Macroeconomics Theory II

Transcription

1 Macroeconomics Theory II Francesco Franco Nova SBE February 2012 Francesco Franco Macroeconomics Theory II 1/31

2 Housekeeping Website TA: none No "Mas-Collel" in macro One midterm, one final, problem sets Francesco Franco Macroeconomics Theory II 2/31

3 Course Two parts: I: Fluctuations/ Core/DSGE II: Imperfections/Periphery Fluctuations part requires fixed investment in Matlab Applied Theory course Francesco Franco Macroeconomics Theory II 3/31

4 Classical, Keynesian, Neo, New, Post What do you know about Macro? Classics, Keynesians, neo-classics, new-classics, new-keneysian... Crisis Francesco Franco Macroeconomics Theory II 4/31

5 Undergraduate Model An undergraduate textbook model (most of them) typically divide the economy in goods market, financial markets, labor market The model is usually static but sometimes contains dynamic features, Tte equilibrium conditions are: Y = a C (Y, r, T, Y Õ, r Õ, T Õ )+a I (Y, r, Y Õ, r Õ )+G M/P = a M d /P(i, Y ) or i = z MR (fi, Y ) fi = E[fi]+z Y (Y, z) and the real interest rate r i fi e. Here a i are the behavioral equation for consumption,c, investment,i, money demand,m d /P and z i are the policies (Monetary rule) or law of nature (technology) Francesco Franco Macroeconomics Theory II 5/31

6 Undergraduate Model In the SR the price level is given, expectations are not realized, the aggregate demand side of the economy determines output In the MR expectations are realized, the aggregate supply side of the economy determines output (which is the equilibrium level of output) Money a ects real variables in the short run but in the medium run the classical neutrality holds Fiscal policy can have opposite e ects in SR and MR Expectations about the future can have real e ects Francesco Franco Macroeconomics Theory II 6/31

7 Undergraduate Model The undergraduate model is useful, because it is simple and is a reduced form of a more microfounded model Too many shortcuts...are we sure of their strength? We cannot talk about welfare which is the measure of what is better or worse in Economics Francesco Franco Macroeconomics Theory II 7/31

8 Graduate Model Methodology: Lucas/Kydland and Prescott agenda: construct a dynamic model that fits historical data and that can be simulated to give reliable estimates of the e ects of future policies on future behavior 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 8/31

9 Graduate Model You can estimate empirically a reduced form model by identifying the vector s t with observable magnitudes and estimate F and G. Forecasting... F depends on policies and all actions of all agents in the system. A policy change involves a shift from F to F Õ. How can we get it? Francesco Franco Macroeconomics Theory II 9/31

10 Graduate Model Distinguish actions of agents a it = a(s t ) and policies z t = z(s t ),thenifs 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(.) More or less our undergraduate model stacked Francesco Franco Macroeconomics Theory II 10/31

11 Graduate Model 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 a given date, when the system is in state s, nature selects an action z and each agent i selects an action a i from an opportunity set i (a i, s,z) that is determined by s, z, and the actions a i of the other agents Francesco Franco Macroeconomics Theory II 11/31

12 Graduate Model Denote the payo of agent i given all of those actions R i (a, s, z). Assume an agent seeks to maximize: E I ÿ Œ J t R i (a t, s t, z t ) t=0 E is mathematical expectation conditioned on the initial information s 0 : Rational expectations Francesco Franco Macroeconomics Theory II 12/31

13 Graduate Model Optimal behavior means solving a Bellman equation: ; i (s) = max R i (a, s, z)+ a i œ i (a i,s,z) < 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, i, z, H and G. Any change in z will induce a change in a and hence on the reduced form F Francesco Franco Macroeconomics Theory II 13/31

14 Graduate Model Need to solve it The system will be successful in simulating the e ects of policy e ects only if preference R i and the technology and the rules of the game are invariant to changes in z We shall put more structure and study more specific cases, but this will be the rule of the game we will play in the first part of the course The new tools developed by the new-classicals dominate the academic work but the facts forced imperfections back in the benchmark mode Francesco Franco Macroeconomics Theory II 14/31

15 Facts Striking historical features of aggregate output Figure: Sustained long run growth Francesco Franco Macroeconomics Theory II 15/31

16 Facts Striking historical features of aggregate output Figure: Recurrent fluctuations around this growth path Francesco Franco Macroeconomics Theory II 16/31

17 Time Series Are cycles and trends conceptually separated? Endogenous-growth vs exogenous growth The systematic study of business fluctuations require that they exhibit some regularities: the events comprising an economic time series must be su ciently dissimilar from each other that more experiences provide additional information su ciently 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 17/31

18 Time Series Ergodic process x: Variance and covariances are independent of time, or more formally that the stochastic process is covariance stationary: µ = E(x t ) (0) =E Ë(x t µ) 2È ( ) =E [(x t µ)(x t µ)], = 1, 2,... (weaker than strict stationarity) 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 Francesco Franco Macroeconomics Theory II 18/31

19 Time Series Non stationarity The first requirement: historical experiences be su ciently unrelated is unlikely to hold in the first figure. This is because the current trend levels of these variables depend on the entire history of these series Think about a deterministic trend which increase by some fixed amount every quarter: y t = + t + t, t = 1,...,T where t is a sequence of independent random variables drawn from a distribution with mean zero and constant variance. Inconsistent with the first figure Francesco Franco Macroeconomics Theory II 19/31

20 Time Series Figure: Linear deterministic trend Francesco Franco Macroeconomics Theory II 20/31

21 Time Series Non stationarity A stochastic trend increases in each quarter by some fixed amount on average, however in any given quarter the change in the trend will deviate from its average by some unforecastable random amount This is a rough definition of a random walk with drift: y t = d + y t 1 + t. With this formulation of a trend change in the trend in one quarter provides a new base from which growth will occur in the next Francesco Franco Macroeconomics Theory II 21/31

22 Time Series We are interested in transforming the series to induce stationarity. To achieve it we filter the series y t : the first di erence =1 L, wherel is the lag operator which is defined by Ly t = y t 1. Apply it to the RW: y t (1 L)y t = y t y t 1 = d + t where L is the lag operator. This first di erence is a linear filter h(l) =1 L, so that yt c = h(l)y t Francesco Franco Macroeconomics Theory II 22/31

23 Time Series 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 a cyclical component and y g t = d + y g t 1 + g t, y c t = fly c t 1 + c t. Applying the first di erence shows that you indeed make the series stationary but you cannot disentangle the two components unless they are orthogonal or perfectly correlated. Usually we rely on the assumption that g t has a small variance relative to c t. In this case we can hope to get the trend out by taking out a smooth curve Francesco Franco Macroeconomics Theory II 23/31

24 Time Series The Hodrick-Prescott filter which can be obtained as the solution of: min {y g t } T +1 t=0 Tÿ Ë!yt yt g t=1 " 2 + #! y g t+1 y g t "! y g t y g t 1"$ 2 È one can show (see King and Rebelo 1993) that in the case for T æœ, h(l) = [1 L]2 # 1 L 1$ [1 L] 2 [1 L 1 ] 2. Francesco Franco Macroeconomics Theory II 24/31

25 Time Series The Baxter and King band-pass filter is a filter designed to isolate the fluctuations that persists for periods of two through eight years. The filter is a double sided moving average h(l) = q K j= K h j L j where the h j are chosen according to an approximately optimal criterion (see Baxter and King 1995) Francesco Franco Macroeconomics Theory II 25/31

26 Time Series A very useful theorem is the Wold decomposition theorem which says that a zero-mean covariance stationary series (or vector of series) can be represented by an infinite moving average : Y t = ÿ j ju 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) process Francesco Franco Macroeconomics Theory II 26/31

27 Time Series Once you have covariance stationary series you can study its time domain properties looking at ( ) as a function of : this is known as the autocovariance function. Stock and Watson look at the recurrent facts of the recovered cyclical components of a selected (exhaustive) list of US economic series. Their cyclical component is thought of as the movements associated with periodicities that are between 6 and 32 quarters. They look at the correlation (fl( ) = ( ) (0) ) between cyclical components of output and other variables: where t are quarters. fl(x c t, y c t+ ), = 6,...,0, If fl is positive and highest for <0, thenx is procyclical and lags If fl is positive and highest for >0, thenx is procyclical and leads Francesco Franco Macroeconomics Theory II 27/31

28 Time Series US comovements Output and Consumption: high and positive Output and Inventory high and positive Output and Export: low Output and Government expenditure (total purchases, defense, non-defense) low High correlation across sectors Francesco Franco Macroeconomics Theory II 28/31

29 Time Series US comovements Output and Employment high and positive. lag suggest movements in output then movement in bodies Output and Hours: high, positive and coincident. Suggest hours before bodies Output and Productivity (Solow Residual and Labor productivity) high and positive, lead Output and Prices: real wage and real interest rate. No movement, slightly procyclical real wage Output and interest rates: nominal (fed, 10y) is prociclycal, lags output. Real interest rate slightly countercyclical Output and inflation (GDP deflator and CPI), high lag Francesco Franco Macroeconomics Theory II 29/31

30 Time Series US comovements Comovements are strong Prices do not move much Relation with inflation, money and productivity. But what is the causality? Francesco Franco Macroeconomics Theory II 30/31

31 References Methods and Problems in Business Cycle Theory (1980), Robert Lucas The state of Macro Olivier J. Blanchard NBER Working Paper No August 2008 Modern Macroeconomic Models as tools for Economic policy, Narayana Kocherlakota, May 2010 Macroeconomics after the Crisis: Time to Deal with the Pretense-of-Knowledge Syndrome, Ricardo Caballero Journal of Economic Perspectives Volume 24, Number 4 Fall 2010 Pages Time Series Analysis, Hamilton Francesco Franco Macroeconomics Theory II 31/31