In the field of fresh produce retail, vegetables generally have a relatively limited shelf life, and their quality deteriorates with time. Most vegetable varieties, if not sold on the day of delivery, become difficult to sell the following day. Therefore, retailers usually perform daily quantitative replenishment based on historical sales data and demand conditions. Vegetable pricing typically uses a "cost-plus pricing" method, with retailers often discounting products affected by transportation loss and quality decline. In this context, reliable market demand analysis is crucial as it directly impacts replenishment and pricing decisions. Given the limited retail space, a rational sales mix becomes essential. This paper first uses data analysis and visualization techniques to examine the distribution patterns and interrelationships of vegetable sales quantities by category and individual item, based on provided data on vegetable types, sales records, wholesale prices, and recent loss rates. Next, it constructs a functional relationship between total sales volume and cost-plus pricing for vegetable categories, forecasts future wholesale prices using the ARIMA model, and establishes a sales profit function and constraints. A nonlinear programming model is then developed and solved to provide daily replenishment quantities and pricing strategies for each vegetable category for the upcoming week. Further, we optimize the profit function and constraints based on the actual sales conditions and requirements, providing replenishment quantities and pricing strategies for individual items on July 1 to maximize retail profit. Finally, to better formulate replenishment and pricing decisions for vegetable products, we discuss and forecast the data that retailers need to collect and analyses how the collected data can be applied to the above issues.

This document replicates the main results from Santos Silva and Tenreyro (2006 in R. The original results were obtained in TSP back in 2006. The idea here is to be explicit regarding the conceptual approach to regression in R. For most of the replication I used base R without external libraries except when it was absolutely necessary. The findings are consistent with the original article and reveal that the replication effort is minimal, without the need to contact the authors for clarifications or incur into data transformations or filtering not mentioned in the article.

In social networks or spatial experiments, one unit's outcome often depends on another's treatment, a phenomenon called interference. Researchers are interested in not only the presence and magnitude of interference but also its pattern based on factors like distance, neighboring units, and connection strength. However, the non-random nature of these factors and complex correlations across units pose challenges for inference. This paper introduces the partial null randomization tests (PNRT) framework to address these issues. The proposed method is finite-sample valid and applicable with minimal network structure assumptions, utilizing randomization testing and pairwise comparisons. Unlike existing conditional randomization tests, PNRT avoids the need for conditioning events, making it more straightforward to implement. Simulations demonstrate the method's desirable power properties and its applicability to general interference scenarios.

We propose a structural model-free methodology to analyze two types of macroeconomic counterfactuals related to policy path deviation: hypothetical trajectory and policy intervention. Our model-free approach is built on a structural vector moving-average (SVMA) model that relies solely on the identification of policy shocks, thereby eliminating the need to specify an entire structural model. Analytical solutions are derived for the counterfactual parameters, and statistical inference for these parameter estimates is provided using the Delta method. By utilizing external instruments, we introduce a projection-based method for the identification, estimation, and inference of these parameters. This approach connects our counterfactual analysis with the Local Projection literature. A simulation-based approach with nonlinear model is provided to add in addressing Lucas' critique. The innovative model-free methodology is applied in three counterfactual studies on the U.S. monetary policy: (1) a historical scenario analysis for a hypothetical interest rate path in the post-pandemic era, (2) a future scenario analysis under either hawkish or dovish interest rate policy, and (3) an evaluation of the policy intervention effect of an oil price shock by zeroing out the systematic responses of the interest rate.

Selective contests can impair participants' overall welfare in overcompetitive environments, such as school admissions. This paper models the situation as an optimal contest design problem with binary actions, treating effort costs as societal costs incurred to achieve a desired level of selectivity. We provide a characterization for the feasible set of selection efficiency and societal cost in selective contests by establishing their relationship with feasible equilibrium strategies. We find that selection efficiency and contestants' welfare are complementary, i.e. it is almost impossible to improve one without sacrificing the other. We derive the optimal equilibrium outcome given the feasible set and characterize the corresponding optimal contest design. Our analysis demonstrates that it is always optimal for a contest designer who is sufficiently concerned with societal cost to intentionally introduce randomness into the contest. Furthermore, we show that the designer can optimize any linear payoff function by adjusting a single parameter related to the intensity of randomness, without altering the specific structure of the contest.

We propose a knowledge operator based on the agent's possibility correspondence which preserves her non-trivial unawareness within the standard state-space model. Our approach may provide a solution to the classical impossibility result that 'an unaware agent must be aware of everything'.

In this paper, I conduct a policy exercise about how much the introduction of a cash transfer program as large as a Norwegian-sized lottery sector to the United States would affect startups. The key results are that public cash transfer programs (like lottery) do not increase much the number of new startups, but increase the size of startups, and only modestly increase aggregate productivity and output. The most important factor for entrepreneurs to start new businesses is their ability.

In this paper, I propose a new general equilibrium model that explains stylized facts about venture capitalists' impact on their portfolio firms. Venture capitalists can help increase firms' productivity, yet they face increasing entry costs to enter. I characterize steady state effort choice, entry threshold, and mass of venture capitalists, and show how they are affected by change in upfront investment, interest rate, and entry costs. The key contribution is that public policy to stimulate startups by subsidizing upfront investments or reducing interest cost have limited success if not accompanied by an increasing supply of experts who can improve business ideas.

Inequalities may appear in many models. They can be as simple as assuming a parameter is nonnegative, possibly a regression coefficient or a treatment effect. This paper focuses on the case that there is only one inequality and proposes a confidence interval that is particularly attractive, called the inequality-imposed confidence interval (IICI). The IICI is simple. It does not require simulations or tuning parameters. The IICI is adaptive. It reduces to the usual confidence interval (calculated by adding and subtracting the standard error times the $1 - \alpha/2$ standard normal quantile) when the inequality is sufficiently slack. When the inequality is sufficiently violated, the IICI reduces to an equality-imposed confidence interval (the usual confidence interval for the submodel where the inequality holds with equality). Also, the IICI is uniformly valid and has (weakly) shorter length than the usual confidence interval; it is never longer. The first empirical application considers a linear regression when a coefficient is known to be nonpositive. A second empirical application considers an instrumental variables regression when the endogeneity of a regressor is known to be nonnegative.

Adam Smith's inquiry into the emergence and stability of the self-organization of the division of labor in commodity production and exchange is considered using statistical equilibrium methods from statistical physics. We develop a statistical equilibrium model of the distribution of independent direct producers in a hub-and-spoke framework that predicts both the center of gravity of producers across lines of production as well as the endogenous fluctuations between lines of production that arise from Smith's concept of "perfect liberty". The ergodic distribution of producers implies a long-run balancing of "advantages to disadvantages" across lines of employment and gravitation of market prices around Smith's natural prices.

When analyzing Bitcoin users' balance distribution, we observed that it follows a log-normal pattern. Drawing parallels from the successful application of Gibrat's law of proportional growth in explaining city size and word frequency distributions, we tested whether the same principle could account for the log-normal distribution in Bitcoin balances. However, our calculations revealed that the exponent parameters in both the drift and variance terms deviate slightly from one. This suggests that Gibrat's proportional growth rule alone does not fully explain the log-normal distribution observed in Bitcoin users' balances. During our exploration, we discovered an intriguing phenomenon: Bitcoin users tend to fall into two distinct categories based on their behavior, which we refer to as ``poor" and ``wealthy" users. Poor users, who initially purchase only a small amount of Bitcoin, tend to buy more bitcoins first and then sell out all their holdings gradually over time. The certainty of selling all their coins is higher and higher with time. In contrast, wealthy users, who acquire a large amount of Bitcoin from the start, tend to sell off their holdings over time. The speed at which they sell their bitcoins is lower and lower over time and they will hold at least a small part of their initial holdings at last. Interestingly, the wealthier the user, the larger the proportion of their balance and the higher the certainty they tend to sell. This research provided an interesting perspective to explore bitcoin users' behaviors which may apply to other finance markets.

One thread of empirical work in social science focuses on decomposing group differences in outcomes into unexplained components and components explained by observable factors. In this paper, we study gender wage decompositions, which require estimating the portion of the gender wage gap explained by career histories of workers. Classical methods for decomposing the wage gap employ simple predictive models of wages which condition on a small set of simple summaries of labor history. The problem is that these predictive models cannot take advantage of the full complexity of a worker's history, and the resulting decompositions thus suffer from omitted variable bias (OVB), where covariates that are correlated with both gender and wages are not included in the model. Here we explore an alternative methodology for wage gap decomposition that employs powerful foundation models, such as large language models, as the predictive engine. Foundation models excel at making accurate predictions from complex, high-dimensional inputs. We use a custom-built foundation model, designed to predict wages from full labor histories, to decompose the gender wage gap. We prove that the way such models are usually trained might still lead to OVB, but develop fine-tuning algorithms that empirically mitigate this issue. Our model captures a richer representation of career history than simple models and predicts wages more accurately. In detail, we first provide a novel set of conditions under which an estimator of the wage gap based on a fine-tuned foundation model is $\sqrt{n}$-consistent. Building on the theory, we then propose methods for fine-tuning foundation models that minimize OVB. Using data from the Panel Study of Income Dynamics, we find that history explains more of the gender wage gap than standard econometric models can measure, and we identify elements of history that are important for reducing OVB.

LASSO introduces shrinkage bias into estimated coefficients, which can adversely affect the desirable asymptotic normality and invalidate the standard inferential procedure based on the $t$-statistic. The desparsified LASSO has emerged as a well-known remedy for this issue. In the context of high dimensional predictive regression, the desparsified LASSO faces an additional challenge: the Stambaugh bias arising from nonstationary regressors. To restore the standard inferential procedure, we propose a novel estimator called IVX-desparsified LASSO (XDlasso). XDlasso eliminates the shrinkage bias and the Stambaugh bias simultaneously and does not require prior knowledge about the identities of nonstationary and stationary regressors. We establish the asymptotic properties of XDlasso for hypothesis testing, and our theoretical findings are supported by Monte Carlo simulations. Applying our method to real-world applications from the FRED-MD database -- which includes a rich set of control variables -- we investigate two important empirical questions: (i) the predictability of the U.S. stock returns based on the earnings-price ratio, and (ii) the predictability of the U.S. inflation using the unemployment rate.

Even though practitioners often estimate Pareto exponents running OLS rank-size regressions, the usual recommendation is to use the Hill MLE with a small-sample correction instead, due to its unbiasedness and efficiency. In this paper, we advocate that you should also apply OLS in empirical applications. On the one hand, we demonstrate that, with a small-sample correction, the OLS estimator is also unbiased. On the other hand, we show that the MLE assigns significantly greater weight to smaller observations. This suggests that the OLS estimator may outperform the MLE in cases where the distribution is (i) strictly Pareto but only in the upper tail or (ii) regularly varying rather than strictly Pareto. We substantiate our theoretical findings with Monte Carlo simulations and real-world applications, demonstrating the practical relevance of the OLS method in estimating tail exponents.