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Nominal income targeting. Consider the simple
where v is velocity, e, 0, and I] are disturbances with zero serial and cross correlation, and all other variables are standard. The information set at time t includes current and past values of G, 0, and 1].
(a) Derive output under a fixed money rule and a fixed nominal income rule.
(b) Under what conditions does a nominal income rule dominate a fixed money rule? What objective function should you use to answer that question?
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- Suppose now the economy is described by a New Keynesian Model, where we assume rational expectations. The equilibrium is described by the following three equations, in order the Dynamic IS, the New Keynesian PC and the Monetary Policy Rule: 1 Y₁ = E₁Y₁+1 = = rt+u!S; Yt Etyt+1 (1) T4+ = BETCH+1+ky tuổi (2) rt = Y¬πt + YyYt + UMP (3) where u¹S, u and u IS MP are white noise, iid disturbances identifying output, infla- tion and interest rate shocks, respectively. Then, 0, ß, к are positive model's (con- volution of) structural parameters and 4 and yy are positive policy parameters. Because of the absence of any backward-looking elements and any information about the future values of the disturbances, Ett+1 = Etyt+1 = 0.Assume that the price level in an economy is stable with expected inflation initially equal to 3% in period 0. Further assume the economy is then hit by an expansion at the beginning of period 1, and employment remains at a constant high level until the beginning of period 4. With ‘time period’ on the xaxis and ‘inflation rate’ on the y-axis: (i) Plot the path of the bargaining gap (assume it is equal to 1%), inflation and expected inflation from period 1 to the end of period 4. (ii) Provide some reasons for why the bargaining gap might disappear after period 4, and state any other assumptions you are making. (iii) Explain how an increase in the central bank’s policy interest rate would affect the exchange rate through the market for financial assets (such as government bonds). What impact would this have on aggregate demand?Prices and aggregate-supply shocks can be added to Poole’s analysis by using the following model: Assume that the central bank’s objective is to minimize and that disturbances are mean-zero, white noise processes. Both the private sector in setting Et-1 πt and the monetary authority in setting its policy instrument must act prior to observing the current values of the disturbances. a. Calculate the expected loss function if it is used as the policy instrument. (Hint: Given the objective function, the instrument will always be set to ensure that expected inflation is equal to zero.) b. Calculate the expected loss function if mt is used as the policy instrument. c. How does the instrument choice comparison depend on i. the relative variances of the aggregate-supply, demand, and money-demand disturbances? ii. the weight on stabilizing output fluctuations l?
- Assuming that at equilibrium real money supply (M$/P) is equal to real money demand (Md /P), which is assumed to be a function of real income (Y), nominal interest rate (R), and technology (A) as follows: MS Y =A- R P (a) Specify the assumptions needed to uphold the prediction of quantity theory of money claiming that the ratio of money to GDP is constant in the long run.e (b) Assuming that the growth rate of Y is 4%, the growth rate of R is 0, and the growth rate of A is -1%, draw a diagram to indicate the relation between growth rate of MS (on the X-axis) and inflation rate (on the Y-axis).Type T or F at the end of the statement to indicate whether it is true or false. Please also provide an explanation for each choice. A) According to the Real Business Cycle Model, actual output generally fluctuates much more than the full-employment level of output. B) According to the Real Business Cycle Model, permanent productivity shocks drive fluctuations in GDP over the business cycle. C) According to the Real Business Cycle Model, decreases in employment during recessions reflect large temporary decreases in labor supply. D) The United States' large current account deficit reflects mainly its large trade deficits with China and Japan. E) Labor productivity in the United States is strongly procyclical, falling during recessions and rising during recoveries.Consider a modified aggregate supply function which takes account for the emergence of random business cycle shocks (ce) with Ele] - O in the sense that The loss function is the same as in exercise 1: L- (n - k)* +(m) Notation: €: random shock; E[e,]: expected value of e; b: constant parameter, all other variables see Exercise 1. Having considered the scenario above complete the following tasks: a) Derive the central bank's preferred inflation rate and explain. b) The result in a) reads as T = b(k – j) – %3D Explain the economic intuition of this result. c) Consider a more conservative central banker whose loss function is represented by L = }(y – k)? + }(7.) k) + (m) Apparently, the preferred inflation rate would read eb 1+b TE = 6(k – y) – What can you say about the relationship between B and b? le i larger or smaller than b? Provide an explanation.
- Consider the following four demand functions for money: (1) InM," = a, +a,InY," +a, In R, + a, In P, + , %3D (2) InM," = B, + BInY, + B, In R, + B, In P, + u,2 (3) InM, = %, +7,InY, + 7, In R, +u,, (4) InM)=6, +6, InR, +u,. where M,", Y,", R, and P, denote, respectively, aggregate nominal money demand, M,", and /P, aggregate national income, long-term interest rate, implicit price deflator. M, Y, = / stand for aggregate real money demand and aggregate real national income. These four money demand equations are estimated for the period 1949-1965 and the following estimated equations are obtained: (1) InM," = 3.999+1.710lnY," – 0.608 In R, – 0.759In P, R = 0.942, SSR = 0.080 (0.469) (1.801) (0.416) (0.651) (2) InM," = 3.999+1.710lnY, –0.608In R, +0.9519 In P, R² =0.942, SSR = 0.080 (1.801) (0.416) (0.469) (0.651) R = 0.902, SSR = 0.081 (3) InM, = 3.760 +1.683lnY, – 0.594 In R, (0.566) (0.353) (0.443) (4) In M)=2.727+0.2201n R, R = 0.129, SSR = 0.102 (0.202) (0.149)How do inflationary expectations influence interest rates on mortgage? Please elaborate by expressing your thoughts about your findings in at leastsuppose a Keynesian macroeconomic model is characterized with the following equations: Y = C + I + G Goods markets C = C = 320 + 0.8YdYd = Y − TI = 40 − 40rG = 80T = 50 Money marketsMoney demand:(M/P)d = 500 + 0.8 − rMoney supply: MSP = 800Derive IS and LM equations and derive equilibrium income level and interest rate.
- he classical model is appropriate for analysis of the economy in the Answer long run, since evidence indicates that money is not neutral in the long run. long run, since real and nominal variables are essentially determined separately in the long run. short run, provided money is not neutral. short run, provided real and nominal variables are highly intertwined.Using the data in the table, integrate the expected relationship of the behavior of inflation with the phases of the economic cycle. You should use the different levels of inflation rate with economic growth and construct graphs to present your analysis arguments.Discuss the Lucas Critique of traditional structural Keynesian macroeconomics. Explain why the Euler Equation below is immune to the Lucas critique and explain its main implications for household consumption. u' (C₁) = (1 + 1) E₁u' (C (+1) Ct is consumption at time t and C++1 is consumption in the next period p> 0 is the rate of time discount (degree of impatience) i is the fixed interest rate on a risk free asset Et is the expectation at time t (today)