Stochastic Shocks Research Articles

Fiscal risk in a monetary union

We present a dynamic and quantitative model of a fiscal solvency crisis in a monetary union. Diverse fiscal policies, which are subject to fiscal limits and stochastic shocks, can threaten a monetary union. The fiscal limits arise due to distortionary taxation and political will. Stochastic shocks are random and could push a fiscally sound policy towards its limit. In equilibrium agents refuse to lend along a path which violates the fiscal limits, creating a fiscal solvency crisis. The dynamics leading to the crisis depend on the policy response to restore lending. We focus on two responses, default and policy switching. We simulate our model to quantify the probability of a fiscal solvency crisis in the European Monetary Union with fiscal variables at end of 2009 values. Our model predicts the Greek crisis which occurred and warns of an Italian one.

Transmission mechanisms of real stochastic shocks in a small open economy

We offer a qualitative evaluation of the transmission mechanisms of two real shocks, a productivity shock and a government expenditure shock in Walrasian business cycle models. The analysis is developed in a monetary small open economy business cycle model, a set-up general enough to study the effects of the two shocks on both real and nominal variables. Qualitative and graphical displays indicate properties of Real Business Cycles that are able to reproduce observed cyclical patterns, independently of the calibration used for different economies. These qualitative findings match the quantitative results found in the literature, and rationalize some disparity findings (such as the cyclicity pattern of prices) and failures (such as the Dunlop–Tarshis observation). We suggest that understanding the underlying qualitative intuitions of these models may be of great help in tackling new puzzles in this area.

The International Transmission of Volatility Shocks: An Empirical Analysis

This paper proposes an empirical model which can be used to estimate the impact of changes in the volatility of shocks to US real activity on the UK economy. The proposed empirical model is a structural VAR where the volatility of structural shocks is time varying and is allowed to affect the level of endogenous variables. Using this extended SVAR model we estimate that a one standard deviation increase in the volatility of the shock to US real GDP leads to a decline in UK GDP growth of 0.1% and a 0.1% increase in UK CPI inflation. We then use a non-linear small open economy New Keynesian business cycle model calibrated to US/UK economies to investigate what kind of stochastic volatility shocks can deliver such behaviour. We find that shocks that generate marginal cost uncertainty – such as foreign wage mark-up and productivity stochastic volatility shocks – can reproduce the macroeconomic aggregate responses obtained by the empirical model. An increase in uncertainty, associated with foreign demand shocks on the other hand has a negligible impact on the domestic economy.

Stochastic shocks in a two-sector Solow model

We study a stochastic, discrete-time, two-sector growth model a-la Solow (1956) characterised by perpetual growth. Assuming that exogenous i.i.d. shocks hit the physical production sector, we show that the capital dynamics can be converted, through an appropriate log-transformation, into an iterated function system converging to an invariant distribution supported on a Cantor set.

A Stochastic Model to account for System Uncertainties applied to an Optimal Harvesting Problem

In the modeling of stochastic nonlinear systems it is often necessary to consider the existence of uncertainties about some parameters of the system or in the distribution implied by the stochastic shocks, and in this setting, the control policy can be obtained by the rules of robust control theory. To present a different way to handle control systems in this scenario, this paper introduces a theoretical framework for continuous-time stochastic nonlinear systems in which the Control Variations Increase the state Uncertainty (CVIU systems). This type of system can be applied in several areas of science and engineering, due to its ability in dealing with complex stochastic systems, for which the dynamics are not completely known. In particular, the paper applies this model to a problem of fishery management in an unknown environment, and establishes a harvesting rule for it based on the CVIU approach. Using dynamic programming and tools from nonsmooth analysis, the control solution indicates the existence of a region in the state space in which the optimal harvesting is of no variation, yielding periods of inaction. This behavior obtained from optimality is somehow expected from the cautionary nature of controlling underdetermined systems.

Political model of social evolution

Almost all democratic societies evolved socially and politically out of authoritarian and nondemocratic regimes. These changes not only altered the allocation of economic resources in society but also the structure of political power. In this paper, we develop a framework for studying the dynamics of political and social change. The society consists of agents that care about current and future social arrangements and economic allocations; allocation of political power determines who has the capacity to implement changes in economic allocations and future allocations of power. The set of available social rules and allocations at any point in time is stochastic. We show that political and social change may happen without any stochastic shocks or as a result of a shock destabilizing an otherwise stable social arrangement. Crucially, the process of social change is contingent (and history-dependent): the timing and sequence of stochastic events determine the long-run equilibrium social arrangements. For example, the extent of democratization may depend on how early uncertainty about the set of feasible reforms in the future is resolved.

Research Note: Long-Lasting Effects and Welfare Costs of Fluctuations

The tourism industry is growing rapidly but is also highly fluctuating. Using China's inbound tourism market as the object and based on the B–N data decomposition theory, this paper adopts the statistics of variance ratio to measure the long-lasting effects of stochastic fluctuations on China's inbound tourism industry. It also discusses the influences of stochastic fluctuations and the decreasing growth rate on the welfare of China's inbound tourism. The conclusion is that undoubtedly China's inbound tourism industry will continue to grow, but the impact of stochastic shocks will endure for a relatively long time. Twenty-four per cent of the long-term fluctuation of China's inbound tourism industry is the result of stochastic shocks, whose effect, in the short term, will continue to be reinforced. Though the elimination of fluctuations will increase welfare by 0.40%, lowering the growth rate will decrease welfare by a larger percentage. If the monthly growth rate decreases by 0.1%, welfare will fall by about 19.37%, 48 times the amount of welfare loss without fluctuation. Therefore, China's inbound tourism business should stick to the long-term policy of facilitating growth, while some administrative and legislative measures should be taken to address the negative impact of stochastic fluctuation appropriately.

Stocks in the Short Run

The existing literature estimates stock-price volatility accumulated over the trading day. We focus on what happens to volatility within the trading day. Using transactions data from 2001 through 2009, we estimate the path of the quadratic variation process in 5-minute increments day by day for the 30 stocks of the DJIA and for an exchange-traded fund (the SPDR) that tracks the S&P 500. Using a Heston (1993) model, we estimate that 80% of the gap between the level of the volatility process and its asymptotic mean is eliminated within 5-minutes. Roughly two-thirds of daily realized volatility can be explained by a deterministic version of the Heston model that begins the trading day far above its equilibrium and converges to a constant. The remaining third reflects stochastic shocks to volatility arriving after trade begins. The asymptotic mean of the SPDR behaves much like the closing value of the VIX, a volatility index based on the S&P 500 stock index. When standardized by our 5-minute volatility estimates, 5-minute log returns are approximately normally distributed.

Inequality and Growth: Understanding the Link through a Simulation

As suggested in the literature, economic growth and inequality may be influenced by common determinants. One set of determinants may be stochastic production shocks, and in particular non-neutral shocks. To communicate this idea to undergraduate students, I present a model in which shocks to the capital stock introduce both growth and inequality. To engage students and reinforce the empirical consequences of this relationship, I employ an online simulation which implements the model. Representative simulation results are presented and discussed herein.

A Theory of Occupational Choice with Endogenous Fertility

Theories based on partial equilibrium reasoning alone cannot explain the widespread negative cross-sectional correlation between parental wages and fertility, without restrictive assumptions on preferences and childcare costs. We argue that incorporating a dynamic general equilibrium analysis of returns to human capital can help explain observed empirical patterns. Other by-products of this theory include explanations for intergenerational mobility without stochastic shocks, connections between mobility and fertility patterns, and locally determinate steady states. Comparative statics exercises on steady states shed light on the effects of education, childcare subsidies, child labor regulations, and income redistribution policy on long run living standards. (JEL H23, I31, J13, J24, J62, J82)

Stochastic technology shocks in an extended Uzawa–Lucas model: closed-form solution and long-run dynamics

We add stochastic technological progress, modelled as a geometric Brownian motion with drift, to an augmented Uzawa–Lucas growth model. Under a particular combination of parameters we derive a closed form solution to the model and analytical expressions which show that uncertainty reduces the optimal levels of consumption and increases the proportion of human capital devoted to producing new human capital.

Endogenous Growth Mechanism as a Source of Medium Term Fluctuations in the Labor Market: Application to the US Economy

Endogenous Growth Mechanism as a Source of Medium Term Fluctuations in the Labor Market: Application to the US Economy

Learning and Judgment Shocks in U.S. Business Cycles

This paper examines the role of judgment shocks in combination with other structural shocks in explaining post-war economic volatility within the context of a New Keynesian model. Agents form expectations using constant gain learning then augment these forecasts with judgment. These judgments may be interpreted as a reaction to current news stories or policy announcements that would influence people's expectations. I allow for the possibility that these judgments be informatively based on information about structural shocks, but judgment itself may also be subject to its own stochastic shocks. I estimate a standard New Keynesian model that includes these shocks using Bayesian simulation methods. To aid in identifying expectational shocks from other structural shocks I include data on professional forecasts along with data on output gap, inflation, and interest rates. I find judgment is largely not informed by macroeconomic fundamentals; most of the variability in judgment is explained by its own stochastic shocks. Impulse response functions from the estimated model illustrate how shocks to judgment destabilize the economy and explain business cycle fluctuations.

Siesta: A Theory of Freelancing

I study the effect of fatigue and innate ability on performance in a model with incomplete contracts, lumpy tasks requiring multiple periods of work and stochastic productivity shocks. I find that increasing ability or reducing fatigue does not lead necessarily to more productive efficiency, since it may exacerbate the incentive for agents take too much on-the-job leisure. In a world with heterogenous agents, the problem may be ameliorated by the introduction of a dual labour market with free-lancers (who can take breaks at their discretion) and regular workers (who work on a fixed schedule).

An Empirical Investigation of Consumption-Based Asset Pricing Models With Stochastic Habit Formation

We econometrically estimate a consumption-based asset pricing model with stochastic internal habit and test it using the generalized method of moments. The model departs from existing models with deterministic internal habit (e.g., Dunn and Singleton (1983), Ferson and Constan- tinides (1991), and Heaton (1995)) by introducing shocks to the coefficients in the distributed lag specification of consumption habit and consequently an additional shock to the marginal rate of substitution. The stochastic shocks to the consumption habit are persistent and provide an additional source of time variation in expected returns. Using Treasury bond returns and broad equity market index returns, we show that stochastic internal habit formation models resolve the dichotomy between the autocorrelation properties of the stochastic discount factor and those of expected returns. Consequently, they provide a better explanation of time-variation in expected returns than models with either deterministic habit or stochastic external habit.

An Empirical Investigation of Consumption-Based Asset Pricing Models with Stochastic Habit Formation

We econometrically estimate a consumption-based asset pricing model with stochastic internal habit and test it using the generalized method of moments. The model departs from existing models with deterministic internal habit (e.g., Dunn and Singleton (1983), Ferson and Constantinides (1991), and Heaton (1995)) by introducing shocks to the coefficients in the distributed lag specification of consumption habit and consequently an additional shock to the marginal rate of substitution. The stochastic shocks to the consumption habit are persistent and provide an additional source of time variation in expected returns. Using Treasury bond returns and broad equity market index returns, we show that stochastic internal habit formation models resolve the dichotomy between the autocorrelation properties of the stochastic discount factor and those of expected returns. Consequently, they provide a better explanation of time-variation in expected returns than models with either deterministic habit or stochastic external habit.

Political Selection and Persistence of Bad Governments

We study dynamic selection of governments under different political institutions, with a special focus on institutional “flexibility.” A government consists of a subset of the individuals in the society. The competence level of the government in office determines collective utilities (e.g., by determining the amount and quality of public goods), and each individual derives additional utility from being part of the government (e.g., rents from holding office). We characterize the dynamic evolution of governments and determine the structure of stable governments, which arise and persist in equilibrium. In our model, perfect democracy, where current members of the government do not have veto power over changes in governments, always leads to the emergence of the most competent government. However, any deviation from perfect democracy, to any regime with incumbency veto power, destroys this result. There is always at least one other, less competent government that is also stable and can persist forever, and even the least competent government can persist forever in office. We also show that there is a nonmonotonic relationship between the degree of incumbency veto power and the quality of government. In contrast, in the presence of stochastic shocks or changes in the environment, a regime with less incumbency veto power has greater flexibility and greater probability that high-competence governments will come to power. This result suggests that a particular advantage of “democratic regimes” (with a limited number of veto players) may be their greater adaptability to changes rather than their performance under given conditions. Finally, we show that “royalty-like” dictatorships may be more successful than “junta-like” dictatorships because in these regimes veto players are less afraid of change.

Nominal Wage Rigidities in a New Keynesian Model with Frictional Unemployment

In this paper, we propose a search and matching model with nominal stickiness a la Calvo in the wage bargaining. We analyze the properties of the model, first, in the context of a typical real business cycle model driven by stochastic productivity shocks and second, in a fully specified monetary DSGE model with various real and nominal rigidities and multiple shocks. The model generates realistic statistics for the important labor market variables.

Preemption in a real option game with a first mover advantage and player-specific uncertainty

Abstract In this paper a two-player real option game with a first-mover advantage is analyzed, where payoffs are driven by a player-specific stochastic state variable. It is shown that there exists an equilibrium which has qualitatively different properties from those in standard real option games driven by common stochastic shocks. The properties of the equilibrium are four-fold: (i) preemption does not necessarily occur, (ii) if preemption takes place, the rent-equalization property holds, (iii) for almost all sample paths it is clear ex-ante which player invests first, and (iv) it is possible that both players invest simultaneously, even if that is not optimal. It is argued from simulations that real option games with a common one-dimensional shock do not provide a good approximation for games with player-specific uncertainty, even if these are highly correlated.

Exchange Rate Crises and Fiscal Solvency

This paper combines insights from generation one currency crisis models and the fiscal theory of the price level (FTPL) to create a dynamic FTPL model of currency crises. The initial fixed‐exchange‐rate policy entails risks due to an upper bound on government debt and stochastic surplus shocks. Agents refuse to lend into a position for which the value of debt exceeds the present value of expected future surpluses. Policy switching, usually combined with currency depreciation, restores fiscal solvency and lending. This model can explain a wide variety of crises, including those involving sovereign default. We illustrate by explaining the crisis in Argentina (2001).