Since it is the dominant paradigm of the business cycle and growth literatures, the stochastic growth model has been used to test the performance of alternative numerical methods. This paper applies the finite element method to this example. I show that the method is easy to apply and, for examples such as the stochastic growth method, gives accurate solutions within a second or two on a desktop computer. I also show how inequality constraints can be handled by redefining the optimization problem with penalty functions.
We estimate a dynamic general equilibrium model of the U.S. economy that includes an explicit household production sector. We use these estimates to investigate two issues. First, we analyze how well the model accounts for aggregate fluctuations. Second, we use the model to study the effects of fiscal policy. We find household production has a significant impact, and reject a nested specification in which changes in the home production technology do not matter for market variables. The model generates very different predictions for the effects of tax changes than similar models without home production.
This paper catalogues formulas that are useful for estimating dynamic linear economic models. We describe algorithms for computing equilibria of an economic model and for recursively computing a Gaussian likelihood function and its gradient with respect to parameters. We display an application to Rosen, Murphy, and Scheinkman's (1994) model of cattle cycles.
We estimate a dynamic general equilibrium model of the U.S. economy that includes an explicit household production sector and stochastic fiscal variables. We use our estimates to investigate two issues. First, we analyze how well the model accounts for aggregate fluctuations. We find that household production has a significant impact and reject a nested specification in which changes in the home production technology do not matter for market variables. Second, we study the effects of some simple fiscal policy experiments and show that the model generates different predictions for the effects of tax changes than similar models without home production.
This paper catalogues formulas that are useful for estimating dynamic linear economic models. We describe algorithms for computing equilibria of an economic model and for recursively computing a Gaussian likelihood function and its gradient with respect to parameters. We apply these methods to several example economies.
We find that the welfare gains to being at the optimum quantity of debt rather than the current U.S. level are small, and, therefore, concerns regarding the high level of debt in the U.S. economy may be misplaced. This finding is based on a model of a large number of infinitely-lived households whose saving behavior is influenced by precautionary saving motives and borrowing constraints. This model incorporates a different role for government debt than is found in standard models, and it captures different cost-benefit trade-offs. On the benefit side, government debt enhances the liquidity of households by providing an additional means of smoothing consumption and by effectively loosening borrowing constraints. On the cost side, the implied taxes have adverse wealth distribution and incentive effects. In addition, government debt crowds out capital via higher interest rates and lowers per capita consumption.
In this appendix, we describe the numerical methods used to compute an equilibrium in the economy with an inelastic labor supply and in the economy with an elastic labor supply (i.e., our benchmark economy). Although the economy with inelastically supplied labor is a special case of the benchmark economy, the equilibrium in the inelastic labor supply case is much easier to compute and is therefore treated separately. In each case, we start with the consumer's problem, assuming the consumer takes prices as given. We then show how the equilibrium prices are determined. To verify that the methods work well with our problem, we apply them to some related test problems that have known solutions.
We ask what fraction of the variation in incomes across countries can be accounted for by investment distortions. In our neoclassical growth model the relative price of investment to consumption is a good measure of the distortions. Using data on relative prices we estimate a stochastic process for distortions and compare the resulting variance of incomes in the model to that in the data. We find that the variation of incomes in the model is roughly 4/5 of the variability of incomes in the data. Our model does well in accounting for 6 key regularities on income and investment in the data.
The paper itself is followed by three appendices: Appendix 1 describing the log-likelihood function, Appendix 2 describing the construction of labor share of income associated with the production of consumption and investment goods, and the Data Appendix.
We construct a quantitative equilibrium model with price setting and use it to ask whether with staggered price setting monetary shocks can generate business cycle fluctuations. These fluctuations include persistent output fluctuations along with the other defining features of business cycles, like volatile investment and smooth consumption. We assume that prices are exogenously sticky for a short period of time. Persistent output fluctuations require endogenous price stickiness in the sense that firms choose not to change prices very much when they can do so. We find that for a wide range of parameter values the amount of endogenous stickiness is small. As a result, we find that in a standard quantitative business cycle model staggered price setting, by itself, does not generate business cycle fluctuations.
The conventional wisdom is that monetary shocks interact with sticky goods prices to generate the observed volatility and persistence in real exchange rates. We investigate this conventional wisdom in a quantitative model with sticky prices. We find that with preferences as in the real business cycle literature, irrespective of the length of price stickiness, the model necessarily produces only a fraction of the volatility in exchange rates seen in the data. With preferences which are separable in leisure, the model can produce the observed volatility in exchange rates. We also show that long stickiness is necessary to generate the observed persistence. In addition, we show that making asset markets incomplete does not measurably increase either the volatility or persistence of real exchange rates.
I argue that low-frequency movements in U.S. base velocity are well explained by standard models of money demand. The model of Gordon, Leeper, and Zha is not standard because they assume a very high interest elasticity. The positive conclusion that they reach about the model’s ability to mimic movements in velocity necessarily implies that predicted movements in interest rates are too smooth.
This chapter reviews the literature that tries to explain the disparity and variation of GDP per worker and GDP per capita across countries and across time. There are many potential explanations for the different patterns of development across countries, including differences in luck, raw materials, geography, preferences, and economic policies. We focus on differences in economic policies and ask to what extent can differences in policies across countries account for the observed variability in income levels and their growth rates. We review estimates for a wide range of policy variables. In many cases, the magnitude of the estimates is under debate. Estimates found by running cross-sectional growth regressions are sensitive to which variables are included as explanatory variables. Estimates found using quantitative theory depend in critical ways on values of parameters and measures of factor inputs for which there is little consensus. In this chapter, we review the ongoing debates of the literature and the progress that has been made thus far.
The central puzzle in international business cycles is that fluctuations in real exchange rates are volatile and persistent. We quantity the popular story for real exchange rate fluctuations: they are generated by monetary shocks interacting with sticky goods prices. If prices are held fixed for at least one year, risk aversion is high, and preferences are separable in leisure, then real exchange rates generated by the model are as volatile as in the data and quite persistent, but less so than in the data. The main discrepancy between the model and the data, the consumption—real exchange rate anomaly, is that the model generates a high correlation between real exchange rates and the ratio of consumption across countries, while the data show no clear pattern between these variables.
Many stock market analysts think that in 1929, at the time of the crash, stocks were overvalued. Irving Fisher argued just before the crash that fundamentals were strong and the stock market was undervalued. In this paper, we use growth theory to estimate the fundamental value of corporate equity and compare it to actual stock valuations. Our estimate is based on values of productive corporate capital, both tangible and intangible, and tax rates on corporate income and distributions. The evidence strongly suggests that Fisher was right. Even at the 1929 peak, stocks were undervalued relative to the prediction of theory.
We derive the quantitative implications of growth theory for U.S. corporate equity plus net debt over the period 1960–2001. There were large secular movements in corporate equity values relative to GDP, with dramatic declines in the 1970s and dramatic increases starting in the 1980s and continuing throughout the 1990s. During the same period, there was little change in the capital-output ratio or earnings share of output. We ask specifically whether the theory accounts for these observations. We find that it does, with the critical factor being changes in the U.S. tax and regulatory system. We find that the theory also accounts for the even larger movements in U.K. equity values relative to GDP in this period.
Mehra and Prescott (1985) found the difference between average equity and debt returns puzzling because it was too large to be a premium for bearing nondiversifiable aggregate risk. Here, we re-examine this puzzle, taking into account some factors ignored by Mehra and Prescott—taxes, regulatory constraints, and diversification costs—and focusing on long-term rather than short-term savings instruments. Accounting for these factors, we find the difference between average equity and debt returns during peacetime in the last century is less than 1 percent, with the average real equity return somewhat under 5 percent, and the average real debt return almost 4 percent. As theory predicts, the real return on debt has been close to the 4 percent average after-tax real return on capital. Similarly, as theory predicts, the real return on equity is equal to the after-tax real return on capital plus a modest premium for bearing nondiversifiable aggregate risk.
There is much debate about the usefulness of the neoclassical growth model for assessing the macroeconomic impact of fiscal shocks. We test the theory using data from World War II, which is by far the largest fiscal shock in the history of the United States. We take observed changes in fiscal policy during the war as inputs into a parameterized, dynamic general equilibrium model and compare the values of all variables in the model to the actual values of these variables in the data. Our main finding is that the theory quantitatively accounts for macroeconomic activity during this big fiscal shock.
We study the large observed changes in labor supply by married women in the United States over the post–World War II period, a period that saw little change in the labor supply by single women. We investigate the effects of changes in the gender wage gap, the quantitative impact of technological improvements in the production of nonmarket goods, and the potential inferiority of nonmarket goods in explaining the dramatic change in labor supply. We find that small decreases in the gender wage gap can simultaneously explain the significant increases in the average hours worked by married women and the relative constancy in the hours worked by single women and by single and married men. We also find that the impact of technological improvements in the household on married female hours and on the relative wage of females to males is too small for realistic values. Some specifications of the inferiority of home goods match the hours patterns, but they have counterfactual predictions for wages and expenditure patterns.
We propose a simple method to help researchers develop quantitative models of economic fluctuations. The method rests on the insight that many models are equivalent to a prototype growth model with time-varying wedges which resemble productivity, labor and investment taxes, and government consumption. Wedges corresponding to these variables—efficiency, labor, investment, and government consumption wedges—are measured and then fed back into the model in order to assess the fraction of various fluctuations they account for. Applying this method to U.S. data for the Great Depression and the 1982 recession reveals that the efficiency and labor wedges together account for essentially all of the fluctuations; the investment wedge plays a decidedly tertiary role, and the government consumption wedge, none. Analyses of the entire postwar period and alternative model specifications support these results. Models with frictions manifested primarily as investment wedges are thus not promising for the study of business cycles. (See Additional Material for a response to Christiano and Davis (2006).)
Gali and Rabanal provide statistical evidence that, in their view, puts into question the real business-cycle paradigm in favor of the sticky-price paradigm. I demonstrate that their statistical procedure is easily misled in that they would reach the same conclusions even if their data had been simulated from an RBC model. I also demonstrate that sticky-price models do a poor job generating U.S.-like business cycles with only shocks to technology, the federal funds rate, and government consumption. This explains why Gali and Rabanal need large unobserved shocks to preferences and to the degree of monopoly power.
With a monetary union in place, many European countries are now debating if and how to coordinate their tax policies. Of particular interest to EU ministers is taxation of mobile factors like capital. Mendoza and Tesar (MT) use a game-theoretic approach to address the question, What is the outcome of tax competition and tax coordination when countries choose the tax on capital income and adjust other tax rates to keep revenues constant? MT predict very large welfare gains (losses) to tax competition for European countries that had high (low) tax rates prior to financial integration. In particular they predict a large gain for the United Kingdom and a large loss for countries in continental Europe. A second finding is that the welfare gains of tax coordination relative to that of tax competition are small. I discuss these findings in light of current policy debates and possible future extensions of this work.
In this paper, we show that ignoring corporate intangible investments gives a distorted picture of the post-1990 U.S. economy. In particular, ignoring intangible investments in the late 1990s leads one to conclude that productivity growth was modest, corporate profits were low, and corporate investment was at moderate levels. In fact, the late 1990s was a boom period for productivity growth, corporate profits, and corporate investment.
In recent financial crises and in recent theoretical studies of them, abrupt declines in capital inflows, or sudden stops, have been linked with large drops in output. Do sudden stops cause output drops? No, according to a standard equilibrium model in which sudden stops are generated by an abrupt tightening of a country’s collateral constraint on foreign borrowing. In this model, in fact, sudden stops lead to output increases, not decreases. An examination of the quantitative effects of a well-known sudden stop, in Mexico in the mid-1990s, confirms that a drop in output accompanying a sudden stop cannot be accounted for by the sudden stop alone. To generate an output drop during a financial crisis, as other studies have done, the model must include other economic frictions which have negative effects on output large enough to overwhelm the positive effect of the sudden stop.
The central finding of the recent structural vector autoregression (SVAR) literature with a differenced specification of hours is that technology shocks lead to a fall in hours. Researchers have used this finding to argue that real business cycle models are unpromising. We subject this SVAR specification to a natural economic test and show that when applied to data from a multiple-shock business cycle model, the procedure incorrectly concludes that the model could not have generated the data as long as demand shocks play a nontrivial role. We also test another popular specification, which uses the level of hours, and show that with nontrivial demand shocks, it cannot distinguish between real business cycle models and sticky price models. The crux of the problem for both SVAR specifications is that available data require a VAR with a small number of lags and such a VAR is a poor approximation to the model’s VAR.
For the 1990s, the basic neoclassical growth model predicts a depressed economy, when in fact the U.S. economy boomed. We extend the base model by introducing intangible investment and non-neutral technology change with respect to producing intangible investment goods and find that the 1990s are not puzzling in light of this new theory. There is micro and macro evidence motivating our extension, and the theory’s predictions are in conformity with U.S. national accounts and capital gains. We compare accounting measures with corresponding measures for our model economy. We find that standard accounting measures greatly understate the 1990s boom.
Real business cycles are recurrent fluctuations in an economy’s incomes, products, and factor inputs—especially labor—that are due to nonmonetary sources. These sources include changes in technology, tax rates and government spending, tastes, government regulation, terms of trade, and energy prices. Most real business cycle (RBC) models are variants or extensions of a neoclassical growth model. One such prototype is introduced. It is then shown how RBC theorists, applying the methodology of Kydland and Prescott (Econometrica 1982), use theory to make predictions about actual time series. Extensions of the prototype model, current issues, and open questions are also discussed.
We make three comparisons relevant for the business cycle accounting approach. We show that in theory, representing the investment wedge as a tax on investment is equivalent to representing this wedge as a tax on capital income as long as the probability distributions over this wedge in the two representations are the same. In practice, convenience dictates that the underlying probability distributions over the investment wedge are different in the two representations. Even so, the quantitative results under the two representations are essentially identical. We also compare our methodology, the CKM methodology, to an alternative one used in Christiano and Davis (2006) and by us in early incarnations of the business cycle accounting approach. We argue that the CKM methodology rests on more secure theoretical foundations. Finally, we show that the results from the VAR-style decomposition of Christiano and Davis reinforce the results of the business cycle decomposition of CKM.