1 Dynamics of the current account in a small open economy microfounded model Lecture 4, MSc Open Economy Macroeconomics Birmingham, Autumn 2015 Tony Yates
2 Main features of the model. Small open economy. Our economy is too small for outcomes to affect world variables like the real rate. Used by central banks like Sweden, Norway. Used in study of small emerging economies. But world variables affect us. Endowment economy, so we don t model production.
3 Punchlines of the lecture Show how the current account, gap between consumption and the endowment, is procyclical if the endowment is stationary. In the data, the opposite is true. Assume instead a non stationary endowment process, where the growth rate is stationary. This makes the model behave better.
4 Points to note about our SOE model Microfounded model aggregate laws of motion for macro time series derived from adding up outcomes of explicit decisions made by individual consumers These decisions made by finding optimal solutions to a consumption saving problem. Contrast with the DMF model where we made educated guesses about the aggregate money, demand and supply functions.
5 Representative consumer Our model is one of infinitely many and infinitely small identical consumers. Known as the representative agent paradigm. Obviously, since everyone is different, counter factual. Various arguments for pursuing it..
6 On the rep agent paradigm If there are complete markets [to insure agents against all shocks] economy behaves as if there were a rep agent, despite differences. Heterogeneous agent is very hard and computational demands initially made it impossible. It s a first step along the road to understanding. Maybe some situations are nevertheless captured ok by representative agent.
7 Current account expresses flow of saving and borrowing Common in popular discourse for gap between consumption and income, current account, to be viewed as bad if there is a negative number. Translates into protectionist and pro export policies. Or, Polonius, Hamlet: neither a borrower nor a lender be. In this model, borrowing and saving are devices for consumption smoothing and beneficial intertemporal trade.
8 Merits of current account deficits CA deficits therefore neither good, nor bad. What would be bad, in this otherwise frictionless model, is inhibiting saving and borrowing. In more complicated models, where saving and borrowing are not arrived at optimally, it might be legitimate to stop them. Eg some models have overborrowing; relatedly, in others agents mis forecast their future incomes.
9 Consumer optimisation max E t t 0 t u c t d t 1 r d t 1 c t y t Consumers maximise infinite sequence of utilities. Ie they are infinitely lived. Lack of realism justified by i) simplicity and ii) think of family dynasties where each cohort cares altruistically about all subsequent ones. y_t is an endowment; we don t model production for simplicity. At this point we don t specify u(.). It s strictly increasing in c, and twice differentiable wrt c.
10 No Ponzi Games Condition lim j E t d t j 1 r j 0 Can t continually run up debts; d>0 means I owe someone. If stream of consumption set optimally, will mean that expect to make sure debts=0. If you have any positive assets left over at the end of time, better to eat them.
11 Dynamic optimisation using the Lagrangian, again. L E 0 t 0 t u c t t d t 1 r d t 1 y t c t Form the Lagrangian, made from i) period utility, and ii) the LM times the budget constraint set=0. Differentiate wrt choice variables d_t,c_t, and set=0. Eliminate LM s to get, in this case, the Euler equation. Here we have uncertainty, so take care with the expectations operator, which, remember, is just a way of averaging over future possible outcomes. u c t 1 r E t u c t 1
12 Two simplifications to gain insight 1 1 r 1 r 1 We equate the financial (1/1+r) and subjective rates of discount. u c 0. 5 c c 2 And we assume quadrative utility. C_bar is a bliss point. Eg eating just the right amount, or a hot bath of just the right temperature. C<c_bar always.
13 Random walk result u c t 1 r E t u c t 1 c t E t c t 1 These simplifications give us the result that consumption is a random walk. Open economy version of Hall (1978). Led to a rich but inconclusive literature connecting this theoretical time series result to actual time series. Inconclusive since it s hard to tell persistent processes from random walks, especiallly if there are breaks.
14 What it means to solve the model This is not yet the solution to the model. We have found the consumers first order condition, which the solution must obey. Solution to model usually refers to deriving expression for endogenous variable consumption [eg] in terms of primitive parameters and exogenous driver, in this case the output endowment.
15 Plan for analysis Derive an infinite period budget constraint, by repeated substitution of the period budget constraint into itself. Use the random walk assumption to substitute out for the infinite period ahead forecasts. This gives us our relationship between c, ca and y.
16 Building the infinite period budget constraint by repeated substitution Rewrite the budget constraint. 1 r d t 1 y t c t d t Then lead 1 period and rearrange. d t y t 1 c t 1 1 r d t 1 1 r Then substitute this into the first line. Then repeat over and over. 1 r d t 1 y t c t y t 1 c t 1 1 r d t 1 1 r 1 r d t 1 y t c t y t 1 c t 1 1 r y t 2 c t 2 1 r 2 d t 2 1 r 2
17 Getting rid of the last d_t+n term using the No Ponzi Games condition. 1 r d t 1 E t s j 0 y t j c t j 1 r j d t s 1 r s This is what we get eventually. lim j E t d t j 1 r j 0 NPG holds with equality at an optimum. 1 r d t 1 E t j 0 yt j c t j 1 r j So the last d_t term disappears.
18 Recap on our goal. 1 r d t 1 E t j 0 yt j c t j 1 r j Now we have the infinite period budget constraint. Remember that the purpose was to get an expression for c_t [actually the current account, defined later] in terms of the exogenous endowment y_t. To do this we have to turn the infinite sequence forecast on the RHS into terms involving only c_t and y_t.. This is what we do next. Starting with c
19 Turning terms in forecasts of c into terms involving just c 1 r d t 1 E t j 0 yt j c t j 1 r j Expand out the sequence of terms involving c on the RHS so we can see more clearly.. E t c t 1 r 0 E t c t 1 1 r 1 E t c t 2 1 r 2...E t c t j 1 r j We turn each one of these forecasts into a term in c_t, using the random walk property of the Euler equation, and what s called the law of iterated expectations.
20 From c_t+j to c_t. E t c t 1 r 0 First term involves only c_t anyway. E t c t c t Expectation at t of something at t is just that thing at t. E t c t 1 1 r 1 Second term involves c_t+1. c t E t c t 1 We can use the Euler Equation directly to substitute out for this
21 Forecasts into current period c: terms further out than t+1. c t E t c t 1 Take our Euler equation. c t 1 E t 1 c t 2 Lead it one period. c t E t E t 1 c t 2 Then substitute it back into the original, un led Euler Equation. E t E t 1 c t 2 E t c t 2 c t Apply the law of iterated expectations, once.
22 Law of iterated expectations In words: The forecast at t, of what you will forecast tomorrow at t+1 something will be the day after that at t+2 is simply the forecast today at t of what you think something will be at t+2. The forecast of a forecast, is simply the forecast. Likewise, the forecast of a forecast of a forecast is also just the forecast.
23 LOIE again Not special to economics. It s a property of integration [which is what an expectation, or a forecast is] and time series processes. Some conditions required, that we won t go into. Satisfied here.
24 LOIE used to transform the term in c_t+3 E t c t 3 1 r 3 Next, we would deal with the term in c_t+3 E t c t 2 E t E t 2 c t 3 Lead the EE by 2 periods and take expectations of both sides. E t c t 2 c t LHS we can substitute for c_t using our result for c_t+2 c t E t c t 3 And by applying LOIE to RHS of the twice led RR, we get this.
25 Concluding process of dealing with the stream of E_t[c_t+j] s 1 r d t 1 E t j 0 yt j c t j 1 r j Recall this was the infinite period budget constraint of the SOE consumer. c t E t c t j 1 r d t 1 j 0 E t y t j 1 r j c t 1 r j We find that all of the future c s=c_t Hence take out of the expectation. rd t 1 c t r E 1 r t j 0 t y t j 1 r j And with algebra of infinite sequence sum, can write like this. Now need to deal with y s.
26 SOE and permanent income hypothesis rd t 1 c t r E 1 r t j 0 t y t j 1 r j With a bit of algebra, using formula for sum of an infinite geometric series, we can take the c_t onto the LHS. This says, roughly, consumption plus interest payments should be equal to the annuity value of our expected future income stream in the small open economy.
27 Dealing with the E[y_t+j] s y t y t 1 t, 1 We assume a stationary autoregressive process for output, which is an endowment. E t y t j j y t This allows us to express every foreast as a function of rho^j*y_t E t y t 1 y t To see why, work out a few individual cases at the start of the sequence. E t y t 2 E t y t 1 2 y t E t y t 3 E t y t 2 2 E t y t 1 3 y t... Note that the forecast today of future shocks to the endowment is zero.
28 Converting the stream of expected future y_t s into y_t s E t j 0 t y t j 1 r j y t j 0 j 1 r j 1 r 1 r y t First substitute in the result we had using the autoregressive process assumption. Then use our high school formula for the sum of an infinite geometric series. And we are done. So we have converted the infinite sequence of ever far ahead forecasts into a set of terms in today s endowment.
29 How consumption responds to the endowment rd t 1 c t r 1 r c t r 1 r y t 1 r 1 r y t r 1 r y t rd t 1 Consumption responds less than one for one with the endowment. Since the shock is temporary, consumers save some of it to consume later. Utility quadratic, so benefit of small increments in later period very large, hence don t eat it all at once.
30 Towards the relationship between the current account and y tb t y t c t Trade balance=endowment less consumption. ca t rd t 1 tb t tb t y t r 1 r y t rd t 1 y t 1 r 1 r rd t 1 tb t 1 1 r y t rd t 1 Current account=balance between funds used to pay foreign debtors, and trade balance Substituting in, we can get the relationship between the trade balance and the endowment y. ca t 1 1 r y t And between the current account and the endowment y
31 The model and the data Model predicts current account is pro cyclical. But the data says the opposite! Many assumptions made along the way. Which one could be the cause of this problem? We ll show that assuming non stationary endowment [stationary growth] can fix it.
32 A hint from our stationary endowment results c t r 1 r y t rd t 1 This was our expression for consumption. y t y t 1 t, 1 This is the stationary assumption we made about the endowment. As rho goes towards 1, consumers spend more and more of the change in y. They know the change is longer lived, so don t have to share the current change in y out over many periods. Tendency for current account to respond positively [ie for saving to rise] with endowment falls. A clue to saving the model.
33 Non stationary endowment process Δy t y t y t 1 Definition of the change in output between periods. Δy t Δy t 1 t,0 1 A stationary autoregressive process for the growth in the endowment. or in other words a non stationary process for the level of the endowment.
34 Recap on what we need to do Take our infinite period budget constraint. That involves expressions in infinite sequence of expectations of income and consumption. Use the EE and LOIE to substitute out for the expected consumption terms Use the endowment process to try to turn the expected endowment terms into current endowment terms. Then we have an equation relating consumption to the endowment. [And therefore the current account, which is saving, related to the endowment]
35 Deriving expression for current account in terms of expected future growth rates rd t 1 c t ca t y t c t rd t 1 r E 1 r t j 0 t y t j 1 r j Take our old infinite period budget constraint. Which still holds even with different endowment process. ca t y t rd t 1 rd t 1 r 1 r E t j 0 t y t j 1 r j Substitute in the defn of the current account. ca t y t r 1 r E t j 0 ca t E t j 1 t t y t j 1 r j  Δy t j 1 r j  Then a bit of trickery to change the term in expected future levels into one involving expected future growth rates. Note sum spans different dates.
36 Deriving expression for ca in terms of growth. E t Δy t j j Δy t We now have a random walk in growth rates. ca t Δy t. 1 r So our sum of an infinite sequence of expected growth rates can be turned into an infinite set of terms in todays growth. And then using the infinite geometric sequence formula into an expression for a single term in today s growth. If output falls [growth negative] current account improves. This makes the model match the data, roughly!
37 Ca dynamics and the persistence of the growth process ca t Δy t. 1 r The more persistent the growth process, ie the higher is rho. the more the current account responds to changes in the growth rate. Leads to a natural question; does our model predict, as we see in the data, that consumption is more variable than output?
38 Variability of consumption and output Plan for the next lot of algebra [!!] Find the variability of output as a function of the variability of the endowment shock Do the same for consumption. Then figure out [for you in an exercise] what conditions lead to consumption variance being larger. Uses result about the variance of an AR(1).
39 Preliminaries: transforming expression for ca back into one for c, y ca t Δy t. 1 r We start with our expression for the current account as a f(dy). ca t y t c t rd t 1 ca t ca t 1 Δy t Δc t r d t 1 d t 2 Find definition of the change in the current account. Then use this to turn our expression ca=f(dy) into one of the form dc=f(dy,dy_ 1) d t 1 d t 2 ca t 1 ca t ca t 1 Δy t Δc t r ca t 1 Δc t Δy t ca t 1 r ca t 1 Δy t Δy t. 1 r Δy 1 r t 1. 1 r
40 Deriving the variance of consumption growth Δc t 1 r 1 r Δy t 1 r 1 r Δy t 1 This comes from collecting terms in y from last expression on previous slide. Δy t Δy t 1 t Δc t 1 r 1 r t Now substitute in our AR(1) for endowment. Our expression for dc=f(shock) 2 Δct 1 r 1 r 2 2 Using classic formula for variances of functions of random variables, we get this formula for the variance of dc. Now for the variance out output.
41 Computing the variance of an AR(1) [in our case for output growth] Δy t Δy t 1 t 2 Δyt For a stationary univariate process, the variance of the series is given by this next expression Formulae like this crop up a lot in macro, because of the connection between macro and time series. It s worth seeing where it comes from
42 Digression: the variance of an AR(1) E x t E x t 2 Definition of the variance for some process x_t E x t 1 t x 2 Substitute in the AR(1) formulae for x_t E x t 2 t 1 t x 2 E 2 x t 2 t 1 t x 2 Use the AR(1) formula again to substitute out for x_t 1 And keep on doing this. x 2 E 3 x t 3 2 t 2 t 1 t x 2
43 Computing the variance of an AR(1)/ctd x 2 E n t n... 2 t 2 t 1 t x 2 E t s 0,s t E t t E t n t n 2, j We assert that errors in different time periods are uncorrelated; That the variance of the shock does not change over time. E x t x 0 And that the expected value of x is zero. [we ll justify this in a moment].
44 Computing the variance of our AR(1) x x 2 2 / 1 2 Since only the squared terms in the variance product are non zero, and they are all the same, the variance reduces to this infinite sum. Which we can evaluate using the usual formula. 2 Δyt This is to remind you that this was the AR(1) endowment growth variance that we stated earlier, and have now proved.
45 Justifying the assertion that the mean of the AR(1) was zero E x t E x t 1 t E x t E x t 1 t E n t n... 2 t 2 t 1 t Substitute in the expression for the AR(1) repeatedly.. And we see that we are taking an expectation of an infinite sequence of errors. E t j 0, j But we assume that the shock at each point in time is mean zero. Hence the expectation, or mean of x_t is 0 too.
46 Back to deciding whether the variance of consumption growth>variance of output growth Δc t 1 r 1 r t This is the expression we worked out for consumption growth as a f(shock). 2 Δct 1 r 1 r 2 2 Using simple algebra of variances we can deduce the variance of consumption growth. 1 r 1 r This is the condition for the variance of consumption growth to be greater than the variance of the growth in the endowment [output]. Note if rho=0 they are the same.
47 Recap We wrote down a small open economy endowment model. We derived the representative agent consumer eulerequation We used an assumption about quadratic utility to get that this EE implies a random walk. We derived an infinite period budget constraint from the each period one.
48 We then used the RW for consumption, and the law of iterated expectations. to turn the infinite period budget constraint into an expression for c or the ca in terms of the exogenous endowment y. We saw that with a stationary y, the ca was procyclical, which is counterfactual. Re deriving using a stationary dy, we got a countercyclical current account.
49 Recap 3 Finally, we worked out conditions under which the variance of consumption growth > variance of output growth. [Noting that in the data this tends to be true for SOEs.] To do this, we used time series econometrics, and the algebra of variances to derive the variance of an AR(1) process, and its mean.
50 Key assumptions Quadratic utility, and the bliss point. Rational expectations. Complete markets and representative agent. Optimising consumers. Endowment economy, no production. SOE is too small to affect rest of the world. Flexible prices. No money, or monetary policy.
51 Comments comparing this to Eggertson Krugman EK we also began with flexible prices, but later introduced sticky prices. And we had an endowment economy. But there we considered two large economies, one borrowing and one lending. The shock to the borrowers did affect the lenders, because it drove down the real rate. In our SOE model, what happens to our SOE agents does not matter for the real rate or the rest of the world in any way. Note here there was no frictions on borrowing by or lending into the SOE.
Current Accounts in Open Economies Obstfeld and Rogoff, Chapter 2 1 Consumption with many periods 1.1 Finite horizon of T Optimization problem maximize U t = u (c t ) + β (c t+1 ) + β 2 u (c t+2 ) +...
Lecture 1: The intertemporal approach to the current account Open economy macroeconomics, Fall 2006 Ida Wolden Bache August 22, 2006 Intertemporal trade and the current account What determines when countries
The Real Business Cycle model Spring 2013 1 Historical introduction Modern business cycle theory really got started with Great Depression Keynes: The General Theory of Employment, Interest and Money Keynesian
Universidad de Montevideo Macroeconomia II Danilo R. Trupkin Class Notes (very preliminar) The Ramsey-Cass-Koopmans Model 1 Introduction One shortcoming of the Solow model is that the saving rate is exogenous
Intertemporal approach to current account: small open economy Ester Faia Johann Wolfgang Goethe Universität Frankfurt a.m. March 2009 ster Faia (Johann Wolfgang Goethe Universität Intertemporal Frankfurt
The Real Business Cycle Model Ester Faia Goethe University Frankfurt Nov 2015 Ester Faia (Goethe University Frankfurt) RBC Nov 2015 1 / 27 Introduction The RBC model explains the co-movements in the uctuations
Chapter 21: The Discounted Utility Model 21.1: Introduction This is an important chapter in that it introduces, and explores the implications of, an empirically relevant utility function representing intertemporal
Chapter 5 Real business cycles 5.1 Real business cycles The most well known paper in the Real Business Cycles (RBC) literature is Kydland and Prescott (1982). That paper introduces both a specific theory
Prof. Dr. Thomas Steger Advanced Macroeconomics II Lecture SS 2012 6. Budget Deficits and Fiscal Policy Introduction Ricardian equivalence Distorting taxes Debt crises Introduction (1) Ricardian equivalence
Lecture 1: current account - measurement and theory What is international finance (as opposed to international trade)? International trade: microeconomic approach (many goods and factors). How cross country
Real Business Cycle Models Lecture 2 Nicola Viegi April 2015 Basic RBC Model Claim: Stochastic General Equlibrium Model Is Enough to Explain The Business cycle Behaviour of the Economy Money is of little
Chapter 8 Inflation This chapter examines the causes and consequences of inflation. Sections 8.1 and 8.2 relate inflation to money supply and demand. Although the presentation differs somewhat from that
Bond valuation A reading prepared by Pamela Peterson Drake O U T L I N E 1. Valuation of long-term debt securities 2. Issues 3. Summary 1. Valuation of long-term debt securities Debt securities are obligations
Phd Macro, 2007 (Karl Whelan) 1 Real Business Cycle Models The Real Business Cycle (RBC) model introduced in a famous 1982 paper by Finn Kydland and Edward Prescott is the original DSGE model. 1 The early
1 CHAPTER 11. AN OVEVIEW OF THE BANK OF ENGLAND QUARTERLY MODEL OF THE (BEQM) This model is the main tool in the suite of models employed by the staff and the Monetary Policy Committee (MPC) in the construction
COLLEGE ALGEBRA Paul Dawkins Table of Contents Preface... iii Outline... iv Preliminaries... Introduction... Integer Exponents... Rational Exponents... 9 Real Exponents...5 Radicals...6 Polynomials...5
Optimal Consumption with Stochastic Income: Deviations from Certainty Equivalence Zeldes, QJE 1989 Background (Not in Paper) Income Uncertainty dates back to even earlier years, with the seminal work of
Lecture 11-1 6.1 The open economy, the multiplier, and the IS curve Assume that the economy is either closed (no foreign trade) or open. Assume that the exchange rates are either fixed or flexible. Assume
Chapter 23 Squares Modulo p Revised Version of Chapter 23 We learned long ago how to solve linear congruences ax c (mod m) (see Chapter 8). It s now time to take the plunge and move on to quadratic equations.
Franck Portier TSE Macro II 29-21 Chapter 3 Real Business Cycles 36 3 The Standard Real Business Cycle (RBC) Model Perfectly competitive economy Optimal growth model + Labor decisions 2 types of agents
Contents Preface 3 The Basics of Interest Theory 9 1 The Meaning of Interest................................... 10 2 Accumulation and Amount Functions............................ 14 3 Effective Interest
MATHEMATICS OF FINANCE AND INVESTMENT G. I. FALIN Department of Probability Theory Faculty of Mechanics & Mathematics Moscow State Lomonosov University Moscow 119992 firstname.lastname@example.org 2 G.I.Falin. Mathematics
Chapter 4 The Optimal Path of Government Debt Up to this point we have assumed that the government must pay for all its spending each period. In reality, governments issue debt so as to spread their costs
A Model of the Current Account Costas Arkolakis teaching assistant: Yijia Lu Economics 407, Yale January 2011 Model Assumptions 2 periods. A small open economy Consumers: Representative consumer Period
Chapter 3 Credit and Business Cycles Here I present a model of the interaction between credit and business cycles. In representative agent models, remember, no lending takes place! The literature on the
Chapter 4 Payment streams and variable interest rates In this chapter we consider two extensions of the theory Firstly, we look at payment streams A payment stream is a payment that occurs continuously,
Chapter 4 Inflation and Interest Rates in the Consumption-Savings Framework The lifetime budget constraint (LBC) from the two-period consumption-savings model is a useful vehicle for introducing and analyzing
Money and Capital in an OLG Model D. Andolfatto June 2011 Environment Time is discrete and the horizon is infinite ( =1 2 ) At the beginning of time, there is an initial old population that lives (participates)
Real Business Cycle Theory Marco Di Pietro Advanced () Monetary Economics and Policy 1 / 35 Introduction to DSGE models Dynamic Stochastic General Equilibrium (DSGE) models have become the main tool for
Name: Number: Nova School of Business and Economics Macroeconomics, 1103-1st Semester 2013-2014 Prof. André C. Silva TAs: João Vaz, Paulo Fagandini, and Pedro Freitas Final Maximum points: 20. Time: 2h.
ECON 20310 Elements of Economic Analysis IV Problem Set 1 Due Thursday, October 11, 2012, in class 1 A Robinson Crusoe Economy Robinson Crusoe lives on an island by himself. He generates utility from leisure
Introduction to Economics, ECON 1:11 & 13 We will now rationalize the shape of the aggregate demand curve, based on the identity we have used previously, AE=C+I+G+(X-IM). We will in the process develop
CHAPTER 1 Compound Interest 1. Compound Interest The simplest example of interest is a loan agreement two children might make: I will lend you a dollar, but every day you keep it, you owe me one more penny.
Lecture 2 Dynamic Equilibrium Models : Finite Periods 1. Introduction In macroeconomics, we study the behavior of economy-wide aggregates e.g. GDP, savings, investment, employment and so on - and their
Intermediate Macroeconomics: The Real Business Cycle Model Eric Sims University of Notre Dame Fall 2012 1 Introduction Having developed an operational model of the economy, we want to ask ourselves the
Discussion of Capital Injection, Monetary Policy, and Financial Accelerators Karl Walentin Sveriges Riksbank 1. Background This paper is part of the large literature that takes as its starting point the
A B I L E N E C H R I S T I A N U N I V E R S I T Y Department of Mathematics General Theory of Differential Equations Sections 2.8, 3.1-3.2, 4.1 Dr. John Ehrke Department of Mathematics Fall 2012 Questions
Wald s Identity by Jeffery Hein Dartmouth College, Math 100 1. Introduction Given random variables X 1, X 2, X 3,... with common finite mean and a stopping rule τ which may depend upon the given sequence,
Financial Development and Macroeconomic Stability Vincenzo Quadrini University of Southern California Urban Jermann Wharton School of the University of Pennsylvania January 31, 2005 VERY PRELIMINARY AND
Money and Public Finance By Mr. Letlet August 1 In this anxious market environment, people lose their rationality with some even spreading false information to create trading opportunities. The tales about
Graduate Macroeconomics 2 Lecture 1 - Introduction to Real Business Cycles Zsófia L. Bárány Sciences Po 2014 January About the course I. 2-hour lecture every week, Tuesdays from 10:15-12:15 2 big topics
1. Differentiation The first derivative of a function measures by how much changes in reaction to an infinitesimal shift in its argument. The largest the derivative (in absolute value), the faster is evolving.
CONSUMPTION Most prominent work on consumption: 1. John Maynard Keynes: consumption and current income 2. Irving Fisher and Intertemporal Choice 3. Franco Modigliani: the Life-Cycle Hypothesis 4. Milton
EC3070 FINANCIAL DERIVATIVES Exercise 1 1. A credit card company charges an annual interest rate of 15%, which is effective only if the interest on the outstanding debts is paid in monthly instalments.
Economics 7344, Spring 2013 Bent E. Sørensen INTEREST RATE THEORY We will cover fixed income securities. The major categories of long-term fixed income securities are federal government bonds, corporate
Lecture 14 More on Real Business Cycles Noah Williams University of Wisconsin - Madison Economics 312 Optimality Conditions Euler equation under uncertainty: u C (C t, 1 N t) = βe t [u C (C t+1, 1 N t+1)
Does Black-Scholes framework for Option Pricing use Constant Volatilities and Interest Rates? New Solution for a New Problem Gagan Deep Singh Assistant Vice President Genpact Smart Decision Services Financial
A Two-Period Model of the Current Account Obstfeld and Rogo, Chapter 1 1 Small Open Endowment Economy 1.1 Consumption Optimization problem maximize U i 1 = u c i 1 + u c i 2 < 1 subject to the budget constraint
Chapter Vector autoregressions We begin by taking a look at the data of macroeconomics. A way to summarize the dynamics of macroeconomic data is to make use of vector autoregressions. VAR models have become
MA Advanced Macroeconomics: 7. The Real Business Cycle Model Karl Whelan School of Economics, UCD Spring 2015 Karl Whelan (UCD) Real Business Cycles Spring 2015 1 / 38 Working Through A DSGE Model We have
Two-State Options John Norstad email@example.com http://www.norstad.org January 12, 1999 Updated: November 3, 2011 Abstract How options are priced when the underlying asset has only two possible
Summing up 4310 ECON4310 Lecture Asbjørn Rødseth University of Oslo 27/11 2013 Asbjørn Rødseth (University of Oslo) Summing up 4310 27/11 2013 1 / 20 Agenda Solow, Ramsey and Diamond Real Business Cycle
ECON 5110 Class Notes Overview of New Keynesian Economics 1 Introduction The primary distinction between Keynesian and classical macroeconomics is the flexibility of prices and wages. In classical models
Lecture 6 Weight Tension Normal Force Static Friction Cutnell+Johnson: 4.8-4.12, second half of section 4.7 In this lecture, I m going to discuss four different kinds of forces: weight, tension, the normal
Introduction to Real Estate Investment Appraisal Maths of Finance Present and Future Values Pat McAllister INVESTMENT APPRAISAL: INTEREST Interest is a reward or rent paid to a lender or investor who has
Induction Margaret M. Fleck 10 October 011 These notes cover mathematical induction and recursive definition 1 Introduction to induction At the start of the term, we saw the following formula for computing
Brunel University Msc., EC5504, Financial Engineering Prof Menelaos Karanasos Lecture Notes: Basic Concepts in Option Pricing - The Black and Scholes Model Recall that the price of an option is equal to
Chapter 4: Vector Autoregressive Models 1 Contents: Lehrstuhl für Department Empirische of Wirtschaftsforschung Empirical Research and und Econometrics Ökonometrie IV.1 Vector Autoregressive Models (VAR)...
3 Introduction to Assessing Risk Important Question. How do we assess the risk an investor faces when choosing among assets? In this discussion we examine how an investor would assess the risk associated
Insurance Michael Peters December 27, 2013 1 Introduction In this chapter, we study a very simple model of insurance using the ideas and concepts developed in the chapter on risk aversion. You may recall
1 Bond Price Arithmetic The purpose of this chapter is: To review the basics of the time value of money. This involves reviewing discounting guaranteed future cash flows at annual, semiannual and continuously
Prof. Dr. Thomas Steger Advanced Macroeconomics II Lecture SS 13 2. Real Business Cycle Theory (June 25, 2013) Introduction Simplistic RBC Model Simple stochastic growth model Baseline RBC model Introduction
WHY THE LONG TERM REDUCES THE RISK OF INVESTING IN SHARES A D Wilkie, United Kingdom Summary and Conclusions The question of whether a risk averse investor might be the more willing to hold shares rather
1 Simple interest 2 5. Time value of money With simple interest, the amount earned each period is always the same: i = rp o We will review some tools for discounting cash flows. where i = interest earned
Econ 116 Mid-Term Exam Part 1 1. True. Large holdings of excess capital and labor are indeed bad news for future investment and employment demand. This is because if firms increase their output, they will
A Review of the Literature of Real Business Cycle theory By Student E XXXXXXX Abstract: The following paper reviews five articles concerning Real Business Cycle theory. First, the review compares the various
Lecture 6 Investment Decisions The Digital Economist Investment is the act of acquiring income-producing assets, known as physical capital, either as additions to existing assets or to replace assets that
A Theory of Capital Controls As Dynamic Terms of Trade Manipulation Arnaud Costinot Guido Lorenzoni Iván Werning Central Bank of Chile, November 2013 Tariffs and capital controls Tariffs: Intratemporal
Geometric Series and Annuities Our goal here is to calculate annuities. For example, how much money do you need to have saved for retirement so that you can withdraw a fixed amount of money each year for
VI. Real Business Cycles Models Introduction Business cycle research studies the causes and consequences of the recurrent expansions and contractions in aggregate economic activity that occur in most industrialized
Choice under Uncertainty Part 1: Expected Utility Function, Attitudes towards Risk, Demand for Insurance Slide 1 Choice under Uncertainty We ll analyze the underlying assumptions of expected utility theory
Chapter 5 MEASURING GDP AND ECONOMIC GROWTH* Key Concepts Gross Domestic Product Gross domestic product, GDP, is the market value of all the final goods and services produced within in a country in a given
6.042/8.062J Mathematics for Comuter Science December 2, 2006 Tom Leighton and Ronitt Rubinfeld Lecture Notes Random Walks Gambler s Ruin Today we re going to talk about one-dimensional random walks. In
Macroeconomics Lecture 1: The Solow Growth Model Richard G. Pierse 1 Introduction One of the most important long-run issues in macroeconomics is understanding growth. Why do economies grow and what determines
We analyze the multiplier effect of fiscal policy changes in government expenditure and taxation. The key result is that an increase in the government budget deficit causes a proportional increase in consumption.
THE FUNDAMENTAL THEOREM OF ARBITRAGE PRICING 1. Introduction The Black-Scholes theory, which is the main subject of this course and its sequel, is based on the Efficient Market Hypothesis, that arbitrages
Theory of Computation Prof. Kamala Krithivasan Department of Computer Science and Engineering Indian Institute of Technology, Madras Lecture No. # 31 Recursive Sets, Recursively Innumerable Sets, Encoding
APPLICATIONS AND MODELING WITH QUADRATIC EQUATIONS Now that we are starting to feel comfortable with the factoring process, the question becomes what do we use factoring to do? There are a variety of classic
Arbitrage 1. Exchange rate arbitrage Exchange rate arbitrage is the practice of taking advantage of inconsistent exchange rates in different markets by selling in one market and simultaneously buying in
UGBA 103 (Parlour, Spring 2015), Section 1 Present Value, Compounding and Discounting Raymond C. W. Leung University of California, Berkeley Haas School of Business, Department of Finance Email: firstname.lastname@example.org
Lecture 8: Asset Markets c 2009 Je rey A. Miron Outline:. Present and Future Value 2. Bonds 3. Taxes 4. Applications Present and Future Value In the discussion of the two-period model with borrowing and
Answers to Text Questions and Problems in Chapter 8 Answers to Review Questions 1. The key assumption is that, in the short run, firms meet demand at pre-set prices. The fact that firms produce to meet
Performance Assessment Task Quadratic (2009) Grade 9 The task challenges a student to demonstrate an understanding of quadratic functions in various forms. A student must make sense of the meaning of relations
Monetary Theory of Inflation and the LBD in Transactions Technology. Constantin T. Gurdgiev Department of Economics, Trinity College, Dublin. The Open Republic Institute, Dublin. email@example.com Draft 1/2003.
Statistics in Retail Finance 1 Overview > So far we have focussed mainly on application scorecards. In this chapter we shall look at behavioural models. We shall cover the following topics:- Behavioural
6.42/8.62J Mathematics for Computer Science Srini Devadas and Eric Lehman May 3, 25 Lecture otes Expected Value I The expectation or expected value of a random variable is a single number that tells you
Your consent to our cookies if you continue to use this website.