Part II: Mixed CCA on Covid-19 Related Policies
Challenge 1: too many indicators on Covid-19 related policies with few information in each indicator to do simple regression.
Mingze Huang
12/18/2021
The sole purpose for this project is to serve as PhD dissertation to fulfill the degree requirements.
There will be two parts in this project:
Transparency on Shadow Banking Regulation
The application of sparse semiparametric canonical correlation analysis for mixed data types on covid-19 government response data
Background: Lack of transparency connected with shadow banking increases risks of losses for banks
Research Object: Modeling Independent Asset Management Subsidiaries in Shadow Banking Regulation
Baseline Model: a two-type banking system introduced by Guillermo Ordoñez (Ordonez 2018)
No assumption on quantity limitation, pure thought experiment by game theory with asymmetric information.
Assumption on Banking Investment Opportunities:
Any banks (or representative bank) have access safe assets on the market: \[ \text{Return on safe assets } (s):\begin{cases}y_{s}\;\;\;p_{s}\\ 0\;\;\;1-p_{s} \end{cases} \]
A fraction of \(\alpha\) banks (or representative bank) have access to superior risky assets: \[ \text{Return on superior risky assets } (r_{s}):\begin{cases}y_{r}\;\;\;p_{s}\\ 0\;\;\;1-p_{s} \end{cases} \]
The rest of \(1-\alpha\) banks (or representative bank) have access to inferior risky assets: \[ \text{Return on inferior risky assets } (r_{i}):\begin{cases}y_{r}\;\;\;p_{r}\\ 0\;\;\;1-p_{r} \end{cases} \] where \(y_{r}>y_{s}\) (both superior and inferior risky assets have higher return than safe assets) and \(p_{s}>p_{r}\) (safe assets have higher successful probability than risky assets).
Assumption on Assets’ Payoffs:
\(p_{s}y_{r}>p_{s}y_{s}>p_{r}y_{r}>1\) (superior risky assets pay more in expectation than safe assets, which in expectation more than inferior risky assets).
\(p_{s}y_{s}>\alpha p_{s}y_{r}+(1-\alpha)p_{r}y_{r}\) (safe assets pay more in expectation than risky assets).
\((1+\kappa)y_{r}>(1+\kappa)y_{s}>R\) (successful assets are enough to repay \(R\)).
\(p_{s}[(1+\kappa)y_{r}-R]>p_{r}[(1+\kappa)y_{r}-R]>p_{s}[(1+\kappa)y_{s}-R]\) (risk-shifting: including funding costs, it is more profitable for banks to invest always in risky assets).
Assumption on Information Structure:
Bank can distinguish \(s\), \(r_{s}\) and \(r_{i}\).
Government can just distinguish between \(s\) and \(r\) (cannot distinguish between \(r_{s}\) and \(r_{i}\)).
Investors cannot distinguish any asset type.
First-best welfare: \[ U^{*}=(1+\kappa)p_{s}(\alpha y_{r}+(1-\alpha)y_{s}) \] In words, the \(\alpha\) fraction of banks (or representative bank) only invest in superior risky assets to have \(y_{r}\) return with probability \(p_{s}\) rather than safe assets; whereas the rest \(1-\alpha\) fraction of banks only invest in safe assets to have \(y_{s}\) return with probablity \(p_{s}\) rather than inferior risky assets.
In the absence of regulation, banks are not differentiated by their participation in different banking systems (pay the same rate for funds \(R\)).
Laissez-faire welfare: \[ U_{LF}=(1+\kappa)[\alpha p_{s}+(1-\alpha)p_{r}]y_{r}<U^{*} \] All banks invest in risky asset no matter it has access to superior or inferior risky assets.
Assumption on standard regulation (risk-weighted capital requirement) on traditional banking: \[ \frac{\kappa}{\omega_{s}E(v_{s})}>\chi>\frac{\kappa}{\omega_{r}E(v_{r})} \] where
Expected value of safe assets: \(E(v_{s})=(1+\kappa)p_{s}y_{s}\).
Expected value of risky assets: \(E(v_{r})=(1+\kappa)[\alpha p_{s}+(1-\alpha)p_{r}]y_{r}\).
Since government cannot distinguish between superior risky assets and inferior risky assets, the capital requirement is so strict that banks cannot hold risky assets if they choose to stay in traditional banking market (even for banks with access to superior risky assets).
By selling part of the asset and recording it as an off-balance sheet asset, banks can avoid investment restrictions as long as requirements do not bind when investing in risky assets. In other words, banks can hold risky asset by becoming shadow banks. \[ \frac{\kappa}{\omega_{s}[E(v_{s})-R_{SB}]}>\frac{\kappa}{\omega_{r}[E(v_{r})-R_{SB}]}>\chi \]
Intuitively, both traditional banking and shadow banking markets are pooling.
Investors (depositors) can only evaluate overall risk in traditional banking and overall risk in shadow banking.
Investors (depositors) cannot distinguish between superior risky assets and inferior risky assets on shadow banking market.
Government cannot distinguish between superior risky assets and inferior risky assets too. So standard regulation (risk-weighted capital requirement) is too strict for banks with superior risky assets to stay in traditional banking system.
Equilibrium in original model:
All banks with access to superior assets finance in shadow banking and invest in superior risky assets.
A fraction of banks with access to inferior risky assets finances in shadow banking and invest in inferior risky assets; while the rest finance in traditional banking and invest in safe assets.
The corresponding reason is intuitive:
By first point of assumption on asset payoffs, superior risky assets pay more in expectation than safe assets, it’s been better to be shadow banks to invest in superior risky assets rather than being traditional banks to invest in safe assets (Although interest rate could be slightly higher on shadow banking market).
By fourth point (risk-shifting) of assumption on asset payoffs, even inferior risky assets are more profitable for banks assuming shadow banking market is pooling (e.g. investors cannot distiguish superior and inferior risky assets so that banks pay same interest rate no matter their asset quality).
Only need one more assumption to address transparency setting in independent asset management subsidiary of banks:
New equilibrium would be also intuitive:
All banks with superior risky assets are going to finance in independent asset management subsidiary since it’s transparent, separate and not subject to captal requirements. By transparency and separation, superior risky assets can show their low risks to investors, so the interest rate could be lower than pooling shadow banking market.
All banks with inferior risky assets are going to finance in traditional banking market rather than shadow banking. Since no superior risky assets on pooling shadow banking market, every investor knows any assets on shadow banking market must be inferior (high risk), that makes interest rate in shadow banking market becomes too high to profit from.
This just the first-best welfare as I mentioned before.
Intellectual Merit: This research could potentially extend current model on shadow banking activities to incorporate discussions on banks’ independent asset management subsidiaries.
Broader Impacts: This research could also provide some theoretical support to government’s efforts on enhancing transparency in asset management industry and gradually transform intransparent shadow banking activities into transparent asset managements.
Research Plan: I can finalize all proofs in three days assuming there is no further changes on assumptions. Possible welfare analysis can be done in another three days by mimicking the welfare analysis in original model.
Timeline: As long as we all agree to follow TAMU PhD dissertation template, everything related to part I can be done in one week.
Research Object: The Association between Government Response Policies and Covid-19 Spread
Data Source: Covid-19 government response data. See code book for coding detail.
| RegionCode | Date | C1_School closing | C2_Workplace closing | C3_Cancel public events | C4_Restrictions on gatherings | C5_Close public transport | C6_Stay at home requirements |
|---|---|---|---|---|---|---|---|
| US_CA | 3/12/2020 | 1 | 0 | 2 | 2 | 0 | 1 |
| US_CA | 3/13/2020 | 2 | 0 | 2 | 2 | 0 | 1 |
| US_CA | 3/14/2020 | 2 | 0 | 2 | 2 | 0 | 1 |
| US_CA | 3/15/2020 | 2 | 0 | 2 | 2 | 0 | 1 |
| US_CA | 3/16/2020 | 2 | 0 | 2 | 4 | 0 | 1 |
| US_CA | 3/17/2020 | 3 | 3 | 2 | 4 | 0 | 2 |
| US_CA | 3/18/2020 | 3 | 3 | 2 | 4 | 0 | 2 |
Challenge 1: too many indicators on Covid-19 related policies with few information in each indicator to do simple regression.
Challenge 2: all indicators are denoted by ordinal variables.
## [1] "C1_School closing:"## [1] 0 1 2 3## [1] "C2_Workplace closing:"## [1] 0 1 2 3## [1] "C3_Cancel public events:"## [1] 0 1 2## [1] "C4_Restrictions on gatherings:"## [1] 0 1 2 3 4## [1] "C5_Close public transport:"## [1] 0 1 2Original solution: simple average index (Hale et al. 2020), which could be biased and lose lots of information in original ordinal indicators. This can be verified by simulation. 
At least zero-inflated (or approximately continuous) indicators for covid-19 spread. 
Latent correlations between policy indicators and covid-19 spread indicators (Huang, Müller, and Gaynanova 2021). Policy indicators are correlated with each other and all correlated to covid-19 spread indicators.
## ordinal levels between 4 and 10 will be approximated by either continuous or truncated type.
## ordinal levels between 4 and 10 will be approximated by either continuous or truncated type.
## ordinal levels between 4 and 10 will be approximated by either continuous or truncated type.Challenge 3: The persistency of policies and covid-19 spread (high auto-correlation or unit root process). The same thing happens on both simple average indexes and individual indicators.
Possible solution could be first order difference. However, it could be even more difficult to see correlation directly.
mixedCCA Yoon, Müller, and Gaynanova (2021) for canonical correlation analysis for mixed data types can be used to estimate correlation between covid-19 related policies and covid-19 spread.
Since precautionary government response policies are supposed to lead to covid-19 spread, I calculate canonical correlation between policies at \(t\) and covid-19 spread at \(t+n\).
Blue states’ government tend to more sensitive to covid-19 spread?
Intellectual Merit: A good application of mixedCCA to social science research if it is not the first one. Also a good application latentcor to social science. Introduce high-dimensional big data methods to social science so that it is not necessary to hand-pick a very small number of variables to serve as explanatory variables.
Broader Impacts: Take good use of Covid-19 government response data and build a better framework to numerically evaluate covid-related policies rather than just scatterplot simple average indexes vs. covid cases.
Research Plan:
Adapt R package mixedCCA to ternary and higher levels ordinal variables. General formula for ordinal/continuous cases has been derived (Quan, Booth, and Wells 2018). I’ve derived ordinal/ordinal and ordinal/zero-inflated cases during summer.
Possibly build a corresponding Python package for mixedCCA and use this as application example. There is a fresh published Python package collects most types of CCA except for mixedCCA(Chapman and Wang 2021).
Try to make PCA for mixed data types to create better policy indexes than simple average indexes if possible.
Timeline: TBD