Neat Examples
Economic Growth Models
CESifo Working Paper No. 11053, April 2024
The authors analytically show that the simplified DICE exhibits a continuum of saddle-point stable steady states, a property that carries over to a large set of (numerical and analytical) IAMs. This novel insight is important because it implies initial conditions of stock variables, notoriously difficult to calibrate, matter for the ultimate steady state.
The figure shows first-best solutions, trajectories in (K, S) plane, starting from a grid of 25 different initial conditions. Terminal conditions require that shadow prices do not change anymore. Downward sloping (blue) curve: continuum of steady states (CSS).
Journal of Economic Theory, 196, September, 2021.
The authors study how zoning deregulation affects household welfare in general equilibrium. Zoning deregulation triggers a temporarily slower growth in housing rents and house prices. This transition process is calculated by applying the relaxation algorithm. The representative household's welfare gain is unequally distributed at the micro level.
Welfare effects of zoning deregulation (homogeneous portfolio) across the earnings and wealth distribution. For details see figure 3 in the paper.
Hémous & Olsen (2020): The Rise of the Machines: Automation, Horizontal Innovation and Income Inequality
American Economic Journal: Macroeconomics (forthcoming)
The authors build an endogenous growth model with automation and horizontal innovation. Over time, the share of automation innovations endogenously increases through an increase in low-skill wages, leading to an increase in the skill premium and a decline in the labor share. They calibrate the model to the US economy and show that it quantitatively replicates the paths of the skill premium, the labor share and labor productivity.
Panel A shows yearly growth rates for GDP, low-skill wages (w) and high-skill wages (v), Panel B the profit ratio of automated and non-automated firms and the relative pay of high-skill and low-skill wages, Panel C the total spending on horizontal innovation and automation as well as the share of products that are automated (G), and Panel D the wage share of GDP for total wages and low-skill wages.
Dalgaard & Strulik (2017): The genesis of the golden age: Accounting for the rise in health and leisure
Review of Economic Dynamics, 2017, Vol. 24, 132–151
The authors develop a life cycle model featuring an optimal retirement decision in the presence of physiological aging. In the model, individuals decide on optimal consumption during life, the age of retirement, and (via health investments) the timing of their death. Accordingly, “years in retirement” is fully endogenously determined. Using the model, the authors can account for the evolution of age of retirement and longevity across cohorts born between 1850 and 1940 in the US.
Resulting life cycle trajectories given the authors calibrations. Solid lines: model prediction. Stars: data.
European Economic Review, 56 (6), 2012, 1180-1199
The authors set up a neoclassical growth model suitable to assess revenue effects of capital taxation. While their results at the aggregate level are broadly consistent with the available literature, the novel disaggregated view on capital taxation has provided new insights. For example, their general equilibrium analysis suggests that corporate taxes can be drastically reduced with little effect on total tax revenue and that the revenue-maximizing tax rate on capital gains is zero.
Laffer Curves for Labor income (left) and corporate income (right). Solid lines: steady-state Laffer curve; dashed lines: NPV Laffer curve. The Laffer curve for taxation of labor income broadly confirms Trabandt and Uhlig (2010). The Laffer curve for taxation of corporate income, in contrast, is relatively flat, in particular the steady-state variant.
Strulik & Trimborn (2010): Anticipated Tax Reforms and Temporary Tax Cuts: A General Equilibrium Analysis
Journal of Economic Dynamics and Control, 34, 2141-2158
The relaxation algorithm is employed to solve a Ramsey model extended by an government sector. Simulations of a preannounced increase in the consumption tax showed a qualitative different pattern depending on the intertemporal elasticity of substitution. Potential applications of this method emerge throughout in economic fields where the reaction on preannounced policy measures is of special interest in the context of perfect foresight optimizing agents.
Reaction of key economic variables with an anticipated increase in a consumption tax for households with a high value of intertemporal elasticity of substitiution.
Journal of Economic Growth, 2009, Vol. 14, 55-78
This paper develops a quality-ladder growth model with overlapping intellectual property rights and capital accumulation to quantitatively evaluate the effects of blocking patents. The model is calibrated to aggregate data of the US economy. Under parameter values that match key features of the US economy and show equilibrium R&D underinvestment, the author finds that reducing the extent of blocking patents by changing the profit-sharing rule would lead to a significant increase in R&D, consumption and welfare.
Socially optimal R&D shares of GDP given the fraction of long-run TFP growth driven by R&D, ξ.
Resource Models
International Economic Review, 2017, 1371 - 1415
Expectations about future energy use, the authors argue, affect the transition from fossil fuels to renewable substitutes because of an interaction between directed innovation and resource scarcity. Fossil-saving technical change erodes the incentives to implement renewables. Conversely, the anticipation of a transition to renewables diminishes the incentives to invest in fossil technology. Two equilibria may arise, one with a transition to renewables and low fossil efficiency and one without renewables and high fossil efficiency. Expectations determine which equilibrium arises.
The panels show the time profiles for fossil fuel use (panel a) and resource-augmenting technical change (panel b) for the two equilibria. If the backstop technology is expected not to become competitive (see the dashed lines), resource extraction starts out relatively low and is monotonically declining over time. Resource-augmenting technical change is relatively high and monotonically increasing over time. On the contrary, if the future implementation of the backstop technology is expected (see the solid lines), current resource extraction is relatively high, whereas resource-augmenting technical change is modest and drops to zero before the backstop technology actually becomes competitive.
Bretschger & Schaefer (2017): Dirty history versus clean expectations: Can energy policies provide momentum for growth
European Economic Review, Vol. 99, 2017, 170-190
The authors study the macroeconomic effects of a policy-induced switch from dirty to clean production. They identify macroeconomic conditions under which policy instruments can trigger a development with sufficient momentum, fostering at the same time economic activity and environmental quality. The model features multiple steady states and a role for history and expectations in the process of equilibrium selection.
The phase diagram illustrates multiple steady states with an overlap region (or region of global indeterminacy). Paper quote: "We employ the Relaxation algorithm since this method is numerically the most efficient one in order to detect a transition path from a certain initial point ... to a steady state ...."
Dugan & Trimborn (2020): The Optimal Extraction of Non-Renewable Resources Under Hyperbolic Discounting
Economics Working Papers 2020-17, Department of Economics, Aarhus University
The authors investigate the consequences of a declining social discount rate on optimal extraction of non-renewable resources and economic growth. They introduce time-consistent hyperbolic utility discounting into models of resource extraction and show that resource use is more conservative under hyperbolic discounting resulting in a permanently higher resource stock.
Resource extration rate for hyperbolic (red line) and exponential (dashed line) discounting While the extraction rate is initially higher under hyperbolic discounting, it is soon overtaken be the extraction rate under exponential discounting. From the intersection point onwards, both extraction rates follow strikingly different paths and converge towards different levels asymptotically
Other Models
Schünemann & Trimborn (2023): Boosting Taxes for Boasting about Houses? Status Concerns in the Housing Market
Journal of Economic Behavior & Organization, 205, pp 120-143
This paper characterizes the optimal time path for housing taxation when households have status concerns for housing. Implementing the tax schedule is associated with a moderate aggregate welfare gain, but has a sizable and diverse impact on household groups’ welfare. We compare the findings to the case in which the utilitarian social planner is constrained to constant housing taxes.
Schünemann, Strulik & Trimborn (2017): The gender gap in mortality: How much is explained by behavior?
Journal of Health Economics, 54, 79-90
Abstract
Journal of International Economics, Vol. 95, 2015, 291-304
Abstract
Journal of Public Economics, Vol. 132, 2015, 79-94
Abstract
Journal of Economic Dynamics and Control, 2013, Vol. 37 (3), 516-534
This paper characterizes the optimal time path of R&D subisidzation in a semi-endogenous growth model. Starting from the initial steady state under current R&D subisidzation in the US, the R&D subsidy should significantly jump upwards and then slightly decrease over time.