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The model with oil price consists of an IS curve, a Phillips curve, an autoregressive process of oil price, and a policy rule for the short term interest rate. The model can be derived from an underlying dynamic stochastic general equilibrium model based on optimizing agents, and the model equations are the concentration of economic content in the DSGE model that is discussed shortly. In that sense, the model is structural. While the model emphasizes the role of forward-looking behavior and rational expectations, it also incorporates a substantial degree of persistence in the form of multiple lags of output and inflation. In line with Salemi (2006), the investigation taken up in this study does not concern the deeper structural parameters in the model.

The model economy consists of the following linearized equations

yt = λEtyt+1+a1yt−1+a2yt−2−b(rt−Etπt+1) +εy,t, (4.1)

πt = α1Etπt+1+α2πt−1+βyt+ηqt+επ,t, (4.2)

qt = ρ1qt−1+εq,t, (4.3)

rt = c1yt−1+c2πt−1+c3rt−1+c4qt−1+c5yt−2+εr,t. (4.4)

The complete model characterizes the equilibrium dynamics of four variables: yt, πt, qt,

andrt. qtis defined as the real oil price. yt,πt, andrtcarry the same definitions presented

in previous paragraph. Each variable is expressed as deviation from its own trend. The stochastic variables επ,t, εy,t, εq,t, and εr,t are serially uncorrelated shocks that account

policy, respectively.

Equation (4.1) is loosely consistent with a linearized Euler condition characterizing the optimal consumption in a dynamic general equilibrium setting. The equation links output during period t to its own expected future and lagged values, and to the value of ex ante real interest rate. b measures the inverse relationship between current output and the real interest rate which reflects intertemporal substitution on the optimization of households. Clarida, Gal´ı and Gertler (1999) show that the presence of expected future output in the IS equation can be explained by the desire of households to smooth consumption. The presence of lagged output in the IS equation can be explained by habit persistence. Habit formation can cause delays between decision making and consumption. Hence aggregate demand and output adjust only partially such that output depends on a combination of its own lagged values, see Svensson (2000).

Equation (4.2) is a Phillips curve governing the dynamic behavior of inflation. The specification that oil is used as an input for producing intermediate goods makes current inflation depend on the real oil price36_{. The Phillips curve also has the appearance of} inflation being partly “backward looking” in spite of the fact that firms are rational and forward looking. Therefore, equation (4.2) takes the form of a hybrid forward- and backward-looking New Keynesian Phillips curve. If the coefficients on lagged inflation and real oil price become zero and drop out of the specification, the equation reduces to the purely forward-looking New Keynesian Phillips curve analyzed by Gal´ı and Gertler

(1999) that links inflation to expected future inflation and output gap.

Equation (4.3) describes the process for the real oil price. In this study, oil price movement is derived to be in the form of a first-order autoregressive driving process, which is in line with many studies, e.g.,Kim and Loungani(1992),Leduc and Sill(2004),

Carlstrom and Fuerst (2005), and De Walque, Smets and Wouters (2005). Therefore,

macroeconomic variables are affected by the oil supply disruption through higher oil prices. Hamilton (1983) suggests that oil price changes prior to 1973 were likely to be exogenous due to oil commissions that insulated the oil prices from movements in oil demand. Montoro (2010) also suggests that during the 1970’s and through the 1990’s the major source of oil price hikes seemed to be on the international supply side, either because of attempts to gain more oil revenue or supply interruptions due to geopolitical events, such as Iranian Revolution and the first Gulf war. However, many studies argue that in the 2000’s the high price of oil is more related to international demand side37_. It would be ideal to use an open economy model with endogenous oil price to estimate preference parameters of the Federal Reserve. This is a case worth exploring, which this study leaves for further research.

Equation (4.4) is the policy rule or reaction function that explains how the central bank sets the short term interest rate. The linearized equation takes a form of theTaylor

(1993) type reaction function and corresponds to the common practice of using the short term interest rate as monetary policy instrument by most central banks. The reaction function also features intrinsic persistence in the policy rate, because such persistence allows monetary policy to achieve a given degree of stabilization with less volatile short- term interest rate. The persistence feature of policy rule is actually followed by many central bank, see Sack and Weiland (2000). Dennis (2006) argues that the error term

εr,t can capture some variables that are omitted by econometricians since they tend to

have less information than the policymakers. Salemi (2006) interprets the disturbance as a term that includes idiosyncratic wisdom of the monetary policy authority. In line with Clarida, Gal´ı and Gertler (1999) and Salemi(2006), the coefficients of the reaction

37_{Within a global economic setting, a list of articles find evidence in support of endogenous responses} of the real price of oil to the global macroeconomic conditions, see e.g., Barsky and Kilian (2004),

Hamilton (2005), Woodford (2007), Kilian(2008), and Kilian (2009). These studies argue that there are additional transmission channels that cause oil prices to affect the macroeconomic variables and all major real oil price increases since the mid-1970’s can be traced to increased global aggregate demand.

function are assumed to be fixed in a policy regime so that policy is time consistent.