This paper proposes a new framework for determining whether a given relationship is nonlinear, what the nonlinearity looks like, and whether it is adequately described by a particular parametric model. The paper studies a regression or forecasting model of the form yt = µ(xt) + et where the functional form of µ(.) is unknown. We propose viewing µ(.) itself as the outcome of a random process. The paper introduces a new stationary random random field m(.) that generalizes finite-differenced Brownian motion to a vector field and whose realizations could represent a broad class of possible forms for µ(.). We view the parameters that characterize the relation between a given realization of m(.) and the particular value of µ(.) for a given sample as population parameters to be estimated by maximum likelihood or Bayesian methods. We show that the resulting inference about the functional relation also yields consistent estimates for a broad class of deterministic functions µ(.). The paper further develops a new test of the null hypothesis of linearity based on the Lagrange multiplier principle and small-sample confidence intervals based on numerical Bayesian methods. An empirical application suggests that properly accounting for the nonlinearity of the inflation-unemployment tradeoff may explain the previously reported uneven empirical success of the Phillips Curve.

Chapter 1 suggests an efficient and simple regression-based approach for consistent estimation of dynamic effects of structural shocks in vector autoregressions (VAR) with proxy variables for the shocks. First, we show that the existing Proxy Structural VAR (Proxy-SVAR) approach using the proxy as an instrument variable yields a consistent estimator of the shape of the impulse-response function (IRF) if and only if the proxy does not have any direct forecasting ability in the VAR. Second, we prove that in the linear model, the shape of the IRF can be consistently estimated by adding the current and past values of the proxy variable in the VAR regardless of its direct forecasting ability or measurement error. Third, we show both theoretically and empirically that the formulation in Gertler and Karadi (2015) misestimates the effect of a monetary policy shock. Applying our unrestricted approach to GK's specification results in a substantially different conclusion from the Proxy-SVAR.

In Chapter 2, We build a Markov-switching structural VAR to estimate state-dependent government spending multipliers in the U.S. We show that the multipliers are statistically larger during recessions than during expansions. Our model has two features. First, we combine quantitative data and qualitative indicators to infer the regimes of the economy across which the multipliers differ. Second, we propose a recursive method to estimate IRFs that allows the economy to switch regimes after the shock. We argue that these two features are important for reconciling the main findings in previous studies.

Chapter 3 extends the Rosen-Roback spatial equilibrium model to show that increasing city-level college share affects welfare distribution by changing both wages and housing costs across individuals with different education levels. Using the PSID from 1980 to 2013, we confirm that high skilled workers gain greater benefits from living in cities with a rising college share, as the increase in their wage premiums outweighs their rent growth. However, earnings increase of the unskilled are completely offset by higher housing rents. In response influxes of college graduates, housing wealth also increases significantly more for college graduates, further widening the welfare gap.

This dissertation consists of three essays on monetary policy and asset prices.

The first chapter proposes a novel methodology to disentangle in real-time the signaling effect of a Fed announcement from exogenous monetary shocks. The method relies on the different ways monetary news and non-monetary news change the short end of the yield curve at high frequency, with the latter informed by market responses to macroeconomic data releases. The estimated revelation of Fed information is strongly correlated with the difference between market forecasts and the Fed’s own forecasts. The policy shock is found to have a bigger effect on the economy than suggested using an instrument without adjustment for the signaling effect.

The second chapter studies the structural forces driving the financial market responses to data releases and Fed announcements. I estimate a coherent, realistic framework that prices Treasury bonds based on macroeconomic fundamentals. The framework explicitly recognizes agents' information frictions in regard to contemporaneous aggregate outcomes, successfully matches the market responses to macroeconomic events and sheds light on the nature of news learned by investors at various events.

The third chapter proposes a state-space approach to decomposing a stock's idiosyncratic volatility into a common component and an idiosyncratic one. The measure of the common idiosyncratic volatility is persistent at the daily frequency. It accounts for idiosyncratic volatilities in sample better than GARCH(1,1) and a principal component approach. It also forecasts the future levels of idiosyncratic volatilities better than GARCH(1,1) in the medium- to long-run. I assess its pricing implication in the cross section of stock returns.

This dissertation aims to apply textual data into economic questions. In Chapter 1, I use politicians' tweets to examine the time-varying effects of political cheap talk on the foreign exchange market and on the stock market. I find that the markets buy the cheap talk stories only at the beginning. In Chapter 2, I design a measure of policy intention for China, and show two examples of the measure. It is found that the policy intention measure could forecast future economic variables. Chapter 3 includes a new measure of monetary shocks from Twitter data which is built with machine learning techniques Convolutional Neural Network. This measure uses the general public anticipation about the interest rate decisions of the Federal Reserve.

In my dissertation, I use cutting-edge time series econometric models to explore how the effects of government spending shocks change with the state of the economy, how to identify the effects of oil price changes induced by different reasons, and why oil price shocks seem to be much less important nowadays than decades ago.

Chapter 1 builds a Markov-switching structural VAR to estimate state-dependent government spending multipliers in the U.S. We show that the multipliers are statistically larger during recessions than during expansions, although smaller than 1 in both periods. Our model has two features. First, we combine quantitative data and qualitative indicators to infer the regimes of the economy across which the multipliers differ. Second, we propose a recursive method to estimate impulse response functions that allows the economy to switch regimes after the shock. We argue that these two features are important for reconciling the main findings in previous studies.

Chapter 2 estimates a standard structural VAR of the global oil market using both external and internal instrumental variables. I find that a negative oil supply shock leads to a delayed but significant decline in economic activity. Whereas oil consumption demand shocks do not have a significant effect on economic activity, a positive shock to oil inventory demand results in significant declines in oil production and economic activity at the same time. Furthermore, I show that oil price movements are mostly driven by shocks to oil consumption demand.

Chapter 3 revisits the evidence in Blanchard and Gali (2010) that the effects of oil price shocks have diminished since the mid-1980s. I show that the apparent instability in the oil price-macroeconomy relationship they find can be accounted for by the endogeneity of oil price changes and the lower energy share in consumption in recent decades. When these two factors are taken into account, the effects of oil price shocks on real economic activity appear to be stable over time. Nevertheless, the impact of oil prices on inflation has noticeably weakened over time.

Chapter 1 examines the effects of bank-driven terminations of bank-borrower relationships on the borrowers' investments by exploiting a matched dataset of Japanese banks and firms. I find that bank-driven terminations significantly decrease investment when the firms facing termination have difficulty in either establishing new relationships or increasing borrowings within their existing relationships. Such termination effects are larger than those due to credit reduction within continuing relationships and are more pronounced for smaller firms. Our findings coincide with previous literature emphasizing financial frictions in the matching process and the importance of relation-specific assets in credit markets.

Chapter 2 investigates the effects of unconventional monetary policy on bank lending, using a bank-firm matched dataset in Japan from 1999 to 2015 by disentangling conventional and unconventional monetary policy shocks employed by the Bank of Japan over the past 15 years. I find that a rise in the share of the unconventional assets held by the Bank of Japan boosts lending to firms with a lower distance-to-default ratio from banks with a lower liquid assets ratio and higher risk appetite. In contrast to the composition shock, the monetary base shock of increasing the Bank of Japan's balance sheet size does not have heterogeneous effects on bank lending. Furthermore, we find that interest rate cuts stimulate lending to risky firms from banks with a higher leverage ratio.

Chapter 3 contributes to the debate about the the effect of bank loan supply shocks on real economy, using bank lending stance shocks derived from the industry-level Short-term Economic Survey of Enterprises (Tankan) survey data in Japan. The identified bank lending stance shocks enable us to investigate the effect of loan supply shocks on the real economy over the past 30 years in a consistent manner using a structural vector auto regressive model, thereby leading to three main conclusions. First, a negative bank loan supply shock, which means a tightening of banks' lending stance, significantly decreases real GDP growth rates.

However, loan supply shocks were not main driving factors for fluctuations of the real economy; the contribution of bank loan supply shocks to GDP is less than 10%.

Third, I find that the economy with a zero lower bound constraint is more vulnerable to an adverse loan supply shock compared to that without the constraint as predicted by existing theoretical models. In a zero lower bound environment, loan supply shocks contribute to approximately 10% of the GDP fluctuations.

In the first chapter, I propose a tractable model of the labor share that emphasizes the

interaction between labor market imperfections and productivity dispersion. I bring the model to

the data using an administrative dataset covering the universe of firms in Canada. As in the data,

most firms have a high labor share, yet the aggregate labor share is low due to the disproportionate

effect of a small fraction of large, extremely productive “superstar firms”. I find that a rise in the

dispersion of productivity across firms leads to a decline of the aggregate labor share in favor of

firm profit. The mechanism is that productivity dispersion effectively shields high-productivity

firms from wage competition. Reduced-form evidence from cross-country and cross-industry

data supports both the prediction and the mechanism. Through the lens of the model, rising productivity dispersion has caused the U.S. labor share to decline starting around 1990.

In the second chapter, we propose a new, systematic approach for analyzing and solving

heterogeneous-agent models with fat-tailed wealth distributions. Our approach exploits the

asymptotic linearity of policy functions and the analytical characterization of the Pareto exponent

to make the solution algorithm more transparent, efficient, and accurate with zero additional

computational cost. As an application, we solve a heterogeneous-agent model that features

persistent earnings and investment risk, borrowing constraint, portfolio decision, and endogenous

Pareto-tailed wealth distribution. We find that a wealth tax is a ”lose-lose” policy: the introduction

of a 1% wealth tax (with extra tax revenue used as consumption rebate) decreases wage by 6.5%,

welfare (in consumption equivalent) by 7.7%, and total tax revenue by 0.72%.

In the third chapter, I propose a model of earnings dynamics and inequality within the

firm. The model combines a production hierarchy with a “rank order tournament” promotion

scheme. I motivate the theory by documenting three sets of facts using proprietary personnel

data. First, most of inequality within the firm is between hierarchy levels rather than within.

Second, there is on average very little upward mobility within the firm. Third, there is important

heterogeneity in earnings trajectories. The model provides a positive theory of these facts and

sheds light on the determinants of inequality within the firm.

A recent paper by Bernanke, Gertler and Watson (1997) suggests that monetary policy could be used to eliminate any recessionary consequences of an oil price shock. This paper challenges that conclusion on two grounds. First, we question whether the Federal Reserve actually has the power to implement such a policy; for example, we consider it unlikely that additional money creation would have succeeded in reducing the Fed funds rate by 900 basis points relative to the values seen in 1974. Second, we point out that the size of the effect that Bernanke, Gertler and Watson attribute to oil shocks is substantially smaller than that reported by other researchers, primarily due to their choice of a shorter lag length than used by other researchers. We offer evidence in favor of the longer lag length employed by previous research, and show that, under this specification, even the aggressive Federal Reserve policies proposed would not have succeeded in averting a downturn.

This dissertation contains three essays exploring how macroeconomists can identify and estimate dynamic causal effects in models where researchers have doubts about identifying assumptions.

Chapter 1 proposes a new Markov Chain Monte Carlo algorithm to estimate a sign-restricted structural vector autoregression on time series that are subject to regime shifts. My approach can incorporate useful prior information about both model parameters and hidden states while transparently imposing sign restrictions. I illustrate my method by revisiting the literature on asymmetric effects of conventional monetary policy during recessions and expansions. My evidence suggests that previous empirical research found asymmetric effects by questionable identification schemes and neglecting changes in the variances of structural shocks. I find little difference in the structural parameters, and thus I do not find evidence of asymmetry.

Chapter 2 studies the method of instrumental variables in set-identified models. I develop a proxy structural vector autoregression in which prior information from both theory and the empirical literature is incorporated about signs and magnitudes of certain parameters and equilibrium impacts. I use my method to investigate the relevance and validity of three popular instruments for monetary policy shocks, developed by Romer and Romer (2004), Sims and Zha (2006), and Smets and Wouters (2007). I find that all of them are strongly relevant but only that of Smets and Wouters is valid. Furthermore, the empirical analysis demonstrates that my framework can combine information from a relevant and valid instrument with prior information about sign restrictions to improve inference about structural impulse-response functions.

Chapter 3 develops new methods to study dynamic causal effects in a data-rich environment. Current development in high-dimensional statistics fails to address the main interest of economists: causal inference with credible assumptions. I first review the literature on high-dimensional linear regression models and dynamic factor models. Then, I develop several new Bayesian numerical algorithms that combine the techniques in high-dimensional statistics with recent advances in dynamic causal inference. In particular, I discuss how to make causal statements from a high-dimensional structural model when researchers have doubts about identifying assumptions. Finally, I extend those algorithms to the case of Markov-switching models to accommodate nonlinearities in economic time series.

In the first two chapters of my dissertation, I study the pricing of risk in commodities futures and bond markets. In the first chapter, I provide a new way to characterize risk in commodities futures markets. I apply my framework to the natural gas futures market and study the consequences of changes in regime on the risk premium. In the second chapter, I study risk pricing in bond yields and investigate whether regime shifts are important for our understanding of bond risk premia and the term structure. I produce novel empirical estimates to characterize risk premia and the term structure of bond yields and natural gas futures contracts. I also propose a new method for estimating Gaussian affine term structure models subject to regime switching, which solves the serious numerical difficulties encountered by other methods in the literature. The third chapter of my dissertation investigates whether forecast aggregation helps in forecasting commodity prices.