Question

Briefly discuss the advantages and disadvantages of using a structural model, relative to using a Structural (Identified) VAR.

Answer 1

Vector self-regression models (VAR) model common dynamics and causal relationships between a set of macroeconomic variables. VAR models are useful for prediction.
Consider a variable automatic regression model that describes the dynamics of only one random variable Y (i.e. national
income) as a linear function of its own past. Based on this model, the expectations of national income depend only on its previous history. However, economic variables
such as national income, employment, prices, money supply, interest rates, etc. interact with each other. For example, movements in interest rates affect the level of
employment, which in turn affects the level of national income. In this multivariate setting, the national income forecast will be a function of a larger set of
information that collects not only the history of national income but also the history of many other variables, such as interest and employment rates. VAR is the
generalization of a single-variable self-regression model to a set of economic variables.

VAR Advantages

Motivation response function and contrast decomposition. An important use of VAR is to determine the effects over time of economic policy. Suppose the monetary
authority shocks interest rates. Questions become: when, for how, and how does the interest rate shock affect employment and production? Motivation functionality is
designed to respond to these questions. The pulse response function describes the response over time of each variable in the VAR to a one-time shock in any variable
while maintaining the stability of all other variables.

The length of delay p is also chosen by statistical testing or by reducing some parameters of information. The VAR model is estimated under the null value and under the alternative and is tested by creating either F statistic (based on a comparison of the sum of the residual squares of the bound and unrestricted specifications) or the non-asymptotic probability test (based on a comparison of the probability function value of the bound and unrestricted specifications).

Classical inference Since the OLS estimator has standard approach properties, it is possible to test any linear constraints, either in one equation or across
equations, with standard t and F statistics. Assume that one is interested in knowing whether the second delay is closely related to the first mining. One writes the
null hypothesis . This is a limitation that only includes the first equation. It is also possible to test limitations involving more than one
equation.

Ease of implementation Since each equation in VAR has the same number of variables on the right side, coefficients of the
total system are easily estimated By applying the OLS to each equation separately, the OLS estimator has standard converging properties.In large samples, the OLS
estimator is a constant and a normal distributor.

Closely related to the pulse propulsion function in contrast analysis. This breakdown indicates that each innovation contributes to the variance of the prediction
error associated with the forecast for each variable in the VAR. A standard time series program provides both pulse response functions and contrast analysis.

Causer Granger test. It is important to know if one or more variables have predictive content to predict a benefit variable (s). For example, in System (1), one might
ask if X is useful in predicting Y. And the corresponding null hypothesis is that all coefficients in deficiency X are zero, that is, H 0: 0 11 = γ 12 = 0. If these
coefficients are statistically zero, someone says that X does not cause Granger-Y or, - X is equivalent, X does not have any predictive content for Y. The zero
hypothesis can be tested using standard F statistics.

VAR disadvantages

Determination of restrictions. This is the point of discussion in VAR structural modeling. The idealistic view is that economic theory should dictate the constraints
that must be imposed. However, Sims said that economic theory was not helpful regarding appropriate identification restrictions, and therefore, estimating the reduced
form is the maximum that can be achieved. Some researchers place restrictions on the coefficients of contemporary variables. Others impose restrictions on the variance
of long-term complications and structural innovations.

Custom specifications. VAR models are criticized for not shedding light on the infrastructure of the economy. Although this criticism is not important when predicting
a VAR target, it is important when the goal is to find causal relationships between macroeconomic variables. Structural VAR is a system of concurrent equations that
aims to analyze causal relationships. For each system variable, there is an equation that explains the simultaneous and dynamic interactions between a whole set of
variables.

Sorting the variables. the impulse response functions will depend on the order of the variables. The
common solution is to transform innovations (for example, using Cholesky decomposition) so that the transformed innovations are not related. The result is that the
system's response to the shock of innovation can now be tracked separately from the inconvenience of other innovations. The transformation also has implications for
the system specifications because the first equation will now have only one current innovation, the second equation will have two current creations, and the third
equation will contain three, and so on. Therefore, the order of the variables is important. There are no rules on how to choose the order of variables. Economic theory
may shed some light, but ultimately the choice of system depends on the questions that the forecaster wants to answer.

The most common limitation of identification is the determination of iterative parameters or the lower triangulation of a contemporary coefficient matrix. it will affect production with some delay depending on the dynamics specified in the VAR model. Less trinity is the most common constraint in time series computer packages.

The solution is known as the low modeland it is VAR in (1) taking into account some parameter limitations. The question is: Is it possible to recover structural parameters from estimated parameters in
reduced form? This is known as the identification problem. Structural VAR in (2) contains fourteen parameters (twelve coefficients and differences for innovation,
assuming variance is zero), while VAR in (1) contains thirteen parameters (ten coefficients, two variables, and variance in innovations). For a unique determination of
structural standards, the researcher needs to restrict the structural VAR.