Researches on Ray Yang, Ph.D.

Regression Discontinuity Design

Wed, 23 Jun 2021 00:00:00 +0000

the Causality Graph

Remove the Differences in Y NOT explained by Treatment and Time

Difference-in-Difference

Wed, 16 Jun 2021 00:00:00 +0000

the Causality Graph

Remove the Differences in Y NOT explained by Treatment and Time

Matching

Wed, 09 Jun 2021 00:00:00 +0000

the Causality Graph

Removing the “Differences in Y explained by X” (to find out the pure effect of Treatment on Y)

Fixed Effects

Wed, 02 Jun 2021 00:00:00 +0000

the Causality Graph

Remove “Differences in X explained by Person” vs. Remove “Differences in Y explained by Person”

Remove Persons’s influence on “the effect of X on Y” step by step

Post-treatment Control

Wed, 26 May 2021 00:00:00 +0000

the Causality Graph

Remove “Differences in X explained by C” vs. Remove “Differences in Y explained by C”

Remove C’s influence on X and Y step by step

Collider Bias

Wed, 19 May 2021 00:00:00 +0000

the Causality Graph

Remove “Differences in X explained by C” vs. Remove “Differences in Y explained by C”

What the model does: Remove C’s influence on X and Y step by step

Instrument Variable

Wed, 12 May 2021 00:00:00 +0000

Causality Graph

Generate the Data for Analysis

# DGP
set.seed(66)
# Z is a binary variable in this case, but it can also be continuous.
df <- data.frame(Z = c(rep(0, 100), rep(1, 100)), 
                 W = rnorm(200)) %>%
  # Z affects X
  mutate(X = .5 + 2*W + 2*Z + rnorm(200)) %>% 
  # Z does NOT affect either Y or W (God's Game)
  mutate(Y = -X + 4*W + 1 + rnorm(200)) %>% 
  group_by(Z) %>%
  mutate(mean_X=mean(X), mean_Y=mean(Y)) %>%
  ungroup()

Visualization

Remove “Differences in X NOT explained by Z” vs. Remove “Differences in Y NOT explained by Z”

Retain “Differences in X and Y explained by Z” step by step

Run the Regression and Check the Estimate of X

library(AER)
# Z is the instrument variable
summary(ivreg(Y ~ X | Z , data = df)) %>% 
  coef() %>% 
  regrrr::to_long_tab()

##   n.r        var_      beta
## 1   1 (Intercept)    1.318*
## 2   1               (0.583)
## 3   2           X -1.089***
## 4   2               (0.300)

Sample Selection Bias

Wed, 12 May 2021 00:00:00 +0000

Causality Graph

DGP

set.seed(66)
# Generate Exogenous Variables
df <- data.frame(X = runif(300) * 10, 
                 W = runif(300) * 5, 
                 U = runif(300) * 2, 
                 Z = c(rep(0, 150), rep(1, 150))) %>%
  # God's Game
  # X (Visible) affects Y, W (Invisible) and U (Invisible) affect Y
  mutate(Y = .1 + .5*X + 0.8*W + 0.2*U + rnorm(300),
  # X (Visible) affects Y, W (Invisible) and U (Invisible) affect Latent Selection Function
  # Z (Visible) affect Latent Selection Function
         select_ = 10 + 3*X + 2*W + 1*U + .5*Z + rnorm(300),
  # Latent Selection Determines the True Selection
         select = ifelse(select_ > mean(select_), 1, 0)
         )

Run Heckman Regression

run_selection <- glm(select ~ X + Z, family = binomial( link = "probit" ), data = df)
df$IMR <- dnorm(run_selection$linear.predictors)/pnorm(run_selection$linear.predictors)
summary(run_selection)

## 
## Call:
## glm(formula = select ~ X + Z, family = binomial(link = "probit"), 
##     data = df)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.0059  -0.1287  -0.0013   0.1240   2.5195  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  -5.4514     0.6613  -8.244   <2e-16 ***
## X             1.0163     0.1213   8.380   <2e-16 ***
## Z             0.6183     0.2704   2.287   0.0222 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 415.03  on 299  degrees of freedom
## Residual deviance: 113.84  on 297  degrees of freedom
## AIC: 119.84
## 
## Number of Fisher Scoring iterations: 8

run_outcome <- lm(Y ~ IMR + X, data = df[which(df$select == 1),])
summary(run_outcome)

## 
## Call:
## lm(formula = Y ~ IMR + X, data = df[which(df$select == 1), ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.4067 -0.8600  0.0496  0.7680  3.4331 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   2.4928     0.8875   2.809  0.00569 ** 
## IMR           0.9237     0.4398   2.100  0.03749 *  
## X             0.4922     0.1099   4.477 1.56e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.338 on 139 degrees of freedom
## Multiple R-squared:  0.1532, Adjusted R-squared:  0.141 
## F-statistic: 12.58 on 2 and 139 DF,  p-value: 9.55e-06

Visualization

Double Check

# Run OLS (which is biased)
run_biased <- lm(Y ~ X, data = df[which(df$select == 1),])
summary(run_biased)

## 
## Call:
## lm(formula = Y ~ X, data = df[which(df$select == 1), ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.5643 -0.9695  0.1065  0.7926  3.2590 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   4.0168     0.5172   7.766 1.55e-12 ***
## X             0.3114     0.0692   4.500 1.42e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.354 on 140 degrees of freedom
## Multiple R-squared:  0.1263, Adjusted R-squared:  0.1201 
## F-statistic: 20.25 on 1 and 140 DF,  p-value: 1.419e-05

# Check the Inclusion Restriction
run_test_instrument <- lm(Y ~ X + Z, data = df[which(df$select == 1),])
summary(run_test_instrument)

## 
## Call:
## lm(formula = Y ~ X + Z, data = df[which(df$select == 1), ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.3369 -0.9958  0.1245  0.8445  3.1289 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.71761    0.54715   6.794 2.93e-10 ***
## X            0.32192    0.06913   4.657 7.42e-06 ***
## Z            0.37117    0.23158   1.603    0.111    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.347 on 139 degrees of freedom
## Multiple R-squared:  0.1422, Adjusted R-squared:  0.1299 
## F-statistic: 11.52 on 2 and 139 DF,  p-value: 2.347e-05

# In Reality, Only God Can Run This Regression (by Knowing about the Truth and Seeing the Invisibles).
run_ture <- lm(Y ~ U + W + X, data = df)
summary(run_ture)

## 
## Call:
## lm(formula = Y ~ U + W + X, data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -3.02525 -0.64811 -0.01175  0.56035  2.71664 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.008025   0.188084   0.043  0.96600    
## U           0.330793   0.099258   3.333  0.00097 ***
## W           0.773520   0.040014  19.331  < 2e-16 ***
## X           0.499843   0.020288  24.637  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9544 on 296 degrees of freedom
## Multiple R-squared:  0.7703, Adjusted R-squared:  0.768 
## F-statistic: 330.9 on 3 and 296 DF,  p-value: < 2.2e-16

Control Variable

Wed, 05 May 2021 00:00:00 +0000

the Causality Graph

Simpson’s Paradox

Remove “Differences in X explained by W” vs. Remove “Differences in Y explained by W”

Remove W’s influence on X and Y step by step

Tracking the Change of Industry Positioning Caused by an Acquisition

Sun, 19 Apr 2020 00:00:00 +0000

1. Motivation

Due to enduring resource heterogeneity, firms tend to hold persistent positionings within an established industry (like commercial banking). However, transformative corporate actions may alter a firm’s asset structure and create a new industry for the acquirer. Thus, we can map out the industry positions and track the position change caused by an acquisition.

2. Mapping the Positioning and Tracking the Movement

2.1 the Biplot

Consider commercial banks as an example. Different banks may hold differently structured financial asset portfolios and occupy different positions. We can assess a bank’s position based on the proportion of cash, commercial loans, mortgage loans, etc., as a percentage in the total asset (i.e., multiple dimensions). A biplot can provide us a quick intuition about how those dimensions relate to one another. However, the relative positions shown on biplot would not be accurate due to the loss of information in dimension reduction.

2.2 the 3-D and 2-D Scatterplots based on MDS

In an alternative approach, we can build distance-based features by exploring the inter-firm distance using multi-dimensional scaling (MDS). On Feb. 12th, 2018, Pacific Premier Bancorp launched an acquisition of Grandpoint Capital. Using this acquisition event as an example, we can first calculate the interfirm distance using MDS and then track how the acquisition shifts a bank’s position (in both a 3-D and 2-D scatter plots).

the Positionings of Big Tech Firms on Industry Presence and Competition Description

Thu, 16 Apr 2020 00:00:00 +0000

In this post, I calculated the positioning of big tech firms based on two metrics, the multiple-industry presence (based on 3-digit SIC codes) versus the competition description (in 10-K filings), and compared the difference between the two approaches.

1 the positioning by industry presence across SIC categories

Scholars have used SIC codes to understand interfirm differences ¹ Big public firms typically straddle across multiple SIC industry categories. So it is straightforward and easy to see their positionings by multiple-industry participation. Accordingly, a firm’s position can be calculated as the sales distribution across multiple SIC industry categories ².

2 the positioning by competition description in 10-K filing

The SIC-code might be “backward-looking,” as firms tend to quite if particular combinations of multiple-industry business lines create economic inefficiencies. Only efficient multi-industry presence survives.

In contrast, the SEC filings may reflect managers’ current understanding of what they do. Especially when they characterize their competition, managers tend to draw their forward-looking expectations on the various forms of competitive threats. Some scholars³ and companies⁴ have used the text-based approach to calculate inter-industry distance.

2.1 calculating positioning based on the competition description

I collected the competition description texts of the largest 17 tech companies. Below are some frequently used words in those statements.

I ran an LDA topic modeling with 11 latent topics, which yields a low perplexity score.

The figure below shows how the 11 topics distribute across terms.

This is the topic loading on the 11 firms’ competition description, which is used to calculate the pairwise distance.

2.2 the final result: positioning by competition description

Here is the positioning map based on the competition description. The graph on the right shows the positioning of American companies. Looking at the results, we can see some interesting differences. The competition description moves some firms closer or further away from one another as compared to the SIC-presence positioning map.

for example:
Teece, D. J., Rumelt, R., Dosi, G., & Winter, S. (1994). Understanding corporate coherence: Theory and evidence. Journal of economic behavior & organization, 23(1), 1-30.

Lien, L. B., & Klein, P. G. (2013). Can the survivor principle survive diversification?. Organization Science, 24(5), 1478-1494.
↩
Litov, L. P., Moreton, P., & Zenger, T. R. (2012). Corporate strategy, analyst coverage, and the uniqueness paradox. Management Science, 58(10), 1797-1815.Lien, L. B., & Klein, P. G. (2013).↩
https://hobergphillips.tuck.dartmouth.edu ↩
Morningstart’s Company Comparables System ↩

Mapping Twitter Topics and Sentiment about FAAMG Companies since Covid-19 Outbreak

Wed, 15 Apr 2020 00:00:00 +0000

1 Motivation

On a whim, I mapped out what people say (the text) and feel (the sentiment) about the top tech companies (FAAMG) on twitter since the Covid-19 outbreak. The keywords and sentiment that are associated with the main topics should differ across these companies.

By no means I am drawing any causal association here. But the story starts with checking the recent price movements of the FAAMG stocks. Obviously, Covid-19 has impacted these companies quite differently.

2 Procedures

2.1 Data Source

For each company, I downloaded 1,000 tweets containing the company name as the hashtag (e.g. “#amazon” for Amazon). I used Python module “tweepy” to stream the data and set the “since” parameter to ‘2020-03-01’, which collects a sample of 1,000 tweets since March 1st.

2.2 Topic Modeling

Using Python module “gensim”, I detected three most significant topics (including Covid-19, business, and daily life), which are named by the associated keywords (most relevant terms).

Using Python module “vaderSentiment”, I computed sentiment scores for each tweet and aggregated the scores by company. The topic-based sentiment scores are used to construct the perceptual map, in which each company takes a different position. Using Python module “nltk”, I find the most frequent topic-based co-occurring words for each company.

3 Results

3.1 Perceptual Map of FAAMG Based on Topic Sentiment

It looks Amazon does well on all topics, especially on Covid-19-related topic. Microsoft and Apple do well on “Business”.

3.2 Keywords Co-occurrence Network on Each Topic

Here are the work keywords co-occurrence patterns for each topic of these companies.

My Research

Mon, 01 Jan 0001 00:00:00 +0000

Check My C.V.