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“Path Forecast Evaluation” (with Massimiliano Marcellino)
Abstract
A path forecast refers to
the sequence of forecasts 1 to H periods into the future. A summary of the
range of possible paths the predicted variable may follow for a given
confidence level requires construction of simultaneous confidence regions
that adjust for any covariance between the elements of the path forecast.
This paper shows how to construct such regions with the joint predictive
density and Scheffé's (1953) S-method. In addition, the joint predictive
density can be used to construct simple statistics to evaluate the local internal
consistency of a forecasting exercise of a system of variables. Monte Carlo
simulations demonstrate that these simultaneous confidence regions provide
approximately correct coverage in situations where traditional error bands,
based on the collection of marginal predictive densities for each horizon,
are vastly off mark. The paper showcases these methods with an application to
the most recent monetary episode of interest rate hikes in the U.S.
macroeconomy.
GAUSS Code:
o
VAR/Direct Forecast
Marginal, Bonferroni and Scheffe Bands based on Stock and Watson’s (2001)
VAR. These
files should be easy to adapt for different applications. [JAE_SW.zip]
o
Stock and Watson
(2001) VAR Monte Carlos (Tables 1 and 2 in the paper). [JAE_MC_SW.zip]
o
AR(1) Monte Carlo
files (Table 3). [JAE_MC_AR.zip]
o
Files that generate
figures 4 and 5 (direct forecast empirical application and counterfactual
simulation). [JAE_FIGS.zip]
Abstract
Inference about an impulse
response is a multiple testing problem with serially correlated coefficient
estimates. This paper provides a method to construct simultaneous confidence
regions for impulse responses to evaluate uncertainty about the shape of the
impulse response; and conditional bands to examine individual significance
levels of impulse response coefficients given propagation trajectories. The
paper also shows how to constrain a subset of impulse response paths to
anchor structural identification of the system; and how to formally test for
the validity of such identifying constraints. Simulation and empirical
evidence illustrate the new techniques. A broad summary of asymptotic results
and simple formulas for a impulse response estimators based on VARs and local
projections are provided to make the methods easily implementable with
commonly available statistical software.
Gauss Code
The code contained in the folder replicates the
figures in the paper. However, I have modified the code slightly from what is
prescribed in the paper to incorporate a refinement due to Holm (1979) that I
used in my “Path Forecast Evaluation” paper with
Massimiliano Marcellino. The figures will look slightly different than in the
paper but the benefit is that if you adapt the code to your own application;
you will have a more up-to-date procedure. [irs_se.zip]
Abstract
A covariance-stationary
vector of variables has a Wold representation whose coefficients can be
semiparametrically estimated by local projections (Jordà, 2005). Substituting
the Wold representations for variables in model expressions generates
restrictions that can be used by the method of minimum distance to estimate
model parameters. We call this estimator projection minimum distance (PMD)
and show that its parameter estimates are consistent and asymptotically
normal. In many cases, PMD is asymptotically equivalent to maximum likelihood
estimation (MLE) and nests GMM as a special case. In fact, models whose ML
estimation would require numerical outines (such as VARMA models) can often
be estimated by simple least-squares routines and almost as efficiently by
PMD. Because PMD imposes no constraints on the dynamics of the system, it is
often consistent in many situations where alternative estimators would be
inconsistent. We provide several Monte Carlo experiments and an empirical
application in support of the new techniques introduced.
Note: GAUSS code for all the procedures in the
paper available by e-mailing
me.
Formerly "Model-Free
Impulse Responses"
Abstract
This paper introduces methods to compute impulse
responses without specification and estimation of the underlying multivariate
dynamic system. The central idea consists in estimating local projections at
each period of interest rather than extrapolating into increasingly distant
horizons from a given model, as it is done with vector autoregressions (VAR).
The advantages of local projections are numerous: (1) they can be estimated
by simple regression techniques with standard regression packages; (2) they
are more robust to misspecification; (3) joint or point-wise analytic
inference is simple; and (4) they easily accommodate experimentation with
highly non-linear and flexible specifications that may be impractical in a
multivariate context. Therefore, these methods are a natural alternative to
estimating impulse responses from VARs. Monte Carlo evidence and an
application to a simple, closed-economy, new-Keynesian model clarify these
numerous advantages.
Abstract
This paper investigates the effects of temporal
aggregation when the aggregation frequency is variable and possibly
stochastic. The results that we report include, as a particular case, the
well-known results on fixed-interval aggregation, such as when monthly data
is aggregated into quarters. A variable aggregation frequency implies that
the aggregated process will exhibit time-varying parameters and non-spherical
disturbances, even when these characteristics are absent from the original
model. Consequently, we develop methods for specification and estimation of
the aggregate models and show with an example how these methods perform in
practice.
Abstract
This
paper contains three useful contributions: (1) it collects a new data-set of
electronic transaction data on soybean futures from the Dalian Futures
Exchange in China that records, not only the usual elements of each
transaction (such as price and size) but also identifies broker and customer
identities, variables not usually obtainable; (2) it presents new econometric
methods for the analysis of dynamic multivariate count data based on the
autoregressive conditional intensity model of Jordà and Marcellino (2000);
and (3) together, the new data and econometric methods allow us to
investigate, in a manner not available before, the determinants and effects
of non-institutional market making (or scalping).
Abstract
This paper shows that greater uncertainty about
monetary policy can lead to a decline in nominal interest rates. In the
context of a limited participation model, monetary policy uncertainty is
modeled as a mean-preserving spread in the distribution for the money growth
process. This increase in uncertainty lowers the yield on short-term maturity
bonds because the household sector responds by increasing liquidity in the
banking sector. Long-term maturity bonds also have lower yields but this
decrease is a result of the effect that greater uncertainty has on the
nominal intertemporal rate of substitution -- which is a convex function of
money growth. We examine the nature of these relations empirically by
introducing the GARCH-SVAR model -- a multivariate generalization of the
GARCH-M model. The predictions of the model are broadly supported by the
data: higher uncertainty in the federal funds rate can lower the yields of
the three- and six-month treasury bill rates.
Abstract
This paper investigates the ability of the Federal Reserve to
manipulate the overnight rate without open market operations (which Demiralp
and Jorda (2000) term the announcement effect), using high-frequency,
open-market-desk data. Using similar data, Hamilton (1997) takes advantage of
forecast errors in the Treasury balance to compute the elasticity of the
federal funds rate to these errors and thus to obtain a measure of the liquidity
effect. Similarly, one can view daily deviations of the federal funds
rate from target as forecast errors in the reserve need (see Taylor, 2000).
By analyzing the manner and the type of operation the Fed uses to maintain
the federal funds rate close to its targeted value and by observing the
pattern of operations on the days surrounding a change in this target, we
provide evidence of the announcement effect. An integral part of the analysis
requires that we provide forecasts of market expectations on future target
changes. We do this in two ways, using federal funds futures data as in
Kuttner (2000) and with the autoregressive conditional hazard model proposed
by Hamilton and Jordá (2000).
e-mail me if you would
like a copy of an alternative set of GAUSS code to estimate ACH models with
the specification in this paper.
Abstract
This paper measures the degree of monetary
policy interdependence between major industrialized countries from a new
perspective. The analysis uses a special data set on central bank issued
policy rate targets for 14 OECD countries. Methodologically, our approach is
novel in that we separately examine monetary interdependence due to (1) the
coincidence in time of when policy actions are executed from (2) the nature
and magnitude of the policy adjustments made. The first of these elements
requires that the timing of events be modeled with a dynamic discrete
duration design. The discrete nature of the policy rate adjustment process
that characterizes the second element is captured with an ordered response
model. The results indicate there is significant policy interdependence among
these 14 countries during the 1980-1998 sample period. This is especially
true for a number of European countries which appeared to respond to German
policy during our sample period. A number of other countries appeared to
respond to U.S. policy, though this number is smaller than that suggested in
preceding studies. Moreover, the policy harmonization we find appears to work
through channels other than formal coordination agreements.
The 1970s and early 1980s witnessed two main approaches to the
analysis of monetary policy. The first is the early new classical
approach of Lucas, based on the assumptions of rational expectations and
market clearing. The second is the atheoretical econometrics of Sims's
VAR program. Both have developed: the new classical approach has
been enriched through various accounts of price stickiness, cost of
adjustment or alternative expectational schemes; the original VAR program has
developed into the structural VAR program. This paper clarifies the
relationship between these two programs. Based on work of Cochrane
(1998), it shows that the typical method of evaluating unanticipated,
unsystematic monetary policy is correct only if the conditions necessary for
Lucas's policy-ineffectiveness proposition hold, while recent methods for
evaluating systematic monetary policy violate Lucas's policy-noninvariance
proposition ("the Lucas critique"). The paper shows how to
construct and estimate (using regime changes) a model in which some agents
form rational-expectations and others follow rules of thumb. In such a
model, monetary policy actions can be validly decomposed into systematic and
unsystematic components and valid counterfactual experiments on alternative
systematic monetary-policy rules can be evaluated.
Abstract
The traditional view of the monetary transmission mechanism
rests on the premise that the Federal Reserve (Fed) controls the level of the
Federal funds rate via open market operations and the liquidity effect. By
contrast, this paper argues that the Fed also manipulates the Federal funds
rate via public disclosures of the new level of the Federal funds rate target
and the "announcement effect.'' We define the announcement effect as the
portion of interest rate movements associated with public statements on interest
rate targets that do not require conventional open market operations for
their support. This paper provides evidence on how the Fed uses the liquidity
effect in conjunction with the announcement effect to execute monetary
policy. In addition, it investigates the implications of the announcement
effect on term structure behavior and the rational expectations hypothesis.
This paper is a general investigation of temporal aggregation in time series
analysis. It encompasses traditional research on time aggregation as a
particular case and extends the analysis to irregular intervals of
aggregation. The Data Generating Process is allowed to evolve at regular,
deterministic-irregular or even stochastic intervals of time (operational
time). The time scale of this process is then transformed to generate the
observational time process. This transformation can be deterministic (such as
the familiar aggregation of monthly data into quarters) or more generally,
stochastic (such as aggregating stock market quotes by the hour). In general,
the observational time model exhibits persistence, time-varying parameters
and non-spherical disturbances. Consequently, we review detection,
specification, estimation and structural inference in this context, provide
new solutions to these issues, and apply our results to high frequency, FX
data.
Data and programs used in the paper
Abstract
This paper is a statistical analysis of the
manner in which the Federal Reserve determines the level of the Federal funds
rate target, one of the most publicized and anticipated economic indicators
in the financial world. The analysis presents two econometric challenges:(1)
changes in the target are irregularly spaced in time; (2) the target is
changed in discrete increments of 25 basis points. The contributions of this
paper are: (1) to give a detailed account of the changing role of the target
in the conduct of monetary policy; (2) to develop new econometric tools for
analyzing time-series duration data; (3) to analyze empirically the
determinants of the target. The paper introduces a new class of models termed
autoregressive conditional hazard processes, which allow one to produce
dynamic forecasts of the probability of a target change. Conditional on a
target change, an ordered probit model produces predictions on the magnitude
by which the Fed will raise or lower the Federal funds rate. By decomposing
Federal funds rate innovations into target changes and nonchanges, we arrive
at new estimates of the effects of a monetary policy "shock.’’
Abstract
How is econometric analysis (of partial
adjustment models) affected by the fact that, while data collection is done
at regular, fixed intervals of time, economic decisions are made at random
intervals of time? This paper addresses this question by modeling the
economic decision making-process as a general point process. Under random-time
aggregation: (1) inference on the speed of adjustment is biased -
adjustments are a function of the intensity of the point process and
the proportion of adjustment; (2) inference on the correlation with exogenous
variables is generally downward biased; and (3) a non-constant intensity of
the point process gives rise to a general class of regime dependent time
series models. An empirical application to test the
production-smoothing-buffer-stock model of inventory behavior illustrates, in
practice, the effects of random-time aggregation.
Abstract
This paper extends previous work in Escribano
and Jorda (1997) and introduces new LM specification procedures to choose
between Logistic and Exponential Smooth Transition Regression (STR) Models.
These procedures are simpler, consistent and more powerful than those
previously available in the literature. An analysis of the properties of
Taylor approximations around the transition function of STR models permits
one to understand why these procedures work better and it suggests ways to
improve tests of the null hypothesis of linearity versus the alternative of
STR-type nonlinearity. Monte-Carlo experiments illustrate the performance of
the different tests introduced. The new procedures are then implemented on a
study of the dynamics of the U.S. unemployment rate.
Abstract
A new LM specification procedure to choose
between Logistic and Exponential Smooth Transition Autoregressive (STAR)
models is introduced. This procedure has better consistency and power
properties than that previously available in the literature. Monte-Carlo
simulations and empirical evidence are provided in support of our claims.
Shorter Papers
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Do
Monetary Aggregates Help Forecast Inflation? Economic Letter, Federal Reserve
Bank of San Francisco, 2007-10
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Comments
by Reuters
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Comments by Dow
Jones Newswires
Abstract
The timing and frequency of many economic events
(the economic time scale) is endogenous to the economic problem that
generates these events and may vary from one event to the next. By contrast,
data collection is done at regular, fixed intervals of calendar time (the
observational time scale). This essay discusses some of the empirical issues
that arise when the economic time scale differs from the observational time
scale. Unlike traditional time aggregation however, the intervals of time
separating economic events are not a fixed constant (say one month). Rather,
they are probably best described as random variables. An example based on
high frequency financial data analyzed at half-hourly intervals illustrates
the major points that arise when economic time evolves stochastically.
A short article prepared for Situación, Banco Bilbao-Vizcaya
Note: Figure captions in Spanish.
Working Papers are in Adobe PDF format. 
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