# 2.2 Panel data models  (Page 2/10)

 Page 2 / 10

## Estimation issues

Hsiao (2003: 27-30) discusses a convenient example of a panel data model that illustrates many of the important issues that arise with panel data. We make use of this example in what follows. Assume that we want to estimate a production function for farm production in order to determine if the farm industry exhibits increasing returns to scale. Assume the sample consists of observations for N farms over T years, giving a total sample size of $NT.$ For simplicity, we assume that the Cobb-Douglas production is an adequate description of the production process. The general form of the Cobb-Douglas production function is:

$q={\alpha }_{0}{I}_{1}^{{\beta }_{1}}\cdots {I}_{k}^{{\beta }_{k}},$

where q is output and ${I}_{j}$ is the quantity of the j-th input (for example, land, machinery, labor, feed, and fertilizer). The parameter, ${\beta }_{j},$ is the output elasticity of the j-th input; the farms exhibit constant returns to scale if the output elasticities sum to one and either increasing or decreasing returns to scale if they sum to a value greater than or less than one, respectively. is the quantity of the j -th input (for example, land, machinery, labor, feed, and fertilizer). The parameter, is the output elasticity of the j -th input; the farms exhibit constant returns to scale if the output elasticities sum to one and either increasing or decreasing returns to scale if they sum to a value greater than or less than one, respectively.

Taking the natural logarithm of (5) gives $\mathrm{ln}q=\mathrm{ln}{\alpha }_{0}+{\beta }_{1}\mathrm{ln}{I}_{1}+\cdots +{\beta }_{k}\mathrm{ln}{I}_{k}.$ We can re-write this equation (adding an error term, as well as farm and year subscripts) giving:

${y}_{it}={\beta }_{0}+{\beta }_{1}{x}_{1it}+\cdots +{\beta }_{k}{x}_{kit}+{\epsilon }_{it,}$

where ${y}_{it}=\mathrm{ln}{q}_{it},$ , ${\beta }_{0}=\mathrm{ln}{\alpha }_{0},$ ${x}_{jit}=\mathrm{ln}{I}_{jit},$ for $j=1,\dots ,k$ and ${\epsilon }_{it}$ is an error term. One way to account for year and time effects is to assume:

${\epsilon }_{it}=\lambda {F}_{i}+\eta {P}_{t}+{\upsilon }_{it},$

where F i is a measure of the unobserved farm specific effects on productivity and P t is a measure of the unobserved changes in productivity that are the same for all farms but vary annually. Substitution of (7) into (6) gives: ${y}_{it}=\left({\beta }_{0}+\lambda {F}_{i}+\eta {P}_{t}\right)+\sum _{j=1}^{k}{\beta }_{j}{x}_{jit}+{\upsilon }_{it}$ or

${y}_{it}={\alpha }_{it}+\sum _{j=1}^{k}{\beta }_{j}{x}_{jit}+{\upsilon }_{it},$

where ${\alpha }_{it}={\beta }_{0}+\lambda {F}_{i}+\eta {P}_{t}.$ Thus, (8) is equivalent to (2). Moreover, if we assume that $\eta =0,$ we get

${y}_{it}={\alpha }_{i}+\sum _{j=1}^{k}{\beta }_{j}{x}_{jit}+{\upsilon }_{it},$

where ${\alpha }_{i}={\beta }_{0}+\lambda {F}_{i}.$ Thus, (9) is equivalent to (1).

## Fixed-effects models

A natural way to make (9) operational is to introduce a dummy variable, D i , for each farm so that the intercept term becomes:

${\alpha }_{i}={\alpha }_{1}+{\alpha }_{2}{D}_{2}+\cdots +{\alpha }_{m}{D}_{m}={\alpha }_{1}+\sum _{j=2}^{m}{\alpha }_{j}{D}_{j},$

where ${D}_{j}=1$ if $j=i$ and 0 otherwise. This substitution is equivalent to replacing the intercept term with a dummy variable for each farm and letting the farm dummy variable “sweep out” the farm-specific effects. In this specification the slope terms are the same for every farm while the intercept term is given for farm j by ${\alpha }_{1}+{\alpha }_{j}.$ Clearly, the intercept term for the first farm is equal to just ${\alpha }_{1}.$ This specification is known as the fixed effect model and is estimated using ordinary least squared (OLS). We can extend the fixed-effects model to fit (8) by including a dummy variable for each time period except one.

In sum, fixed-effects models assume either (or both) that the omitted effects that are specific to cross-sectional units are constant over time or that the effects specific to time are constant over the cross-sectional units. This method is equivalent to including a dummy variable for all but one of the cross-sectional units and/or a dummy variable for all but one of the time periods.

how environment affect demand and supply of commodity ?
Wht at the criteria for market ?
Amos
what is difference between monitory policy and fiscal policy?
monetary policy is a policy thrust by National Govt(CBN) to influence government spending, purchase &taxes
Frank
necessity of economics
I will say want,choice,opportunity cost,scarcity,scale of preference
Alao
what is monopoly market.How price output are determined under monopoly market
bisham
b) Monopoly market is an impecfect market where s single firm having the innovation to produce a particular commodity.Prices are determined through output since there are no other competitive.
Frank
Monopoly market:firm has market power & does not respond to market price
Frank
Explain the process of price determination under perfect competition market with suitable diagram
Price determination under perfect competition via this process :firms have no market power to influence price rather firms respond to market price.
Frank
price is different from demand- demand is amount of commodity
demand is amount /quantity of commodity a potential buyer is willing to buy at a given price at market
Frank
demand is a desire of customer on commodity with the ability to pay it and willing to buy it at given price of commodity
Harika
demand is price of what
show that shortrun average cost
what is economics
what is money
Mbah
what is money
Mbah
Difine macro economics
agaba
money is a medium of exchange between goods and services,maybe inform of currency.
Wesonga
Economics is study of how human beings strive to satisfy numerous wants using limited available resources.
Wesonga
how do you find the maximum number of workers the firms should employ order to produce where there are increasing returns
Jane
what are implications of computing national income?.
agaba
pl
MUDASIRU
what is the formulae for calculating national income
MUDASIRU
it calculated by value added method
Praveen
classify the production units like agriculture, banking, transport etc
Praveen
money is anything that is generally acceptetable for human
Ogbaji
Estimate the net value added(NVA) at fixed cost by each industrial structure
Praveen
definition of unemployment
what are the causes of unemployment?
The main causes of unemployment are listed below. 1. Frictional unemployment 2. Cyclical unemployment 3. Structural unemployment
assani
We can also categorize the causes on a broader sense as: 1. Political and 2. Social cause As unemployeement root causes are embaded in this two.
Yonathan
would opportunity cost exist if there was no scarcity?
assani
yes just because the opportunity cost arose when there is Alternative to choose among the alternatives.
I am thinking that, if our resources were unlimited, then there wouldn't be any need to forgo some wants. Hence the inexistence if opportunity cost
assani
Politics
Job
politics has done what?
assani
consider time assani
Mary
I'm Emmanuel,...I taught the main cause is the change in gov't.
Emmanuel
...Lack of capital to set up a firm respectively
Emmanuel
🙈
Emmanuel
I would like to bring in Educational levels can also be the cause the cause of the problem respectively
Emmanuel
I think the main causes of unemployment is lack of INFRASTRUCTURAL DEVELOPMENT OVER POPULATION OVER DEPENDENT ON GOVERNMENT LACK OF SELF EMPOWERMENT...
ananti
lack of skills among the new generation is the serious issue.
Vishal
Where I come from , I don't see why education or personal aspects seem to do with unimployment, technically the motivation and eigerness in all works of live is there , dispite the cultural influence and physical bearriors;the thing we lacking is Government Support and open market ethics.
Joe
sorry about that-(repation). We have a over powering ethical political system that's displacing the marketing asspects of economy and causing large scale unemployment right across the board...
Joe
can someone Explain Expansionary Monetary Policy and Contractionary Monetary Policy Using one of the instrument of Monetary Policy? Please am kinda lost here?. ta
using a graph show the case of substitute and compliment goods
can anyone give me a simple explanation to Five Sector Macroeconomics?
Emmanuel
Can someone please define what economics is
economics simply is a social science subject that study human behavior.
dajan
economics is a social science which studies human behaviour as a relationship between ends and scarce means that has alternative uses
Alao
Can someone please tell me how to calculate GDP
Emmanuel
emmanual kapal to calculate GDP (Gross Domestic Product) has three method in calculating it (1)income approach (2) expenditure approach (3) value added method
Alao
thanks Alae
Emmanuel
u are welcome
Alao
in basic terms economics is revered to as battery system, it date back to when Men sees the need to exchange sapless goods and produce to gain , either wealth , basic necessities or to establish trading ties for personal benefit or social asspects in terms of coexistence and continuity, future .
Joe
what is the law of demand
keep other thing constant, when the price increases demand decrease when the price decreases demand increases of the commodity.
sj
all things being equal,quantity demanded decrease as price increase and increase as price decrease
Seth
there's practial joke to it ..." the higher the demand ; scarcity, increase in production and drop in quality"... quite the controversy - for example China vs Europe, United States and we are all boxed up in between somewhere...
Joe
Other thing remain constant the low price of commodity the high quantity of commodity and vice versa is true
Baraka
Explain Effective demand
What is effective demand
Anita
like Modi is in demand...best example of effective demand
Pranav
Don't get you
Anita
Anita you mean you don't get me or who?
Onyeking
level of demand that represents a real intention to purchase by people with the means to pay
Pranav
Got questions? Join the online conversation and get instant answers!