Title: Individual Assignment
Course: Monetary Economics and Macroeconomy
Question 1 Simple Taylor Rule Estimation
1. Download the data set EstimTaylorRule_Data_AA .csv (available on Canvas) for country AA of your choice (UK: United Kingdom, US: United States). Use it to perform a simple OLS estimation of the Taylor rule
it = φy gy,t + φπ πt + εt ,
where it is the (policy) interest rate, gy,t is real GDP growth, and πt is in ation.
(a) Report the estimated values for the coe cients φy and φπ . Does φπ satisfy the Taylor principle?
(b) Draw a graph plotting the estimated Taylor rule (ˆ(1)t ) against the actual interest rate.
The data set contains two time series for real GDP growth (percentage change from a year earlier, and percentage change from the previous quarter at an annual rate) and two time series for in ation (headline in ation, and core in ation, which excludes food and energy). You may use whichever pair you prefer.
2. Describe two problems or disadvantages of this approach to estimating a Taylor Rule. (Hint: Think about (i) structural breaks, (ii) endogeneity).
Question 2 Simple New Keynesian Model
Consider the baseline New Keynesian model. The model can be described by the following equations:
The rst equation is the IS curve, the second is the Phillips curve, and the third is the monetary policy rule. We have
where ω is the fraction of rms that cannot change prices. β ∈ (0, 1) is the discount factor, σ > 0 is the inverse of the intertemporal elasticity of substitution, and ϕπ > 1 measures how strongly monetary policy reacts to in ation. Equations (IS), (PC), and (MP) determine the dynamic paths of the endogenous variables {xt ,πt , it } , given the exogenous shocks {vt , ut }.
1. Brie y describe the economic intuition behind the three equations.
2. Combine (MP) with (IS) and (PC) to eliminate it from the system and rewrite the
remaining two equations in matrix form as
where A is a 2 × 2 matrix and B is a 2 × 1 vector. What are A and B?
3. Show that the assumption ϕπ > 1 is crucial to ensure uniqueness of the equilibrium. Hint: you have to show that both roots of the characteristic equation λ2 −tr (A) λ+ det(A) = 0 are larger than one in absolute value, where tr(A) denotes the trace of the matrix A and det(A) is the determinant. Discuss the economic intuition.
4. Assume that the monetary policy shock ut follows a stationary autoregressive pro- cess
ut = ρuut-1 + εt , with − 1 < ρu < 1
where εt is an i.i.d. normal innovation with mean zero. For simplicity, set the shock to the IS curve equal to zero, i.e. vt = 0 for all t. Solve for the equilibrium paths of xt and πt using the method of undetermined coe cients. In particular, conjecture that in equilibrium
xt = ψxu ut
and
πt = ψπuut
Substitute these conjectures into the IS-PC-MP equations and solve for the unde- termined coe cients ψxu ,ψπu.
5. Let us analyze the economy's response to an increase in ut (i.e. a contractionary monetary policy shock).
(a) Show analytically that ψxu < 0, ψπu < 0 for all admissible parameter values. What is the economic intuition?
(b) Derive analytically the equilibrium paths for the nominal interest rate it and for the real interest rate rt = it - Et πt+1 . A friend of yours claims: Clearly, a positive shock to ut will induce an increase in both the real and the nominal interest rate. Is this statement true or false? Explain.
6. Now use the computer (Matlab or Excel) to simulate the response of the economy to a unit increase in ut. Speci cally, in period t = 1 we have u1 = 1, then u2 = ρu , u3 = ρu(2), and so on. Assume the following parameter values: β = 0.99, ϕπ = 1.5,
σ = 1, ω = 0.8 and ρu = 0.5. Show the impulse responses of {xt ,πt , it , rt } in a single chart. How would your ndings change if ω = 0.4? Discuss the economic intuition. (Hint: recall that ω is the fraction of rms that cannot change prices).