# What is the difference between SVAR and VAR

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## by DM

Learn things especially in coding need a practice. Lets put it into work then. Today we are going to enthusiatly dig deeper between what is VAR and what is structural VAR.

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PhD is when you are trying to explain something and get so enthusiatly love about it.

# The difference between VAR and SVAR

## VAR or vector autoregression

Var or vector autoregression or unstructured vector autoregression is a way of learning the relationship between one variable without any structural limitation such as time. However, the problem with VAR only is that sometimes, there is no particular rule on seeing both two data related to each other. For example, in monetary policy, let's say we want to control the inflation of the price; as we expect that inflation will rise, the monetary authority will increase its instrument, the interest rate, and expect the commodity price to go down. It turns out that the price is not going down and rising instead. Then without any rule in concluding, opening the tide of economic mystery, we will complete that raising the interest rate will also increase the inflation or commodity price.

Learn in the video below.

## SVAR or Structural vector autoregression

Meanwhile, Structural vector autoregression is similar to vector autoregression but with much more constraint—for example, time. One of the differences is in the sample. For example, the government attempted to reduce inflation by increasing the interest rate. In the unstructured vector autoregression, when the result of increasing the interest rate makes the inflation go up, we just read it as it is, which will create an erroneous conclusion. Meanwhile, in structure vector autoregression, we have a time duration that can help explain when the price increases and in which period the inflation goes down or starts to take effect, and whether it's significant.

### Some explanations in the video format

Here I found a couple of great videos about SVAR

1. Why SVAR

Svar is a fascinating development in macroeconomics from Christopher Sims. From this video, for example, when the bank anticipates inflation while buying release more money, the inflation still rises. The wrong conclusion is that the interest rate hike led to inflation. But it turns out the monetary policy is an endogenous reaction to expected inflation.  The same issue occurred with fiscal policy; for example, we expect that there will be a reduction in private demand and, therefore, an increase in public spending, and the output will still decline. The wrong conclusion will be public spending will cause the work to fall. However, fiscal policy reacted endogenously with the reduction in production.  To measure the effect of policy, we need to identify or isolate purely exogenous independent movements and how the economy reacts to them. It calls impulse reaction.&nbsp Therefore we need to identify the structural model that isolates the exogenous variable from the model. After the economy is hit by the shock, getting the structural model is called identification.  According to Sims (1986) Identification is the interpretation of historically observed variation in data in a way that allows the variation to be used to predict the consequences of an action not yet undertaken.  After the structure is identified, one can predict inflation and output growth. And we can expect the fiscal effect on GDP.

2. The calculation behind SVAR

ok

How to identify purely exogenous shocl

Lets say we have

$AX_t = \beta_0+\beta X_{t-1} + u_t$

From the explanation above it can be interpreted that the vector $$X$$ relies on its lag itself and structural shock $u$.

if we assume that X has 2 variables which is GDP gap y and interest rate r: it become

$X_t = \begin{bmatrix} y \\ r\end{bmatrix}$

and make the system become

$\begin{matrix} y_t + a_{12} r_t = \beta_{10}+\beta_{11} y_{t-1}+\beta_{12} r_{t-1}+ u_{yt} \\a_{21} y_t + r_t = \beta_{20}+\beta_{21} y_{t-1}+\beta_{22}r_{t-1}+ u_{rt} \end{matrix}$

Where it can be written in matrix form

$\begin{bmatrix} 1 & a_{12} \\ a_{21} & 1 \end{bmatrix} \begin{bmatrix} y_t \\ r_t \end{bmatrix} = \begin{bmatrix} \beta_{10} \\ \beta_{20} \end{bmatrix} \begin{bmatrix} \beta_{11} & \beta_{12} \\ \beta_{21} & \beta_{22}\end{bmatrix} \begin{bmatrix} y_{t-1} \\ r_{t-1} \end{bmatrix} +\begin{bmatrix} u_{yt} \\ u_{rt} \end{bmatrix}$

where

$A = \begin{bmatrix} 1 & a_{12} \\ a_{21} & 1 \end{bmatrix}$

What is identity matrices, check this video also

And also what is inverse matrices

How to find inverse matrix

Test the matrix

In Matrix A, the constants 1 and 1 showing a contemporaneous relationship.

$\begin{matrix} 1 & 2 & 3 \\ a & b & c \end{matrix}$

test the matrix

$\begin{bmatrix} 1 & 2 & 3 \\ a & b & c \end{bmatrix}$

$\begin{bmatrix} 1 & 2 & 3 \\ a & b & c \end{bmatrix}$

3.

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# Analysis of correlation and significance of parameters

## Correlation

The study of the significance of the impact of input parameters on output parameters should begin with the analysis of the correlation of individual parameters. Three basic dependencies can be checked:

#### How to calculate the correlation using their original formula

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Correlation coefficients are used to measure how strong a relationship is between two variables. There are several types of correlation coefficient, but the most popular is Pearson’s. Pearson’s correlation (also called Pearson’s R) is a correlation coefficient commonly used in linear regression. If you’re starting out in statistics, you’ll probably learn about Pearson’s R first. In fact, when anyone refers to the correlation coefficient, they are usually talking about Pearson’s.

#### VARs package in R

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Need to check it out

#### VAR in stata

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This one is interesting

#### SVAR model example

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SVAR model example can be found in literature of macroeconomic.

#### VAR vs SVAR risk

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This topic also need to look back at

#### SVAR model in R

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Its interesting topic that I havent dig deeper

#### Library VARs

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Well if you using Matlab, the library is available in Matlab website

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