Lecture 3 Current Account Dynamics

8/12/2019 Lecture 3 Current Account Dynamics

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Current account dynamics



Outline

• Three main topics

– The fundamental equation of the current account

– The consequences of uncertainty

– Current account sustainability



Extending the two period model• Natural to ask if the insights of the two period

model hold up to more realistic assumptions – Long/infinite time horizons –

Stochastic setting, e.g. output fluctuations

• Makes use of dynamic programming techniques

• We will draw parallels with the modern theory ofconsumption and link to asset pricing theory.



Long horizons (with certainty)

• Small open economy facing an exogenouslygiven real interest rate on world capitalmarkets

• Representative agent maximizes (timeseparable) utility from life time consumption

• A production economy with no depreciation.



What should we expect?

1. Euler equation for consumption should hold2. Marginal product condition for capital should

hold3. There should be separation of investment

and consumption

• Let the economy start at date t , with givencapital K t and a stock of foreign assets, B t



Optimization

• As before, we maximize lifetime utility subjectto an inter-temporal budget constraint.

• With time-separable utility, we maximize



• The intertemporal budget constraint can beobtained by “forward substitution”

• Recall the current account identity



• We can rearrange this:

• Substitute forward one period:

• And plug back in above for B t+1 :



•

But we have to go through a similar process toeliminate B t+2 , Bt+3 , etc all the way to T to get

Rearrange once more and



First order conditions

• As with the two period model, we canmaximize utility by substituting for C t

• We exploit the current account identity yetagain:





• Finally, note that – Lenders will not let the agent die with unpaid debt – And it cannot (by definition) be optimal if our

agent leaves this world at T with unused resources

• So Bt+T+1 =0. But if T ∞, does this mean debtcan be rolled over permanently?



Transversality condition• We asymptotically use up all our resources

• If the limit is ne.g.ative, the present value of what weconsume and invest exceeds the present value of output.We continually borrow to make interest payments.

• If the limit is positive, then the opposite holds andresources aren’t being used. We cannot be at a utilitymaximum.



Fundamental equation of the CA

• Current account imbalances in an inter-temporally solvent economy reflect deviationsof output, consumption, investment andgovernment spending from their “permanentlevels”

• Consider the case β=1/1+r. In this case, theEuler equation reminds us that optimalconsumption is constant.



• Also recall that the sum of an infinitegeometric series is

• We can capture “permanent” by consideringthe annuity value of the variables in the model

• So noting that Cs is constant for all s, we have

x s

1

1 x s 0



• And we can rearrange so that

• where

• And applying the geometric sum yields



• We can also express permanent consumptionas

• And upon recalling the definition of thecurrent account we obtain



So what??

• Suppose output rises above the “permanent”level. Rather than increasing consumption,individuals accumulate foreign assets to smooth

consumption – the country runs a CA surplus• And if investment needs are unusually high, then

people borrow abroad to cushion consumption

instead of using domestic savings• CA imbalances reflect deviations of Y, I, G from

their permanent levels.



• Note that assuming β≠1/1+r does not changethe basic insight of the model

• But letting r vary (e.g. in a two country setting)complicates the analysis as foreign assetholdings will depend on r and “permanent”r*.

• Should current account deficits be a cause ofconcern if they reflect optimal consumptionand investment decisions?



Stochastic version of the model

• Now suppose that our (infinitely lived)economy is subject to stochastic shocks

• Y, I and G are random variables and the shockterms are i.i.d.

• Now the representative agent maximizesexpected lifetime utility



• He still faces the current account identity,which we manipulate forwards to obtain theintertemporal budget constraint:



• The transversality condition again rules outthe possibility that the debtor can foreverrollover debt:

• Budget constraint shows that present value ofexpenditure equals the present value ofincome + wealth.



Optimization problem

• We plug in the period 1 current accountidentity to express the problem inunconstrained fashion:

• And the Euler condition looks familiar:



Fundamental equation

• Using the same approach as before, thefundamental equation of the CA is



Does consumption follow a randomwalk?

• Suppose β=1/1+r and that u(c t) = ct – 0.5c t2

• Notice that the Euler condition implies thatthe agent smooths marginal utility ofconsumption in expectation

• And



• With quadratic utility, people make decisionsunder uncertainty “as if” future randomvariables turn out equal to their conditionalmeans. [certainty equivalence]

• At each point in time, the agent expects tomaintain a constant level of consumption.



Current account sustainability

• In order for a country to keep its foreigncreditors happy, the present value of itsresource transfers must equal the value of theinitial foreign debt.

• To see this, rearrange the infinite horizonbudget constraint:



• Suppose an economy grows at rate g, so thatYs+1=(1+g)Ys

•

And suppose it wants to maintain a constantforeign debt/gdp ratio, i.e

• Which can be written as:



• We can identify the size of the trade surpluswe need to maintain a constant debt/gdp ratioby using the current account identity



• The trade balance need only to compensatethe difference between the interest to be paidon the debt and the growth rate of theeconomy

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Lecture 3 Current Account Dynamics