Yankun Wang Cornell University Oct 2009 What is VAR A var p model is with and Originally proposed by Sims 1980 Efficient way of summarizing information contained in the data ID: 276565
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Slide1
VAR Models
Yankun
Wang, Cornell University, Oct 2009Slide2
What is VAR?
A
var
(p) model is: with andOriginally proposed by Sims (1980)Efficient way of summarizing information contained in the dataUseful for forecastingConduct economically interesting analysis under meaningful identification restrictionsSlide3
Outline:
Reduced form VAR
Wold
TheoremSpecificationEstimationPresentation of ResultsStructural VAR
IdentificationPotential extension to “Evaluation of Currency Regimes: the Unique Role of Sudden Stops”by
Assaf Razin and Yona RubinsteinSlide4
The Wold
Theorem
Wold
Theorem: Every stationary process can be written as the sum of two components: a deterministic part and an MA(∞) part.As a result:
Every stationary process can be written as a VAR process of infinite order. Potential Problem:
In reality, we can only deal with finite order. Slide5
Specification
What is the appropriate lag length in the VAR?
Three criterions:
Akaike information criterion (AIC)Schwarz criterion (SIC)Hannan-Quinn criterion (HQC)
( all functions of m, T, and variance-covariance matrix)In practice: Fix an upper bound of lag length q (12), choose the q which minimizes one of the information criterionAIC is inconsistent
For T>20, SIC and HQC will always choose smaller models than AICSlide6
Estimation
Multivariate GLS estimates are the same as equation by equation OLS estimates.
For unrestricted VAR models: ML estimates and equation by equation OLS estimates coincide.
When a VAR is estimated under some restrictions, ML estimates are different from OLS estimates; ML estimates are consistent and efficient if the restrictions are true. Slide7
Presentation of Results
It is rare to report estimated VAR coefficients.
Instead:
Impulse responsesForecast error variance decomposition: assess the relative contribution of different shocks to fluctuations in varablesHistorical Decomposition: given the path of one specific shock, how will the variables evolve?Slide8
Structural VARs
Suppose we have estimated the following reduced form VAR:
with .
! : u is just reduced form residuals, no economic meaning.Solution: Assume , where is the vector of fundamental shocks, then naturally:Lack m(m-1)/2 restrictions to exactly identify D. Slide9
Short-Run Timing Restrictions
Example: Suppose m=3: output, inflation and interest rate:
Criticism: hard to justify from theoretical foundations
In practice: try to switch the ordering the variablesSlide10
Long-run Impact Restrictions
Classical example: Blanchard and
Quah
( 1989)Suppose two variable system: output growth and unemploymentTotal long run impact matrix: Assume: accumulated long-run effect of demand shocks on is zero, Slide11
Sign Restrictions
Restricting the sign (and/or shape) of structural responses.
Faust (1998), Canova and De
Nicolo (2002) and Uhlig(2005)Informally used in research ( e.g. monetary shocks must generate a liquidity effect): this approach makes it explicitMore justifiable by theoretical model: DSGEs seldom deliver all zero restrictions, but lots of sign restrictions usableSlide12
Example:
Uhlig
(2005)
Contractionary Policy: Responses of prices and nonborrowed reserves are not positive and those of the federal funds rate are not negativeSlide13
Razin and Rubinstein:
Output
Growth Rate
Prob
of Sudden Stop/Currency
Crisis
Flexible Exchange Rate Regime
Capital Account Liberalization
-
-
-
+
+Slide14
Could we extend this framework to a dynamic analysis?
What are the variables to include?
[growth rate of output;
change/level of exchange rate regime; change/level of capital account liberalization; probability of crisis]What are the shocks we want to identify? One choice: shocks interpreted according to variablesSlide15
How to Identify the Structural Shocks
?
Shock run restriction?
Long run restriction?Sign restriction?Available convention: Exchange rate shock from flexible to peg should increase crisis probability; Capital Account Liberalization shock from less to more free capital flow should increase crisis probability What are their effects on output?
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