By David Fan , Isabelle Tao , Lucy Cao and Emma Lu

This work won the first place at the Wharton Hackathon during September 21st-27th.

We are so happy for team Woahhhh. Congratulations!

## Executive Summary & Key Takeaways

### Background

The COVID-19 pandemic has forced many countries to use lockdowns as a public health measure to prevent further spread of the disease, often at the expense of slowed economic activities. The lockdown-induced trade-off between economic and health outcomes has underscored the importance to evaluate the **effectiveness of lockdowns**.

We focus on the US economy given its leading world count in COVID-19 cases and its economy’s influence on the global economy. In addition, US states have experienced varying levels of lockdown success, allowing for further investigation. We evaluated the health and economic outcomes of different US state lockdown policies that vary in **duration and stringency**, adjusted based on the states’ characteristics, to determine the optimal lockdown policies that would maximize both health and economic outcomes.

### Methodology

To understand the effects of lockdown, we first created created an index that tracks multiple health and economic indicators for each of the 50 states when the lockdown policies were imposed. This was done by first standardizing these metrics and feeding them through a Principal Component Analysis (PCA).

Then we selected control variables (Population Density, Population Size, Political Leaning, and Share of Population above 65 years old) that might also play a part on lockdown outcomes independent of government intervention. Finally, lever variables (Duration and Stringency of lockdown) were selected for their direct relationship to the characteristic of the lockdown.

We further analyzed the relative variable importance between the nuisance and lever variables, generated Partial Dependence Plots to understand each lever’s marginal effects, and conducted a case study to understand the synergies between potential government interventions.

### Key Observations

**Lockdown length is more important than lockdown stringency to contain the virus.**

Our analysis shows that the longer the length of the lockdown, the more effective the lockdown is. Stringency on the other hand, has an inverse effect on the health index. This means that states with more stringent lockdowns actually promotes more rebellious behavior which causes more deaths, hospitalizations and spikes in cases.**Lockdown length and stringency are both not strongly correlated with decline in GDP and increase in unemployment.**

While it is common to assume that the longer the lockdown, the worse the length of the state of the economy, our analysis shows that that is not the case. Given alternative consumption methods (online shopping) and alternative working options (work from home), consumption and productivity can still be sustained. This is aligned with results globally: the actual or expected drop in GDP, across OECD countries is not as strongly correlated with lockdown lengths or stringency. (McKinsey Analytics)**The most effective lockdown duration is between 55 and 60 days.**

We found that there is a golden period where lockdowns are the most effective. When the lockdown is below 55 days, it’s insufficient to cause a decline in cases. When the lockdown is above 60 days, there is essentially no effect for both health index and economic index.

### Next Steps

First, we hope to incorporate more granular county level data, so we can add in more control variables and obtain results that are of higher statistical significance. Second, we hope to extend these results globally to check if our observations apply to global situations.

## Modeling

### Background & Analytical Approach

#### Introduction

COVID-19 lockdowns have been implemented around the world for public health reasons. While lockdowns are undoubtedly an **effective public health measure**, they also **limit economic activities** and **negatively affect economic growth**. For example, the US, leading the world charts with over 7 million COVID-19 cases, had a GDP fall of 32.9% (annualized rate) in Q2 2020, the lowest since 1947.

Policymakers are faced with the challenge of **balancing the health and economic trade-off**. If a lockdown is lifted too quickly, it could cause a re-surge in cases, resulting in more lockdowns. Alternatively, a lockdown that is too long could cause detriments to the economy that will take years to recover. Our knowledge of the lockdown’s effectiveness is limited and there are few historical data references. With over six months of current data and different states employing different policies, it is possible to **empirically assess the outcomes** from these lockdowns to derive additional understandings of the **optimal trade-off**.

We aim to **create a model that stimulates real-world reactions at the state-level** towards different lockdown policies. The model will allow policymakers to **forecast lockdown effectiveness and economic impacts**. Our model can also be used as an **evidence-based argument to improve policy adherence**.

#### Analytical Approach

While COVID-19 lockdowns have garnered much interest from health and economic experts, there still remain many gaps in the literature of assessing the effect of lockdown measure that we aim to investigate.

#### Index Construction

First, we needed a metric that will allow us to measure the **health and economic outcomes of lockdowns**. Since outcomes can be measured using many indicators, we created **two indices that combined relevant variables** to track the health and economic outcomes of a state’s lockdown policy.

These indicators were created through **factor analysis** where we utilized the top Principal Component across individual indicators. This served 2 main purposes; first, we want to be able to **isolate the underlying latent state of either health or economics that causes the observables** as opposed to relying on the observed metrics themselves. This is because metrics observed (death, cases in the health cases, or GDP and unemployment in the econ cases) are subjected to some degree of randomness and may therefore individually exhibit variation that would add noise to our data. Secondly, the creation of indexes lessens additional model we need to run in order to incorporate various health outcomes, drastically simplifying the process.

### Index Construction & Variable Selection

#### Health Index

The Health Index is created to access the coronavirus cases in states during the lockdown. The higher the absolute number of the health index, the worse the performance of the lockdown. Given that this measure is a gradient, we opted to focus on the percentage decline of 3 key health attributes: **daily number of deaths**, **number of hospitalized**, and **number of cases**.

We obtained the decline rate of each of these 3 health attributes during the lockdown using the following method. First, we obtained the **highest number for each of these 3 metrics** during the lockdown. Next, we extracted these **3 metrics on the last day** of the lockdown. Lastly, we divided the final day metric by the maximum metric to get the gradient change during the period.

In simple terms, the **higher the gradient change ratio, the less effective the lockdown is**, because the lockdown did not improve the health metric as expected. If the ratio is low, it indicates that the lockdown is effective in lowering the cases from the peak.

As indicated earlier, we wanted to combine these 3 high level metrics into one overall indicator. **This was done by first standardizing these metrics and feeding them through a Principal Component Analysis (PCA)**. As expected, the leading principal component was able to explain **52% of the variation** in these metrics, making it a fair representation of the underlying health traits. The loading score of the aforementioned indicator are all around 0.5, indicating that a one unit increase in health index correspond to half a standard deviation increase gradient change, pointing to a less effective lockdown.

#### Economic Index

Similar to the health index, the economic index is created to gauge the overall decline in state economic condition.

This measure was done with the use of gradient change for 2 metrics: GDP decline from 2019 Q4 to 2020 Q1, and unemployment rate increase fromFebruary 2020 to April 2020.

Since both metrics were already in their natural percentage format, rescaling is no longer necessary. We simply performed our factor analysis using **PCA on both these gradients**.

**The leading component using the PCA was able to explain 71% of the total variation in the gradient** once again, making a viable candidate to represent the underlying economic drivers. The loading vectors for GDP change is -0.7 and 0.7 for unemployment change. This means as one unit of economic index increases, we would expect the **GDP to decrease by 0.7%** while **unemployment rate to increase by 0.7%**.

#### Control Variables and Lever Variables

After constructing the indexes needed for our target variable, we now move on to create the left hand side of our equation, or the x-variables.

When considering our x-variables, we looked at **variables that may affect our aforementioned indexes independent of any kind of intervention that the government attempts**. We refer to these variables as our **control variables**. While it may be ideal to include as many control variables as possible to create impartial results, since we are using state level dataset with limited amount of observations (50 states at most), to avoid the curse of dimensionality problem, **we opted to only include 4 main control variables**: **Population Density**, **Population**, **Political Leaning** and **Share of Population above 65 years old**. These variables are selected due to how they may directly affect the indexes at hand without the Gov’t intervention.

For our lever variables, we selected two main characteristic related lockdown: **the length of the lockdown and the relative stringency of lockdown** which is anchored on two characteristics: 1) Whether the state required masks and 2) whether the state implemented a penalty for violating the rules.

### Model Performance & Feature Interpretations

#### Initial Model Performance

We performed an initial linear regression model to assess the relationship between lockdown length and the health index. We found that the linear regression model gave us an **r-squared of 0.279** and we also found **the lockdown length variable to be statistically significant** with a p-value of 0.035. Similarly, we fitted a second linear regression model to **evaluate the relationship between lockdown length and the economic index**. We found that this linear regression model had an r-squared of 0.262. In this model, we found that **the republican feature is statistically significant with a p-value of 0.020**.

#### Improved Model Performance

We then performed a **random forest model to account for potentially non-linear relationships between the variables and the indices** as well as increase predictive power of our modeling. Moreover, through partial dependence plots we can better understand the marginal effect of the length and stringency of lockdown on economic and health outcomes. We first performed a 20% split on the data set, with 80% of the data in the training set and 20% of the data in the test set.

This model gave us a **better predictive ability overall for our dataset**. This includes a 0.9 r-squared for our training dataset and a 0.4 r-squared for our test dataset when predicting the health indexes and 0.75 r-squared for our training dataset and a 033 r-squared for our test dataset when predicting the econ indexes. We then set out to draw additional inference from the model.

#### Variable Relative Importance

First we aim to analyze the variable importance information within our two models. Starting off with the health index model.

Weight | Feature |
---|---|

0.5357 ± 0.4113 | Lockdown Length |

0.0115 ± 0.2518 | Population 2019 |

0.0106 ± 0.0108 | Added Levels |

0.0096 ± 0.0161 | Republican |

-0.0015 ± 0.0055 | Democrat |

-0.0565 ± 0.1245 | Density |

-0.1444 ± 0.1540 | Share_65 |

It is apparent from the variable importance plot that **the lockdown length is by far the most important variable** in our dataset superseding even the control variables that we have included. **This generally is in line with our hypothesis that the length of lockdown will very likely benefit the states in terms of containing the spread of the virus.**

**Stringency of lockdowns**, on the other hand, represented by the added levels variable, **ranks third in importance**, indicating that it does somewhat still have an effect on the indexes but just not as apparent as the length itself. This can be an artifact of the majority perception of lockdown such that most individuals are likely to abide by the rules regardless of stringency.

For the econ model on the other hand,

Weight | Feature |
---|---|

-0.0026 ± 0.0118 | Added Levels |

-0.0053 ± 0.0516 | Republican |

-0.0567 ± 0.1146 | Population 2019 |

-0.0960 ± 0.5125 | Density |

-0.1043 ± 0.0286 | Democrat |

-0.2388 ± 0.3275 | Share_65 |

-0.4528 ± 1.1405 | Lockdown Length |

the variable importance is rather interesting. No individual variable stood out too strongly in terms of how irreplaceable it is in our model. It is especially quite interesting to see that the Lockdown Length actually did not seem to impact the econ index at all from a variable importance point of view. These results regardless should be taken with a grain of salt given the huge variation around the weight of these variables. Nonetheless, an insight from this point of view is that the economic downfall during COVID may not necessarily be as related to the lockdown given the rise of alternative consumption methods and alternative work opportunities.

### Partial Dependence Plots

We now want to take a deep-dive into the health index model and examine the two lever variables of interest that we have identified: Lockdown length and stringency. This is specifically done for the health index case as it is in there that both lockdown length and added levels were most significant.

The deep dive into the partial dependence plots shed light on something extremely interesting. As expected, the **partial dependence plots for the lockdown periods follows a negative relationship with the health index** (i.e., as lockdown length increases, we see a greater reduction in cases from the peak). The effect is actually not fully continuous but **there is a sharp increase in effectiveness of lockdown at around 55-60 days and later remains flat**. While not conclusive, this gives us an idea to the ideal lockdown period.

Another interesting insight that emerged is that **lockdown stringency actually may trigger an inverse reaction** that governments do not expect. Specifically, we saw that as stringency increases, the health index actually rose gradually, indicating a less effective lockdown. This is likely due to individuals feeling too suppressed and constrained by the lockdown and end up not abiding by the lockdown rules altogether.

#### Case Studies

In order to better understand the effect of lockdown length on the health and economic outcomes, we decided to look more closely at how states health and economic indices change when lockdown lengths are altered. For Texas, with an original 30-day lockdown, we predicted the health index to be 0.82. However, when we extend this lockdown period to 60 days, the health index decreases to -0.61 and when we further extend this lockdown period to 90 days, the health index decreases to -0.84. **This result is consistent with our finding that longer lockdowns lead to better containment of the disease and better health outcomes.** We also took a look at the economic index and found that adjusting the lockdown period does not drastically affect the economic index. For the state of Alabama, we notice that the economic index with the original 26-day lockdown is predicted to be -1.43 while an extension of the lockdown to 40 days gives us an economic index of -0.21 and an extension to 60 days gives us a new prediction of -0.05.

### Conclusion & Next Steps

This study from a theoretical level showed that **lockdown length, stringency and efficiency is not a purely additive function**. Lockdown length and stringency does not have a positive linear function with improved health outcomes. Instead, the the best approach to achieve an efficient lockdown is often a **combination the right length with a lesser emphasis on stringency**. Furthermore we also explored and realized that the lockdown length and stringency does not drastically affect the economic status of states due to the rise of other opportunities.

In the future, we wish to extend this study to a county but also a global level in order to incorporate more control variables but also allow us to create statistical models with more confidence from more observations.