O Problem Set 7 - Solution

O.1 Readings - Public Debt, Say’s Law

  1. Q: Paul Krugman, Multipliers and Reality, New York Times Blog Post, June 3, 2015. What is the Chicago school’s argument against Keynesian multipliers? Why is it wrong, in Paul Krugman’s opinion? A: The Chicago school’s argument against Keynesian multiplier rests on Ricardian equivalence. As I said during class, Ricardian equivalence implies that when the government cuts taxes, or engages in government spending, then consumers anticipate higher taxes in the future, and therefore cut spending today, anticipating that public debt will have to be repaid someday (they consume according to the discounted present value of their future ncomes). However, Paul Krugman argues that this argument is actually wrong, because consumers are not that rational and forward looking. People do not even know about very important government programs, so how would they be engaged in the kind of rational, forward-looking decisions that many economists think they are engaged in? As a consequence, it is just not true that government spending is offset one for one by lower private expenditures.

  2. Q: Glutology - Say’s Law: Supply Creates its Own Demand. The Economist, August 10, 2017. What view was Jean-Baptiste Say fighting? What poses a problem for Jean-Baptiste Say’s vision? A: Jean-Baptiste Say was fighting the view, very prevalent in his time, that “general gluts” could occur. This is because after the downfall of Napoleon, government spending was cut both in Britain as well as in France and in the rest of Europe, so that many former soldiers were forced to find alternative employment elsewehere. Britain was accused of inundating foreign markets, very much like China is blamed for exporting cheap products today. (we will see later in the chapter on “open economy” that we can make sense of this more precisely later) What poses a problem for Say’s vision, according to The Economist article, is if people produced goods in order to store value (that is, if they want to save instead of consuming), which interrupts the flow of goods on which Say’s vision relies. The article talks about the fact that people would hoard money, instead of spending it.

  3. Q: Overlapping Generations: Kicking the road down an endless road. The Economist, August 31, 2017. How is a financial bubble similar in many ways to public debt, and to a pay-as-you-go system? How is it different? A: A financial bubble is similar in many ways to public debt and to pay-as-you-go system, in that similarly to these two schemes, it tends to redistribute money away from young people, at the benefit of old people. In the case of public debt, it reduces the capital stock which the young people can buy, because they know have to buy the public debt (and the old benefit from the corresponding transfers). In the case of a pay-as-you-go system, they know are being taxed more on their wages through social security (in the U.S., it is called OASDI), which is used to pay current retirees. Similarly, you can think of financial bubbles as redistributing money from the young to the old, if the old are selling the overvalued assets (such as real estate in Los Angeles, or equities in 401(k)s) and the young are buying the overvalued assets, thereby transferring value to them. In fact, this argument comes back often in the public debate, where high house prices for example are thought to be bad for the younger generation of first-time homebuyers.

  4. Q: Greg Mankiw, The National Debt Is Still a Problem, New York Times, June 20, 2019. Why is National Debt still a problem according to Greg Mankiw? How do you make sense of his arguments through the overlapping-generations model? A: Greg Mankiw thinks that debt is a problem because debt is not being built up in order to invest for future generations (and he includes military expenditures in those), this is just a debt that our children will need to pay. This is not a debt which is being increased to combat a temporary downturn either. To him, the Trump deficits are being implemented in an already heated economy, with high rates of employment. His arguments can be understood through the lens of the overlapping generations model, as a struggle between the young and the old generations: the old are taking on government debt at the expense of the young, who one day will need to pay the bill. Because Greg Mankiw thinks that the government debt will need to be repaid by future generations, he probably thinks that the situation of \(r<g\) is not going to persist in the future, and that the government will not stay stable if it is not reimbursed.

  5. Q: Alex Williams. “Why Don’t Rich People Just Stop Working?”, New York Times, October 17, 2019. How is this article connected to the issue of “Say’s law”, and to Keynesian economics? A: This article is connected to the issue of “Say’s law” in the sense that it shows that unlike what many economists assume, saving is not always done having in mind future consumption (including that of one’s children). Some high-income people seem to just enjoy working, which means that they supply labor, without demanding anything in return for this labor. As a consequence, not only do they not consume today but more importantly, they do not intend to consume anytime later in the future. The result is that their saving does not create any demand for new investment: firms will sell less today, and they will not be able to sell more in the future (in fact, they probably will sell less in the future too) so they will not want to invest more.

O.2 A Budget Surplus and a Trade Deficit

  1. Aggregate consumption is given as shown in lecture 9 by: \[C=C_0 -\left(\underline{c}_{1}\underline{T}_0+\bar{c}_{1}\bar{T}_0\right)+c_1 (1-t_1) Y,\] where we have defined the average MPC \(c_1\) as a function of \(\underline{c}_1\) and \(\bar{c}_1\) by: \[c_{1} \equiv \frac{\lambda\underline{c}_{1}+\left(1-\lambda\right)\gamma\bar{c}_{1}}{\lambda+(1-\lambda)\gamma}.\] Using that \(Z\) is \(C+I+G+X-M\), we get: \[ \begin{aligned} Z &=C+I+G+X-M\\ &=C_0 -\left(\underline{c}_{1}\underline{T}_0+\bar{c}_{1}\bar{T}_0\right)+c_1 (1-t_1) Y + b_{0}+b_{1}Y+G + x_1 Y^{*} - m_1 Y\\ Z &=\left[C_0 -\left(\underline{c}_{1}\underline{T}_0+\bar{c}_{1}\bar{T}_0\right)+ b_{0} + G + x_1 Y^{*} \right]+ \left(c_1(1-t_1) + b_1-m_1\right) Y \end{aligned} \] Equating output to demand \(Z = Y\) gives the value for output: \[Y=\frac{1}{1-\left(1-t_{1}\right)c_{1}-b_{1}+m_1}\left[C_0-\underline{c}_{1}\underline{T}_{0}-\bar{c}_{1}\bar{T}_{0}+b_{0}+G + x_1 Y^{*}\right].\] A reduction in taxes on the poor \(\Delta\underline{T}_{0}<0\), with an offsetting increase in taxes on high income earners \(\Delta \bar{T}_0 = -\Delta\underline{T}_{0}\) such that aggregate taxes are zero (\(\Delta T_0=\Delta\underline{T}_{0}+\Delta\bar{T}_{0}=0\)) therefore leads to a change in output given by: \[ \begin{aligned} \boxed{\Delta Y=\frac{\underline{c}_{1}-\bar{c}_{1}}{1-\left(1-t_{1}\right)c_{1}-b_{1}+m_1}\Delta\bar{T}_{0}}. \end{aligned} \]

  2. Using the value for aggregate taxes \(\Delta\underline{T}_{0}+\Delta\bar{T}_{0}=0\), we now get that aggregate taxes are higher because of automatic stabilizers, just as in lecture 9: \[ \begin{aligned} \Delta T&=\Delta\underline{T}_{0}+\Delta\bar{T}_{0}+t_1\Delta Y\\ &=t_1 \Delta Y\\ \Delta T&=\frac{t_1\left(\underline{c}_{1}-\bar{c}_{1}\right)}{1-\left(1-t_{1}\right)c_{1}-b_{1}+m_1}\Delta\bar{T}_{0}>0. \end{aligned} \] This unambiguously leads to a reduction in the public deficit, or an increase in public saving, as in lecture 9, because of automatic stabilizers, since \(\Delta\left(T-G\right)=\Delta T\): \[ \begin{aligned} \boxed{\Delta\left(T-G\right)=\frac{t_1\left(\underline{c}_{1}-\bar{c}_{1}\right)}{1-\left(1-t_{1}\right)c_{1}-b_{1}+m_1}\Delta\bar{T}_{0}}. \end{aligned} \]

  3. An increase in output leads to a trade deficit because some of the additional demand of the low income falls on imported goods so that \(\Delta NX = -m_1 \Delta Y\) which implies: \[ \begin{aligned} \boxed{\Delta NX =- \frac{m_1\left(\underline{c}_{1}-\bar{c}_{1}\right)}{1-\left(1-t_{1}\right)c_{1}-b_{1}+m_1}\Delta\bar{T}_{0}}. \end{aligned} \] Therefore, since \(\Delta\bar{T}_{0}>0\), we have both a trade deficit and a budget surplus: \[\boxed{\Delta NX <0, \qquad \Delta (T-G) > 0}.\]

  4. Again, the change in net exports \(NX\) are equal to the change in total saving minus the change in investment: \[\Delta NX = \Delta S+ \Delta (T-G)- \Delta I.\] Therefore, the fact that an increase in the government surplus comes together with a trade deficit is somewhat of a puzzle: everything else being equal, an increase in government surplus should lead to a trade surplus, because it increases total saving. (everything else equal \(\Delta NX = \Delta (T-G)\)) In order to understand this “puzzle”, we first compute the change in investment, which depends on output through \(I = b_0+b_1Y\) so that \(\Delta I = b_1 \Delta Y\), implying: \[ \begin{aligned} \boxed{\Delta I=\frac{b_1\left(\underline{c}_{1}-\bar{c}_{1}\right)}{1-\left(1-t_{1}\right)c_{1}-b_{1}+m_1}\Delta\bar{T}_{0}>0}. \end{aligned} \] The increase in investment consecutive to redistributive policies does contribute to explaining the puzzle. Indeed, there was an investment boom at the end of Bill Clinton’s presidency. For example, you can read this Paul Krugman op-ed, where he gives this argument:

At the time, Martin Feldstein famously linked the two, calling them “twin deficits.” While this oversimplified matters – in the late 1990s we ran both budget surpluses and trade deficits, thanks to booming investment – the logic made sense.

  1. Private saving \(S\) is: \[ \begin{aligned} S &= Y-T-C\\ &=Y-\left(\left(\underline{T}_{0}+\bar{T}_{0}\right)+t_1 Y\right) - \left(C_0 -\left(\underline{c}_{1}\underline{T}_0+\bar{c}_{1}\bar{T}_0\right)+c_1 (1-t_1) Y\right)\\ &=Y - t_1 Y - c_1(1-t_1)Y-C_0 - \left(\underline{T}_{0}+\bar{T}_{0}\right)+\left(\underline{c}_{1}\underline{T}_0+\bar{c}_{1}\bar{T}_0\right)\\ S&=(1-t_1)(1-c_1)Y-C_0 - \left(\underline{T}_{0}+\bar{T}_{0}\right)+\left(\underline{c}_{1}\underline{T}_0+\bar{c}_{1}\bar{T}_0\right) \end{aligned} \] Therefore: \[ \begin{aligned} \Delta S &= (1-t_1)(1-c_1)\Delta Y + \underline{c}_{1}\Delta \underline{T}_0+\bar{c}_{1}\Delta \bar{T}_0\\ &=\frac{(1-t_1)(1-c_1)\left(\underline{c}_{1}-\bar{c}_{1}\right)}{1-\left(1-t_{1}\right)c_{1}-b_{1}+m_1}\Delta\bar{T}_{0}-(\underline{c}_1-\bar{c}_1)\Delta \bar{T}_0\\ &=\left[\frac{(1-t_1)(1-c_1)}{1-\left(1-t_{1}\right)c_{1}-b_{1}+m_1}-1\right](\underline{c}_1-\bar{c}_1)\Delta \bar{T}_0\\ &=\left[\frac{(1-t_1)(1-c_1)-\left(1-\left(1-t_{1}\right)c_{1}-b_{1}+m_1\right)}{1-\left(1-t_{1}\right)c_{1}-b_{1}+m_1}\right](\underline{c}_1-\bar{c}_1)\Delta \bar{T}_0\\ &=\left[\frac{-t_1+b_1-m_1}{1-\left(1-t_{1}\right)c_{1}-b_{1}+m_1}\right](\underline{c}_1-\bar{c}_1)\Delta \bar{T}_0\\ \Delta S&=\frac{(-t_1+b_1-m_1)\left(\underline{c}_{1}-\bar{c}_{1}\right)}{1-c_1(1-t_1)-b_1+m_1}\Delta \bar{T}_0 \end{aligned} \] The sign of the change in private saving is ambiguous: \[\boxed{\Delta S=\frac{(-t_1+b_1-m_1)\left(\underline{c}_{1}-\bar{c}_{1}\right)}{1-c_1(1-t_1)-b_1+m_1}\Delta \bar{T}_0}.\] However, if \(m_1=b_1\) as in the numerical application, then private saving decreases, which also contributes to explaining the puzzle: private saving move against public saving, which tends to increase the trade deficit.

  2. The net effect on net exports can be given as: \[ \begin{aligned} \Delta NX &= \Delta S + \Delta (T-G) + \Delta I\\ &=\frac{(-t_1+b_1-m_1) + t_1 - b_1}{1-\left(1-t_{1}\right)c_{1}-b_{1}+m_1}\left(\underline{c}_{1}-\bar{c}_{1}\right)\Delta\bar{T}_{0}\\ \Delta NX &= - \frac{m_1}{1-\left(1-t_{1}\right)c_{1}-b_{1}+m_1}\left(\underline{c}_{1}-\bar{c}_{1}\right)\Delta\bar{T}_{0} \end{aligned} \] We find the same expression as in question 3: \[\boxed{\Delta NX = - \frac{m_1}{1-\left(1-t_{1}\right)c_{1}-b_{1}+m_1}\left(\underline{c}_{1}-\bar{c}_{1}\right)\Delta\bar{T}_{0}}\]

  3. Assuming that \(m_1=1/6\), \(b_1=1/6\), \(t_1=1/4\), \(\underline{c}_{1}=1\), \(\bar{c}_{1}=1/3\), \(\gamma=9\), \(\lambda=0.9\), the average marginal propensity to consume is: \[ \begin{aligned} c_1 &= \frac{\lambda\underline{c}_{1}+\left(1-\lambda\right)\gamma\bar{c}_{1}}{\lambda+(1-\lambda)\gamma}\\ &= \frac{\lambda}{\lambda+(1-\lambda)\gamma}\underline{c}_{1} + \frac{\left(1-\lambda\right)\gamma}{\lambda+(1-\lambda)\gamma}\bar{c}_{1}\\ &= \frac{0.9}{0.9+0.1 \cdot 9}\cdot 1 + \frac{0.1 \cdot 9}{0.9+0.1 \cdot 9}\cdot \frac{1}{3}\\ &= \frac{1}{2}\cdot 1 + \frac{1}{2}\cdot \frac{1}{3}\\ c_1 &= \frac{2}{3}. \end{aligned} \] If redistribution is given by \(\Delta \bar{T}_0 = 1\), we get an increase in output which is given by: \[ \begin{aligned} \Delta Y &= \frac{\underline{c}_{1}-\bar{c}_{1}}{1-\left(1-t_{1}\right)c_{1}-b_{1}+m_1}\Delta\bar{T}_{0}\\ &=\frac{1}{1-(2/3) \cdot (1- 1/4)-1/6+1/6} \cdot \left(1-\frac{1}{3}\right) \cdot 1\\ &= 2 \cdot \frac{2}{3} \cdot 1\\ \Delta Y &= \frac{4}{3} \end{aligned} \] The change in the trade balance \(\Delta NX\) can be decomposed as:

  • A change in private saving \(\Delta S\): \[ \begin{aligned} \Delta S &= (-t_1+b_1-m_1) \cdot \Delta Y\\ &=\left(-\frac{1}{4} + \frac{1}{6} - \frac{1}{6}\right) \cdot \frac{4}{3}\\ \Delta S &=-\frac{1}{3} \end{aligned} \]
  • A change in public saving \(\Delta (T-G)\): \[ \begin{aligned} \Delta (T-G) &= t_1 \cdot \Delta Y\\ &=\frac{1}{4} \cdot \frac{4}{3}\\ \Delta (T-G) &=\frac{1}{3} \end{aligned} \]
  • A change in investment \(\Delta I\): \[ \begin{aligned} \Delta I &= b_1 \cdot \Delta Y\\ &=\frac{1}{6} \cdot \frac{4}{3}\\ \Delta I &=\frac{2}{9}. \end{aligned} \] The sum of all these contributions is: \[ \begin{aligned} \boxed{\Delta NX=\Delta S + \Delta (T-G)-\Delta I=-\frac{1}{3}+\frac{1}{3}-\frac{2}{9}=-\frac{2}{9}}. \end{aligned} \] Note that this same expression can be obtained using that \(\Delta NX = -m_1 \Delta Y\) directly: \[ \begin{aligned} \Delta NX&=-m_1 \Delta Y\\ &=-\frac{1}{6} \cdot \frac{4}{3} \\ \Delta NX&=-\frac{2}{9}. \end{aligned} \]

O.3 Coordination of Economic Policies

  1. Given \(Y^{*}\), aggregate demand is: \[ \begin{aligned} Z &=C+I+G+X-M\\ &=\left(10+0.8 \cdot (Y-T)\right)+\left(8+0.1Y\right) + \left(g_0+0.1Y\right) + 0.1Y^{*} - 0.1Y\\ &=10+0.8 \cdot (Y-10-0.5Y)+8+0.1Y + g_0+0.1Y + 0.1Y^{*} - 0.1Y\\ Z &= 0.5Y + 10 + g_0+ 0.1Y^{*} \end{aligned} \] Setting \(Y=Z\) gives: \[ \begin{aligned} \boxed{Y=20+2 \cdot g_0+ 0.2 \cdot Y^{*}}. \end{aligned} \]

  2. Assuming that foreign output is given, the multiplier is 2 since: \[ \begin{aligned} \boxed{\Delta Y=2 \cdot \Delta g_0}. \end{aligned} \] Note that foreign output cannot be fixed when government spending changes in the home economy: because of imports, a stimulus in the home economy necessarily increases output in the foreign economy. The rest of this problem shows why.

  3. If we were to close the economy, then demand would be: \[ \begin{aligned} Z &=C+I+G\\ &=10+0.8(Y-10-0.5Y)+8+0.1Y + g_0+0.1Y\\ Z &= 0.6Y + 10 + g_0 \end{aligned} \] Setting \(Y=Z\) gives: \[\boxed{Y= 25 + 2.5 \cdot g_0}.\] Therefore, the multiplier is 2.5 since \[\boxed{\Delta Y=2.5 \cdot \Delta g_0}.\] In a closed economy, the multiplier would be higher because all the increase in income would be feeding domestic demand: there would be no “leakage” of aggregate demand.

  4. We similarly have: \(Y^{*}=20+2g_0^{*}+ 0.2Y.\) Therefore: \[ \begin{aligned} Y&=20+2g_0+ 0.2Y^{*}\\ &=20+2g_0+ 0.2\left(20+2g_0^{*}+ 0.2Y\right)\\ Y&=24+2g_0+0.4g_0^{*}+0.04Y \end{aligned} \] This gives output \(Y\), and symmetrically foreign output \(Y^{*}\): \[ \begin{aligned} Y&=\frac{24}{0.96}+\frac{2}{0.96}g_0+\frac{0.4}{0.96}g_0^{*} \\ Y^{*}&=\frac{24}{0.96}+\frac{2}{0.96}g_0^{*}+\frac{0.4}{0.96}g_0. \end{aligned} \] Finally: \[ \begin{aligned} \boxed{Y\approx25+2.08 \cdot g_0+0.42 \cdot g_0^{*}} \qquad \boxed{Y^{*}\approx25+2.08 \cdot g_0^{*}+0.42 \cdot g_0}. \end{aligned} \]

  5. The multiplier is now given by \(2/0.96 \approx 2.08\). Indeed: \[ \begin{aligned} \boxed{\Delta Y = \frac{2}{0.96}\Delta g_0 \approx 2.08 \cdot \Delta g_0}. \end{aligned} \] This is higher than \(2\). The reason is that increasing \(G\) in the home economy increases \(M\) from the foreign economy and therefore, \(Y\) in the foreign economy, which in turn increases demand for \(X\) in the home economy.

  6. We have the following two equations for \(Y\) and \(Y^{*}\): \[Y = 20 + 2 \cdot g_0 + 0.2 \cdot Y^{*}\] and: \[Y^{*}=20+2 \cdot g_0^{*} + 0.2 \cdot Y.\] The second equation says that whenever output increases by $1 in the home economy, this leads output to increase by $0.2 in the foreign economy. In turn, this increase of $0.2 in the foreign economy leads to an increase of $\(0.2 \cdot 0.2 = 0.04\) in the home economy. Therefore, when output increases by $1 in the home economy, then through the spillover effects it leads to an increase in $0.04 in the home economy. In turn, this $0.04 increase leads to a further $\(0.04 \cdot 0.04 = 0.04^2\) increase, etc. Finally, we get a total spillover effect for 1 dollar given by: \[\boxed{1+0.2\cdot 0.2 + (0.2\cdot 0.2)^2 + ... = \frac{1}{1-0.04} = \frac{1}{0.96} \approx 1.04}.\] This explains why the open economy multiplier is \(1/0.96\) times the open economy multiplier without spillovers (that is, the open economy multiplier taking foreign output as given), so that: \[ \begin{aligned} \boxed{\Delta Y = \frac{2}{0.96} \cdot \Delta g_0\approx 2.08 \cdot \Delta g_0}. \end{aligned} \]

  7. U.S.’s government spending increases Germany’s exports, and after the multiple rounds: \[\Delta Y^{*} = 0.42 \cdot \Delta g.\] The impact on Germany’s surplus is: \[ \begin{aligned} \Delta (T^{*}-G^{*}) &= \Delta T^{*} - \Delta G^{*}\\ &= 0.5 \cdot \Delta Y^{*} - 0.1 \cdot\Delta Y^{*}\\ &= 0.4 \cdot \Delta Y^{*}\\ &= 0.4 \cdot 0.42 \cdot \Delta g \\ \Delta (T^{*}-G^{*}) &= 0.168 \cdot \Delta g \end{aligned} \] Therefore, U.S.’s government spending leads to a surplus in Germany’s budget, given as a function of U.S.’s increase in government spending by: \[\boxed{\Delta (T^{*}-G^{*}) = 0.168 \cdot \Delta g}.\]

  8. The multiplier for a coordinated increase in government spending, such that \(\Delta g_0 = \Delta g_0^{*}\) is given by: \[ \begin{aligned} \Delta Y&=\frac{2}{0.96} \Delta g_0 + \frac{0.4}{0.96} \Delta g_0^{*}\\ &=\frac{2.4}{0.96} \Delta g_0 \\ \Delta Y&= 2.5 \cdot \Delta g_0 \end{aligned} \] The multiplier for a coordinated increase in government spending is \(2.5\). Note that this is equal to the closed economy multiplier, which is intuitive.

  9. The multiplier is higher. If government spending is coordinated, then exports in the home economy increase, which contributes to boosting output further. The aggregate demand leakage, increasing imports, is offset by an expansion abroad, increasing exports.

  10. There is a free-rider problem because all countries have an incentive to wait other countries to do more Keynesian stimulus. When the U.S. does a Keynesian stimulus, this stimulus benefits Germany in the form of increased GDP in Germany, and their government surplus. Therefore, this non-cooperative game can lead to too little stimulus.

  11. Donald Trump believes that Germany is not doing enough to boost aggregate demand, and that this explains the U.S.’s unfavorable trade balance. Again, whether you think that his complaint is legitimate depends on whether you think that global aggregate demand is deficient, or not. Many economists take the view that if Germany is willing to lend to the U.S., and always produce more than it consumes, then Germany is not acting in its best interest, and the U.S. should simply be consuming these “free” goods (same with China). As you know, I am more agnostic. I think that the question is whether supply indeed creates its own demand, and whether people care more about production or about consumption. This controversy dates back to at least Adam Smith against the mercantilists, in the eighteenth century.

O.4 Readings - Open Economy

  1. John Maynard Keynes. Proposals for a Revenue Tariff (March 7, 1931). Q: What are the main arguments, in J.M. Keynes’ opinion, in favor of a revenue tariff? How would you use the model seen in the class to show this? A: J.M. Keynes argues that the U.K. has a lot of slack in 1931 (“a vast body of persons in idleness”, “one quarter of our industrial plant closed down and one quarter of our industrial workers unemployed”), and thinks that to solve this problem there are two possible courses of action. One is an expansionist policy (in terms of the model seen in class, think \(\Delta G>0\) or \(\Delta T<0\)), which would however increase government debt and the trade deficit (\(\Delta NX <0\)). To the extent that the trade deficit needs to be financed by foreign investors, this could be difficult (if investors panick, for example). A second option is to cut costs (reduce wages), which might reduce aggregate demand by redistributing income between different classes, in a way which is adverse to employment. As a consequence, J.M. Keynes proposes a “substantial revenue tariff”, applied very broadly (“no discriminating protective taxes”). The advantage of such a possibility, to him would be a “substitution of home-produced goods for goods previously imported”, which would expand employment. In terms of the model seen in the class, the best way to see this is to assume that the marginal propensity to import \(m_1\) has fallen with the tariff, which increases the Keynesian multiplier given by: \[\text{Multiplier}(m_1) = \frac{1}{1-c_1(1-t_1)-b_1+m1} \quad \Rightarrow \quad \frac{\partial\text{Multiplier}}{\partial m_1}<0.\]

  2. Robert J. Barro, Stimulus Spending Keeps Failing; If austerity is so terrible, how come Germany and Sweden have done so well?, Wall Street Journal, May 9, 2012. Q: What are Robert Barro’s main arguments against the Keynesian view? What would a Keynesian economist respond? (some of these arguments are given by Barro himself, but dismissed; you should find other arguments) A: According to Robert J. Barro, Germany and Sweden have done very well macroeconomically, despite having moved to rough budget balance from 2009 to 2011. In contrast, Greece, Portugal, Italy, and Spain did not do so well despite having large budget deficits. Robert Barro concedes that because of automatic stabilizers (\(t_1\) in the class), low GDP could be causing large deficits, and not the other way around, but he still argues it’s suggestive. Similarly, Japan has had disappointing GDP growth since the 1990s despite having now more than 200% of GDP in public debt. A Keynesian economist would respond again, that high public debt results largely from Japan’s dismal economic performance, and that things would have been even worse without high public deficits. Robert Barro responds in anticipation that “a little evidence would be nice.” Another response that a Keynesian economist would actually give would be to say that the reason why Germany and Sweden have done so well is that they have largely benefited from growth in their external demand, themselves due to other countries implementing Keynesian aggregate demand stimulating policies during the period. And indeed, both Germany’s and Sweden’s net exports have substantially increased during that period, or at least they have stayed strong, as shown here https://data.worldbank.org/indicator/BN.GSR.GNFS.CD?locations=DE for Germany and there https://data.worldbank.org/indicator/BN.GSR.GNFS.CD?locations=SE for Sweden (you can see both here).

  3. Ben Bernanke. Germany’s trade surplus is a problem. Brookings Blog. April 3, 2015. Q: Why does Germany have such a large trade surplus? Why is Germany’s trade surplus a problem according to Ben Bernanke? A: The German trade surplus results from the undervaluation of the euro, coming from the fact that Germany belongs to a currency union. It is further reinforced by policies (tight fiscal policies, for example) that suppresses the country’s domestic spending, including spending on imports. According to Ben Bernanke, the world is generally short of aggregate demand. In that environment, Germany’s trade surplus is problem, in that it is adding to the world excess of saving relative to investment.

  4. “Why Germany’s current-account surplus is bad for the world economy”, The Economist, July 8, 2017. Q: What are the main arguments given by The Economist, which explain Germany’s large trade surpluses? Can you think of other arguments? A: The main argument given by The Economist, which explains Germany’s large trade surpluses, is that Germany saves more than it invests. Saving is high in Germany, according to The Economist, largely because of a decade-old accord between unions and business in favour of wage restraint to keep export industries competitive. In turn, this fall in wages resulting in low prices (for concreteness, cheaper BMWs) as well as high profits tends to keep aggregate demand rather low, which compresses imports. (“Pay restraint means less domestic spending and fewer imports.”) The Economist also argues that public investment is too low in Germany: Germany could spend more on school building and roads, or on high-speed internet. Other arguments that one could think of to explain Germany’s large trade surpluses is Germany’s slow move from a largely pay-as-you-go system (like social security in the U.S.) to a funded system, which was implemented in the 2000s in order to solve a looming pension crisis (with high population ageing). As a result of this, just like we studied before, the saving rate increased substantially: this is because the new generations of young people had to both continue to pay taxes to finance the last generation of social security for the old, as well as put some money on the side for their own retirement (in practice, the pensions of the old were reduced, too, which also contributed to depress consumption).

  5. Simon Tilford. “Germany Is an Economic Masochist.”, Foreign Policy, August 21, 2019. Q: Denying the role of competitiveness, the author argues that “Germany produces far more than it consumes, because the country saves far more than it invests.” Explain why this argument is correct, but incomplete at the same time. A: This argument is both correct because mechanically \(NX = S-I\) and at the same time incomplete. First, it is incomplete because everything depends on everything else in macroeconomics. For example, we have learned that if government spending decreases \(\Delta G<0\) (austerity), then we simultaneously generally get a recession, lower private saving, higher public saving, with an ambiguous effect on total saving, while investment falls as well. So when we say that the “country saves far more than it invests”, we seem to be saying that investment needs are fixed - independently of the level of demand - and that saving just need to equal those needs, otherwise it is considered to be “in excess”. In the Keynesian model, this is incorrect. Similarly, regressive redistributive policies, like the one which were discussed in The Economist article, clearly lead to lower public saving (since \(\Delta(T-G) = \Delta T = t_1 \Delta Y<0\)), but higher private saving (since this raises the rich’s disposable income, and they save more out of this income), and lower investment. In practice, Germany is probably doing a mix of both austerity, and regressive redistribute policies, so that indeed both public saving and private saving increase (therefore total saving increase), and investment falls. Second, this argument is also incomplete because how much imbalance between saving and investment results from a local aggregate demand shock, very much depends on the propensity to import, which itself depends on competitiveness (how much consumers prefer to buy foreign goods, relative to locally-produced goods; and this probably depends on relative prices). In the limit, when \(m_1=0\), then \(\Delta S\) and \(\Delta I\) need to be equal. In contrast, when \(m_1\) is very large (the economy is not very competitive), then any given negative aggregate demand shock leads to a substantial disconnect between \(\Delta S\) and \(\Delta I\) since \(\Delta NX = \Delta S - \Delta I\). Note: You way be wondering why we focus so much on Germany’s trade surplus in this class. Note that The Economist compares Germany’s current account surplus with China’s, arguing that it is actually bigger in dollar terms, which you can also do on your own here https://data.worldbank.org/indicator/BN.GSR.GNFS.CD?locations=DE-CN. Thus, Germany’s increase in saving is a big factor behind the saving glut at the world level.