What are structural vector autoregression (SVAR) models?

Structural Vector Autoregression (SVAR) models are multivariate time series models that implement identification restrictions based on economic theory and/or other sensible assumptions. Some of the common restrictions implemented in the literature are Short-run restrictions, long-run restrictions, and sign restrictions. In this video, we will focus on long-run restrictions and will inspire our work on a paper written by Enders and Lee (1997). 

Structural Vector Autoregressive Models

Structural VAR is a variant of unrestricted VAR models, and is one method for forecasting several variables within a system. While in a conventional unrestricted VAR, we let time series data talk and behave on its own, a structural var model, on the other hand, enforces a few key constraints which establish conditions on how particular variables will behave. For models without recursion, or over-identified structural VAR models, whether the linear restrictions are specified on A or B is of importance. Recursive models are probably the most common structural VAR models identified with a short-run constraint of impact effects from a structural shock. Many svar models apply short run restrictions. For example, short-run restrictions can help to conduct monetary policy. According to economic theory, in the short run, a shock on the interest rate will not have any effects on the rest of the variables in the economy. However, after some periods, gdp or inflation will respond to structural shocks. If we observe the impulse response function, we will see how inflation does not respond to shocks in the short run. This is a property very common in macro models.

Another sort of restriction that we will analyze today, are long run restrictions. Long run restrictions will impose that in the long run, nominal variables have no effects on real variables. To do so, we will replicate a model by Enders and Lee (1997), where they study how nominal and real exchange rate decompose over time. We will follow the var approach that we covered in previous tutorials. In the eviews software we will estimate a reduced form stationary var. After the var estimation, we will select the appropriate lag length and impose the appropriate long run restrictions. Our structural vector autoregression model is ready!

Structural Var example: Enders and Lee (1997) summary

Using a technique developed by Blanchard and Quah (long run restrictions identification), the authors break down the movements of the real and nominal exchange rates into components caused by real and nominal factors. The authors find that Nominal shocks had only minor effects on real and nominal two-way exchange rates between the United States and Canada, Japan, and Germany. Also, there is little evidence for an overshooting in exchange rates. Lastly, the authors conclude that Real shocks of demand, not supply, are what are responsible for the fluctuations in the exchange rate, and a structural model of the determination of the exchange rate must take into account such shocks as a major underlying factor.

What you will learn by watching this tutorial:

By watching this video tutorial you will learn:

• Stationarity

• Requirements to use Long-Run Restrictions

• How to estimate the SVAR model

• Lag Length Criteria

• How to display structural impulse response functions

• How to implement the long-run restrictions

• Structural Variance Decomposition

Structural Vector Autoregression (SVAR) models: Blanchard and Quah (1989)

In 1989, Blanchard and Quah (1989), proposed a new identification strategy for the parameters of a structural var. They proposed imposing restrictions on how shocks influence endogenous variables “in the long run”, and suggested limiting the responses of a variable to a shock.

A long run restriction is commonly associated with the concept of long run neutrality. Classical Macroeconomic Hypothesis specify that in the long run, permanent changes in nominal variables have no effect on real variables.

Examples

1. Permanent changes in the nominal money stock has no effect on the level of real output in the long run.

2. Permanent changes in the rate of inflation has no long-run effect on unemployment. (i.e, Picture a vertical Phillips Curve in the long run)

3. Permanent changes in the inflation rate has no long-run effect on the real interest rate. (Fisher Relationship in the long-run).

Preliminary Conclusions

Having provided diverse examples, imposing a long run restriction in our structural var model, implies limiting the cumulated responses of an endogenous variable in the model to a shock. For example, Blanchard and Quah (1989) estimated a bivariate VAR using Real GNP and Unemployment. The authors identified two shocks in the model: “supply shock” and “demand shock”. The demand shock has no effect on real GNP in the long run, while a supply shock will have permanent effects. 

Example: Real and Nominal Exchange Rates

In our example, inspired on Enders & Lee (1997), we will try to decompose real and nominal exchange rate movements. We will see how real and nominal shocks affect real and nominal exchange rate movements. Please download the dataset to replicate the content. 

Overview of the Model

• There are two shocks: Nominal and Real shocks.

• Real shocks can cause permanent effects in the real exchange rate, but Nominal shocks can only affect the exchange rate in the short run.

• Picture a country that doubles their money supply. Price level and nominal exchange rate will double in the long run, while the real exchange rate will remain unaffected.

Data

• We will estimate the model for Japan.

• We will use Quarterly Data: Period 1973:01–2019:04

Requirements for the permanent effect

In order to use long run restrictions within an SVAR framework, at least one of the variables in our system needs to be non stationary (Cannot be I(0). It has has to be I(1)). Why?

• If the data we are using is stationary in levels, the
  long-run impacts of shocks to the levels of the series are always zero.

• In other words, I(0) variables have no permanent components.

Note: Although we require at least one of the variables to be non stationary in levels, when estimating the model, the variables must be in a stationary form (i.e., applying differences).

Test for Stationarity

Having mentioned the requirements for the permanent effect, ensure to test for the stationarity of the variables. Ensure at least one of them is I(1). Ensure to conduct and report:

1. Graph Analysis

2. Correlogram Analysis

3. Formal Tests: ADF, Phillips-Perron.