Public Policy, Household Finance and the Macroeconomy

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(255) PUBLIC POLICY, HOUSEHOLD FINANCE AND THE MACROECONOMY. Jakob Almerud.

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(257) Public Policy, Household Finance and the Macroeconomy Jakob Almerud.

(258) ©Jakob Almerud, Stockholm University 2018 ISBN print 978-91-7977-250-1 ISBN PDF 978-91-7977-251-8 ISSN 1404-3491 Picture on the back cover: Konjunkturinstitutet Printed in Sweden by Universitetsservice US-AB, Stockholm 2018 Distributor: Department of Economics, Stockholm University.

(259) Till Liv och Alva.

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(261) Abstract The thesis contains four separate essays, spanning questions of the interaction between public policy, household nance and the macroeconomy. The rst essay, Optimal Public Policy in a Multi-Sector Economy with Asymmetric Shocks, shows how scal policy can complement monetary policy. It is shown that scal policy can be used to improve macroeconomic outcomes and make the economy more ecient. Since scal policy, in general, includes more instruments than monetary policy, it is possible to neutralize several frictions in the economy simultaneously. This is shown in a general equilibrium model with dynastic households, where rms face monopolistic competition, sticky prices, productivity shocks and cost-push shocks. The second essay, On the Design of Mortgage Default Legislation, asks how dierent types of mortgage contracts interact with dierent types of mortgage default policies regarding the probability of a default on home-owner's mortgage. The dierent types of mortgage contracts analyzed are xed rate annuity mortgages, adjustable rate amortized mortgages and adjustable rate non-amortized mortgages. The mortgage default policies span from non-recourse (where the mortgage lender takes all the default risk) to full recourse (where the borrower takes all the default risk). It is shown that a borrower friendly non-recourse policy is, as the one implemented in many parts of the United States, not necessarily borrower friendly due to its eect on the risk premium. This is investigated in a model with nitely lived households and an endogenous risk premium. The third essay, On The Empirical Relevance of Cointegration Between Stock Market Returns and Labor Income on Optimal Portfolio Choice, investigates how nitely lived households optimally choose a portfolio consisting of riskfree bonds and risky equity, and how this choice is aected by the long-run correlation between risky (cumulative) equity returns and stochastic labor income. More specically, I investigate if the empirical cointegration (longrun correlation) between the two variables is strong enough to aect the optimal portfolio choice. It is shown that it is not. Cointegration exists between the two variables, but the speed-of-adjustment back to the cointegration equilibrium is to slow to have a signicant eect on the households' optimal portfolios. The fourth essay, Solving Dynamic Programming Problems Using Stochastic Grids and Nearest-Neighbor Interpolation, describes a new computational method, which is used in the second and third essays. The method is developed to solve models with nitely lived households who face a complex economic environment. Post-state decision rules for the households are used together with simulated stochastic grids over the exogenous variables. By simulating the grids it is possible to reduce the number of grid points that the model is solved for, thereby making it signicantly faster to solve models with many exogenous state variables..

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(263) Sammanfattning på svenska Denna avhandling innehåller fyra uppsatser, som tillsammans spänner över ämnena penningoch nanspolitik, bolånereglering och hushållens nansiella val. Sammantaget diskuteras de olika val som den oentliga sektorn och hushållen gör och bör göra. I den första uppsatsen diskuteras hur nanspolitik kan användas som ett komplement till penningpolitik för att stabilisera ekonomin runt dess optimala bana. Ett vanligt resultat inom litteraturen är att det räcker med penningpolitik för att nå denna optimala bana. Detta gäller dock bara om ekonomin är strukturerad på ett specikt sätt. Om ekonomin istället är något mer komplex än det som vanligen antas så räcker det inte längre med penningpolitik för att nå optimum. Om man däremot ger nanspolitiken utrymme i modellen så går det att få ett optimalt utfall, givet att de som utformar nanspolitiken har rätt nanspolitiska instrument att arbeta med. Jag visar i en teoretisk så kallad Nykeynesiansk modell att man med hjälp av en kombination av sektorspecika skatter och subventioner kan uppnå det optimala utfallet i ekonomin. Detta gäller dock inte om det tar tid för nanspolitiken att implementeras. Det är dock ändå värt att föra politiken, eftersom det ekonomiska utfallet ändå blir bättre än vad den skulle blivit utan den förda politiken. I den andra uppsatsen, som är skriven tillsammans med Roine Vestman och Anders Österling, diskuteras hur olika typer av bolånelagstiftning som hanterar skuldbördan vid en situation där hushållen slutar betala räntorna på sina bolån. Vidare undersöks vilket reglering som, utifrån ett hushålls perspektiv, är den optimala lagstiftningen. Detta undersöks givet era olika typer av bolånekontrakt (fasta eller rörliga räntor, amorteringsfritt eller amorterade bolån). Den ena extremen vad gäller reglering är att banken tar all risk i bolånekontraktet. Om hushållen ställer in sina betalningar så har banken möjlighet att ta kontraktet på bostaden, men de har inte möjlighet att få någonting utöver bostaden för att täcka ytterligare förluster. Detta är en vanlig lagstiftning i många delstater i USA. Den andra extremen är att banken har möjlighet att ta alla tillgångar och inkomster som hushållet förfogar över för att täcka den potentiella skulden till banken. Vi undersöker vilken lagstiftning och vilket typ av bolån som hushållen föredrar i en teoretisk så kallad livscykelmodell. Det visar sig i vår analys att hushåll föredrar hård lagstiftning eftersom detta sänker de riskpremier som hushållen måste betala. De hushåll som inte ställer in sina betalningar betalar för de hushåll som gör det genom riskpremien. Ju hårdare lagstiftningen är, desto färre ställer in sina betalningar, och desto lägre blir riskpremien, och därmed hushållens räntebetalningar till banken. I den tredje uppsatsen utreds hur hushållets optimala val mellan två typer av tillgångar, obligationer med en fast ränta samt en aktieindexfond, påverkas av att det nns en långsiktig korrelation mellan avkastningen på aktier och löneökningarna i ekonomin. Om en sådan korrelation nns så kan det betyda att hushållen bör spara betydligt mindre i aktier än.

(264) annars. Jag utreder detta genom att använda en teoretisk livscykelmodell samt genom att skatta en regressionsmodell som innehåller aggregerade löner samt aktieindex på amerikansk data mellan 1929-2016. Jag skattar den långsiktiga korrelationen i regressionsmodellen och använder sedan värdena från det skattade sambandet i den teoretiska modellen för att utreda eekten på det optimala portföljvalet. En tidigare uppsats har visat att sådan korrelation kan ha stora eekter. Jag börjar med att replikera den tidigare uppsatsen, och visar sedan att det skattade sambandet i en modell som är i stort sett identisk med deras inte har någon signikant eekt på det optimala portföljvalet. I den fjärde uppsatsen, som är skriven tillsammans med Anders Österling, utvecklar vi en ny metod för att lösa teoretiska livscykelmodeller numeriskt. Denna metod används i den andra och tredje uppsatsen. Med hjälp av metoden går det att lösa modeller som är mer komplexa än vad som tidigare gått att lösa. Vi använder sedan metoden på ett ekonomiskt problem för att illustrera dess användbarhet..

(265) Contents -1.. Acknowledgments. 0.. Introduction. 1.. Optimal Public Policy in a Multi-Sector Economy with Asymmetric Shocks. 2.. On the Design of Mortgage Default Legislation. 3.. On the Empirical Relevance of Cointegration Between Stock Market Returns and Labor Income on Optimal Portfolio Choice. 4.. Solving Dynamic Programming Problems Using Stochastic Grids and NearestNeighbor Interpolation.

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(267) Acknowledgments Writing a thesis is often a solitary task. Nevertheless, there are many persons which, without them, no thesis would have come about. All of them deserve a proper thank you. First and foremost I would like to thank my supervisor, Paul Klein. He has the ability to ask the central questions, the ones that force you to rethink your own work, dig deeper into the answers and (hopefully) come out on top of your own research. For this I am very grateful. He made me a better researcher and his guidance has been above reproach. I would also like to thank my second supervisor and co-author, Roine Vestman, who let me into his and Anders Österling's project regarding mortgage defaults, and who has the ability to think strategically in almost every situation, always keeping in mind what is ahead, and how to go to get there. I would also like to thank Annika Alexius for taking me under her wings during the period I was ying around in Ph.D. student's no-mans-land, and Martin Flodén for being there at the start of my thesis journey. Furthermore, I would like to thank Johan Söderberg for the good talks, especially the ones about the rst essay in this thesis and the ones about Bruce Springsteen. I am greatly indebted to Ducktor Österling, for half of my thesis is also his thesis. The long and tiresome journey would have been so much longer, so much more tiresome, and include much fewer semla buns without him. Thank you for the coding, the bad jokes, the music and the unhealthy foodish things. There are two other persons who I met on my Ph.D. journey that I would like to mention in particular. During the years that I was enrolled in the PhD-program, they were both very important for me, and they continue to be so. Their support during the PhD-student period has been invaluable. It all began a long long time ago, in an oce (not too) far far away. Thank you Theodoros Rapanos for being my oce mate, for being such a good fellow, for not talking too much about research with me, and for introducing me to the concept of Bad Movie Night. Without you, I would never have seen wondrous movies such as Birdemic and Shark Exorcist. Thank you André Richter, for being a constant support, for always giving insightful advice on questions regarding both research and life in general, for holding so high spirits, for being such a good fellow, for always being prepared to discuss strange issues, and for making the Bad Movie Nights even more enjoyable. And thank you both for the burgers. Many people have made my Ph.D. journey a lot more fun (and interesting) than it would have been without them. A special thanks go to Spiros Sichlimiris and Paola Di-Casola, and also to Ana-Maria Ceh. I would also like to especially mention my friends and colleagues that started the Ph.D. studies with me, several of them who have become good friends; Niels-Jakob Harboe-Hansen, Mounir Karadja, Leda Pateli, Christoer Milonas, Luca Facchinello, Audi 1. 1 Here, I think it is appropriate to mention that one could probably randomly re-shue all scenes in the movie Shark Exorcist without in any signicant way changing the movie experience..

(268) Baltrunaite, Ricardo Lopez-Aliouchkin, Luca Facchinello, Egle Karmaziene, Erik Lundin, Mengyi Cao and Mathias Pronin. Someone who should have been mentioned might have been forgotten, but I promise that it was a concious choice, but rather an absent-minded head that was to blame. Furthermore, I would like to thank Thomas Eisensee for luring me into the policy world. Who could know that so much interesting stu happened there, and that there was so much to learn!? In addition, I would like to thank Konjunkturinstitutet's running group for keeping me in (somewhat) good shape during the nal months of this thesis work. I would also like to thank the administrative sta at the Department of Economics for their help with the tricky administrative business. I would especially like to thank Anne Jensen and Ingela Arvidsson. Without the support of my loving family, I would never be where I am today. My father has always believed that I could be whatever I want in life. For that I am very grateful, and his belief has denitely left its mark. My mother has always been supporting in my endeavors, also when they might not have lead to great things. Especially she was there for me during a time when I really needed her, but didn't really understand it myself. The support from my siblings Markus, Mikaela and Isak has been above reproach my whole life, and for that, I am very grateful. The biggest thank of them all, for everything, goes to my wife Linn. Without her, I would have been lost in ways that she can not even imagine (or perhaps she can, since she, in some dimensions, knows me better than I know myself). She had made me a better person, a smarter individual and a happier man. Slutligen, mina älskade döttrar Liv och Alva. Utan er vore världen en mycket blekare plats. Bara det faktum att ni nns i den gör mina dagar mycket ljusare. Mina tankar strövar ofta iväg över både värld och universum, men de hittar alltid tillbaka till er, deras hem. I det hemmet nns även mitt hjärta, som aldrig lämnar det. Jakob Almerud April 2018.

(269) Introduction. This thesis contains four self-contained essays. The essays span dierent topics, but share the common feature that all questions in the thesis are analyzed using computational applied theoretical simulation models. The rst two essays investigate how dierent public policies affect welfare, and how to conduct policy in an optimal fashion. In the rst essay, I investigate how scal policy can be used in complement with monetary policy to improve macroeconomic outcomes. In the second essay, the focus is shifted away from the macroeconomy to individual households and their nancial decisions. In the essay, which is co-authored with Roine Vestman and Anders Österling, we investigate how dierent types of mortgage default policies interact with dierent types of mortgage contracts regarding the households' choice to default on their mortgages. Even though the focus is not directly on the macroeconomy, a macroeconomic environment is still present. A change in that macroeconomic environment directly aects the households' nancial decisions. The third and fourth essays also investigate the households' nancial decisions. In the third essay, I investigate how households optimally choose between risky equity and risk-free bonds in their asset portfolios if there is a long-run correlation between the returns to equity and the wage income that they receive. I also investigate if the empirical long-run correlation is strong enough to matter for the households' nancial decisions. In the fourth essay, which is written together with Anders Österling, we develop a method to solve computational economic models such as the ones used in the second and third essays in a more ecient way than has previously been done. As the computational eciency increases, it becomes easier for the computer to solve the models, which has as a consequence that it is possible to build more complex and realistic models, being more similar to the world that the models are built to investigate. Below follows a more detailed descriptions of the four essays.. Essay No 1: Optimal Public Policy in a Multi-Sector Model with Asymmetric Shocks: Academics have studied, and policy makers have conducted, monetary and scal policy (public policy) as tools for stabilizing the economy at least since the days of John Maynard Keynes. Since the welfare loss of economic recessions is seen as larger than the welfare gains of booms, it is possible to improve the general welfare by conducting counter-cyclical public policy to reduce size of the swings in output around its growth-trend. A modern view of stabilization policy is, however, that it might not be possible to improve welfare by stabilizing economic output completely around its trend. Such a policy could lead to the economy acting in a less ecient manner, thereby reducing welfare. Instead, it is recognized that the economy is aected by dierent frictions (for example matching frictions, informational frictions and price frictions). The goal of public policy in such an economy.

(270) should then be to (as far as possible) neutralize the negative eects of those frictions, thereby pushing the economy closer to its frictionless counterfactual self. One commonly used framework which is used to analyze how to conduct policy given dierent frictions, especially price frictions, is the New Keynesian framework.. In such a. framework, it is commonly assumed that rms are not able to react immediately to changes in the economic environment, which means that the price level can not adjust optimally to such changes. Within the framework, the use of monetary policy as a policy tool has been analyzed extensively. Fiscal policy as a tool to achieve similar outcomes is, however, less frequently analyzed (with Correia et al. (2008) and Correia et al. (2013) as two notable exceptions). In the essay, I try to ll (a portion of) that gap. I investigate how state-dependent scal policy, i.e. a scal policy that responds to changes in the economic environment, for example, an economy that goes into a recession, can be used to reduce, or under some conditions completely neutralize, the negative eects of the frictions that distort the economic outcomes. The analysis builds on an idea presented by Correia et al. (2013), who show that statedependent scal policy can be used as a tool when monetary policy is constrained by the zero-lower bound on the nominal interest rates. An economy at the lower bound is, however, not the only potentially case for scal policy as a useful tool. The usefulness depends on the structure of the economy. To show this, I build a New Keynesian model that includes several dierent types of production goods, where the sectors that produce the goods are hit by shocks which are not correlated between sectors. The rms in each sector are subject to monopolistic competition and price stickiness. In such an environment, it is not possible to reach the rst-best outcome, i.e. the outcome where all negative eects of the frictions are neutralized, with only monetary policy as a tool. However, by introducing the appropriate scal instruments it is possible to reach the rst-best. This does, however, hinge on that the scal authority is able to respond immediately after a shock has hit the economy. In reality this might be dicult, since it is often the case that changes in scal policy have to go through a time-consuming political process. Therefore, it is also investigated how to conduct policy when scal policy is restricted by an implementation lag. It is shown that it is still benecial to conduct state-dependent scal policy if such a lag is included.. Essay No 2: On the Design of Mortgage Default Legislation: This essay is co-authored with Roine Vestman and Anders Österling. We investigate how dierent types of mortgage contracts interact with dierent types of mortgage default policies regarding the probability of a default on a home-owner's mortgage, and which is the best policy-combination from the home-owner's perspective. The legislation regulating the consequences of a home-owner defaulting on his or her mortgage diers signicantly between countries and between dierent states within the United States (U.S.). On one end of the spectrum lies for example many U.S. states, having socalled non-recourse regimes, meaning that the mortgage lender has no ability to claim any.

(271) outstanding debt that is left after a forced sale of the home (the underlying security of the mortgage). On the other end lies for example Sweden, where the mortgage lender has the right to claim all of the home owner's assets to cover their loss. Which policy that is optimal from the home-owner's perspective is however uncertain. Furthermore, it might depend on the type of mortgage contract. To be able to answer that question, we develop a model consisting of home-owners who are modeled from the year that they buy their home and to the end of the duration of the mortgage contract. The home-owners choose how much to consume, save, and how much to work. Furthermore, every year they choose if they should stay in their home, sell it to become renters, or if they should default on their mortgage. The mortgage default policies span from non-recourse to full recourse. With non-recourse policy, the mortgage lender takes all the default risk since there is no cost for the household (except for the mortgage lender claiming the house) to default on their mortgage. With full recourse, the mortgage lender is able to claim all of the defaulting household's assets and income, up to the dierence between the value of the mortgage and the value of the home. Hence, the households bear all the risk of the default. The dierent types of mortgage contracts that we consider are xed rate annuity mortgages (FRM), adjustable rate amortized mortgages (ARM) and adjustable rate non-amortized mortgages (IO). Households with FRM mortgages have a xed nominal interest rate, and do therefore face ination risk. If ination is high the real interest rate of the mortgage decreases. Simultaneously, the mortgage levels decrease in real terms since the mortgage contract is written in nominal terms. The real interest rates of households that have ARM and IO mortgages are not aected by ination, but are instead aected by changes in the real short-term interest rate. Increased ination does however decrease the mortgage levels in real terms also for households with ARM and IO mortgages. Due to the dierences in household behavior given dierent policies and dierent types of mortgages, the home-owners face a dierent risk premium for every default legislation/mortgage type combination. The main result in the essay that a borrower friendly policy, as the nonrecourse policy implemented in many states in the United States, is actually not borrowerfriendly due to its eect on the risk premium. Households that do not default on their mortgages pay for the households that do default via a higher risk premium. Therefore, households prefer recourse to non-recourse, since it leads to reduced interest rate payments on their mortgages. Furthermore, we show that households prefer mortgages including amortization if the default cost is low, since the amortization reduces the probability of default, thereby decreasing the risk premium. However, if the cost of default is high, the households instead prefer IO mortgages.. Essay No 3: On the Empirical Relevance of Cointegration Between Stock Market Returns and Labor Income on Optimal Portfolio Choice. In the third essay, I investigate how the optimal choice of an asset portfolio that consists of.

(272) risk-free bonds and risky equity is aected by long-run correlation, or so-called cointegration, between cumulative equity returns and aggregate labor income. 2 This is important because it has implications on for example how pension funds should be allocated, so as to minimize the risk of the household loosing both labor income and future pensions. It does also have implications for how the household should allocate their savings for a rainy day (so-called precautionary savings). Assume that there is a long-run correlation between equity income and labor income, and that there is a sharp decline in stock market prices, i.e. a stock market crash. If this, because of the cointegration, is followed by labor income decreasing drastically, the assets that was hold for a rainy day is not worth much when that rainy day arrives. The standard optimal portfolio choice result found in the nance literature, which disregards such long-run correlation, states that households should invest heavily in equity when young, and then reduce their equity share as they grow older. However, that result is at odds with empirical observations of how households act, giving rise to a so-called puzzle that has caught the interest of many researchers. One study where this result has been reversed is Benzoni et al. (2007). They study the cointegration between aggregate labor income and equity dividends. Finding such a cointegration, they continue by making the assumption that the total return on equity perfectly follows the evolution of dividend payouts, and show that the cointegration between the two variables leads to dramatic eects on the optimal portfolio choice compared to the standard result in the literature. Instead of investing heavily in equity, households should invest nothing in equity when young. Furthermore, they should increase, rather than decrease, the equity share in their portfolio as they grow older. The assumption of total returns being perfectly correlated with dividend payouts is however at odds with the data, as shown by for example Shiller (1981) and Shiller (1987). Furthermore, investors rather care about total returns than only about dividends. Therefore I estimate a type of cointegration model, a Vector Error Correction (VEC) model, using data on the United States aggregate labor income and cumulative total equity returns. The estimated values in the VEC model are then used in a theoretical model where households solve a portfolio problem between the ages 20 and 64 (after which they are assumed to retire, thereby no longer caring about labor income).. The portfolio consists of a risk-free bond. and an stock market index fund. In contrast to Benzoni et al. (2007), the households do not choose to save only in bonds when young. Instead their behavior lies much closer to the standard result. Hence, I do not nd any evidence for the long-run correlation between the two variables being important enough for the households to take it into account when choosing how to save for the future.. Essay No 4: Solving dynamic programming problems using stochastic grids and nearest-neighbor interpolation The fourth essay is co-authored together with Anders Österling, and is a pre-requisite for the 2. With equity I mean assets traded on the stock market..

(273) second and third essay. The real world, and the actions taken by the inhabitants in it, is a very complex place. Economists try to understand it by reducing the world into something more manageable. When doing this, a large part of it have to be abstracted from, and it is the economist's job to include the relevant elements needed to answer the question that he or she is studying, and to abstract from the rest. When doing this, the economist creates a small, manageable model economy. As the power of computers have exploded during the last decades, these model economies have become more complex, introducing more elements from the real world into them. Another way of being able to introduce more elements is by increasing the eciency of the solution methods used to solve the economic models. This is done in the paper. We develop a method that can be used to computationally solve economic simulation models. With the method, it is possible to solve a certain class of economic models more quickly, and using less computational power, than before. This means that it is possible to include more elements to the model, making it more realistic than if those elements would be excluded. With the method, we are able to solve so-called life-cycle models, where the economic agents live for a certain amount of periods and then die, with many exogenous disturbances (for example several dierent shocks to a household's labor income together with an uncertain interest rate and uncertain future ination) using a standard personal computer. This has been hard to do before, which means that answers to questions including these features have become become more accessible to the economist. We build on a method to solve an economic consumption/savings problem of a nitely live household, introduced by Carroll (2006) to solve the kinds of models. On top of that, we introduce a number of economic shock processes that aect the household's labor income. These shock processes are called exogenous state variables. The standard way of solving a model with such state variables is to introduce a deterministic discrete space that includes values which the process can take, on which the model is then solved. If there are several shock processes, every shock has its own discrete space, and the model is solved for each combination of elements in those discrete spaces. Instead of using that approach, we simulate paths of the shock processes beforehand, solving the models on the simulated paths instead of on deterministic grids. This way, we are able to reduce the number of points that the model is solved for signicantly, thereby increasing the solution speed of the model. Furthermore, we make use of nearest neighbor interpolation to nd policy functions where the economic environment is similar to the economic environment for which the model is solved. We show that it is possible to solve non-linear life-cycle models including at least eight exogenous state variables relatively quickly on a standard desktop computer. We then apply the method to a consumption/savings problem in a life-cycle setting, where agents face a much more complicated wage earnings process than the one commonly assumed in the the kind of model framework we are using. The process that we use was estimated by Guvenen et al. (2015), and lies much closer to what we see in actual data than the one.

(274) that is commonly used. We compare the patterns of consumption and savings to of those of a model using the standard process.. References Benzoni, L., Collin-Dufresne, P., and Goldstein, R. S. (2007).. Portfolio Choice over the. Life-Cycle when the Stock and Labor Markets Are Cointegrated.. The Journal of Finance,. LXII(5). Carroll, C. D. (2006). The method of endogenous gridpoints for solving dynamic stochastic optimization problems.. Economics Letters, 91:312320.. Correia, I., Farhi, E., Nicolini, J. P., and Teles, P. (2013). Unconventional scal policy at the zero bound.. American Economic Review , 103(4):11721211.. Correia, I., Nicolini, J., and Teles, P. (2008). Optimal Fiscal and Monetary Policy: Equivalence Results.. Journal of Political Economy , 116(1):141170.. Guvenen, F., Karahan, F., Ozkan, S., and Song, J. (2015). What Do Data on Millions of U.S. Workers Reveal about Life-Cycle Earnings Risk? Shiller, R. J. (1981). Do Stock Prices Move Too Much to be Justied by Subsequent Changes in Dividends? Shiller, R. J. (1987). 235(4784):3337.. The volatility of stock market prices.. Science (New York, N.Y.),.

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