This dissertation introduces advanced statistical and econometric methods in two distinct areas of non-market valuation: benefit transfer (BT) and hedonic analysis. While the first and the third chapters address the challenge of estimating the societal benefits of prospective environmental policy changes by adopting locally weighted regression (LWR) technique in an environmental valuation context, the second chapter combines the output from traditional hedonic regression and matching estimators and provides guidance on the choice of model with low risk of bias in housing market studies. The economic and societal benefits associated with various environmental conservation programs, such as improvement in water quality, or increment in wetland acreages, can be directly estimated using primary studies. However, conducting primary studies can be highly resource-intensive and time-consuming as they typically involve extensive data collection, sophisticated models, and a considerable investment of financial and human resources. As a result, BT offers a practical alternative, which involves employing valuation estimates, functions, or models from prior primary studies to predict the societal benefit of conservation policies at a policy site. Existing studies typically fit one single regression model to all observations within the given metadata and generate a single set of coefficients to predict welfare (willingness-to-pay) in a prospective policy site. However, a single set of coefficients may not reflect the true relationship between dependent and independent variables, especially when multiple source studies/locations are involved in the data-generating process which, in turn, degrades the predictive accuracy of the given meta-regression model (MRM). To address this shortcoming, we employ the LWR technique in an environmental valuation context. LWR allows an estimation of a different set of coefficients for each location to be used for BT prediction. However, the empirical exercise carried out in the existing literature is rigorous from a computational perspective and is cumbersome for practical adaptation. In the first chapter, we simplify the experimental setup required for LWR-BT analysis by taking a closer look at the choice of weight variables for different window sizes and weight function settings. We propose a pragmatic solution by suggesting "universal weights" instead of striving to identify the best of thousands of different weight variable settings. We use the water quality metadata employed in the published literature and show that our universal weights generate more efficient and equally plausible BT estimates for policy sites than the best weight variable settings that emerge from a time-consuming cross-validation search over the entire universe of individual variable combinations. The third chapter expands the scope of LWR to wetland meta-data. We use a conceptually similar set of weight variables as in the first chapter and replicate the methodological approach of that chapter. We show that LWR, under our proposed weight settings, generates substantial gain in both predictive accuracy and efficiency compared to the one generated by standard globally-linear MRM. Our second chapter delves into a separate yet interrelated realm of non-market valuation, i.e., hedonic analysis. Here, we explore the combined inferential power of traditional hedonic regression and matching estimators to provide guidance on model choice for housing market studies where researchers aim to estimate an unbiased binary treatment effect in the presence of unobserved spatial and temporal effects. We examine the potential sources of bias within both hedonic regression and basic matching. We discuss the theoretical routes to mitigate these biases and assess their feasibility in practical contexts. We propose a novel route towards unbiasedness, i.e., the "cancellation effect" and illustrate its empirical feasibility while estimating the impact of flood hazards on housing prices. / Doctor of Philosophy / This dissertation introduces novel statistical and econometric methods to better understand the value of environmental resources that do not have an explicit market price, such as the benefits we get from the changes in water quality, size of wetlands, or the impact of flood risk zoning in the sales price of residential properties. The first and third chapters tackle the challenge of estimating the value of environmental changes, such as cleaner water or more wetlands. To figure out how much people benefit from these changes, we can look at how much they would be willing to pay for such improved water quality or increased wetland area. This typically requires conducting a primary survey, which is expensive and time-consuming. Instead, researchers can draw insights from prior studies to predict welfare in a new policy site. This approach is analogous to applying a methodology and/or findings from one research work to another. However, the direct application of findings from one context to another assumes uniformity across the different studies which is unlikely, especially when past studies are associated with different spatial locations. To address this, we propose a ``locally-weighting" technique. This places greater emphasis on the studies that closely align with the characteristics of the new (policy) context. Determining the weight variables/factors that dictate this alignment is a question that requires an empirical investigation. One recent study attempts this locally-weighting technique to estimate the benefits of improved water quality and suggests experimenting with different factors to find the similarity between the past and new studies. However, their approach is computationally intensive, making it impractical for adaptation. In our first chapter, we propose a more pragmatic solution---using a "universal weight" that does not require assessing multiple factors. With our proposed weights in an otherwise similar context, we find more efficient and equally plausible estimates of the benefits as previous studies. We expand the scope of the local weighting to the valuation of gains or losses in wetland areas in the third chapter. We use a conceptually similar set of weight variables and replicate the empirical exercise from the first chapter. We show that the local-weighting technique, under our proposed settings, substantially improves the accuracy and efficiency of estimated benefits associated with the change in wetland acreage. This highlights the diverse potential of the local weighting technique in an environmental valuation context. The second chapter of this dissertation attempts to understand the impact of flood risk on housing prices. We can use "hedonic regression" to understand how different features of a house, like its size, location, sales year, amenities, and flood zone location affect its price. However, if we do not correctly specify this function, then the estimates will be misleading. Alternatively, we can use "matching" technique where we pair the houses inside and outside of the flood zone in all observable characteristics, and differentiate their price to estimate the flood zone impact. However, finding identical houses in all aspects of household and neighborhood characteristics is practically impossible. We propose that any leftover differences in features of the matched houses can be balanced out by considering where the houses are located (school zone, for example) and when they were sold. We refer to this route as the "cancellation effect" and show that this can indeed be achieved in practice especially when we pair a single house in a flood zone with many houses outside that zone. This not only allows us to accurately estimate the effect of flood zones on housing prices but also reduces the uncertainty around our findings.

Shuffled linear regression concerns itself with linear models with an unknown correspondence between the input and the output. This correspondence is usually represented by a permutation matrix II*. The model we are interested in has one more complication which is that the design matrix is itself latent and is observed with noise. This is considered as a type of errors-in-variables (EIV) model. Our interest lies in the recovery of the permutation matrix. We propose an estimator for II* based on the total least squares (TLS) technique, a common method of estimation used in EIV model. The estimation problem can be viewed as approximating one matrix by another of lower rank and the quantity it seeks to minimize is the sum of the smallest singular values squared. Due to identifiability issue, we evaluate the proposed estimator by the normalized Procrustes quadratic loss which allows for an orthogonal rotation of the estimated design matrix. Our main result provides an upper bound on this quantity which states that it is required that the signal-to-noise ratio to go to infinity in order for the loss to go to zero. On the computational front, since the problem of permutation recovery is NP-hard to solve, we propose a simple and efficient algorithm named alternating LAP/TLS algorithm (ALTA) to approximate the estimator, and we use it to empirically examine the main result. The main idea of the algorithm is to alternate between estimating the unknown coefficient matrix using the TLS method and estimating the latent permutation matrix by solving a linear assignment problem (LAP) which runs in polynomial time. Lastly, we propose a hypothesis testing procedure based on graph matching which we apply in the field of digital humanities, on character social networks constructed from novel series.

Thesis advisor: M. Utku Ünver / Thesis advisor: Tayfun Sönmez / This thesis is a collection of three essays in market design concerning designs of matching markets with aggregate constraints, affirmative action schemes, and investigating boundaries of simultaneous efficiency-stability relaxation for one-to-one matching mechanisms.In Chapter 1, I establish and propose a possible solution for a college housing crisis, a severe ongoing problem taking place in many countries. Every year many colleges provide housing for admitted students. However, there is no college admissions process that considers applicants’ housing needs, which often results in college housing shortages. In this chapter, I formally introduce housing quotas to the college admissions problem and solve it for centralized admissions with common dormitories. The proposed setting is inspired by college admissions where applicants apply directly to college departments, and colleges are endowed with common residence halls. Such setting has many real-life applications: hospital/residents matching in Japan (Kamada and Kojima, 2011, 2012, 2015), college admissions with scholarships in Hungary (Biró, 2012), etc. A simple example shows that there may not be a stable allocation for the proposed setting. Therefore, I construct two mechanisms that always produce some weakened versions of a stable matching: a Take-House-from-Applicant-stable and incentive compatible cumulative offer mechanism that respects improvements, and a Not-Compromised-Request-from-One-Agent-stable (stronger version of stability) cutoff minimising mechanism. Finally, I propose an integer programming solution for detecting a blocking-undominated Not-Compromised-Request-from-One-Agent-stable matching. Building on these results, I argue that presented procedures could serve as a helpful tool for solving the college housing crisis. In Chapter 2, I propose a number of solutions to resource allocation problems in an affirmative action agenda. Quotas are introduced as a way to promote members of minority groups. In addition, reserves may overlap: any candidate can belong to many minority groups, or, in other words, have more than one trait. Moreover, once selected, each candidate fills one reserve position for each of her traits, rather than just one position for one of her traits. This makes the entire decision process more transparent for applicants and allows them to potentially utilize all their traits. I extend the approach of Sönmez and Yenmez (2019) who proposed a paired-admissions choice correspondence that works under no more than two traits. In turn, I allow for any number of traits focusing on extracting the best possible agents, such that the chosen set is non-wasteful, the most diverse, and eliminates collective justified envy. Two new, lower- and upper-dominant choice rules and a class of sum-minimizing choice correspondences are introduced and characterized. In Chapter 3, I implement optimization techniques for detecting the efficient trade off between ex-post Pareto efficiency (for one side of a two-sided matching market) and ex-ante stability for small one-to-one matching markets. Neat example (Roth, 1982) proves that there is no matching mechanism that achieves both efficiency (for one side of the one-to-one matching market) and stability. As representative mechanisms I choose deferred-acceptance for stability, and top trading cycles for Pareto efficiency (both of them are strategy-proof for one side of the market). I compare performances of a randomized matching mechanism that simultaneously relaxes efficiency and stability, and a convex combination of two representative mechanisms. Results show that the constructed mechanism significantly improves efficiency and stability in comparison to mentioned convex combination of the benchmark mechanisms. / Thesis (PhD) — Boston College, 2023. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Economics.

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