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Showing papers in "International Economic Review in 2018"


Journal ArticleDOI
TL;DR: This paper developed a model of industry dynamics based on putty-clay technology that is consistent with these findings and found that restaurant exit and entry both rise following a minimum wage increase.
Abstract: We document two new findings about the industry‐level response to minimum wage hikes. First, restaurant exit and entry both rise following a hike. Second, there is no change in employment among continuing restaurants. We develop a model of industry dynamics based on putty‐clay technology that is consistent with these findings. In the model, continuing restaurants cannot change employment, and thus industry‐level adjustment occurs gradually through exit of labor‐intensive restaurants and entry of capital‐intensive restaurants. Interestingly, the putty‐clay model matches the small estimated short‐run disemployment effect of the minimum wage found in other studies, but produces a larger long‐run disemployment effect.

111 citations


Journal ArticleDOI
TL;DR: In this article, the authors identify a "border effect" in the absence of a border and find that trade between East- and West-Japan is 23.1% -51.3% lower than trade within both country parts.
Abstract: Over the last 20 years the trade literature repeatedly documented the trade-reducing effects of inter- and intra-national borders. Thereby, the puzzling size and persistence of observed border effects from the beginning raised doubts on the role of underlying political borders. However, when observed border effects are not caused by political trade barriers, why should their spatial dimension then inevitably coincide with the geography of present or past political borders? This paper identifies a "border effect" in the absence of a border. Thereby, the finding that trade between East- and West-Japan is 23.1% - 51.3% lower than trade within both country parts, is established in the absence of an obvious east-west division due to historical borders, cultural differences or past civil wars. From a rich set of explanatory variables post-war agglomeration processes, reflected by the contemporaneous structure of Japan's business and social networks, rather than cultural differences, shaped by long-lasting historical shocks, are identified as an explanation for the east-west bias in intra-Japanese trade.

98 citations


Journal ArticleDOI
TL;DR: In this paper, the authors estimate country-specific terms of trade shocks using data from 38 poor and emerging countries and find that terms-of-trade shocks explain only 10 percent of movements in aggregate activity.
Abstract: According to conventional wisdom, terms of trade shocks represent a major source of business cycles in emerging and poor countries. This view is largely based on the analysis of calibrated business-cycle models. We argue that the view that emerges from empirical SVAR models is strikingly different. We estimate country-specific SVARs using data from 38 poor and emerging countries and find that terms-of-trade shocks explain only 10 percent of movements in aggregate activity. We then build a fully-fledged, open economy model with three sectors, importables, exportables, and nontradables, and use data from each of the 38 countries to obtain country-specific estimates of key structural parameters, including those defining the terms-of-trade process. In the estimated theoretical business-cycle models terms-of-trade shocks explain on average 30 percent of the variance of key macroeconomic indicators, three times as much as in SVAR models.

91 citations


Journal ArticleDOI
TL;DR: The authors showed that subjects are correlation averse over lotteries with intertemporal income profiles, and used this theoretical structure to guide the design of a series of experiments that allow them to identify and estimate inter-temporal correlation aversion.
Abstract: Convenient assumptions about qualitative properties of the intertemporal utility function have generated counter-intuitive implications for the relationship between atemporal risk aversion and the intertemporal elasticity of substitution. If the intertemporal utility function is additively separable then the latter two concepts are the inverse of each other. We review a theoretical specification with a long lineage in the literature on multi-attribute utility and use this theoretical structure to guide the design of a series of experiments that allow us to identify and estimate intertemporal correlation aversion. Our results show that subjects are correlation averse over lotteries with intertemporal income profiles.

72 citations


Journal ArticleDOI
TL;DR: In this article, the authors examine four sources of uncertainty in exchange rate forecasting models: (i) random variations in the data, (ii) estimation uncertainty, (iii) uncertainty about the degree of time-variation in coefficients, and (iv) uncertainty regarding the choice of the predictor.
Abstract: In a unified framework, we examine four sources of uncertainty in exchange rate forecasting models: (i) random variations in the data, (ii) estimation uncertainty, (iii) uncertainty about the degree of time-variation in coefficients, and (iv) uncertainty regarding the choice of the predictor. We find that models which embed a high-degree of coefficient variability yield forecast improvements at horizons beyond 1-month. At the 1-month horizon, and apart from the standard variance implied by unpredictable fluctuations in the data, the second and third sources of uncertainty listed above are key obstructions to predictive ability. The uncertainty regarding the choice of the predictors is negligible.

55 citations


Journal ArticleDOI
TL;DR: In this paper, the authors compare first price auctions with ex post screening of bid responsiveness and average bid auctions (ABAs), in which the bidder closest to the average bid wins.
Abstract: This article contrasts two auction formats often used in public procurement: first price auctions with ex post screening of bid responsiveness and average bid auctions (ABAs), in which the bidder closest to the average bid wins. The equilibrium analysis reveals that their ranking is ambiguous in terms of revenues, but the ABA is typically less efficient. Using a data set of Italian public procurement auctions run alternately under the two formats, a structural model of bidding is estimated for the subsample of first price auctions and used to quantify the efficiency loss under counterfactual ABAs.

52 citations


Journal ArticleDOI
TL;DR: In this paper, a large sample of laboratory subjects was used to investigate the relationship between the digit ratio (2D:4D), a biomarker for pre-natal testosterone exposure, and individual risk taking.
Abstract: Using a large (n=704) sample of laboratory subjects, we systematically investigate the links between the digit ratio - a biomarker for pre-natal testosterone exposure - and two measures of individual risk taking: (i) risk preferences over lotteries with real monetary incentives, and (ii) self-reported risk attitude. The digit ratio (also called 2D:4D) is the ratio of the length of the index finger to the length of the ring finger, and we consider both hands’ digit ratios. Previous studies have found that the digit ratio correlates with risk taking in some subject samples, but not others. In our sample, we find that both the right-hand and the left-hand digit ratio are significantly associated with risk preferences: subjects with lower digit ratios tend to choose riskier lotteries. Neither digit ratio, however, is associated with self-reported risk attitude.

47 citations


Journal ArticleDOI
TL;DR: In this paper, the causes and consequences of political centralization and fragmentation in China and Europe were studied, and it was shown that a severe and unidirectional threat of external invasion fostered centralization in China, whereas Europe faced a wider variety of smaller external threats and remained fragmented.
Abstract: This article studies the causes and consequences of political centralization and fragmentation in China and Europe. We argue that a severe and unidirectional threat of external invasion fostered centralization in China, whereas Europe faced a wider variety of smaller external threats and remained fragmented. Political centralization in China led to lower taxation and hence faster population growth during peacetime compared to Europe. But it also meant that China was more vulnerable to occasional negative population shocks. Our results are consistent with historical evidence of warfare, capital city location, tax levels, and population growth in both China and Europe.

46 citations


Journal ArticleDOI
TL;DR: In this paper, a model with search and matching frictions and heterogeneous workers was established to evaluate a reform of the public sector wage policy in steady-state and the model was calibrated to the UK economy based on Labour Force Survey data.
Abstract: A model with search and matching frictions and heterogeneous workers was established to evaluate a reform of the public sector wage policy in steady-state. The model was calibrated to the UK economy based on Labour Force Survey data. A review of the pay received by all public sector workers to align the distribution of wages with the private sector reduces steady-state unemployment by 1.4 percentage points.

40 citations


Journal ArticleDOI
TL;DR: This paper developed a model of trade agreements with renegotiation and imperfectly verifiable information, which yields predictions on how the dispute outcome depends on the contracting environment and how it correlates with the optimal contract form.
Abstract: We develop a model of trade agreements with renegotiation and imperfectly verifiable information. In equilibrium, trade disputes can occur and can be resolved in a variety of ways: Governments may settle “early†or trigger a court ruling, and in the latter case, they may implement the ruling or reach a post†ruling settlement. The model yields predictions on how the dispute outcome depends on the contracting environment and how it correlates with the optimal contract form. We find support for a key prediction of our model using data on the outcomes of actual trade disputes in the General Agreement on Tariffs and Trade/World Trade Organization.

39 citations


Journal ArticleDOI
TL;DR: The authors proposed a new VAR identication scheme that enables disentangling labor supply shocks from wage bargaining shocks by imposing robust sign- restrictions that are derived from a New Keynesian model with endogenous labor force par- ticipation.
Abstract: We propose a new V AR identication scheme that enables us to disentangle labor supply shocks from wage bargaining shocks. Identication is achieved by imposing robust sign- restrictions that are derived from a New Keynesian model with endogenous labor force par- ticipation. According to our analysis on US data over the period 1985-2014, labor supply shocks and wage bargaining shocks are important drivers of output and unemployment both in the short run and in the long run. These results suggest that identication strategies used in estimated New Keynesian models to disentangle labor market shocks may be misguided. We also analyze the behavior of the labor force participation rate through the lenses of our model. Wend that labor supply shocks are the main drivers of the participation rate and account for about half of its decline in the aftermath of the Great Recession.

Journal ArticleDOI
TL;DR: In this paper, the authors studied the interaction between government debt and banking markets and highlighted the spillover from fragility in debt markets on banks and, through government bailout of troubled banks, spillovers from banks to the debt market.
Abstract: This paper studies the interaction of government debt and banking markets. Both markets are known to be fragile: excessively responsive to fundamentals and prone to strategic uncertainty. Our analysis highlights the spillover from fragility in debt markets on banks and, through government bailout of troubled banks, spillovers from banks to the debt market. This interaction, termed a ‘diabolic loop’, is driven by government willingness to bail out banks and the resulting incentives for banks not to self-insure through equity buers. We provide conditions such that the ‘diabolic loop’ is a Nash Equilibrium of the interaction between banks and the government.

Journal ArticleDOI
TL;DR: This article conducted a theoretical analysis of why individuals provide care and attention to their elderly parents using a two-period overlapping generations model with endogenous saving and a "contest success function" and test this model using micro data from a Japanese household survey.
Abstract: In this paper, we conduct a theoretical analysis of why individuals provide care and attention to their elderly parents using a two-period overlapping generations model with endogenous saving and a “contest success function” and test this model using micro data from a Japanese household survey, the Osaka University Preference Parameter Study. To summarize our main findings, we find that the Japanese are more likely to live with (or near) their elderly parents and/or to provide care and attention to them if they expect to receive a bequest from them, which constitutes strong support for the selfish bequest motive or the exchange motive (much stronger than in the United States), but we find that their caregiving behavior is also heavily influenced by the strength of their altruism toward their parents and social norms.

Journal ArticleDOI
TL;DR: This paper found that workers do trade off the incented output (quantity) at the expense of the non-incented one (quality) as a result of a piece rate bonus scheme.
Abstract: A well-recognized problem in the multitasking literature is that workers might substantially reduce their effort on tasks that produce unobservable outputs as they seek the salient rewards to observable outputs. Since the theory related to multitasking is decades ahead of the empirical evidence, the economic costs of standard incentive schemes under multitasking contexts remain largely unknown. This study provides empirical insights quantifying such effects using a field experiment in Chinese factories. Using more than 2200 data points across 126 workers, we find sharp evidence that workers do trade off the incented output (quantity) at the expense of the non-incented one (quality) as a result of a piece rate bonus scheme. Consistent with our theoretical model, treatment effects are much stronger for workers whose base salary structure is a flat wage compared to those under a piece rate base salary. While the incentives result in a large increase in quantity and a sharp decrease in quality for workers under a flat base salary, they result only in a small increase in quantity without affecting quality for workers under a piece rate base salary.

Journal ArticleDOI
TL;DR: In this paper, the authors examine a dynamic, two-sided, one-one-to-one matching market where agents on both sides interact over a period of time and define and identify sufficient conditions for the existence of a dynamically stable matching, which may require revisions to initial assignments.
Abstract: We examine a dynamic, two‐sided, one‐to‐one matching market where agents on both sides interact over a period of time. We define and identify sufficient conditions for the existence of a dynamically stable matching, which may require revisions to initial assignments. A generalization of the deferred acceptance algorithm can identify dynamically stable outcomes in a large class of economies, including cases with intertemporal preference complementarities. We relate our analysis to market unraveling and to common market design applications, including the medical residency match.

Journal ArticleDOI
TL;DR: In this article, the authors studied the state-dependence of the output and welfare effects of shocks to government purchases in a canonical medium scale DSGE model and found that the welfare multiplier is quite volatile and procyclical.
Abstract: This paper studies the state-dependence of the output and welfare effects of shocks to government purchases in a canonical medium scale DSGE model. When monetary policy is characterized by a Taylor rule, the output multiplier (the change in output for a one unit change in government spending) is countercyclical but close to constant across states of the business cycle, whereas the welfare multiplier (the consumption equivalent change in a measure of aggregate welfare for the same change in government spending) is quite volatile and procyclical. These results are robust to different means of fiscal finance. When the nominal interest rate is unresponsive to economic conditions, such as would be the case at the zero lower bound, both the output and welfare multipliers are larger and move significantly more across states than under a Taylor rule. The welfare multiplier is still procyclical under passive monetary policy, albeit less so than under a Taylor rule.Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Journal ArticleDOI
TL;DR: In this article, a variety of structural vector autoregression (VAR) models have been proposed to identify credit supply shocks and the performance of these models can vary substantially, with some identification schemes producing particularly misleading results.
Abstract: In the aftermath of the recent financial crisis, a variety of structural vector autoregression (VAR) models have been proposed to identify credit supply shocks. Using a Monte Carlo experiment, we show that the performance of these models can vary substantially, with some identification schemes producing particularly misleading results. When applied to U.S. data, the estimates from the best performing VAR models indicate, on average, that credit supply shocks that raise spreads by 10 basis points reduce GDP growth and inflation by 1% after one year. These shocks were important during the Great Recession, accounting for about half the decline in GDP growth.

Journal ArticleDOI
TL;DR: In this article, a dynamic general equilibrium model of intermediation in the FOREX market is proposed, where immediate trade between ultimate buyers and sellers of foreign currencies is obstructed by search frictions due to geographic dispersion.
Abstract: The FOREX market is an over-the-counter market (in fact, the largest in the world) characterized by bilateral trade, intermediation, and significant bid-ask spreads. The existing international macroeconomics literature has failed to account for these stylized facts largely due to the fact that it models the FOREX as a standard Walrasian market, therefore overlooking some important institutional details of this market. In this paper, we build on recent developments in monetary theory and finance to construct a dynamic general equilibrium model of intermediation in the FOREX market. A key concept in our approach is that immediate trade between ultimate buyers and sellers of foreign currencies is obstructed by search frictions (e.g., due to geographic dispersion). We use our framework to compute standard measures of FOREX market liquidity, such as bid-ask spreads and trade volume, and to study how these measures are affected both by macroeconomic fundamentals and the FOREX market microstructure. We also show that the FOREX market microstructure critically affects the volume of international trade and, consequently, welfare. Hence, our paper highlights that modeling the FOREX as a frictionless Walrasian market is not without loss of generality.

Journal ArticleDOI
TL;DR: Using nearly 50 years of data from Framingham Heart Study male participants, longevity consequences of different lifetime smoking patterns are evaluated by jointly estimating smoking behavior and health outcomes over the life cycle, by richly including smoking and health histories, and by flexibly incorporating correlated unobserved heterogeneity.
Abstract: Using data from Framingham Heart Study participants interviewed and examined at frequent intervals over much of their adult lifetime, we discover a relationship between smoking and mortality that differs significantly in magnitude from findings in the medical and epidemiological literature. We attribute the finding of smaller deleterious health impacts of smoking to a failure by previous studies to appropriately account for the non- random nature of lifetime smoking patterns and health histories. We provide causal and consistent estimates of the expected longevity consequences of current smoking, smoking cessation, smoking duration, and smoking experience by jointly modeling individual health heterogeneity, by including supply-side factors such as cigarette advertising and prices, and by allowing for permanent and time-varying unobserved heterogeneity in a flexible yet comprehensive multiple equation joint estimation procedure. We simulate our estimated empirical model under a variety of lifetime smoking patterns, and we compare the resulting mortality differences to the epidemiological literature that treats smoking behavior as random. Our results suggest that difference-in-means statistics significantly overstate the expected longevity loss from various patterns of lifetime smoking. For comparison, the (biased) unconditional difference-in-means in age of death between lifelong smokers and nonsmokers is 9.3 years in our research sample, while simulations from our estimated dynamic model suggest the difference is only 4.3 years. Additionally, our results examine the importance of smoking cessation and relapse avoidance.

Journal ArticleDOI
Ming Gao1
TL;DR: This paper developed a general model for mixed two-sided markets and showed that a monopolist platform's incentive to bundle and its optimal pricing strategy are determined by simple formulas using familiar price elasticities of demand, which embody the bundling effect, and price-cost margins adjusted for network externalities.
Abstract: When a consumer can appear on both sides of a two‐sided market, such as a user who both buys and sells on eBay, the platform may want to bundle the services it provides to two sides. I develop a general model for such “mixed” two‐sided markets and show that a monopolist platform's incentive to bundle and its optimal pricing strategy are determined by simple formulas using familiar price elasticities of demand, which embody the bundling effect, and price‐cost margins adjusted for network externalities, which incorporate “two‐sidedness.” The optimal pricing rule in such markets generalizes the familiar Lerner formula.

Journal ArticleDOI
TL;DR: In this article, the authors explored the relationship between competitiveness and stress and found that more competitive subjects exhibit higher stress responses than their less competitive counterparts in the computation tasks under both tournament and piece rate.
Abstract: This study explores the relationship between competitiveness and stress. In Experiment 1, we observe a higher response of cortisol—the primary stress hormone—to the computation task coupled with tournament than to the computation task with piece rate. Moreover, more competitive subjects exhibit higher stress responses than their less competitive counterparts in the computation tasks under both tournament and piece rate. In Experiment 2, we find that exogenously induced stress does not significantly affect competitiveness. Overall, our findings reveal an important trade‐off between tournament and piece rate in terms of stress response with implications on the design of incentive contracts.

Journal ArticleDOI
TL;DR: In this paper, a Bayesian SVAR analysis is used to show that an increase in government purchases raises private consumption, the real wage and total factor productivity (TFP) while reducing inflation, which is hard to reconcile with both neoclassical and New-Keynesian models.
Abstract: Using a Bayesian SVAR analysis, we document that an increase in government purchases raises private consumption, the real wage and total factor productivity (TFP) while reducing inflation. Each of these facts is hard to reconcile with both neoclassical and New-Keynesian models. We extend a standard New-Keynesian model to allow for skill accumulation through past work experience, following Chang, Gomes and Schorfheide (2002). An increase in government spending increases hours and induces skill accumulation and higher measured TFP and real wages in subsequent periods. Future marginal costs fall lowering future expected inflation and, through the monetary policy rule, the real interest rate. Consumption increases as a result.

Journal ArticleDOI
TL;DR: This paper developed a dynamic rational expectations general equilibrium framework that links house value to fundamental economic variables such as income growth, demographics, migration, and land supply, and applied the framework to Beijing, finding that the equilibrium house price and rent under reasonable parameterizations of the model are substantially lower than the data.
Abstract: This article develops a dynamic rational expectations general equilibrium framework that links house value to fundamental economic variables such as income growth, demographics, migration, and land supply. Our framework handles nonstationary dynamics as well as structural changes in fundamentals that are commonplace in transition economies. Applying the framework to Beijing, we find that the equilibrium house price and rent under reasonable parameterizations of the model are substantially lower than the data. We explore potential explanations for the discrepancies between the model and the data.

Journal ArticleDOI
TL;DR: In this paper, the authors studied the transmission of possibly false information by rational agents who seek the truth, and showed how a social network can serve as a filter, where the messages that circulate may be incorrect but sufficiently informative as to the correct decision.
Abstract: Why do people spread rumors? This paper studies the transmission of possibly false information---by rational agents who seek the truth. Unbiased agents earn payoffs when a collective decision is correct in that it matches the true state of the world, which is initially unknown. One agent learns the underlying state and chooses whether to send a true or false message to her friends and neighbors who then decide whether or not to transmit it further. The papers hows how a social network can serve as a filter. Agents block messages from parts of the network that contain many biased agents; the messages that circulate may be incorrect but sufficiently informative as to the correct decision.

Journal ArticleDOI
TL;DR: This article investigated the extent to which religions'supposed pronatalism is detrimental to growth via the fertility/education channel using censuses from South-East Asia, and they first estimate an empirical model of fertility and show that having a religious affiliation significantly raises fertility.
Abstract: Through indirect inference, we investigate the extent to which religions’supposed pronatalism is detrimental to growth via the fertility/education channel. Using censuses from South-East Asia, we first estimate an empirical model of fertility and show that having a religious affiliation significantly raises fertility. This effect is stronger for couples with intermediate to high education levels. We next use these estimates to identify the parameters of a structural model of fertility choice. On average, Catholicism is the most pro-child religion (increasing spending on children), followed by Buddhism, while Islam has a strong pro-birth component (redirecting spending from quality to quantity). We show that pro-child religions depress growth in the early stages by lowering saving, physical capital, and labor supply. These effects account for 10% to 50% of the actual growth gaps between countries over 1950-1980. At later stages of growth, pro-birth religions lower human capital accumulation, explaining between 10% and 20% of the gap between Muslim and Buddhist countries over 1980-2010.

Journal ArticleDOI
TL;DR: In this paper, the authors present and estimate a model of the transfer and renewal of patents that, under some assumptions, allows them to quantify the gains resulting from the transfer of patents.
Abstract: The “market for patents”—the sale of patents—is an often discussed source of incentives to invest in R&D. This article presents and estimates a model of the transfer and renewal of patents that, under some assumptions, allows me to quantify the gains resulting from the transfer of patents. The gains from trade measure the private benefits of reallocating the ownership of a patent from the original patentee to a new owner for whom the patent has a higher value. In addition, I study the effect that lowering transaction costs has on the proportion of patents traded and the gains from trade.

Journal ArticleDOI
TL;DR: In this article, the authors develop a model of patent trolls to understand various litigation strategies employed by nonpracticing entities and discuss policy implications including legal fee shifting and the use of injunctive relief.
Abstract: This article develops a model of patent trolls to understand various litigation strategies employed by nonpracticing entities (NPEs). When an NPE faces multiple potential infringers who use related technologies, it can gain a credible threat to litigate even when it has no such credibility vis-a-vis any single potential infringer in isolation. This is due to an information externality generated by an early litigation outcome for subsequent litigation. Successful litigation creates an option value against future potential infringers through Bayesian updating. We discuss policy implications including legal fee shifting and the use of injunctive relief.

Journal ArticleDOI
TL;DR: In this paper, instead of giving all the trading power to those students with the highest priority for a school, the authors argue for the distribution of the trading rights of all slots of each school: This allows them to trade in a thick market where additional constraints can be accommodated by choosing an appropriate pointing rule.
Abstract: A particular adaptation of Gale's top trading cycles (TTC) procedure applied to school choice, the so‐called TTC mechanism, has attracted much attention both in theory and practice due to its superior efficiency and incentive features. We discuss and introduce alternative adaptations of Gale's original procedure that can offer improvements over TTC in terms of equity, along with various other distributional considerations. Instead of giving all the trading power to those students with the highest priority for a school, we argue for the distribution of the trading rights of all slots of each school: This allows them to trade in a thick market where additional constraints can be accommodated by choosing an appropriate pointing rule. We propose a particular mechanism of this kind, the equitable top trading cycle (ETTC) mechanism, which is also Pareto efficient and group strategy‐proof just like TTC and eliminates avoidable justified envy situations. ETTC generates significantly fewer justified envy situations than TTC both in simulations and the lab.

Journal ArticleDOI
TL;DR: The authors determined that exchange rate returns are driven by a two-factor model, i.e., a dollar factor and a euro factor, and that exchange rates are thus driven by global, U.S., and eurozone stochastic discount factors.
Abstract: Using recently developed model selection procedures, we determine that exchange rate returns are driven by a two‐factor model. We identify them as a dollar factor and a euro factor. Exchange rates are thus driven by global, U.S., and euro‐zone stochastic discount factors. The identified factors can also be given a risk‐based interpretation. Identification motivates multilateral models for bilateral exchange rates. Out‐of‐sample forecast accuracy of empirically identified multilateral models dominates the random walk and a bilateral purchasing power parity fundamentals prediction model. Twenty‐four‐month‐ahead forecast accuracy of the multilateral model dominates those of a principal components forecasting model.

Journal ArticleDOI
TL;DR: A theory of pruning and formulas for pruning of any order is provided and it is related to results described by Judd (1998) on perturbing dynamical systems.
Abstract: Often, numerical simulations for dynamic, stochastic models in economics are needed. Kim et al. (Journal of Economic Dynamics and Control 32 2008, 3397–414) proposed “pruning” to deal with the challenge of generating explosive paths when employing second‐order approximations. In this article, we provide a theory of pruning and formulas for pruning of any order. Our approach builds on Judd's Numerical Methods in Economics (1998), chapter 13. We provide a comparison to existing methods.