Advanced Macroeconomics An Easy Guide An application The small open economy

An application The small open economy The Neoclassical Growth Model ( is more than just a growth model . It provides us with a powerful tool to think about a number of questions in , which require us to think dynamically So lets now put it to work ! We will do so in a simple but important application understanding the capital accumulation dynamics for a small open economy . As we will see shortly , in an open economy the capital lation process is by the possibility of using foreign savings . This really allows countries to move much faster in the process of capital accumulation ( if in doubt ask the Norwegians ! and is one of the main reasons why integrating into world capital markets is often seen as a big positive for any economy . The use of foreign savings ( or the accumulation of assets abroad ) is in the economy current account , so the applied to a small open economy can be thought of as yielding a model of the behaviour of the current account . The current account provides a measure of how fast the country is building foreign assets ( or foreign debt ) and as such it is a key piece to assess the sustainability of policies . We will also see that the adjustment of the current account to different shocks can lead to surprising and unexpected results . Finally , the framework can be used to analyse , for example , the role of stabilisation funds in small open economies . Some basic identities A quick refresher that introduces the concept of the current account . A good starting point is to start with the basic identities , which you have seen before in your introductory and intermediate macro courses . Recall the relationship between ( Gross National Product , the amount that is paid to a country residents ) and ( Gross Domestic Product , the amount of goods produced in a particular country ) How to cite this book chapter , and , A . 2021 . Advanced An Easy Guide . An application The small open economy , London Press . DOI . License .

42 AN APPLICATION THE SMALL OPEN ECONOMY where is the position held by residents in foreign assets ( net of domestic assets held by foreigners ) and is the rate of return paid on those assets . In other words , is the total ( net ) interest payments made by foreigners to residents . Notice that countries with foreign assets will have a which is larger than , whereas countries with debt will have a which is smaller than their . Starting from the output equation we have that , where , I , and , stand , as usual , for consumption , investment , government expenditures , exports and imports . This can be rewritten as , The side ( is roughly the current account CA ( the trade balance plus the net income on net foreign assets , which is typically called primary income , add up to the current account ) The equation says that the current account is equal to the difference between what the economy saves ( and what it invests ( I ) Another alternative is to write this as , Absorption CA , which clearly shows that a current account is the difference between income and absorption , In mon parlance if a country spends more than it earns , it runs a current account deficit , Importantly , and as we will see over and over again , this does not mean that current account are bad ! They simply mean that a country is using debt and , as always , whether that is a good or a bad thing hinges on whether that is done in a sustainable way . To that out , we need to embed these accounting identities into an model of how consumption and investment are chosen given current and future output . As luck would have it , this is exactly what the is ! The Ramsey problem for a small open economy VVe will solve the ( benevolent central planner ) Ramsey problem for a small open economy . The key conclusions are ( i ) consumption can be perfectly smoothed ( ii ) the capital stock can adjust immediately via foreign borrowing , and thus becomes independent of domestic savings . This is because the current account allows the economy to adjust to shocks while maintaining optimal levels of consumption and capital stock . Here is where we will start using , right away , what we learnt in the previous chapter . As before , there is one representative household whose members consume and produce . Population growth is now assumed to be for simplicity initial population is to , so that all quantities are in per capita terms ( in letters ) There is one good , and no government . The key difference is that now the economy is open , in the sense that foreigners can buy domestic output , and domestic residents can buy foreign output . Whenever domestic income exceeds domestic

AN APPLICATION THE SMALL OPEN ECONOMY 43 expenditure , locals accumulate claims on the rest of the world , and vice versa . These claims take the form of an bond , in units of the only good . The economy is also small , in the sense that it does not affect world prices ( namely the interest rate ) and thus takes them as given . We will assume also that the country faces a constant interest rate . The constancy of is a key ing feature of the small country model . However , this is a strong assumption if a country borrows a lot , probably its country risk would increase and so would the interest rate it would have to pay but we will keep this assumption for now . We will return to issues of risk when we talk about tion and investment , in ( Chapters 13 and 14 . The utility function is exactly as before ( with ) re ( The resource constraint of the economy is , The novelty is that now domestic residents own a stock 17 , of the bond , whose rate of return is , which is a constant from the standpoint of the small open economy What is the current account in this representation ?

It is income ( which ( minus consumption , minus investment I , In other words , it is equal to 17 ' A surplus is equivalent to an increase in foreign bond holdings . In the open economy , we also have to impose a game ( condition ( or solvency condition ) yr ( This condition again , not to be confused with the transversality condition ( we met in the chapter did not apply to the benevolent central planner ( in the last chapter because they could not borrow in the context of a closed economy . It did apply to the consumers in the equilibrium though , and here it must apply to the economy as a whole . It means that the economy not run a Ponzi scheme with the rest of the world by borrowing money to pay interest on its outstanding debt . In other words , this rules out explosive trajectories of debt accumulation under the assumption that foreigners would eventually stop lending money to this pyramid scheme . A useful transformation total domestic assets per capita as a , 17 , Then , becomes 51 , and ( becomes , aT )

44 AN APPLICATION THE SMALL OPEN ECONOMY Solution to consumer problem The consumer ( 45 ) subject to ( and ( for given and be . The for the problem can be written as ( Note is one control variable ( jumpy ) and now is another control variable ( also jumpy ) It is now a that is the state variable ( sticky ) the one that has to follow the equation of motion . A is the costate variable ( the multiplier associated with the budget constraint , also jumpy ) The costate has the same intuitive interpretation as before the marginal value as of time of an additional unit of the state ( assets , in this case ) Here is a question for you to think about why is capital a jumpy variable now , while it used to be sticky in the closed economy ?

The order conditions are then ( and 1113 a , Using ( in ( we obtain ( CI ) Dividing both sides by ( CI ) and using the of the elasticity of substitution , gets us to our equation for the dynamic behaviour of consumption ( This equation says that consumption is constant only if , which we assume from now on . Notice that we can do this because and are exogenous . This assumption eliminates any inessential dynamics ( including endogenous growth ) and ensures a It follows then that consumption is constant , Solving for the stock of domestic capital ( says that the marginal product of ( capital is constant and equal to the interest rate on bonds . Intuitively , the marginal return on both assets is . This means that capital is always at its steady state level , which is by '

AN APPLICATION THE SMALL OPEN ECONOMY 45 This means , in turn , that domestic per capita income is constant , and given by ( Note that the capital stock is completely independent of savings and consumption decisions , which is a crucial result of the small open economy model . One should invest in capital according to its rate of return ( which is by the return on bonds ) and raise the necessary resources not out of savings , but out of debt . The steady state consumption and current account Now that you have the level of income you should be able to compute the level of consumption . How do we do that ?

By solving the differential equation that is the budget constraint ( which we can rewrite as 51 , rat ( using the solutions for optimal consumption and capital stock . Using our strategy of integrating factors , we can multiply both sides by , and integrate the resulting equation between and ate ( Now evaluate this equation as oo . Considering the and the , it follows that mo ( We can also the optimal level of debt at each time period . It is easy to see that a , is kept constant at ac , from which it follows that 19 , be . The current account is zero . In other words , the delivers a growth model with no growth , as we saw in the last chapter , and a model of the current account dynamics without current account surpluses or . Not so fast , though ! We saw that the did have predictions for growth outside of the . Let look at the transitional dynamics here as well , and see what we can learn . The inexistence of transitional dynamics There are no transitional dynamics in this model output per capita converges instantaneously to that of the rest of the world ! Suppose that initial conditions are and be . But , condition ( 419 ) says that capital must always be equal to , Hence , in the first instant , capital must jump up from to , How is this accomplished ?

Domestic residents purchase the necessary quantity of capital ( the single good ) abroad and instantaneously install it . Put differently , the speed of adjustment is infinite . How do the domestic residents pay for this new capital ?

By drawing down their holdings of the bond . If Ako ko , then ( ko ) Note that this transaction does not affect initial net national assets , since Aka Aka Ako .

46 AN APPLICATION THE SMALL OPEN ECONOMY An example Suppose now that the production function is given by ( Ak , A , a 31 . This means that condition ( is aA ( so that the level of capital on the is . which is increasing in A and decreasing in , Using this solution for the capital stock we can write ) as ( Ez ( A ) with ( A ) increasing in A . It follows that consumption can be written as mo ( A ) mo ( 002 ( A ) with ( A ) Productivity shocks and the current account Suppose the economy initially has total factor productivity A , with corresponding optimal stock of capital ( and consumption level ( At time there is an unanticipated and permanent fall in productivity from A to AL , where AL A ( maybe because this economy produced oil , guano , or diamonds and its price has come down ) This means , from ( that ( A ) falls from ( AH ) to ( AL ) Capital holdings are reduced residents sell capital in exchange for bonds , so after the shock they have ( where ( was the optimal stock of capital before the shock . Assets are unchanged on impact . From ( it follows that consumption adjusts instantaneously to its new ( and lower ) value ( mo ( AL ) mo ( a ) AH ) for all . What happens to the current account ?

After the instantaneous shock , assets remain unchanged , and , is zero , The economy immediately converges to the new , where the current account is in balance . At this point , you must be really disappointed don we ever get any interesting current account dynamics from this model ?

Actually , we do ! Consider a transitory fall in productivity at time , from A to , with productivity eventually returning to A after some time Well , it should be clear that consumption will fall , but not as much as in the permanent case . You want to smooth consumption , and you understand that things will get back to normal in the future , so you don have to bring it down so much now . At the same time , the capital stock does adjust down fully , otherwise its return would be below what the domestic household could get from bonds . If current output falls just as in the permanent case , but consumption falls by less , where is the difference ?

A simple inspection of ( AN APPLICATION THE SMALL OPEN ECONOMY 47 reveals that la has to fall below zero its a ! Quite simply , residents can smooth consumption , in spite of the negative shock , by borrowing resources from abroad . Once the shock reverts , the current account returns to zero , while consumption remains unchanged . In the new , consumption will remain lower relative to its initial level , and the difference will pay for the interest incurred on the debt accumulated over the duration of the shock or more generally , the reduction in net foreign asset income . This example underscores the role of the current account as a mechanism through which an can adjust to shocks . It also highlights one feature that we will see over and over again the optimal response and resulting dynamics can be very different depending on whether a shock is manent or transitory Sovereign wealth funds This stylised model actually allows us to think of other simple policy responses . Imagine a country that has a stock of resources , like Furthermore let imagine that this stock of copper is being extracted in a way that it will disappear in a amount of time . The optimal program is to consume the net present value of the copper over the future . So , as the stock of copper declines the economy should use those resources to accumulate other assets . This is the surplus rule implemented by Chile to compensate for the depletion of their resources . In fact , Chile also has a rule to identify transitory from permanent shocks , with the implication that all transitory increases ( decreases ) in the price level have to be saved ( spent ) Does this provide a rationale for some other sovereign wealth funds ?

The discussion above suggests that a country should consume 00 , where is the value of the resources extracted in period This equation says that a country should value its resources ( which are the equivalent of the ao above , an initial stock of assets ) and consume the real return on it . Is that how actual sovereign funds work ?

Well , the Norwegian sovereign fund rule , for instance , does not do this . Their rule is to spend at time tthe real return of the assets accumulated until then I , This rule can only be if you expect no further discoveries and treat each new discovery as a surprise , Alternatively , one could assume that the future is very uncertain , so one does not want to commit debt ahead of time . We will come back to this precautionary savings idea in our study of consumption in Chapter 11 . In any event , the key lesson is that studying our stylised models can help clarify the logic of existing policies , and where and why they depart from our basic assumptions . What have we learned ?

The provides the starting point for a lot of dynamic analysis , which is why it is one of the workhorse models of modern . In this chapter , we have seen how it provides us , in the context of a small open economy , with a theory of the current account . When

48 AN APPLICATION THE SMALL OPEN ECONOMY an economy has access to international capital markets , it can use them to adjust to shocks , while smoothing consumption and maintaining the optimal capital stock . Put simply , by borrowing and lending ( as by the current account ) the domestic economy need not rely on its own savings in order to make adjustments . This brings to the forefront a couple of important messages . First , current account ( contrary to much popular perception ) are not inherently bad . They simply mean that the economy is making use of resources in excess of its existing production capacity . That can make a lot of sense , if the economy has accumulated assets or otherwise expects to be more productive in the future , Second , access to capital markets can be a very positive force . It allows economies to adjust to shocks , thereby reducing volatility in consumption . It is important to note that this conclusion is ing from a model without risk or uncertainty , without in capital markets , and where decisions are being taken by a benevolent central planner , We will lift some of those assumptions later in the book , but , while we will not spend much more time talking about open economies , it is ant to keep in mind those here as well . Third , we have seen how the adjustment to permanent versus transitory shocks can be very ent . We will return to this theme over and over again over the course of this book . Last but not least , we have illustrated how our stylised models can nevertheless illuminate actual policy discussions , This will , again , be a recurrent theme in this book . What next ?

The analysis of the current account has a long pedigree in economics . As the counterpart of current accounts are either capital or changes in Central Bank reserves it has been the subject of much controversy . Should capital accounts be ?

Is there a sequence of ?

Can in capital markets or incentive distortions make these markets not operate as smoothly and as we have portrayed here ?

The literature on moral hazard , the policy discussion on , and , as a result , all the discussion on sovereign debt , which is one key mechanism countries , smooth consumption over time . The presentation here follows and Fischer ( 1989 ) but if you want to start easy you can check the textbook by Caves et al . 2007 ) which covers all the policy issues . and ( 1996 ) is the canonical textbook in international . More recently , you can dwell in these discussions by checking out ( 2013 ) and and ( 2017 ) Last , but not least , the celebrated paper by and ( 2007 ) distinguishes between shocks to put and shocks to trends in output growth , showing that the latter are relevant empirically and help understand the current account dynamics in emerging economies . Notes We should add secondary income , but we will disregard for the analysis , The fact that current accounts seem to be typically quite small relative to the size of the economy , so that savings is roughly similar to investment , is called the puzzle , Think about what happens , for instance , if . We would have consumption increasing at a rate . This patient economy , with relatively low , would start accumulating assets . But in this case , should we expect that the assumption that it is a small economy would keep being appropriate ?

What if ?

This impatient economy would borrow heavily to enjoy a high level of AN APPLICATION THE SMALL OPEN ECONOMY 49 consumption early on , and consumption would asymptotically approach zero as all income would be devoted to debt payments not a very interesting case . Is this example mere coincidence , or related to the fact that one of us is from Chile , which is a major exporter of copper ?

We will let you guess . References , 2007 ) Emerging market business cycles The cycle is the trend . Journal of Political Economy , 115 ( Fischer , 1989 ) Lectures on . MIT Press . Caves , 2007 ) World trade An introduction . Pearson . 1996 ) Foundations . MIT Press . 2017 ) Open economy . Princeton University Press . 2013 ) Open economy in developing countries . MIT Press .