Working Papers   


    We derive a fully nonlinear optimal income tax schedule in the presence of a private insurance market. The optimal tax formula is expressed in terms of sufficient statistics---such as the Frisch elasticity of labor supply, social preferences, and hazard rates of the income distributions---as in the standard Mirrleesian taxation without private insurance (e.g., Saez (2001)). However, in the presence of a private market, the standard sufficient statistics are no longer sufficient. The optimal tax rate also depends on how private savings interact with public insurance---through substitution and crowding in/out. Based on our formula, we compute the optimal tax schedule using a quantitative general equilibrium model calibrated to reproduce the U.S. income distribution.


      We develop a quantitative heterogeneous-agents general equilibrium model that reproduces the income inequalities of 32 countries in the Organization for Economic Co-operation and Development. Using this model, we compute the optimal income tax rate for each country under the equal-weight utilitarian social welfare function. We simulate the voting outcome for the utilitarian optimal tax reform for each country. Finally, we uncover the Pareto weights in the social welfare functions of each country that justify the current redistribution policy.


        The standard life-cycle models of household portfolio choice have difficulty generating a realistic age profile of risky share. These models not only imply a high risky share on average but also a steeply decreasing age profile, whereas the risky share is mildly increasing in the data. We introduce age-dependent labor-market uncertainty into an otherwise standard model. A great uncertainty in the labor market---high unemployment risk, frequent job turnovers, and an unknown career path---prevents young workers from taking too much risk in the financial market. As labor-market uncertainty is resolved over time, workers start taking more risk in their financial portfolios.


        We consider a matching model of employment with wages that are flexible for new hires, but sticky within matches. We depart from standard treatments of sticky wages by allowing effort to respond to the wage being too high or low. Shimer (2004) and others have illustrated that employment in the Mortensen-Pissarides model does not depend on the degree of wage flexibility in existing matches. But this is not true in our model. If wages of matched workers are stuck too high in a recession, then firms will require more effort, lowering the value of additional labor and reducing new hiring. 

        We develop a heterogeneous-agent general equilibrium model that incorporates both intensive and extensive margins of labor supply. A nonconvexity in the mapping between time devoted to work and labor services distinguishes between extensive and intensive margins. We consider calibrated versions of this model that differ in the value of a key preference parameter for labor supply and the extent of heterogeneity. The model is able to capture the salient features of the empirical distribution of hours worked, including how individuals transit within this distribution. We then study how the various specifications influence labor supply responses to aggregate technology shocks. We find that abstracting from intensive margin adjustment has large effects on the volatility of aggregate hours even if intensive margin fluctuates relatively little.



        Published Papers

        We identify cyclical turning points for 74 U.S. manufacturing industries and uncover new empirical regularities: (1) Industries tend to comove between expansion and contraction phases over the business cycle; (2) Clusters of industry turning points are highly asymmetric between peaks and troughs: troughs are much more concentrated and sharper than peaks; (3) The temporal pattern of phase shifts across industries supports the spillovers through input-output linkages; and (4) Macroeconomic shocks, such as unanticipated changes in monetary policy, government spending, oil prices, and financial conditions, are significant drivers of industrial phase shifts. 

        Many successful examples of economic development, such as South Korea, exhibit long periods of sustained capital accumulation. This process is characterized by a gradually rising investment rate along with a moderate rate of return to capital, both of which are strongly at odds with the standard neoclassical growth model that predicts an initially high and then declining investment rate with an extremely high return to capital. We show that minor modifications of the neoclassical model go a long way toward accounting for the transition dynamics of the South Korean economy. Our modifications recognize that (i) agriculture (which makes up a large share of the aggregate economy in the early stage of development) does not rely much on capital and (ii) the relative price of capital declined substantially during the transition period. 

        We develop a multi-country quantitative model of the global distribution of current account and external balances. Countries accumulate domestic capital and foreign assets to smooth consumption over time against exogenous productivity shocks in the presence of liquidity constraints. In equilibrium, optimal consumption and investment responses to persistent productivity shocks imply a degree of intertemporal substitution across countries that can explain up to one-third of the current account dispersion in the data.

        Data from a heterogeneous-agents economy with incomplete asset markets and  indivisible labor supply are simulated under various fiscal policy regimes and an approximating representative-agent model is estimated. Preference and technology parameter estimates of the representative-agent model are not invariant to policy changes and the bias in the representative-agent model's policy predictions is large compared  to predictive intervals that reflect parameter  uncertainty. Since it is not always feasible to account for  heterogeneity explicitly, it is important to  recognize the possibility that the parameters of a highly aggregated model may not be invariant with respect to policy changes.


        Worker heterogeneity in productivities and labor supplies are introduced into a Diamond-Mortensen-Pissarides model. The model identifies workers who earn high wages and work high hours when employed as those with strong market comparative advantage, that is, high rents from being employed. The model is calibrated to match average rates of separation, job finding, and employment across men in the SIPP data. The model predicts a big shift in separations toward workers with weak comparative advantage during recessions. But the data show that workers with strong comparative advantage also display sizable employment fluctuations. Our results imply that aggregate employment fluctuations are not explained by the responses of workers with small rents to employment.


        Using a standard incomplete-markets model, we compute the welfare of two socio-economic systems: laissez-faire and egalitarianism. The egalitarian system (in which after-tax wages are compressed) provides insurance against income risks but at the cost of inefficiency: it undermines productive workers' incentives to work. When the stochastic process of idiosyncratic productivity shocks are calibrated to match the earnings inequality, the egalitarian society yields a much higher welfare as the insurance benefit dominates the efficiency loss. However, when the idiosyncratic productivity shocks are calibrated to capture the ex-post heterogeneity of earnings only, households are better off under laissez-faire if the labor supply is elastic enough. Transition between the two regimes is computed. When the wage compression is removed from the egalitarian steady state, the inequality emerges quickly and reaches its laissez-faire steady state in 20 year.

        We construct a family model of labor supply that features adjustment along both the intensive and extensive margin. Intensive margin adjustment is restricted to two values: full time work and part-time work. Using simulated data from the steady state of the calibrated model, we examine whether standard labor supply regressions can uncover the true value of the intertemporal elasticity of labor supply parameter. We find positive estimated elasticities that are larger for women and that are highly significant, but they bear virtually no relationship to the underlying preference parameters.


        We model worker heterogeneity in the rents from being employed in a Diamond-Mortensen-Pissarides model of matching and unemployment. We show that heterogeneity, reflecting differences in match quality and worker assets, reduces the extent of fluctuations in separations and unemployment. We find that the model faces a trade-off--it cannot produce both realistic dispersion in wage growth across workers and realistic cyclical fluctuations.


        Accounting for observed fluctuations in aggregate employment, consumption, and real wage using optimality conditions of a representative household often requires preferences that are incompatible with economic priors (e.g., Mankiw, Rotemberg, and Summers 1985). This discrepancy between the equilibrium model and the aggregate data is often viewed as evidence of the failure of labor-market clearing. We argue that such a conclusion is premature. We construct a model economy where all prices are flexible and all markets clear at all times but household decisions are not readily aggregated because of incomplete capital markets and the indivisible nature of labor supply. We demonstrate that if we were to explain the model-generated aggregate time series using decisions of a ``fictitious'' stand-in household, such a household is likely to have a non-concave or unstable utility.



        Whether technological progress raises or lowers aggregate employment in the short run has been the subject of much debate in recent years. We show that cross-industry differences in inventory holding costs, demand elasticities, and price rigidities potentially all affect employment decisions in the face of productivity shocks. In particular, the employment response to a permanent productivity shock is more likely to be positive the less costly it is to hold inventories, the more elastic industry demand is, and the more flexible prices are. Using data on 458 4-digit U.S. manufacturing industries over the period 1958-1996, we find statistically significant effects of variations in inventory holdings and demand elasticities on short-run employment responses, but less conclusive evidence pertaining to the effects of measured price stickiness..



        We show that a simple heterogeneous-agent economy with incomplete capital markets and indivisible labor can exhibit a strong increase in aggregate employment and consumption without a corresponding movement in wages. In the presence of aggregate productivity shifts, the interaction between partial insurance and indivisible labor results in a very low employment-productivity correlation and creates a time-varying wedge between the real wage and the marginal rate of substitution in consumption and leisure. Our results caution against viewing the measured wedge as an inefficiency due to a failure of labor-market clearing or as a fundamental driving force behind business cycles.

        Reply to "Comments on Heterogeneity and Aggregation: Implications for Labor Market Fluctuations". 



        The time series fit of dynamic stochastic general equilibrium (DSGE) models often suffers from restrictions on the long-run dynamics that are at odds with the data. Relaxing these restrictions can close the gap between DSGE models and vector autoregressions. This paper modifies a simple stochastic growth model by incorporating permanent labor supply shocks that can generate a unit root in hours worked. Using Bayesian methods we estimate two versions of the DSGE model: the standard specification in which hours worked are stationary and the modified version with permanent labor supply shocks. We find that the data support the latter specification.



        We find that technology's effect on  employment varies greatly across manufacturing industries. Some industries exhibit a temporary reduction in employment in response to a permanent increase in TFP, whereas far more industries exhibit an employment increase in response to a permanent TFP shock. This raises serious questions about existing work that finds that a labor productivity shock has a strong negative effect on employment. There are tantalizing and interesting differencesbetween TFP and labor productivity. We argue that TFP is a more natural measure of technology because labor productivity reflects shifts in the input mix as well as in technology.



        At the aggregate level, the labor-supply elasticity depends on the reservation-wage distribution. We present a model economy where workforce heterogeneity stems from idiosyncratic productivity shocks. The model economy exhibits the cross-sectional earnings and wealth distributions that are comparable to those in the micro data. We find that the aggregate labor-supply elasticity of such an economy is around 1, greater than a typical micro estimate. While the model is parsimonious, it provides a reconciliation between the micro and macro labor-supply elasticities.



        Studying the incentives and constraints in the non-market sector – that is, home production – enhances our understanding of economic behaviour in the market. In particular, it helps us to understand (a) small variations of labour supply over the life cycle, (b) the low correlation between employment and wages over the business cycle, and (c) large income differences across countries.



        The labor supply elasticity of an individual household and the aggregate labor supply elasticity of all households can differ significantly. If individual households not only decide on their hours worked, but also on whether to work or not, then the aggregate labor supply is determined not only by the willingness to substitute leisure over time, but also by the distribution of reservation wages. We present a model economy where earnings and wealth distributions are comparable to those in the micro data. We find that the aggregate labor supply elasticity of such an economy is around 1 which is greater than the typical micro estimates but smaller than those often assumed in the aggregate models.

        • Trends in Unemployment Rates in Korea: A Search-Matching Model Interpretation (joint with Changyong Rhee and Jaeryang Nam), Journal of the Japanese and International Economies, 18 (2) 241-163, 2004.


        We investigate the steady decline in aggregate unemployment rates in Korea since the 1960's.  We argue that a pronounced decrease in the intensity of reallocation shocks, which resulted in a downward trend in the natural rate of unemployment, has been an important factor in this decline.  Our claim is based on a structural search-matching model, the times series of job-separation and job-finding rates, and sectoral-shift measures that we construct from a micro data for the past three decades.


        We investigate the role of labor-supply shifts in economic fluctuations. We propose a new identification scheme for innovations to labor-supply schedule, which does not rely on a form of households' utility function. According to a VAR analysis of post-war U.S. data, the labor-supply shift accounts for about half the variation in hours and one-fifth of variation in output. To assess the role of labor-supply shifts in a more structural framework, predictions from a home production model with stochastic variation in home technology are compared to those from the VAR. We ask whether recent U.S. recessions are associated with unusually high productivity in non-market activity. Two recessions out of six recessions in the past 40 years are consistent with this interpretation.


        We examine the impact of wage stickiness when employment has an effort as well as hours dimension.  Despite wages being predetermined, the labor market clears through the effort margin.  Consequently, welfare costs of wage stickiness are potentially much, much smaller.


        This paper suggests that skill accumulation through past work experience, or "learning-by-doing'', can provide an important propagation mechanism in a dynamic stochastic general equilibrium model, as the current labor supply affects future productivity. Our econometric analysis uses a Bayesian approach to combine micro-level panel data with aggregate time series. Formal model evaluation shows that the introduction of the LBD mechanism improves the model's ability to fit the dynamics of aggregate output and hours.

        • Cyclical Movements in Hours and Effort Under Sticky Wages (joint with Mark BilsInternational Economic Journal, 15:2; 1-26, 2001.


        We examine the response of a sticky-wage economy to various real and nominal shocks.  In addition to variations in hours, we allow for an endogenous response in worker effort per hour.  Despite wages being predetermined, the labor market clears through the effort margin.  We find that the ability of a sticky-wage model to mimic U.S. business cycles is much improved by allowing for reasonable effort movements.  The model also provides a ready explanation for the finding that TFP is negatively affected by nominal shocks.

        • Decomposition of Hours based on Extensive and Intensive Margins of Labor (joint with Noh-sun Kwark), Economics Letters, 72, 361-367, 2001.


        We decompose underlying disturbances in total hours into three kinds: disturbances that shift the aggregate employment in the long- run, those that change the sectoral composition of employment in the long-run, and those that cause temporary movement of hours around the steady-state. Our identifying restriction exploits the distinctive nature of the two margins of labor: employment and hours per worker. According to the variance decomposition from a VAR based on Post-War U.S. monthly data, we find that aggregate and sectoral disturbances are roughly equally important in the cyclical fluctuation in aggregate hours.

        The importance of sticky prices in business cycle fluctuations has been debated for many years. But we argue, based on a large empirical literature from the 1950's and 60's, that it is necessary to distinguish the response of price to an increase in factor prices from its response to an increase in marginal cost generated by an expansion in production. Consistent with that earlier literature, we find for 450 U.S. manufacturing industries that prices do respond more dramatically to increases in costs driven by changes in factor prices than to an increase in marginal cost precipitated by expansions in output. We explore two models that can potentially explain these findings. Both break the link between price and marginal cost, thereby generating what one might naively interpret as average-cost pricing. The first is driven by firms pricing to limit entry. The second is driven by firms pricing to limit non-price competition within their market.

        Two investment anomalies in aggregate home production models are investigated: excess volatility and comovement. Adjustment cost in capital accumulation reduces both volatility and the negative correlation in investments on capital goods in the market and at home. Investments comove to the extent that durable goods and time are good substitutes in consumption activities. Consumers substitute durable goods for time at home when the opportunity cost of time is high during booms. Based on the Consumer Expenditure Survey, I show that households' expenditure shares on durable goods are negatively associated with household leisure, indicating that durable goods are relatively good substitutes for time.

        The standard equilibrium models of business cycles face a puzzling fact that total hours vary greatly over the business cycle without much variation in aggregate wages. The model augments the standard RBC model to include Lucas span of control. Distinction between market and non-market and managerial and non-managerial work makes aggregate wage far less cyclical than individual wages. A weak cross-sectional comparative advantage between market and home production can increase aggregate labor supply elasticity substantially. As a result, the model provides a reconciliation between data and equilibrium macroeconomics.



        “Detecting Home Production by Baxter and Rotz” (NBER Meeting at Minneapolis FED),

        “Product Market Regulation and Market Work by Feng and Rogerson ” (IMF and University of Tokyo),

        “Marginal Worker and Aggregate Elastiticy of Labor Supply by Gurio and Noual ” (AEA Meeting, Chicago),

        “Complementarity and Transition to Modern Economic Growth by Kim and Jung ” (KAEA Meeting, Chicago),

        “An Inventory Theoretic Approach to the New Keyensian Phillips Curve by Jung and Yun ” (AEA Meeting, New Orleans),

        “Investment-Specific Technological Change in Japan by Braun and Shioji” (SJE Conference, Seoul National University),