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Recursive macroeconomic theory, Lars Ljungqvist and Thomas J. Sargent; The MIT Press, Cambridge, MA, 2000, pp. 737, $60.
Journal of Economic Dynamics & Control 25 (2001) 1451–1456 www.elsevier.nl/locate/econbase
Book review Recursive macroeconomic theory, Lars Ljungqvist and Thomas J: Sargent; The MIT Press; Cambridge; MA; 2000; pp: 737; $60: Dynamic stochastic models play a key role in current macroeconomic theories. These models make it possible to incorporate in a structured manner features thought to be essential to understand economic systems: shocks that are propagated through the system, expectations about future events that a9ect current economic behavior, and expectations about actions taken by agents or institutions that a9ect decisions which are in turn being predicted by other agents. These models can be used to understand the behavior of observed macroeconomic time series and, when they are built using microeconomic foundations, to make predictions about the response of the economic system to changes in government policies. Simple stochastic dynamic models are unfortunately not even capable of explaining some minimal set of observed characteristics of macroeconomic time series like the average value of the short-term interest rates, the average value of the equity premium, and the cyclical behavior of employment, prices, and wages. During the last two decades the empirical performance of these models has been considerably improved by incorporating sensible features such as heterogeneous agents, incomplete markets, frictions, and bounded rationality. By moving away from the standard models, these models quickly become di:cult to analyze. Considerable progress can be made if one focuses on recursive formulations of the problem in which agents faced with the same set of observed state variables would behave in the same way. Consider the following standard (deterministic) in
max ∞ ? t U (ct );
{ct ; kt+1 }t=0 t=0
s:t:
kt+1 + ct = Akt ; k0 given:
∞ Here, the solutions are sequences {ct }∞ t=0 and {kt+1 }t=0 . The recursive approach would search for solutions of the form ct = c(kt ) and kt+1 = k(kt ) so that faced with the same value for the state variable kt agents would behave in the same way.
0165-1889/01/$ - see front matter ? 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 5 - 1 8 8 9 ( 0 1 ) 0 0 0 1 9 - 7
1452
Book review / Journal of Economic Dynamics & Control 25 (2001) 1451–1456
Even recursive models become complicated very fast. For example, determining the set of state variables can be nontrivial. Moreover, for a given set of state variables, the functional form of the solutions is typically unknown and there could be multiple solutions. These issues are important because the properties of the model can depend strongly on the selected solution. For example, consider the claim of the recently developed
Book review / Journal of Economic Dynamics & Control 25 (2001) 1451–1456
1453
somewhat challenging. 1 Chapter 6 analyzes a typical investment problem and this framework is used to carefully review the de
1454
Book review / Journal of Economic Dynamics & Control 25 (2001) 1451–1456
reoptimize. The authors introduce the concept of Nash equilibrium, discuss several di9erent timing conventions, and show how crucial these assumptions about the timing are for the results. Models with money: Chapter 17 introduces money into the model using a shopping time technology that has real money balances as one of its inputs. With this framework the authors review monetary doctrines about the e9ects of sustained de
i i ) s:t: cii + M i =pi ≤ !1 ; ci+1 ≤ M i =pi+1 + !2 ∀i ¿ 0; max ln(cii ) + ln(ci+1
i cii ; ci−1 ;Mi
where !1 ¡ !2 and in equilibrium M i = M . Typically, even this simple problem is simpli
As in Chapter 4 of Blancard and Fisher (1989).
Book review / Journal of Economic Dynamics & Control 25 (2001) 1451–1456
1455
2M /(!1 (1 − !2 =!1 )). Ljungqvist and Sargent provide here, as elsewhere in the book, a more thorough presentation of the problem and show that the full set of solutions is given by t 2M !1 +c pt = !1 (1 − !2 =!1 ) !2 for any scalar c ≥ 0. The more complete approach taken by Ljungvist and Sargent throughout the book makes it possible to obtain a richer understanding of the predictions of dynamic models. Since we typically have no arguments to prefer the simpler solutions to the more complicated solutions this is the right way to analyze these models. Of course, it also means that relative to other macroeconomic text books less space is devoted to discussions of economic issues. While Stokey and Lucas (1989) focus on theoretical aspects of proving theorems about the existence of solutions and their properties, Ljungqvist and Sargent focus much more on the practical aspects of developing and analyzing a rich set of dynamic problems. Compared to Sargent (1979) and Sargent (1987) the book is much of more of a comprehensive text book and less of a set of lecture notes. By developing a thorough analysis of stochastic dynamic models and by avoiding simplifying short cuts the authors have written a book that is bound to become an obligatory resource for all students who plan on working with stochastic dynamic models. Besides being an ideal educational tool, the book is also an excellent source to review both the technical and economic aspects of many classic and contemporaries problems 3 that are part of the literature on stochastic dynamic macroeconomic models. References Blancard, O.J., Fisher, S., 1989. Lectures on Macroeconomics. The MIT Press, Cambridge, MA. Hosios, A.J., 1990. On the e:ciency of matching and related models of search and unemployment. Rev. Economic Studies 57, 279–298. Kiotaki, N., Wright, R., 1989. On money as a medium of exchange. Journal of Political Economy 97 (4), 927–954. Pissarides, Christopher, A., 1990. Equilibrium Unemployment. Basil Blackwell, Cambridge, MA. Romer, D., 1996. Advanced Macroeconomics. The McGraw-Hill Companies Inc., New York. Sargent, T.J., 1979. Macroeconomic Theory. Academic Press, New York. Sargent, T.J., 1987. Dynamic Macroeconomic Theory. Harvard University Press, Cambridge, MA. Stokey, N., Lucas Jr., R.E. 1989. Recursive Methods in Economic Dynamics. Harvard University Press, Cambridge, MA. 3 Examples are the Hansen–Jagannathan bounds, the
1456
Book review / Journal of Economic Dynamics & Control 25 (2001) 1451–1456
Townsend, R.M., 1980. Models of Money with Spatially Separated Agents. In: Models of Monetary Economies. Kareken, J.H., Wallace, N., (Eds.), Federal Reserve Bank of Minneapolis, Minneapolis, pp. 265 –303. Walsh, C.E., 1998. Monetary Theory and Policy. The MIT Press, Cambridge, MA.
Wouter J. Den Haan Department of Economics, University of California at San Diego, La Jolla, CA 92093-0508, USA National Bureau of Economic Research, Cambridge, USA Centre for Economic Policy Research, London, UK E-mail address: [email protected] (W.J. Den Haan)
Book review Recursive macroeconomic theory, Lars Ljungqvist and Thomas J: Sargent; The MIT Press; Cambridge; MA; 2000; pp: 737; $60: Dynamic stochastic models play a key role in current macroeconomic theories. These models make it possible to incorporate in a structured manner features thought to be essential to understand economic systems: shocks that are propagated through the system, expectations about future events that a9ect current economic behavior, and expectations about actions taken by agents or institutions that a9ect decisions which are in turn being predicted by other agents. These models can be used to understand the behavior of observed macroeconomic time series and, when they are built using microeconomic foundations, to make predictions about the response of the economic system to changes in government policies. Simple stochastic dynamic models are unfortunately not even capable of explaining some minimal set of observed characteristics of macroeconomic time series like the average value of the short-term interest rates, the average value of the equity premium, and the cyclical behavior of employment, prices, and wages. During the last two decades the empirical performance of these models has been considerably improved by incorporating sensible features such as heterogeneous agents, incomplete markets, frictions, and bounded rationality. By moving away from the standard models, these models quickly become di:cult to analyze. Considerable progress can be made if one focuses on recursive formulations of the problem in which agents faced with the same set of observed state variables would behave in the same way. Consider the following standard (deterministic) in
max ∞ ? t U (ct );
{ct ; kt+1 }t=0 t=0
s:t:
kt+1 + ct = Akt ; k0 given:
∞ Here, the solutions are sequences {ct }∞ t=0 and {kt+1 }t=0 . The recursive approach would search for solutions of the form ct = c(kt ) and kt+1 = k(kt ) so that faced with the same value for the state variable kt agents would behave in the same way.
0165-1889/01/$ - see front matter ? 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 5 - 1 8 8 9 ( 0 1 ) 0 0 0 1 9 - 7
1452
Book review / Journal of Economic Dynamics & Control 25 (2001) 1451–1456
Even recursive models become complicated very fast. For example, determining the set of state variables can be nontrivial. Moreover, for a given set of state variables, the functional form of the solutions is typically unknown and there could be multiple solutions. These issues are important because the properties of the model can depend strongly on the selected solution. For example, consider the claim of the recently developed
Book review / Journal of Economic Dynamics & Control 25 (2001) 1451–1456
1453
somewhat challenging. 1 Chapter 6 analyzes a typical investment problem and this framework is used to carefully review the de
1454
Book review / Journal of Economic Dynamics & Control 25 (2001) 1451–1456
reoptimize. The authors introduce the concept of Nash equilibrium, discuss several di9erent timing conventions, and show how crucial these assumptions about the timing are for the results. Models with money: Chapter 17 introduces money into the model using a shopping time technology that has real money balances as one of its inputs. With this framework the authors review monetary doctrines about the e9ects of sustained de
i i ) s:t: cii + M i =pi ≤ !1 ; ci+1 ≤ M i =pi+1 + !2 ∀i ¿ 0; max ln(cii ) + ln(ci+1
i cii ; ci−1 ;Mi
where !1 ¡ !2 and in equilibrium M i = M . Typically, even this simple problem is simpli
As in Chapter 4 of Blancard and Fisher (1989).
Book review / Journal of Economic Dynamics & Control 25 (2001) 1451–1456
1455
2M /(!1 (1 − !2 =!1 )). Ljungqvist and Sargent provide here, as elsewhere in the book, a more thorough presentation of the problem and show that the full set of solutions is given by t 2M !1 +c pt = !1 (1 − !2 =!1 ) !2 for any scalar c ≥ 0. The more complete approach taken by Ljungvist and Sargent throughout the book makes it possible to obtain a richer understanding of the predictions of dynamic models. Since we typically have no arguments to prefer the simpler solutions to the more complicated solutions this is the right way to analyze these models. Of course, it also means that relative to other macroeconomic text books less space is devoted to discussions of economic issues. While Stokey and Lucas (1989) focus on theoretical aspects of proving theorems about the existence of solutions and their properties, Ljungqvist and Sargent focus much more on the practical aspects of developing and analyzing a rich set of dynamic problems. Compared to Sargent (1979) and Sargent (1987) the book is much of more of a comprehensive text book and less of a set of lecture notes. By developing a thorough analysis of stochastic dynamic models and by avoiding simplifying short cuts the authors have written a book that is bound to become an obligatory resource for all students who plan on working with stochastic dynamic models. Besides being an ideal educational tool, the book is also an excellent source to review both the technical and economic aspects of many classic and contemporaries problems 3 that are part of the literature on stochastic dynamic macroeconomic models. References Blancard, O.J., Fisher, S., 1989. Lectures on Macroeconomics. The MIT Press, Cambridge, MA. Hosios, A.J., 1990. On the e:ciency of matching and related models of search and unemployment. Rev. Economic Studies 57, 279–298. Kiotaki, N., Wright, R., 1989. On money as a medium of exchange. Journal of Political Economy 97 (4), 927–954. Pissarides, Christopher, A., 1990. Equilibrium Unemployment. Basil Blackwell, Cambridge, MA. Romer, D., 1996. Advanced Macroeconomics. The McGraw-Hill Companies Inc., New York. Sargent, T.J., 1979. Macroeconomic Theory. Academic Press, New York. Sargent, T.J., 1987. Dynamic Macroeconomic Theory. Harvard University Press, Cambridge, MA. Stokey, N., Lucas Jr., R.E. 1989. Recursive Methods in Economic Dynamics. Harvard University Press, Cambridge, MA. 3 Examples are the Hansen–Jagannathan bounds, the
1456
Book review / Journal of Economic Dynamics & Control 25 (2001) 1451–1456
Townsend, R.M., 1980. Models of Money with Spatially Separated Agents. In: Models of Monetary Economies. Kareken, J.H., Wallace, N., (Eds.), Federal Reserve Bank of Minneapolis, Minneapolis, pp. 265 –303. Walsh, C.E., 1998. Monetary Theory and Policy. The MIT Press, Cambridge, MA.
Wouter J. Den Haan Department of Economics, University of California at San Diego, La Jolla, CA 92093-0508, USA National Bureau of Economic Research, Cambridge, USA Centre for Economic Policy Research, London, UK E-mail address: [email protected] (W.J. Den Haan)