Research Articles
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Regime-Switching Models and Recent Work
- A Trade-off Between Monetary Policy Transmission and Systemic Risk (Journal of Monetary Economics, Forthcoming; NBER Working Paper 34056, 2025)
By Kaiji Chen, Yiqing Xiao, and Tao Zha
Abstract: We study how interbank funding links monetary policy transmission to systemic risk in a banking system with heterogeneous access to deposit funding. Using bank-level data from China, we show that monetary policy easing reallocates liquidity through the interbank market: large banks raise household demand deposits and lend in the interbank market, while small banks expand loans through interbank borrowing. During economic downturns, greater reliance on interbank funding is associated with higher systemic risk. To interpret these facts, we build a structural model with deposit-rich and deposit-poor banks and interbank rollover risk. The model shows that monetary policy easing reallocates liquidity and boosts lending, but also raises run risk. It reveals a macroprudential trade-off: a regulatory limit on interbank funding weakens monetary policy transmission but reduces systemic risk.
Note: A non-technical article published by ChinaVox appears in this column. - Algorithm-Driven SVARs: Navigating the Wilderness of Big Data (NBER Working Paper 35604, 2026 (August); Paper on arXiv)
By Yucheng Yang and Tao Zha
Abstract: Every SVAR result is conditional on two choices: the restrictions that identify the shock and the variables on which they operate. The literature disciplines the first; the second is chosen by hand. We develop a Bayesian methodology that constructs information sets, uses an out-of-sample criterion, and retains the largest system it admits. Under recursive identification, output rises with housing production rather than household credit alone. For monetary policy, an anchor-free joint Bayesian proxy SVAR with multiple instruments strengthens the credit spread channel. A core system augmented with the selected corporate spread identifies expected default risk as a potent transmission margin. - Sharpening Economic Interpretation with HARS (NBER Working Paper 35483, 2026 (July))
By Dawis Kim and Tao Zha
Abstract: We develop a unified framework that combines shock volatility with sign and narrative restrictions and provides the theoretical foundation for the computationally efficient sampler HARS. HARS preserves the heteroskedastic likelihood and can be combined with any posterior simulator for the heteroskedastic model. In monetary policy, oil market, and fiscal policy models, the same restrictions deliver substantively different economics once shock heteroskedasticity is accounted for. Homoskedastic SVARs put uncertainty in the wrong place, pushing shock-scale variation into impulse-response uncertainty. Heteroskedasticity sharpens dynamic responses, alters economic conclusions, and restores 90% credible intervals as a practical standard for economic inference. - Does Fiscal Policy Matter for Stock-bond Return Correlation? (Journal of Monetary Economics, 2022 (May), 128, 20-34)
By Erica X.N. Li, Tao Zha, Ji Zhang, and Hao Zhou
Abstract: Switching between monetary and fiscal regimes is incorporated in a general-equilibrium model to explain three stylized facts: (1) a positive correlation of stock and bond returns in 1971–2001 and a negative correlation after 2001, (2) a negative correlation of consumption and inflation in 1971–2001 and a positive correlation after 2001, and (3) the coexistence of a positive bond risk premium and a negative correlation of stock and bond returns. While the technology shock drives the positive stock-bond and negative consumption-inflation correlations in the monetary regime, the investment shock drives the negative stock-bond and positive consumption-inflation correlations in the fiscal regime. - Four Stylized Facts About COVID-19 (International Economic Review, 2024, 65 (1), 3-42)
By Andrew G. Atkeson, Karen A. Kopecky, and Tao Zha
Abstract: We develop a Bayesian method for estimating the dynamics of COVID-19 deaths and uncover four key findings that highlight limitations in current structural epidemiological models. (i) Death growth rates declined rapidly from high levels during the initial 30 days of the epidemic worldwide. (ii) After this initial period, these rates fluctuated substantially around 0%. (iii) The cross-location standard deviation of death growth rates decreased sharply in the first 10 days but remained elevated afterward. (iv) These insights apply to both effective reproduction numbers and their cross-location variability as captured by epidemiological models. Our method is also applicable to the study of other epidemics. - Perturbation Methods for Markov-Switching DSGE Models (Quantitative Economics, 2016, 7, 637-669)
By Andrew Foerster, Juan Rubio-Ramirez, Daniel F. Waggoner, and Tao Zha
Abstract: Markov-switching DSGE (MSDSGE) modeling has become a growing body of literature on economic and policy issues related to structural shifts. This paper develops a general perturbation methodology for constructing high-order approximations to the solutions of MSDSGE models. Our new method, called “the partition perturbation method,” partitions the Markov-switching parameter space to keep a maximum number of time-varying parameters from perturbation. For this method to work in practice, we show how to reduce the potentially intractable problem of solving MSDSGE models to the manageable problem of solving a system of quadratic polynomial equations. This approach allows us to first obtain all the solutions and then determine how many of them are stable. We illustrate the tractability of our methodology through two revealing examples. - Sources of Macroeconomic Fluctuations: A Regime-switching DSGE Approach (Quantitative Economics, 2011, 2, 251-301)
By Zheng liu, Daniel F. Waggoner, and Tao Zha
Abstract: We examine the sources of macroeconomic economic fluctuations by estimating a variety of richly parameterized DSGE models within a unified framework that incorporates regime switching both in shock variances and in the inflation target. We propose an efficient methodology for estimating regime-switching DSGE models. Our counterfactual exercises show that changes in the inflation target are not the main driving force of high inflation in the 1970s. The model that best fits the U.S. time-series data is the one with synchronized shifts in shock variances across two regimes and the fit does not rely on strong nominal rigidities. We provide evidence that a shock to the capital depreciation rate, which resembles a financial shock, plays a crucial role in accounting for macroeconomic fluctuations. - Understanding Regime-Switching Rational Expectations Models (Journal of Economic Theory, 2009, 144, 1849-1867)
By Roger E. A. Farmer, Daniel F. Waggoner, and Tao Zha
Abstract: We develop a set of necessary and sufficient conditions for equilibria to be determinate in a class of forward-looking Markov-switching rational expectations models and we develop an algorithm to check these conditions in practice. We use three examples, based on the new-Keynesian model of monetary policy, to illustrate our technique. Our work connects applied econometric models of Markov-switching with forward looking rational expectations models and allows an applied researcher to construct the likelihood function for models in this class over a parameter space that includes a determinate region and an indeterminate region. - Were Regime Switches in US Monetary Policy? (American Economic Review, 2006, 96 (1), 54-81)
By Christopher A. Sims and Tao Zha
Abstract: A multivariate model, identifying monetary policy and allowing for simultaneity and regime switching in coefficients and variances, is confronted with US data since 1959. The best fit is with a version that allows time variation in structural disturbance variances only. Among versions that allow for changes in equation coefficients also, the best fit is for a one that allows coefficients to change only in the monetary policy rule. That version allows switching among three main regimes and one rarely and briefly occurring regime. The three main regimes correspond roughly to periods when most observers believe that monetary policy actually differed, but the differences among regimes are not large enough to account for the rise, then decline, in inflation of the 70’s and 80’s. In versions that insist on changes in the policy rule, the estimates imply monetary targeting was central in the early 80’s, but also important sporadically in the 70’s.
Financial Sectors and the Macroeconomy
- A Trade-off Between Monetary Policy Transmission and Systemic Risk (Journal of Monetary Economics, Forthcoming; NBER Working Paper 34056, 2025)
By Kaiji Chen, Yiqing Xiao, and Tao Zha
Abstract: We study how interbank funding links monetary policy transmission to systemic risk in a banking system with heterogeneous access to deposit funding. Using bank-level data from China, we show that monetary policy easing reallocates liquidity through the interbank market: large banks raise household demand deposits and lend in the interbank market, while small banks expand loans through interbank borrowing. During economic downturns, greater reliance on interbank funding is associated with higher systemic risk. To interpret these facts, we build a structural model with deposit-rich and deposit-poor banks and interbank rollover risk. The model shows that monetary policy easing reallocates liquidity and boosts lending, but also raises run risk. It reveals a macroprudential trade-off: a regulatory limit on interbank funding weakens monetary policy transmission but reduces systemic risk.
Note: A non-technical article published by ChinaVox appears in this column. - Atlanta Fed Conference in Honor of Christopher Sims, Nobel Laureate: A Celebration of a Lifetime of Scholarship
May 10–11, 2024
Summary: In May 2024, the Federal Reserve Bank of Atlanta hosted a two-day conference in honor of Christopher Sims, Nobel Laureate, organized by Eric Leeper and Tao Zha. The program brought together an extraordinary group of scholars and friends to celebrate Chris’s profound influence on economics, econometrics, and macroeconomics, with presentations by leading economists including Lars Peter Hansen, Thomas Sargent, and many others. Looking back, this gathering feels all the more meaningful as a chance to honor Chris Sims in person and to celebrate the intellectual generosity, friendship, and lasting legacy that shaped so many of us. - Monetary Stimulus Amidst the Infrastructure Investment Spree: Evidence from China’s Loan-Level Data (Journal of Finance, 2023, 78 (2), 1147-1204)
By Kaiji Chen, Haoyu Gao, Patrick C. Higgins, Daniel F. Waggoner, and Tao Zha
Abstract: We study how a fiscal expansion via infrastructure investment influences the dynamic impacts of monetary stimulus on credit allocation. We develop a two-stage approach and apply it to the Chinese economy using a confidential loan-level dataset that covers all sectors. We find that infrastructure investment significantly weakened the transmission of monetary policy to credit allocated to private firms while reinforcing its effects on loans to state-owned firms. This fiscal-monetary interaction channel is key to understanding the preferential credit access enjoyed by state-owned firms during the stimulus period. Consequently, monetary stimulus crowded out private investment and decreased capital allocation efficiency. - A Theory of Housing Demand Shocks (Journal of Economic Theory, 2022, 203, 1-32 (105484))
By Ding Dong, Zheng Liu, Pengfei Wang, and Tao Zha
Abstract: Housing demand shocks in standard macroeconomic models are a primary source of house price fluctuations, but these models struggle to generate the observed large volatility of house prices relative to rents. We provide a microeconomic foundation for reduced-form housing demand shocks using a tractable heterogeneous-agent framework. In our model with heterogeneous beliefs, an expansion of credit supply raises the housing demand of optimistic buyers and boosts house prices without affecting rents. A credit supply shock also leads to a positive correlation between house trading volumes and house prices. The theoretical mechanism and model predictions are supported by empirical evidence, and the results are robust to alternative specifications of heterogeneity. - Discount Shock, Price–Rent Dynamics, and the Business Cycle (International Economic Review, 2020, 61 (3), 1229-1252)
By Jianjun Miao, Pengfei Wang, and Tao Zha
Abstract: The price-rent ratio in commercial real estate is highly volatile, and its variation comoves with the business cycle. To account for these facts, we develop a dynamic general equilibrium model that introduces a rental market and incorporates a liquidity constraint on individual firms’ production as a key element. Our estimation identifies the discount shock as the most important factor driving price-rent dynamics and linking developments in the real estate market to those in the broader economy. We illustrate the importance of the liquidity premium and endogenous TFP in the nexus between the financial and real sectors. - The Nexus of Monetary Policy and Shadow Banking in China (American Economic Review, 2018, 108 (12), 3891-3936)
By Kaiji Chen, Jue Ren, and Tao Zha
Abstract: We study how monetary policy in China influences banks’ shadow banking activities. We develop and estimate an endogenously switching monetary policy rule that is based on institutional facts and is at the same time tractable in the spirit of Taylor (1993). This development, along with two newly constructed micro banking datasets, enables us to establish the following empirical evidence: contractionary monetary policy during 2009–2015 caused shadow banking loans to rise rapidly, offsetting the expected decline of traditional bank loans and hampering the effectiveness of monetary policy on total bank credit. We advance a theoretical explanation of our empirical findings.
Note: A non-technical summary published by VoxEU appears in this column. - Land Prices and Unemployment (Journal of Monetary Economics, 2016 (June), 80, 86-105)
By Zheng Liu, Jianjun Miao, and Tao Zha
Abstract: We integrate the housing market and the labor market in a dynamic general equilibrium model with credit and search frictions. We argue that the labor channel, combined with the standard credit channel, provides a strong transmission mechanism that can deliver a potential solution to the Shimer (2005) puzzle. The model is confronted with U.S. macroeconomic time series. The estimation results account for two prominent facts observed in the data. First, land prices and unemployment move in opposite directions over the business cycle. Second, a shock that moves land prices also generates the observed large volatility of unemployment. - Land-Price Dynamics and Macroeconomic Fluctuations (Econometrica, 2013, 81 (3), 1147-1184)
By Zheng liu, Pengfei Wang, and Tao Zha
Abstract: We argue that positive co-movements between land prices and business investment are a driving force behind the broad impact of land-price dynamics on the macroeconomy. We develop an economic mechanism that captures the co-movements by incorporating two key features into a DSGE model: We introduce land as a collateral asset in firms’ credit constraints and we identify a shock that drives most of the observed fluctuations in land prices. Our estimates imply that these two features combine to generate an empirically important mechanism that amplifies and propagates macroeconomic fluctuations through the joint dynamics of land prices and business investment. - Identifying Monetary Policy in a Small Open Economy Under Flexible Exchange Rates (Journal of Monetary Economics, 1997, 39, 433-448)
By David O. Cushman and Tao Zha
Abstract: Previous empirical studies on the effects of monetary policy shocks in small open economies have generated puzzling dynamic responses in various macroeconomic variables. This paper argues that these puzzles arise from an identification of monetary policy that is inappropriate for such economies. To address this, it is proposed that a structural model be estimated to explicitly account for the features of a small open economy. Such a model is applied to Canada, yielding tightly estimated results overall. The dynamic responses to the identified monetary policy shock are consistent with standard theory and highlight the exchange rate as a transmission mechanism.
Development and the Chinese Economy
- A Trade-off Between Monetary Policy Transmission and Systemic Risk (Journal of Monetary Economics, Forthcoming; NBER Working Paper 34056, 2025)
By Kaiji Chen, Yiqing Xiao, and Tao Zha
Abstract: We study how interbank funding links monetary policy transmission to systemic risk in a banking system with heterogeneous access to deposit funding. Using bank-level data from China, we show that monetary policy easing reallocates liquidity through the interbank market: large banks raise household demand deposits and lend in the interbank market, while small banks expand loans through interbank borrowing. During economic downturns, greater reliance on interbank funding is associated with higher systemic risk. To interpret these facts, we build a structural model with deposit-rich and deposit-poor banks and interbank rollover risk. The model shows that monetary policy easing reallocates liquidity and boosts lending, but also raises run risk. It reveals a macroprudential trade-off: a regulatory limit on interbank funding weakens monetary policy transmission but reduces systemic risk.
Note: A non-technical article published by ChinaVox appears in this column. - Deposit Regulation and Monetary Transmission in China (NBER Working Paper 31396, 2025)
By Kaiji Chen, Yiqing Xiao, and Tao Zha
Abstract: In well-developed financial markets, retail deposits and wholesale funding comove negatively in response to monetary policy changes. This negative comovement weakens the transmission of monetary policy. By contrast, our study finds that in emerging markets such as China, where deposit rate ceilings are regulated, (i) retail deposits and wholesale funding comove positively as the policy rate changes, and (ii) wholesale funding strengthens the transmission of monetary policy to bank lending. We develop a theoretical model that highlights the significant influence of deposit regulation on monetary policy transmission in the context of the world’s largest emerging market economy. - Aggregate and Distributional Impacts of LTV Policy in China (Quantitative Economics, Forthcoming, 2025; NBER Working Paper 28092, 2025)
By Kaiji Chen, Qing Wang, Tong Xu, and Tao Zha
Abstract: We study how China’s loan-to-value (LTV) policy affects mortgage markets and household consumption, focusing on an abrupt and unprecedented relaxation in LTV limits for secondary houses from 2014Q4 to 2016Q3. Using a rich dataset of over three million loan-level records from a major Chinese commercial bank, supplemented by survey data on urban household finances, we analyze how this policy shift influenced mortgage demand, house prices, and consumption across household groups and at the aggregate level. We find that this LTV relaxation, aimed at promoting housing investments, spurred a mortgage boom, especially in primary home mortgages, while crowding out household consumption among middle-aged, high-education households. Motivated by these findings, we develop and calibrate a dynamic equilibrium model that distinguishes between primary homes for housing services and secondary houses for investment. When the LTV limit for secondary houses is relaxed, demand for these properties surges, increasing house prices and capital gains. Unlike prior literature, we identify a housing investment channel in which these capital gains enable existing homeowners—particularly middle-aged and high-income households—to upsize their primary residences. Rising house prices then drive further demand and mortgage borrowing, amplifying the effects of the LTV policy change and reducing these households’ non-housing consumption. - China’s Macroeconomic Development: The Role of Gradualist Reforms (Journal of Economic Literature, 2025)
By Kaiji Chen and Tao Zha
Abstract: This paper provides analytic guides to recent literature on China’s macroeconomic development, emphasizing the critical role of the gradualist reform approach. Our analysis suggests that from 1978 to 1997, the gradualist approach contributed to China’s aggregate total factor productivity and economic growth primarily through policies that facilitated the reallocation of surplus labor from agriculture to non-agricultural sectors. Since 1998, the government’s focus shifted, with various reforms encouraging large enterprises, whether state-owned or privately-owned, to enter capital-intensive sectors, making capital deepening the main driver of economic growth. While this strategy sustained China’s GDP growth, it also increased trade tensions with global partners, created barriers to transitioning to a consumption-led economy, and threatened China’s long-term financial stability, casting long shadows over the Chinese economy. - Constructing Quarterly Chinese Time Series Usable for Macroeconomic Analysis (Journal of International Money and Finance, 2024, 143, 1-18 (103052))
By Kaiji Chen, Patrick C. Higgins, and Tao Zha
Abstract: During episodes such as the global financial crisis and the COVID-19 pandemic, China experienced notable fluctuations in GDP growth and key expenditure components. To explore the primary sources of these fluctuations, we construct a comprehensive dataset of GDP and its components in both nominal and real terms at a quarterly frequency. Applying two SVAR models to this dataset, we uncover the principal drivers of China’s economic fluctuations across different episodes. In particular, our findings reveal the stark and enduring impacts of consumption-constrained shocks on GDP and all of its components—especially household consumption—both during and in the aftermath of the COVID-19 pandemic. - The Challenging Transition from Investment- to Consumption-Led Growth in China (NBER Reporter, 2024 (July), 24-27)
By Tao Zha
Abstract: This article analyzes the evolution of China’s growth model, highlighting the country’s shift from productivity-led to investment-driven growth and the mounting challenges in transitioning toward a consumption-based economy. The study attributes China’s rapid expansion after 1998 largely to preferential credit policies and pro-growth monetary policy that favored capital-intensive sectors, particularly through state-owned enterprises. These policies led to rising investment and real estate booms, often at the cost of household consumption and private sector vitality. It illustrates how expansionary policies, such as relaxed mortgage regulations, triggered speculative housing cycles, contributing to inequality and financial risk. With consumption remaining sluggish despite policy efforts, and the COVID-19 pandemic introducing persistent “consumption-constrained shocks,” the article underscores the fragility of China’s current growth model and the need for structural reforms to foster sustainable, consumption-led development. - Macroeconomic Effects of China’s Financial Policies (Handbook of China’s Financial System, 2020 (Chapter 6), 151-182, Princeton University Press)
By Kaiji Chen and Tao Zha
Abstract: The Chinese economy has undergone three major phases: the 1978-1997 period marked as the SOE-led economy, the 1998-2015 phase as the investment-driven economy, and the new normal economy since 2016. All three economies have been shaped by the government’s financial policies, defined as a set of credit policy, monetary policy, and regulatory policy. We analyze the macroeconomic effects of these financial policies throughout the three phases and provide the stylized facts to substantiate our analysis. The stylized facts differ qualitatively across different phases or economies. We argue that the impacts of China’s financial policies work through transmission channels different from those in developed economies and that a regime switch from one economy to another was driven mainly by regime changes in financial policies. - Forecasting China’s Economic Growth and Inflation (China Economic Review, 2016, 41, 46-61)
By Patrick C. Higgins, Tao Zha, and Karen Zhong
Abstract: Although macroeconomic forecasting forms an integral part of the policymaking process, there has been a serious lack of rigorous and systematic research in the evaluation of out-of-sample model-based forecasts of China’s real GDP growth and CPI inflation. This paper fills this research gap by providing a replicable forecasting model that beats a host of other competing models when measured by root mean square errors, especially over long-run forecast horizons. The model is shown to be capable of predicting turning points and to be usable for policy analysis under different scenarios. It predicts that China’s future GDP growth will be of L-shape rather than U-shape. - Trends and Cycles in China’s Macroeconomytrends and Cycles in China’s Macroeconomy (NBER Macroeconomics Annual, 2016, 30, 1-84)
By Chun Chang, Kaiji Chen, Daniel F. Waggoner, and Tao Zha
Abstract: We make four contributions in this paper. First, we provide a core set of macroeconomic time series usable for systematic research on China. Second, we document, through various empirical methods, robust findings about striking patterns of trend and cycle. Third, we build a theoretical model that accounts for these facts. Fourth, the model’s mechanisms and assumptions are corroborated by institutional details, disaggregated data, and banking time series, all of which are distinctive of Chinese characteristics. We argue that preferential credit policy for promoting heavy industries accounts for the unusual cyclical patterns as well as the post-1990s economic transition, characterized by a persistently rising investment rate, a declining labor income share, and a growing foreign surplus. The departure of our theoretical model from standard ones offers a constructive framework for studying China’s modern macroeconomy.
Note: A non-technical description of this paper, published by VoxEU.org (CEPR’s policy portal), appears in this column. - China’s Growth Prospects: Discussion of Loren Brandt’s Paper (The 2015 Asia Economic Policy Conference (AEPC) Series on Policy Challenges in a Diverging Global Economy, 2015 (November 19–20), Federal Reserve Bank of San Francisco)
By Tao Zha
Abstract: This commentary on Loren Brandt’s firm-level analysis of China’s productivity argues that, while China’s past growth has been driven by massive investment—particularly in heavy industry—it has come at the expense of consumption and has been sustained by policies favoring large, often inefficient firms over more dynamic private enterprises. This imbalance is largely the result of deliberate credit policies and institutional priorities, rather than genuine productivity improvements. The commentary emphasizes the need for financial reforms—especially those aimed at redirecting capital flows toward more productive uses—as essential for achieving sustainable, long-term growth, even if such reforms entail short-term economic pain.
Econometric Theory and Application
- Algorithm-Driven SVARs: Navigating the Wilderness of Big Data (NBER Working Paper 35604, 2026 (August); Paper on arXiv)
By Yucheng Yang and Tao Zha
Abstract: Every SVAR result is conditional on two choices: the restrictions that identify the shock and the variables on which they operate. The literature disciplines the first; the second is chosen by hand. We develop a Bayesian methodology that constructs information sets, uses an out-of-sample criterion, and retains the largest system it admits. Under recursive identification, output rises with housing production rather than household credit alone. For monetary policy, an anchor-free joint Bayesian proxy SVAR with multiple instruments strengthens the credit spread channel. A core system augmented with the selected corporate spread identifies expected default risk as a potent transmission margin. - Sharpening Economic Interpretation with HARS (NBER Working Paper 35483, 2026 (July))
By Dawis Kim and Tao Zha
Abstract: We develop a unified framework that combines shock volatility with sign and narrative restrictions and provides the theoretical foundation for the computationally efficient sampler HARS. HARS preserves the heteroskedastic likelihood and can be combined with any posterior simulator for the heteroskedastic model. In monetary policy, oil market, and fiscal policy models, the same restrictions deliver substantively different economics once shock heteroskedasticity is accounted for. Homoskedastic SVARs put uncertainty in the wrong place, pushing shock-scale variation into impulse-response uncertainty. Heteroskedasticity sharpens dynamic responses, alters economic conclusions, and restores 90% credible intervals as a practical standard for economic inference. - January 2026 IMF Mission Teaching Materials:
(a) Likelihood -> Bayes bridge: a two-variable illustration
(b) Intuitive explanation of the Kalman filter
(c) Summary and recap of all the DSGE lectures - Structural Vector Autoregressions: Theory of Identification and Algorithms for Inference (Review of Economic Studies, 2010, 77 (2), 665-696)
By Juan Rubio-Ramirez, Daniel F. Waggoner, and Tao Zha
Abstract: SVARs are widely used for policy analysis and to provide stylized facts for dynamic general equilibrium models. Yet there have been no workable rank conditions to ascertain whether an SVAR is globally identified. When identifying restrictions, such as long-run restrictions, are imposed on impulse responses, there have been no efficient algorithms for small-sample estimation and inference. To fill these important gaps in the literature, this paper makes four contributions. First, we establish general rank conditions for global identification of both overidentified and exactly identified models. Second, we show that these conditions can be checked as a simple matrix-filling exercise and that they apply to a wide class of identifying restrictions, including linear and certain nonlinear restrictions. Third, we establish a very simple rank condition for exactly identified models that amounts to a straightforward counting exercise. Fourth, we develop a number of efficient algorithms for small-sample estimation and inference, especially for SVARs with sign and nonlinear restrictions. - Methods for Inference in Large Multiple-equation Markov-switching Models (Journal of Econometrics, 2008, 146 (2), 255-274)
By Christopher A. Sims, Daniel F. Waggoner, and Tao Zha
Abstract: Inference for hidden Markov chain models in which the structure is a multiple-equation macroeconomic model raises a number of difficulties that are not as likely to appear in smaller models. One is likely to want to allow for many regimes in the Markov chain, without allowing the number of free parameters in the transition matrix to grow as the square as the number of regimes, but also without losing a convenient form for the posterior distribution of the transition matrix. Calculation of marginal data densities for assessing model fit is often difficult in high-dimensional models, and seems particularly difficult in these models. This paper gives a detailed explanation of methods for maximizing posterior density and initiating MCMC simulations that provide some robustness against the complex shape of the likelihood in these models. These difficulties and remedies are likely to be useful generally for Bayesian inference in large time series models. - A Gibbs Sampler for Structural Vector Autoregressions (Journal of Economic Dynamics & Control, 2003, 28, 349–366)
By Daniel F. Waggoner and Tao Zha
Structural VAR modeling has played an important role in empirical macroeconomics. The importance sampler used in the existing literature, however, can be prohibitively inefficient for obtaining accurate finite-sample inferences. In this paper, we develop a Gibbs sampler for Bayesian inference of structural VARs that restrict the covariance matrix of reduced-form residuals. Our method is computationally efficient compared to the existing method and can be readily applied. We show, by example, that inferences based on the importance sampler can seriously distort economic interpretations. - Conditional Forecasts in Dynamic Multivariate Models (Review of Economics and Statistics, 1999, 81 (4), 639-651)
By Daniel F. Waggoner and Tao Zha
Abstract: In the existing literature, conditional forecasts in the vector autoregressive (VAR) framework have not been commonly presented with probability distributions (densities). This paper develops Bayesian methods for computing the exact finite-sample distribution of conditional forecasts. It broadens the class of conditional forecasts to which the methods can be applied. The methods work for both structural and reduced-form VAR models and, in contrast to common practices, account for parameter uncertainty in finite samples. Empirical examples under both a flat prior and a reference prior are provided to show the use of these methods. - Block Recursion and Structural Vector Autoregressions (Journal of Econometrics, 1999, 90,291-316)
By Tao Zha
Abstract: In applications of structural VAR modeling, finite-sample properties may be difficult to obtain when certain identifying restrictions are imposed on lagged relationships. As a result, even though imposing some lagged restrictions makes economic sense, lagged relationships are often left unrestricted to make statistical inference more convenient. This paper develops block Monte Carlo methods to obtain both maximum likelihood estimates and exact Bayesian inference when certain types of restrictions are imposed on the lag structure. These methods are applied to two examples to illustrate the importance of imposing restrictions on lagged relationships. - Bayesian Methods for Dynamic Multivariate Models (International Economic Review, 1998, 39 (4), 949-968)
By Christopher A. Sims and Tao Zha
Abstract: If dynamic multivariate models are to be used to guide decision-making, it is important that probability assessments of forecasts or policy projections be provided. When identified Bayesian vector autoregression (VAR) models are presented with error bands in the existing literature, both conceptual and numerical problems have not been addressed in an internally consistent way. In this paper, we develop methods to introduce prior information into both reduced-form and structural VAR models without introducing substantial new computational burdens. Our approach makes it feasible to use a single, large dynamic framework (for example, 20-variable models) for policy projection tasks.
Learning and Escape Dynamics
- Policy Contagion: What Do We Learn from Financial Reforms? (International Economic Review, Forthcoming, 2025)
By Nan Li, Chris Papageorgiou, Tong Xu, and Tao Zha
Abstract: We use financial reforms as a case study to understand the temporal clustering of policy changes across countries, shedding light on the broader phenomenon of global policy contagion. We constructed a comprehensive database of domestic financial reforms spanning 90 countries from 1973 to 2014. Using this dataset, we estimate a semi-structural model that incorporates key factors identified in the literature. We find that (1) geopolitical influence and cross-country learning drove the global surge in reforms during the 1990s, and (2) reversals of financial reforms in developing countries after the global financial crisis reflected shifting beliefs about their growth effects. - The Conquest of South American Inflation (Journal of Political Economy, 2009, 117 (2), 211-256)
By Thomas Sargent, Noah Williams, and Tao Zha
Abstract: We infer determinants of Latin American hyperinflations and stabilizations by using the method of maximum likelihood to estimate a hidden Markov model that potentially assigns roles both to fundamentals in the form of government deficits that are financed by money creation and to destabilizing expectations dynamics that can occasionally divorce inflation from fundamentals. Our maximum likelihood estimates allow us to interpret observed inflation rates in terms of variations in the deficits, sequences of shocks that trigger temporary episodes of expectations driven hyperinflations, and occasional superficial reforms that cut inflation without reforming deficits. Our estimates also allow us to infer the deficit adjustments that seem to have permanently stabilized inflation processes. - Learning, Adaptive Expectations, and Technology Shocks (Economic Journal, 2009, 119 (536), 377-405)
By Kevin Huang, Zheng Liu, and Tao Zha
Abstract: When rational expectations are replaced by adaptive expectations, we prove that the self-confirming equilibrium is the same as the steady state rational expectations equilibrium, but that dynamics around the steady state are substantially different between the two equilibria. We show that, in contrast to Williams(2003), the differences are driven mainly by the lack of the wealth effect and the strengthening of the intertemporal substitution effect, not by escapes. As a result, adaptive expectations substantially alter the amplification and propagation mechanisms and allow technology shocks to exert much more impact on macroeconomic variables than do rational expectations. - Shocks and Government Beliefs: the Rise and Fall of American Inflation (American Economic Review, 2006, 96 (4), 1193-1224)
By Thomas Sargent, Noah Williams, and Tao Zha
Abstract: We use a Bayesian Markov Chain Monte Carlo algorithm jointly to estimate the parameters of a `true’ data generating mechanism and those of a sequence of approximating models that a monetary authority uses to guide its decisions. Gaps between a true expectational Phillips curve and the monetary authority’s approximating non-expectational Phillips curve models unleash inflation that a monetary authority that knows the true model would avoid. A sequence of dynamic programming problems implies that the monetary authority’s inflation target evolves as its estimated Phillips curve moves. Our estimates attribute the rise and fall of post WWII inflation in the US to an intricate interaction between the monetary authority’s beliefs and economic shocks. Shocks in the 1970s made the monetary authority perceive a tradeoff between inflation and unemployment that ignited big inflation. The monetary authority’s beliefs about the Phillips curve changed in ways that account for Volcker’s conquest of US inflation. - Modest Policy Interventions (Journal of Monetary Economics, 2003, 50 (8), 1673-1700)
By Eric M. Leeper and Tao Zha
Abstract: We present a theoretical and empirical framework for computing and evaluating linear projections conditional on hypothetical paths of monetary policy. A modest policy intervention does not significantly shift agents’ beliefs about policy regime and does not induce the changes in behavior that Lucas (1976) emphasizes. Applied to an econometric model of U.S. monetary policy, we find that a rich class of interventions routinely considered by the Federal Reserve is modest and their impacts can be reliably forecasted by an identified linear model. Modest interventions can shift projected paths and probability distributions of macro variables in economically meaningful ways.