence RL is included in the model and its estimation. 2.7 Summary of Model Specification Our brief presentation of the model highlights several points. First, although our model considers production and expenditure decisions in a bit more detail, it shares many similar features with other DSGE models in the literature, such as imperfect competition, nominal price and wage rigidities, and real frictions like adjustment costs and habit-persistence. The rich specification of structural shocks (to aggregate and investment-specific productivity, aggregate and sector-specific risk premiums, and mark-ups) and adjustment costs allows our model to be brought to the data with some chance of finding empirical validation. Within EDO, fluctuations in all economic variables are driven by thirteen structural shocks. It is most convenient to summarize these shocks into five broad categories: 10 Page 11 of 68 Authorized for public release by the FOMC Secretariat on 1/10/2020 • Permanent technology shocks: This category consists of shocks to aggregate and investmentspecific (or fast-growing sector) technology. • A labor supply shock: This shock affects the willingness of to supply labor. As was apparent in our earlier description of the unemployment rate and in the presentation of the structural drivers below, this shock captures very persistent movements in unemployment that the model judges are not indicative of wage pressures. While EDO labels such movements labor supply shocks, an alternative interpretation would descrbie these as movements in unemployment that reflect persistent strucutral features not otherwise captured by the model. • Financial, or intertemporal, shocks: This category consists of shocks to risk premia. In EDO, variation in risk premia – both the premium households’ receive relative to the federal funds rate on nominal bond holdings and the additional variation in discount rates applied to the investment decisions of capital intermediaries – are purely exogenous. Nonetheless, the specification captures aspects of related models with more explicit financial sectors (e.g., Bernanke, Gertler, and Gilchrist (1999)), as we discuss in our presentation of the model’s properties below. • Markup shocks: This category includes the price and wage markup shocks. • Other demand shocks: This category includes the shock to autonomous demand and a monetary policy shock. 3 Estimation: Data and Properties 3.1 Data The empirical implementation of the model takes a log-linear approximation to the first-order conditions and constraints that describe the economy’s equilibrium, casts this resulting system in its state-space representation for the set of (in our case 13) observable variables, uses the Kalman filter to evaluate the likelihood of the observed variables, and forms the posterior distribution of the parameters of interest by combining the likelihood function with a joint density characterizing some prior beliefs. Since we do not have a closed-form solution of the posterior, we rely on Markov-Chain Monte Carlo (MCMC) methods. The model is estimated using 13 data series over the sample period from 1984:Q4 to 2011:Q4. The series are: 1. The civilian unemployment rate (U ); 2. The growth rate of real gross domestic product (∆GDP ); 3. The growth rate of real consumption expenditure on non-durables and services (∆C); 4. The growth rate of real consumption expenditure on durables (∆CD); 5. The growth rate of real residential investment expenditure (∆Res); 6. The growth rate of real business investment expenditure (∆I); 11 Page 12 of 68 Authorized for public release by the FOMC Secretariat on 1/10/2020 7. Consumer price inflation, as measured by the growth rate of the Personal Consumption Expenditure (PCE) price index (∆PC,total ); 8. Consumer price inflation, as measured by the growth rate of the PCE price index excluding food and energy prices (∆PC,core ); 9. Inflation for consumer durable goods, as measured by the growth rate of the PCE price index for durable goods (∆Pcd ); 10. Hours, which equals hours of all persons in the non-farm business sector from the Bureau of Labor Statistics (H);5 11. The growth rate of real wages, as given by compensation per hour in the non-farm business sector from the Bureau of Labor Statistics divided by the GDP price index (∆RW ); 12. The federal funds rate (R). 13. The yield on the 2-yr. U.S. Treasury security (RL). Our implementation adds measurement error processes to the likelihood implied by the model for all of the observed series used in estimation except the short-term nominal interest rate series. 3.2 Variance Decompositions and impulse responses We provide detailed variance decompositions and impulse response in Chung, Kiley, and Laforte (2011), and only highlight the key results here. Volatility in aggregate GDP growth is accounted for primarily by the technology shocks in each sector, although the economy-wide risk premium shock contributes non-negligibly at short horizons. Volatility in the unemployment rate is accounted for primarily by the economy-wide risk premium and business investment risk premium shocks at horizons between one and sixteen quarters. Technology shocks in each sector contribute very little, while the labor supply shock contributes quite a bit a low frequencies. The large role for risk premia shocks in the forecast error decomposition at business cycle horizons illustrates the importance of this type of “demand” shock for volatility in the labor market. This result is notable, as the unemployment rate is the series most like a “gap” variable in the model – that is, the unemployment rate shows persistent cyclical fluctuations about its long-run value. Volatility in core inflation is accounted for primarily by the markup shocks. Volatility in the federal funds rate is accounted for primarily by the economywide risk premium (except in the very near term, when the monetary policy shock is important). Volatility in expenditures on consumer non-durables and non-housing services is, in the near horizon, accounted for predominantly by economy-wide risk-premia shocks. In the far horizon, volatility is accounted for primarily by capital-specific and economy-wide technology shocks. Volatilities in expenditures on consumer durables, residential investment, and nonresidential investment are, in the near horizon, accounted for predominantly by their own sector 5 We remove a low-frequency trend from hours. We first pad the historical series by appending 40 quarterly observations which approach the most recent 40-quarter moving average of the data at a rate of 0.05 percent per quarter. We then extract a trend from this padded series via the Hodrick-Prescott filter with a smoothing parameter of 6400; our model is not designed to capture low frequency trends in population growth or labor force participation. 12 Page 13 of 68 Authorized for public release by the FOMC Secretariat on 1/10/2020 specific risk-premium shocks. At farther horizons, their volatilities are accounted for by technology shocks. Figure 4: Impulse Response to a One Standard Deviation Shock to the Aggregate Risk Premium. −0.2 −0.2 −0.4 −0.6 −0.8 −0.4 Real Durables Real Consumption Real GDP −0.2 −0.3 −0.4 −0.5 −0.6 −0.8 −1 −1.2 −1.4 −1 −0.6 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 −0.5 −1.5 −2 0 −0.2 −1 −0.4 Hours Real Investment Real Housing −1 −2 −0.6 −0.8 −2.5 −3 −3 −4 −1 5 10 15 20 5 10 15 20 0.005 −0.02 0.4 Core PCE inflation Fed Funds −0.06 −0.08 −0.1 Unemployment 0 −0.04 −0.005 −0.01 −0.015 −0.02 0.3 0.2 0.1 −0.025 −0.12 5 10 15 20 5 10 15 20 With regard to impulse responses, we highlight the responses to the most important shock, the aggregate risk premium, in figure 4. As we noted, this shock looks like a traditional demand shock, with an increase in the risk premium lowering real GDP, hours worked, and inflation; monetary policy offsets these negative effects somewhat by becoming more accommodative. As for responses to other disturbances, the impulse responses to a monetary policy innovation captures the conventional wisdom regarding the effects of such shocks. In particular, both household and business expenditures on durables (consumer durables, residential investment, and nonresidential investment) respond strongly (and with a hump-shape) to a contractionary policy shock, with more muted responses by nondurables and services consumption; each measure of inflation responds gradually, albeit more 13 Page 14 of 68 Authorized for public release by the FOMC Secretariat on 1/10/2020 quickly than in some analyses based on vector autoregressions (VARs).6 Shocks to sectoral risk premia principally depress spending in the associated category of expenditure (e.g., an increase in the residential risk premium lowers residential investment), with offsetting positive effects on other spending (which is “crowded in”). Following an economy-wide technology shock, output rises gradually to its long-run level; hours respond relatively little to the shock (in comparison to, for example, output), reflecting both the influence of stick prices and wages and the offsetting income and substitution effects of such a shock on households willingness to supply labor. Figure 5: Innovations to Exogenous Processes 0 −1 0.2 Funds Rate Shock 1 20 Labor Supply Wage Markup Exog. Demand 10 5 0 10 0 −10 −5 −20 2 0 −1 −2 2000 1 0 −1 2010 1990 2 1 0 −1 −2 1990 2000 2010 1990 2000 2010 2000 50 0 −50 1990 2000 2000 −0.4 2010 1 0 −1 2010 1990 Capital Risk−Premium 1 1990 −0.2 Invest. Price Markup 2010 2000 1990 2000 2010 1990 2000 2010 1990 2000 2010 2 1 0 −1 −2 2010 1 1 Risk−premium 2000 Non−Invest. Price Markup 1990 Durables Risk−Premium Housing Risk−Premium 2010 2 1990 Term Premium 2000 Overall TFP Capital Goods Technology 1990 0 0 −1 2010 0.5 0 −0.5 1990 2000 2010 0.2 0 −0.2 6 This difference between VAR-based and DSGE-model based impulse responses has been highlighted elsewhere – for example, in the survey of Boivin, Kiley, and Mishkin (2010). 14 Page 15 of 68 Authorized for public release by the FOMC Secretariat on 1/10/2020 Figure 6: Exogenous Drivers 2 1 0 −1 2 TFP Tech. Exog. Demand Risk−premium 2 1 0 −1 1 0 −1 −2 1990 1 0 −1 −2 0 −1 −2 −3 0 −2 −4 1990 2000 1990 2000 2010 1990 2000 2010 1990 2000 2010 50 0 −50 2010 100 0.5 0 50 0 −50 −100 −0.5 1990 3.3 2 Labor Supply 1 2010 4 2010 2−y Term premium 2000 2000 Durables Risk−Premium 2010 2 1990 Capital Risk−Premium 2000 Housing Risk−Premium Capital−specific Tech. 1990 2000 2010 1990 2000 2010 Estimates of Latent Variable Paths Figures 5 and 6 report modal estimates of the model’s structural shocks and the persistent exogenous fundamentals (i.e., risk premia and autonomous demand). These series have recognizable patterns for those familiar with U.S. economic fluctuations. For example, the risk premia jump at the end of the sample, reflecting the financial crisis and the model’s identification of risk premia, both economy-wide and for housing, as key drivers. Of course, these stories from a glance at the exogenous drivers yield applications for alternative versions of the EDO model and future model enhancements. For example, the exogenous risk premia can easily be made to have an endogenous component following the approach of Bernanke, Gertler, and Gilchrist (1999) (and indeed we have considered models of that type). At this point we view incorporation of such mechanisms in our baseline approach as premature, pending ongoing research on financial frictions, banking, and intermediation in dynamic general equilibrium models. Nonetheless, the EDO model captured the key financial disturbances during the last several years in its current specification, and examining the endogenous factors that explain these developments will be a topic of further study. 15 Page 16 of 68 Authorized for public release by the FOMC Secretariat on 1/10/2020 References [Bernanke, Gertler, and Gilchrist (1999)] Bernanke, B., M. Gertler, and S. Gilchrist. 1999. The financial accelerator in a quantitative business cycle framework, In: John B. Taylor and Michael Woodford, Editor(s), Handbook of Macroeconomics, Elsevier, 1999, Volume 1, Part 3, Pages 1341-1393. [Beveridge and Nelson (1981)] Beveridge, S. and C.R. Nelson. 1981. A new approach to the decomposition of economic time series into permanent and transitory components with particular attention to measurement of the business cycle, Journal of Monetary Economics vol. 7, Pages 151-174. [Boivin et al. (2010)] Boivin, J., M. Kiley, and F.S. Mishkin. 2010. How Has the Monetary Transmission Mechanism Evolved Over Time? In B. Friedman and M. Woodford, eds., The Handbook of Monetary Economics, Elsevier. [Carlstom et al (2012)] Carlstrom, Charles T., Timothy S. Fuerst and Matthias Paustian. 2012. How inflationary is an extended period of low interest rates?, Federal Reserve Bank of Cleveland Working Paper 1202. [Chung et al. (2011)] Chung, Hess, J.P. Laforte, David L. Reifschneider, and John C. Williams. 2010. Have We Underestimated the Likelihood and Severity of Zero Lower Bound Events. Federal Reserve Bank of San Francisco Working Paper 2011-01 http://www.frbsf.org/publications/economics/papers/2011/wp11-01bk.pdf [Edge, Kiley, and Laforte (2008)] Edge, R., Kiley, M., Laforte, J.P., 2008. Natural rate measures in an estimated DSGE model of the U.S. economy. Journal of Economic Dynamics and Control vol. 32(8), Pages 2512-2535. [Edge, Kiley, and Laforte (2010)] Edge, R., Kiley, M., Laforte, J.P., 2010. A comparison of forecast performance between Federal Reserve staff forecasts, simple reduced-form models, and a DSGE model. Journal of Applied Econometrics vol. 25(4), Pages 720-754. [Fisher (2006)] Fisher, Jonas D. M., 2006. The Dynamic Effects of Neutral and Investment-Specific Technology Shocks. Journal of Political Economy, University of Chicago Press, vol. 114(3), Pages 413-451. [Gali (2011)] Gali, Jordi, 2011. The Return Of The Wage Phillips Curve. Journal of the European Economic Association vol. 9(3), pages 436-461. [Hall (2010)] Hall, Robert E., 2010. Why Does the Economy Fall to Pieces after a Financial Crisis? Journal of Economic Perspectives vol. 24(4), Pages 3-20. http://www.aeaweb.org/articles.php?doi=10.1257/jep.24.4.3 [Kiley (2007)] Kiley, M., 2007. A Quantitative Comparison of Sticky-Price and Sticky-Information Models of Price Setting. Journal of Money, Credit, and Banking 39, Pages 101-125. 16 Page 17 of 68 Authorized for public release by the FOMC Secretariat on 1/10/2020 [Kiley (2010a)] Kiley, M., 2010a. Habit Persistence, Non-separability between Consumption and Leisure, or Rule-of-Thumb Consumers: Which Accounts for the Predictability of Consumption Growth? The Review of Economics and Statistics vol. 92(3), Pages 679-683. [Kiley (2010b)] Kiley, M., 2010b. Output Gaps. Federal Reserve Board Finance and Economics Discussion Series (FEDS), 2010-27. [Kydland and Prescott (1982)] Kydland, Finn and Prescott, Edward. 1982. Time-to-build and Aggregate Fluctuations. Econometrica vol. 50(6), Pages 1345 - 1370. [Laforte (2007)] Laforte, J., 2007. Pricing Models: A Bayesian DSGE Approach to the U.S. Economy. Journal of Money, Credit, and Banking vol. 39, Pages 127-54. [Smets and Wouters (2007)] Smets, F., Wouters, R., 2007. Shocks and Frictions in the US Busines Cycles: A Bayesian DSGE Approach. American Economic Review, American Economic Association, vol. 97(3), Pages 586-606. [Wieland and Wouters (2010)] Wieland, Volker and Wolters, Maik H, 2010. The Diversity of Forecasts from Macroeconomic Models of the U.S. Economy. CEPR Discussion Papers 7870, C.E.P.R. Discussion Papers. 17 Page 18 of 68 Authorized for public release by the FOMC Secretariat on 1/10/2020 Detailed Philadelphia (PRISM) Forecast Overview March 2014 Keith Sill Forecast Summary The FRB Philadelphia DSGE model denoted PRISM, projects that real GDP growth will run at a fairly strong pace over the forecast horizon with real output growth peaking at about 4.2 percent in 2015. Core PCE inflation is projected to be contained at below 2 percent through 2016. For this forecast round, we have implemented the assumption that the forecasted federal funds rate is pinned down by current futures market projections through mid-2015. The funds rate is unconstrained beginning in 2015Q3, and rises to about 1.5 percent in 2015Q4. Many of the model’s variables continue to be well below their steady-state values. In particular, consumption, investment, and the capital stock are low relative to steady state, and absent any shocks, the model would predict a rapid recovery. These state variables have been below steady state since the end of the recession. The relatively slow recovery to date and the low inflation that has recently characterized U.S. economic activity require the presence of shocks to offset the strength of the model’s internal propagation channels. The Current Forecast and Shock Identification The PRISM model is an estimated New Keynesian DSGE model with sticky wages, sticky prices, investment adjustment costs, and habit persistence. The model is similar to the Smets & Wouters 2007 model and is described more fully in Schorfheide, Sill, and Kryshko 2010. Unlike in that paper though, we estimate PRISM directly on core PCE inflation rather than projecting core inflation as a non-modeled variable. Details on the model and its estimation are available in a Technical Appendix that was distributed for the June 2011 FOMC meeting or is available on request. The current forecasts for real GDP growth, core PCE inflation, and the federal funds rate are shown in Figures 1a-1c along with the 68 percent probability coverage intervals. The forecast uses data through 2013Q4 supplemented by a 2014Q1 nowcast based on the latest Macroeconomic Advisers forecast. For example, the model takes 2014Q1 output growth of 2 percent as given and the projection begins with 2014Q2. PRISM continues to anticipate a fairly strong rebound in real GDP growth, which rises to 4.2 percent by early-2015. Output growth tapers off only modestly in 2016 with Q4/Q4 growth at 4.1 percent. Thus, the output growth forecast for this round is a bit stronger than the December projection. While output growth is fairly robust, core PCE inflation stays contained at below 2 percent through the forecast horizon. Based on the 68 percent coverage interval, the model sees a minimal chance of deflation or recession (measured as negative quarters of real GDP growth) over the next 3 years. The federal Page 1 of 24 Page 19 of 68 Authorized for public release by the FOMC Secretariat on 1/10/2020 funds rate is constrained near the zero bound through mid-2015. Thereafter, the model dynamics take over and the funds rate rises gradually to 2.7 percent in 2016Q4, which is a slightly weaker projection for the funds rate than in December. . The key factors driving the projection are shown in the forecast shock decompositions (shown in Figures 2a-2e) and the smoothed estimates of the model’s primary shocks (shown in Figure 3, where they are normalized by standard deviation). The primary shocks driving abovetrend real output growth over the next 3 years are labor supply shocks (labeled Labor), marginal efficiency of investment shocks (labeled MEI), and financial shocks in the form of discount factor shocks (labeled Fin). Over the course of the recession and recovery PRISM estimated a sequence of large positive shocks to leisure (negative shocks to labor supply) that have a persistent effect on hours worked and so pushed hours well below steady state. As these shocks unwind hours worked rebounds strongly over the forecast horizon and so leads to higher output growth. As seen in Figure 3, the model estimates a sequence of largely negative discount factor shocks since 2008. All else equal, these shocks push down current consumption and push up investment, with the effect being very persistent. Consequently, the de-trended level of consumption (nondurables + services) remains below the model’s estimated steady state at this point. As these shocks wane over the projection period, consumption growth runs at an average pace of about 2.6 percent over the next three years. The negative discount factor shocks worked to strengthen investment in 2010 and 2011, but investment was pushed well below steady state by adverse MEI shocks over 2007 to 2009. Indeed, recent weakness in investment growth is accounted for in the model, in part, by negative MEI shocks over the last 7 quarters (see Figure 3). Looking ahead though the model projects a rebound in investment growth as these shocks unwind: the principal shocks driving strong investment growth over the forecast horizon are efficiency of investment shocks and labor shocks. There is a net strong positive contribution to investment growth over the next 3 years as historical shocks work their way through the system (and MEI shocks are a negative contributor to consumption growth over the forecast horizon). Note though that the unwinding of the discount factor shocks that contributed positively to investment growth over 2009-2011 leads to a downward pull on investment growth over the next three years. Investment growth runs at about an 8 percent pace in 2015 easing back to about a 5 percent pace by the end of 2016. The forecast for core PCE inflation is largely a story of upward pressure from the unwinding of negative labor supply shocks and MEI shocks being offset by downward pressure from the waning of discount factor shocks. Negative discount factor shocks have a strong and persistent negative effect on marginal cost and inflation in the estimated model. Compared, for example, to a negative MEI shock that lowers real output growth by 1 percent, a negative discount factor shock that lowers real output growth by 1 percent leads to a 3 times larger drop in inflation that is more persistent. The negative discount factor shock leads to capital deepening and higher labor productivity. Consequently, marginal cost and inflation fall. The negative effect of discount factor shocks on inflation is estimated to have been quite significant since the end of Page 2 of 24 Page 20 of 68 Authorized for public release by the FOMC Secretariat on 1/10/2020 2008. As these shocks unwind over the projection period there is a decreasing, but still substantial, downward effect on inflation over the next three years (these shocks have a very persistent effect on inflation). Partly offsetting the downward pressure on inflation from discount factor shocks is the upward pressure coming from the unwinding of negative labor supply shocks. Labor supply shocks that push down aggregate hours also serve to put upward pressure on the real wage and hence marginal cost. The effect is persistent -- as the labor supply shocks unwind over the forecast horizon they exert a waning upward push to inflation. On balance the effect of these opposing forces is to keep inflation below 2 percent through the forecast horizon. The Unconditional Forecast Pinning down the federal funds rate at current market expectations through mid-2015 (using fully anticipated monetary policy shocks) has a modest impact on the PRISM forecast for output growth and inflation. Figures 4a-c show the forecast and shock decompositions for the unconditional forecast (ie, a forecast that does not constrain the funds rate path). The forecasted path for real GDP growth is marginally weaker compared the conditional forecast for the next 3 years under a less-accommodative monetary policy. The projection for core PCE inflation is a bit stronger than in the conditional forecast, even though the federal funds rate begins to rise immediately, reaching about 2.7 percent by the end of 2015 and 3.4 percent by the end of 2016. Thus, the inflation forecast is somewhat stronger if the funds rate is not constrained at the ZLB through mid-2014. The fact that the forecast with a substantially more accommodative policy has a weaker inflation path and only slightly stronger output growth is counter intuitive. It is the case in the PRISM model that an anticipated easing of monetary policy in the future does lead to an immediate jump in current period output and inflation – the economy strengthens with the easier policy. Compared to the unconditional forecast, an anticipated easing of monetary policy leads to a stronger economy and higher inflation today. Why then the weaker inflation projection in PRISM under the funds-rate-constrained policy? The reason is that history is locked down in the model. For example, output growth in 2014Q1 is given at 2 percent and inflation is 1.3 percent in both the unconditional and conditional forecasts since it is treated as historical data (recall that we use a nowcast for 2014Q1 as data to update the March projection). An easing of future monetary policy, by construction, cannot change 2014Q1 output growth or inflation – or indeed their history. Consequently, the model re-weights shocks so that negative TFP, discount factor, and MEI shocks offset the stimulus from anticipated easier monetary policy in order to keep the history of output growth and inflation unchanged. The persistence of the re-weighted TFP, discount factor, and MEI shocks then shows through as the model projection unfolds. If we were to instead allow the PRISM model variables that map into data observations to immediately adjust in response to an anticipated easing of policy, the economic forecast would look significantly stronger. Page 3 of 24 Page 21 of 68 Authorized for public release by the FOMC Secretariat on 1/10/2020 As implemented though, leaving the funds rate unconstrained in the forecast shifts the historical shock decomposition to give an expected path for output growth that is broadly similar and inflation that is somewhat higher compared to the conditional forecast. With inflation running at about target and strong output growth, PRISM forecasts that the funds rate should begin rising immediately, reaching 3.4 percent by the end of 2016 -- roughly 70 basis points above the constrained path federal funds rate at that point. References Schorfheide, Frank, Keith Sill, and Maxym Kryshko. 2010. “DSGE model-based forecasting of non-modelled variables.” International Journal of Forecasting, 26(2): 348-373. Smets, Frank, and Rafael Wouters. 2007. “Shocks and Frictions in U.S. Business Cycles: A Bayesian DSGE Approach.” American Economic Review, 97(3): 586-606. Page 4 of 24 Page 22 of 68 Authorized for public release by the FOMC Secretariat on 1/10/2020 Figure 1a Real GDP Growth 10 8 6 4 2 0 -2 -4 -6 -8 -10 2008 2009 2010 2011 2012 2013 2014 Page 5 of 24 Page 23 of 68 2015 2016 2017 2018 Authorized for public release by the FOMC Secretariat on 1/10/2020 Figure 1b Core PCE Inflation 6 5 4 3 2 1 0 -1 2008 2009 2010 2011 2012 2013 2014 Page 6 of 24 Page 24 of 68 2015 2016 2017 2018 Authorized for public release by the FOMC Secretariat on 1/10/2020 Figure 1c Fed Funds Rate 8 6 4 2 0 -2 -4 2008 2009 2010 2011 2012 2013 2014 Page 7 of 24 Page 25 of 68 2015 2016 2017 2018 Authorized for public release by the FOMC Secretariat on 1/10/2020 Figure 2a Conditional Forecast Conditional Forecast: Real GDP Growth 10 5 0 ‐5 ‐10 ‐15 ‐20 2008 2009 TFP 2010 Gov 2011 MEI 2012 2013 MrkUp shocks: TFP: Gov: MEI: MrkUp: Labor: Fin: Mpol: Total factor productivity growth shock Government spending shock Marginal efficiency of investment shock Price markup shock Labor supply shock Discount factor shock Monetary policy shock Page 8 of 24 Page 26 of 68 2014 Labor 2015 Fin 2016 Mpol Authorized for public release by the FOMC Secretariat on 1/10/2020 Figure 2b Conditional Forecast Core PCE Inflation 3 3 2 2 1 1 0 0 ‐1 ‐1 ‐2 ‐2 ‐3 ‐3 ‐4 ‐4 ‐5 ‐5 2008 2009 TFP 2010 Gov 2011 MEI 2012 2013 MrkUp shocks: TFP: Gov: MEI: MrkUp: Labor: Fin: Mpol: Total factor productivity growth shock Government spending shock Marginal efficiency of investment shock Price markup shock Labor supply shock Discount factor shock Monetary policy shock Page 9 of 24 Page 27 of 68 2014 Labor 2015 Fin 2016 Mpol Authorized for public release by the FOMC Secretariat on 1/10/2020 Figure 2c Conditional Forecast Conditional Forecast: Fed Funds Rate 4 4 2 2 0 0 ‐2 ‐2 ‐4 ‐4 ‐6 ‐6 ‐8 ‐8 2008 2009 TFP 2010 Gov 2011 MEI 2012 2013 MrkUp shocks: TFP: Gov: MEI: MrkUp: Labor: Fin: Mpol: Total factor productivity growth shock Government spending shock Marginal efficiency of investment shock Price markup shock Labor supply shock Discount factor shock Monetary policy shock Page 10 of 24 Page 28 of 68 2014 Labor 2015 Fin 2016 Mpol Authorized for public release by the FOMC Secretariat on 1/10/2020 Figure 2d Conditional Forecast Conditional Forecast: Real Consumption Growth 10 5 0 ‐5 ‐10 ‐15 2008 2009 TFP 2010 Gov 2011 MEI 2012 2013 MrkUp shocks: TFP: Gov: MEI: MrkUp: Labor: Fin: Mpol: Total factor productivity growth shock Government spending shock Marginal efficiency of investment shock Price markup shock Labor supply shock Discount factor shock Monetary policy shock Page 11 of 24 Page 29 of 68 2014 Labor 2015 Fin 2016 Mpol Authorized for public release by the FOMC Secretariat on 1/10/2020 Figure 2e Conditional Forecast Conditional Forecast: Real Investment Growth 30 20 10 0 ‐10 ‐20 ‐30 ‐40 ‐50 2008 2009 TFP 2010 Gov 2011 MEI 2012 2013 MrkUp shocks: TFP: Gov: MEI: MrkUp: Labor: Fin: Mpol: Total factor productivity growth shock Government spending shock Marginal efficiency of investment shock Price markup shock Labor supply shock Discount factor shock Monetary policy shock Page 12 of 24 Page 30 of 68 2014 Labor 2015 Fin 2016 Mpol Authorized for public release by the FOMC Secretariat on 1/10/2020 Figure 3 Smoothed Shock Estimates for Conditional Forecast Model (normalized by standard deviation) labor shock discount factor shock 4 5 2 0 0 -2 2005 2010 2015 -5 2005 TFP shock 2010 2015 mei shock 4 2 2 0 0 -2 -2 2005 2010 2015 2005 Page 13 of 24 Page 31 of 68 2010 2015 Authorized for public release by the FOMC Secretariat on 1/10/2020 Figure 4a Unconditional Forecast Unconditional Forecast: Real GDP Growth 10 5 0 ‐5 ‐10 ‐15 ‐20 2008 2009 TFP 2010 Gov 2011 MEI 2012 2013 MrkUp shocks: TFP: Gov: MEI: MrkUp: Labor: Fin: Mpol: Total factor productivity growth shock Government spending shock Marginal efficiency of investment shock Price markup shock Labor supply shock Discount factor shock Monetary policy shock Page 14 of 24 Page 32 of 68 2014 Labor 2015 Fin 2016 Mpol Authorized for public release by the FOMC Secretariat on 1/10/2020 Figure 4b Unconditional Forecast Unconditional Forecast: Core PCE Inflation 3 3 2 2 1 1 0 0 ‐1 ‐1 ‐2 ‐2 ‐3 ‐3 ‐4 ‐4 ‐5 ‐5 2008 2009 TFP 2010 Gov 2011 MEI 2012 2013 MrkUp shocks: TFP: Gov: MEI: MrkUp: Labor: Fin: Mpol: Total factor productivity growth shock Government spending shock Marginal efficiency of investment shock Price markup shock Labor supply shock Discount factor shock Monetary policy shock Page 15 of 24 Page 33 of 68 2014 Labor 2015 Fin 2016 Mpol Authorized for public release by the FOMC Secretariat on 1/10/2020 Figure 4c Unconditional Forecast Unconditional Forecast: Federal Funds Rate 6 6 4 4 2 2 0 0 ‐2 ‐2 ‐4 ‐4 ‐6 ‐6 ‐8 ‐8 2008 2009 TFP 2010 Gov 2011 MEI 2012 2013 MrkUp shocks: TFP: Gov: MEI: MrkUp: Labor: Fin: Mpol: Total factor productivity growth shock Government spending shock Marginal efficiency of investment shock Price markup shock Labor supply shock Discount factor shock Monetary policy shock Page 16 of 24 Page 34 of 68 2014 Labor 2015 Fin 2016 Mpol Authorized for public release by the FOMC Secretariat on 1/10/2020 Figure 5 Smoothed Shock Estimates from Unconstrained Forecast Model (normalized by standard deviation) labor shock discount factor shock 4 5 2 0 0 -2 2005 2010 2015 -5 2005 TFP shock 2010 2015 mei shock 4 2 2 0 0 -2 -2 2005 2010 2015 2005 Page 17 of 24 Page 35 of 68 2010 2015 Authorized for public release by the FOMC Secretariat on 1/10/2020 Impulse Responses to TFP shock output growth consumption growth 1 1 0.5 0.5 0 0 5 10 15 0 0 investment growth 0.5 0 0 0 5 10 15 -0.5 0 inflation 0.05 0 0 0 5 15 5 10 15 nominal rate 0.05 -0.05 10 aggregate hours 2 -2 5 10 15 -0.05 0 Page 18 of 24 Page 36 of 68 5 10 15 Authorized for public release by the FOMC Secretariat on 1/10/2020 Impulse Response to Leisure Shock output growth consumption growth 2 2 0 0 -2 0 5 10 15 -2 0 investment growth 0 0 -1 0 5 10 15 -2 0 inflation 0.4 0.2 0.2 0 5 15 5 10 15 nominal rate 0.4 0 10 aggregate hours 5 -5 5 10 15 0 0 Page 19 of 24 Page 37 of 68 5 10 15 Authorized for public release by the FOMC Secretariat on 1/10/2020 Impulse Responses to MEI Shock output growth consumption growth 2 0.2 0 0 -2 0 5 10 15 -0.2 0 investment growth 10 1 0 0.5 -10 0 5 10 15 0 0 inflation 0.4 0 0.2 0 5 10 15 5 10 15 nominal rate 0.1 -0.1 5 aggregate hours 10 15 0 0 Page 20 of 24 Page 38 of 68 5 10 15 Authorized for public release by the FOMC Secretariat on 1/10/2020 Impulse Responses to Financial Shock output growth consumption growth 1 2 0 0 -1 0 5 10 15 -2 0 investment growth 0.5 0 0 0 5 10 15 -0.5 0 inflation 1 0.2 0.5 0 5 15 5 10 15 nominal rate 0.4 0 10 aggregate hours 5 -5 5 10 15 0 0 Page 21 of 24 Page 39 of 68 5 10 15 Authorized for public release by the FOMC Secretariat on 1/10/2020 Impulse Responses to Price Markup Shock output growth consumption growth 0.5 0.5 0 0 -0.5 0 5 10 15 -0.5 0 investment growth 0 0 -0.1 0 5 10 15 -0.2 0 inflation 0.5 0 0 0 5 15 5 10 15 nominal rate 1 -1 10 aggregate hours 1 -1 5 10 15 -0.5 0 Page 22 of 24 Page 40 of 68 5 10 15 Authorized for public release by the FOMC Secretariat on 1/10/2020 Impulse Responses to Unanticipated Monetary Policy Shock output growth consumption growth 0.5 0.5 0 0 -0.5 0 5 10 15 -0.5 0 investment growth 0.2 0 0 0 5 10 15 -0.2 0 inflation 1 0 0 0 5 15 5 10 15 nominal rate 0.1 -0.1 10 aggregate hours 1 -1 5 10 15 -1 0 Page 23 of 24 Page 41 of 68 5 10 15 Authorized for public release by the FOMC Secretariat on 1/10/2020 Impulse Responses to Govt Spending Shock output growth consumption growth 2 0.5 0 0 -2 0 5 10 15 -0.5 0 investment growth 0.4 0 0.2 0 5 10 15 0 0 inflation 0.04 0.01 0.02 0 5 15 5 10 15 nominal rate 0.02 0 10 aggregate hours 0.2 -0.2 5 10 15 0 0 Page 24 of 24 Page 42 of 68 5 10 15 Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 Overview The FRBNY DSGE model forecast is obtained using data released through 2013Q4 augmented with the FRBNY 2014Q1 forecast for real GDP growth, core PCE inflation and growth in total hours, and with values of the federal funds rate and the spread between Baa corporate bonds and the 10-year Treasury yields based on 2014Q1 observations. The expected future federal funds rates are constrained to equal market expectations, as measured by OIS rates, through 2015Q2. The FRBNY DSGE projections for real activity and inflation are little changed relative to the December ones. Overall, the model continues to project moderate growth in economic activity and inflation below 2 percent throughout the forecast horizon. The subdued real GDP and inflation outlook is driven by continued headwinds from the financial crisis, as captured by persistent shocks to the marginal efficiency of investment (MEI), and by the fading effects of past accommodative monetary policy. In addition, reductions in labor supply are also projected to contribute to lower GDP growth. General Features of the Model The FRBNY DSGE model is a medium-scale, one-sector, dynamic stochastic general equilibrium model. It builds on the neoclassical growth model by adding nominal wage and price rigidities, variable capital utilization, costs of adjusting investment, and habit formation in consumption. The model follows the work of Christiano, Eichenbaum, and Evans (2005) and Smets and Wouters (2007), but also includes credit frictions, as in the financial accelerator model developed by Bernanke, Gertler, and Gilchrist (1999). The actual implementation of the credit frictions closely follows Christiano, Motto, and Rostagno (2009). In this section, we briefly describe the microfoundations of the model, including the optimization problem of the economic agents and the nature of the exogenous processes. The innovations to these processes, which we refer to as “shocks,” are the drivers of macroeconomic fluctuations. The model identifies these shocks by matching the model dynamics with six quarterly data series: real GDP growth, core PCE inflation, the labor share, aggregate FRBNY DSGE Group, Research and Statistics Page 43 of 68 1 Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 hours worked, the effective federal funds rate (FFR), and the spread between Baa corporate bonds and 10-year Treasury yields. Model parameters are estimated from 1984Q1 to the present using Bayesian methods. Details on the structure of the model, data sources, and results of the estimation procedure can be found in Del Negro et al. (2013). The economic units in the model are households, firms, banks, entrepreneurs, and the government. (Figure 1 describes the interactions among the various agents, the frictions and the shocks that affect the dynamics of this economy.) Households supply labor services to firms. The utility they derive from leisure is subject to a random disturbance, which we call “labor supply” shocks (this shock is sometimes also referred to as a “leisure” shock). Labor supply shocks capture exogenous movements in labor supply due to such factors as demographics and labor market imperfections. The labor market is also subject to frictions because of nominal wage rigidities. These frictions play an important role in the extent to which various shocks affect hours worked. Households also have to choose the amount to consume and save. Their savings take the form of deposits to banks and purchases of government bills. Household preferences take into account habit persistence, a characteristic that affects their consumption smoothing decisions. Monopolistically competitive firms produce intermediate goods, which a competitive firm aggregates into the single final good that is used for both consumption and investment. The production function of intermediate producers is subject to “total factor productivity” (TFP) shocks. Intermediate goods markets are subject to price rigidities. Together with wage rigidities, this friction is quite important in allowing demand shocks to be a source of business cycle fluctuations, as countercyclical mark-ups induce firms to produce less when demand is low. Inflation evolves in the model according to a standard, forward-looking New Keynesian Phillips curve, which determines inflation as a function of marginal costs, expected future inflation, and “mark-up” shocks. Mark-up shocks capture exogenous changes in the degree of competitiveness in the intermediate goods market. In practice, these shocks capture unmodeled inflation pressures, such as those arising from fluctuations in commodity prices. Financial intermediation involves two actors, banks and entrepreneurs, whose interaction captures imperfections in financial markets. These actors should not be interpreted in a literal sense, but rather as a device for modeling credit frictions. Banks take deposits from households and lend them to entrepreneurs. Entrepreneurs use their own wealth and the loans from banks to acquire capital. They then choose the utilization level of capital and FRBNY DSGE Group, Research and Statistics Page 44 of 68 2 Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 rent the capital to intermediate good producers. Entrepreneurs are subject to idiosyncratic disturbances in their ability to manage the capital. Consequently, entrepreneurs’ revenue may not be enough to repay their loans, in which case they default. Banks protect against default risk by pooling loans to all entrepreneurs and charging a spread over the deposit rate. Such spreads vary endogenously as a function of the entrepreneurs’ leverage, but also exogenously depending on the entrepreneurs’ riskiness. Specifically, mean-preserving changes in the volatility of entrepreneurs’ idiosyncratic shocks lead to variations in the spread (to compensate banks for changes in expected losses from individual defaults). We refer to these exogenous movements as “spread” shocks. Spread shocks capture financial intermediation disturbances that affect entrepreneurs’ borrowing costs. Faced with higher borrowing costs, entrepreneurs reduce their demand for capital, and investment drops. With lower aggregate demand, there is a contraction in hours worked and real wages. Wage rigidities imply that hours worked fall even more (because nominal wages do not fall enough). Price rigidities mitigate price contraction, further depressing aggregate demand. Capital producers transform general output into capital goods, which they sell to the entrepreneurs. Their production function is subject to investment adjustment costs: producing capital goods is more costly in periods of rapid investment growth. It is also subject to exogenous changes in the “marginal efficiency of investment” (MEI). These MEI shocks capture exogenous movements in the productivity of new investments in generating new capital. A positive MEI shock implies that fewer resources are needed to build new capital, leading to higher real activity and inflation, with an effect that persists over time. Such MEI shocks reflect both changes in the relative price of investment versus that of consumption goods (although the literature has shown the effect of these relative price changes to be small), and most importantly financial market imperfections that are not reflected in movements of the spread. Finally, the government sector comprises a monetary authority that sets short-term interest rates according to a Taylor-type rule and a fiscal authority that sets public spending and collects lump-sum taxes to balance the budget. Exogenous changes in government spending are called “government” shocks (more generally, these shocks capture exogenous movements in aggregate demand). All exogenous processes are assumed to follow independent AR(1) processes with different degrees of persistence, except for i.i.d. “policy” shocks, which are exogenous disturbances to the monetary policy rule. FRBNY DSGE Group, Research and Statistics Page 45 of 68 3 Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 Figure 1: Model Structure productivity shocks Firms wage rigidities utilization capital labor supply shocks intermediate goods price rigidities mark-up shocks labor Final Goods Producers Capital Producers MEI shocks investment adjustment costs investment Entrepreneurs consumption Banks Households deposits loans credit frictions spread shocks bills habit persistence Government interest rate policy policy shocks FRBNY DSGE Group, Research and Statistics Page 46 of 68 gov’t spending shocks 4 Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 The Model’s Transmission Mechanism In this section, we illustrate some of the key economic mechanisms at work in the model’s equilibrium. We do so with the aid of the impulse response functions to the main shocks hitting the economy, which we report in figures 8 to 14. We start with the shock most closely associated with the Great Recession and the severe financial crisis that characterized it: the spread shock. As discussed above, this shock stems from an increase in the perceived riskiness of borrowers, which induces banks to charge higher interest rates for loans, thereby widening credit spreads. As a result of this increase in the expected cost of capital, entrepreneurs’ borrowing falls, hindering their ability to channel resources to the productive sector via capital accumulation. The model identifies this shock by matching the behavior of the ratio of the Baa corporate bond rate to the 10-year Treasury rate, and the spread’s comovement with output growth, inflation, and the other observables. Figure 8 shows the impulse responses of the variables used in the estimation to a onestandard-deviation innovation in the spread shock. An innovation of this size increases the observed spread by roughly 35 basis points (bottom right panel). This leads to a reduction in investment and consequently to a reduction in output growth (top left panel) and hours worked (top right panel). The fall in the level of hours is fairly sharp in the first year and persists for many quarters afterwards, leaving the labor input not much higher than at the trough five years after the impulse. Of course, the effects of this same shock on GDP growth, which roughly mirrors the change in the level of hours, are much more short-lived. Output growth returns to its steady state level about two years after the shock hits, but it barely moves above it after that, implying no catch up of the level of GDP towards its previous trend (bottom left panel). The persistent drop in the level of economic activity due to the spread shock also leads to a prolonged decline in real marginal costs - which in this model map one-to-one into the labor share (middle left panel)- and, via the New Keynesian Phillips curve, in inflation (middle right panel). Finally, policymakers endogenously respond to the change in the inflation and real activity outlook by cutting the federal funds rate (left panel on the third row). Very similar considerations hold for the MEI shock, which represents a direct hit to the ‘technological’ ability of entrepreneurs to transform investment goods into productive capital, rather than an increase in their funding cost. Although the origins of these two shocks are different, the fact that they both affect the creation of new capital implies very similar effects on the observable variables, as shown by the impulse responses in figure 9. In particular, a FRBNY DSGE Group, Research and Statistics Page 47 of 68 5 Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 positive MEI shock also implies a very persistent increase in investment, output and hours worked, as well as in the labor share and hence inflation. The key difference between the two impulses, which is also what allows us to tell them apart empirically, is that the MEI shock leaves spreads virtually unchanged (bottom right panel). Another shock that plays an important role in the model, and whose estimated contribution to the Great Recession and its aftermath increased in light of the latest data revisions, is the TFP shock. As shown in figure 10, a positive TFP shock has a large and persistent effect on output growth, even if the response of hours is muted in the first few quarters (and slightly negative on impact). This muted response of hours is due to the presence of nominal rigidities, which prevent an expansion of aggregate demand sufficient to absorb the increased ability of the economy to supply output. With higher productivity, marginal costs and thus the labor share fall, leading to lower inflation. The policy rule specification implies that this negative correlation between inflation and real activity, which is typical of supply shocks, produces offsetting forces on the interest rate, which as a result moves little. These dynamics make the TFP shock particularly suitable to account for the first phase of the recovery, in which GDP growth was above trend, but hours and inflation remained weak. With the recent softening of the expansion, though, the role of TFP shocks is fading. The last shock that plays a relevant role in the current economic environment is the mark-up shock, whose impulse response is depicted in figure 11. This shock is an exogenous source of inflationary pressures, stemming from changes in the market power of intermediate goods producers. As such, it leads to higher inflation and lower real activity, as producers reduce supply to increase their desired markup. Compared to those of the other prominent supply shock in the model, the TFP shock, the effects of markup-shocks feature significantly less persistence. GDP growth falls on impact after mark-ups increase, but returns above average after about one year, and the effect on the level of output is absorbed in a little over four years. Inflation is sharply higher, but only for a couple of quarters, leading to a temporary spike in the nominal interest rate, as monetary policy tries to limit the passthrough of the shock to inflation. Unlike in the case of TFP shocks, however, hours fall immediately, mirroring the behavior of output. FRBNY DSGE Group, Research and Statistics Page 48 of 68 6 Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 Forecasts Core PCE Inflation Real GDP Growth 2014 (Q4/Q4) March Dec 0.9 0.9 (0.4,1.4) (0.3,1.5) 2.7 2.5 (0.6,4.1) (-0.5,4.3) Unconditional 2015 (Q4/Q4) March Dec 1.3 1.4 (0.5,2.0) (0.5,2.1) 1.9 1.6 (-1.3,4.5) (-1.8,4.4) Forecast 2016 (Q4/Q4) March Dec 1.7 1.7 (0.8,2.5) (0.8,2.5) 1.7 1.5 (-1.3,4.8) (-1.6,4.8) 2017 (Q4/Q4) March 1.9 (1.1,2.7) 1.9 (-1.1,5.2) Core PCE Inflation Real GDP Growth 2014 (Q4/Q4) March Dec 1.0 0.9 (0.5,1.4) (0.3,1.5) 2.0 2.0 (-0.1,3.4) (-0.9,3.9) Conditional Forecast* 2015 (Q4/Q4) 2016 (Q4/Q4) March Dec March Dec 1.2 1.3 1.6 1.7 (0.4,1.9) (0.4,2.0) (0.8,2.4) (0.8,2.4) 1.9 1.7 1.9 1.7 (-1.3,4.6) (-1.8,4.5) (-1.2,5.0) (-1.5,5.0) 2017 (Q4/Q4) March 1.9 (1.0,2.7) 2.1 (-1.0,5.3) *The unconditional forecasts use data up to 2013Q4, the quarter for which we have the most recent GDP release, as well as the federal funds rate and spreads data for 2014Q1. In the conditional forecasts, we further include the 2014Q1 FRBNY projections for GDP growth, core PCE inflation, and growth in total hours worked as additional data points. Numbers in parentheses indicate 68 percent probability intervals. We detail the forecast of three main variables over the horizon 2014-2017: real GDP growth, core PCE inflation and the federal funds rate. To obtain the forecast we set federal funds rate expectations equal to market expectations for the federal funds rate (as measured by OIS rates) through 2015Q2. We capture policy anticipation by adding anticipated monetary policy shocks to the central bank’s reaction function starting in 2008Q4, the beginning of the zero bound period, following the methodology of Laseen and Svensson (2009). We estimate the standard deviation of the anticipated shocks as in Campbell et al. (2012), but use only post-2008Q4 data. The table above presents Q4/Q4 forecasts for real GDP growth and inflation for 20142017, with 68 percent probability intervals. We include two sets of forecasts. The unconditional forecasts use data up to 2013Q4, the quarter for which we have the most recent GDP release, as well as the federal funds rate and spreads data for 2014Q1 (we use the average realizations for the quarter up to the forecast date). In the conditional forecasts, we further include the 2014Q1 FRBNY staff projections for GDP growth, core PCE inflation, and hours worked as additional data points (as of March 4, projections for 2014Q1 are 1.6 percent for output growth, 1.2 percent for core PCE inflation, and 0.6 percent growth for hours worked). Treating the 2014Q1 staff forecasts as data allows us to incorporate information about the current quarter into the DSGE forecasts for the subsequent quarters. FRBNY DSGE Group, Research and Statistics Page 49 of 68 7 Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 In addition to providing the current forecasts, the table reports the forecasts included in the DSGE memo forwarded to the FOMC in advance of its December 2013 meeting. Figure 2 presents quarterly forecasts, both unconditional (left panels) and conditional (right panels). In the graphs, the black line represents data, the red line indicates the mean forecast, and the shaded areas mark the uncertainty associated with our forecast as 50, 60, 70, 80 and 90 percent probability intervals. Output growth and inflation are expressed in terms of percent annualized rates, quarter to quarter. The interest rate is the annualized quarterly average of the daily series. The bands reflect both parameter and shock uncertainty. Figure 3 compares the current forecasts with the September forecasts. Our discussion will mainly focus on the conditional forecasts, which are those reported in the memo to the FOMC. The model continues to project moderate growth in economic activity, with output growth in the neighborhood of 2 percent throughout the forecast horizon. Relative to December, the GDP growth forecast for 2014 (Q4/Q4) remains unchanged at 2.0 percent, while the forecasts for 2015 and 2016 (Q4/Q4) are higher by two tenth of a percent, at 1.9 percent, compared to last December’s forecast of 1.7 percent for each of these years. For 2017, the model forecasts 2.1 percent GDP growth. For inflation, the mean core PCE inflation for 2014 is projected to be 1.0 percent, slightly higher than the 0.9 percent projected last December. For 2015 and 2016, however, inflation forecasts are lowered to 1.2 and 1.6 percent, respectively, compared to the December forecasts of 1.3 and 1.7 percent, respectively. Inflation is projected to reach 1.9 percent in 2017. Despite being on an upward trajectory, inflation is projected to remain below the FOMC long-run goal of 2 percent throughout the whole forecast horizon. Uncertainty around real GDP growth and inflation forecasts has diminished slightly, due primarily to a reduction in downside risks. For GDP growth, the 68 percent bands cover the intervals -0.1 to 3.4 percent in 2014, -1.3 to 4.6 percent in 2015 and -1.2 to 5.0 in 2016. For inflation, the 68 percent probability bands range from 0.4 to 2.4 percent throughout 2016. Finally, as mentioned above, we constrain the federal funds rate expectations through 2015Q2 to be equal to the expected federal fund rate as measured by the OIS rates on March 4; after that the federal funds rate rises gradually and is forecasted to reach 1.8 percent at the end of 2016. FRBNY DSGE Group, Research and Statistics Page 50 of 68 8 Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 Figure 2: Forecasts 5 0 0 −5 −5 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Core PCE Inflation 3 3 2 2 1 1 0 0 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Output Growth 5 5 0 0 −5 −5 Percent Q−to−Q Annualized 5 Percent Q−to−Q Annualized Conditional Output Growth Percent Q−to−Q Annualized Percent Q−to−Q Annualized Unconditional 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Core PCE Inflation 3 3 2 2 1 1 0 0 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Interest Rate 4 4 2 2 0 0 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Percent Annualized Percent Annualized Interest Rate 4 4 2 2 0 0 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Black lines indicate data, red lines indicate mean forecasts, and shaded areas mark the uncertainty associated with our forecast as 50, 60, 70, 80, and 90 percent probability intervals. FRBNY DSGE Group, Research and Statistics Page 51 of 68 9 Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 Figure 3: Change in Forecasts 5 0 0 −5 −5 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Core PCE Inflation 3 3 2 2 1 1 0 0 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Output Growth 5 5 0 0 −5 −5 Percent Q−to−Q Annualized 5 Percent Q−to−Q Annualized Conditional Output Growth Percent Q−to−Q Annualized Percent Q−to−Q Annualized Unconditional 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Core PCE Inflation 3 3 2 2 1 1 0 0 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Interest Rate 5 5 4 4 3 3 2 2 1 1 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Percent Annualized Percent Annualized Interest Rate 5 5 4 4 3 3 2 2 1 1 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Solid (dashed) red and blue lines represent the mean and the 90 percent probability intervals of the current (previous) forecast. FRBNY DSGE Group, Research and Statistics Page 52 of 68 10 Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 Interpreting the Forecasts We use the shock decomposition shown in Figure 4 to interpret the forecasts. This figure quantifies the importance of each shock for output growth, core PCE inflation, and the federal funds rate (FFR) from 2007 on, by showing the extent to which each of the disturbances contributes to keeping the variables from reaching their long-run values. Specifically, in each of the three panels the solid line (black for realized data, red for mean forecast) shows the variable in deviation from its steady state (for output, the numbers are per capita, as the model takes population growth as exogenous; for both output and inflation, the numbers are quarter-to-quarter annualized). The bars represent the contribution of each shock to the deviation of the variable from steady state, that is, the counterfactual values of output growth, inflation, and the federal funds rate (in deviations from the mean) obtained by setting all other shocks to zero. By construction, for each observation the bars sum to the value of the solid line. The figure shows that all three variables of interest are currently below their steady-state values, and are forecasted to remain so through the end of the forecast horizon. The outlook is driven by three main factors. First, headwinds from the financial crisis, as captured by shocks to the marginal efficiency of investment (MEI), continue to depress real activity, and hence result in low real marginal costs, and low inflation, five years after the crisis. The economy experienced large spread shocks during the Great Recession and a sequence of adverse MEI shocks afterwards. Given that the MEI shocks have persistent effects on output growth and inflation, they continue to negatively affect the forecasts for these variables through the end of the forecast horizon. Second, while accommodative monetary policy, particularly forward-guidance about the future path of the federal funds rate (captured here by anticipated policy shocks), has played an important role in counteracting these headwinds, and has lifted output and inflation in past years, the impact of past forward guidance announcements on the level of output has now begun to wane. This implies a negative effect of policy on GDP growth, starting in 2014 and for the remainder of the forecasting horizon. Third, the model estimates that reductions in labor supply will also contribute to lower GDP growth. The combination of these three factors explains why output growth is still below its long-run average at the end of 2016. The role played by MEI shocks is quite evident in the shock decomposition for inflation and interest rates, which shows that MEI shocks (azure bars) play a key role in keeping these two variables below steady state. This feature of the DSGE forecast is less evident for FRBNY DSGE Group, Research and Statistics Page 53 of 68 11 Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 real output growth, as the contribution of MEI shocks seems small, particularly toward the end of the forecast horizon. However, recall that a small, but still negative, effect on output growth implies that the effect of the MEI shocks on the level of output is getting larger, even several quarters after the occurrence of the shock. This is evident in the protracted effect of MEI shocks on the output level, shown in the impulse responses of Figure 9 discussed above. In turn, the fact that economic activity is well below trend pushes inflation and consequently interest rates below steady state (given the Fed’s reaction function). More insights on the interpretation of the “financial” shocks—MEI and spread shocks— comes from Figure 5. This figure shows the recent history of the shocks, expressed in standard deviation units. The panel labeled “Spread” shows that during the Great Recession there were two large positive spread shocks, one in 2007 and one at the time of Lehman’s default. These shocks raise spreads and have negative impact on economic activity (see Figure 8). The panel labeled “MEI” in Figure 5 shows that MEI shocks were mostly negative from 2009 onwards, that is, after the end of the recession. Negative MEI shocks persistently depress economic activity (see Figure 9). The FRBNY model projects the FFR to be roughly 2 percent by the end of 2016, about 2 percentage points below its steady state value. This forecast is mostly driven by the endogenous response of policy to the weak economy, rather than by policy shocks. In fact, about two thirds of the FFR deviation from steady state (close to 1.5 percentage points) is accounted for by the negative contribution of MEI shocks, which, similarly to the headwinds invoked in Fed communication, represent an extremely persistent impairment of the ability of the economy to add to its productive capital stock as it emerges from the Great Recession. Anticipated policy shocks add about 70 basis points of accommodation. In this respect, the DSGE forecast is quite consistent with the December Summary of Economic Projections (SEP), which show a majority of FOMC participants expecting the FFR to be at or below 2 percent in 2016, while inflation and unemployment are projected to be close to target. Unlike the SEP, however, the large and persistent undershooting of the longer-run level of the FFR in the model is not sufficient to achieve the Committee’s objectives even by the end of 2016. Indeed, the model sees GDP growth about one percentage point below steady state and inflation about a quarter of a percentage point below target by the end of 2016. This evidence points to the fact that the level of the FFR is not by itself fully indicative of policy accommodation, as the low rate largely reflects projections of continued weakness in output growth and in inflation. FRBNY DSGE Group, Research and Statistics Page 54 of 68 12 Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 Shocks to monetary policy have been largely expansionary in recent history. These shocks include both contemporaneous and anticipated deviations from the feedback rule, and are shown in Figure 6 (expressed in percent). The contemporaneous policy shocks (on the top left of Figure 6) were large and accommodative before the beginning of the zero bound period. After 2008Q4 the estimated contemporaneous policy shocks become negligible, not surprisingly, and policy accommodation is achieved via forward guidance, which the model captures through anticipated shocks. Since the anticipated shocks are realized at different horizons, but interact with one another, it is difficult to assess their overall impact from Figure 6. The orange bars in Figure 4, however, show their cumulative impact, which currently amounts to about 70 basis points of policy accommodation. The impact of forward guidance, combined with interest rate smoothing in the policy rule, which limits quarterto-quarter adjustments, implies that the renormalization path is lower than that implied by the estimated rule. Policy shocks have played an important role in sustaining inflation and output both in the immediate aftermath of the recession and in the recent period. However, the impact of policy on the level of output started to wane at the end of 2012. This implies that the effect of policy on growth is actually negative after that, which explains why growth is still at or below trend by the end of 2016. This is partly because the stimulative effect of forward guidance is front-loaded, with its largest impact at the time it is first implemented. Forecasts without Incorporating Federal Funds Rate Expectations As mentioned above, we add federal funds rate expectations from 2008Q4 through 2015Q2 to the usual set of observables, to incorporate market expectations and forward guidance into our outlook (see Del Negro et al. (2013) for details). The inclusion of this information is made possible by including anticipated shocks in the central bank’s reaction function, following Laseen and Svensson (2009). The model can therefore match the information about federal funds rate expectations in two different ways: (i) via the anticipated policy shocks, which capture pre-announced deviations from the estimated policy rule (as in “we expect interest rates to be low because monetary policy is unusually accommodative”); and (ii) by changing its assessment of the state of the economy (as in “we expect interest rates to be low because the state of the economy is worse than previously estimated”). The two channels capture the exogenous and endogenous component of monetary policy, respectively. FRBNY DSGE Group, Research and Statistics Page 55 of 68 13 Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 We discussed the first channel – the effect of anticipated shocks – in the previous section. Figure 7 shows unconditional (left panels) and conditional (right panels) forecasts without incorporating federal funds rate expectations (solid lines) as well as our baseline forecasts (dashed lines). The figure shows that the model interprets the data on expected future federal funds rates as signaling a relatively weak state of the economy and a sluggish expansion in the next few years: forecasts are a bit more optimistic when disregarding the information provided by expected future federal funds rates. In particular, output growth and inflation forecasts are slightly higher, despite a tighter monetary policy. Lift-off occurs sooner in the model when expected future federal funds rates are not constrained, with the federal funds rate reaching almost 1.0 percent at the end of 2014 and almost 2.5 percent by the end of 2016. FRBNY DSGE Group, Research and Statistics Page 56 of 68 14 Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 Output Growth (deviations from mean) 0 0 −5 −5 −10 −10 Percent Q−to−Q Annualized Percent Q−to−Q Annualized Percent Q−to−Q Annualized Figure 4: Shock Decomposition 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Core PCE Inflation (deviations from mean) 1 1 0 0 −1 −1 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Interest Rate (deviations from mean) 0 0 −2 −2 −4 −4 2007 2008 2009 2010 2011 2012 Spread MEI TFP Policy 2013 Mark−Up 2014 2015 Gov’t 2016 2017 Labor The shock decomposition is presented for the conditional forecast. The solid lines (black for realized data, red for mean forecast) show each variable in deviation from its steady state. The bars represent the shock contributions; specifically, the bars for each shock represent the counterfactual values for the observables (in deviations from the mean) obtained by setting all other shocks to zero. FRBNY DSGE Group, Research and Statistics Page 57 of 68 15 ] Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 Figure 5: Shock Histories Labor 1 0 0 −1 −1 −2 −2 2 2 0 0 −2 −2 2007−1 2008−1 2009−1 2010−1 2011−1 2012−1 2013−1 2014−1 MEI Demand 1 1 0 0 −1 −1 −2 −2 Standard Deviations 2007−1 2008−1 2009−1 2010−1 2011−1 2012−1 2013−1 2014−1 0.5 0.5 0 0 −0.5 −0.5 2007−1 2008−1 2009−1 2010−1 2011−1 2012−1 2013−1 2014−1 2007−1 2008−1 2009−1 2010−1 2011−1 2012−1 2013−1 2014−1 Mark−Up Spread 2 Standard Deviations Standard Deviations 1 2 1 1 0 0 −1 −1 2007−1 2008−1 2009−1 2010−1 2011−1 2012−1 2013−1 2014−1 Standard Deviations Standard Deviations Standard Deviations TFP 6 6 4 4 2 2 0 0 −2 −2 2007−1 2008−1 2009−1 2010−1 2011−1 2012−1 2013−1 2014−1 FRBNY DSGE Group, Research and Statistics Page 58 of 68 16 Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 Figure 6: Anticipated Shock Histories 0 −0.1 −0.1 −0.2 −0.2 −0.3 −0.3 0 Percent 0 −0.05 −0.05 −0.1 −0.1 2007−1 2008−1 2009−1 2010−1 2011−1 2012−1 2013−1 2014−1 Ant 2 Ant 3 0.1 0 0 0.1 0.1 0 0 −0.1 −0.1 −0.1 2007−1 2008−1 2009−1 2010−1 2011−1 2012−1 2013−1 2014−1 Ant 5 0.1 0.1 0.05 0.05 0 −0.05 Percent 0.05 0 −0.1 2007−1 2008−1 2009−1 2010−1 2011−1 2012−1 2013−1 2014−1 Ant 4 Percent 0 2007−1 2008−1 2009−1 2010−1 2011−1 2012−1 2013−1 2014−1 0.1 Percent Ant 1 0.1 Percent Percent Money 0.1 0 0.05 0 −0.05 −0.05 −0.1 −0.1 −0.05 2007−1 2008−1 2009−1 2010−1 2011−1 2012−1 2013−1 2014−1 2007−1 2008−1 2009−1 2010−1 2011−1 2012−1 2013−1 2014−1 Percent Ant 6 0.1 0.1 0.05 0.05 0 −0.05 0 −0.05 2007−1 2008−1 2009−1 2010−1 2011−1 2012−1 2013−1 2014−1 FRBNY DSGE Group, Research and Statistics Page 59 of 68 17 Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 Figure 7: Effect of Incorporating FFR Expectations 5 0 0 −5 −5 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Core PCE Inflation 3 3 2 2 1 1 0 0 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Output Growth 5 5 0 0 −5 −5 Percent Q−to−Q Annualized 5 Percent Q−to−Q Annualized Conditional Output Growth Percent Q−to−Q Annualized Percent Q−to−Q Annualized Unconditional 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Core PCE Inflation 3 3 2 2 1 1 0 0 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Interest Rate 4 4 2 2 0 0 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Percent Annualized Percent Annualized Interest Rate 4 4 2 2 0 0 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Solid (dashed) red lines represent the mean for the forecast without (with) incorporating FFR expectations. Solid and dashed blue lines represent the relative 90 percent probability intervals. FRBNY DSGE Group, Research and Statistics Page 60 of 68 18 Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 Figure 8: Responses to a Spread Shock Aggregate Hours Percent Annualized Percent Annualized Output Growth 0.5 0 −0.5 −1 0 4 8 0 −0.5 −1 12 0 Percent 0 −0.2 −0.4 0 4 8 12 0 −0.2 0 4 Percent Annualized Percent Annualized 4 8 8 12 Spread −0.2 0 12 0.2 Interest Rate 0 −0.4 8 Core PCE Inflation Percent Annualized Labor Share 4 12 0.4 0.2 0 0 4 8 12 Percent Annualized Output Level 0 −0.5 −1 0 4 8 12 FRBNY DSGE Group, Research and Statistics Page 61 of 68 19 Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 Figure 9: Responses to an MEI Shock Aggregate Hours Percent Annualized Percent Annualized Output Growth 1.5 1 0.5 0 0 4 8 12 1 0.5 0 0 Percent 0.4 0.2 0 0 4 8 12 0.2 0 0 4 Percent Annualized Percent Annualized 4 8 8 12 Spread 0.2 0 12 0.4 Interest Rate 0.4 0 8 Core PCE Inflation Percent Annualized Labor Share 4 12 0.2 0.1 0 0 4 8 12 Percent Annualized Output Level 1.5 1 0.5 0 0 4 8 12 FRBNY DSGE Group, Research and Statistics Page 62 of 68 20 Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 Figure 10: Responses to a TFP Shock Aggregate Hours Percent Annualized Percent Annualized Output Growth 2 1 0 −1 0 4 8 12 2 1 0 −1 0 Percent 0.5 0 −0.5 −1 0 4 8 12 0 −0.2 0 4 Percent Annualized Percent Annualized 4 8 8 12 Spread 0 0 12 0.2 Interest Rate 0.1 −0.1 8 Core PCE Inflation Percent Annualized Labor Share 4 12 0.1 0 −0.1 0 4 8 12 Percent Annualized Output Level 2 1 0 0 4 8 12 FRBNY DSGE Group, Research and Statistics Page 63 of 68 21 Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 Figure 11: Responses to a Mark-up Shock Aggregate Hours Percent Annualized Percent Annualized Output Growth 0.5 0 −0.5 −1 0 4 8 12 0.5 0 −0.5 −1 0 Percent 0 −0.5 −1 0 4 8 12 0.5 0 −0.5 0 4 Percent Annualized Percent Annualized 4 8 8 12 Spread 0 0 12 1 Interest Rate 0.5 −0.5 8 Core PCE Inflation Percent Annualized Labor Share 4 12 0.01 0 −0.01 −0.02 0 4 8 12 Percent Annualized Output Level 0 −0.5 −1 0 4 8 12 FRBNY DSGE Group, Research and Statistics Page 64 of 68 22 Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 Figure 12: Responses to a Monetary Policy Shock Aggregate Hours Percent Annualized Percent Annualized Output Growth 0.5 0 −0.5 −1 0 4 8 12 0 −0.5 −1 0 Percent 0 −0.1 −0.2 0 4 8 12 0 −0.1 0 4 Percent Annualized Percent Annualized 0 4 8 8 12 Spread 0.5 0 12 0.1 Interest Rate 1 −0.5 8 Core PCE Inflation Percent Annualized Labor Share 4 12 0.04 0.02 0 −0.02 0 4 8 12 Percent Annualized Output Level 0 −0.5 −1 0 4 8 12 FRBNY DSGE Group, Research and Statistics Page 65 of 68 23 Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 Figure 13: Responses to a Labor Supply Shock Aggregate Hours Percent Annualized Percent Annualized Output Growth 0.5 0 −0.5 −1 0 4 8 12 0 −0.5 −1 −1.5 0 Percent 1 0.5 0 −0.5 0 4 8 12 0.2 0 0 4 Percent Annualized Percent Annualized 4 8 8 12 Spread 0.1 0 12 0.4 Interest Rate 0.2 0 8 Core PCE Inflation Percent Annualized Labor Share 4 12 0 −0.05 −0.1 0 4 8 12 Percent Annualized Output Level 0 −0.5 −1 0 4 8 12 FRBNY DSGE Group, Research and Statistics Page 66 of 68 24 Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 Figure 14: Responses to a Government Spending Shock Aggregate Hours Percent Annualized Percent Annualized Output Growth 2 1 0 −1 0 4 8 12 0.4 0.2 0 0 Percent 0.2 0.1 0 0 4 8 12 0.04 0.02 0 0 4 Percent Annualized Percent Annualized 4 8 8 12 Spread 0.05 0 12 0.06 Interest Rate 0.1 0 8 Core PCE Inflation Percent Annualized Labor Share 4 12 0 −0.01 −0.02 0 4 8 12 Percent Annualized Output Level 0.4 0.2 0 0 4 8 12 FRBNY DSGE Group, Research and Statistics Page 67 of 68 25 Authorized for public release by the FOMC Secretariat on 1/10/2020 FRBNY DSGE Model: Research Directors Draft March 5, 2014 References [1] Bernanke, Ben, Mark Gertler and Simon Gilchrist, “The Financial Accelerator in a Quantitative Business Cycle Framework,” in J.B. 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Svensson, “Anticipated Alternative InstrumentRate Paths in Policy Simulations,” NBER Working Paper No. w14902, 2009. [8] Smets, Frank and Raphael Wouters, “Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach,” American Economic Review, 2007, 97 (3), 586 – 606. FRBNY DSGE Group, Research and Statistics Page 68 of 68 26
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