**Estimating Vector Autoregression Model with The U.S. Federal Funds Rate, Nominal Interest Rate, Exchange Rate and Industrial Production as Endogenous Variables**

**Based of the lectures of Dr. Rokon Bhuiyan, CSUF
**

Once you have the time series data for these variables you need to upload them into Eviews and follow these steps:

Figure1: Select Estimate VAR from the Quick Menu

Figure 2: Here the ff-rate is the Federal Funds Rate, interest_rate is the Nominal Interest Rate, exchange_rate is the trade weighted Exchange Rate, and the ip is the Industrial Production Index for the United States

Figure 3: The EViews estimates of the VAR model with 3 lags on every variable along with the coefficient estimation, standard error of the coefficient, and the t-statistic of the coefficient.

**Choleski Decomposition of the Contemporaneous Effect Matrix and Estimation of Impulse Responses to Monetary Shocks**

The limitations of the Choleski Decomposition is that once can only choose an upper or a lower triangular matrix to equate the number of equations with the number of unknowns. Since Industrial Production is not contemporaneously affected by financial variables, an upper triangular matrix appears to be the more consistent with economic theory. After all the other option would imply that the Federal Funds Rate is not contemporaneously affected by the market interest rate, exchange rate, or industrial production which is not the case. The Federal Reserve looks at all these variables when deciding monetary policy in the United States.

Figure 4: The Contemporaneous Affect upper Triangular Matrix and the Reduced for Errors in term of Reduced and Structural Error Terms to Calculate the shock.

The last four equations can be estimated in EViews but must first be translated into EViews Language and an placed into an Impulse Estimator.

Figure 5: The Contemporaneous Affect Matrix written in programming code that EViews can understand.

Figure 6: After Pressing “O.K.” an estimate of the equations will present itself much like in the VAR estimation above.

Once you have the estimate press the “Impulse” button above and enter the impulse as the Federal Funds Rate and all the other variable in the Response section.

Now that we have the code we can use the following command to estimate the shocks and observe the following puzzling results/

**Summary of SVAR impulse responses vs. Theoretical Expectations**

*Response of Federal Funds Rate to an Increase in the Federal Funds Rate*

An increase in the Federal Funds rate is statistically significant for up to 10 months. This is consistent with the fact that once the Fed begins increasing interest rates it continues to do so consistently until it has stymied of the threat of inflation. The maximum of the graph occurs at the fourth month and then slowly there is a decay in the federal funds rate.

*Response of the Market Interest Rate to an Increase in the Federal Funds Rate*

Once there is a increase in the Federal Funds rate there is also an increase in the market interest rate. This is consistent since the cost of bank borrowing is an important determinant in the amount of interest banks charge on their loans. The Market Interest rate mirrors the impulse response of the Federal Funds rate and is also statistically significant up to the 10^{th} month.

*Response of the Exchange Rate to an Increase in the Federal Funds Rate*

The response of the Exchange Rate to an Increase in the Federal Funds Rate is a little more ambiguous than the last two example. According to economic theory, a contractionary monetary policy shock should cause the home currency to appreciate (Exchange rate to Decrease), which is what happens in the graph on the previous page. The problem occurs in the length of time the graph says that the currency depreciates for 2 months. This would imply that an arbitrage opportunity exist for two months which seems unlikely. If this is the case then this would be an example of the Delayed Overshooting puzzle.

*Response of Industrial Production to an Increase in the Federal Funds Rate*

Industrial Production is shown to react immediately to an increase in the Federal Funds Rate and this is clearly false in the direction, magnitude, and speed of the change. An increase in the Federal Funds Rate tends to lower investment and a decrease in investment reduces industrial output and employment over time. The amount of time for Industrial Production to decrease from an increase in the Federal Funds rate is surely longer than one month. This graph reacts instantaneously and in the wrong direction.

These puzzles could be from ommitted variable biased and most certainly the specification of the contemporaneous affect matrix. A better matrix can be constructed that is more in line with economic theory and that eliminates these puzzles, can you think of a better specification of zeros in the contemporaneous affect matrix to get more realistic results?