Meaning: The quote by Thomas Sargent, a renowned economist, alludes to the challenges and trade-offs associated with maximizing the likelihood function in economic modeling, particularly during the 1980s. To provide a comprehensive understanding of the quote, it is essential to delve into the context of likelihood function maximization in economics and its significance in modeling.

Likelihood function maximization is a fundamental concept in econometrics and statistical modeling. It involves the process of finding the parameter values that maximize the likelihood function, which represents the probability of observing the data given a specific statistical model. By maximizing the likelihood function, economists and researchers aim to estimate the parameters of their models, allowing for the identification of relationships and patterns within the data.

During the 1980s, the field of econometrics and economic modeling experienced significant advancements in computational techniques and statistical methods. As a result, economists were increasingly able to develop more complex and sophisticated models to analyze economic phenomena. However, this era also presented challenges related to the computational resources and techniques available at the time.

Sargent's quote reflects the notion that there were instances in the 1980s when maximizing the likelihood function posed considerable difficulties. The complexity of certain models and the computational constraints of the era made it impractical or even detrimental to pursue maximum likelihood estimation in some cases. This difficulty may have arisen from the high dimensionality of the parameter space, nonlinearity of the likelihood function, or the limitations of available computational tools.

Moreover, Sargent's reference to the potential of "blowing our model out of the water" underscores the precarious nature of model estimation and the potential consequences of pushing the limits of likelihood function maximization. In the context of economic modeling, pushing a model "out of the water" implies that attempting to maximize the likelihood function could lead to unrealistic or unsubstantiated parameter estimates, rendering the model unreliable or invalid for making meaningful inferences about the real-world economic processes.

The quote also hints at the delicate balance between model complexity and computational feasibility. In some cases, the pursuit of maximum likelihood estimation may have been deemed impractical if the computational burden outweighed the potential benefits of more accurate parameter estimates. Economists and researchers faced the challenge of weighing the trade-offs between model sophistication and the practical limitations of available computational resources.

Furthermore, the quote reflects the pragmatic approach that economists had to adopt in navigating the complexities of model estimation and computational constraints during that time. It highlights the recognition that, in certain circumstances, it was necessary to acknowledge the limitations of likelihood function maximization and exercise caution to avoid compromising the integrity of the economic models being developed.

In conclusion, Thomas Sargent's quote encapsulates the challenges and considerations surrounding likelihood function maximization in economic modeling during the 1980s. It serves as a reminder of the practical constraints and trade-offs that economists faced when striving to balance model complexity with computational feasibility. By understanding the context and implications of the quote, we gain insights into the evolving landscape of econometrics and the nuanced decision-making processes involved in model estimation and parameter estimation in economics.