Time-series cross-section model

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# Time-series cross-section model
### Thierry Warin, PhD
### quantum simulations<a style="color:#6f97d0">*</a>

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# Outline

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### outline

1. Time-series cross-section model

2. Fixed effects

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# Time-series cross-section model

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# Time-series cross-section model

```r
mydata1 <- readr::read_csv("https://warin.ca/datalake/courses_data/qmibr/session5/panel_data_1.csv")
head(mydata1,4)
```

```
## # A tibble: 4 x 45
##     obs name    country  year lngdppc3    va    ps    ge    rq    rl    cc   inv
##   <dbl> <chr>     <dbl> <dbl>    <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1     1 Albania       1  1989     6.76    NA    NA    NA    NA    NA    NA 44.8 
## 2     2 Albania       1  1990     6.52    NA    NA    NA    NA    NA    NA 49.8 
## 3     3 Albania       1  1991     6.01    NA    NA    NA    NA    NA    NA  9.51
## 4     4 Albania       1  1992     5.56    NA    NA    NA    NA    NA    NA  7.44
## # … with 33 more variables: gns <dbl>, lninfl <dbl>, govrev <dbl>,
## #   govexp <dbl>, fb <dbl>, strfb <dbl>, netdebt <dbl>, grossdebt <dbl>,
## #   cab <dbl>, ief <dbl>, property <dbl>, integrity <dbl>, taxburden <dbl>,
## #   govspend <dbl>, busfreedom <dbl>, labfreedom <dbl>, monfreedom <dbl>,
## #   tradefreedom <dbl>, invfreedom <dbl>, finfreedom <dbl>, dcr <dbl>,
## #   emplpop <dbl>, schooling1 <dbl>, to <dbl>, fdinet <dbl>, secondenrol <dbl>,
## #   tertenrol <dbl>, incomeind <dbl>, lfp <dbl>, schooling2 <dbl>,
## #   oldagedep <dbl>, remittances <dbl>, gci <dbl>
```

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# Time-series cross-section model

```r
library(plm)
mydata_1_random <- plm(grossdebt ~ busfreedom + finfreedom + invfreedom, data = mydata1, index = c("country", "year"), model = "random")
```

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# Time-series cross-section model

```r
summary(mydata_1_random)
```

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<img src="./images/regression2b.png" width="100%" style="display: block; margin: auto;" />
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# Fixed effects

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# Fixed effects

In terms of estimation techniques, we need to use time-series cross-section based techniques. First, we need to go through a couple of checkings. Among the first ones, we need to see whether we need a fixed-effects or a random-effects model.

FE explore the relationship between predictor and outcome variables within an entity (country, person, company, etc.).

Each entity has its own individual characteristics that may or may not influence the predictor variables (for example, being a male or female could influence the opinion toward certain issue; or the political system of a particular country could have some effect on trade or GDP; or the business practices of a company may influence its stock price).

When using FE we assume that something within the individual may impact or bias the predictor or outcome variables and we need to control for this. This is the rationale behind the assumption of the correlation between entity’s error term and predictor variables.

FE remove the effect of those time-invariant characteristics so we can assess the net effect of the independent variable on the outcome variable.

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# Fixed effects

Another important assumption of the FE model is that those time-invariant characteristics are unique to the individual and should not be correlated with other individual characteristics.

Each entity is different therefore the entity’s error term and the constant (which captures individual characteristics) should not be correlated with the others. If the error terms are correlated, then FE is no suitable since inferences may not be correct and you need to model that relationship (probably using random-effects), this is the main rationale for the Hausman test.

```r
# Running a panel data with fixed effects
fixed <- plm(grossdebt ~ busfreedom + finfreedom + invfreedom,
             data = mydata1, index = c("country", "year"), model = "within")
# Running a panel data with random effects
random <- plm(grossdebt ~ busfreedom + finfreedom + invfreedom,
              data = mydata1, index = c("country", "year"), model = "random")
```

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# Fixed effects

```r
# Running the Hausman test
phtest(fixed, random)
```

```
## 
## 	Hausman Test
## 
## data:  grossdebt ~ busfreedom + finfreedom + invfreedom
## chisq = 5.4333, df = 3, p-value = 0.1427
## alternative hypothesis: one model is inconsistent
```

Considering the results of the Hausman test with a `\(p-value >0.05\)`, we need a random effects model.