Question

Consider the following money demand function for the US m=0.72m-1+ wr w=0.27+0.191,-0.045rb -0.019rc where m is the log of real money holdings. I, is the log of aggregate real income, rb, is the log of interest rate on bank holdings and re, is the log of the interest rate on commercial paper. You may treat w, as deterministic for the purposes of this question. This model was estimated using quarterly data. Find the effect of a one unit increase in I, on real money holdings two quarters from now. What about one year from now? (Hint: read Hamilton ch.1) 2 For the following stochastic process: Y-0.86-1+0.56-2 E()=0,t, E(G), otherwise. (a) Compute the first three autocovariances and autocorrelations. (b) Determine if it is stationary. 3 Determine if the following difference equations are convergent or divergent. (a) 0.5-11.2-2 (b) = 0.9-1+0.1-2 4 For the 5th order stochastic difference equation: 0.8-1 -0.42-2 +0.571-3-1.21-4 +0.22-5 (a) Determine the stability. You may use Stata or R (b) Rewrite this equation in vector first difference equation form. Using this form determine if it satisfies stability condition. 5 Download Turkish Industrial Production Index (2015-100, historical series, total industry, 1986.01- 2023.01) monthly series from TUIK website. Download both unadjusted series and seasonally and calender adjusted series (there is a table containing both at the TUIK website). You may use either Stata or R (but R may be easier). Your code should be reproducible, i.e.. I should be able to reproduce everything you did including reading data from the excel file. (a) For both adjusted and unadjusted series, draw the time-series graphs, and the sample correlo- gram and interpret. (b) From the TUIK website (under the title "metaveri") describe how the industrial production index is seasonally and calender adjusted. Which software programs and procedures do they use? (c) Use the adjusted series and separate the sample into two: period 2010.01-2016.12 as the esti- mation (training) set and 2017.01-2019.12 as the evaluation set (do not use observations before 2010 and after 2019). Compute one-period ahead forecasts using time series cross-validation method and compare the performance of naive (with and without drift), and seasonal naive methods. Which one of these performs the best according to RMSE criterion?

Answer 1

The concepts of real GDP and aggregate demand are key elements in macroeconomic analysis. The Keynesian cross model depicts how equilibrium real GDP is determined in the economy, and the rational expectations theory might impact the efficacy of monetary policy. To find the equilibrium, one needs to equalize the aggregate expenditure with real GDP.

Step-by-step explanation:

Within the context of macroeconomics, and specifically in relation to the Keynesian cross model and the concepts of real GDP and aggregate demand, there are several important facets to consider when analyzing the effects of monetary policy and finding economic equilibrium.

Firstly, in the Keynesian framework, an increase in the money supply can initially lead to a higher level of real GDP, indicating a boost in aggregate demand. However, according to the rational expectations theory, agents in the economy anticipate future policy actions and adjust their behavior accordingly, which might result in a different outcome than the traditional Keynesian prediction.

To find the economic equilibrium or the level of real GDP that the economy will reach, the Keynesian cross model approach involves setting aggregate expenditures equal to real GDP. This is demonstrated by the algebraic expression AE = C + I + G + X - M, where C is consumption, I is investment, G is government spending, X is exports, and M is imports. Calculating the equilibrium level of output then involves solving for Y when AE equals Y.