Macroeconomics Theory II

Transcription

1 Macroeconomics Theory II Francesco Franco FEUNL February 2016 Francesco Franco Macroeconomics Theory II 1/23

2 Housekeeping. Class organization. Website with notes and papers as no "Mas-Collel" in macro and there are many alternatives. TA: none. :-( One midterm: 50%, one final 50%, 4-6 problem sets 10%. Francesco Franco Macroeconomics Theory II 2/23

3 Structure. Two parts. Two parts: I: Benchmark, II: Dark Corners. Benchmark: DSGE. Dark Corners: harder to solve. Francesco Franco Macroeconomics Theory II 3/23

4 Facts The recorded history since However NAS starts in 1947 (dotted line) after effort during the 20 s-30 s. Data measurement or two different DGP? Francesco Franco Macroeconomics Theory II 4/23

5 Facts The recorded history since The Great Moderation again two DGP? Francesco Franco Macroeconomics Theory II 5/23

6 Macroeconomics Theory. Neo-classical synthesis: 1947 s-1970 s/1980 s Long-Run: Neoclassical, Short-Run: Keynesian. Benchmmark short run model typically divides the economy in goods market, financial markets and labor market. The model is usually static but sometimes contains dynamic features. The equilibrium conditions are: Y = a C (Y, r, T, Y 0, r 0, T 0 )+a I (Y, r, Y 0, r 0 )+G + NX (e, Y ) M/P = a M d /P(i, Y ) or i = z MR (p, Y ) p = p e + z Y (Y, z) and the real interest rate r i p e and p e is the expected inflation (tipycally adaptive during that period but the extended to rational expectations). Here a i are the behavioral equation for consumption,c, investment,i,moneydemand,m d /P and z i are the policies (Monetary rule) or law of nature (technology). Francesco Franco Macroeconomics Theory II 6/23

7 Break Stagflation Francesco Franco Macroeconomics Theory II 7/23

8 Macroeconomics Theory. Rational expectations, microfoundations and equilibrium: 1970 s/1980 s - today Lucas (1976) : technically, movements about trend in gross national product in any country can be well described by a stochastically disturbed difference equation of very low order...those regularities which are observed are in the co-movements among different aggregative time series...business cycles are all alike. Francesco Franco Macroeconomics Theory II 8/23

9 Equilibrium Business cycles. Models as laboratory like first keynesian macro-models (Adelmans) Lucas methodological agenda: construct a microfounded rational expectation dynamic model for short-run or business-cycle. Microfoundations allow to compute welfare measures. Rational expectations and microfoundations allow to compute the implications of future policies on future behavior and vice versa. The model should be an explicit description of the way the economy evolves through time. This achieved by spelling out stochastic systems described by the law of motion of the state of the system s t s t+1 = F (s t, e t ), where e t is a vector of exogenous shocks drawn from G (e). Francesco Franco Macroeconomics Theory II 9/23

10 Equilibrium Business cycles. Microfoundations Distinguish actions of agents a it = a(s t ) and policies z t = z(s t ), then if s t+1 = H(z t, a t, s t, e t ) we can express F as F (s t, e t )=H(z(s t ), a(s t ), s t, e t ). This is progress (structural) if H(.) and a(.) do not change in responses to (known) changes in z(.). Francesco Franco Macroeconomics Theory II 10/23

11 Equilibrium Business cycles. Microfoundations and Rational Expectations Lucas critique: there is no reason to expect that the function a(.) remain invariant under changes in the function z(.). Solution builds a more formal structure. Let us assume that at agivendate,whenthesystemisinstates, natureselectsan action z and each agent i selects an action a i from an opportunity set W i (a i, s,z) that is determined by s, z, and the actions a i of the other agents. Denote the payoff of agent i given all of those actions R i (a, s, z). Assume an agent seeks to maximize: ) E ( Â t=0 b t R i (a t, s t, z t ). E is mathematical expectation conditioned on the initial information s 0 :Rational expectations. Francesco Franco Macroeconomics Theory II 11/23

12 Equilibrium Business cycles. Microfoundations and Rational Expectations and equilibrium. Optimal behavior means solving a Bellman equation: ˆ n i (s) = R i (a, s, z)+b max a i 2W i (a i,s,z) n i (H(z(s), a, s, e))dg (e). The system is in equilibrium when each agent i chooses the action a i that attains the RHS of the Bellman equation given the actions chosen by all other agents. The nature of such an equilibrium will depend on R i, W i, z, H and G. Anychangeinz will induce a change in a and hence on the reduced form F. Francesco Franco Macroeconomics Theory II 12/23

13 Equilibrium Business cycles. Theoretical sources of disturbances or shocks. Lucas (1976): e are monetary shocks. Agents are confused and are uncertain about aggregate versus temporary/permanent idiosyncratic shocks. Prototype of news shocks. Robert Lucas. An Equilibrium Model of the Business Cycle JPE, 1975, Vol. 83, no. 6 Kydland and Prescott (1982): e is an aggregate technology shock. Prototype of supply shocks. Time to Build and Aggregate Fluctuations Econometrica, 1982, Volume 50, Issue 6 Francesco Franco Macroeconomics Theory II 13/23

14 Rational Expecations Econometrics. Empirical analysis: time series. Sargent (2005): A rational expectation model is a likelihood. Maximize it. Remember that the reduced form model can ba casted as s t+1 = F (s t, e t ), where e t is a vector of exogenous shocks drawn from G (e). Infact linear approximations of non-linear model or linear specifications in empirical models are the standard: s t+1 = As t + Bh t x t = Cs t + De t Maximum Likelihood methods Lars Peter Hansen, Thomas J. Sargent, Formulating and estimating dynamic linear rational expectations models, Journal of Economic Dynamics and Control, Volume 2, 1980, Pages 7-46 Francesco Franco Macroeconomics Theory II 14/23

15 Dynamic Macro Econometrics. Empirical analysis: time series. Sargent (2005) But after about five years of doing likelihood ratio tests on rational expectations models, I recall Bob Lucas and Ed Prescott both telling me that those tests were rejecting too many good models. Calibration: RBC literature, take estimates from some previous study and pretend that they are known numbers. SVAR: Agnostic data approach to recover e t. Sims, C. A.. (1980). Macroeconomics and Reality. Econometrica, 48(1), Blanchard, O. J., & Quah, D.. (1989). The Dynamic Effects of Aggregate Demand and Supply Disturbances. The American Economic Review, 79(4), Francesco Franco Macroeconomics Theory II 15/23

16 Time Series. Requirements. Are cycles and trends conceptually separated? Less clear today: hysteresis. The systematic study of business fluctuations require that they exhibit some regularities: the events comprising an economic time series must be sufficiently dissimilar from each other that more experiences provide additional information and sufficiently similar that combining individual events can help to understand the underlying economic structure. This requirement is the essence of the technical assumptions that a time series is stationary and ergodic. Francesco Franco Macroeconomics Theory II 16/23

17 Time Series. Requirements. Ergodic process x: Variance and covariances are independent of time, or more formally that the stochastic process is covariance stationary: µ = E (x t ) g(0) =E h(x t µ) 2i g(t) =E [(x t µ)(x t t µ)], t = 1, 2,... Reasonable? Sometimes not: some episodes appear to be unique: Great depression, Wars...You can handle them with a deeper process that generates such episodes infrequently. But given the length of the series we have this point is not so Francesco Franco Macroeconomics Theory II 17/23

18 Time Series. Stationarity. In general we can think of an economic series as: y t = y g t + y c t Where y g t is a growth component and y c t acyclicalcomponentand y g t = d + y g t 1 + eg t, y c t = ry c t 1 + e c t. Applying the first difference shows that you indeed make the series stationary but you cannot disentangle the two components unless they are orthogonal or perfectly Francesco Franco Macroeconomics Theory II 18/23

19 Time Series. Detrending. We are interested in transforming the series to induce stationarity. To achieve it we filter the series y t :The first difference D = 1 L, where L is the lag operator which is defined by Ly t = y t 1. Apply it to the RW: Dy t (1 L)y t = y t y t 1 = d + e t where L is the lag operator. This first difference is a linear filter h(l) =1 L, so that y c t = h(l)y t Francesco Franco Macroeconomics Theory II 19/23

20 Time Series. Detrending. Usually we rely on the assumption that et g has a small variance relative to et c.inthiscasewecanhopetogetthetrendoutby taking out a smooth curve: The Hodrick-Prescott filter which can be obtained as the solution of: min {y g t } T +1 t=0 T h  (y t yt g ) 2 + l y g t+1 yt g yt g y g t 1 t=1 one can show (see King and Rebelo 1993) that in the case for T!, h(l) = l [1 L]2 1 L l [1 L] 2 [1 L 1 ] 2. 2 i Francesco Franco Macroeconomics Theory II 20/23

21 Time Series. Wold decomposition. AveryusefultheoremistheWolddecompositiontheoremwhich says that a zero-mean covariance stationary series (or vector of series) can be represented by an infinite moving average : Y t = Â j Y j u t j + k t where Y t is a vector of variables of interest, u t is also a vector of iid, mean 0, constant variance and k t is a deterministic component. This is convenient because an infinite MA can be well approximated by an ARMA(p,q) or even AR(p) Francesco Franco Macroeconomics Theory II 21/23

22 Time Series. Cyclical properties Once you have covariance stationary series you can study its time domain properties looking at g(t) as a function of t : this is known as the autocovariance function. Stock and Watson look at cyclical component is thought of as the movements associated with periodicities that are between 6 and 32 quarters. They look at the correlation (r(t) = g(t) ) between cyclical g(0) components of output and other variables: where t are quarters. r(x c t, y c t+t), t = 6,...,0, If r is positive and highest for t < 0, then x is procyclical and lags. If r is positive and highest for t > 0, then x is procyclical and leads. Francesco Franco Macroeconomics Theory II 22/23

23 Schedule. Schedule for MaThII, Spring 2016 Date Topics 1. Introduction and Facts 2. The Neoclassical Stochastic Growth Model 3. RBC 4. Money in RBC 6. NKM 7. Monetary Policy 8. Fiscal Policy 9. Open Economy 10. Labour markets 11. Financial markets 12. Estimation Francesco Franco Macroeconomics Theory II 23/23