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Finance and Economics Discussion Series: Data for paper 2010-29

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Documentation of the Estimated, Dynamic, Optimization-based (EDO) Model of the U.S. Economy: 2010 Version

Hess T. Chung, Michael T. Kiley, and Jean-Philippe Laforte

Figure 1: Model Overview

This figure presents a flow chart of the model's structure. In the center of the figure are monopolistically competitive intermediate goods producers (of the model's two goods, CBI and KB), who produce their goods using labor and capital input (from households and capital intermediaries, respectively) and who sell their output to final goods producers for each good. The final goods producers sell their goods to households and the intermediaries who purchase consumer durable capital, residential capital, and non-residential capital. Each of the three capital intermediaries rent their capital to either the household (durables and residential capital) or firms (non-residential capital). Finally, the central bank sets the short-term nominal interest rates, which affects all other entities in the model.

Figure 2: Impulse Responses: Federal Funds Rate

This figure presents the response of 8 variables to a 1 percent (not at an annual rate) shock to the federal funds rate over 24 quarters. Real GDP falls a bit less than 1 percent in the initial few quarters and the returns to baseline; Real consumption falls a bit less than 0.5 percent in the initial few quarters and the returns to baseline; Real durables consumption falls a bit more than 1.0 percent in the initial few quarters and the returns to baseline; Real housing investment falls a bit more than 1.0 percent in the first couple of years and slowly returns to baseline; Real (nonresidential) investment falls about 3.0 percent in the first year and slowly returns to baseline; the response of hours follows the contour of the response of GDP (with a proportionality factor of about 1.3); the federal funds rate rises about 0.8 percent initially and returns to baseline in less than two years; and inflation (on a core or overall PCE price basis) falls less than 0.05 percent in the first year and then returns to baseline.

Figure 3: Impulse Responses: Risk premium

This figure presents the response of 8 variables to a 1 percent (not at an annual rate) shock to the risk premium. Real GDP falls about 1.5 percent in the initial few quarters and the returns to baseline after about three years; Real consumption falls a bit less than 0.8 percent in the initial few quarters and the returns to baseline in about three years; Real durables consumption falls a bit less than 2.0 percent in the initial few quarters and the returns to baseline in about three years; Real housing investment falls about 2.0 percent in the first several years and slowly returns to baseline; Real (nonresidential) investment falls about 5.0 percent in the first year and returns to baseline after about three years; the response of hours follows the contour of the response of GDP (with a proportionality factor of about 1.3); the federal funds rate falls about 0.4 percent in the first year and returns to baseline in about three years; and inflation (on a core or overall PCE price basis) falls about 0.1 percent in the first year and then returns to baseline.

Figure 4: Impulse Responses: Housing risk premium

This figure presents the response of 8 variables to a 1 percent (not at an annual rate) shock to the housing risk premium. Real GDP falls slowly to about 0.2 percent below baseline after two years and the returns to baseline slowly; Real consumption increases about 0.5 percent above baseline over two years and the returns to baseline slowly; Real durables consumption increases about 1.5 percent above baseline over two years and the returns to baseline slowly; Real housing investment falls about 8.0 percent in the first two years and slowly returns to baseline; Real (nonresidential) investment increases about 1.5 percent above baseline over two years and the returns to baseline slowly; the response of hours follows the contour of the response of GDP (with a proportionality factor of about 1.3); the federal funds rate falls less than 0.1 percent over the 6 years shown; and inflation (on a core or overall PCE price basis) falls less than 0.05 percent over the 6 years shown.

Figure 5: Impulse Responses: Durables risk premium

This figure presents the response of 8 variables to a 1 percent (not at an annual rate) shock to the durables risk premium. All 7 variables other than durables consumption (Real GDP, Real consumption, Real housing investment, Real nonresidential investment, hours, the federal funds rate, and inflation) respond by very small amounts. Real durables consumption falls about 1/4 percent initially and quickly returns to baseline.

Figure 6: Impulse Responses: Capital risk premium

This figure presents the response of 8 variables to a 1 percent (not at an annual rate) shock to the capital (nonresidential) risk premium. Real GDP falls about 1.0 percent in the initial few quarters and the returns to baseline after about three years; Real consumption increases about 0.8 percent in the initial few quarters and the returns to baseline in about three years; Real durables consumption increases a bit more than 2.0 percent in the initial few quarters and the returns to baseline in about three years; Real housing investment rises about 2.0 percent in the first several years and slowly returns to baseline; Real (nonresidential) investment falls about 10.0 percent in the first year and returns to baseline after about three years; the response of hours follows the contour of the response of GDP (with a proportionality factor of about 1.3); the federal funds rate falls a bit more than 0.1 percent in the first year and returns to baseline in about three years; and inflation (on a core or overall PCE price basis) increases about 0.05 percent in the first year and then returns to baseline.

Figure 7: Impulse Responses: Exogenous Demand

This figure presents the response of 8 variables to a 1 percent (not at an annual rate) shock to exogenous demand. Real GDP increases about 0.15 percent (less than the share of exogenous demand in overall demand, 0.2, indicating a multiplier below 1). The responses of the other 7 variables are relatively muted (that is, responses for Real consumption, Real durables consumption, Real nonresidential investment, hours, the federal funds rate, and inflation).

Figure 8: Impulse Responses: Non-Investment Price Markup

This figure presents the response of 8 variables to a 1 percent (not at an annual rate) shock to the non-investment price markup. Real GDP falls about 0.1 percent in the initial few quarters and the returns to baseline after about three years; Real consumption falls about 0.15 percent in the initial few quarters and the returns to baseline in about three years; Real durables consumption increases a bit more than 0.2 percent in the initial two years and the returns to baseline in about three years; Real housing investment falls about 0.5 percent in the first several years and slowly returns to baseline; Real (nonresidential) investment rises about 0.5 percent over the first two years and returns to baseline thereafter; the response of hours follows the contour of the response of GDP (with a proportionality factor of about 1.3); the federal funds rate rises a bit more than 0.1 percent in the first year and returns to baseline in about three years; and inflation (on a core or overall PCE price basis) increases about 0.25 percent initially and then returns to baseline.

Figure 9: Impulse Responses: Investment Price Markup

This figure presents the response of 8 variables to a 1 percent (not at an annual rate) shock to the investment price markup. Real GDP falls about 0.1 percent in the initial few quarters and the returns to baseline after about three years; Real consumption rises about 0.08 percent in the initial few quarters and the returns to baseline in about three years; Real durables consumption falls about 0.4 percent in the initial two years and the returns to baseline in about three years; Real housing investment rises about 0.25 percent in the first several years and slowly returns to baseline; Real (nonresidential) investment falls about 0.8 percent over the first year and returns to baseline thereafter; the response of hours follows the contour of the response of GDP (with a proportionality factor of about 1.3); the federal funds rate rises a bit more than 0.1 percent in the first year and returns to baseline in about three years; and inflation (on a core or overall PCE price basis) increases about 0.04 percent initially and then returns to baseline.

Figure 10: Impulse Responses: Wage markup

This figure presents the response of 8 variables to a 1 percent (not at an annual rate) shock to the wage markup. All 8 variables (Real GDP, Real consumption, Real durables consumption, Real housing investment, Real nonresidential investment, hours, the federal funds rate, and inflation) respond by very small amounts (less than about 0.1 percent).

Figure 11: Impulse Responses: Capital Goods Technology

This figure presents the response of 8 variables to a 1 percent (not at an annual rate) shock to the capital goods technology. Real GDP increases about 0.4 percent on impact and rises further to about 0.55 percent above baseline permanently; Real consumption increases about 0.1 percent on impact and rises further to about 0.2 percent above baseline by the end of six years; Real durables consumption increases about 0.9 percent on impact and further to more than 1 percent by the end of six years; Real housing investment rises about 0.3 percent on impact and slowly thereafter; Real (nonresidential) investment rises about 0.8 percent on impact and by 1.4 percent after three years; the response of hours is muted, at about 0.1 percent on impact and peaking at about 0.15 percent; the federal funds rate falls a very small amount; and inflation (on a core or overall PCE price basis) falls a very small amount.

Figure 12: Impulse Responses: Overall TFP

This figure presents the response of 8 variables to a 1 percent (not at an annual rate) shock to overall total factor productivity (TFP). Real GDP increases about 0.8 percent on impact and rises further to about 1.2 percent above baseline after six years; Real consumption increases about 0.3 percent on impact and rises further to about 0.8 percent above baseline by the end of six years; Real durables consumption increases about 1.2 percent on impact and further to more than 1.4 percent above baseline after one year, and then slowly falls to around 1 percent above baseline; Real housing investment rises about 1.2 percent on impact and slowly thereafter, remaining nearly 3 percent above baseline after six years; Real (nonresidential) investment rises about 1.5 percent on impact and by nearly 2.5 percent after two years; the response of hours is muted, at about 0.1 percent on impact and peaking at about 0.4 percent at about two years; the federal funds rate falls about 0.1 percent in the first year; and inflation (on a core or overall PCE price basis) falls about 0.1 percent in the first year.

Figure 13: Smoothed Observables and Data

This figure presents the data (blue line) and smoothed model observables (black line, which equal the data minus the model's estimated measurement error for that data) along with confidence intervals for the smoothed observables over the period 1984Q$ to 2008Q4; in each case the data have had their means or trends removed. Real GDP growth follows its familiar path, with declines in the recessions of the early 1990s, early 2000s, and in 2008; the smoothed observable largely follows the same path. Real nondurables consumption growth follows a path similar to that of GDP but with lower volatility; the smoothed observable largely follows the same path. Real nonresidential investment growth is volatile and showed an especially large decline around the early 2000s recession; the smoothed observable largely follows the same path. Real durables consumption growth is volatile, with its most pronounced decline over this sample in 2008; the smoothed observable largely follows the same path. Real housing investment declined strongly in the early 1990s and after 2005; the smoothed observable largely follows the same path. The growth of the real wage is volatile with no clear cyclical pattern; the smoothed observable largely follows the same path. Aggregate hours (per capita, detrended) peaks before each recession and falls during the recessions and for awhile after the recessions. PCE inflation is much more volatile than its smoothed observable, reflecting the absence of food and energy prices from the model. Core PCE inflation is higher through the early 1990s (that is above zero, which corresponds to above 2 percent at an annual rate, as that is the model's steady-state rate of inflation); the smoothed observable largely follows the same path. Finally, investment good inflation (that is, inflation in the PCE durables price index) looks similar to the core PCE inflation measure; the smoothed observable largely follows the same path.

Figure 14: Innovations to Exogenous Processes

This figure presents the innovations to the exogenous processes in the model (risk premium, exogenous demand, wage markup, funds rate shock, capital goods technology, overall TFP, non-investment price markup, investment price markup, housing risk premium, durables risk premium, capital risk premium) . All of these innovations should be independently and identically distributed; as a result, there should not be evident patterns in the innovations. For the most part this is true, with the innovations looking likely random paths.

Figure 15: Exogenous Drivers

This figure presents the exogenous drivers in the model. All of these are AR(1) processes and hence could have interesting cyclical properties. The risk premium rises sharply during each recession; exogenous demand is very strong in the early 1990s and weak from 2003 to 2006; the housing risk premium rose sharply after 2004; the durables risk premium is volatile and random; the capital risk premium rose after 2000 and remained high after that point.

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