Research Database

This is a survey of simulation methods in economics, with a specific focus on integration problems. It describes acceptance methods, importance sampling procedures, and Markov chain Monte Carlo methods for simulation from univariate and multivariate distributions and their application to the approximation of integrals. The exposition gives emphasis to combinations of different approaches and assessment of the accuracy of numerical approximations to integrals and expectations. The survey illustrates these procedures with applications to simulation and integration problems in economics.

This paper generalizes the normal probit model of dichotomous choice by introducing mixtures of normals distributions for the disturbance term. By mixing on both the mean and variance parameters and by increasing the number of distributions in the mixture these models effectively remove the normality assumption and are much closer to semiparametric models. When a Bayesian approach is taken, there is an exact finite-sample distribution theory for the choice probability conditional on the covariates. The paper uses artificial data to show how posterior odds ratios can discriminate between normal and nonnormal distributions in probit models. The method is also applied to female labor force participation decisions in a sample with 1,555 observations from the PSID. In this application, Bayes factors strongly favor mixture of normals probit models over the conventional probit model, and the most favored models have mixtures of four normal distributions for the disturbance term.

Dynamic general equilibrium models that include explicit household production sectors provide a useful framework within which to analyze a variety of macroeconomic issues. However, some implications of these models depend critically on parameters, including the elasticity of substitution between market and home consumption goods, about which there is little information in the literature. Using the PSID, we estimate these parameters for single males, single females, and married couples. At least for single females and married couples, the results indicate a high enough substitution elasticity that including home production will make a significant difference in applied general equilibrium theory.

A traditional explanation for why sovereign governments repay debts is that they want to keep good reputations so they can easily borrow more. Bulow and Rogoff show that this argument is invalid under two conditions: (i) there is a single debt relationship, and (ii) regardless of their past actions, governments can earn the (possibly state-contingent) market rate of return by saving abroad. Bulow and Rogoff conjecture that, even under condition (ii), in more general reputation models with multiple relationships and spillover across them, reputation may support debt. This paper shows what is needed for this conjecture to be true.

Most empirical studies of the static CAPM assume that betas remain constant over time and that the return on the value-weighted portfolio of all stocks is a proxy for the return on aggregate wealth. The general consensus is that the static CAPM is unable to explain satisfactorily the cross-section of average returns on stocks. We assume that the CAPM holds in a conditional sense, i.e., betas and the market risk premium vary over time. We include the return on human capital when measuring the return on aggregate wealth. Our specification performs well in explaining the cross-section of average returns.

This paper provides an exact Bayesian framework for analyzing the arbitrage pricing theory (APT). Based on the Gibbs sampler, we show how to obtain the exact posterior distributions for functions of interest in the factor model. In particular, we propose a measure of the APT pricing deviations and obtain its exact posterior distribution. Using monthly portfolio returns grouped by industry and market capitalization, we find that there is little improvement in reducing the pricing errors by including more factors beyond the first one.

Statistical inference in multinomial multiperiod probit models has been hindered in the past by the high dimensional numerical integrations necessary to form the likelihood functions, posterior distributions, or moment conditions in these models. We describe three alternative approaches to inference that circumvent the integration problem: Bayesian inference using Gibbs sampling and data augmentation to compute posterior moments, simulated maximum likelihood (SML) estimation using the GHK recursive probability simulator, and method of simulated moment (MSM) estimation using the GHK simulator. We perform a set of Monte-Carlo experiments to compare the performance of these approaches. Although all the methods perform reasonably well, some important differences emerge. The root mean square errors (RMSEs) of the SML parameter estimates around the data generating values exceed those of the MSM estimates by 21 percent on average, while the RMSEs of the MSM estimates exceed those of the posterior parameter means obtained via agreement via Gibbs sampling by 18 percent on average. While MSM produces a good agreement between empirical RMSEs and asymptotic standard errors, the RMSEs of the SML estimates exceed the asymptotic standard errors by 28 percent on average. Also, the SML estimates of serial correlation parameters exhibit significant downward bias.

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.

This paper evaluates the argument that differences in physical and intangible capital can account for the large international income differences that characterize the world economy today. The finding is that they cannot. Savings rate differences are of minor importance. What is all-important is total factor productivity. In addition, the paper presents industry evidence that total factor productivities differ across countries and time for reasons other than differences in the publicly available stock of technical knowledge. These findings lead me to conclude a theory of TFP is needed. This theory must account for differences in TFP that arise for reasons other than growth in the stock of technical knowledge.

This paper presents a full characterization of the equilibrium value set of a Ramsey tax model. More generally, it develops a dynamic programming method for a class of policy games between the government and a continuum of consumers. By selectively incorporating Euler conditions into a strategic dynamic programming framework, we wed two technologies that are usually considered competing alternatives, resulting in a dramatic simplification of the problem.

We provide a brief review of the techniques that are based on the Generalized Method of Moments (GMM) and used for evaluating capital asset pricing models. We first develop the CAPM and multi-beta models and discuss the classical two-stage regression method originally used to evaluate them. We then describe the pricing kernel representation of a generic asset pricing model; this representation facilitates use of the GMM in a natural way for evaluating the conditional and unconditional versions of most asset pricing models. We also discuss diagnostic methods that provide additional insights.

This paper explores some macroeconomic implications of including household production in an otherwise standard real business cycle model. We calibrate the model based on microeconomic evidence and long run considerations, simulate it, and examine its statistical properties Our finding is that introducing home production significantly improves the quantitative performance of the standard model along several dimensions. It also implies a very different interpretation of the nature of aggregate fluctuations.

We document properties of business cycles in ten countries over the last hundred years, contrasting the behavior of real quantities with that of the price level and the stock of money. Although the magnitude of output fluctuations has varied across countries and periods, relations among variables have been remarkably uniform. Consumption has generally been about as variable as output, and investment substantially more variable, and both have been strongly procyclical. The trade balance has generally been countercyclical. The exception to this regularity is government purchases, which exhibit no systematic cyclical tendency. With respect to the size of output fluctuations, standard deviations are largest between the two world wars. In some countries (notably Australia and Canada) they are substantially larger prior to World War I than after World War II, but in others (notably Japan and the United Kingdom) there is little difference between these periods. Properties of price levels, in contrast, exhibit striking differences between periods. Inflation rates are more persistent after World War II than before, and price level fluctuations are typically procyclical before World War II, countercyclical afterward. We find no general tendency toward increased persistence in money growth rates, but find that fluctuations in money are less highly correlated with output in the postwar period.

This paper is motivated by empirical observations on the comovements of currency velocity, inflation, and the relative size of the credit services sector. We document these comovements and incorporate into a monetary growth model a credit services sector that provides services that help people economize on money. Our model makes two new contributions. First, we show that direct evidence on the appropriately defined credit service sector for the United States is consistent with the welfare cost measured using an estimated money demand schedule. Second, we provide welfare cost of inflation estimates that have some new features.

Recent literature suggests that historical accidents can trap economies in inefficient equilibria. In a prototype model in the literature, there are two locations, the productive South and the unproductive North. By accident of history, the industry starts in the North. Because of agglomeration economies, the industry may reside in the North forever—an inefficient outcome. This paper modifies the standard model by assuming there is a continuum of locations between the North and the South. Productivity gradually increases as one moves South. There is a unique long-run equilibrium in this economy where all agents locate at the most productive locations.

Unit root tests against trend break alternatives are based on the premise that the dating of the trend breaks coincides with major economic events with permanent effects on economic activity, such as wars and depressions. Standard economic theory, however, suggests that these events have large transitory, rather than permanent, effects on economic activity. Conventional unit root tests against trend break alternatives based on linear ARIMA models do not capture these transitory effects and can result in severely distorted inference. We quantify the size distortions for a simple model in which the effects of wars and depressions can reasonably be interpreted as transitory. Monte Carlo simulations show that in moderate samples, the widely used Zivot-Andrews (1992) test mistakes transitory dynamics for trend breaks with high probability. We conclude that these tests should be used only if there are no plausible economic explanations for apparent trend breaks in the data.

Measured aggregate U.S. consumption does not behave like a martingale. This paper develops and tests two variants of the permanent income model that are consistent with this fact. In both variants, we assume agents make decisions on a continuous time basis. According to the first variant, the martingale hypothesis holds in continuous time and serial persistence in measured consumption reflects only the effects of time aggregation. We investigate this variant using both structural and atheoretical econometric models. The evidence against these models is far from overwhelming. This suggests that the martingale hypothesis may yet be a useful way to conceptualize the relationship between aggregate quarterly U.S. consumption and income. According to the second variant of the permanent income model, serial persistence in measured consumption reflects the effects of exogenous technology shocks and time aggression. In this model, continuous time consumption does not behave like a martingale. We find little evidence against this variance of the permanent income model. It is difficult, on the basis of aggregate quarterly U.S. data, to convincingly distinguish between the different continuous time models considered in the paper.

This paper examines the sets of feasible allocations in a large class of economic environments in which commitment is impossible (the standard definition of feasibility is adapted to take account of the lack of commitment). The environments feature either memory or money. Memory is defined as knowledge on the part of an agent of the full histories of all agents with whom he has had direct or indirect contact in the past. Money is defined as an object that does not enter preferences or production and is available in fixed supply. The main proposition proves that any allocation that is feasible in an environment with money is also feasible in the same environment with memory. Depending on the environment, the converse may or may not be true. Hence, from a technological point of view, money is equivalent to a primitive form of memory.

We explore the welfare consequences of different taxation schemes in an economy where agents are debt-constrained. If agents default on their debt, they are banned from future credit markets, but retain their private endowments which are subject to income taxation. A change in the tax system changes the severity of punishment from default and, hence, leads to a limitation of possible risk sharing via private contracts. The welfare consequences of a change in the tax system depend on the relative magnitudes of increased risk sharing forced by the new tax system and the reduced risk sharing in private insurance markets. We quantitatively address this issue by calibrating an artificial economy to US income and tax data. We show that for a plausible selection of the structural parameters of our model, the change to a more redistributive tax system leads to less risk sharing among individuals and lower ex-ante welfare.

This paper surveys implementation theory when players have incomplete or asymmetric information, especially in economic environments. After the basic problem is introduced, the theory of implementation is summarized. Some coalitional considerations for implementation problems are discussed. For economies with asymmetric information, cooperative games based on incentive compatibility constraints or Bayesian incentive compatible mechanisms are derived and examined.

We look for the scale effects predicted by some theories of trade and growth based on the dynamic returns to scale that arise from learning by doing, investment in human capital, or development of new products. We find little empirical evidence of a relation between the growth rate of GDP per capita and the measures of scale implied by the theory. Restricting attention to the manufacturing sector, however, we find a significant relation between the growth rate of output per worker and the relevant scale variables. We also find that growth rates are significantly related to measures of intra-industry trade.

This paper develops a simple model of sovereign debt in which defaulting nations are excluded from capital markets and regain access by making partial repayments. This is consistent with the historical evidence that defaulting countries return to international loan markets soon after a settlement, but after varying periods of exclusion.

In empirical studies of the CAPM, it is commonly assumed that, (a) the return to the value-weighted portfolio of all stocks is a reasonable proxy for the return on the market portfolio of all assets in the economy, and (b) betas of assets remain constant over time. Under these assumptions, Fama and French (1992) find that the relation between average return and beta is flat. We argue that these two auxiliary assumptions are not reasonable. We demonstrate that when these assumptions are relaxed, the empirical support for the CAPM is very strong. When human capital is also included in measuring wealth, the CAPM is able to explain 28% of the cross sectional variation in average returns in the 100 portfolios studied by Fama and French. When, in addition, betas are allowed to vary over the business cycle, the CAPM is able to explain 57%. More important, relative size does not explain what is left unexplained after taking sampling errors into account.

This paper develops the quantitative implications of optimal fiscal policy in a business cycle model. In a stationary equilibrium the ex ante tax rate on capital income is approximately zero. There is an equivalence class of ex post capital income tax rates and bond policies that support a given allocation. Within this class the optimal ex post capital tax rates can range from being close to i.i.d. to being close to a random walk. The tax rate on labor income fluctuates very little and inherits the persistence properties of the exogenous shocks and thus there is no presumption that optimal labor tax rates follow a random walk. The welfare gains from smoothing labor tax rates and making ex ante capital income tax rates zero are small and most of the welfare gains come from an initial period of high taxation on capital income.

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.

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.

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.

A tax distorted real business cycle model is parameterized, calibrated, and solved numerically in an attempt to measure the size of Harberger Triangles relative to Okun Gaps. In particular, the model constructed is used to study, quantitatively, the impact of various distortional government tax and subsidy schemes. It is shown that the government can use tax policy to stabilize cyclical fluctuations, and this is done for the economy being studied. The benefits of implementing such a stabilization policy are calculated and compared with the size of the welfare gains realized from reducing various tax distortions.

This paper investigates the characteristics of stationary single-price equilibrium in a monetary random-matching model where agents can hold an arbitrary amount of divisible money and where production is costly. At such an equilibrium, agents’ money holdings are endogenously determined and uniformly bounded. A refinement of weakly undominated strategies is argued to be necessary. It is shown that a continuum of single-price equilibria indexed by the aggregate real-money balance exists if one such equilibrium exists. Equilibria with different money-holdings upper bounds, hence different distributions, but with identical aggregate real-money balances, can coexist.

We consider a class of dynamic games in which each player's actions are unobservable to the other players and each player's actions can influence a state variable that is unobservable to the other players. We develop an algorithm that solves for the subset of sequential equilibria in which equilibrium strategies depend on private information only through the privately observed state.

We consider a dynamic, stochastic equilibrium business cycle model which is augmented to reflect seasonal shifts in preferences, technology, and government purchases. Our estimated parameterization implies implausibly large seasonal variation in the state of technology: rising at an annual rate of 24% in the fourth quarter and falling at an annual rate of 28% in the first quarter. Furthermore, our findings indicate that variation in the state of technology of this magnitude is required if the model is to explain the main features of the seasonal cycle.

We develop a model of a representative democracy in which a legislature makes collective decisions about local public goods expenditures and how they are financed. In our model of the political process legislators defer to spending requests of individual representatives, particularly committee chairmen, who tend to promote spending requests that benefit their own districts. Because legislators do not fully internalize the tax consequences of their individual spending proposals, there is a free rider problem, and as a result spending is excessively high. This leads legislators to prefer a higher level of debt to restrain excessive future spending.

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.

We show that valuing performance is equivalent to valuing a particular contingent claim on an index portfolio. In general the form of the contingent claim is not known and must be estimated. We suggest approximating the contingent claim by a series of options. We illustrate the use of our method by evaluating the performance of 130 mutual funds during the period 1968–82. We find that the relative performance rank of a fund is rather insensitive to the choice of the index, even though the actual value of the services of the portfolio manager depends on the choice of the index.

We use a calibrated model of the dynamics of organization capital and industry evolution to measure the size of investment in organization capital in the steady state and the dynamics of organization capital during the transition following a major reform. We find that, in the steady state, aggregate net investment in organization capital is roughly one-fifth of measured output. During the initial phase of transition, the failure rate of plants rises 200-400 percent, measured output and aggregate productivity stagnate, physical investment falls, and net investment in organization capital rises between 300 and 500 percent above its steady-state level.

We develop a model of commodity money and use it to analyze the following two questions motivated by issues in monetary history: What are the conditions under which Gresham’s Law holds? And, what are the mechanics of a debasement (lowering the metallic content of coins)? The model contains light and heavy coins, imperfect information, and prices determined via bilateral bargaining. There are equilibria with neither, both, or only one type of coin in circulation. When both circulate, coins may trade by weight or by tale. We discuss the extent to which Gresham’s Law holds in the various cases. Following a debasement, the quantity of reminting depends on the incentives offered by the sovereign. Equilibria exist with positive seigniorage and a mixture of old and new coins in circulation.

This paper surveys the fundamental principles of subjective Bayesian inference in econometrics and the implementation of those principles using posterior simulation methods. The emphasis is on the combination of models and the development of predictive distributions. Moving beyond conditioning on a fixed number of completely specified models, the paper introduces subjective Bayesian tools for formal comparison of these models with as yet incompletely specified models. The paper then shows how posterior simulators can facilitate communication between investigators (for example, econometricians) on the one hand and remote clients (for example, decision makers) on the other, enabling clients to vary the prior distributions and functions of interest employed by investigators. A theme of the paper is the practicality of subjective Bayesian methods. To this end, the paper describes publicly available software for Bayesian inference, model development, and communication and provides illustrations using two simple econometric models.

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 paper, I estimate the impact on aggregate labor productivity of having government, rather than private industry, produce investment goods. This policy was pursued to varying degrees by Egypt, India, Turkey, among others. The policy has a large impact because there is both a direct effect (on the production function in the investment sector) and a secondary effect (on the economywide capital stock per worker). I estimate that this policy alone accounted for about one-third of Egypt's aggregate labor productivity gap with the United States during the 1960s.

The Economics of QWERTY suggests that historical accidents can trap economies in inefficient equilibria. This paper suggests that such accidents do not have the force that proponents claim. The paper presents a mechanism that may unravel a locational advantage caused by an historical accident. In the model, there are agglomeration benefits from concentrating industry in a particular location because it enables a large variety of local suppliers to emerge. Firms differ by the extent to which they purchase from local suppliers. Low-tier firms purchase little; high-tier firms purchase more. When the industry migrates, the lowest-tier products move first.

Energy use is inelastic in time-series data, but elastic in international cross-section data. Two models of energy use reproduce these elasticities: a putty-putty model with adjustment costs developed by Pindyck and Rotemberg (1983) and a putty-clay model. In the Pindyck-Rotemberg model, capital and energy are highly complementary in both the short run and the long run. In the putty-clay model, capital and energy are complementary in the short run, but substitutable in the long run. We highlight the differences in the cross-section implications of the models by considering the effect of an energy tax on output in both models. In the putty-putty model, an energy tax that doubles the price of energy leads to a fall in output in the long run of 33%. In contrast, the same tax in the putty-clay model leads to a fall in output of only 5.3%.

This study examines common stock prices around ex-dividend dates. Such price data usually contain a mixture of observations—some with and some without arbitrageurs and/or dividend capturers active. Our theory predicts that such mixing will result in some nonlinear relation between percentage price drop and dividend yield—not the commonly assumed linear relation. This prediction and another important prediction of theory are supported empirically. In a variety of tests, marginal price drop is not significantly different from the dividend amount. Thus, over the last several decades, one-for-one marginal price drop has been an excellent (average) rule of thumb.

The notion of skilled-biased technological change is often held responsible for the recent behavior of the U.S. skill premium, or the ratio between the wages of skilled and unskilled labor. This paper develops a framework for understanding this notion in terms of observable variables and uses the framework to evaluate the fraction of the skill premium's variation that is caused by changes in observables. A version of the neoclassical growth model is used in which the key feature of aggregate technology is capital-skill complementarity: the elasticity of substitution is higher between capital equipment and unskilled labor than between capital equipment and skilled labor. With this feature, changes in observables can account for nearly all the variation in the skill premium over the last 30 years. This finding suggests that increased wage inequality results from economic growth driven by new, efficient technologies embodied in capital equipment.

We analyze a model in which there is socially inefficient competition among people. In this model, self-enforcing social norms can potentially control the inefficient competition. However, the inefficient behavior often cannot be suppressed in equilibrium among those with the lowest income due to the ineffectiveness of sanctions against those in the society with the least to lose. We demonstrate that in such cases, it may be possible for society to be divided into distinct classes, with inefficient behavior suppressed in the upper classes but not in the lower.

There is now an extensive literature regarding the efficient design of incentive mechanisms in dynamic environments. In this literature, there are no exogenous links across time periods because either privately observed shocks are assumed time independent or past private actions have no influence on the realizations of current variables. The absence of exogenous links across time periods ensures that preferences over continuation contracts are common knowledge, making the definition of incentive compatible contracts at a point in time a simple matter. In this paper, we present general recursive methods to handle environments where privately observed variables are linked over time. We show that incentive compatible contracts are implemented recursively with a threat keeping constraint in addition to the usual temporary incentive compatibility conditions.

We study the general equilibrium effects of social insurance on the transition in a model in which the process of moving workers from matches in the state sector to new matches in the private sector takes time and involves uncertainty. As to be expected, adding social insurance to an economy without any improves welfare. Contrary to standard intuition, however, adding social insurance may slow transition. We show that this result depends crucially on general equilibrium interactions of interest rates and savings under alternative market structures.

We examine whether the Mortensen-Pissarides matching model can account for the business cycle facts on employment, job creation, and job destruction. A novel feature of our analysis is its emphasis on the reduced-form implications of the matching model. Our main finding is that the model can account for the business cycle facts, but only if the average duration of a nonemployment spell is relatively high—about nine months or longer.

Several recent papers provide strong empirical support for the view that an expansionary monetary policy disturbance generates a persistent decrease in interest rates and a persistent increase in output and employment. Existing quantitative general equilibrium models, which allow for capital accumulation, are inconsistent with this view. There does exist a recently developed class of general equilibrium models which can rationalize the contemporaneous response of interest rates, output, and employment to a money supply shock. However, a key shortcoming of these models is that they cannot rationalize persistent liquidity effects. This paper discusses the basic frictions and mechanisms underlying this new class of models and investigates one avenue for generating persistence. We argue that once a simplified version of the model in Christiano and Eichenbaum (1991) is modified to allow for extremely small costs of adjusting sectoral flow of funds, positive money shocks generate long-lasting, quantitatively significant liquidity effects, as well as persistent increases in aggregate economic activity.

We integrate search theory into an equilibrium framework in a new way and argue that the result is a simple but powerful tool for understanding many issues related to bilateral matching. We assume for much of what we do that utility is less than perfectly transferable. This turns out to generate multiple equilibria that do not arise in a standard model, with transferable utility, unless one adds increasing returns. We also provide simple conditions for uniqueness that apply to models with or without transferable utility or increasing returns. Examples, applications, and extensions are discussed.

Data augmentation and Gibbs sampling are two closely related, sampling-based approaches to the calculation of posterior moments. The fact that each produces a sample whose constituents are neither independent nor identically distributed complicates the assessment of convergence and numerical accuracy of the approximations to the expected value of functions of interest under the posterior. In this paper methods for spectral analysis are used to evaluate numerical accuracy formally and construct diagnostics for convergence. These methods are illustrated in the normal linear model with informative priors, and in the Tobit-censored regression model.

This research compares several approaches to inference in the multinomial probit model, based on Monte-Carlo results for a seven choice model. The experiment compares the simulated maximum likelihood estimator using the GHK recursive probability simulator, the method of simulated moments estimator using the GHK recursive simulator and kernel-smoothed frequency simulators, and posterior means using a Gibbs sampling-data augmentation algorithm. Each estimator is applied in nine different models, which have from 1 to 40 free parameters. The performance of all estimators is found to be satisfactory. However, the results indicate that the method of simulated moments estimator with the kernel-smoothed frequency simulator does not perform quite as well as the other three methods. Among those three, the Gibbs sampling-data augmentation algorithm appears to have a slight overall edge, with the relative performance of MSM and SML based on the GHK simulator difficult to determine.

We characterize the values of government debt and the debt’s maturity structure under which financial crises brought on by a loss of confidence in the government can arise within a dynamic, stochastic general equilibrium model. We also characterize the optimal policy response of the government to the threat of such a crisis. We show that when the country’s fundamentals place it inside the crisis zone, the government is motivated to reduce its debt and exit the crisis zone because this leads to an economic boom and a reduction in the interest rate on the government’s debt. We show that this reduction may be quite gradual if debt is high or the probability of a crisis is low. We also show that, while lengthening the maturity of the debt can shrink the crisis zone, credibility-inducing policies can have perverse effects.

In this paper we develop alternative ways to compare asset pricing models when it is understood that their implied stochastic discount factors do not price all portfolios correctly. Unlike comparisons based on chi-squared statistics associated with null hypotheses that models are correct, our measures of model performance do not reward variability of discount factor proxies. One of our measures is designed to exploit fully the implications of arbitrage-free pricing of derivative claims. We demonstrate empirically the usefulness of methods in assessing some alternative stochastic factor models that have been proposed in asset pricing literature.

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.

We provide new evidence that models of the monetary transmission mechanism should be consistent with at least the following facts. After a contractionary monetary policy shock, the aggregate price level responds very little, aggregate output falls, interest rates initially rise, real wages decline by a modest amount, and profits fall. We compare the ability of sticky price and limited participation models with frictionless labor markets to account for these facts. The key failing of the sticky price model lies in its counterfactual implications for profits. The limited participation model can account for all the above facts, but only if one is willing to assume a high labor supply elasticity (2 percent) and a high markup (40 percent). The shortcomings of both models reflect the absence of labor market frictions, such as wage contracts or factor hoarding, which dampen movements in the marginal cost of production after a monetary policy shock.

This paper provides new evidence that state policies play a role in the location of industry. The paper classifies a state as pro-business or anti-business depending upon whether or not the state has a right-to-work law. The paper finds that, on average, there is a large abrupt increase in manufacturing activity when crossing a state border from an anti-business state into a pro-business state.

We propose a constructive, multivariate framework for assessing agreement between (generally misspecified) dynamic equilibrium models and data, a framework which enables a complete second-order comparison of the dynamic properties of models and data. We use bootstrap algorithms to evaluate the significance of deviations between models and data, and we use goodness-of-fit criteria to produce estimators that optimize economically relevant loss functions. We provide a detailed illustrative application to modeling the U.S. cattle cycle.

Following are the technical appendixes for “Banking in Computable Equilibrium Economies” by Javier Díaz-Giménez, Edward C. Prescott, Terry Fitzgerald, and Fernando Alvarez, in Journal of Economic Dynamics and Control 16 (1992), 533–59. Technical Appendix I, by Fernando Alvarez, describes the procedures used to construct the balance sheets reported in Tables 1 and 2 in page 536 and 537 of the paper. Technical Appendix II, by Terry Fitzgerald, describes the computational procedures used in this paper.

The welfare-maximizing income tax structure, rate of money creation, and amounts of intergenerational transfers are jointly determined for given rates of government consumption. When government consumption is zero, it is found for the parameter values examined that the income tax structure is progressive, the rate of money change is negative, and positive transfers are made to the old. As government consumption increases, the tax structure’s progressivity declines and turns increasingly regressive, the rate of money change rises, and transfers decrease. It is found that the bulk of the increase in government consumption is optimally financed by a cut in transfers.

We document and attempt to explain the observation that automobile insurance premiums vary dramatically across local markets. We argue high premiums can be attributed to the large numbers of uninsured motorists in some cities, while at the same time, the uninsured motorists can be attributed to high premiums. We construct a simple noncooperative equilibrium model, where limited liability can generate inefficient equilibria with uninsured drivers and high, yet actuarially fair, premiums. For certain parameterizations, an optimal full insurance equilibrium and inefficient high price equilibria with uninsured drivers exist simultaneously, consistent with the observed price variability across seemingly similar cities.

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.

According to previous studies, the demand-liability feature of national bank notes did not present a problem for note-issuing banks because the nonbank public treated notes and other currency as perfect substitutes. However, that view, when combined with nonbindingness of the collateral restriction against note issue, itself an implication of the fact that some eligible collateral was not used for that purpose, implies that the safe short-term interest rate is pegged at the tax rate on note circulation. Since evidence on short-term interest rates is inconsistent with such a peg, that view must be rejected.

We describe several methods for approximating the solution to a model in which inequality constraints occasionally bind, and we compare their performance. We apply the methods to a particular model economy which satisfies two criteria: It is similar to the type of model used in actual research applications, and it is sufficiently simple that we can compute what we presume is virtually the exact solution. We have two results. First, all the algorithms are reasonably accurate. Second, on the basis of speed, accuracy and convenience of implementation, one algorithm dominates the rest. We show how to implement this algorithm in a general multidimensional setting, and discuss the likelihood that the results based on our example economy generalize.

It is well documented that on average, stock prices drop by less than the value of the dividend on ex-dividend days. This has commonly been attributed to the effect of tax clienteles. We use data from the Hong Kong stock market where neither dividends nor capital gains are taxed. As in the U.S.A. the average stock price drop is less than the value of the dividend; specifically, in Hong Kong the average dividend was HK $0.12 and the average price drop was HK $0.06. We are able to account for this both theoretically and empirically through market microstructure based arguments.

There is an old wisdom that reductions in tariffs force changes on producers that lead to costless, or nearly so, increases in productivity. We construct a technology-ladder model that captures this wisdom. As in other technology-ladder models, time spent in research helps propel an industry up a technology-ladder. In contrast to the literature, we include another activity that plays a role in determining an industry's position on the technology-ladder: attempts to obstruct the research program of rivals (through regulations, for example). In this world, reductions in tariffs between countries lead producers to spend more time in research and less in obstruction of rivals.

We present a 2-country model with heterogeneous agents in which changes in a country’s monetary policy affect real interest rates, relative prices of traded and nontraded goods and real exchange rates. Nontransitory real effects of monetary policy stem solely from a friction (country-specific reserve requirements) that generates separate demands for a country’s money and bonds. Without violating the classical assumptions of individual rationality and flexible prices, the model’s implications seem qualitatively in accord with the U.S. experience of the 1980s: a monetary policy tightening leading to a rise in the real interest rate and to an initial rise in the real value of the dollar which is subsequently reversed. In the model a monetary policy change leads to different welfare effects for agents born at different times, living in different countries, or participating on different sides of a market. The welfare of some agents can be affected more by relative price changes than by real interest rate changes.

Applied general equilibrium models with imperfect competition and economies of scale have been extensively used for analyzing international trade and development policy issues. They offer a natural framework for testing the empirical relevance of propositions from the industrial organization and new trade theoretical literature. This paper warns model builders and users that considerable caution is needed in interpreting the results and deriving strong policy conclusions from these models: in this generation of applied general equilibrium models, nonuniqueness of equilibria is not a theoretical curiosum, but a potentially serious problem. Disregarding this may lead to dramatically wrong policy appraisals.

We investigate, by Monte Carlo methods, the finite sample properties of GMM procedures for conducting inference about statistics that are of interest in the business cycle literature. These statistics include the second moments of data filtered using the first difference and Hodrick-Prescott filters, and they include statistics for evaluating model fit. Our results indicate that, for the procedures considered, the existing asymptotic theory is not a good guide in a sample the size of quarterly postwar U.S. data.

It is often argued that with a positively skewed income distribution (median less than mean) majority voting would result in higher tax rates than maximizing average welfare and, hence, lower aggregate savings. We reexamine this view in a capital accumulation model, in which distorting redistributive taxes provide insurance against idiosyncratic shocks and income distributions evolve endogenously. We find small differences of either sign between the tax rates set by a majority voting and a utilitarian government, for reasonable parametric specifications, despite the fact that model simulations produce positively skewed distributions of total income across agents.

This paper explores the extent to which the Mexican government's inability to roll over its debt during December 1994 and January 1995 can be modeled as a self-fulfilling debt crisis. In the model there is a crucial interval of debt for which the government, although it finds it optimal to repay old debt if it can sell new debt, finds it optimal to default if it cannot sell new debt. If government debt is in this interval, which we call the crisis zone, then we can construct equilibria in which a crisis can occur stochastically, depending on the realization of a sunspot variable. The size of this zone depends on the average length of maturity of government debt. Our analysis suggests that for a country, like Mexico, with a very short maturity structure of debt, the crisis zone is large and includes levels of debt as low as that in Mexico before the crisis.

This paper studies the quantitative properties of fiscal and monetary policy in business cycle models. In terms of fiscal policy, optimal labor tax rates are virtually constant and optimal capital income tax rates are close to zero on average. In terms of monetary policy, the Friedman rule is optimal—nominal interest rates are zero—and optimal monetary policy is activist in the sense that it responds to shocks to the economy.

An economic experiment consists of the act of placing people in an environment desired by the experimenter, who then records the time paths of their economic behavior. Performing experiments that use actual people at the level of national economies is obviously not practical, but constructing a model economy and computing the economic behavior of the model’s people is. We refer to such experiments as computational experiments because the economic behavior of the model’s people is computed. In this essay, we specify the steps in designing a computational experiment to address some well posed quantitative question. We emphasize that the computational experiment is an econometric tool used in the task of deriving the quantitative implications of theory.

A unified growth theory is developed that accounts for the roughly constant living standards displayed by world economies prior to 1800 as well as the growing living standards exhibited by modern industrial economies. Our theory also explains the industrial revolution, which is the transition from an era when per capita incomes are stagnant to one with sustained growth. We use a standard growth model with one good and two available technologies. The first, denoted the Malthus technology, requires land, labor, and reproducible capital as inputs. The second, denoted the Solow technology, does not require land. We show that in the early stages of development, only the Malthus technology is used, and, due to population growth, living standards are stagnant despite technological progress. Eventually, technological progress causes the Solow technology to become profitable, and both technologies are employed. In the limit, the economy behaves like a standard Solow growth model.

In this paper, we build a model of the transition following large-scale economic reforms that predicts both a substantial drop in output and a prolonged pause in physical investment as the initial phase of the optimal transition following the reform. We model reform as a change in policy which induces agents to close existing enterprises using old technologies of production and to open up new enterprises adopting new technologies of production. The central idea of our paper is that it is costly to close old enterprises and open new enterprises because, in doing so, information capital built up about old enterprises is lost and time must pass before information capital about new enterprises can be acquired. Thus, an acceleration of the pace of industry evolution leads in the short run to a net loss of information capital, a drop in productivity, a recession, and a fall in physical investment. We calibrate our model of industry evolution, information capital, and transition to match micro data on industry evolution in the United States and macro data from the United States, Japan, and the former communist countries of Europe. We find that the loss of information capital that accompanies a major acceleration in the pace of industry evolution in an economy leads initially to a decade of recession and a five year pause in physical investment before the benefits of reform are realized.

The marginal cost of plant capacity, measured by the price of equity, is significantly procyclical. Yet, the price of a major intermediate input into expanding plant capacity, investment goods, is countercyclical. The ratio of these prices is Tobin's q. Following convention, we interpret the fact that Tobin's q differs from unity at all, as reflecting that there are diminishing returns to expanding plant capacity by installing investment goods ("adjustment costs"). However, the phenomenon that interests us is not just that Tobin's q differs from unity, but also that its numerator and denominator have such different cyclical properties. We interpret the sign switch in their covariation with output as reflecting the interaction of our adjustment cost specification with the operation of two shocks: one which affects the demand for equity and another which shifts the technology for producing investment goods. The adjustment costs cause the two prices to respond differently to these two shocks, and this is why it is possible to choose the shock variances to reproduce the sign switch. These model features are incorporated into a modified version of a model analyzed in Boldrin, Christiano and Fisher (1995). That model incorporates assumptions designed to help account for the observed mean return on risk free and risky assets. We find that the various modifications not only account for the sign switch, but they also continue to account for the salient features of mean asset returns. We turn to the business cycle implications of our model. The model does as well as standard models with respect to conventional business cycle measures of volatility and comovement with output, and on one dimension the model significantly dominates standard models. The factors that help it account for prices and rates of return on assets also help it account for the fact that employment across a broad range of sectors moves together over the cycle.

This is a note on the analysis of inflation and taxation in Cooley and Hansen’s cash-in-advance economy described in their paper “The Welfare Costs of Moderate Inflations.” Basic issues concerning the costs and consequences of inflation are considered, their results are assessed, and some directions for extensions are suggested.

We ask whether a two-country real business cycle model can account simultaneously for domestic and international aspects of business cycles. With this question in mind, we document a number of discrepancies between theory and data. The most striking discrepancy concerns the correlations of consumption and output across countries. In the data, outputs are generally more highly correlated across countries than consumptions. In the model we see the opposite.

This paper explores the consequences of new information technologies, such as bar codes and computer-tracking of inventories, for the optimal organization of retail. The first result is that there is a complementarity between the new information technology and frequent deliveries. This is consistent with the recent move in the retail sector toward higher-frequency delivery schedules. The second result is that adoption of the new technology tends to increase store size. This is consistent with recent increases in store size and the success of the superstore model of retail organization.

The founding fathers of the Econometric Society defined econometrics to be quantitative economic theory. A vision of theirs was the use of econometrics to provide quantitative answers to business cycle questions. The realization of this dream required a number of advances in pure theory—in particular, the development of modern general equilibrium theory. The econometric problem is how to use these tools along with measurement to answer business cycles questions. In this essay, we review this econometric development and contrast it with the econometric approach that preceded it.

The question of the existence and uniqueness of a stationary equilibrium for distorted versions of the standard neoclassical growth model is addressed in this paper. The conditions presented guaranteeing the existence and uniqueness of nontrivial equilibrium for the class of economies under study are simple and intuitively appealing, while the existence and uniqueness proof developed is elementary. Examples are presented illustrating that economies with distortional taxation, endogenous growth with externalities, and monopolistic competition can all fit into the framework developed.

Technology change is modeled as the result of decisions of individuals and groups of individuals to adopt more advanced technologies. The structure is calibrated to the U.S. and postwar Japan growth experiences. Using this calibrated structure we explore how large the disparity in the effective tax rates on the returns to adopting technologies must be to account for the huge observed disparity in per capita income across countries. We find that this disparity is not implausibly large.

We extend the analysis of Kiyotaki and Wright, who study an economy in which the different commodities that serve as media of exchange are determined endogenously. Kiyotaki and Wright consider only symmetric, steady-state, pure-strategy equilibria, and find that for some parameter values no such equilibria exist. We consider mixed-strategy equilibria and dynamic equilibria. We prove that a steady-state equilibrium exists for all parameter values and that the number of steady-state equilibria is generically finite. We also show, however, that there may be a continuum of dynamic equilibria. Further, some dynamic equilibria display cycles.

Many economists have worried about changes in the demand for money, since money demand shocks can affect output variability and have implications for monetary policy. This paper studies the theoretical implications of changes in money demand for the nonneutrality of money in the limited participation (liquidity) model and the predetermined (sticky) price model. In the liquidity model, we find that an important connection exists between the nonneutrality of money and the relative money demands of households and firms. This model predicts that the real effect of a money shock rose by 100 percent between 1952 and 1980, and subsequently declined 65 percent. In contrast, we find that the nonneutrality of money in the sticky price model is invariant to changes in money demands or other monetary factors. Several researchers have concluded from VAR analyses that the effects of money shock over time are roughly stable. This view is consistent with the predictions of the sticky price model, but is harder to reconcile with the specific pattern of time variation predicted by the liquidity model.

We argue that the rationalization gains often predicted by static applied general equilibrium models with imperfect competition and scale economies are artificially boosted by an unrealistic treatment of fixed costs. We introduce sunk costs into one such model calibrated with real-world data. We show how this changes the oligopoly game in a way significant enough to affect, both qualitatively and quantitatively, the outcome of a trade liberalization exercise.

In this paper we propose a general equilibrium model where heterogeneous agents specialize either in legitimate market activities or in criminal activities and majority rule determines the share of income redistributed and the expenditures devoted to the apprehension of criminals. We calibrate our model to the U.S. economy in 1990, and we conduct simulation exercises to evaluate the effectiveness of expenditures on police protection and income redistribution at reducing crime. We find that while expenditures on police protection reduce crime, it is possible for the crime rate to increase with redistribution. We also show that economies that adopt relatively more generous redistribution policies may have either higher or lower crime rates than economies with relatively less generous redistribution policies, depending on the characteristics of their wage distribution and on the efficiency of their apprehension technology.

I argue that Farmer and Guo's one-sector real business cycle model with indeterminacy and sunspots fails empirically and that its failure is inherent in the logic of the model taken together with some simple labor market facts.

This paper essentially puts together procedures that are used in the computation of equilibria in models with a very large number of heterogeneous agents. It is not a complete description of all procedures used in the literature. It describes procedures that deal with infinitely lived agent versions of the growth model with and without aggregate uncertainty, overlapping generations models, and dynamic political economy models.

In this paper we analyze the efficacy of seignorage as a tax associated with various monetary arrangements in a computable general equilibrium model. For the economies examined, we find that seignorage tax is not a good one relative to a tax on labor income. If the after-tax real return is –5 percent, as it was in the 1974–1978 period, welfare is approximately 0.5 percent of consumption lower than it would be if the after-tax return were zero.

Many unions in the United States have for several years engaged in what is known as pattern bargaining—a union determines a sequence for negotiations with firms within an industry where the agreement with the first firm becomes the take-it-or-leave-it offer by the union for all subsequent negotiations. In this paper, we show that pattern bargaining is preferred by a union to both simultaneous industrywide negotiations and sequential negotiations without a pattern. In recent years, unions have increasingly moved away from patterns that equalized wage rates across firms when these patterns did not equalize interfirm labor costs. Allowing for interfirm productivity differentials within an industry, we show that for small interfirm productivity differentials, the union most prefers a pattern in wages, but for a sufficiently wide differential, the union prefers a pattern in labor costs.

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.

The goal of this paper is to extend the analysis of strategic bargaining to nonstationary environments, where preferences or opportunities may be changing over time. We are mainly interested in equilibria where trade occurs immediately, once the agents start negotiating, but the terms of trade depend on when the negotiations begin. We characterize equilibria in terms of simply dynamical systems, and compare these outcomes with the myopic Nash bargaining solution. We illustrate the practicality of the approach with an application in monetary economics.

This paper considers Marshall's argument that geographic concentration of industry facilitates specialization. I use Census data on manufacturing plants to examine the relationship between localization of industry and vertical disintegration. I find that establishments located near other establishments within the same industry tend to make more intensive use of purchased inputs than establishments without own-industry neighbors. This relationship only holds among industries that are geographically concentrated; having neighbors makes no difference in geographically dispersed industries. I argue that this pattern is consistent with a model in which increased opportunity for specialization is the reason some industries localize.

We find support for a negative relation between conditional expected monthly return and conditional variance of monthly return, using a GARCH-M model modified by allowing (i) seasonal patterns in volatility, (ii) positive and negative innovations to returns having different impacts on conditional volatility, and (iii) nominal interest rates to predict conditional variance. Using the modified GARCH-M model, we also show that monthly conditional volatility may not be as persistent as was thought. Positive unanticipated returns appear to result in a downward revision of the conditional volatility whereas negative unanticipated returns result in an upward revision of conditional volatility.

This study uses data from the Panel Survey of Income Dynamics (PSID) to address a number of questions about life cycle earnings mobility. It develops a dynamic reduced form model of earnings and marital status that is nonstationary over the life cycle. The study reaches several firm conclusions about life cycle earnings mobility. Incorporating non-Gaussian shocks makes it possible to account for transitions between low and higher earnings states, a heretofore unresolved problem. The non-Gaussian distribution substantially increases the lifetime return to post-secondary education, and substantially reduces differences in lifetime wages attributable to race. In a given year, the majority of variance in earnings not accounted for by race, education and age is due to transitory shocks, but over a lifetime the majority is due to unobserved individual heterogeneity. Consequently, low earnings at early ages are strong predictors of low earnings later in life, even conditioning on observed individual characteristics.

Our study examines whether there is a systematic relationship between the monetary standard under which a country operates and the rate of inflation it experiences. It also explores whether there are other properties of inflation, money, and output that differ between economies operating under a commodity standard and economies operating under a fiat standard. The basis for our study is price, money, and output data for 15 countries that have operated under both types of monetary standards. For each of these countries the data cover 80 years, and for most the data cover more than 100 years. With these data we are able to establish several facts about the differences in inflation, money growth, and output growth between economies operating under commodity standards and those operating under fiat standards. Specifically, we find that the following facts emerge when comparing commodity standards to fiat standards: inflation, money growth, and output growth are all lower; growth rates of monetary aggregates are less highly correlated with each other; growth rates of monetary aggregates are less highly correlated with inflation; and growth rates of monetary aggregates are more highly correlated with output growth.

This paper considers model worlds in which there is a continuum of individuals who form finite-sized associations to undertake joint activities. We show how, through a suitable choice of commodity space, restrictions on the composition of feasible groups can be incorporated into the specification of the consumption and production sets of the economy. We also show that if there are a finite number of types, then the classical results from the competitive analysis of convex finite-agent economies can be reinterpreted to apply.

This paper analyses the effects of open market operations on interest rates in a model in which agents must pay a fixed cost to exchange assets and cash. Asset markets are endogenously segmented in that some agents choose to pay the fixed cost and some do not. When the fixed cost is zero, the model reduces to the standard one in which persistent money injections increase nominal interest rates, flatten the yield curve, and lead to a downward-sloping yield curve on average. In contrast, if markets are sufficiently segmented, then persistent money injections decrease interest rates, steepen or even twist the yield curve, and lead to an upward-sloping yield curve on average.

This essay distills the differences between zero inflation proponents and critics to three main questions: Can the central bank make a credible commitment to maintaining a stable price level? Should monetary policy be used to reduce the tax on capital income? And would reducing uncertainty about inflation produce significant social benefits? Proponents of zero inflation answer all three questions yes, while critics answer no. The essay reviews both answers for each question and suggests that the disagreements are at least partly due to inadequacies in economic models. The essay repeats the author's view, argued in an earlier study, that when other policy options are considered, the overall benefits of a zero inflation policy shrink close to zero, and may even become negative.

This paper analyzes the U.S. congressional proposal to instruct the Federal Reserve to, in the next five years, lower inflation to zero from its current rate of around 5 percent. The paper concludes that, when other policy options are considered, the zero inflation policy is not advisable. Its benefits would be very small—possibly negative—while its costs would probably be significant. Other, more direct policy options could produce most of the same benefits with fewer costs. Among these alternative policies are deregulating interest rates on demand deposits, paying interest on financial institution reserves, lowering the federal tax rate on capital income, and indexing the federal tax code to inflation.

This article contends that the various measures of the contribution of technology shocks to business cycles calculated using the real business cycle modeling method are not corroborated. The article focuses on a different and much simpler method for calculating the contribution of technology shocks, which takes account of facts concerning the productivity/labor input correlation and the variability of labor input relative to output. Under several standard assumptions, the method predicts that the contribution of technology shocks must be large (at least 78 percent), that the labor supply elasticity need not be large to explain the observed fluctuation in labor input, and that the contribution of technology shocks can be estimated fairly precisely. The method also estimates that the contribution of technology shocks could be lower than 78 percent under alternative assumptions.