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Materiale didattico per il corso di Econometria per la politica economia del prof. Roberto Golinelli. Trattasi di slides in lingua inglese a cura del docente, all'interno delle quali sono affrontati i seguenti argomenti: il modello statistico, le previsioni e l'informazione; previsione e disaggregazione;... Vedi di più

Esame di Econometria per la politica economica docente Prof. R. Golinelli

Anteprima

ESTRATTO DOCUMENTO

Forecasting and disaggregation

• The level of y functional disaggregation relates

t

the variable of interest with the variables on

which it is based (i.e. its components).

• Instead of an univariate model for y , we can use

t

a set of different models for disaggregate

forecasts; then aggregation of the components.

• Examples: demand components (or supply GDP

models). Sectors to forecast IPI. Geographic area:

single-country (region) vs area-wide models.

• Question: disaggregation provides more

information or only noise? No general theorems,

the choices are specific: it is empirical issue.

• Examples: Baffigi et al (2004), Golinelli&Pastorello (2002).

5

The two main statistical competitors

• In more complex indicator (statistical) models, y

t

data information is augmented by other time

series P , available up to t: I = ( y ; P ).

t t t t

• If P includes few indicators pre-selected by the

t

practitioner on the basis of her skills and

experience, we have the Selected indicator Model

(SM) or the Bridge Model (BM).

• If P is very large (including up to 100-200

t

indicators) we have alternative Factor based

Models (FM). In this case we define P = X .

t t 6 3

Bridge (selected-indicator) models

• BM deliver early forecasts by using the information of few

timely indicators through linear dynamic equations, where

the target (e.g. GDP) or its components are explained by

suitable short term indicators, selected on the basis of

researchers experience and statistical testing procedures.

• BM for GDP can be seen as tools to ‘translate’ the noisy and

timely information of short-term indicators into the more

coherent and complete ‘language’ of NA. Since indicators

cover a wide range of short run macroeconomic phenomena,

they can be used in different bridge equations for the main

GDP components (namely, C, G, I, S, X and M, ‘demand-

side’ BM where GDP is predicted by the NA income–

expenditure identity), or directly at aggregate GDP level

(‘supply-side’ BM, where GDP is forecast by a single bridge

equation).

• IPI is GDP main (coincident) indicator in supply side BM.

7

Forecasting GDP with BM & auxiliary models

• The following cases mimic as close as possible the actual activity

of forecasting. Since one-quarter ahead GDP forecasts with BM

require the knowledge of the conditioning indicator data for that

quarter, we suggest four alternative cases, depending on monthly

data availability (T is the last quarter of the estimation sample):

• (1) The pure one-step ahead forecast: one-quarter ahead (T+1)

GDP forecast when all the conditioning indicators are unknown. In

this case such indicators have to be forecast three-months ahead by

an auxiliary model.

• (2) Forecast with one month known: one-quarter ahead GDP

forecast when the conditioning indicators are known only for the

first month of the quarter T+1 (in this case indicators have to be

forecast two-months ahead by an auxiliary model).

• (3) Forecast with two months known: one-quarter ahead GDP

forecast when the conditioning indicators are known for two

months of the quarter T+1 (in this case indicators have to be

forecast one-month ahead by an auxiliary model).

• (4) Forecast with all months known (nowcast): one-quarter ahead

GDP forecast when the conditioning indicators for the quarter T+1

8

are fully known (in this case, the auxiliary models are not used). 4

Factor based models

Factor analysis and principal components analysis (PCA) are

two longstanding methods for summarizing the main sources

of variation and covariation among N variables in X:

The relationship describes the N×1 vector X using a k×1

t

and an error term e .

vector of unobserved factors F

t t

Empirical content is given to this relation by assuming that

k is much smaller than N and the elements of e are only

t

weakly correlated; this implies that covariances between

the (many) elements of X are explained, in large part, by

t

the (few) factors in F . A single variable in X is predicted

t t

with the ad hoc equation: 9

The equation above describes the forecast h-steps ahead

using the factors, autoregressive lags, and an forecast error

u . Because X does not enter this equation directly, the

t+h t

elements of X are useful for predicting Y only because they

t

contain information about F . This equation is a factor-

t

augmented autoregression (FAAR).

With FM forecasts of the target are computed through the

first k principal components of the N indicators in the large

data set of indicators (N>>k). The main advantage of this

approach is to exploit not only the information content of

the single variables but their covariance as well, without

incurring in the “curse of dimensionality” as in unrestricted

vector autoregressive models. Problem: the composition of

the indicators sample. 10 5

The ragged edge problem with FM

• Issue: incomplete data on current and immediate past

values of indicators are available because they are

released at different times within the period t to t+1.

• What strategy to deal with non-synchronous data

releases?

1. Shifting operator: all indicators with missing

observations for the latest period are shifted in time so

as to have a balanced panel.

2. Forecasting the missing observations with

autoregressive (AR) models

3. Use the EM algorithm which not only guarantees a

coherent solution to the jagged edge issue, but also

provides forecasts of missing observations that are

efficient (they exploit all available information) and

consistent with the factor estimates. 11

Discussion

The BM-FM alternative to the use of AR models

represents a good example of the trade-off

simple/complex models depicted in previous lecture.

If the increase of information (because of the exploitation

of additional predictors) is effective, we expect an

improvement of the forecasting ability of both BM and

FM over the simple AR model.

Since the AR model is nested in the BM, the comparison

can be made both in- and out-of-sample. Given that the

same is not always true for AR vs FM comparison, we

can only rely on out-of-sample comparisons.

BM can tell the story of the forecasts, FM does not. More

discussion and comparisons in Bulligan-Golinelli-Parigi.

12 6

Forecasting with real-time data

• Forecasting literature often compares the performance of

competing models through pseudo out-of-sample forecasting

exercises with the latest available data rather than the real-

time data actually at the forecaster’s command (main

reference: Croushore & Stark works).

• A real-time data-set – i.e. a collection of data vintages that

gives the modeler a snapshot of the macroeconomic data

available at any given date in the past – makes it possible to

take into account the revision process applied by statistical

institutes after the first published data.

• For example, the preliminary GDP estimate of the same

quarter is updated until, after a number of both statistical and

definitional changes, all relevant information is incorporated

and a stable measure is reached: the “actual” or final GDP

estimate for that quarter. Thus, data revisions imply two

possible alternative targets in prediction: (i) the first release

or (ii) the final GDP data. 13

A sketch of real-time data

• The problem of data revisions: we can use preliminary

(e.g. only the 1st releases) or final data if e.g. our

forecast purpose is in the field of financial markets

(reacting to preliminary data publication), or of

driving policy maker decisions respectively.

• Statistical agencies usually revise their preliminar data

as new information is available because of:

1. statistical revisions (new information)

2. definitional (benchmark) revisions (base, account…)

• Until, after a number of revisions, all relevant

information is incorporated and a stable measure is

of that period .

reached (?): the “actual” or final data 14 7

vintage, v

1 2 3 4 f

period, t T+1 1 T+2 2 T+3 3 T+4 4 T+f f

y y y y .... y

1 1 1 1 1 1

T 1 T+1 2 T+2 3 T+3 4 T+f-1 f

2 y y y y .... y

2 2 2 2 2

T-1 1 T 2 T+1 3 T+2 4 T+f-2 f

3 y y y y .... y

3 3 3 3 3

T-2 1 T-1 2 T 3 T+1 4 T+f-3 f

4 y y y y .... y

4 4 4 4 4

.... .... .... .... .... .... ....

3 1 4 2 5 3 6 4 f+2 f

T-1 y y y y .... y

T-1 T-1 T-1 T-1 T-1

2 1 3 2 4 3 5 4 f+1 f

T y y y y .... y

T T T T T

1 1 2 2 3 3 4 4 f f

T+1 y y y y .... y

T+1 T+1 T+1 T+1 T+1

1 2 2 3 3 4 f-1 f

T+2 n.a. y y y .... y

T+2 T+2 T+2 T+2

1 3 2 4 f-2 f

T+3 n.a. n.a. y y .... y

T+3 T+3 T+3

1 4 f-3 f

T+4 n.a. n.a. n.a. y .... y

T+4 T+4

.... .... .... .... .... .... ....

st

1 release 1 f

T+f n.a. n.a. n.a. n.a. .... y T+f

nd

2 vintage Latest available

vintage 15

A real-time data-set

Alternative data to forecast

v

Vintage y series represent the state-of-art at the time of

publication. Observations are homogeneous over t (but

not in quality: old data are better than recent ones)

v

y growth rate calculation is straightforward:

×

o v o v o’ v

dy = 100 ( y / y – 1)

t t t-1

o

Release y series includes data revised for the same

number of times which come from different vintages;

observations are not homogeneous over t (but they are

in quality)

o o v

y growth rates need collecting dy (growth-within)

t

→ What is the effect of data revisions on the simulated

models predicting ability? 16 8


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DESCRIZIONE DISPENSA

Materiale didattico per il corso di Econometria per la politica economia del prof. Roberto Golinelli. Trattasi di slides in lingua inglese a cura del docente, all'interno delle quali sono affrontati i seguenti argomenti: il modello statistico, le previsioni e l'informazione; previsione e disaggregazione; modelli factor based; il test di Giacomini e White; il test di razionalità.


DETTAGLI
Corso di laurea: Corso di laurea magistrale in politica amministrazione e organizzazione
SSD:
Università: Bologna - Unibo
A.A.: 2011-2012

I contenuti di questa pagina costituiscono rielaborazioni personali del Publisher Atreyu di informazioni apprese con la frequenza delle lezioni di Econometria per la politica economica e studio autonomo di eventuali libri di riferimento in preparazione dell'esame finale o della tesi. Non devono intendersi come materiale ufficiale dell'università Bologna - Unibo o del prof Golinelli Roberto.

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