1---
 2meta: 
 3  date: false
 4  reading_time: false
 5title: "Truncated Sample"
 6date: 2023-10-05
 7description: "A sample from which some observations have been systematically excluded"
 8tags: ["Sampling Methods", "Econometrics", "Data Analysis"]
 9---
10
11## Background
12
13In statistical and econometric analyses, an understanding of sampling methods is crucial. The concept of a "truncated sample" addresses specific situations where data collection is limited to a subset of the possible observations.
14
15## Historical Context
16
17The use of truncated samples has been critical since the early developments in regression analysis and estimation methods. Researchers noticed that traditional estimation techniques did not yield expected or reliable results when applied to truncated data, prompting further studies into the effects and corrections of such sampling methods.
18
19## Definitions and Concepts
20
21A **truncated sample** is a sample from which some observations have been systematically excluded. Unlike a censored sample, where observations are only partially missing (e.g., a known upper/lower boundary), a truncated sample means these data points are wholly absent from the collected sample.
22
23An example of a truncated sample might be analyzing only households with income below a specified level. Households with income above this threshold are entirely omitted, affecting the representativeness of the sample.
24
25## Major Analytical Frameworks
26
27### Classical Economics
28
29In classical economics, robust data is paramount for accurate models. Truncated samples can introduce bias that affects the estimation of economic models.
30
31### Neoclassical Economics
32
33In neoclassical frameworks, where optimization and utility functions are central, truncated samples could skew predictions and interpretations due to systematic exclusions of certain data points.
34
35### Keynesian Economics
36
37Keynesian models often rely on comprehensive aggregate data. Therefore, truncated samples could potentially misrepresent consumption and savings behaviors, fundamental in Keynesian analysis.
38
39### Marxian Economics
40
41Marxian economics, with its focus on classes and exploitation theory, may encounter significant analytical gaps if the sample excludes higher-income groups, impeding holistic class-based analysis.
42
43### Institutional Economics
44
45This branch examines how institutions shape economic behavior. Truncated samples can inhibit the understanding of institutional impacts across different segments of the population.
46
47### Behavioral Economics
48
49Behavioral economics, which studies psychological, social, and emotional factors on economic decisions, could be deeply affected by truncated samples, as exclusion of specific segments might obscure critical behavioral insights.
50
51### Post-Keynesian Economics
52
53Post-Keynesians emphasize historical time, uncertainty, and fundamental unpredictability in economies. Truncated samples could thus distort the understanding of large-scale economic dynamics.
54
55### Austrian Economics
56
57Austrian economics, focusing on individual actions and subjectivism, could find truncated samples problematic, as incomplete data might lead to inaccurate individual behavior modeling.
58
59### Development Economics
60
61Development economics relies heavily on comprehensive data across various income groups to understand poverty, growth, and development. Truncated samples could miss out on significant trends and policy impacts.
62
63### Monetarism
64
65Monetarist theories, emphasizing the role of governments in controlling the amount of money in circulation, may be affected by truncated samples impacting inflation and money supply analysis, leading to incorrect policy prescriptions.
66
67## Comparative Analysis
68
69Using truncated samples restricts the scope of data, introducing bias and inconsistency into traditional estimation methods like ordinary least squares (OLS). It's crucial for economists to understand the full impact of truncation and apply appropriate adjustments such as truncation correction techniques.
70
71## Case Studies
72
73Case studies exploring truncation include public health surveys excluding high-income respondents or financial analyses omitting extreme incomes. Each illustrates the challenges and required methodological adjustments.
74
75## Suggested Books for Further Studies
76
77- **"Econometrics by Example" by Damodar Gujarati:** A practical guide addressing how to handle different types of econometric data.
78- **"Truncated and Censored Samples in Surveying and Data Analysis" by Neil John:** Detailed methodologies for dealing with limited datasets.
79- **"The Craft of Economic Modelling" by Asami Nakagawa:** Comprehensive strategies in economic modeling, discussing estimators and truncated samples.
80
81## Related Terms with Definitions
82
83- **Censored Sample:** A sample where some variables are partly observed, known only to lie above or below a certain threshold.
84- **Sample Bias:** The effect that results when certain members of a population are systematically more (or less) likely to be included in a sample.
85- **Ordinary Least Squares (OLS):** A method for estimating the parameters in a linear regression model.
86- **Consistency:** An estimative attribute referring to the property that as more data becomes available, the estimator converges to the true parameter value.