Before we perform the simulation, we need to collect data on the endogenous and exogenous variables up to the quarter preceding the beginning of the simulation. These data constitute the initial state of the simulation. One may understand their role, for example, by observing inflation equation (4.4). One
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One year ahead expectations for inflation, as derived from the capital markets, are calculated by the difference between the (nominal) yield to maturity of an un-indexed one-year bond (Makam) and the real yield to maturity of a one-year CPI-indexed bond.
of the factors in the equation is lagged inflation (πct-1). Thus, the inflation rate at the initial state affects the derived inflation rate in the first quarter of the simulation.
At the beginning of this phase, we need to determine the quarter in which the simulation will begin. The choice is not trivial because at the time the forecast is produced, some of the data are known in real time (e.g., nominal exchange rate and interest rates) while other statistics are published at a lag of several months. (GDP data, for example, are released at a two-month lag.) For the most part, we begin the simulation in the following quarter. Therefore, when updating the data (for both endogenous and exogenous variables), we have to make some assumptions that will allow us to “close” the quarter preceding the beginning of the simulation.62
In the example that follows, the simulation was performed in the middle of September 2006. Since the interest rate for the entire third quarter was already known, we chose to begin the simulation in the fourth quarter.
In what follows we describe the sources of data for the four endogenous variables of the model:
Inflation (πct) is the quarterly percent change in the Consumer Price Index (annualized). Adjustment for seasonality is made on the basis of seasonal factors that are estimated in the inflation equation. The CPI is reported at a two-week lag. To close the quarter preceding the beginning of the simulation, we must fill in up to two CPIs that were not published. We do this by availing
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For example, if at the end of September 2006 we wish to perform a simulation starting from the fourth quarter of 2006, we must make an assumption about the September CPI (which is not published until October 15) – in order to determine the rate of inflation in the third quarter, which is a part of the initial state for the simulation.
ourselves of professional forecasters’ outlooks and a monthly model developed by the Bank of Israel's Monetary Department.63
In the example, we assumed that the September CPI (not published at the time that the forecast was performed) declined by 0.2 percent. The assumption was based on the aforementioned Monetary Department monthly model. Following this assumption, we found that inflation in the third quarter (annualized, seasonally adjusted) was 1.1 percent.
Nominal sheqel/dollar exchange rate (et) from which the (annualized) nominal rate of depreciation is also derived. We assume that there is no seasonality in the evolution of the exchange rate. The rate is reported in real time. To close a quarter, we need to make an assumption about the behavior of the rate up to one or one-half months ahead. For the most part, we assume that it will remain at the average level that it had established in recent weeks.
In the example, we assumed an average dollar exchange rate in the second half of September 2006 of 4.39 sheqels. (In the first half of September, it fluctuated in the 4.36– 4.40 sheqels range.) Accordingly, we found that appreciation continued in the third quarter of 2006 much as it had in the second quarter (9.6 percent in the third quarter as against 13.2 percent in the second quarter, both in annual terms). These appreciations explain the relatively low inflation rate in the third quarter of 2006.
The output gap (yt) is based on domestic gross product of the business sector in constant prices. Initial output data are reported at a two-month lag. Accordingly, the closing of a quarter for the initial state is based on the Bank
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See
of Israel’s growth outlooks. We calculate the gap using the HP filter64 as follows:
[
log( )−HP(log( t))]
∗100= Y Y
yt t
where Yt is business-sector output in constant prices.
To surmount the end-of-sample problem of the HP filter, we extend the output series, prior to applying the HP filter, on the basis of real development outlooks by the Bank of Israel's Research Department and judgment assumptions. By so doing, we dampen the effect of the latest output data on the output gap estimate at the initial state of the simulation.
In the example: By September, National Accounts data had been released for the first half of 2006 only. We “extended” the output series on the assumption that business-sector product would grow by 4.5 percent during the entire year and by 4.0 percent in subsequent years. By using the HP filter, we found that the output gap in the third quarter of 2006 was –0.3 percent.65
Nominal interest rate (it) – We use the Bank of Israel’s (effective) nominal interest rate, which is known in real time. Occasionally, in order to close a quarter before the simulation begins, we need to make a judgmental assumption about the interest rate for the next month.
The nominal interest rate, as stated, was known for the entire third quarter of 2006 and rested on average at 5.4 percent.
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Hodrick-Prescott filter. 65