Dynamic AD and Dynamic AS - PDF Free Download

Dynamic AD and Dynamic AS Pedro Serôdio July 21, 2016

Inadequacy of the IS curve The IS curve remains Keynesian in nature. It is static and not explicitly microfounded. An alternative, microfounded, Dynamic IS curve (DIS) has been developed, and is currently used in modern New Keynesian models. To be consistent with modern macro, the demand curve 1. must incorporate agents forward-looking behaviour 2. so, must be based on a dynamic (not just static) model 3. old IS-LM model has a Keynesian IS curve that embodies only static response of the level of investment today to the level of the real interest rate. The New Keynesian dynamic IS (DIS) curve is the basis of all modern macro models.

Foundations of the dynamic IS schedule Because the DIS is such an important component of modern macro, it is worth understanding its formal derivation.

Foundations of the dynamic IS schedule Because the DIS is such an important component of modern macro, it is worth understanding its formal derivation. Deriving the DIS is fairly straightforward and helps clarify why modern New Keynesian macro emphasises consumption rather than the Keynesian investment channel in the monetary transmission mechanism. We model consumers intertemporal optimisation using the normal budget constraint and indifference curves. From these, we derive an IS curve in which current income depends on future income and the real interest rate.

Aggregate Demand and Aggregate Supply 2-period model, t = 1, 2. Initial wealth is W. C 2 C 1

Aggregate Demand and Aggregate Supply C 2 2-period model, t = 1, 2. Initial wealth is W. Consumption per period is C t, t = 1, 2. C 1

Aggregate Demand and Aggregate Supply C 2 2-period model, t = 1, 2. Initial wealth is W. Consumption per period is C t, t = 1, 2. Income per period is Y t, t = 1, 2. C 1

Aggregate Demand and Aggregate Supply C 2 2-period model, t = 1, 2. Initial wealth is W. Consumption per period is C t, t = 1, 2. Income per period is Y t, t = 1, 2. Real interest rate is r on savings from t 1 to t 2. According to the budget constraint, C 2 = (W + Y 1 C 1 )(1 + r) + Y 2 C 1

Indifference curves Individual s discount factor is β. C 2 Ū C 1

Indifference curves C 2 Individual s discount factor is β. Utility, looking forward from period 1, is U = U(C 1 ) + βu(c 2 ). Ū C 1

Indifference curves C 2 Individual s discount factor is β. Utility, looking forward from period 1, is U = U(C 1 ) + βu(c 2 ). We can define the implicit function U = 0 and use the implicit function theorem to find: Ū C 1 C 2 = 1 U C 1 C 1 β U = MRS C 2 which is the slope of the indifference curve.

Optimisation C 2 In order to maximise utility, agents will equate the marginal rate of substitution (MRS) with the marginal rate of transformation (MRT), which yields: MRS = 1 β U C 1 U C 2 = (1 + r) = MRT C 2 C 1 Ū C 1 This gives rise to the Euler equation for consumption, an expression that characterises the optimal path of consumption over time: U C 1 = (1 + r)βu C 2

Deriving the dynamic IS Assume a particular form for the utility function that implies: U = C σ, where σ is known as the (constant) coefficient of relative risk aversion (CRRA) (implies an isoelastic, or constant elasticity of substitution (CES), utility function). Using this functional form and linearising along the long run values, we get: σc t = r σc e t+1 + r t. We can use the fact that the income-expenditure equation implies: y t = c t + i t + g t (in log terms) and replace that into the expression for consumption. In the New Keynesian model, investment is a function of the capital stock and, consequently, responds to changes to the real interest rate (just like the standard IS). Here, we make the assumption that investment simply replaces depleted stock, so that it is always constant.

Deriving the dynamic IS That means we can write the dynamic IS schedule as: σ(y t g t i t ) = r σ(y e t+1 g e t+1 i e t+1) + r t. y t = g t + y e t+1 g e t+1 1 σ (r t r)

Deriving the dynamic IS That means we can write the dynamic IS schedule as: σ(y t g t i t ) = r σ(y e t+1 g e t+1 i e t+1) + r t. y t = g t + y e t+1 g e t+1 1 σ (r t r) This equation again implies a negative relationship between output and the real interest rate, just like the standard IS schedule.

Deriving the dynamic IS To summarise, so far: A New Keynesian dynamic IS (DIS) curve can be derived from a simple microeconomic model of an intertemporally optimising representative consumer with rational expectations. Basically, the DIS says that the output gap depends on expectations of future output gaps and today s real interest rate.

Deriving the dynamic AD We can use the monetary policy rule we used in the IS-MP model to characterise the conduct of monetary policy in the New Keynesian model.

Deriving the dynamic AD We can use the monetary policy rule we used in the IS-MP model to characterise the conduct of monetary policy in the New Keynesian model. Doing so allows us to derive a relationship between inflation and output similar to the one derived in previous models. The two equilibrium conditions are: y t ȳ = g t + (y e t+1 ȳ) g e t+1 1 σ (r t r) r t = r + φ π (π t π T ) + φ y (y t ȳ) While the expression for output is: yt 1 [ ] = σ(g t + yt+1 e g e σ + φ t+1) φ π (π π T ) + φ y ȳ y Note that there is a negative relationship between inflation and output, as in the IS-MP model discussed before.

Dynamic AS We saw in the preceding section how the Phillips curve allowed us to derive an upward sloping aggregate supply schedule.

Dynamic AS We saw in the preceding section how the Phillips curve allowed us to derive an upward sloping aggregate supply schedule. In standard New Keynesian models prices, rather than wages, are assumed to be sticky due to a variety of possible reasons. Menu costs: the increase in profits from changing prices is small for any given firm but, due to aggregate demand externalities, this cost can be much larger for the economy as a whole. Firms don t change prices frequently. (problem: if all firms are the same, they will all either adjust or not adjust so, every period, prices are either infinitely flexible or completely fixed)

Dynamic AS Information asymmetries I: firms receive incomplete information regarding whether prices reflect demand for their own product or an increase in the general price level. They will respond by changing prices somewhat, but not enough to prevent all of the additional demand, and will therefore increase production too. Information asymmetries II: firms do not receive a signal to adjust their prices and, therefore, keep them constant for a number of periods.

Dynamic AS The latter case is by far the most common in the literature.

Dynamic AS The latter case is by far the most common in the literature. Because only some firms update their price, the general price will reflect that fact: some firms will change prices to reflect economic conditions while other firms simply keep last period s prices constant. This implies: p t = θp t + (1 θ)p t 1 where θ is the fraction of firms changing their price and p is the optimal price. The problem of finding the optimal price, p, is very complex, but it can be shown that, in combination with the expression above, that leads to the so-called New Keynesian Phillips Curve: π t = βπ e t+1 + κ(y t ȳ)

We can combine the new Phillips curve with the dynamic IS schedule to complete the DAD-DAS model. π t = βπt+1 e + κ(y t ȳ) yt 1 [ ] = σ(g t + yt+1 e g e σ + φ t+1) φ π (π π T ) + φ y ȳ y

We can combine the new Phillips curve with the dynamic IS schedule to complete the DAD-DAS model. π t = βπt+1 e + κ(y t ȳ) 1 [ ] y t = σ(g t + yt+1 e g e σ + φ t+1) φ π (π π T ) + φ y ȳ y

We can combine the new Phillips curve with the dynamic IS schedule to complete the DAD-DAS model. π t = βπt+1 e + κ(y t ȳ) 1 [ ] y t = σ(g t + yt+1 e g e σ + φ t+1) φ π (π π T ) + φ y ȳ y This model has a representation in (y, π) space that is exactly identical to the IS-MP model described above. Why is it a more useful model than any of those that we discussed previously? In short, because this version of the model allows us to think about the impact of expectations on macroeconomic variables, and how policy makers can attempt to manage these in order to achieve their policy goals (e.g., forward guidance).

Equilibrium r MP 1 r 1 r MP 0 DIS 0 DIS 1 Let s examine the impact of a policy where the central bank announces that it intends to raise its inflation target. ȳ y π LRAS DAS 1 DAS 0 π T 1 π T ȳ DAD 0 DAD 1 y

Equilibrium r MP 1 MP 0 r 1 r Let s examine the impact of a policy where the central bank announces that it intends to raise its inflation target. π ȳ LRAS DIS 1 DIS 0 y DAS 1 DAS 0 If the announcement is believed (and even if the central bank does not adjust their policy rule), then DIS shifts out to DIS 1. π T 1 π T DAD 1 DAD 0 y ȳ