data project final adjust
Jingshu Zhao
11/9/2020
#check countries selected in the data
length(unique(main$Country))## [1] 20Quasi-Experimental Designs
We are aimed to find solution for following reasearch questions: 1. Has COVID-19 impacted the economy and if so, which factors has it affected? 2. How well have the measures taken by the government to combat COVID-19 affected the economy (Covariates) 3. Is there any difference in the effectiveness of measures taken by governments in countries with differing levels of per capita income in their effect on the economy (Factor)
Hotelling T Square is a good approach for #1.
- Has COVID-19 impacted the economy and if so, which factors has it affected?
We have collected the information for 20 countries which are heavily impacted by COVID-19. The countries are from different per capita income level which we have classified as high, medium, low.
Economic factors includes Purchasing Managers Index (PMI), composite, Consumer Price Index (CPI), Share Price Index, Unemployment Rate and government support factors includes Stringency Index, Government Response Index, and Economic Support Index based on population per country data are collected from OCT. 2019 through current.
To answer first part of question 1, Hotelling T square is a good approach: In the first test, we are testing if the global economy has impact by COVID-19 overall.
#Hypothesis:
H0: There’s no significant in the monthly change in Purchasing Manager Index (PMI), Consumer Price Index (CPI), Share Price Index (SPI), and Unemployment Rate between the pre-covid and post-covid period.
H1:There is a significant difference in the monthly change in Purchasing Manager Index (PMI), Consumer Price Index (CPI), Share Price Index (SPI), and Unemployment Rate between the pre-covid and post-covid period
And we have chosen 0.05 as the test significant level
main_test = main %>% filter(Period != "COVID Month")
m1 = with(main_test, HotellingsT2(cbind( PMI_PCT,CPI_PCT,SharePriceIndex_PCT,UnempRate_PCT) ~ Period))
m1##
## Hotelling's two sample T2-test
##
## data: cbind(PMI_PCT, CPI_PCT, SharePriceIndex_PCT, UnempRate_PCT) by Period
## T.2 = 7.0139, df1 = 4, df2 = 55, p-value = 0.0001229
## alternative hypothesis: true location difference is not equal to c(0,0,0,0)Since the p < 0.05, we reject the null hypothesis. We can conclude COVID-19 has a big impacted on both government measures and economic factors for all.
To testing the factors impact by COVID-19, we introduce one-way manova here.
##Manova
p1 <- manova(cbind(PMI_PCT,CPI_PCT,SharePriceIndex_PCT,UnempRate_PCT) ~ Period, data=main_test)
summary(p1, test="Pillai")## Df Pillai approx F num Df den Df Pr(>F)
## Period 1 0.33779 7.0139 4 55 0.0001229 ***
## Residuals 58
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Since p < 0.05, the COVID-19 have impacted all the factors.
summary.aov(p1, test="Pillai")## Response PMI_PCT :
## Df Sum Sq Mean Sq F value Pr(>F)
## Period 1 2.4170 2.41700 19.7 4.114e-05 ***
## Residuals 58 7.1159 0.12269
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Response CPI_PCT :
## Df Sum Sq Mean Sq F value Pr(>F)
## Period 1 3.15e-06 3.1459e-06 0.2981 0.5871
## Residuals 58 6.12e-04 1.0552e-05
##
## Response SharePriceIndex_PCT :
## Df Sum Sq Mean Sq F value Pr(>F)
## Period 1 0.07512 0.075122 11.623 0.001191 **
## Residuals 58 0.37488 0.006463
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Response UnempRate_PCT :
## Df Sum Sq Mean Sq F value Pr(>F)
## Period 1 0.00007113 7.1128e-05 1.5081 0.2244
## Residuals 58 0.00273557 4.7165e-05
##
## 97 observations deleted due to missingnessWe have learnt, in general, government measures include strigency index, government response index, and economic support index have put into significant effort because of COVID-19. The economic factors that impacted greatly by COVID-19 are PMI and Share price index.
- How well have the measures taken by the government to combat COVID-19 affected the economy (Covariates)
##Check Correlation
The government support factors which are meant to combat COVID-19 and offer supports to affected economy. Thus, we have graph following three correlation charts based on each individual index: Strigency index, government response index, and economic support index.
main[is.na(main)] <- 0
main_str = as.data.frame(c(main[,16],main[,19:22]))
main_gov = as.data.frame(c(main[,17],main[,19:22]))
main_eco = as.data.frame(main[,18:22])
corrplot(cor(main_str), method="circle")
corrplot(cor(main_gov), method="shade")
corrplot(cor(main_eco), method="square")
##Manova
- Is there any difference in the effectiveness of measures taken by governments in countries with differing levels of per capita income in their effect on the economy (Factor) Based on Data dictionary,
Stringency Index: The strictness of lockdown style policies that primarily restrict people’s behaviour Government Response Index: The overall response of governments across all indicators measured by the Oxford study Economic Support Index: Records measures such as income support and debt relief And the scale for all three government measures are from 0 - 100.
Since we are applying MANOVA to testing the effectiveness on economic factors before and after governmeasures. We’ll bucket the government measures into: Low (0-50, refering pre-covid) and High (51-100, refering post-covid)
main$SI = ifelse(main$StringencyIndex < 50,'Low','High')
main$GI = ifelse(main$GovernmentResponseIndex < 50, 'Low','High')
main$EI = ifelse(main$EconomicSupportIndex < 50, 'Low','High')#Hypothesis: H0: There’s no significant difference on economic factors before and after applying government measures H1:There’s significant difference on economic factors before and after applying government measures
We apply manova through pillai, if p < 0.05, it stands the government measures do provide significant help to these economic factors.
High = main %>% filter(PCI_Type == "High")
manRes1 <- manova(cbind(PMI_PCT,CPI_PCT,SharePriceIndex_PCT,UnempRate_PCT) ~ SI*GI*EI - SI:GI:EI, data=High)
summary(manRes1, test="Pillai")## Df Pillai approx F num Df den Df Pr(>F)
## SI 1 0.06368 1.1393 4 67 0.3456780
## GI 1 0.26336 5.9885 4 67 0.0003509 ***
## EI 1 0.00801 0.1353 4 67 0.9687670
## SI:GI 1 0.34340 8.7600 4 67 9.478e-06 ***
## SI:EI 1 0.02822 0.4863 4 67 0.7456989
## GI:EI 1 0.07778 1.4127 4 67 0.2392836
## Residuals 70
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The result shows the interation between strigency index and government response index provides the greatest help to the high per capital countries followed by the interaction between government reponse index and econmoic support index.
summary.aov(manRes1, test="Pillai")## Response PMI_PCT :
## Df Sum Sq Mean Sq F value Pr(>F)
## SI 1 0.3541 0.35407 3.2083 0.07759 .
## GI 1 0.0886 0.08858 0.8026 0.37339
## EI 1 0.0146 0.01461 0.1324 0.71706
## SI:GI 1 0.1619 0.16192 1.4672 0.22987
## SI:EI 1 0.0157 0.01573 0.1425 0.70693
## GI:EI 1 0.0071 0.00710 0.0643 0.80051
## Residuals 70 7.7254 0.11036
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Response CPI_PCT :
## Df Sum Sq Mean Sq F value Pr(>F)
## SI 1 0.00000621 6.2050e-06 0.4820 0.48983
## GI 1 0.00000552 5.5230e-06 0.4290 0.51464
## EI 1 0.00000000 2.0000e-09 0.0001 0.99132
## SI:GI 1 0.00000091 9.0900e-07 0.0706 0.79119
## SI:EI 1 0.00000379 3.7890e-06 0.2943 0.58922
## GI:EI 1 0.00003856 3.8558e-05 2.9948 0.08794 .
## Residuals 70 0.00090125 1.2875e-05
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Response SharePriceIndex_PCT :
## Df Sum Sq Mean Sq F value Pr(>F)
## SI 1 0.000799 0.000799 0.2233 0.6380
## GI 1 0.080843 0.080843 22.5860 1.039e-05 ***
## EI 1 0.001595 0.001595 0.4457 0.5066
## SI:GI 1 0.126738 0.126738 35.4081 9.580e-08 ***
## SI:EI 1 0.005507 0.005507 1.5387 0.2190
## GI:EI 1 0.005267 0.005267 1.4715 0.2292
## Residuals 70 0.250554 0.003579
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Response UnempRate_PCT :
## Df Sum Sq Mean Sq F value Pr(>F)
## SI 1 0.0000401 4.0144e-05 0.2340 0.6300
## GI 1 0.0000163 1.6314e-05 0.0951 0.7587
## EI 1 0.0000033 3.3120e-06 0.0193 0.8899
## SI:GI 1 0.0000176 1.7568e-05 0.1024 0.7499
## SI:EI 1 0.0000002 2.2000e-07 0.0013 0.9716
## GI:EI 1 0.0000030 2.9820e-06 0.0174 0.8955
## Residuals 70 0.0120066 1.7152e-04It shows share price index is affected significantly by government measures.
For Medium per capita countries,
Mid = main %>% filter(PCI_Type == "Medium")
manRes2 <- manova(cbind(PMI_PCT,CPI_PCT,SharePriceIndex_PCT,UnempRate_PCT) ~ SI*GI*EI - SI:GI:EI, data=Mid)
summary(manRes1, test="Pillai")## Df Pillai approx F num Df den Df Pr(>F)
## SI 1 0.06368 1.1393 4 67 0.3456780
## GI 1 0.26336 5.9885 4 67 0.0003509 ***
## EI 1 0.00801 0.1353 4 67 0.9687670
## SI:GI 1 0.34340 8.7600 4 67 9.478e-06 ***
## SI:EI 1 0.02822 0.4863 4 67 0.7456989
## GI:EI 1 0.07778 1.4127 4 67 0.2392836
## Residuals 70
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1We have found a similar finding as high per capita income countries. That is the interation between strigency index and government response index provides the greatest help to the high per capital countries, and the interaction between government reponse index and econmoic support index also provides significant help.
summary.aov(manRes2, test="Pillai")## Response PMI_PCT :
## Df Sum Sq Mean Sq F value Pr(>F)
## SI 1 0.3957 0.39575 1.6141 0.2098
## GI 1 0.1321 0.13208 0.5387 0.4664
## EI 1 0.4631 0.46311 1.8888 0.1755
## SI:GI 1 0.3370 0.33701 1.3745 0.2466
## SI:EI 1 0.1580 0.15801 0.6445 0.4259
## Residuals 50 12.2590 0.24518
##
## Response CPI_PCT :
## Df Sum Sq Mean Sq F value Pr(>F)
## SI 1 0.00000042 4.2400e-07 0.0278 0.8683
## GI 1 0.00000295 2.9510e-06 0.1931 0.6623
## EI 1 0.00000684 6.8430e-06 0.4477 0.5065
## SI:GI 1 0.00004652 4.6520e-05 3.0437 0.0872 .
## SI:EI 1 0.00000004 4.1000e-08 0.0027 0.9588
## Residuals 50 0.00076421 1.5284e-05
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Response SharePriceIndex_PCT :
## Df Sum Sq Mean Sq F value Pr(>F)
## SI 1 0.000000 0.000000 0.0000 0.99885
## GI 1 0.023355 0.023355 4.3875 0.04129 *
## EI 1 0.007157 0.007157 1.3446 0.25173
## SI:GI 1 0.044249 0.044249 8.3128 0.00579 **
## SI:EI 1 0.003715 0.003715 0.6979 0.40745
## Residuals 50 0.266149 0.005323
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Response UnempRate_PCT :
## Df Sum Sq Mean Sq F value Pr(>F)
## SI 1 0.00003735 3.7354e-05 0.6970 0.4078
## GI 1 0.00000325 3.2480e-06 0.0606 0.8066
## EI 1 0.00000001 7.0000e-09 0.0001 0.9910
## SI:GI 1 0.00002357 2.3573e-05 0.4399 0.5102
## SI:EI 1 0.00000109 1.0900e-06 0.0203 0.8872
## Residuals 50 0.00267957 5.3591e-05It also shows share price index is significantly affected by government measures.
For Low per capital income countries,
Low = main %>% filter(PCI_Type == "Low")
manRes3 <- manova(cbind(PMI_PCT,CPI_PCT,SharePriceIndex_PCT,UnempRate_PCT) ~ SI*GI*EI - SI:GI:EI, data=Low)
summary(manRes3, test="Pillai")## Df Pillai approx F num Df den Df Pr(>F)
## SI 1 0.265451 3.4331 4 38 0.01721 *
## GI 1 0.012303 0.1183 4 38 0.97517
## EI 1 0.142394 1.5773 4 38 0.20013
## Residuals 41
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The results indicate the interation between strigency index and government response index provids the greatest help to the low per capital countries followed by the interaction between Stringency index and economic support index.
summary.aov(manRes3, test="Pillai")## Response PMI_PCT :
## Df Sum Sq Mean Sq F value Pr(>F)
## SI 1 0.1301 0.130059 1.4935 0.2286
## GI 1 0.0008 0.000755 0.0087 0.9263
## EI 1 0.2206 0.220616 2.5335 0.1191
## Residuals 41 3.5703 0.087080
##
## Response CPI_PCT :
## Df Sum Sq Mean Sq F value Pr(>F)
## SI 1 0.00003893 3.8926e-05 1.4406 0.23693
## GI 1 0.00001181 1.1808e-05 0.4370 0.51227
## EI 1 0.00010209 1.0209e-04 3.7782 0.05881 .
## Residuals 41 0.00110785 2.7021e-05
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Response SharePriceIndex_PCT :
## Df Sum Sq Mean Sq F value Pr(>F)
## SI 1 0.061085 0.061085 10.3099 0.002574 **
## GI 1 0.000005 0.000005 0.0009 0.976220
## EI 1 0.001547 0.001547 0.2611 0.612093
## Residuals 41 0.242921 0.005925
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Response UnempRate_PCT :
## Df Sum Sq Mean Sq F value Pr(>F)
## SI 1 0.0000006 5.7900e-07 0.0034 0.9536
## GI 1 0.0000023 2.2720e-06 0.0134 0.9083
## EI 1 0.0000351 3.5131e-05 0.2078 0.6509
## Residuals 41 0.0069302 1.6903e-04It shows PMI, CPI, and share price index are affected by government measures.