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Authorized for public release by the FOMC Secretariat on 1/8/2021 BOARD OF GOVERNORS OF THE FEDERAL RESERVE SYSTEM DIVISION OF MONETARY AFFAIRS FOMC SECRETARIAT Date: June 5, 2015 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. Page 1 of 1 Authorized for public release by the FOMC Secretariat on 1/8/2021 The Current Outlook in EDO: June FOMC Meeting (Class II – Restricted FR) Taisuke Nakata∗ June 3, 2015 1 The EDO Forecast from 2015 to 2017 Given recent data (including expectations for the federal funds rate), the EDO model projects real GDP growth of 1.5 percent in 2015, about 11/4 percentage point lower than the growth rate of potential output. Subsequently, real GDP growth picks up and average 21/4 percent through the end of the forecast period. The unemployment rate rises to 53/4 percent by the end of 2015, exceeds 6 percent in the first half of 2016, and reaches 61/4 percent in the first quarter of 2017 (Figures 1 and 3).1 Growth in output is held down by two factors. First, the model regards the market-expected federal funds rate path as accommodative relative to the estimated rule; the waning of this unusual accommodation restrains growth. Second, the model attributes the slow-down in economic activity in the first quarter of 2015 to a sharp decline in total factor productivity, whose effects continue to weigh on GDP growth until the beginning of next year. Output growth in the first half of 2015 is now estimated to have been much weaker than the model would have anticipated in March. The model views this weakness as persistent, and output growth has revised down on average by 1/4 percent in the second half of 2015 and 2016 since the March round. The gradual increase in projected inflation over the forecast horizon is due to the gradual increase in wages, which is driven by the slowly dissipating negative markup shock. The model has interpreted ∗ Taisuke Nakata (taisuke.nakata@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 June 2015 Tealbook projection through 2015:Q2 and market expectations that the federal funds rate will remain at its effective lower bound through the third 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 2014: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 1 of 62 Authorized for public release by the FOMC Secretariat on 1/8/2021 Figure 1: Recent History and Forecasts EDO Projection Summary Real GDP Core PCE price index Percent change, a.r. 6 6 4 4 2 2 0 0 -2 -2 -4 -4 Percent change, a.r. 2.5 2.0 1.5 1.5 1.0 1.0 0.5 0.5 0.0 0.0 -0.5 -0.5 -1.0 -1.0 -1.5 -1.5 -2.0 -6 2012 2013 2014 2015 2016 -6 2017 2.5 2.0 -2.5 -2.0 2012 2013 2014 2015 2016 2017 -2.5 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 2012 2013 2014 2015 2016 2017 -5 2015 Q4/Q4 Real GDP (a) Credible set (c) Federal Funds Rate (b) Credible set (c) 2017 Q4/Q4 1.5 2.0 2.6 -.8-3.7 -.3-3.9 .6-4.5 Core PCE Price index (a) 1.6 Credible set (c) 2016 Q4/Q4 1.3-1.8 1.9 2.1 1.2-2.4 1.3-2.6 0.3 1.0 1.6 .0-1.1 .0-2.5 .0-3.5 (a) Q4/Q4 percent change, (b) Q4 level, (c) 68 percent Red, solid line -- Data (through 2015:Q2) and projections; Blue, solid line -- Previous projection (March, 2014, as of 2015:Q1); Black, dashed line -- Steady-state or trend values Contributions (bars): Red -- Financial; Blue -- Technology; Silver -- Monetary policy; Green -- Other the surprising strength of inflation since the March round as driven by the above-mentioned decline in total factor productivity. The inflation rate has revised up 1/4 percentage point on average over the forecast horizon. The unemployment rate rises through early 2015, driven largely by the weak demand conditions. By the end of the forecast, however, a substantial portion of the elevated unemployment rate is accounted for by 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 2 of 62 Authorized for public release by the FOMC Secretariat on 1/8/2021 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 3 of 62 Authorized for public release by the FOMC Secretariat on 1/8/2021 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. The 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, first, an aggregate risk-premium, or natural rate of interest, shock driving a wedge between the short-term policy rate and the interest rate faced by private decisionmakers (as in Smets and Wouters (2007)) and, second, fluctuations in the discount factor/risk premia faced by 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. 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 4 Page 4 of 62 Authorized for public release by the FOMC Secretariat on 1/8/2021 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: ∞ X cnn E0 β t ς cnn ln(Etcnn (i)−hEt−1 (i))+ς cd ln(Ktcd (i)) t=0 +ς r ln(Ktr (i)) −ς l 1+ν kb (Lcbi t (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 in the early 2000s recession and the most recent downturn. Many other models do not distinguish between developments across these categories of spending. 5 Page 5 of 62 Authorized for public release by the FOMC Secretariat on 1/8/2021 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 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 6 Page 6 of 62 Authorized for public release by the FOMC Secretariat on 1/8/2021 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 2015:Q2) 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 is characterized by monopolistic competition. As a result, unemployment arises in equilibrium – some 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 7 of 62 -2 Authorized for public release by the FOMC Secretariat on 1/8/2021 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). 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 8 Page 8 of 62 Authorized for public release by the FOMC Secretariat on 1/8/2021 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 + .017mcst + θts + 0.76Et πt+1 πtp,s = 0.22πt−1 (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 interest rate Rt to its target level R̄t ρr Rt = (Rt−1 ) R̄t 1−ρr 9 Page 9 of 62 exp [rt ] , (5) Authorized for public release by the FOMC Secretariat on 1/8/2021 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: • Permanent technology shocks: This category consists of shocks to aggregate and investmentspecific (or fast-growing sector) technology. 10 Page 10 of 62 Authorized for public release by the FOMC Secretariat on 1/8/2021 • A labor supply shock: This shock affects the willingness 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); 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 ); 11 Page 11 of 62 Authorized for public release by the FOMC Secretariat on 1/8/2021 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 at 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 specific risk-premium shocks. At farther horizons, their volatilities are accounted for by technology shocks. 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, 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 12 of 62 Authorized for public release by the FOMC Secretariat on 1/8/2021 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 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 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 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). 13 Page 13 of 62 Authorized for public release by the FOMC Secretariat on 1/8/2021 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 −1 Funds Rate Shock 0 0.2 20 Labor Supply Wage Markup Exog. Demand 10 1 5 0 10 0 −10 −5 −20 2010 2 Overall TFP 0 −1 −2 0 −1 2010 1990 Durables Risk−Premium Housing Risk−Premium 2000 1 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 2000 2000 1990 2000 2010 1990 2000 2010 1990 2000 2010 2 1 0 −1 −2 2010 1 1 Risk−premium 1990 2010 2 1990 Term Premium 2000 Non−Invest. Price Markup Capital Goods Technology 1990 0 0 −1 2010 0.5 0 −0.5 1990 2000 2010 0.2 0 −0.2 3.3 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 14 Page 14 of 62 Authorized for public release by the FOMC Secretariat on 1/8/2021 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 2 0 −2 −4 1990 0 −1 −2 −3 2000 1990 2000 2010 1990 2000 2010 1990 2000 2010 50 0 −50 2010 100 0.5 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 0 50 0 −50 −100 −0.5 1990 2000 2010 1990 2000 2010 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 15 of 62 Authorized for public release by the FOMC Secretariat on 1/8/2021 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 16 of 62 Authorized for public release by the FOMC Secretariat on 1/8/2021 [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 17 of 62 Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 Summary of the Forecasts The FRBNY model forecasts are obtained using data released through 2015Q1, augmented for 2015Q2 with the FRBNY staff forecasts 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 10-year Treasury yields based on 2015Q2 observations. Note that we do not constrain the expected federal funds rate to be equal to market expectations, as measured by OIS rates, beyond 2015Q2. The 2015Q2 staff projections and spreads are those that were available on May 26. The FRBNY DSGE forecast for output growth is weaker in the short run than it was in March, reflecting the weaker than expected 2015Q1 GDP data. The model projects the economy to grow 1.1 percent in 2015, a sharp downward revision from the 2.4 percent projected in March. The growth forecasts for 2016 and 2017 are 2.0 and 2.3 percent, respectively, only slightly weaker than the March projections. Conversely, inflation, as measured both by the GDP and the core PCE deflators, was stronger in Q1 than expected, yielding higher short run forecasts than in March. Inflation projections are 1.2 percent for 2015, up from 0.9 percent in March, while for 2016 and 2017 they are 1.2 and 1.3 percent, respectively. The model attributes the forecast errors for 2015Q1 to largely temporary factors – transitory technology shocks for GDP growth and mark-up shocks for inflation which explains why the medium run forecasts are very similar to the March projections. The broader story behind the forecasts is unchanged relative to March: The headwinds that slowed down the economy in the aftermath of the financial crisis are finally abating, resulting in an increase of the natural rate of interest toward positive ranges and a gradual closing of the output gap the difference between output and natural output. The gap is closing only slowly, however, resulting in growth that is barely above potential, and in weak inflation projections. Inflations convergence to the FOMC long-run objective is contingent on projected increases in future real wages and marginal costs. In the absence of accelerating wages, inflation projections would be even weaker. The model projects the federal funds rate to reach 2.4 percent by the end of 2017, well below its steady state value. This relatively shallow path after lift-off is mostly driven by FRBNY DSGE Group, Research and Statistics Page 18 of 62 1 Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 the endogenous response of policy to weak inflation, according to the historical reaction function estimated by the model. However, past forward guidance on interest rates, which is estimated to have provided consistent support to GDP growth and inflation over the last several years, also contributes to maintaining a lower expected future federal funds rates than is implied by the historical reaction function. The estimated natural real rate of interest has been well below the actual real rate during and after the crisis, indicating that the zero lower bound imposed a constraint on interest-rate policy. Currently, the natural rate is close to the actual real rate, suggesting that policy is still not particularly accommodative. Uncertainty around the forecasts is significant, particularly for GDP growth. The width of the 68 percent probability interval for GDP growth is 2.7 percentage points in 2015, ranging from -0.5 to 2.2 percent, and widens to 5.2 percentage points in 2017 from -0.4 to 4.8 percent. The 68 percent probability intervals for inflation range from 0.9 to 1.6 percent in 2015 and from 0.5 to 2.2 percent in 2017. 1 The Model and Its Transmission Mechanism General Features of the Model The FRBNY DSGE model is a medium scale, one-sector dynamic stochastic general equilibrium model which is based on the New Keynesian model with financial frictions used in Del Negro et al. (2015). The core of the model is based on the work of Smets and Wouters (2007) and Christiano et al. (2005): It builds on the neo-classical growth model by adding nominal wage and price rigidities, variable capital utilization, costs of adjusting investment, and habit formation in consumption. The model also includes credit frictions as in the financial accelerator model developed by Bernanke et al. (1999), where the actual implementation of the credit frictions follows closely Christiano et al. (2014), and a time-varying inflation target following Del Negro and Schorfheide (2012). In contrast to these papers, the model features both a deterministic and a stochastic trend in productivity. Finally, it accounts for forward guidance in monetary policy by including anticipated policy shocks as in Laseen and Svensson (2011). 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 macroecoFRBNY DSGE Group, Research and Statistics Page 19 of 62 2 Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 nomic fluctuations. The model identifies these shocks by matching the model dynamics with numerous quarterly data series: real GDP growth, real consumption growth, real investment growth, real wage growth, hours worked, inflation in the personal consumption expenditures deflator and inflation in the GDP deflator, the federal funds rate (FFR), the 10-year nominal Treasury bond yield, 10-year survey-based inflation expectations, credit spreads (Baa - 10year Treasury bond yield), and data on total factor productivity. In addition, from 2008Q4 to 2015Q2, we use market expectations of future federal funds rates. Model parameters are estimated from 1960Q1 to the present using Bayesian methods. 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 derive utility from leisure, supply labor services to firms, and set wages in a monopolistically competitive fashion. The labor market is subject to frictions because of nominal wage rigidities. In addition, we allow for exogenous disturbances to wage markups, labeled “wage mark-up” shocks, which capture exogenous changes in the degree of competitiveness in the labor market, or other exogenous movements in the labor supply. Households, who discount future utility streams, also have to choose how much to consume and save. Their savings take the form of deposits to banks and purchases of government bills. Household preferences feature habit persistence, a characteristic that affects their consumption smoothing decisions. In addition, “discount factor” shocks drive an exogenous wedge between the change in the marginal utility of consumption and the riskless real return. These shocks possibly capture phenomena like deleveraging, or increased risk aversion. 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, which affect both the temporary and the permanent component of the level of total factor productivity. 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 with indexing, which determines inflation as a function of marginal costs, expected future inflation, past inflation, and “price mark-up” shocks. Markup shocks capture exogenous changes in the degree of competitiveness in the intermediate FRBNY DSGE Group, Research and Statistics Page 20 of 62 3 Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 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 to entrepreneurs. Entrepreneurs use their own wealth and the loans from banks to acquire capital. They then choose the utilization level of capital and 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 interFRBNY DSGE Group, Research and Statistics Page 21 of 62 4 Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 est 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 mark-up shocks which have also a moving-average component, disturbances to government spending which are allowed to be correlated with total factor productivity disturbances, and exogenous disturbances to the monetary policy rule, or “policy” shocks, which are assumed to be i.i.d. FRBNY DSGE Group, Research and Statistics Page 22 of 62 5 Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 Figure 1: Model Structure productivity shocks Firms wage rigidities utilization capital wage mark-up shocks intermediate goods price rigidities mark-up shocks labor MEI shocks Capital Producers investment adjustment costs Final Goods Producers investment Entrepreneurs consumption disc. factor shocks Banks loans credit frictions spread shocks deposits Households bills habit persistence Government interest rate policy policy shocks FRBNY DSGE Group, Research and Statistics Page 23 of 62 gov’t spending shocks 6 Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 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 6 to 11. We start with the shocks most closely associated with the Great Recession and the severe financial crisis that characterized it: the discount factor shock and the spread shock. The discount factor shock reflects the sudden desire by households to cut down on their consumption and save more. This may capture the fact that households want to reduce their debt level, or their increased pessimism about future economic conditions. Figure 6 shows the impulse responses of the variables used in the estimation to a one-standard-deviation innovation in the discount factor shock. Such a shock results in a decline in consumption (fourth panel in left column), and hence in aggregate demand, which leads to a decrease in output growth (top left panel), hours worked (top right panel), and real wage growth. The implied reduction in marginal costs induces measures of inflation to fall (see inflation of GDP and PCE deflators, in second and third rows). In addition, the discount factor shock implies an increase in credit spread (fifth panel in left row) which causes investment growth to contract. Monetary policy typically attempts to mitigate the decline in activity and inflation by lowering the FFR, but is unable to fully offset the shock. The other key shock, the spread 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 yield, and the spread’s comovement with output growth, inflation, and the other observables. Figure 7 shows the impulse responses to a one-standard-deviation innovation in the spread shock. An innovation of this size increases the observed spread by roughly 25 basis points (fifth panel in left column). 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 barely higher than at the trough four 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 less than three years after the shock hits, FRBNY DSGE Group, Research and Statistics Page 24 of 62 7 Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 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, and, via the New Keynesian Phillips curve, in inflation. Finally, policymakers endogenously respond to the change in the inflation and real activity outlook by cutting the federal funds rate (right panel on the third row). 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. The impulse responses to MEI shocks, shown in Figure 8, also feature a decrease in investment, output and hours worked, as well as in real wages, although these are less persistent than in the case of spread shocks. Inflation responds little however, as marginal costs are expected revert back to steady state relatively quickly. One key difference between the responses to spread and MEI shocks which 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 is the stationary TFP shock (the model features shocks to both the level and the growth rate of productivity – we discuss here the former). As shown in Figure 9, 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. The last shock that plays a relevant role in the current economic environment is the price mark-up shock, whose impulse response is depicted in Figure 10. 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 FRBNY DSGE Group, Research and Statistics Page 25 of 62 8 Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 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 26 of 62 9 Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 Forecasts Core PCE Inflation Real GDP Growth 2015 (Q4/Q4) June March 0.8 0.9 (0.5,1.2) (0.4,1.4) 0.8 2.4 (-0.9,1.9) (-0.0,3.9) Unconditional Forecast 2016 (Q4/Q4) 2017 (Q4/Q4) June March June March 1.0 1.1 1.3 1.4 (0.3,1.8) (0.3,1.8) (0.4,2.1) (0.5,2.2) 2.1 2.3 2.3 2.3 (-0.9,4.2) (-0.6,4.6) (-0.3,4.9) (-0.3,4.8) 2018 (Q4/Q4) June March 1.5 1.6 (0.5,2.3) (0.7,2.4) 2.4 2.3 (-0.1,5.2) (-0.3,5.1) Core PCE Inflation Real GDP Growth 2015 (Q4/Q4) June March 1.2 0.9 (0.9,1.6) (0.4,1.4) 1.1 2.4 (-0.5,2.2) (-0.1,3.7) Conditional Forecast* 2016 (Q4/Q4) 2017 (Q4/Q4) June March June March 1.2 1.1 1.3 1.4 (0.4,1.9) (0.3,1.9) (0.5,2.2) (0.5,2.2) 2.0 2.3 2.3 2.3 (-0.8,4.2) (-0.6,4.6) (-0.4,4.8) (-0.3,4.9) 2018 (Q4/Q4) June March 1.5 1.6 (0.6,2.4) (0.7,2.4) 2.4 2.3 (-0.2,5.1) (-0.3,5.1) *The unconditional forecasts use data up to 2015Q1, the quarter for which we have the most recent GDP release, as well as the federal funds rate and spreads data for 2015Q2. In the conditional forecasts, we further include the 2015Q2 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 2015-2018: real GDP growth, core PCE inflation and the federal funds rate. From 2008Q4 to 2015Q2, we capture policy anticipation setting federal funds rate expectations equal to market expectations for the federal funds rate (as measured by OIS rates), and by adding anticipated monetary policy shocks to the central bank’s reaction function, as in Laseen and Svensson (2011). We estimate the standard deviation of the anticipated shocks as in Campbell et al. (2012). Beyond 2015Q2, we do not constrain the expected federal funds rate to equate market expectations. The table above presents Q4/Q4 forecasts for real GDP growth and inflation for 20152018, with 68 percent probability intervals. We include two sets of forecasts. The unconditional forecasts use data up to 2015Q1, the quarter for which we have the most recent GDP release, as well as the federal funds rate and spreads data for 2015Q2 (we use the average realizations for the quarter up to the forecast date). In the conditional forecasts, we further include the 2015Q2 FRBNY staff projections for GDP growth, core PCE inflation, and hours worked as additional data points (as of May 26, quaterly annualized projections for 2015Q2 are 1.8 percent for output growth and 1.6 percent for core PCE inflation). Treating the 2015Q2 staff forecasts as data allows us to incorporate information about the current quarter into the DSGE forecasts for the subsequent quarters. In addition to providing the FRBNY DSGE Group, Research and Statistics Page 27 of 62 10 Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 current forecasts, the table reports the forecasts included in the DSGE memo forwarded to the FOMC in advance of its March 2015 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 March forecasts. Our discussion will mainly focus on the conditional forecasts, which are those reported in the memo to the FOMC. The FRBNY DSGE forecast changed importantly since March, reflecting weaker than expected 2015Q1 GDP data and somewhat stronger than expected inflation data, as shown in Figure 3. The trajectory of output growth is weaker in 2015 and to a lesser extent in 2016, while inflation forecasts have been revised up during that period. Relative to March, the GDP growth forecast for 2015 (Q4/Q4) decreased from 2.4 to 1.1, and the forecasts for 2016 and 2017 (Q4/Q4) are at around 2.0 and 2.3 percent, respectively. For inflation, the incoming data for April has led to a significant increase in the nowcast for 2015Q2 (1.6 percent for core PCE inflation). This implies that core PCE inflation for 2015 is projected to be 1.2 percent, higher than the 0.9 percent projected in March. Inflation returns to the long term objective of 2 percent over the forecast horizon. The point forecasts are 1.2 for 2016 and 1.3 for 2017, near the March point forecasts. Uncertainty around the real GDP growth, as measured by the 68 percent bands, has diminished somewhat for output and inflation. For GDP growth, the 68 percent bands cover the intervals -0.5 to 2.2 percent in 2015, -0.8 to 4.2 in 2016, and -0.4 to 4.8 in 2017. For inflation, the 68 percent probability bands range from 0.5 to 2.2 percent throughout 2017. 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 May 26; after that the federal funds rate rises gradually and is forecasted to be around 1.6 percent at the end of 2016 and around 2.3 percent by the end of 2017. Finally, note that the June conditional and unconditional forecasts are quite different from one another, over the near term. While the conditional forecast assumes a 1.8 percent growth in real GDP and a relatively rapid increase in core PCE prices in 2015Q2, the unconditional forecast shows a much weaker GDP growth in the near term and a more gradual increase in inflation. FRBNY DSGE Group, Research and Statistics Page 28 of 62 11 Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 Figure 2: Forecasts 5 0 0 −5 −5 2007 2009 2011 2013 2015 2017 2019 Core PCE Inflation 3 3 2 2 1 1 0 0 2007 2009 2011 2013 2015 2017 2019 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 2009 4 4 2 2 2013 2015 2017 0 2019 Percent Annualized Percent Annualized 6 2011 2015 2017 2019 3 3 2 2 1 1 0 0 2007 2009 2011 2013 2015 2017 2019 Interest Rate 6 2009 2013 Core PCE Inflation Interest Rate 0 2007 2011 6 6 4 4 2 2 0 2007 2009 2011 2013 2015 2017 0 2019 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 29 of 62 12 Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 Figure 3: Change in Forecasts 5 0 0 −5 −5 2007 2009 2011 2013 2015 2017 2019 Core PCE Inflation 3 3 2 2 1 1 0 0 2007 2009 2011 2013 2015 2017 2019 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 2009 4 4 2 2 2013 2015 2017 2019 Percent Annualized Percent Annualized 6 2011 2015 2017 2019 3 3 2 2 1 1 0 0 2007 2009 2011 2013 2015 2017 2019 Interest Rate 6 2009 2013 Core PCE Inflation Interest Rate 2007 2011 6 6 4 4 2 2 2007 2009 2011 2013 2015 2017 2019 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 30 of 62 13 Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 Interpreting the Forecasts We use the shock decomposition shown in Figure 4 to interpret the forecasts. This figure quantifies the importance of the most important shocks 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. We should note that the impact of some shocks have been aggregated. For example, the “financial” shock (purple) captures both shocks to the spread as well as shocks to the discount factor. The dynamics behind the FRBNY DSGE forecast can be described as follows. The headwinds from the financial crisis, which are captured in the model by the contribution of the financial (purple) and MEI (azure) shocks, are finally waning, implying that both shocks have a positive contribution on output growth. The impact of financial shocks on the level of output is still negative throughout the forecast horizon, however, as can be inferred from their negative contribution to inflation. In fact, Figure 4 shows that financial shocks are mostly responsible for the slow return of inflation to the 2 percent target, and for the interest rate being below its steady state value. Figure 5 shows the output gap – the difference between output and its “natural” level (the counterfactual level of output in absence of nominal rigidities, mark-up shocks, and financial frictions) – and the corresponding “natural” rate of interest through history. The natural interest rate remains near zero, but has risen recently consistently with the waning of the headwinds from the financial crisis. The output gap however remains negative, mostly because of the lagged effect of financial shocks, and closes only gradually, which explains the slow return of inflation to target. While total factor productivity shocks contributed negatively to economic activity in late 2007 and 2008, these shocks have instead pushed GDP up significantly in 2009 and 2010. In 2015Q1, as was the case in 2014Q1, the sharp drop in real GDP growth is mainly attributable to a temporary drop in total factor productivity. Over the past several years, FRBNY DSGE Group, Research and Statistics Page 31 of 62 14 Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 the negative impact of the headwinds mentioned above has been partly compensated by expansionary monetary policy. In particular, 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, lifting both output and inflation. However, the positive effect of this policy accommodation on the level of output has been negligible over the most recent quarters. Since monetary policy is neutral in the long run in this model, the impact of policy accommodation on the level of output will wane eventually, and has already begun to do so by the end of 2014, implying a negative effect on growth. As a consequence of forward guidance the renormalization path is somewhat slower than that implied by the estimated rule, as indicated by the yellow bars in the shock decomposition for interest rates. The comparison between the estimated natural real rate of interest and the actual real rate of interest, shown in Figure 5, is revealing in regard to the stance of policy. The natural rate of interest has been well below the actual real rate during and after the crisis, indicating that the zero lower bound imposed a constraint on interest-rate policy. Currently, the natural rate is close to the actual real rate, suggesting that policy is still not particularly accommodative. The shock decomposition for inflation also shows that mark-up shocks (green bars), which capture the effect of exogenous changes in marginal costs such as those connected with fluctuations in commodity prices, play an important role. These shocks tend to have a fairly persistent impact on inflation. Recent negative mark-up shocks, likely reflecting declines in oil prices, contribute to push inflation down relative to target by at least half of a percentage point during the current year and the next one. The rise in inflation in 2015Q1 is partly explained by a temporary reversal of mark-up shocks, consistently with the fact that oil prices stopped falling. The temporary decrease in productivity in 2015Q1 also helps explaining the increase in inflation. FRBNY DSGE Group, Research and Statistics Page 32 of 62 15 Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 Output Growth (deviations from mean) 0 0 −5 −5 −10 2007 −10 2019 2008 2009 2010 2011 2012 2013 2014 Core PCE Inflation (deviations from mean) 2015 2016 2017 2018 0.5 0.5 0 0 −0.5 −0.5 −1 −1 −1.5 2007 Percent Q−to−Q Annualized Percent Q−to−Q Annualized Percent Q−to−Q Annualized Figure 4: Shock Decomposition 2008 2009 2010 2011 2012 2013 2014 Interest Rate (deviations from mean) 2015 2016 2017 2018 −1.5 2019 0 0 −2 −2 −4 2007 2008 2009 2010 Gov’t 2011 2012 Financial 2013 TFP 2014 Mark−Up 2015 2016 Policy 2017 2018 −4 2019 MEI 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 33 of 62 16 ] Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 Figure 5: Output Gap and the Natural Interest Rate Output Gap 10 8 6 4 2 0 −2 −4 −6 −8 −10 1960 1970 1980 1990 2000 2010 2020 2030 Natural Rate & Ex-Ante Real Rate FRBNY DSGE Group, Research and Statistics Page 34 of 62 17 Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 Figure 6: Responses to a Discount Factor Shock Aggregate Hours Percent Annualized Percent Annualized Output Growth 0.3 0.2 0.1 0 −0.1 0 4 8 0.8 0.6 0.4 0.2 0 12 0 4 Real Wage Growth Percent Annualized Percent Annualized 0.04 0.02 0 −0.02 0 4 8 0.03 0.02 0.01 0 12 0 4 Percent Annualized Percent Annualized 0.03 0.02 0.01 4 8 0.15 0.1 0.05 0 4 0.4 0.2 0 4 8 0.2 0.1 0 −0.1 12 0 4 Percent Annualized Percent Annualized −0.05 4 8 0.02 0.01 0 12 0 Percent Annualized Percent Annualized 0.04 0.02 4 8 4 8 12 Total Factor Productivity, Util.Unadjusted 0.06 0 12 0.03 Long Rate 0 8 Long Inf 0 0 12 0.3 Spread −0.1 8 Investment Growth Percent Annualized Percent Annualized Consumption Growth 0 12 0.2 0 12 0.6 −0.2 8 Interest Rate 0.04 0 12 0.04 Core PCE Inflation 0 8 GDP Deflator 0.03 0.02 0.01 0 −0.01 12 0 FRBNY DSGE Group, Research and Statistics Page 35 of 62 4 8 12 18 Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 Figure 7: Responses to a Spread Shock Output Growth Aggregate Hours 0.02 0 −0.02 0 4 12 x 10 0 4 −3 8 4 5 x 10 −5 −10 0 4 Percent Annualized 0.02 0.01 0 0 4 0 −0.05 8 0.4 0.2 0 −0.2 12 Percent Annualized Percent Annualized 0 −0.02 −0.04 0 4 5 0 −5 −10 0 0 4 8 12 −6 2 0 4 8 12 −3 Total Factor Productivity, Util.Unadjusted x 10 1 0 −1 −2 12 8 Long Inf −4 Long Rate x 10 4 x 10 −2 −8 12 Percent Annualized Percent Annualized −3 8 0 −3 Spread −0.06 12 Investment Growth 0.05 4 8 0.6 Percent Annualized Percent Annualized Consumption Growth 0 12 0.03 −0.01 12 0.1 −0.1 8 Interest Rate −5 8 12 0 12 0 4 8 GDP Deflator Core PCE Inflation x 10 0 0 −3 2 −10 0 Real Wage Growth 4 5 0.1 −0.1 6 0 Percent Annualized 8 0.2 Percent Annualized Percent Annualized −3 8 0.3 Percent Annualized Percent Annualized 0.04 0 FRBNY DSGE Group, Research and Statistics Page 36 of 62 4 8 12 19 Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 Figure 8: Responses to an MEI Shock Aggregate Hours 0.2 0.1 0 −0.1 1 Percent Annualized Percent Annualized Output Growth 0.3 0 4 8 0.5 0 −0.5 12 Percent Annualized Percent Annualized 0.03 0.02 0.01 0 −0.01 0 4 5 x 10 4 8 x 10 −4 −6 0 4 0.1 0.05 0 Percent Annualized Percent Annualized 0.1 0 8 0 4 0 Percent Annualized Percent Annualized 0.02 8 0 0 −4 0 Percent Annualized Percent Annualized 0 −0.01 −0.015 4 8 4 8 12 Total Factor Productivity, Util.Unadjusted −0.005 0 12 −2 −6 12 8 Long Inf x 10 Long Rate −0.02 4 −3 0.04 4 12 1 −1 12 0.06 0 8 2 Spread 0 12 Investment Growth 0.05 4 8 0.15 Consumption Growth 0 12 −2 −0.05 12 0.15 −0.05 8 GDP Deflator Interest Rate −5 0 4 Core PCE Inflation 0 −10 0 −8 12 Percent Annualized Percent Annualized −3 8 0 −3 Real Wage Growth 0.03 0.02 0.01 0 −0.01 12 0 FRBNY DSGE Group, Research and Statistics Page 37 of 62 4 8 12 20 Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 Figure 9: Responses to a TFP Shock Aggregate Hours 0 −0.2 −0.4 −0.6 0.6 Percent Annualized Percent Annualized Output Growth 0.2 0 4 8 0.4 0.2 0 −0.2 12 0 4 0.02 0 −0.02 −0.04 0 4 8 0.03 0.02 0.01 0 12 0 4 Percent Annualized Percent Annualized 0.03 0.02 0.01 4 8 0.05 0 4 0.2 0 −0.2 4 5 −5 −10 0 −0.2 0 4 8 0.005 0 Percent Annualized Percent Annualized 0.01 8 4 8 12 Total Factor Productivity, Util.Unadjusted 0.02 4 12 0.01 0 12 0.03 0 8 0.015 Long Rate 0 4 Long Inf 0 −15 0 −0.1 Spread x 10 12 0.1 −0.3 12 Percent Annualized Percent Annualized −3 8 8 Investment Growth Percent Annualized Percent Annualized Consumption Growth 0 12 0.1 0 12 0.4 −0.4 8 Interest Rate 0.04 0 12 0.04 Core PCE Inflation 0 8 GDP Deflator Percent Annualized Percent Annualized Real Wage Growth 0.5 0 −0.5 −1 12 0 FRBNY DSGE Group, Research and Statistics Page 38 of 62 4 8 12 21 Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 Figure 10: Responses to a Price Mark-up Shock Aggregate Hours Percent Annualized Percent Annualized Output Growth 0.05 0 −0.05 −0.1 −0.15 0 4 8 0.1 0 −0.1 −0.2 −0.3 12 0 4 0.2 0.1 0 −0.1 −0.2 0 4 8 0.2 0.1 0 −0.1 12 0 4 0.1 0 8 0.1 0.05 0 −0.05 12 0 4 0 −0.05 −0.1 0 4 8 0 −0.1 −0.2 −0.3 12 Percent Annualized Percent Annualized −0.005 4 15 x 10 0 4 8 8 12 Long Inf 5 0 0 4 8 12 Total Factor Productivity, Util.Unadjusted 5 0 4 x 10 Long Rate 10 −5 10 −5 12 Percent Annualized Percent Annualized −3 8 0 −3 0 0 12 0.1 Spread −0.01 8 Investment Growth Percent Annualized Percent Annualized Consumption Growth 0.05 −0.15 12 0.15 Percent Annualized Percent Annualized 0.2 4 8 Interest Rate 0.3 0 12 0.3 Core PCE Inflation −0.1 8 GDP Deflator Percent Annualized Percent Annualized Real Wage Growth 0.01 0 −0.01 −0.02 −0.03 12 0 FRBNY DSGE Group, Research and Statistics Page 39 of 62 4 8 12 22 Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 Figure 11: Responses to a Monetary Policy Shock Aggregate Hours Percent Annualized Percent Annualized Output Growth 0.2 0 −0.2 −0.4 −0.6 0 4 8 0 −0.2 −0.4 −0.6 −0.8 12 0 −0.01 −0.02 0 4 8 x 10 −4 4 8 x 10 −5 −10 0 4 0.1 0.05 0 0 4 Percent Annualized Percent Annualized 0 −0.4 8 0 −0.5 −1 12 Percent Annualized Percent Annualized 0.01 0 4 8 0 2 0 −1 0 Percent Annualized Percent Annualized 0.02 0.01 0.005 4 8 4 8 12 Total Factor Productivity, Util.Unadjusted 0.015 0 12 1 −2 12 8 Long Inf x 10 Long Rate 0 4 −3 0.02 0 12 0.5 Spread −0.01 8 Investment Growth −0.2 4 12 0.15 Consumption Growth 0 8 0.2 12 0.2 −0.6 12 Interest Rate 0 0 8 GDP Deflator Core PCE Inflation −2 −6 4 0 12 Percent Annualized Percent Annualized −3 2 5 Percent Annualized Percent Annualized 0.01 −0.03 0 −3 Real Wage Growth 0.02 0 −0.02 −0.04 12 0 FRBNY DSGE Group, Research and Statistics Page 40 of 62 4 8 12 23 Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 Figure 12: Shock Histories b g 2 0 0 Standard Deviations Standard Deviations 2 −2 −2 2007 2008 2009 2010 2011 2012 2013 2014 2015 1 1 0 0 −1 −1 Standard Deviations Standard Deviations 0 0 −2 −2 −4 −4 z 2007 2008 2009 2010 2011 2012 2013 2014 2015 1 0 0 −1 −1 2 1 1 0 0 −1 −1 λw Standard Deviations 1 2 2007 2008 2009 2010 2011 2012 2013 2014 2015 λf Standard Deviations 2 2007 2008 2009 2010 2011 2012 2013 2014 2015 µ 2 2 0 0 −2 −2 −4 −4 2007 2008 2009 2010 2011 2012 2013 2014 2015 2007 2008 2009 2010 2011 2012 2013 2014 2015 σ rm w 1 1 0 0 −1 −1 2007 2008 2009 2010 2011 2012 2013 2014 2015 Standard Deviations Standard Deviations 2 2 2 0 0 −2 −2 2007 2008 2009 2010 2011 2012 2013 2014 2015 FRBNY DSGE Group, Research and Statistics Page 41 of 62 24 Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 Figure 13: Anticipated Shock Histories Ant 2 0.1 0.1 0 0 −0.1 Percent Percent Ant 1 0.1 0.1 0 0 −0.1 −0.1 −0.1 2007 2008 2009 2010 2011 2012 2013 2014 2015 2007 2008 2009 2010 2011 2012 2013 2014 2015 Ant 3 Ant 4 0.05 0 0 −0.05 −0.05 −0.1 −0.1 0 0 −0.05 −0.05 −0.1 −0.1 2007 2008 2009 2010 2011 2012 2013 2014 2015 2007 2008 2009 2010 2011 2012 2013 2014 2015 Ant 5 Ant 6 0.05 0.05 0 −0.05 −0.05 −0.1 −0.1 2007 2008 2009 2010 2011 2012 2013 2014 2015 Percent 0 Percent 0.05 0.05 Percent Percent 0.05 0 0 −0.05 −0.05 −0.1 −0.1 2007 2008 2009 2010 2011 2012 2013 2014 2015 FRBNY DSGE Group, Research and Statistics Page 42 of 62 25 Authorized for public release by the FOMC Secretariat on 1/8/2021 FRBNY DSGE Model: Research Directors Draft June 05, 2015 References Bernanke, B. S., M. Gertler, and S. Gilchrist (1999): “The Financial Accelerator in a Quantitative Business Cycle Framework,” in Handbook of Macroeconomics, ed. by J. B. Taylor and M. Woodford, Amsterdam: North-Holland, vol. 1C, chap. 21, 1341–93. Campbell, J. R., J. D. Fisher, and A. Justiniano (2012): “Monetary Policy Forward Guidance and the Business Cycle,” Federal Reserve Bank of Chicago Working Paper. Christiano, L. J., M. Eichenbaum, and C. L. Evans (2005): “Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy,” Journal of Political Economy, 113, 1–45. Christiano, L. J., R. Motto, and M. Rostagno (2014): “Risk Shocks,” American Economic Review, 104, 27–65. Del Negro, M., M. P. Giannoni, and F. Schorfheide (2015): “Inflation in the Great Recession and New Keynesian Models,” American Economic Journal: Macroeconomics, 7, 168–196. Del Negro, M., R. B. Hasegawa, and F. Schorfheide (2014): “Dynamic Prediction Pools: An Investigation of Financial Frictions and Forecasting Performance,” NBER Working Paper 20575. Del Negro, M. and F. Schorfheide (2012): “DSGE Model-Based Forecasting,” FRBNY Working Paper. Laseen, S. and L. E. Svensson (2011): “Anticipated Alternative Policy-Rate Paths in Policy Simulations,” International Journal of Central Banking, 7, 1–35. Smets, F. and R. Wouters (2007): “Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach,” American Economic Review, 97, 586 – 606. FRBNY DSGE Group, Research and Statistics Page 43 of 62 26 Authorized for public release by the FOMC Secretariat on 1/8/2021 Detailed Philadelphia (PRISM) Forecast Overview June 2015 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 3.7 percent in mid-2017. Core PCE inflation is projected to be contained at below 2 percent through 2017. For this forecast round, we have implemented the assumption that the forecasted federal funds rate is pinned down by current futures market projections through 2015Q3. The funds rate is unconstrained beginning in 2015Q4, and rises to about 0.75 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 pace of growth and low inflation that have characterized U.S. economic performance over the past few years 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 2015Q1 supplemented by a 2015Q2 nowcast based on the latest Macroeconomic Advisers forecast. For example, the model takes 2015Q2 output growth of 2 percent as given and the projection begins with 2015Q3. PRISM anticipates that growth accelerates to about 2.6 percent by the end of 2015. Output growth then rises gradually to a peak of about 3.7 percent in 2017Q2. Overall, the output growth forecast for this round is a bit weaker compared with March projection due to the weaker-than-expected GDP data for 2015Q1. 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. Page 1 of 19 Page 44 of 62 Authorized for public release by the FOMC Secretariat on 1/8/2021 The federal funds rate is constrained near the zero bound through 2015Q3. Thereafter, the model dynamics take over and the funds rate rises gradually to 2.5 percent in 2016Q4 and 3.3 percent in 2017Q4. This path is similar to the March projection. The key factors driving the projection are shown in the forecast shock decompositions (Figures 2a-2e) and the smoothed estimates of the model’s primary shocks (shown in Figure 3, where they are normalized by standard deviation). Over the last two quarters, negative shocks to TFP have been the primary factor holding back real output growth. As these shocks unwind, output growth rises with additional contributions from the unwinding of government spending, investment and labor supply shocks. 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 unwind over the projection period, consumption growth gradually accelerates from about 1.4 percent in 2015 to 3 percent at the end of 2017. The model attributes the moderate strength in investment growth (gross private domestic + durable goods consumption) to the gradual unwinding of a history of negative MEI shocks since the start of the recession (see Figures 2e and 3). Consequently, the principal shocks driving investment growth over the forecast horizon are efficiency of investment shocks with an additional boost from labor shocks. Offsetting these factors to some extent are financial shocks: the unwinding of the discount factor shocks leads to a downward pull on investment growth over the next three years. Investment growth runs at about a 3 percent pace at the end of 2015, rising to near 4 percent in 2017. 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 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). Page 2 of 19 Page 45 of 62 Authorized for public release by the FOMC Secretariat on 1/8/2021 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 slightly below 2 percent through the forecast horizon. The federal funds rate is projected to rise fairly quickly once the constraint from market expectations is removed in 2015Q4. The model attributes the low level of the funds rate to a combination of monetary policy, discount factor and MEI shock dynamics. After 2015Q3, the positive contribution from labor supply shocks is more than offset by discount factor shock dynamics, keeping the funds rate below its steady state level through 2017. 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 3 of 19 Page 46 of 62 Authorized for public release by the FOMC Secretariat on 1/8/2021 Figure 1a Real GDP Growth 10 8 6 4 2 0 -2 -4 -6 -8 -10 2008 2009 2010 2011 2012 2013 2014 Page 4 of 19 Page 47 of 62 2015 2016 2017 2018 Authorized for public release by the FOMC Secretariat on 1/8/2021 Figure 1b Core PCE Inflation 6 5 4 3 2 1 0 -1 2008 2009 2010 2011 2012 2013 2014 Page 5 of 19 Page 48 of 62 2015 2016 2017 2018 Authorized for public release by the FOMC Secretariat on 1/8/2021 Figure 1c Fed Funds Rate 8 6 4 2 0 -2 -4 2008 2009 2010 2011 2012 2013 2014 Page 6 of 19 Page 49 of 62 2015 2016 2017 2018 Authorized for public release by the FOMC Secretariat on 1/8/2021 Figure 2a Conditional Forecast percent Real GDP Growth 8 8 6 6 4 4 2 2 0 0 -2 -2 -4 -4 -6 -6 2010 2011 2012 2013 2014 2015 2016 2017 Date tech gov mei mrkp 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 7 of 19 Page 50 of 62 labor fin mpol Authorized for public release by the FOMC Secretariat on 1/8/2021 Figure 2b Conditional Forecast percent Core PCE Inflation 4 4 3 3 2 2 1 1 0 0 -1 -1 -2 -2 -3 2010 -3 2011 2012 2013 2014 2015 2016 2017 Date tech gov mei mrkp 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 19 Page 51 of 62 labor fin mpol Authorized for public release by the FOMC Secretariat on 1/8/2021 Figure 2c Conditional Forecast percent Fed Funds Rate 6 6 4 4 2 2 0 0 -2 -2 -4 -4 2010 2011 2012 2013 2014 2015 2016 2017 Date tech gov mei mrkp 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 19 Page 52 of 62 labor fin mpol Authorized for public release by the FOMC Secretariat on 1/8/2021 Figure 2d Conditional Forecast percent Real Consumption Growth 6 6 4 4 2 2 0 0 -2 -2 -4 -4 -6 -6 2010 2011 2012 2013 2014 2015 2016 2017 Date tech gov mei mrkp 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 19 Page 53 of 62 labor fin mpol Authorized for public release by the FOMC Secretariat on 1/8/2021 Figure 2e Conditional Forecast percent Real Investment Growth 30 30 20 20 10 10 0 0 -10 -20 2010 -10 -20 2011 2012 2013 2014 2015 2016 2017 Date tech gov mei mrkp 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 19 Page 54 of 62 labor fin mpol Authorized for public release by the FOMC Secretariat on 1/8/2021 Figure 3 Smoothed Shock Estimates for Conditional Forecast Model (normalized by standard deviation) labor shock discount factor shock 4 5 2 0 0 -5 -2 2005 2010 2015 2020 2005 2010 2015 2020 mei shock TFP shock 4 2 2 0 0 -2 -2 -4 2005 2010 2015 2020 2005 Page 12 of 19 Page 55 of 62 2010 2015 2020 Authorized for public release by the FOMC Secretariat on 1/8/2021 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 13 of 19 Page 56 of 62 5 10 15 Authorized for public release by the FOMC Secretariat on 1/8/2021 Impulse Response to Leisure Shock consumption growth output growth 2 2 0 0 -2 0 5 10 15 -2 0 investment growth 5 0 0 -1 -5 0 5 10 15 -2 0 0.4 0.2 0.2 0 5 10 15 5 10 15 nominal rate inflation 0.4 0 5 aggregate hours 10 15 0 0 Page 14 of 19 Page 57 of 62 5 10 15 Authorized for public release by the FOMC Secretariat on 1/8/2021 Impulse Responses to MEI Shock output growth consumption growth 2 0.2 0 0 -2 0 5 10 15 -0.2 0 investment growth 1 0 0.5 0 5 10 15 0 0 inflation 0.4 0 0.2 0 5 15 5 10 15 nominal rate 0.1 -0.1 10 aggregate hours 10 -10 5 10 15 0 0 Page 15 of 19 Page 58 of 62 5 10 15 Authorized for public release by the FOMC Secretariat on 1/8/2021 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 16 of 19 Page 59 of 62 5 10 15 Authorized for public release by the FOMC Secretariat on 1/8/2021 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 17 of 19 Page 60 of 62 5 10 15 Authorized for public release by the FOMC Secretariat on 1/8/2021 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 18 of 19 Page 61 of 62 5 10 15 Authorized for public release by the FOMC Secretariat on 1/8/2021 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 19 of 19 Page 62 of 62 5 10 15
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